Studying evolved stars with Herschel observations

Studying evolved stars with Herschel observations João Manuel da Silva Santos Dissertação de Mestrado apresentada à Faculdade de Ciências da Universidade do Porto Mestrado em Astronomia 2016 Studying evolved stars with Herschel observations João Manuel da Silva Santos MSc FCUP 2016 2.º CICLO Studying evolved stars with Herschel observations João Manuel da Silva Santos Mestrado em Astronomia Departamento de Física e Astronomia 2016 Orientador Carmen Sánchez Contreras, Research Scientist Centro de Astrobiología (CAB), CSIC-INTA Coorientador Pedro Garcia Lario, Research Scientist European Space Astronomy Centre (ESAC) Todas as correções determinadas pelo júri, e só essas, foram efetuadas. O Presidente do Júri, Porto, ______/______/_________ Faculdade de Ciências da Universidade do Porto Departamento de Física e Astronomia Studying evolved stars with Herschel observations Master’s degree in Astronomy João Manuel da Silva Santos Supervisor: Carmen Sanchez Contreras, CAB/INTA-CSIC Co-supervisor: Pedro Garcia Lario, ESAC 2015/2016 Acknowledgments This work would not have been possible without the opportunity and financing provided by ESAC Human Resources and the Science Operations Department in collaboration with the ESAC Faculty and the ESA Education Office. I would like to thank my supervisor Dr. Carmen Sánchez Contreras for her tireless support and for being always so helpful, steering me in the right direction. I thank my co-supervisor Dr. Pedro García-Lario for his mentoring and comments during the progress of this work. I leave a word of gratitude to Jésus Medina (PhD student) for providing the spectral data and with whom I used to meet almost weekly to discuss the progress of our work. I also would like to thank the Herschel/PACS expert Dr. Elena Puga for the enlightening meetings and advice. I thank my friends from CAB and ESAC for their comments and thoughts, and for contributing for the most amazing trainee experience. Finally I want to thank my parents for their unconditional support. This accomplishment would not have been possible without them. João Santos Abstract A systematic inspection of the far-infrared (FIR) properties of evolved stars allows not only to constrain physical models, but also to understand the chemical evolution that takes place in the end of their lives. In this work we intend to study the circumstellar envelopes (CSE) on a sample of stars in the THROES catalogue from AGB/post-AGB stars to planetary nebulae using photometry and spectroscopy provided by the PACS instrument on-board Herschel telescope. In the first part we are interested in obtaining an estimate of the size of FIR emitting region and to sort our targets in two classes: point-like and extended. Secondly, we focus on the molecular component of the envelope traced by carbon monoxide (CO) rotational lines. We conduct a line survey on a sample of evolved stars by identifying and measuring flux of both 12CO and 13CO isotopologues in the PACS range, while looking at the overall properties of the sample. Lastly, we will be interested in obtaining physical parameters of the CSE, namely gas temperature, mass and mass-loss rate on a sample of carbon stars. For that, we make use of PACS large wavelength coverage, which enables the simultaneous study of a large number of CO transitions, to perform the rotational diagram analysis. We report the detection of CO emission in a high number of stars from the catalogue, which were mostly classified as point-like targets with a few exceptions of planetary nebulae. High Jrotational number transitions were detected in a number of targets, revealing the presence of a significant amount of hot gas (T∼400−900 K) and high mass-loss rates. We conclude that Herschel/PACS is in a privileged position to detect a new population of warmer gas, typically missed in sub-mm/mm observations. Keywords: Evolved stars; Circumstellar envelope, far-infrared, mass-loss rate Resumo Uma inspeção sistemática das propriedades de estrelas evoluídas no infra-vermelho longínquo (FIR) permite não só refinar modelos físicos como também perceber a evolução química na fase final das suas vidas. Neste trabalho pretende-se estudar o envelope circum-estelar (CSE) numa amostra de estrelas do catálogo THROES, desde AGB/post-AGB até nebulosas planetárias, usando fotometria e espetroscopia do instrumento PACS a bordo do telescópio Herschel. Primeiramente, estamos interessados em estimar a dimensão da região que emite no FIR, separando objetos pontuais de extensos. De seguida, concentramo-nos na componente molecular do envelope, em particular na medição do fluxo de transições rotacionais dos isotopólogos da molecula de monóxido de carbono: 12CO e13CO. Por último, estamos interessados em obter parâmetros físicos do CSE, nomeadamente temperatura, massa de gás e taxa de perda de massa num conjunto de estrelas de carbono. Para tal, fazendo uso da grande cobertura de comprimento de onda de Herschel/PACS que nos permite estudar um grande número de transições simultaneamente, analisamos o chamado diagrama rotacional. Detetou-se emissão de CO num número elevado de objetos do catálogo, maioritariamente classificados como objetos pontuais excetuando algumas nebulosas planetárias. Encontraram-se transições correspondentes a elevados níveis rotacionais que revelam a presença de uma quantidade significativa de gás quente (T∼400 −900 K) assim como taxas de perda de massa elevadas. Conclui-se que Herschel/PACS é capaz de identificar uma nova população de gás quente tipicamente não detetável em observações no sub-mm/mm. Palavras-chave: Estrelas evoluídas, envelope circum-estelar, infravermelho longínquo, taxa de perda de massa FCUP Studying evolved stars with Herschel observations 2.14 Comparison between sizes from spectral cubes and photometry. . . . . . . . 39 3.1 PACS continuum subtracted spectra of 3 carbon-rich stars. . . . . . . . . . 45 3.2 PACS continuum subtracted spectra of 3 oxygen-rich stars. . . . . . . . . . 46 3.3 Generalized-cross-validation statistic. . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Continuum subtraction of the spectrum of CIT 6. . . . . . . . . . . . . . . . 53 3.5 Line’sFWHMofCIT6.............................. 57 3.6 CO line fluxes versus continuum fluxes. . . . . . . . . . . . . . . . . . . . . . 59 3.7 Part of the PACS range spectrum of AFGL 2688. . . . . . . . . . . . . . . . 61 3.8 A PACS-PACS color-color diagram. . . . . . . . . . . . . . . . . . . . . . . . 63 3.9 Spectral energy distribution of NGC 6537. . . . . . . . . . . . . . . . . . . . 64 4.1 HST images of HD 44179 and IRAS 16594-4656. . . . . . . . . . . . . . . . 73 4.2 Rotational diagram of AFGL 618 with ISO data. . . . . . . . . . . . . . . . 80 4.3 Rotational diagrams for a sample of C-rich stars. . . . . . . . . . . . . . . . 82 4.3 Continued...................................... 83 4.3 Continued...................................... 84 4.4 Change in the opacity correction with size variation. . . . . . . . . . . . . . 86 4.5 The effect of the optical depth on the rotational diagram of IRC+10216. . . 87 4.6 Rotational diagram of AFGL 2688 for different expansion velocities. . . . . 88 4.7 Analysis of regression residuals. . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.8 Testing BIC and AIC for model selection. . . . . . . . . . . . . . . . . . . . 92 4.9 Rotational diagrams with 2 temperature components. . . . . . . . . . . . . . 93 4.10 Rotational diagrams with 2 temperature components. . . . . . . . . . . . . . 94 4.11 Temperature histograms and ratios. . . . . . . . . . . . . . . . . . . . . . . . 97 4.12 Rotational diagrams of 13CO........................... 98 4.13 Temperature versus mass-loss. . . . . . . . . . . . . . . . . . . . . . . . . . . 101 B.1 PACS spectrometer FWHM as a function of the wavelength (from HSA). . . 181 B.2.2Gaussian models in photometry maps. . . . . . . . . . . . . . . . . . . . . . 182 B.3.1Photometry maps of extended sources. . . . . . . . . . . . . . . . . . . . . . 200 FCUP Studying evolved stars with Herschel observations B.4.1Fitting 12CO spectral lines in the carbon-rich AGB CIT 6. . . . . . . . . . . 204 B.5.1PACS range spectra of C-rich stars. . . . . . . . . . . . . . . . . . . . . . . . 207 List of Tables 1.1 Number of fully-reduced, available spectra in the THROES catalogue for eachclass...................................... 12 2.1 Average PACS FWHM derived for the spectrometer and photometer (scan speed 20"/s) using Neptune and Vesta observations respectively. . . . . . . 24 2.2 Gaussian parameters of 2 PN. . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3 FWHM comparison for 20 targets. . . . . . . . . . . . . . . . . . . . . . . . 40 3.1 Atomic and ionic fine-structure lines in the far-infrared. . . . . . . . . . . . 47 3.2 COlinesstatistics. ................................ 58 3.3 COisotopologueratio............................... 62 4.1 Characterisation of the PACS spectrometer observations. . . . . . . . . . . . 68 4.2 Properties of the stars in the sample. . . . . . . . . . . . . . . . . . . . . . . 76 4.3 Rotational diagram results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 4.4 Rotational diagram results for a double component fit. . . . . . . . . . . . . 96 4.5 Mass-loss rate in a sample of carbon stars. . . . . . . . . . . . . . . . . . . . 100 A.1 Stars in the THROES catalogue. . . . . . . . . . . . . . . . . . . . . . . . . 115 A.2 IRAS fluxes in 4 bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 A.3 Spectrometer beam size as a function of wavelength. . . . . . . . . . . . . . 121 A.4 Photometer beam size in two bands. . . . . . . . . . . . . . . . . . . . . . . 126 A.5 Fit parameters from HPF photometry maps. . . . . . . . . . . . . . . . . . . 128 A.6 Fit parameters from JScanam photometry maps in the blue and red bands. 130 A.7 Major axis, minor axis, position angle and FWHM from Jscanam maps. . . 132 FCUP Studying evolved stars with Herschel observations A.8 Continuum fluxes at selected wavelengths. . . . . . . . . . . . . . . . . . . . 135 A.9 Tabulated 12CO rotational transitions. . . . . . . . . . . . . . . . . . . . . . 142 A.10 Tabulated 13CO rotational transitions. . . . . . . . . . . . . . . . . . . . . . 143 A.11COlinefitting. ..................................145 A.12 Results of the rotational diagram without weights. . . . . . . . . . . . . . . 180 Acronyms & Abbreviations AGB Asymptotic-giant-branch AIC Akaike’s information criterion BIC Bayesian information criterion CI Confidence interval CSE Circumstellar envelope FIR Far infra-red FWHM Full width at half maximum GCV Generalized cross-validation HPF High-pass filter HSA Herschel Science Archive HST Hubble Space Telescope IRAS Infrared Astronomical Satellite LTE Local thermodynamic equilibrium MIR Mid infra-red NIR Near infra-red PACS Photoconductor Array Camera and Spectrometer PN Planetary nebula PPN Pre-planetary nebula PSF Point spread function RMSE root-mean-square error SNR Signal-to-noise ratio THROES Catalogue of Herschel Observations of Evolved Stars WD White-dwarf FCUP Studying evolved stars with Herschel observations FCUP 1 Studying evolved stars with Herschel observations Chapter 1 Introduction 1.1 Post-main sequence evolution of low-to-intermediate-mass stars As the hydrogen in the stellar core is depleted, the star drifts away from the mainsequence in the Hertzsprung-Russell diagram. Soon it begins to fuse helium in its core producing carbon and oxygen while burning hydrogen in a surrounding spherical shell. This process causes the star to gradually grow in size and luminosity, but to decrease its effective temperature. This marks the beginning of the red giant phase where the convective motions in the upper layers start to alter the chemical composition at the surface. These flows bring material from the core to the top inducing convective mixing in a phenomenon known as "dredge-up" that has been studied with spectroscopy for many evolved stars. 1.1.1 From the AGB to the WD stage The fate of these stars depends critically on their mass. Asymptotic giant branch (AGB) stars are an advanced evolutionary phase of low-to-intermediate mass stars powered by nuclear burning. At this stage the core is electron-degenerate, made of carbon and oxygen. The He-core phase was about 10 times shorter than the H-core burning phase, and this following phase will be even shorter. For stars with initial (main-sequence) mass of less than 8 M, carbon does not ignite, so the C/O core contracts, becoming increasingly electron-degenerate. This means that during the early AGB phase, the He shell burning FCUP 2 Studying evolved stars with Herschel observations Fig. 1.1: Schematic diagram of an AGB star (Decin, 2012) showing some physical mechanisms that take place in these stars and in their environment. The distance is in units of stellar radius R∗. dominates the energy output of the star. A recent review about the evolution throughout the asymptotic giant branch was presented by Herwig (2005). Figure 1.1 shows a schematic view from the inside of an AGB star to its surroundings. A "tiny" core is surrounded by an extended envelope up to several hundred R∗= R. The gas and dust that are able to escape the gravitational attraction form a cool (<1500 K), stellar wind best studied in the infrared. These stellar winds and the mass loss process in general, create huge extended circumstellar shells extending up to 3 pc in some cases. To understand the wind acceleration mechanisms and to derive the intricate structure of the envelopes, it is important to understand the later evolutionary stages of the bulk of stars in our Galaxy. Indeed, using a standard Salpeter initial mass function (IMF), 97% of all stars will eventually go through the AGB phase where mass-loss dominates stellar evolution, i.e., the star cannot be regarded as a sphere of gas in hydrostatic equilibrium anymore. The effect of nucleosynthesis and subsequent convective mixing determine the abundance structure of the stellar layers. Thermodynamic equilibrium and non-equilibrium reactions as well as ion-molecule reactions and dust condensation take place. FCUP 3 Studying evolved stars with Herschel observations Fig. 1.2: Evolutionary tracks in a Hertzprung-Russell diagram of a 2 Mstar (Herwig, 2005). The numbers indicate the logarithm of the approximate duration of each phase. The final phase of AGB evolution is characterised by thermonuclear flashes, or pulses, causing instabilities. Every time a dominant nuclear burning event occurs, a dredge-up may follow. After the first event in the end of the H-burning phase, another convective mixing can be induced in the end of the He-burning phase. A later, third event actually originates a class of star named carbon-star, that we will study further on. The actual physics of AGB stars and their properties are beyond the scope of this thesis. Instead, we will be interested in studying the circumstellar shells, privileged by the view of the Herschel Space Observatory. Once a solar-like star has exhausted its nuclear fuel, its core collapses into a white dwarf (WD) and the outer layers are expelled as a planetary nebula. In between, there is a short-lived stage (∼103yr) named pre-planetary nebula (PPN) that is observationally quite distinct. This subject was reviewed, for example, by Winckel (2003). Figure 1.2 depicts the evolutionary tracks of a 2 Mstar from the main sequence to the WD stage. Post-AGB (or PPN) stars are stars that are not massive enough to fuse carbon, but are still too cold to ionise the circumstellar envelope (CSE) ejected during the AGB phase. One of the most well studied PPNs is AFGL 618 (e.g. Sánchez Contreras et al. 2002; 2004; Bujarrabal et al. 2010; Soria et al. 2013). The shape of the circumstellar envelope is more often than not far from spherical symmetry with constant mass-loss rate. FCUP 10 Studying evolved stars with Herschel observations Fig. 1.6: Filter transmissions of the PACS photometer (Poglitsch et al. 2010). The reference wavelengths are 70 (blue), 100 (green) and 160 (red) µm. 2013). An example of the scientific capabilities of the photometer were showcased in two papers (Mayer et al. 2013; 2014) where the authors report the detection of Archmidean spirals around R Aqr, W Aql and π1Gruis (PI GRU), thus presenting solid evidence of a binary companion in all of them. The final photometry products, namely high-pass-filter maps and Jscanam maps used in this thesis were downloaded from the public Herschel Science Archive (HSA) and they were not reprocessed. 1.3.2 PACS spectrometer The spectrometer is a medium resolution, integral field unit that uses two Ge-Ga photoconductors arrays with 16 ×25 pixels (Poglitsch et al. 2010). One usually adopts the word "pixel" for the spectral pixels, while calling the 5×5array "spaxels", which stands for "spatial pixels". However, in this work we will use at times both terms indistinctly, though the context will provide its clear meaning. The spaxel size is 9.400 ×9.400, hence the field-of-view is of 4700 ×4700. Figure 1.7 depicts the spectrometer concept. The integral-field unit provides 25 spectra in a large area of the sky in the 51-220 µmwavelength range. A diffraction grating is a reflective optical element with parallel, equally spaced grooves. For PACS the grating is 32 cm long and has 8.5±0.05 grooves per mm which means that 2720 FCUP 11 Studying evolved stars with Herschel observations Fig. 1.7: Integral-field spectrometer concept. Credit: PACS observer Manual. grooves cover the length of the grating. PACS spectrometer has a resolving power R=λ/∆λbetween 940 and 5500, i.e. a wavelength-dependent spectral resolution of ∼55 −320 km s−1. There are three main observing modes: (1) - chopped line spectroscopy (for single lines); (2) - chopped range spectroscopy (large range) and (3) - wavelength switching mode, for single lines in extended sources. Recently the unchopped mode was also added. The PACS spectrometer flux calibration accuracy is constrained by detector response drifts and pointing jitter, limiting both the absolute flux accuracy and relative accuracy within a band. The accuracy to assume when comparing relative line fluxes within a spectral band is around 10% between 70 −100 µmand 20% between 100 −190 µm. There is also another source of uncertainty when comparing flux in different spaxels of typically 10%. PACS has been crucial to reveal the gas and dust content of circumstellar envelopes around AGB/post-AGB stars. In this context it allowed, for example, the discovery of the 69 µmfeature attributed to crystalline olivine, or forsterite, in a sample of 48 targets (Blommaert et al. 2014). It also revealed the impressive molecular content of IRC+10216, one of the most well studied AGB stars (Decin et al., 2010), with the detection of very high FCUP 12 Studying evolved stars with Herschel observations rotational level transitions of SiO, SiS and CO. More recenlty it permitted the detection of warm H2Ovapor in carbon-rich AGB stars (Lombaert et al. 2016). All PACS spectra used in this thesis were already fully reduced and available through the THROES website. 1.4 The THROES catalogue THROES stands for "caTalogue of HeRschel Observations of Evolved Stars" and contains a collection of Herschel PACS and SPIRE6spectra of over 100 evolved stars from AGBs to PPN and PN (Ramos-Medina et al. in prep.). Most stars are classified as lowto-intermediate mass stars (<8 M), but there are also few massive, hypergiant stars. Table A.1 summarises the number of stars organised in several classes in the catalogue with downloadable spectrum. Table 1.1: Number of fully-reduced, available spectra in the THROES catalogue for each class. Class number O-rich 22                  AGB (43) C-rich 16 S 4 C/S 1 OH/IR 15 post-AGB/PPN 28 PN 26 unclassified 1 total 113 At the moment of writting there are 113 stars in the catalogue with fully reduced spectrum, mostly AGB stars of types oxygen rich (O-rich), carbon rich (C-rich) and S type. The classification of MGE 4218 is not known with certainty so it was catalogued as a probable C or S (C/S) type. The only unclassified star in the catalogue is a blue supergiant7 (HDE 269006). The remaining targets are PPN and PN in almost equal numbers. 6SPIRE - Spectral and Photometric Imaging Receiver is another Herschel instrument. 7SIMBAD classification. FCUP 13 Studying evolved stars with Herschel observations Fig. 1.8: An example of the spectrometer raster for the point-like target π1Gruis. A cube slice at a selected wavelength channel is shown in the top left corner. 1.4.1 Data reduction and science ready products All PACS range spectra used in this thesis were already available through the catalogue website and fully reduced. To build the catalogue, the data was obtained from the Herschel Science Archive (HSA) and the reduction was done interactively using the HIPE8software. At the moment of writing, in the catalogue one can download 2 types of spectral data: (1) - rebinned cubes (figure 1.8) which contain one spectrum store in each spaxel of the 5×5array and (2) - 1D spectra which are the central spaxel with point-source correction applied and scaled to the flux level of the central 3×3superspaxel. In this thesis we used both products. In the example shown in figure 1.8 one sees that the actual usable spectra are found in the centre of the array, while the outer spaxels only contain background noise. This is, of course, what one expects to find for a point-like target. Moreover, in the website one can display the (FIR) SED of a star and compare fluxes observed with PACS to previous missions such as IRAS and AKARI. Although PACS spectrometer observed between 51 −210 µmit suffered from spectral leakage (order overlap) in the ranges 51 −55 µm,95 −105 µmand 190 −210 µmso the continuum shapes and flux densities in those ranges are not reliable. For that reason, these small ranges were cropped out of the final spectra. Another issue sometimes seen is a dip in the continuum that looks like a broad absorption feature situated between 62 −63 µm. This is interpreted as a filter artifact9. 8Herschel Interactive Processing Environment (Ott, 2010) 9http://herschel.esac.esa.int/twiki/bin/view/Public/DpKnownIssues FCUP 14 Studying evolved stars with Herschel observations 1.4.2 Characterisation of the sample of stars As mentioned before, the catalogue contains stars of various spectral types and evolutionary stages, thus different physical-chemical conditions in the CSE which we intend to investigate. In this section we expose the most important features that are relevant for this study. The classic IRAS two-colour diagram is a way to infer the dust/gas properties of the CSE. Photometric data in IRAS bands at 12, 25, 60 and 100 µmare also provided in the THROES website and in the appendix in table A.2. Following van der Veen & Habing (1988), IRAS colours are defined as: [12] −[25] = −2.5 log Fλ(12) Fλ(25)(1.1) [25] −[60] = −2.5 log Fλ(25) Fλ(60)(1.2) where Fλis the flux at a given wavelength. Figure 1.9 presents the IRAS two-colour diagram for the THROES targets with boxplots for each class. The AGB class (represented by black symbols) is further divided into 3 chemical types: O-rich, S and C-rich, corresponding to spectral types M, S and C respectively. The size of the boxplot is defined by the inter-quartile range (IQR) from Q1= 25th to Q3= 75th percentiles, while the whiskers extend to the most extreme data points not considered outliers, i.e., points that are outside Q1−1.5×IQR or Q3+ 1.5×IQR. If the data is normally distributed this corresponds to ±2.7σthat is 99.7% coverage. We see a clear separation between some classes. While AGB stars occupy the bottom left corner of the diagram with negative colours, the OH/IR and PN groups cluster around the centre, although the latter has greater scatter. Regarding AGBs, there is a notorious difference between the median colours of the sample of oxygen stars and carbon stars, which is probably a consequence of different dust properties because oxygenand carbon-rich dust have different emissivities. The median [25]-[60] colours are -1.8 and -1.5 for the O-rich and C-rich groups respectively. Since these colours are linked to the black-body dust-cooling continuum, the diagram also provides a comparison between temperature conditions in the CSE. Hence, a distinction is also very clear in terms of tem- FCUP 15 Studying evolved stars with Herschel observations Fig. 1.9: IRAS color-color diagram of the THROES sample. The dashed line is the empiric relation for O-rich and OH/IR stars (see text). perature, with the AGBs populating the hotter, lower left side of the diagram, while on the right side we find mainly PPN and PN with cold (T<200 K) dust emission. Van der Veen & Habing (1988) concluded that O-rich and OH/IR stars follow a evolutionary track towards increasing IRAS colours, and found the following empiric relation: [25] −[60] = −2.15 + 0.35 e1.5 ([12]−[25]) (1.3) which is draw in figure 1.9 as well. So the points located to the right of the main cluster of O-rich stars at [12] −[25] ∼ −1in our sample are likely to be relatively older stars. At that time the authors interpreted this trend as evidence that a star with a given mass starts the evolutionary track at the lower left side of the diagram and then evolves to the upper right to become a OH/IR star, with increasing mass-loss rates. There is 1 OH/IR star which is flagged as an outlier because it seems unusually cold Variability is another characteristic of many evolved stars and it is linked to radial FCUP 16 Studying evolved stars with Herschel observations pulsations and mass-loss. In fact, most of the AGB stars in this sample are known to be variable. There are several Mira variables10 (e.g. omi Cet, AFGL 3116, etc.), semiregular11 (e.g. U Hya, CIT 6, etc.) and RV Tau variables12 (e.g. U Mon, AC Her, etc). The complete list of targets can be found in table A.1 in the appendix. In what regards spectral features, namely atomic/ionic and molecular lines, we devote a section to the identification of the most common chemical species found in our spectra in chapter 3. To sum up, THROES contains a heterogeneous sample of evolved stars whose study allows to draw a complete picture of the physical-chemical conditions in the end of their lives. 1.5 Outline of the thesis This thesis is essentially divided in three parts. Each chapter starts with a brief introduction to the topic and in the end a summary is presented with the main conclusions. In the first part, we are interested in obtaining an estimate of the angular size of our targets, or at least an upper limit for point-like sources. For that, we fitted spectral cubes and photometry maps with a 2D-Gaussian model and established comparisons whenever possible. This procedure and discussion can be found on chapter 2. In the second part we explore the molecular content of these targets and conduct a CO survey in our spectra, while looking for correlations between line fluxes and continuum fluxes. We present a PACS colour-colour diagram that is able to separate stars in different evolutionary stages. We also compute isotopologue ratios. In chapter 4, we estimate physical conditions such as temperature and column density . Focusing on CO lines, we obtained the so-called rotational diagram for a sample of carbon-rich targets spanning several evolutionary stages from AGB stars to planetary nebulae. We also estimate the mass-loss rate from the derived gas mass. In chapter 5 we present final remarks and future prospects. 10Miras have very regular pulsations with an average period of ∼400 days (V-band) 11Semi-regular stars show irregularities in their pulsations (20-2000 days) 12They are very luminous stars (few thousand L) with periodicity of 40-150 days. FCUP 17 Studying evolved stars with Herschel observations Chapter 2 Point-like and extended far-infrared sources Our initial sample of PACS range observations stored in the THROES catalogue is diverse, containing 113 objects in different evolutionary stages. We want to estimate the angular extent of the emission traced by PACS and further classify them as point-like or extended targets compared to PACS field-of-view. The method we present here is to fit a Gaussian model directly to spectral cubes. We will present the main issues regarding this procedure and how to partly overcome them. Moreover, we perform the same routine in photometry counterparts to assess the reliability of the procedure and we compare the results. 2.1 PACS point-spread-function First of all, we have to understand how the images are produced. The point-spreadfunction, hereafter PSF, is the response of an imaging system to a point source and it is crucial to understand an astronomical observation. In other words, it describes how the observed flux is smeared by the optics. Whereas in ground based telescopes the PSF is dominated by the astronomical seeing (except in radio wavelengths), in space, Herschel is actually diffraction-limited (Poglitsch et al. 2010), i.e., it is capable of observing at its theoretical limit. Thus an Herschel observation will be limited by its maximum angular resolution. In our case the resulting image will be a convolution (notated ∗) of the observed flux, the PSF and the effect of the FCUP 18 Studying evolved stars with Herschel observations PACS squared detector array: image =true image ∗P SF ∗pixel size (2.1) At this point it is important to refer that the spectrometer usually does not properly sample (spatially) the PSF with a single pointing due to the large spaxel size. We will address this issue further on. In what follows we will indistinctly use the terms PSF and beam as synonyms of the same entity. We first focused on measuring the PSF size for both PACS spectrometer and photometer, instead of taking the commonly assumed values in literature. Essentially we will be measuring the term [PSF ∗pixel size] in equation 2.1, which will be different for both instruments. Obviously the true PSF of a given observation may differ from the model due to pointing jitter and other effects, but at least by doing this in a systematic way we get a grasp of the range of possible values one can expect to find. This allows not only a deeper understanding of the instrumental response, but also a way to better separate true point-like from extended sources. The first ones should have a FWHM comparable to the PSF while the extended sources would fill the 4700 ×4700 spectrometer field-of-view (FOV). 2.1.1 A 2D elliptical Gaussian model The inner-part of the of the diffraction pattern can be approximated by a 2-dimensional Gaussian function f(x, y)for its simplicity and efficiency. The model is given by: f(x, y) = Pexp −A(x−xo)2+ 2B(x−xo)(y−yo) + C(y−yo)2 (2.2) with: A=cos2θ 2σ2 x +sin2θ 2σ2 y (2.3) B=sin 2θ 4σ2 x−sin 2θ 4σ2 y (2.4) C=sin2θ 2σ2 x +cos2θ 2σ2 y (2.5) where Pis the peak intensity, x0and y0are the peak coordinates, θis the position angle measured counterclockwise and σxand σyare the dispersion (or width) of the gaussian in FCUP 19 Studying evolved stars with Herschel observations two orthogonal directions, which will be either the major or minor axis depending on the axis from where the rotation starts. The FWHM = 2√2 ln 2 σ∼2.355 σis then computed for both directions so that we get the major axis of the ellipse aand the minor axis b, at half-intensity. Figure 2.1 depicts a 81 ×81 resolution image with a mock, unit-normalisedgaussian distribution. Fig. 2.1: Gaussian model validation with mock data; left: 2D-gaussian distribution; right: Visualisation in 3D. To perform the fit we used a Trust-Region-Reflective numeric algorithm (e.g. review from Yuan 2015) which is basically a mathematical optimization operation in the leastsquares sense, very effective for solving non-linear problems. Given the variance σ2 i(not to be confused with the gaussian width) associated with each data point, the weights are defined as: wi= 1/σ2 i. The code was implemented in MATLAB by making use of the function fit1. To check the goodness of fit we analysed the root-mean-squared-error (RMSE), also know as the standard error of the regression, which is defined as the square root of the sum of the squared residuals divided by the number of degrees of freedom. The latter is defined as the number of response values minus the number of parameters. The RMSE should be small in a good fit. 1http://es.mathworks.com/help/curvefit/fit.html FCUP 26 Studying evolved stars with Herschel observations Fig. 2.5: Example of a 5×5PACS rebinned cube (left) and two interpolated cubes (right) at λ∼155µm. This target is the pre-planetary nebula AFGL 618. From left to right the spaxel size is 9.400,4.700 and 300. extended. In addition, not only the position angle is harder to be perceived with such little resolution, it can also be artificially produced due to the uneven grid of the spectrometer footprint. To improve this procedure, we also performed the fit in interpolated cubes obtained using HIPE task specInterpolate. In this kind of cube the number of spaxels is increased to a desired value. An example of these cubes is illustrated in figure 2.5. 2.2.1 Fitting channel by channel We want to model the 5×5×Ncube that contains 25 spectra of a given object in 2 or 4 wavelength ranges, depending on how the observation was carried. For each layer of the cube, i.e. each wavelength step, we obtain a 5×5image and perform the Gaussian fit. We obtain an average FWHM, notated Φ = √a.b, by averaging the derived major and minor axis at half-maximum for each wavelength step. Additionally, we compute a weighted average around selected wavelengths to directly compare to our beam size. For an arbitrary parameter, x: ¯x=Pn i=1 xiσ−2 i Pn i=1 σ−2 i (2.9) so that the variance of the mean is given by; σ2 ¯x=1 Pn i=1 σ−2 i (2.10) We deconvolve the obtained average size with the corresponding beam FWHM (table 2.1) using: FCUP 27 Studying evolved stars with Herschel observations 200 400 600 800 1000 a) flux (Jy) 8 9 10 11 12 13 14 b) √a.b (arcsec) beam size wavelength (µm) 60 80 100 120 140 160 0 2 4 6 8 10 12 c) Φd(arcsec) Fig. 2.6: Fitting rebinned cubes layer-by-layer: the case study of AFGL 618. Top: PACS range spectra; Middle: average FWHM; Bottom: deconvolved size. The shaded area corresponds to 2σbounds. Φd=qΦ2−Φ2 PSF (2.11) at selected wavelengths, with errors given approximately by: δΦd= (Φ2−Φ2 PSF)−1/2 qΦ2δ2 Φ+ Φ2 PSFδ2 ΦPSF (2.12) Note that equation 2.12 does not include absolute flux calibration errors. Next we present a case study to exemplify the fitting across wavelength of AFGL 618. Figure 2.6 shows a PACS range spectra in the top pannel, the average FWHM in the middle and the deconvolved size in the bottom. For displaying purposes the entire range was FCUP 28 Studying evolved stars with Herschel observations deconvolved using the linear regression models, so that one can see that when subtracting the PSF from the image, the derived FWHM remains approximately constant with wavelength. AFGL 618 is regarded as a point-like target as observed with Herschel/PACS instrument. However, we see that for wavelengths shorter than 100 µmits average FWHM is systematically larger than the beam, well beyond the formal errors. We believe this is just a consequence of the square detector footprint blurring the image, as we know that its effect dominates in this range. In the reddest part of the spectra, the beam size increases almost linearly and so it does the Gaussian size of AFGL 618. However, in this portion of the spectrum, the measured size pretty much agrees with the beam size at a confidence level of 2σ. The sudden drops in size are due to channels with null variance for which the weighted-least-squares method fails. We also note that the estimated standard errors here are much larger than before, about 1-2". An interesting feature that can be seen in few targets is what we call "extended line emission". In AFGL 618 it is pretty clear that some lines are slightly more extended than the continuum (figure 2.6). The ionised species found in the spectra of NGC 6537 are also a good example of extended emission. In figure 2.7 we show the spectral cube layers around an ionised carbon line ([CII]) where we see a clear difference in the flux contours compared to the continuum region. These larger sizes at line positions are rare and definitely not common in molecular emission. In other cases we observe that the derived FWHM stays constant with wavelength while in other targets the FWHM decreases at line positions. Regibo (2012) only found the latter case in their sample and attributes this effect to the instrumental design. The fitting procedure was repeated, when possible, for the remaining targets in the catalogue. About 30 targets were excluded because they were not observed in the entire PACS range, but in rather small portions of the spectrum (∼3µmbands) so the fit results are not trustworthy. The FWHM was deconvolved at selected wavelengths by averaging it around an arbitrarily small number of channels. We chose 30, which is about 0.5 µm. The fit was also performed in continuum modelled cubes, i.e., cubes that contain spectra without spectral lines to verify if they impact significantly the derived FWHM. This was FCUP 29 Studying evolved stars with Herschel observations 157.377 m 0 10 20 157.47 m 0 10 20 157.437 m 0 10 20 157.467 m 0 10 20 157.57 m 0 10 20 157.537 m 0 10 20 157.567 m 0 10 20 157.597 m 0 10 20 157.627 m 0 10 20 157.657 m 0 10 20 30 157.697 m 0 20 40 157.727 m 0 20 40 157.757 m 0 20 40 60 157.787 m 0 20 40 60 157.817 m 0 20 40 157.847 m 0 10 20 30 157.877 m 0 10 20 157.917 m 0 10 20 157.947 m 0 10 20 157.977 m 0 10 20 1587 m 0 10 20 158.037 m 0 10 20 158.067 m 0 10 20 158.097 m 0 10 20 158.137 m 0 10 20 continuum continuum Fig. 2.7: Flux density contours around the [CII] line (157.7µm),in NGC 6537. The red box encloses the channels closer to the line peak position. achieved by fitting a low-order polynomial to the spectra and masking out the lines using HIPE. We concluded that due to averaging their effect is mitigated, hence the reported sizes across wavelength reflect the FWHM of the continuum. The fitting routine for this kind of data is much more sensitive to the peak intensity and flux ratios between the central and outer spaxels. For example, the fit is usually not good for very faint and noisy targets and it may fail to converge in targets where the peak intensity is not centred in the array. In particular, for point-like targets the relative (statistical) uncertainty in the FWHM can be quite high (up to 40%). It is difficult to evaluate the goodness of the fit in these conditions so a careful comparison with other data, methods and even literature is needed to assess the reliability of this procedure. This was achieved by comparing the FWHM for a "control-sample" of 20 targets for which we have photometry data. Before that we will explain in the next section how we used interpolated cubes to overcome the sampling limitation. FCUP 30 Studying evolved stars with Herschel observations 2.2.2 Interpolated cubes HIPE has an algorithm - specInterpolate3that is able to do a linear interpolation to increase spatial resolution. However we are not interested in increasing the sampling too much, otherwise we would be including artifacts and unpredictable interpolation errors that HIPE currently does not provide. Thus we chose to double the spatial resolution so that the spaxel corresponds to 4.700. Note that single pointing observations do not allow reconstruction of the true morphology of the target, thus we regard our interpolated cubes as merely reasonable approximations. 2.3 Photometry maps We cross-matched our target’s table with entries in the HSA and we found 45 observed targets with PACS photometer, most of them first published in Cox et al. (2012). We obtained a total of 180 photometry maps of two types: scanamorphous maps (Jscanam) and high-pass-filter (HPF). An inspection of the data made us exclude objects that do not show a centrally peaked flux, for that a Gaussian model would be inappropriate. They exhibit instead bright arcs and rings, such is the case of NGC 40 and NGC 6781, two extended PN. We devote a section to extended targets further on. We ended up with a total of 37 targets, among which AGBs and PPNs and we performed the 2D-Gaussian fit in blue and red bands. Figure 2.8 shows an example of Jscanam maps in the blue and red bands of the AGB star X Her. Filaments and arcs are visible in the FIR image of this target which was interpreted as a consequence of interaction between wind ejected by the star and the interstellar medium (Jorissen et al. 2011). All sorts of interesting features can be found in some of these photometry maps, but we will focus on deriving the FWHM of the inner emission. As mentioned before, the aim of this procedure is to assess the reliability of the sizes obtained from fitting spectral cubes, but we could not help noticing some correlations and other interesting aspects revealed by photometry maps. 3http://herschel.esac.esa.int/hcss-doc-13.0/load/pacsspec/html/P drgS.Chp.4d.pointV Sraster.html FCUP 31 Studying evolved stars with Herschel observations Fig. 2.8: Photometry postcard obtained from the Herschel Science Archive (adapted) for the AGB star X Her. Left: Blue JScanam map; right: Red Jscanam map. 2.3.1 High-pass-filter vs Jscanam We want to assess an eventual dependence of the derived parameters on the map-maker algorithm. We considered high-pass-filter (used for point-like sources) and Jscanam maps (used for point-like and extended). There is a third type named UNIMAP which is not available for every target in the HSA because it is not the default algorithm. In HPF maps a small-sized filter is used to boost point source sensitivity, so that the wings of the PSF and faint extended emission disappear, plus overall flux losses can occur (Popesso et al. 2012). This could be an issue if the target is not masked a priori. Jscanam is the (jython-) HIPE implementation of the scanamorphos algorithm developed by Helene Roussel4. Since PACS photometer detectors are bolometers5, their signal is dominated by the low-frequency, uncorrelated 1/f noise (e.g. Graciá et al. 2015). In order to solve this problem, Jscanam maps combine scan plus cross-scan observing modes, where the region of interest is observed first in a given scan direction and then scanned again in a perpendicular direction. Besides the 6 parameters in equation 2.5, we define the flux Fwhich corresponds to the volume under the gaussian surface as: 4http://www2.iap.fr/users/roussel/herschel 5Bolomoters measure the power of incident radiation via heating of materials with a temperature dependent electrical resistance. FCUP 32 Studying evolved stars with Herschel observations F= 2πPσxσy(2.13) with standard errors given by: δF ≈FsδP P2 +δσx σx2 +δσy σy2 (2.14) In figure 2.9 we compare peak intensities, flux (not background subtracted) and FWHM obtained from these 2 types of photometry maps in both blue and red bands. These results are listed in tables A.5 and A.6 in the appendices. Overall the fitted peak intensities and integrated fluxes agree within the absolute flux uncertainties (<10%) with the obvious exception of R Cas which has a measured peak 30% higher in high-pass-filter maps. This goes against the global trend which is the inverse scenario with the Jscanan maps providing larger peak intensities in both bands. This could be related to the lack of source masking prior to filter usage. Indeed, the best agreement between these 2 map-makers was found on targets where we are sure that the masking was performed since the mask is made available in the downloadable products from the archive. U Hya is the second faintest target in this 37-target sample and the derived fluxes obtained from the two maps disagree above 10% in the red band, despite agreeing very well in the blue band. Naturally, the discrepancy is also seen the size ratio. An inspection of the data does not reveal apparent problems in U Hya neither in R Cas, so a probable explanation for this behaviour lies on the map-maker algorithms themselves. Another noticeable pattern is that peak intensities are always higher in the blue band, spanning a couple of orders of magnitude. Furthermore, when we compare the derived FWHM from these 2 map-makers we see that the ratio is mostly above 1, with the highpass-filter maps resulting in slightly larger FWHMs (up to 6%). Thus, when the integrated flux is computed, these two quantities balance each other as expressed in equation 2.13 in such way that the flux ratio is around 1 with smaller scatter. We conclude that the difference in FWHM obtained from high-pass-filter maps and Jscanan maps is not meaningful for our purposes and it is, in fact, of about only 2% in the blue band and 1% in the red band on average. Nevertheless to avoid improper masking FCUP 33 Studying evolved stars with Herschel observations PHPF (Jy/px) 10-2 10-1 100101102 PHPF / PJSCANAM 0.8 0.9 1 1.1 1.2 1.3 FHPF (Jy) 10-1 100101102 FHPF/FJSCANAM 0.8 0.9 1 1.1 1.2 1.3 1.4 ΦHPF (arcsec) 4 6 8 10 12 14 16 ΦHPF / ΦJSCANAM 0.88 0.9 0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 R CAS R CAS R CAS U HYA HD 161796 NML TAU W ORI AFGL 3116 IRAS 17347-3139 X HER HD 235858 U HYA NGC 6302 NGC 6302 Fig. 2.9: Results comparison between HPF maps and Jscanam maps. Blue and red points correspond to results obtained for the blue and red bands respectively. Left: peak intensity ratio (top) and flux ratio (bottom). Right: FHWM ratio. issues we decided to use only Jscanan maps in what follows. 2.3.2 Correlations from photometry maps In figure 2.10 we compare the blue and red FWHM. We observe that there is a linear correlation between the FWHM in two bands (Φ70 and Φ160). The density curves intend to show the FWHM and peak intensity scatter. Essentially one verifies that there is a larger scatter in the red band FWHM compared to the blue band, whereas the inverse occurs when one compares peak intensities. The largest target in this 37-targets sample is NGC 6302 with a FWHM of Φ70 = 9.900 and Φ160 = 15.100, in the blue and red bands respectively. This young planetary nebula also shows the highest red-to-blue flux ratio being 40% brighter in the red band. The FIR excess is probably consequence of cold dust. NGC 6302 could be a great target to compare to spectroscopy imaging results to photometry due to its extension, but a PACS/spectrometer mispointing prevents us from doing proper analysis. The brightest targets are, by far, AFGL 2688 and IRC+10216 which seem to be somewhat extended in the blue band with Φ70 = 6.900 and Φ70 = 6.800 respectively (ΦPSF = 5.500). It is interesting that while IRC+10216 is circular with an ellipticity e= 1 −b/a =0.05, consistent with the observed spherical shells (e.g. Cernicharo et al. 2015), AFGL 2688 has FCUP 34 Studying evolved stars with Herschel observations P (Jy/px) 0 10 20 30 40 50 60 70 Φ (arcsec) 5 6 7 8 9 10 11 12 13 14 15 70 µm 160 µm Φ70 (arcsec) 6 8 10 Φ160 (arcsec) 11 12 13 14 15 Fig. 2.10: Peak intensity versus FWHM obtained for Jscanam maps. The color code corresponds to the blue and red photometric bands. The smaller pannel illustrates the correlation between the derived sizes in both bands. a difference between major and minor axis of 0.9", which translates into a ellipticity of 0.12. We found an elongation along a position angle of 58◦, in agreement with the thermal emission observed in the radio at P.A=53◦(Jura et al. 2000). One of the puzzling features of this nebula is the fact that the symmetry axis of the optical and near-infrared lobes is at P.A=15◦, but the symmetry axis at radio wavelengths, including CO emission, is at P.A=53◦−60◦(Goto et al. 2002). So does it seems to be the case of FIR emission. Here it is important to note that the emission we observe with PACS photometer is a superposition of the continuum together with spectral lines, namely the dominant carbon-monoxide lines. In the red band the ellipticity of AFGL 2688 slightly increases and yet the FWHM is consistent with the PSF FWHM derived for Vesta. The P.A increases to 73◦, but this result is intrinsically not so accurate due to the camera’s larger pixel. Figure 2.11 shows the linear correlation between red band and blue band fluxes. We found that most targets are brighter in the blue band with the exception of NGC 6302 and IRAS 22036+5306. HD 44179 (The red rectangle) has a Fred/Fblue ≈1. FCUP 35 Studying evolved stars with Herschel observations Fblue (Jy) 100101102103 Fred (Jy) 10-1 100 101 102 103 Fred = 0.74 Fblue Fig. 2.11: Relation between the integrated flux in the blue and red bands. The red line corresponds to the best linear least-squares fit. 2.3.3 Extended sources: rings and arcs To finish the topic regarding photometry maps, we present some final considerations about extended sources revealed through this data. Figure 2.12 shows an example of planetary nebula in which the extended FIR emission is clearly not well modelled by a Gaussian function. The remaining 7 PN can be found in the appendix of figures. Some of them exhibit arcs such NGC 40 and NGC 6445. The largest target in the complete sample is definitely NGC 6781 with an angular distance between intensity peaks in the E-W direction of approximately 10000. On the other hand, NGC 7026 looks more compact and fits inside PACS field-of-view. But since it shows double-peaked emission in the blue band it was also separated from the remaining targets. Although the blue band photometry reveals interesting features, in some cases in the red band that information is lost due to halving of angular resolution. Thus in the red band one can approximate the observed flux density distribution of NGC 7009 and NGC 7026 by a 2D-Gaussian quite well. The results are shown in table 2.2 and figure 2.13. The error bars are the propagated statistical uncertainties. These are good examples to compare with PACS spectroscopy imaging. FCUP 42 Studying evolved stars with Herschel observations like with the exception of 8 PN and 1 OH/IR star. The fit is completely bad6for about 30% of the sample, so these results are inconclusive. The extended sources identified in this work are: PN MZ3, NGC 6781, NGC 40, NGC 6543, NGC 6545, NGC 3242, NGC 6826 and IRAS 19312+1950. At least two sources, IC 418 and NGC 7026, are semi-extended, but still not properly sampled by PACS. 2.5 Summary •We studied the spectrometer PSF by fitting a 2D-Gaussian model to Neptune mapping observations with the newest calibration files. •We also fitted Vesta observations to measure the inner size of the photometer’s PSF for several positions in the field-of-view. •We used photometry maps to find extended sources. After excluding 8 planetary nebulae that show bright rings and other features we obtained the FWHM of 37 targets by fitting the same Gaussian model. •We concluded that reliable and equivalent estimates of the FWHM can be obtained from HPF and Jscanam maps. •We fitted two types of spectral cubes: rebinned and interpolated, and found that most targets in the THROES catalogue are point-like. In fact, only 9/72 appear to be extended sources. For the remaining 35 targets in the catalogue the fit is inconclusive. •From the comparison of sizes derived from red band photometry and spectral cubes we concluded that the latter provide a FWHM 10% higher on average. 6Very high RMSE and a variation in the size of up to 10” in adjacent wavelength channels. FCUP 43 Studying evolved stars with Herschel observations Chapter 3 CO and other spectral features in evolved stars In this chapter we analyse the spectra of 107 stars in the THROES catalogue by identifying the most common spectral features1, namely molecular and atomic/ionic (finestructure) lines, while conducting a survey of CO emission. The main goal in this chapter is to fit CO lines that will be used to infer physical conditions of the CSE in chapter 4. PACS observations are best suited for tracing a warmer gas component in the circumstellar shells and outflows around evolved stars, usually missed in sub-mm/mm observations. 3.1 Features in PACS spectra In general, PACS range spectra are crowded with prominent emission lines. Line emission occurs when atoms or ions make a transition from one bound electronic state to another bound state at a lower energy. Additionally, vibrational and rotational states of molecules can be excited either by collisions or by radiation, also giving rise to emission lines upon de-excitation. Because these 2 modes have much smaller energy separations than those of electronic states, the vibrational and rotational transitions occur from the infrared to the millimetre-wave regions of the electromagnetic spectrum instead of the visible and near-UV as in the case of electronic transitions. The chemical species found in THROES targets and their relative line strengths are expected to vary according to the evolutionary stage and spectral type. 1We do not cover solid-state (dust) features in this thesis. FCUP 44 Studying evolved stars with Herschel observations 3.1.1 Molecular lines In figure 3.1 we compare the continuum subtracted2spectrum of 3 C-rich stars in the THROES catalogue spanning different evolutionary stages from AGB to PN. Straightaway we see significant differences such as the richer molecular content in the youngest star (CIT 6) relatively to the PN IRAS 21282+5050 as expected. Noticeably, that is the main difference between the emission line spectra of AGBs and PNs with the latter being almost devoided of molecular lines and yet showing strong ionic emission. Since molecules were not expected to survive in the hostile, ionised environment of PN, the first detection of CO in a PN (NGC 7027) was a surprising discovery (Mufson et al. 1975). In fact, in this case the amount of molecular gas mass inferred from the first CO transition appears to be about 10 times higher than the mass of ionised gas. Anyway, the presence of CO is probably the remnants of the molecular gas of the AGB phase. The strongest molecular features in the AGB and PPN spectra in figure 3.1 belong to CO isotopologues and HCN. However, in the case of O-rich AGB stars there are number of brighter lines of different chemical species. In figure 3.2 we show 3 examples of O-rich stars (NML Tau, AFGL 6815 and NGC 7026) of different evolutionary stages. A number of strong lines in the spectrum of NML Tau (or IK Tau) appear to correspond to H2O(both orthoand para-water) and OH. Some fainter lines could be SiO, SO or SO2typically found in O-rich targets. Line identification is not an easy task since there are several hundred predicted lines in this wavelength range that frequently overlap. In the O-rich PPN AFGL 6815 (also known as Cotton Candy Nebula) CO is dominant, despite multiple weaker unidentified lines being present, whereas in NGC 7026 CO rotational lines do not exist in the PACS range. 3.1.2 Atomic/ionic lines There are essentially two processes (besides cosmic rays) that can convert molecules back to atoms and ions: (1) - the stronger (UV) stellar radiation field that induces pho2This procedure is explained in the next section. FCUP 45 Studying evolved stars with Herschel observations 0 20 40 60 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO HCN HCN HCN Flux (Jy) -50 0 50 100 Flux (Jy) λ(µm) 56 58 60 62 64 66 68 70 72 0 200 400 600 800 Flux (Jy) AFGL 2688 IRAS 21282+5050 CIT 6 AGB PPN PN [OI] 0 20 40 60 80 100 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO HCN HCN HCN HCN HCN HCN HCN HCN HCN HCN HCN HCN 13CO 13CO 13CO 13CO 13CO Flux (Jy) -25 0 25 50 75 Flux (Jy) λ(µm) 75 80 85 90 95 0 10 20 30 40 Flux (Jy) 0 20 40 60 80 100 12CO 12CO 12CO 12CO 12CO 12CO 12CO HCN HCN HCN HCN HCN HCN HCN HCN HCN 13CO 13CO 13CO 13CO 13CO 13CO 13CO Flux (Jy) 0 30 60 90 120 Flux (Jy) λ(µm) 105 110 115 120 125 130 135 0 3 6 9 Flux (Jy) 0 20 40 60 80 100 12CO 12CO 12CO 12CO 12CO HCN HCN HCN HCN HCN HCN HCN 13CO 13CO 13CO 13CO 13CO 13CO CS CS CS CS CS CS CS CS CS Flux (Jy) 0 100 200 300 Flux (Jy) λ(µm) 145 155 165 175 185 0 50 100 150 200 250 Flux (Jy) [OI] [CII] Fig. 3.1: PACS continuum subtracted spectra of 3 carbon-rich stars of different evolutionary stages.: CIT 6 (orange), AFGL 2688 (blue) and IRAS 21282+5050 (green). FCUP 46 Studying evolved stars with Herschel observations 0 50 100 150 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO Flux (Jy) -10 0 10 Flux (Jy) λ(µm) 56 58 60 62 64 66 68 70 72 0 200 400 600 Flux (Jy) NML Tau AFGL 6815 NGC 7026 AGB PPN PN [NIII] [OI] 0 50 100 150 200 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO 12CO H2O H2O H2O Flux (Jy) -5 0 5 10 Flux (Jy) λ(µm) 75 80 85 90 95 0 400 800 1200 1600 Flux (Jy) [OIII] 0 30 60 90 120 12CO 12CO 12CO 12CO 12CO 12CO 12CO H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O Flux (Jy) 0 5 10 Flux (Jy) λ(µm) 105 110 115 120 125 130 135 0 5 10 15 20 Flux (Jy) [NII] 0 30 60 90 120 12CO 12CO 12CO 12CO 12CO H2O H2O H2O H2O H2O H2O H2O H2O H2O H2O OH OH OH 13CO 13CO 13CO 13CO 13CO Flux (Jy) 0 10 20 30 Flux (Jy) λ(µm) 145 155 165 175 185 0 10 20 30 40 Flux (Jy) [OI] [CII] Fig. 3.2: PACS continuum subtracted spectra of 3 oxygen-rich stars of different evolutionary stages.: NML Tau (red), AFGL 6815 (blue) and NGC 7026 (purple). FCUP 47 Studying evolved stars with Herschel observations Table 3.1: Atomic and ionic fine-structure lines in the far-infrared (Kwok 2000). Ion Wavelength (µm) Energy (eV) [SI] 56.311 0 [NIII] 57.317 29.60 [PII] 60.64 10.48 [OI] 63.184 0 [FII] 67.2 17.42 [SiI] 68.473 0 [OIII] 88.356 35.12 [AlI] 89.237 0 [FeIII] 105.37 16.19 [NII] 121.898 14.53 [SiI] 129.682 0 [OI] 145.525 0 [CII] 157.741 11.26 todissociation; (2) - shocks resulting from the interaction between slow and fast winds. In a simplified way, both mechanisms originate atoms, which can be further ionised giving rise to many permitted transitions in the NIR and strong forbidden lines like [OIII] at 88 µmand [CII] at 158 µm. The latter are example of fine-structure lines corresponding to transitions between states of the same multiplets (Kwok 2000). In table 3.1 we tabulate the most common lines in the far-infrared. Atomic and ionic lines are characteristic of PN and they do not show up in AGB’s spectra. The most prominent features in the spectra of IRAS 21282+5050 and CPD-568032 and other C-rich PN are [OI] and [CII], while in NGC 7026 (O-rich) we find even higher-degree ionised species, in particular [OIII] as shown in figure 3.2. From other studies in literature, the first two PN are known to be very compact, low-excitation PN (e.g. Kwok et al. 1993); Chesneau et al. 2006). In contrast, NGC 6537 (not displayed) is an extreme opposite case being a huge high-excitation, slightly O-rich PN (Lawrence et al. 1999; Edwards & Ziurys 2013). In its spectrum we found higher ionised species such as [NIII] and [OIII]. The FIR emission of NGC 7026 seems to be more compact (figure 2.12) than NGC 6537, but their spectra have some similarities namely the presence of a larger variety of lines compared to FCUP 48 Studying evolved stars with Herschel observations IRAS 21282+5050. In the two displayed PPN (AFGL 2688 and AFGL 6815) spectra in figures 3.1 and 3.2 we do not detect atomic/ionic lines which is an indication that the central star is not hot enough to ionise the bulk of the CSE. Further on we will study in greater detail another C-rich PPN named AFGL 618. The PACS spectra of AFGL 2688 and AFGL 618 are similar, being dominated by CO lines. Other molecules are visible such as HCN and CS amongst some other faint lines of unidentified species. However, there are already significant differences between these 2 PPN, namely the presence of ionised gas in the latter revealed by the [OI] lines at 63 µmand 146 µm. This is an indication that AFGL 618 is already entering the PN stage. A more detailed view over the 3 C-rich targets plotted in figure 3.1 will be given in chapter 4. Note that the spectrum of every single star in the THROES catalogue cannot be displayed and studied here in detail, but can be accessed through the catalogue website. 3.2 Identifying and fitting CO lines Carbon-monoxide is one of the most important molecules in astronomy. Despite being the most common molecule in the Universe, H2is a homonuclear, linear molecule with no permanent dipole moment, thus all the low-lying energy levels are quadrupole transitions with small transition probabilities, but relatively high excitation energies. This means they are only excited in high temperatures or strong UV radiation fields conditions. Therefore, the most abundant molecule that carries most of the gas mass and plays a key role in the thermal balance and gas-phase chemistry, is practically invisible to direct observation. Consequently, we rely on the so-called "tracer" species, generally CO, to study CSE chemistry and ISM across the galaxy. CO is a very stable molecule because it is held together by a triple (polar) covalent bound (figure 1.4). However, it can be excited to rotational levels above the ground state by radiation or collisions (namely with H2). The energy levels3of the rotational states of a diatomic molecule (such as CO) are given by: 3Obtained (RJ) by solving the Schrödinger equation ˆ HΨ = EΨof the rigid rotor. FCUP 49 Studying evolved stars with Herschel observations EJ=~ 2IJ(J+ 1) (3.1) where J= 0,1,2... is the rotational quantum number, Iis the moment of inertia and his the Planck constant. In this case the lowest rotational transition, J= 1 →0, has a frequency of 115 GHz, or a wavelength of 2600 µm, which is well outside Herschel range. In fact, the first detectable CO transition falling within Herschel/PACS range is the J= 14 →13 at ∼186 µm. The complete list of CO transitions in PACS range can be found in table A.9. CO can be found in several isotopologue forms. The most common one is 12C16O, while others such as 13C16O,12C18Oor 12C17Oare far less abundant. One of the most important observational quantities to measure is the 12CO/13CO ratio as it can be used to trace past star formation history. It is believed, for instance, that the 12CO/13CO ratio evolves as consequence of nucleosynthesis in AGB stars and there is observational evidence that the ejecta from AGB stars dominates the evolution of the isotopologue-ratio in the local ISM (Ramsted & Olofsson 2014, and references therein). This ratio derived for stars in different evolutionary stages is usually different. Although this ratio is not so well constrained for M-type stars (O-rich AGBs) and PN, it is well known for carbon AGB stars through measurements of photospheric molecular NIR lines (Lambert et al. 1986; Ohnaka & Tsuji 1996) and CO observations in the radio (e.g. Schöier & Olofsson 2000). While Lambert et al. (1986) found that the 12CO/13CO ratio is between 30-70, Schöier & Olofsson (2000) found lower ratios by a factor of 2 for the same targets. Based on optical data Abia & Isern (1997) estimated ratios in the range 20–35 for most carbon stars in their sample. In what regards OH/IR stars Delfosse et al. (1997) estimated much lower ratios (∼4) suggesting these are massive stars where the hot bottom burning process has converted 12Cinto 14N. More recently, Ramsted & Olofsson (2014) consistently estimated the 12CO/13CO ratio in a relatively larger sample of stars of 3 spectral types (M, S and C) and derived a median ratio of 13, 26 and 34 respectively, while not finding any correlation whatsoever with mass-loss rate. In this chapter we fitted the rotational line profiles of 12CO and 13CO isotopologues in the ground vibrational state. For that, the first step involves subtracting the continuum. FCUP 50 Studying evolved stars with Herschel observations 3.2.1 Continuum subtraction No standard parametric function is able to accurately reproduce the shape of the continuum of most targets in the entire PACS/spectrometer range. While a simple degree-one or -two polynomial fits rather well the region above 100 µm, that is surely not the case of the bluest, bumpy part of the spectrum. A non-parametric method is then needed for this purpose. One of the most popular ways to do it is by using splines which are piecewisedefined polynomials. A drawback of this approach is that one has to choose the number of nodes where the pieces connect, i.e., a smoothing parameter that controls the appearance of the fit. So, if we want to process the entire sample of THROES targets this is definitely not the fastest or pratical way to do it. Alternatively, we used local-regression which has been applied in a number of fields, but not so much in astronomy. For that we used a free R package called locfit4(Loader 1999). Basically the difference between local-regression and standard regression techniques is that instead of finding the parameters of a given model to minimise the squared sum of residuals of the entire data set, it computes a weighted least-squares in a sliding window using a polynomial (degree 2 by default) in a nearest-neighbours fashion. Note that a smoothing parameter (0< α ≤1) also exists in local-regression and it is related with the proportion of data to use in each fit. To assess the performance of the fit we employed generalized cross-validation (GCV, Craven & Wahba 1979) and computed the GCV statistic defined as: GCV =n n P i=1 (Yi−ˆµ(xi))2 (n−tr(H))2(3.2) where Yiis the polynomial model, nis the number of models and tr(H)is the trace of the hat matrix5. The denominator is called "equivalent degrees of freedom"6. The best smoothing parameter is the one that minimises the GCV statistic as depicted in figure 3.3. 4http://www.statistik.lmu.de/ leiten/Lehre/Material/GLM0708/Tutorium/locfit.pdf 5The diagonal elements of the hat matrix are called "leverages" and describe the influence the response value on the fitted value. 6The concept of degrees of freedom for non-parametric models is complex, because there is not a number of parameters, so they are empirically determined and result in numbers that are not necessarily integers. FCUP 51 Studying evolved stars with Herschel observations degrees of freedom 0 10 20 30 40 50 60 70 GCV 60 60.5 61 61.5 62 62.5 α 0.9 0.3 0.15 0.11 0.9 0.07 0.05 α 0 0.5 1 degrees of freedom 0 20 40 60 80 Fig. 3.3: Generalized-cross-validation statistic as a function of the degrees of freedom and smoothing parameter. The best αis the one that minimzes the GCV. In this example, we are fitting a portion of the spectrum of the C-rich AGB CIT6. We also used fitting weights inversely proportional to the variance, i.e., wi= 1/σ2 ias well as robust bisquare weighting to reduce the effect of outliers. So in the end the method is best named as non-parametric-local-robust-regression. The smoothing degree αchosen by GCV, although mathematically valid, might still not be the one that best suits one’s needs in reality, hence reflecting the difficulty of purely data-based bandwidth selection. For example, in some cases the GCV curve is flat beyond a certain degree of freedom. Fortunately we were able to quickly fit and subtract the continuum in a sample of 107 out of 113 stars7and over-fitting occurred in just few cases, which were properly identified and corrected by choosing by hand a different smoothing. Of course one could argue that one could choose the number of nodes in spline fitting with cross-validation as well, but local regression proved to be faster and more efficient. An example of the continuum subtraction is shown in figure 3.4 for the AGB star CIT 6. This local fitting routine was important to correctly recover line profiles that sit on top of bumpy regions of the spectrum, especially in the range 55 −75 µm. The continuum 7The excluded OBSIDS are mispointing or off-center observations of extended PN. FCUP 58 Studying evolved stars with Herschel observations Table 3.2: Number of targets with detected (SNR ≥5)Jup = 14 (186 µm) and Jup = 25 (105 µm) CO transitions in each class. Class J= 14 →13 J= 25 →24 O-rich 14/16 (88%)          AGB 24/28 (86%) 5/16 (31%)          AGB 14/27 (52%) C-rich 7/9 (78%) 6/8 (75%) S 3/3 (100/%) 3/3 (100/%) OH/IR 2/5 (40%) 0/5 (0%) PPN 9/22 (41%) 6/22 (27%) PN 3/17 (18%) 2/17 (12%) total 39/72 (54%) 22/71 (31%) dust and gas emission mechanisms. The strongest CO lines were found in 3 of the targets with the brightest continua: IRC+10216 (AGB star), AFGL 618 and AFGL 2688 (2 PPN), followed by the AGB stars IRAS 19312+1950 and CIT 6. This trend is not new. In fact, the strongest FIR sources are also the strongest CO emitters (e.g. Bujarrabal et al. 1992). AGBs are amongst the targets with the brightest continuum and the faintest. The 3 PNs were found to have Jup = 14 and Jup = 16 with approximately the same strength, but distinct continuum fluxes. However, in the case of PNs a smaller range of transitions was found relatively to the average of AGBs and PPN. We found strong linear correlations12 (R2>0.85) between the measured line fluxes and continuum flux in AGB stars. The slope of the linear trend changes with wavelength in the following way: FJ14 = 0.50.6 0.4Fcont [AGB] (3.10) FJ16 = 0.30.4 0.2Fcont [AGB] (3.11) FJ28 = 0.0190.022 0.017 Fcont [AGB] (3.12) FJ31 = 0.00990.011 0.0087 Fcont [AGB] (3.13) where the lower and upper bounds on the slope are 95% CIs. The reason why there is such a deviation from the linear prediction could be due to the underestimation of line 12In regression analysis the square of Pearson’s R (correlation coefficient) is the coefficient of determination that estimates the explained fraction of variance in the data. FCUP 59 Studying evolved stars with Herschel observations Fcont (Jy) 100101102103 FJ14 (Jy) 10-2 100 102 104 Fcont (Jy) 100101102103 FJ16 (Jy) 10-2 100 102 104 Fcont (Jy) 100101102103 FJ28 (Jy) 10-2 100 102 104 AGB OH/IR PPN PN Fcont (Jy) 100101102103 FJ31 (Jy) 10-2 100 102 104 λ∼186µm λ∼84µm λ∼93µm λ∼163µm Fig. 3.6: CO Jup = 14,Jup = 16,Jup = 28 and Jup = 31 line flux versus continuum flux under the line peak. The black and red lines are least-squares fits to the AGBs and PPNs respectively. fluxes because of opacity effects or there are simply different gas-to-dust ratios in different targets. In the case of PPNs, the correlations are weaker with R2= 0.75 and R2= 0.65 in FJ14 and FJ16 respectively. The linear models are given by: FJ14 = 0.190.26 0.12 Fcont [PPN] (3.14) FJ16 = 0.0980.14 0.05 Fcont [PPN] (3.15) In the bottom panels, due to the lack of points the fit is not good and the correlation coefficient is very low. We avoided the constant term in the linear regression because it is rather uncertain and it does not change the derived slope upon its exclusion. Also, its physical meaning is hard to interpret. To sum up, we conclude that CO rotational lines are stronger at longer wavelengths in absolute terms and relatively to the continuum. FCUP 60 Studying evolved stars with Herschel observations IRAS 19312+1950 is an interesting case. This OH/IR star is one of the brightest targets in the catalogue, but in spite of showing the forth strongest Jup = 14 CO line, we did not find a wide range of transitions. In fact, this particular transition is unusually strong with the subsequent quickly decaying in such way that in the bottom panels of figure 3.6 it does not appear. The last transition we found was the J= 24 →23. This raises the question if there is a line blend with some other species, greatly increasing the intensity of the feature at 186 µm, though we are not aware of known line at that wavelength. A more likely explanation could be the existence of a large amount of cold gas traced by lower J lines and very few hot gas in proportion. IRC+10216 (or CW Leo) is, notably, the star that shows the strongest CO lines and the richer chemical content in this sample. In opposition, HD 235858 reveals only 4 faint transitions in an otherwise featureless spectrum. Next, we fitted 13CO rotational lines. Since this isotopologue is much less abundant than 12CO and the latter is already scarce in most THROES targets in PACS range, we only found 13 stars (18% of the sample) with 13CO transitions with SNR≥5. A number of them are blended with known species such as HCN and 12CO and other unidentified lines. This means that adding to their relatively smaller signal-to-noise ratio, their integrated fluxes have higher degree of uncertainty. From these 13 stars, 11 are AGB stars and 2 are PPN. As with 12CO, IRC+10216 shows the strongest 13CO lines. Figure 3.7 illustrates an example of fitted 13CO profiles in the case of AFGL 2688, where we found isotopologue transitions from Jup = 15 to Jup = 21. The line fitting parameters of the remaining targets can be found in table A.11 in the appendices. 3.3.2 12CO/13CO isotopologue ratio Due to somewhat different molecular properties, the 13CO probes regions slightly different from those sampled with 12CO (De Beck et al. 2010). Furthermore, since 13CO is less abundant than 12CO, the CSE is optically thinner to those lines, meaning that 13CO transitions can provide, in principle, a reliable diagnostic for the envelope’s density structure. On the other hand, since they are fainter, their signal-to-noise ratio is much lower, FCUP 61 Studying evolved stars with Herschel observations λ(µm) 140 145 150 155 160 165 170 175 180 185 190 F (Jy) 0 50 100 150 200 250 300 350 151.2 151.4 151.6 151.8 0 5 10 15 170.1 170.2 170.3 170.4 170.5 0 5 10 15 J= 18 →17 J= 16 →15 12CO 12CO 13CO 13CO 12CO 12CO 12CO Fig. 3.7: Part of the PACS range spectrum (continuum subtracted) of AFGL 2688 showing the fitted 13CO lines; 12CO lines are labelled for comparison. i.e., the relative uncertainty is much higher. With the fluxes we derived by fitting both isotopologues, we can determine the isotopologue ratio 12CO/13CO in a straightforward way by simply dividing the measured line fluxes for the same transition in both species. This ratio is then corrected for the Einstein coefficient and frequency difference by a factor of ∼0.92. For optically thin rotational lines the 12CO/13CO ratio should provide a good estimate of the abundance ratio. If we further assume that all carbon is locked in CO, then the 12CO/13CO can yield directly the 12C/13Cisotopic ratio. Beware that any optical depth effects would decrease the ratio, i.e., the isotopic ratio would be underestimated. Schoier et al. (2000) argue that only detailed radiative transfer analysis is able to provide trustworthy abundance ratios, which is beyond the scope this thesis. Anyway, the very high Jtransitions should be less affected by optical depth effects. The 12CO/13CO flux ratio was computed for 13 targets using the first 4 transitions of 13CO within PACS range and the results are summarised in table 3.3. The uncertainty13 results from the error propagation of the integrated flux and it is dominated by the flux uncertainty of 13CO lines. Some scatter in the ratio for the same target as traced by different rotational transitions is visible. The targets with the highest ratios are, as expected (e.g. Milam et al. 2009), C-rich stars, namely AFGL 618, AFGL 2688 and CIT 6. Estimates of this ratio can be found in literature, but this type of analysis is sensitive 13No flux calibration uncertainties were added (typically <20%). FCUP 62 Studying evolved stars with Herschel observations Table 3.3: CO isotopologue ratio for several transitions in the PACS range. The ellipsis mark undetected 13CO or bad fits. 12CO/13CO Target Name J = 15 →14 J = 16 →15 J = 17 →16 J = 18 →17 average AFGL 2688 17±4 23±5 18±5 8±2 17 AFGL 3068 4±2 . . . . . . . . . 4 AFGL 3116 7±3 4±0.4 4.5±0.5 4±2 5 AFGL 618 19±3 21±2 29±8 16±3 21 CIT 6 9±1 9±1 7±1 3.7±0.5 7 EP Aqr 1.5±0.3 1.7±0.4 . . . 6±2 3 IRAS 15194-5115 2±1 5±2 2.2±0.2 2±1 3 IRC+10216 5±1 7.1±0.5 4±1 5±3 5 KHI CYG . . . 6±1 6±1 8±2 7 NML TAU 5±1 . . . . . . . . . 5 OMI CET 2.5±0.5 3±1 5±1 6±2 4 R CAS 4±1 3±2 . . . . . . 3 R DOR 2.3±0.4 1±1 . . . . . . 2 to the particular transition studied or even telescope used (e.g. Schoier & Olofsson 2000). De Beck et al. (2010) used JCMT and APEX data observing from Jup = 2 to Jup = 6 to obtain the isotopologue ratio for a sample of AGB stars. Their uncertainties are of ∼28% and 42% depending on the spectral line. Using IRAM 30m, OSO, APEX and JCMT data Ramstedt & Olofsson (2014) computed 12CO/13CO flux ratios for the same transitions but in a larger set of AGB stars of the 3 main spectral types (M, S and C). The uncertainties should be of the same order. We conclude that our ratios are systematically smaller than the ones derived from low J observations, following the trend of decreasing ratios with decreasing wavelength. This could be due to optical depth effects are an actual 13Cenrichment due to a late ejection of material that is located closer to the central star in a region probed by these higher JCO lines. 3.3.3 PACS colour-colour diagram As a sub-product of the line fitting we obtained useful information regarding the continuum of our targets. In the introduction we presented an IRAS two-colour diagram (figure FCUP 63 Studying evolved stars with Herschel observations Fig. 3.8: A PACS-PACS color-color diagram. Points outside the whiskers in the box plot diagrams are regarded as outliers. 1.9) to characterise the sample of stars and we concluded that they can be distinguished in terms of IRAS colours as reflex of their MIR and FIR properties. Analogously, using the continuum models of PACS spectra we extracted fluxes at selected wavelengths: [60, 70, 160, 170] µmand we defined PACS colours in the following way: [60] −[70] = −2.5 log Fλ(60) Fλ(70)(3.16) [160] −[170] = −2.5 log Fλ(160) Fλ(170)(3.17) We found that we are still able to separate the different types of stars with PACS colours (figure 3.8). Moreover, their location in the diagram provides important hints about the shape of their SED, hence the temperature of the dust-cooling continuum. AGB stars have the sharpest slopes between 60-70 µm(<[60] −[70] >∼ −0.38) meaning that they are in the Rayleigh Jeans limit and their SED peaks at shorter wavelengths compared to PPN FCUP 64 Studying evolved stars with Herschel observations and PN. The median colours of C-rich and O-rich stars are also different as depicted in the boxplot diagrams. No excess at 170 µmrelative to 160 µmwas found in any class meaning that the flux in this wavelength region is steadily decreasing. However, we found an excess at 70 µmwhich translates into a [60] −[70] >0in 2 PN and 1 OH/IR star. This indicates that the peak of the SED is at longer wavelengths. These targets are NGC 6537, NGC 6781 and IRAS 19312+1950. For example, if we look at the spectrum of NGC 6537 (figure 3.9) we see that the flux increases from 55 µmuntil ∼65 µmfrom where it slightly decreases reaching a plateau just before further decreasing from 90 µmonwards. According to Wien’s law14 a peak between 60 −70 µmcorresponds to a temperature of 40-50 K. So we conclude that probably NGC 6537 has a large amount of cold dust. Matsuura et al. (2005) drew the same conclusions using ISAAC, ISO/SWS and IRAS data. At the bottom left corner of the diagram there are 3 targets (OH 32.8-0.3, IRAS 19067+0811 and NGC 3242) which show very blue colours. An inspection of their data reveals a nearly flat noisy spectrum in the longer wavelengths region. wavelength (µm) 100101102103104105 Flux (Jy) 10-2 10-1 100 101 102 103 PACS NGC 6537 Fig. 3.9: Spectral energy distribution (SED) of NGC 6537 with PACS spectrum overlaid. The red points are IRAS fluxes and the black points are other photometry data such as 2MASS, AKARI, WISE, SDSS, VISTA, MSX and SCUBA (VizieR data). 14Wien’s law: λmax =2.8977729 ×10−3[m.K] T[K] FCUP 65 Studying evolved stars with Herschel observations 3.4 Summary •We conducted a CO line survey on a sample of 72 evolved stars of different evolutionary stages from the THROES catalogue with the aim of deriving physical parameters of the molecular CSE. •We confirmed that CO dominates the FIR spectra of carbon AGB stars, but in oxygen AGBs a number of comparably strong lines are seen. Some unidentified lines are probably OH, H2O, SiO and SO among others. •We identified atomic/ionic lines in the spectra of PN and concluded that the most common species are [NIII], [OI], [OIII], [NII] and [CII]. •We modelled the continuum spectra using a non-parametric method from where we obtained fluxes at selected wavelengths and drew a colour-colour diagram. PACS colours separate rather well targets in different evolutionary stages. •After subtracting the continuum from our spectra we fitted 12CO and 13CO lines. The former isotopologue was found in about 54% of the sample, while the latter was found in just 18% of the stars. CO is rare in our sample of planetary nebulae and CO lines are relatively fainter in oxygen stars. •Very high Jrotational lines were found in 9 targets which is a probable indication of a significant amount of gas under relatively high temperature conditions. •There is a correlation between line and continuum fluxes as showed in previous studies. The brightest FIR sources were found to be the strongest CO emitters. The scatter in these relations could be due to optical depth effects and/or very different gas-to-dust mass ratios. •The 12CO/13CO ratio was computed for a smaller number of targets and it is lower than what is found in literature from low JCO observations. •The SEDs of stars in different evolutionary stages have characteristic shapes as revealed by a PACS two-colour diagram plotted using continuum fluxes. FCUP 67 Studying evolved stars with Herschel observations Chapter 4 Physical conditions in carbon-rich CSEs In this chapter we estimate physical parameters of the CSE such as temperature and total gas mass using the rotational diagram. We focused in greater detail on a group of C-rich stars spanning different evolutionary stages from the sample of targets studied in chapter 3 for which we obtained CO line fluxes. 4.1 A sample of carbon-rich stars From the sub-sample of 39 targets that show CO emission we selected all of the stars with carbon-dominated chemistry, i.e., not only C-rich AGBs but also PPN and PN known to be carbon enriched to study in greater detail. These targets are classified as 7 AGB stars, 5 PPN and 2 PN making a total of 14 stars. Their PACS range spectra can be found in the appendix in figure B.5.1. In this section we briefly review some of their properties in what regards their morphology and chemistry. Table 4.1 summarises some basic information with respect to the observations. In what follows we adopt the distances listed in table 4.2 taken from literature. The distance has great influence in some derived quantities so one has to be cautions when comparing results to research literature where consensus is not always achieved. FCUP 74 Studying evolved stars with Herschel observations he analysed its PACS spectrum1and identified spectral lines belonging to CO, HCN, CS, SiS and H2O. Then he derived a mass-loss rate of ˙ M = 1.05 ×10−6Myr−1in good agreement with Knapp et al. (1997; 2000). 4.1.11 IRAS 16594-4656 (The Water Lily Nebula) IRAS 16594-4656, also known as the Water Lily Nebula, hosts a central star with Teff ∼10300 K (Mishra et al. 2005). It was first identified as a PPN on the basis of its IRAS colours with its NIR/MIR emission being dominated by PAHs. These spectral features plus the detection of CO molecular emission in its envelope with velocity ∼16 km s−1confirmed its C-rich chemistry (García-Hernández et al. 2006, and references therein). These authors used the imaging mode of TIMMI2 installed on ESO 3.6m to obtaine MIR images of this source and found an elliptical nebula with its major axis oriented along the east-west direction at a P.A =80oand extending out to at least 3.500 ×2.100, coincident with the orientation of bipolar outflows identified in HST optical images. In fact, while complex multilobe structure (figure 4.1) is seen in the optical V band and in the NIR H band, H2is traced in a clear bipolar, peanut-shaped outflow (Hrivnak et al. 2008). A model with mass-loss of 1×10−5Myr−1fits reasonably well CO J= 1 →0, J= 2 →1and J= 3 →2line profiles (Woods et al. 2005). 4.1.12 AFGL 2688 (The Egg Nebula) AFGL 2688 (or CRL 2688) also known as the Egg Nebula, is a PPN who exhibits bipolar, optical lobes (figure 1.3) and multiple concentric arcs. The central star is completely obscured. (Sahai et al. 1998; Ishigaki et al. 2012). Jura et al. (2000) found an elongated structure (5.600 ×1.900) at P.A∼53◦in cm-wavelength studies, while reporting that the visible outflows lies at P.A∼15◦, resulting from scattered light. A compact CO core of ∼200 expanding at ≥10 km s−1and shocked H2distributed orthogonally to the optical 1Actually we are using the same observation in this thesis, although it was reprocessed with more up-to-date calibration files. FCUP 75 Studying evolved stars with Herschel observations lobes were reported by Cox et al. (2000) who used the IRAM interferometer. Cox et al. (1996) presented the ISO LWS spectrum of AFGL 2688 and drew the same conclusions as we did in the previous chapter: the FIR spectrum of this PPN is dominated by CO lines and no atomic/ionised lines are yet seen, indicating that the central star is still not hot enough to ionise the gas envelope in preparation for the PN phase. The authors also argue that the molecular gas is heated by shocks and cools via NIR ro-vibrational H2 and FIR CO lines. The mass of shocked H2gas was estimated to be ∼5×10−3M. The dynamical age of the nebula and mass-loss rate were estimated to be ∼350 yr and ˙ M= 3 ×10−5Myr−1, respectively (Ueta et al. 2006; Lo et al. 1976). 4.1.13 CPD-568032 CPD-56◦8032 (or Hen 3-1333) is a young PN that hosts a Wolf-Rayet central star of the WC10 type. Moreover, there is evidence for dual-chemistry, namely carbon-rich and oxygen-rich dust grains in the CSE (Danehkar & Parker 2015, and references therein). Using the UCL echelle spectrograph De Marco et al. (1997) found a nebular expansion velocity of ∼30 km s−1by modelling Hαand Hβlines and estimated a dynamical age of ∼100 yr. These authors also used HST (Hβband) images and found a nebular size of ∼200. De Marco & Crowther (1998) found a mass-loss rate of ˙ M = 4 ×10−6Myr−1. 4.1.14 IRAS 21282+5050 IRAS 21282+5050 is an unusual, young, low-excitation planetary nebula, that shows one of the highest IR excesses among it’s class (Kwok et al. 1993). It was considered by (Cohen & Jones 1987) as a very compact source with a Wolf-Rayet central star of the spectral type O7-WC11. The first size estimate of IRAS 21282+5050 came from Likkel et al. (1988) who derived a diameter of ∼1000 in CO (J= 1 →0and J= 2 →1) observations. Using high resolution optical imaging Kwok et al. (1993) measured a size of approximately ∼700 ×500 oriented in the N-S direction, while Bregman et al. (1992) found a very compact nebula (∼500) in the K band. FCUP 76 Studying evolved stars with Herschel observations Table 4.2: Properties of the stars in the sample: distance, luminosity, effective temperature and mass-loss rate. Target name d (pc) L (L) Teff (K) ˙ M (Myr−1) IRC+10216 120b9800b2000m1.5×10−5 CIT 6 410a8165a2445a6×10−6 IRAS 15194-5115 500b8900b2400m1.5×10−5 AFGL 2513 1760g8470g2500m2×10−5 V CYG 366b6000b2581m1.6×10−6 AFGL 3068 1300b10900b2000m2.5×10−5 AFGL 3116 630b9600b2000m7×10−6 AFGL 618 900d10000d30000d5.5×10−5 HD 44179 710h6050h7750h10−8−10−2 V HYA 495a17539a2160a1×10−6 IRAS 16594-4656 1600i6000i10000k1×10−5 AFGL 2688 340c5500c7250j3×10−5 CPD-56o8032 1350f5000f30000f4×10−6 IRAS 21282+5050 2440e4000e30000n6×10−5 References: (a)Bergeat & Chevallier (2005), (b)Ramstedt et al. (2014), (c)Balick et al. (2012), (d)Sánchez Contreras et al. (2004), (e)Vickers et al. (2014), (f)Chesneau et al. (2006), (g)Guandalini et al. (2006), (h)Men’shchikov et al. (2006), (i)García-Hernández et al. (2006), (j)Ishigaki et al. (2012), (k)Mishra et al. (2015), (l)Sahai & Chronopoulos (2010), (m)De Beck et al. (2010), (n)Hasegawa & Kwok (2003); see text for ˙ M The mass-loss rate was first estimated by Likkel et al. (1988) in about ˙ M=6× 10−5Myr−1and later confirmed by Meixner et al. (1998) who assumed a distance of 2 kpc. 4.2 Rotational diagram analysis We performed the rotational diagram (or population diagram) analysis whose details are well explained in Goldsmith & Langer (1999). Essentially, for a molecule in LTE, the population of each level Nucan be described by a single rotation temperature Trot that matches the gas kinetic temperature as given by the Boltzmann distribution: FCUP 77 Studying evolved stars with Herschel observations Nu=Ntot Z(Trot)gue−Eu/kTrot (4.1) where Ntot is the total number density of the species, Z(T)is the partition function, guare the statistical weights and kis the Boltzmann constant. In the case of CO, the partition function can be approximate by: Z(T)≈Trot 2.77 + 1/3(4.2) The optical depth τat the line centre of a given transition is defined by: τ=Aijλ3Ncol u 8πV ×(e(hc/(λkT )) −1) (4.3) where V=vexp√π/(2plog 2) [km s−1]with vexp being the expansion velocity of the gas, Ncol uis the column density of the upper level and Aij is the Einstein A-coefficient for spontaneous emission. In the case of optically thick emission, an optical depth correction factor Cτshould be added. It can be defined as: Cτ=τ 1−e−τ(4.4) to be multiplied by the number of molecules and allowing us to rewrite equation 4.1 in the following way: ln Nu gu= ln Ntot Z(T)−Eu kT −ln Cτ(4.5) where the left hand-side is proportional to the integrated line flux Fas defined in equation 3.6 such that: Nu=4πFλd2 Aijhc (4.6) where dis the distance, his the Planck constant and cis the speed of light. To the statistical uncertainty of the line flux computed using equation 3.7 (table A.11) we add FCUP 78 Studying evolved stars with Herschel observations in quadrature an average flux calibration uncertainty2(cal) of 15% so that the standard errors3are given by: δNu=scal 100 ×F2 +δF F2 (4.7) such that the error in the y-coordinate (y≡ln(Nu/gu)) is simply: δy =δNu Nu (4.8) After plotting the logarithm of the number of molecules per statistical weight (y) versus the energy of the upper transition divided by the Boltzmann constant Eu k, we fit a straight line whose slope and y-intercept are related to the temperature and number of gas molecules, respectively. To convert the latter to column density, an assumption of the size of the CSE is needed. For that we used data from literature and our own estimates of the first part of this work. The transition constants involved in these calculations, namely Einstein coefficients and statistical weights can be found in table A.9 in the appendices. Note that this is a coupled problem because to correct the diagram for the opacity one has to calculate line optical depths τthat require an input temperature and column density. The approach we followed in this work was to compute a first guess of the temperature and column density using equation 4.5 without the opacity correction term, i.e. ln Cτ= 0. Then, after computing the opacity corrected line fluxes, we execute a second iteration and check the impact on the temperature and column density parameters. It keeps going iteratively until convergence is reached, which was defined in terms of a relative, maximum change of 30% in the derived parameters. Moreover, this has to be repeated for a range of different values of gas expansion velocity. If vexp is too high, then the opacity correction might be unimportant. On the other hand, if vexp is small (<20 km s−1) the correction could be significant. Here we tried a range of expansion velocities: [10, 20, 30, 40] km s−1. The fit was performed by making use of the function lm in the R stats package4. We investigated the impact of fitting weights on the regression parameters. They are defined 2PACS Observer’s Manual, v.2.5.1, 2013 3Note that the distance is a major source of uncertainty that cannot be accounted in most cases. 4https://stat.ethz.ch/R-manual/R-devel/library/stats/html/stats-package.html FCUP 79 Studying evolved stars with Herschel observations as usually: wi= 1/σ2 iwhere we devalue points with higher variance σ2 i. Therefore, we perform the fit with and without fitting weights and both results ought to be reported. This is important when comparing results to literature. At times, as we will present further on, a straight line does not quite properly fit the entire range of excitation temperatures. This could be an indication that lines are optically thick or that the LTE approximation is simply not valid. Alternatively, there could be, in fact, several temperature components corresponding to different regions of the CSE since our observations are not spatially resolved. We convert the total number of CO molecules Nto CO mass by simply multiplying it by the mass of a CO molecule (mCO ∼4.65 ×10−23 g). To estimate the mass of molecular hydrogen, i.e., gas envelope mass, we adopted the fractional abundance relative to the CO of fCO = 8 ×10−4(e.g. Teyssier et al. 2006) and used the following formula: MH2=Ntot fCO mH2(4.9) such that the uncertainty propagates as: δMH2=δN NMH2(4.10) We obtained rotational diagrams for 12CO and in some cases for 13CO as well. 4.2.1 Code validation The code was validated by reproducing the results of Justtanont et al. (2000) (hereafter J2000) who used ISO data to plot the rotational diagram (without opacity correction) of AFGL 618. In addition, since this target is also in our sample we compare our rotational diagram with J2000 in figure 4.2. Two points were excluded from their data5around 1800 K (at ∼100 µm) because we don’t have PACS counterparts. Note that CO lines were previously detected only up to Jup = 37, but here we find them until Jup = 45. Adopting a distance of 1.8kpc, J2000 derived a temperature of T= 700 K, a number of molecules 5The slight difference in the ISO temperature relative to the one reported in J2000 is probably due to the exclusion of 2 data points. FCUP 80 Studying evolved stars with Herschel observations Eu/k (K) 0 1000 2000 3000 4000 5000 6000 ln(Nu/gu) 104 105 106 107 108 109 110 111 112 113 114 ISO, Justtanont (2000) PACS blend T = 732 ±36 (K) N = 3.8(±0.8) ×1051 T = 693 ±43 (K) N = 5(±1) ×1051 d=1.8kpc Fig. 4.2: 12CO rotational diagram of AFGL 618 with ISO data (Justtanont et al. 2000) and with our PACS data. For this comparison (only) we adopted the distance d = 1.8 kpc. of N= 4.4×1051, which implies a CO mass of ∼10−4Min good agreement with our PACS data. 4.2.2 A single temperature component In a first approach we want to fit just one straight line to the data and compare the results with and without opacity correction. To compute the column density we need to input a size. To decide on the size of the CO emitting region we take a look at the sizes we derived from photometry maps in the second chapter of this thesis (table A.6). For CIT 6, from both blue and red band photometry, we obtain a deconvolved size (equation 2.11) of ∼300 which agrees with the shells observed in the NIR up to ∼400. For AFGL 3116, we obtain a somewhat smaller size of ∼2.500, but essentially agrees with the PSF within 1σ. AFGL 618 was found to be point-like as well. Probably the FIR emission also arises from the dense core (<200) seen in other studies as mentioned before. AFGL 2688 is significantly larger than the photometer PSF in the blue band and we find a deconvolved size of ∼400. However, in the red band, it agrees with the beam size within the uncertainty. The size of 400 agrees with the elongated structure seen FCUP 81 Studying evolved stars with Herschel observations in radio wavelengths, but perhaps the CO region is even more compact since a CO core is known to exist at the scale of ∼200. In principle, the size of the CO emitting region could be smaller than what traced by the photometric bands which encloses both continuum and line emission within the bandwidth. IRC+10216 is also larger than the photometer PSF in both bands, but while in blue band we obtained a deconvolved size of ∼400, in the red band we get ∼5.800. It seems appropriate to adopt a larger size for this source relatively to the other AGBs. Regarding the remaining targets, AFGL 3068, HD 44179, IRAS 151945115, V Hya and IRAS 16594-4656 were all found to be point-like. Because these sizes are qualitatively not very different, we experiment in a first approach a reasonable size of 300 for all of them, and later we study the impact of this assumption on the derived quantities. In what regards the 2 PN, we do not have photometry data, but we know that the temperature conditions do not require a size as small as in AGB stars. Nevertheless, both IRAS 21282+5050 and CPD-568032 are known to be very compact nebulae so we set both sizes equal to 500. Furthermore, note that the size of the emitting region could be different for each transition, so in this approximation all observed CO lines are assumed to come from the same region. We also assume that the observed 12CO and 13CO lines come from a region with the same size. Firstly, we study the rotational diagram of 12CO. In figure 4.3 we present the rotational diagrams (without opacity correction) of the 14 targets where we see a range o 12CO transitions following a linear trend under different temperature conditions. Qualitatively we found what is expected with PNs showing the coldest gas given the smaller number of detected CO lines, whereas AGBs and some PPNs possess the hottest gas. To apply the opacity correction we used for AGB stars vexp = 20 km s−1, for PPN we took vexp = 40 km s−1and for PN we assumed vexp = 30 km s−1. In table 4.3 we compile the rotational diagram results for the 14 targets with and without opacity correction. In the appendix (table A.12) we list the results of the linear regression without fitting weights which produces significant changes in some cases. We conclude that for this choice of parameters, the opacity correction is small in this sample of stars and it has a negligible impact on the rotational diagram. However, FCUP 82 Studying evolved stars with Herschel observations Eu/k (K) 1000 2000 3000 4000 5000 6000 ln(Nu/gu) 101 102 103 104 105 106 107 108 109 110 T=692K CIT 6 Eu/k (K) 500 1000 1500 2000 2500 3000 3500 4000 4500 ln(Nu/gu) 102 103 104 105 106 107 108 109 T=671K AFGL 3116 Eu/k (K) 500 1000 1500 2000 2500 3000 ln(Nu/gu) 103 104 105 106 107 108 109 110 111 T=342K AFGL 2688 Eu/k (K) 1000 2000 3000 4000 5000 6000 ln(Nu/gu) 102 104 106 108 110 112 114 T=651K AFGL 618 Eu/k (K) 500 600 700 800 900 1000 1100 1200 1300 ln(Nu/gu) 107 108 109 110 111 112 T=173K IRAS 21282+5050 Eu/k (K) 500 1000 1500 2000 2500 ln(Nu/gu) 105 106 107 108 109 110 111 T=378K CPD-56º8032 Fig. 4.3: Rotational diagrams for the sample of C-rich stars with a fitted, single temperature component. Circles mark known line blends. FCUP 83 Studying evolved stars with Herschel observations Eu/k (K) 500 1000 1500 2000 2500 3000 3500 4000 ln(Nu/gu) 102 103 104 105 106 107 108 109 T=533K IRC+10216 no data Eu/k (K) 500 1000 1500 2000 2500 ln(Nu/gu) 105 106 107 108 109 110 111 T=465K AFGL 3068 Eu/k (K) 500 1000 1500 2000 2500 3000 3500 ln(Nu/gu) 102 103 104 105 106 107 108 T=566K V CYG Eu/k (K) 500 1000 1500 2000 2500 3000 3500 ln(Nu/gu) 104 105 106 107 108 109 110 T=621K AFGL 2513 Eu/k (K) 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 ln(Nu/gu) 104 104.5 105 105.5 106 106.5 107 107.5 T=454K HD 44179 Eu/k (K) 500 1000 1500 2000 2500 3000 3500 ln(Nu/gu) 104 105 106 107 108 109 110 111 112 T=484K IRAS 16594-4656 Fig. 4.3: Continued. FCUP 90 Studying evolved stars with Herschel observations is still small for the adopted size of 3" and down to 1". For a size of 1" the maximum optical depth is ∼0.43 and the temperature changes by 5% and the number of molecules varies by 21% relatively to the uncorrected rotational diagram. However, if the high J CO emission comes from an even more compact region, then significant optical depth effects are expected. Finally, if we take the value of vexp = 16 km s−1for the expanding envelope of IRAS 16594-4656 observed through low JCO transitions (García-Hernández et al. 2006) we draw the same type of conclusions, i.e., only a combination of low velocities and small sizes (<1") would produce large optical depths. c) CO fractional abundance The fractional abundance fCO has no impact on the rotational diagram, it only influences the conversion from CO mass to H2mass. So to compare with literature, one simply scales the results with a different conversion ratio. With these ideas in mind, we note that the derived gas temperature should be regarded as an upper limit, while the number of molecules/column density should be taken as a lower limit of the true temperature and density conditions of the gas in the CSE of these stars. 4.2.4 Significance of a multi-component fit Despite being a good representation of the general trend in the data, a single straight line does not fit equally well the entire range of CO transitions in some targets. This deviation from prediction can have several origins as mentioned before. AFGL 618 is the target where that is more clearly visible. To demonstrate that, we can visualise the regression residuals as plotted below. The two charts in figure 4.7 are just different ways of showing the same issue: the residuals are not normally distributed, as they are not randomly distributed around zero on the leftmost chart and they deviate from the theoretical straight line on the normal Q-Q plot6. Moreover they seem to indicate a slope change at around Eu/k ∼2000 K. It is common in literature to split the rotational diagram in 2 or more segments corre6The Q-Q plot is used to compare quantiles of two distributions. FCUP 91 Studying evolved stars with Herschel observations 1000 3000 5000 −1 0 1 2 3 residuals Eu/k (K) standardized residuals −2 −1 0 1 2 −1 0 1 2 3 Normal Q−Q Plot Theoretical Quantiles standardized residuals Fig. 4.7: Analysis of regression residuals in the rotational diagram of AFGL 618. The color code is related to the wavelength with red being longer wavelengths and blue corresponding to shorter ones. sponding to several temperature components (e.g. Wesson et al. 2010; Zhang et al. 2013). However, it is not always clear by eye whether that slope change is present or not and where the breakpoint is located. For that reason we used statistical tests to automatically find structural changes in classical linear regression and assess their significance. To do so, we used strucchange package7(Zeileis et al. 2002) implemented in R. There is an extensive literature about this topic, namely about empirical fluctuation processes, but essentially the methods consist in minimising the residual sum of squares (RSS) by sectioning and fitting different portions of the data . Some of these tools are widely used in economy and medicine to look for changes in time series. In our case, it can be used to test the change in the slope of a straight line fitted to the data. Obviously, the more we split the data in segments the smaller the sum of residuals will be. However, that would lead to an undesired over-fit that really does not represent the data. To overcome that, one can use the Bayesian information criteria (BIC) or even Akaike’s Information Criteria (AIC) to obtain an optimal number of breakpoints, as they will penalize model complexity. These quantities are defined as follows: BIC = −2 ln(ˆ L) + k. ln(n)(4.11) AIC = −2 ln(ˆ L)+2k(4.12) where ˆ Lis the maximum of the Likelihood function, kis the number of parameters and n 7https://www.jstatsoft.org/article/view/v007i02 FCUP 92 Studying evolved stars with Herschel observations x 0 10 20 30 40 y -10 0 10 20 30 40 50 number of breakpoints 0 1 2 3 4 5 RSS 100 150 200 BIC & AIC 180 200 220 RSS AIC BIC x 0 10 20 30 40 y -20 0 20 40 60 80 number of breakpoints 0 1 2 3 4 5 RSS 500 1000 BIC & AIC 200 250 RSS AIC BIC single slope + Gaussian noise double slope + Gaussian noise Fig. 4.8: Testing BIC and AIC for model selection with mock data. The number of breakpoints in the data is given by the minimum of BIC and AIC. is the sample size. So we see that due to the term k. ln(n)BIC will penalize complicated models more severely than AIC. Under the assumption that errors are independent and normally distributed, BIC and AIC can be rewritten as function of the RSS as follows (Maindonald & Braun 2010): BIC = nln(RSS/n) + kln(n)(4.13) AIC = nln(RSS/n)+2k(4.14) Another approach is to use F-statistic8maximum (Andrews & Ploberger 1994), which is designed to test against a single structural change in the data. The F-statistic is basically the ratio of explained variance to the unexplained variance and it will produce an equivalent result to BIC if a 2-segment partition is assumed. The best way to visualise the applicability of the criteria aforementioned is by plotting the RSS for a range of breakpoints, while looking for a minimum in the BIC (or AIC) curve. We have tested some these methods by generating mock data of straight lines plus some random Gaussian noise as exemplified in figure 4.8. Usually BIC and AIC agree in 8The F-test is used to test if two populations variance are equal. FCUP 93 Studying evolved stars with Herschel observations Eu/k (K) 0 1000 2000 3000 4000 5000 6000 ln(Nu/gu) 100 101 102 103 104 105 106 107 108 109 110 CIT 6 T = 490 ±28 K N = 1.0(±0.2) ×1050 MCO = 2.3(±0.4) ×10−6M⊙ T = 842 ±60 K N = 4(±1) ×1049 MCO = 1.0(±0.2) ×10−6M⊙ Eu/k (K) 0 1000 2000 3000 4000 5000 ln(Nu/gu) 102 103 104 105 106 107 108 109 110 T = 494 ±36 K N = 8(±1) ×1049 MCO = 1.8(±0.3) ×10−6M⊙ T = 797 ±57 K N = 3.4(±0.9) ×1049 MCO = 8(±2) ×10−7M⊙ AFGL 3116 Eu/k (K) 500 1000 1500 2000 2500 3000 ln(Nu/gu) 102 103 104 105 106 107 108 109 110 111 T = 270 ±11 K N = 5.0(±0.8) ×1050 MCO = 1.2(±0.2) ×10−5M⊙ AFGL 2688 Eu/k (K) 0 1000 2000 3000 4000 5000 6000 ln(Nu/gu) 103 104 105 106 107 108 109 110 111 112 113 AFGL 618 T = 416 ±21 K N = 2.2(±0.3) ×1051 MCO = 5.1(±0.8) ×10−5M⊙ T = 923 ±48 K N = 3.4(±0.7) ×1050 MCO = 7(±2) ×10−6M⊙ Fig. 4.9: Rotational diagrams with 2 temperature components (coloured lines) and single temperature fit (dashed line). Circles mark known line blends which were excluded from the fit. the number of breakpoints, but in this case, for this level of noise, AIC incorrectly states that there must be a breakpoint on the simple straight line, while in the other situation where a change in the slope was introduced, it finds that any number of breakpoints larger than 1 would equally well represent the data. This is, as expected, a consequence of the much more permissive nature of AIC. On the other hand, the minimum of BIC on the left side is correctly at null number of breakpoints, whereas on the right side it suggests the existence of 1 breakpoint. Hereinafter we only use BIC, but note that BIC is not immune to over-fitting, hence supervision is required. Given the small number of points we are not interested in splitting the diagram too much as it would, in fact, violate one of the conditions upon derivation of FCUP 94 Studying evolved stars with Herschel observations Eu/k (K) 500 1000 1500 2000 2500 3000 3500 4000 ln(Nu/gu) 102 103 104 105 106 107 108 109 IRC+10216 T = 302 ±30 K N = 1.5(±0.4) ×1050 MCO = 3.5(±0.9) ×10−6M⊙ T = 642 ±34 K N = 4(±1) ×1049 MCO = 1.0(±0.2) ×10−7M⊙ Eu/k (K) 500 1000 1500 2000 2500 3000 3500 ln(Nu/gu) 104 105 106 107 108 109 110 AFGL 2513 T = 439 ±34 K N = 2.1(±0.5) ×1050 MCO = 5(±1) ×10−6M⊙ T = 1176 ±120 K N = 3.4(±0.9) ×1049 MCO = 8(±2) ×10−7M⊙ Eu/k (K) 500 1000 1500 2000 2500 3000 3500 ln(Nu/gu) 104 105 106 107 108 109 110 111 112 IRAS 16594-4656 T = 586 ±21 K N = 2.2(±0.3) ×1050 MCO = 5.3(±0.7) ×10−6M⊙ T = 227 ±5 K N = 1.6(±0.1) ×1051 MCO = 3.7(±0.3) ×10−5M⊙ Eu/k (K) 1000 2000 3000 4000 5000 ln(Nu/gu) 101 102 103 104 105 106 107 108 109 T = 501 ±34 K N = 8(±1) ×1049 MCO = 1.8(±0.3) ×10−6M⊙ T = 949 ±40 K N = 2(±0.4) ×1048 MCO = 5.7(±0.9) ×10−7M⊙ V HYA Fig. 4.10: Rotational diagrams of 12CO with 2 temperature components (coloured lines) and single temperature fit (dashed line). Circles mark known line blends which were excluded from the fit. equation 4.11 that nk. This means we will not apply this statistical test to targets with only a few transitions detected (e.g. PNs). Because this method is sensitive to outliers, it is important to exclude points affected by line blend that clearly deviate from the linear trend. Lastly, beware that the BIC criteria does not prove that more than a different temperature component exists, it only highlights hidden patterns in the residuals which could be originated simply by heteroskedasticity in the data. Nevertheless, this approach is still useful to process a large set of observations in an automatic way, liberating the observer from deciding where to split the diagram. The F-statistic is then used to confirm BIC and quantify significance with a p-value. The significance level was set to α= 0.01. Finally, we present the results of the rotational diagram with 2 temperature components FCUP 95 Studying evolved stars with Herschel observations in figures 4.9 and 4.10. CIT 6 and AFGL 3116 share very similar conditions with a warm component of around ∼500 K and a hot component9of ≥800 K. AFGL 618 has a colder warm component of 416 K and a hot component of more than 900 K. For AFGL 2688 the BIC criterion found an obvious breakpoint but we decided not to to fit the second component for Eu/k > 2000 K because of the lack of points. In this case there is mass of CO gas of ∼10−5Mat relatively cold (<300 K) temperatures. In IRC+10216, although BIC clearly suggests a slope change10, the F-test says it is not particularly significant with a p-value of 0.009, just marginally below a 1% significance cutoff. The inclusion of missing data in the range of excitation temperatures 1000 −1500 K would clarify this conclusion. IRAS 16594-4656 is an interesting case because the breakpoint was found at much smaller excitation temperature producing a much colder (∼230 K) first-temperature-component than any other target. Concerning V Cyg, the F-test fails to reject the null hypothesis which means that the slope change is unlikely. A visual inspection of the rotational diagram helps confirming that. Figure 4.11 shows the temperature histograms for the single components and split temperature components. The single least-squares fit corresponds to a sort of average temperature between low and high rotational levels. When we split the diagram in 2 components we see a bi-modal distribution of temperatures around ∼400 K and ∼850 K which we call "warm" and "hot". On the right side, we compare the temperature and mass derived from the 2 fitted lines in some targets. The warm component is up to ∼7times more massive than the hot component which can be hotter by a factor of nearly 3. If we assume that the temperature profile is given by a power-law of the type T∝r−αwhere r is the radial distance (e.g. Teyssier et al. 2006) and that the mass-loss rate and expansion velocity are constant, we find a direct power-law relation between temperature and mass with α≈0.5which fits the data quite well. Note that a large difference in the temperature between the warm and hot components can thus be an indication of very different radial distances of the emission which goes against our initial assumption that every transition comes from a region with the same size. Nevertheless, to obtain an accurate density law 9We call the cold component the one usually traced in radio observations T<100K. 10rotational diagram without opacity correction FCUP 96 Studying evolved stars with Herschel observations Table 4.4: Rotational diagram results for a double component fit. Target Name T (K) NCO (molecules) Ncol (cm−2) MH2( M) IRC+10216 302±30 1.5(±0.4) ×1050 4(±1) ×1018 3.2(±0.8) ×10−4 642±34 4(±1) ×1049 1.0(±0.2) ×1018 9.0(±2) ×10−5 CIT 6 490±28 1.0(±0.2) ×1050 3.7(±0.6) ×1017 2.0(±0.3) ×10−4 842±60 4(±1) ×1049 1.4(±0.4) ×1017 8(±2) ×10−5 AFGL 3116 494±36 8(±1) ×1049 1.2(±0.2) ×1017 1.7(±0.3) ×10−4 797±57 3.4(±0.9) ×1049 5(±2) ×1016 7(±2) ×10−5 AFGL 2688 270±11 5.0(±0.8) ×1050 2.7(±0.4) ×1018 1.1(±0.2) ×10−3 ... ... ... ... AFGL 618 416±21 2.2(±0.3) ×1051 1.7(±0.3) ×1018 4.6(±0.7) ×10−3 923±48 3.4(±0.7) ×1050 2.6(±0.5) ×1017 8(±2) ×10−4 AFGL 2513 439±34 2.1(±0.5) ×1050 4.3(±0.9) ×1016 4.5(±0.8) ×10−4 1176±120 3.4(±0.9) ×1049 7(±1) ×1015 8(±2) ×10−5 IRAS 16594 227±51.6(±0.1) ×1051 3.9(±0.3) ×1017 3.4(±0.3) ×10−3 586±21 2.2(±0.3) ×1050 5.6(±0.7) ×1016 4.7(±0.6) ×10−4 V Hya 501±34 8(±1) ×1049 2.0(±0.3) ×1017 1.7(±0.3) ×10−4 949±40 2(±0.4) ×1048 6(±1) ×1016 5.3(±0.8) ×10−5 in the envelope of these objects, detailed radiative transfer models are needed. FCUP 97 Studying evolved stars with Herschel observations Mhot/Mwarm 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 Thot/Twarm 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 1Thot Twarm 2∝1Mhot Mwarm 2−0.5 Fig. 4.11: Results of rotational diagrams. Left: Histograms of derived temperatures: single components (grey) and double components (red and blue for the coldest and hottest respectively); Right: temperature ratio versus mass ratio of the 2 fitted components. The red curve is the least-squares power-law fit. FCUP 98 Studying evolved stars with Herschel observations 4.2.5 The optically thinner 13CO Because 13CO emission is optically thinner, the opacity correction is not as important as in the previous 12CO rotational diagrams. Therefore, physical parameters derived from 13CO lines are somewhat more reliable. However, this isotopologue produces very faint, i.e., low SNR lines in PACS range and their flux is more severely affected by line blend as explained in the previous chapter. These drawbacks cancel out the advantages of performing similar analysis using 13CO rotational lines. In addition, only a few transitions were detected in a small number of stars. For completeness, we present in figure 4.12 rotational diagrams of 13CO in the sample of carbon stars. The constants used in this calculation are listed in table A.10 in the appendix. The regression parameters have associated a much larger uncertainty than before, preventing us from taking robust conclusions. However, in the case of IRC+10216 we found a good agreement between temperatures derived from 12CO and 13CO. Eu/k (K) 600 800 1000 1200 ln(Nu/gu) 103.5 104 104.5 105 105.5 106 106.5 Eu/k (K) 600 800 1000 1200 ln(Nu/gu) 104.5 105 105.5 106 106.5 107 Eu/k (K) 600 800 1000 1200 ln(Nu/gu) 106.5 107 107.5 108 108.5 Eu/k (K) 600 800 1000 1200 ln(Nu/gu) 104 104.5 105 105.5 106 106.5 13CO 13CO 13CO 13CO T = 561 ±197 K N = 1.0(±0.7) ×1049 IRC+10216 AFGL 618 AFGL 2688 IRAS 15194-5115 T = 369 ±212 K N = 5(±7) ×1049 T = 375 ±115 K N = 7(±6) ×1048 T = 289 ±97 K N = 1(±1) ×1049 Fig. 4.12: Rotational diagrams of 13CO in a sample of carbon stars. FCUP 99 Studying evolved stars with Herschel observations 4.3 Mass-loss rate in evolved stars The mass-loss rate in AGB stars ranges between 10−8−10−5Myr−1(De Beck et al. 2010), mainly in semi-regular variables and Miras, while OH/IR have optically opaque envelopes formed by intense mass loss that can reach up to ∼10−4Myr1. In theory, the mass-loss should be lower in PN. We can estimate the mass-loss rate in a straightforward way using the gas mass we derived from the rotational diagram and an assumption on the expansion velocity and size of the emitting region. If we further assume (for simplicity) that the mass-loss is spherically symmetric and that the density is uniform, then the amount of mass crossing the surface of radius rin an amount of time tis given by: dM =ρdV =ρ4πr2vexpdt dM dt ≡˙ M= 3MH2 vexp r (4.15) Using the parameters listed in table 4.3, we computed the mass-loss rate for the 14 stars. Then, using the gas mass derived from the diagram splitting in two different temperature components, we recompute different estimates corresponding to the hottest temperature and the coldest temperature of the gas, which then yield a minimum and maximum massloss rate. The results can be found in table 4.5. Overall, our results agree with the literature. For example, De Beck et al. (2010) derived a mass-loss rate of 5.9×10−6Myr−1and 4.6×10−6Myr−1for CIT 6 and AFGL 3116 respectively. The mass-loss rate of AFGL 2688 and AFGL 618 are known from previous studies to be 1.7×10−4Myr−1and 2×10−4Myr−1respectively (e.g. Milam et al. 2009, and references therein). However, the authors adopted different distances for the 2 PPN, but if we scale our values with their distances we obtain similar results. In the case of CPD-568032, De Marco & Crowther (1998) found ˙ M=4×10−6Myr−1. Meixner et al. (1998) obtained 6×10−5Myr−1for IRAS 21282+5050, in good agreement with our results. Ramstedt & Olofsson (2014) found a mass-loss rate for IRC+10216 of 1.5×10−5Myr−1in good agreement with ours. 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Target name R.A (deg) DEC (deg) Class Variability AC Her 277.5676 21.8668 PPN RV Tau variable AFGL 2019 268.3282 -26.9436 O-rich AGB Semi-regular AFGL 2403 292.6228 19.8447 OH/IR x AFGL 2513 302.3093 31.4291 C-rich AGB Mira Cet AFGL 2688 315.5781 36.6938 PPN x AFGL 3068 349.8016 17.1931 C-rich AGB Mira Cet AFGL 3116 353.6152 43.5506 C-rich AGB Mira Cet AFGL 4106 155.8311 -59.5346 PPN x AFGL 4202 223.1012 -62.0721 C-rich AGB x AFGL 4259 301.5947 27.0362 OH/IR x AFGL 618 70.7236 36.1147 PPN x AFGL 6815 259.583 -32.4556 PPN x AQ Sgr 293.5791 -16.3741 C-rich AGB Semi-regular BD +303639 293.6884 30.5163 PN x CIT 6 154.0094 30.5718 C-rich AGB Semi-regular CPD-568032 257.2536 -56.9133 PN x CPD-642939 219.292 -64.8013 PPN x EP Aqr 326.6327 -2.2127 O-rich AGB Semi-regular g her 247.1606 41.8816 O-rich AGB Semi-regular FCUP 122 Studying evolved stars with Herschel observations neptune 55 9.37 ±0.02 8.49 ±0.02 8.92 ±0.03 neptune 55 9.33 ±0.02 8.63 ±0.02 8.97 ±0.03 neptune 55 9.01 ±0.02 8.54 ±0.02 8.77 ±0.03 neptune 55 9.02 ±0.02 8.51 ±0.02 8.76 ±0.03 neptune 62 9 ±0.02 8.54 ±0.02 8.77 ±0.03 neptune 62 9.16 ±0.02 8.57 ±0.02 8.86 ±0.03 neptune 62 8.74 ±0.02 8.61 ±0.02 8.67 ±0.03 neptune 62 8.99 ±0.02 8.49 ±0.02 8.74 ±0.03 neptune 62 9.69 ±0.02 8.8 ±0.02 9.23 ±0.03 neptune 62 9.45 ±0.02 8.62 ±0.02 9.02 ±0.03 neptune 62 9.34 ±0.02 8.55 ±0.02 8.93 ±0.03 neptune 62 9.45 ±0.02 8.81 ±0.02 9.12 ±0.03 neptune 62 9.33 ±0.02 8.52 ±0.02 8.91 ±0.03 neptune 62 9.15 ±0.02 8.3 ±0.02 8.71 ±0.03 neptune 62 9.57 ±0.02 8.36 ±0.02 8.94 ±0.03 neptune 68 8.87 ±0.02 8.56 ±0.02 8.72 ±0.02 neptune 68 8.74 ±0.02 8.48 ±0.02 8.61 ±0.02 neptune 68 8.55 ±0.02 8.31 ±0.02 8.43 ±0.03 neptune 68 8.51 ±0.02 8.22 ±0.02 8.37 ±0.03 neptune 68 9.45 ±0.02 8.67 ±0.02 9.05 ±0.03 neptune 68 9.07 ±0.02 8.44 ±0.02 8.75 ±0.03 neptune 68 9.05 ±0.02 8.32 ±0.02 8.67 ±0.03 neptune 68 9.35 ±0.02 8.66 ±0.02 9 ±0.03 neptune 68 8.94 ±0.02 8.4 ±0.02 8.67 ±0.03 neptune 68 8.84 ±0.02 8.24 ±0.02 8.54 ±0.03 neptune 68 9.16 ±0.02 8.24 ±0.02 8.69 ±0.03 neptune 73 8.63 ±0.02 8.32 ±0.02 8.48 ±0.03 neptune 73 8.59 ±0.02 8.25 ±0.02 8.42 ±0.02 neptune 73 8.56 ±0.02 8.21 ±0.02 8.38 ±0.03 neptune 73 8.49 ±0.02 8.22 ±0.02 8.35 ±0.03 neptune 73 9.25 ±0.02 8.52 ±0.02 8.88 ±0.03 neptune 73 9.04 ±0.02 8.4 ±0.02 8.71 ±0.03 neptune 73 8.97 ±0.02 8.24 ±0.02 8.6 ±0.03 neptune 73 9.06 ±0.02 8.38 ±0.02 8.71 ±0.03 neptune 73 9.01 ±0.02 8.29 ±0.02 8.64 ±0.03 neptune 73 8.73 ±0.02 8.12 ±0.02 8.42 ±0.03 FCUP 123 Studying evolved stars with Herschel observations neptune 73 9.09 ±0.02 8.35 ±0.02 8.71 ±0.03 neptune 75 9.11 ±0.02 8.4 ±0.02 8.75 ±0.02 neptune 75 8.74 ±0.02 8.35 ±0.02 8.54 ±0.03 neptune 75 8.8 ±0.02 8.57 ±0.02 8.69 ±0.03 neptune 75 8.95 ±0.02 8.63 ±0.02 8.79 ±0.03 neptune 75 9.27 ±0.02 8.63 ±0.02 8.94 ±0.03 neptune 75 9.27 ±0.02 8.69 ±0.02 8.97 ±0.03 neptune 75 9.35 ±0.02 8.66 ±0.02 9 ±0.03 neptune 75 9.1 ±0.02 8.64 ±0.02 8.86 ±0.03 neptune 75 8.81 ±0.02 8.66 ±0.02 8.73 ±0.03 neptune 75 8.9 ±0.02 8.63 ±0.02 8.77 ±0.03 neptune 75 9.56 ±0.02 8.76 ±0.02 9.15 ±0.03 neptune 84 8.85 ±0.02 8.4 ±0.02 8.62 ±0.03 neptune 84 8.81 ±0.02 8.34 ±0.02 8.57 ±0.03 neptune 84 8.91 ±0.02 8.29 ±0.02 8.59 ±0.03 neptune 84 8.79 ±0.02 8.27 ±0.02 8.53 ±0.03 neptune 84 9.46 ±0.02 8.58 ±0.02 9.01 ±0.03 neptune 84 9.13 ±0.02 8.45 ±0.02 8.78 ±0.03 neptune 84 9.22 ±0.02 8.37 ±0.02 8.79 ±0.03 neptune 84 9.22 ±0.02 8.49 ±0.02 8.85 ±0.03 neptune 84 9.17 ±0.02 8.3 ±0.02 8.72 ±0.03 neptune 84 9.1 ±0.02 8.33 ±0.02 8.71 ±0.03 neptune 84 9.59 ±0.02 8.49 ±0.02 9.02 ±0.03 neptune 94 9.08 ±0.02 8.46 ±0.02 8.77 ±0.03 neptune 94 9.1 ±0.02 8.48 ±0.02 8.79 ±0.03 neptune 94 9.12 ±0.02 8.58 ±0.02 8.84 ±0.03 neptune 94 9.21 ±0.02 8.67 ±0.02 8.94 ±0.03 neptune 94 9.38 ±0.02 8.63 ±0.02 9 ±0.03 neptune 94 9.29 ±0.02 8.46 ±0.02 8.87 ±0.03 neptune 94 9.44 ±0.02 8.45 ±0.02 8.94 ±0.03 neptune 94 9.23 ±0.02 8.59 ±0.02 8.91 ±0.03 neptune 94 9.17 ±0.02 8.44 ±0.02 8.8 ±0.03 neptune 94 9.13 ±0.02 8.42 ±0.02 8.77 ±0.03 neptune 94 9.79 ±0.02 8.6 ±0.02 9.17 ±0.03 neptune 110 10.29 ±0.02 8.92 ±0.02 9.58 ±0.03 neptune 110 9.86 ±0.02 8.79 ±0.02 9.31 ±0.02 FCUP 124 Studying evolved stars with Herschel observations neptune 110 9.61 ±0.02 8.98 ±0.02 9.29 ±0.03 neptune 110 9.72 ±0.02 8.93 ±0.02 9.32 ±0.02 neptune 110 10.5 ±0.02 8.9 ±0.02 9.67 ±0.03 neptune 110 10.01 ±0.02 8.9 ±0.02 9.44 ±0.03 neptune 110 9.89 ±0.02 8.91 ±0.02 9.39 ±0.03 neptune 110 9.89 ±0.02 8.88 ±0.02 9.37 ±0.03 neptune 110 9.98 ±0.02 8.96 ±0.02 9.45 ±0.03 neptune 110 9.87 ±0.02 8.8 ±0.02 9.32 ±0.03 neptune 110 10.09 ±0.02 8.87 ±0.02 9.46 ±0.03 neptune 125 10.81 ±0.02 9.36 ±0.01 10.06 ±0.02 neptune 125 10.74 ±0.01 9.46 ±0.01 10.08 ±0.02 neptune 125 10.32 ±0.02 9.36 ±0.01 9.83 ±0.02 neptune 125 10.6 ±0.02 9.31 ±0.01 9.93 ±0.02 neptune 125 10.94 ±0.02 9.67 ±0.01 10.28 ±0.02 neptune 125 10.83 ±0.02 9.55 ±0.02 10.17 ±0.02 neptune 125 10.38 ±0.02 9.31 ±0.02 9.83 ±0.02 neptune 125 10.73 ±0.02 9.52 ±0.02 10.1 ±0.02 neptune 125 10.48 ±0.02 9.35 ±0.01 9.9 ±0.02 neptune 125 10.51 ±0.02 9.28 ±0.02 9.88 ±0.02 neptune 136 11.14 ±0.01 9.63 ±0.01 10.36 ±0.02 neptune 136 10.51 ±0.01 9.41 ±0.01 9.94 ±0.02 neptune 136 10.4 ±0.02 9.49 ±0.01 9.94 ±0.02 neptune 136 10.28 ±0.02 9.48 ±0.01 9.87 ±0.02 neptune 136 10.92 ±0.01 9.76 ±0.01 10.32 ±0.02 neptune 136 10.5 ±0.02 9.51 ±0.01 9.99 ±0.02 neptune 136 10.47 ±0.02 9.48 ±0.01 9.96 ±0.02 neptune 136 11.05 ±0.02 9.83 ±0.01 10.42 ±0.02 neptune 136 10.43 ±0.01 9.57 ±0.01 9.99 ±0.02 neptune 136 10.27 ±0.01 9.38 ±0.01 9.81 ±0.02 neptune 136 10.86 ±0.01 9.47 ±0.01 10.14 ±0.02 neptune 145 11.2 ±0.01 9.73 ±0.01 10.44 ±0.02 neptune 145 10.58 ±0.01 9.49 ±0.01 10.02 ±0.02 neptune 145 10.66 ±0.01 9.67 ±0.01 10.15 ±0.02 neptune 145 10.8 ±0.01 9.83 ±0.01 10.3 ±0.02 neptune 145 10.98 ±0.01 9.85 ±0.01 10.4 ±0.02 neptune 145 10.59 ±0.01 9.75 ±0.01 10.16 ±0.02 FCUP 125 Studying evolved stars with Herschel observations neptune 145 10.68 ±0.01 9.76 ±0.01 10.21 ±0.02 neptune 145 10.98 ±0.01 9.88 ±0.01 10.42 ±0.02 neptune 145 10.75 ±0.01 9.87 ±0.01 10.3 ±0.02 neptune 145 10.56 ±0.01 9.78 ±0.01 10.16 ±0.02 neptune 145 10.76 ±0.01 9.78 ±0.01 10.26 ±0.02 neptune 150 11.29 ±0.01 10.34 ±0.01 10.81 ±0.02 neptune 150 10.62 ±0.01 10.2 ±0.01 10.41 ±0.02 neptune 150 10.92 ±0.01 10.5 ±0.01 10.71 ±0.02 neptune 150 11.46 ±0.01 10.45 ±0.01 10.94 ±0.02 neptune 150 10.95 ±0.01 10.41 ±0.01 10.68 ±0.02 neptune 150 10.78 ±0.01 10.42 ±0.01 10.6 ±0.02 neptune 150 11.14 ±0.01 10.67 ±0.01 10.9 ±0.02 neptune 150 10.88 ±0.01 10.51 ±0.01 10.69 ±0.02 neptune 150 10.71 ±0.01 10.56 ±0.01 10.63 ±0.02 neptune 150 10.99 ±0.01 10.68 ±0.01 10.83 ±0.02 neptune 150 11.57 ±0.01 10.51 ±0.01 11.03 ±0.02 neptune 168 12.06 ±0.01 10.67 ±0.01 11.34 ±0.02 neptune 168 11.44 ±0.01 10.45 ±0.01 10.93 ±0.01 neptune 168 11.72 ±0.01 10.81 ±0.01 11.26 ±0.02 neptune 168 11.98 ±0.01 10.9 ±0.01 11.43 ±0.02 neptune 168 11.8 ±0.01 10.74 ±0.01 11.26 ±0.02 neptune 168 11.52 ±0.01 10.88 ±0.01 11.19 ±0.02 neptune 168 11.69 ±0.01 10.95 ±0.01 11.31 ±0.02 neptune 168 11.83 ±0.01 10.89 ±0.01 11.35 ±0.02 neptune 168 11.58 ±0.01 10.89 ±0.01 11.23 ±0.01 neptune 168 11.51 ±0.01 10.99 ±0.01 11.25 ±0.01 neptune 168 11.74 ±0.01 10.96 ±0.01 11.34 ±0.02 neptune 187 13.21 ±0.02 11.66 ±0.01 12.41 ±0.02 neptune 187 12.51 ±0.01 11.4 ±0.01 11.94 ±0.02 neptune 187 12.89 ±0.01 12.19 ±0.01 12.54 ±0.02 neptune 187 13.51 ±0.02 12.4 ±0.01 12.94 ±0.02 neptune 187 12.99 ±0.01 11.54 ±0.01 12.24 ±0.02 neptune 187 13.02 ±0.01 12.09 ±0.01 12.55 ±0.02 neptune 187 12.68 ±0.01 11.9 ±0.01 12.28 ±0.02 neptune 187 12.92 ±0.01 11.61 ±0.01 12.25 ±0.02 neptune 187 12.6 ±0.01 11.8 ±0.01 12.19 ±0.02 FCUP 126 Studying evolved stars with Herschel observations neptune 187 12.64 ±0.01 12.1 ±0.01 12.37 ±0.02 neptune 187 12.65 ±0.02 11.83 ±0.01 12.23 ±0.02 A.4 PACS/Photometer PSF Table A.4: Photometer beam size in two bands; a is the major axis, b is the minor axis, ΦPSF (arcsec) = √a.b =FWHM and angle is the array-to-map angle. Target Band a (arcsec) b (arcsec) ΦPSF (arcsec)angle note Vesta Blue 5.53±0.02 5.1±0.02 5.31±0.03 +63 Vesta Blue 5.31±0.02 5.0±0.02 5.15±0.03 +63 recentered Vesta Blue 5.74±0.02 5.43±0.02 5.58±0.03 +63 recentered Vesta Blue 6.29±0.02 5.49±0.02 5.88±0.03 +42 Vesta Blue 5.89±0.02 5.05±0.02 5.46±0.03 +42 Vesta Blue 5.6±0.02 4.91±0.02 5.25±0.03 +42 recentered Vesta Blue 6.0±0.02 5.34±0.02 5.66±0.03 +42 recentered Vesta Blue 6.4±0.02 5.56±0.02 5.96±0.03 -42 Vesta Blue 6.01±0.02 5.12±0.02 5.55±0.03 -42 Vesta Blue 5.77±0.02 4.8±0.02 5.26±0.03 -42 recentered Vesta Blue 6.16±0.02 5.24±0.02 5.68±0.03 -42 recentered Vesta Red 12.12±0.03 10.73±0.03 11.41±0.04 +63 Vesta Red 11.29±0.03 9.87±0.03 10.56±0.04 +63 Vesta Red 11.27±0.03 9.72±0.03 10.47±0.04 +63 recentered Vesta Red 12.13±0.03 10.59±0.03 11.33±0.05 +63 recentered Vesta Red 12.35±0.03 10.44±0.03 11.35±0.04 +42 Vesta Red 11.51±0.03 9.59±0.03 10.5±0.04 +42 Vesta Red 11.41±0.03 9.47±0.03 10.4±0.05 +42 recentered Vesta Red 12.28±0.03 10.35±0.03 11.27±0.05 +42 recentered Vesta Red 12.37±0.03 10.48±0.03 11.39±0.04 -42 Vesta Red 11.53±0.03 9.64±0.03 10.54±0.04 -42 Vesta Red 11.47±0.03 9.56±0.03 10.47±0.05 -42 recentered Vesta Red 12.31±0.04 10.41±0.03 11.32±0.05 -42 recentered FCUP 127 Studying evolved stars with Herschel observations A.5 Photometry fitting The next tables contain information relative to the fit parameters obtained from photometry maps (HPF and JScanam) for our targets. The data was obtained from the HSA. Note that U Mon and IRAS 10178-5958 were not observed in the blue (70µm)band, so we only provide the results in the red band. The reported standard errors correspond to the propagated statistical uncertainties only, i.e, they do not include absolute flux calibration errors. Figures 2.9 and 2.10 were generated using tables A.5 and A.6. FCUP 128 Studying evolved stars with Herschel observations Table A.5: Fitting parameters from HPF photometry maps in the red and blue bands: peak intensity (P), flux (F) and FWHM (Φ). HPF Target OBSID P70 (Jy/px) F70 (Jy) Φ70 (00)P160 (Jy/px) F160 (Jy) Φ160 (00) AFGL2688 1342195837 72.3±0.3 383±3 6.89±0.05 24.06±0.04 338±1 11.27±0.04 AFGL3068 1342188378 7.79±0.01 28.2±0.1 5.72±0.02 1.302±0.002 18.85±0.05 11.44±0.03 AFGL3116 1342188490 2.267±0.004 9.88±0.04 6.28±0.02 0.409±0.001 7.3±0.03 12.69±0.05 AFGL618 1342193132 48.4±0.1 163±1 5.52±0.03 10.407±0.02 132.0±0.6 10.71±0.04 CIT6 1342210620 4.89±0.01 20.9±0.1 6.2±0.03 0.938±0.003 16.7±0.1 12.67±0.09 IRC+10216 1342186298 65.2±0.2 351±2 6.99±0.04 12.75±0.03 218±1 12.42±0.06 EPAQR 1342195460 0.868±0.002 3.45±0.02 5.99±0.03 0.1711±0.004 2.55±0.01 11.61±0.06 HD235858 1342196757 2.459±0.005 9.38±0.05 5.87±0.03 0.355±0.001 5.36±0.03 11.68±0.05 HD44179 1342185549 6.49±0.007 21.80±0.06 5.51±0.01 1.618±0.001 22.07±0.05 11.1±0.02 HD56126 1342207151 1.578±0.004 6.59±0.04 6.15±0.04 0.257±0.001 3.671±0.03 11.36±0.09 HD 161796 1342183565 4.949±0.007 16.93±0.05 5.56±0.02 0.745±0.001 9.78±0.02 10.89±0.02 IRAS15194-5115 1342190247 3.303±0.007 13.45±0.06 6.07±0.03 0.615±0.001 10.33±0.06 12.32±0.06 IRAS16342-3814 1342216493 14.66±0.02 47.4±0.2 5.41±0.02 3.957±0.005 52.6±0.1 10.96±0.03 IRAS16594-4656 1342193052 2.954±0.004 13.09±0.04 6.33±0.02 0.598±0.001 9.26±0.03 11.84±0.04 IRAS17347-3139 1342241406 5.222±0.006 17.14±0.05 5.45±0.01 1.34±0.005 19.3±0.2 11.41±0.1 IRAS22036+5306 1342198911 5.077±0.007 16.47±0.05 5.41±0.02 1.415±0.002 19.22±0.05 11.08±0.03 KHICYG 1342188320 1.568±0.003 6.336±0.03 6.04±0.03 0.3346±0.0005 5.1±0.02 11.74±0.03 NGC6302 1342250872 12.44±0.02 140.7±0.6 10.11±0.04 7.27±0.02 192.3±0.9 15.46±0.07 NMLCYG 1342195485 30.81±0.06 108.1±0.5 5.63±0.02 5.73±0.02 80.5±0.6 11.26±0.08 FCUP 129 Studying evolved stars with Herschel observations NMLTAU 1342190343 6.26±0.01 25.9±0.1 6.12±0.02 0.867±0.002 14.40±0.06 12.25±0.05 OMICET 1342190335 6.01±0.01 23.2±0.1 5.9±0.03 1.084±0.002 15.67±0.07 11.43±0.05 PIGRU 1342196799 1.109±0.003 4.774±0.03 6.24±0.04 0.236±0.001 3.52±0.03 11.6±0.08 RCAS 1342222422 2.518±0.006 9.85±0.06 5.95±0.03 0.522±0.001 8.03±0.04 11.79±0.06 RLEP 1342190304 0.538±0.001 2.145±0.011 6±0.03 0.1190±0.0003 1.74±0.01 11.5±0.06 RTCAP 1342231102 0.1210±0.0003 0.398±0.002 5.45±0.03 0.0258±0.0001 0.328±0.002 10.74±0.05 STHER 1342188324 0.236±0.001 1.209±0.007 6.81±0.03 0.0511±0.0001 0.849±0.004 12.25±0.05 TXCAM 1342217395 2.151±0.006 10.02±0.07 6.49±0.04 0.422±0.001 6.02±0.04 11.36±0.06 UHYA 1342212001 0.319±0.001 1.167±0.009 5.75±0.04 0.0678±0.0003 0.861±0.008 10.71±0.09 V1943SGR 1342208468 0.604±0.001 2.019±0.01 5.5±0.02 0.1279±0.0003 1.677±0.009 10.88±0.06 VCYG 1342188462 0.924±0.002 3.55±0.02 5.89±0.03 0.1821±0.0005 2.975±0.017 12.15±0.07 VHYA 1342211997 2.393±0.005 8.69±0.04 5.73±0.02 0.453±0.001 6.411±0.029 11.3±0.05 WORI 1342229983 0.338±0.001 1.181±0.006 5.62±0.02 0.0751±0.0001 1.008±0.004 11.02±0.04 WXPSC 1342188486 3.522±0.007 14.53±0.06 6.11±0.02 0.56±0.001 9.919±0.047 12.66±0.06 XHER 1342188322 0.702±0.001 2.62±0.01 5.81±0.02 0.1303±0.0002 2.002±0.009 11.79±0.05 YCVN 1342188330 0.418±0.001 1.486±0.006 5.67±0.02 0.09989±0.0001 1.378±0.005 11.22±0.04 IRAS10178-5958 1342237204 — — — 0.813±0.001 12.847±0.024 11.95±0.02 UMon 1342243117 — — — 0.242±0 3.003±0.006 10.59±0.02 FCUP 130 Studying evolved stars with Herschel observations Table A.6: Fitting parameters from JScanam photometry maps in the blue and red bands: peak intensity (P), flux (F) and FWHM (Φ). JScanam Target P70 (Jy/px) F70 (Jy) Φ70 (00) P160 (Jy/px) F160 (Jy) Φ160 (00) AFGL2688 69.4±0.2 371±2 6.95±0.04 24.44±0.03 337.4±0.8 11.17±0.03 AFGL3068 8.46±0.02 27.7±0.1 5.44±0.02 1.393±0.002 18.93±0.06 11.08±0.03 AFGL3116 2.47±0.005 9.67±0.05 5.95±0.03 0.443±0.001 7.29±0.04 12.2±0.05 AFGL618 46.8±0.1 160±1 5.56±0.03 10.52±0.02 132.0±0.5 10.65±0.03 CIT6 4.91±0.01 20.8±0.1 6.19±0.03 0.951±0.002 15.96±0.09 12.32±0.06 IRC+10216 67.9±0.2 350±2 6.83±0.04 12.73±0.03 219±1 12.46±0.06 EPAQR 0.919±0.002 3.41±0.02 5.79±0.03 0.1827±0.0004 2.57±0.01 11.27±0.05 HD235858 2.58±0.004 9.29±0.04 5.71±0.02 0.401±0.002 6.14±0.09 11.77±0.2 HD44179 7.026±0.008 21.58±0.06 5.27±0.01 1.708±0.001 22.01±0.05 10.79±0.02 HD56126 1.575±0.003 6.58±0.03 6.14±0.02 0.254±0.001 3.60±0.02 11.32±0.06 HD 161796 4.767±0.009 17.62±0.08 5.8±0.03 0.753±0.001 9.82±0.03 10.86±0.06 IRAS15194-5115 3.551±0.008 13.20±0.07 5.27±0.02 0.642±0.002 10.58±0.07 12.2±0.07 IRAS16342-3814 15.57±0.02 47.8±0.2 6.1±0.02 4.219±0.007 54.0±0.2 10.75±0.04 IRAS16594-4656 3.162±0.005 13.01±0.05 5.26±0.01 0.652±0.001 9.20±0.04 11.29±0.04 IRAS17347-3139 5.585±0.007 17.08±0.05 5.34±0.02 1.448±0.008 18.8±0.2 10.83±0.12 IRAS22036+5306 5.23±0.01 16.51±0.07 5.75±0.03 1.511±0.002 19.08±0.06 10.69±0.03 KHICYG 1.698±0.004 6.22±0.03 9.9±0.05 0.361±0.001 5.191±0.02 11.4±0.04 NGC6302 12.85±0.03 139.3±0.7 5.59±0.02 7.624±0.018 191±1 15.05±0.08 NMLCYG 31.02±0.05 107.2±0.4 5.74±0.03 5.778±0.01 80.8±0.4 11.24±0.05 FCUP 131 Studying evolved stars with Herschel observations NMLTAU 6.96±0.02 25.4±0.1 5.95±0.03 0.941±0.002 14.27±0.06 11.7±0.04 OMICET 5.95±0.01 23.3±0.1 6.18±0.03 1.085±0.002 15.90±0.07 11.51±0.05 PIGRU 1.129±0.003 4.77±0.03 5.88±0.03 0.2411±0.0004 3.58±0.02 11.59±0.05 RCAS 1.895±0.004 7.24±0.04 6.11±0.03 0.43±0.001 6.14±0.02 11.36±0.04 RLEP 0.53±0.001 2.192±0.012 5.5±0.02 0.1207±0.0003 1.769±0.01 11.51±0.06 RTCAP 0.1193±0.003 0.400±0.002 6.63±0.04 0.0258±0.0001 0.328±0.002 10.74±0.05 STHER 0.253±0.001 1.23±0.008 6.4±0.03 0.0556±0.0002 0.909±0.006 12.15±0.07 TXCAM 2.159±0.004 9.79±0.04 5.66±0.03 0.416±0.001 6.15±0.03 11.56±0.05 UHYA 0.329±0.001 1.165±0.007 5.55±0.02 0.0658±0.0004 1.046±0.013 12.0±0.1 V1943SGR 0.59±0.001 2.009±0.009 5.78±0.02 0.1291±0.0003 1.728±0.01 11±0.06 VCYG 0.952±0.002 3.542±0.02 5.8±0.03 0.199±0.001 3.21±0.03 12.1±0.1 VHYA 2.347±0.004 8.73±0.04 5.8±0.02 0.448±0.001 6.66±0.03 11.6±0.05 WORI 0.334±0.001 1.173±0.006 5.63±0.02 0.0752±0.0001 0.993±0.004 10.92±0.04 WXPSC 3.848±0.008 14.15±0.07 5.76±0.03 0.602±0.001 9.86±0.05 12.16±0.06 XHER 0.759±0.002 2.59±0.01 5.54±0.02 0.1474±0.0004 2.05±0.01 11.22±0.06 YCVN 0.44±0.001 1.506±0.007 5.56±0.02 0.1109±0.0003 1.357±0.007 10.51±0.05 IRAS10178-5958 — — — 0.887±0.001 12.83±0.03 11.43±0.02 UMon — — — 0.2444±0.0004 3.183±0.013 10.85±0.04