A Radial Velocity Study of the Planetary System of π Mensae: Improved Planet Parameters for π Mensae c and a Third Planet on a 125 Day Orbit

A Radial Velocity Study of the Planetary System of πMensae: Improved Planet Parameters for πMensae c and a Third Planet on a 125 Day Orbit Artie P. Hatzes 1 , Davide Gandolfi 2 , Judith Korth 3 , Florian Rodler 4 , Silvia Sabotta 5 , Massimiliano Esposito 1 , Oscar Barragán 6 , Vincent Van Eylen 7 , John H. Livingston 8 , Luisa Maria Serrano 2 , Rafael Luque 9 , Alexis M. S. Smith 10 , Seth Redfield 11 , Carina M. Persson 12 , Martin Pätzold 13 , Enric Palle 14,15 , Grzegorz Nowak 14,15 , Hannah L. M. Osborne 7 , Norio Narita 8,14,16,17,18 , Savita Mathur 14,15 , Kristine W. F. Lam 19 , Petr Kabáth 20 , Marshall C. Johnson 21 , Eike W. Guenther 22 , Sascha Grziwa 13 , Elisa Goffo 1,2 , Malcolm Fridlund 12,23 , Michael Endl 24 , Hans J. Deeg 14,15 , Szilard Csizmadia 10 , William D. Cochran 24 , Lucía González Cuesta 14,15 , Priyanka Chaturvedi 1 , Ilaria Carleo 11 , Juan Cabrera 10 , Paul G. Beck 25 , and Simon Albrecht 26 1 Thüringer Landessternwarte, Sternwarte 5, D-07778 Tautenburg, Germany; [email protected] 2 Dipartimento di Fisica, Università degli Studi di Torino, via Pietro Giuria 1, I-10125, Torino, Italy 3 Department of Space, Earth and Environment, Astronomy and Plasma Physics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden 4 European Southern Observatory (ESO), Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago De Chile, Chile 5 Landessternwarte, Zentrum für Astronomie der Universität Heidelberg, Königstuhl 12, D-69117 Heidelberg, Germany 6 Sub-department of Astrophysics, Department of Physics, University of Oxford, Oxford, OX1 3RH, UK 7 Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey, RH5 6NT, UK 8 Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 9 Instituto de Astrofísica de Andalucía (IAA-CSIC), E-18008, Granada, Spain 10 Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse 2, D-12489 Berlin, Germany 11 Astronomy Department and Van Vleck Observatory, Wesleyan University, Middletown, CT 06459, USA 12 Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, SE-439 92 Onsala, Sweden 13 Rheinisches Institut für Umweltforschung an der Universität zu Köln, Aachener Strasse 209, D-50931 Köln, Germany 14 Instituto de Astrofísica de Canarias, C/Vía Láctea s/n, E-38205 La Laguna, Spain 15 Departamento de Astrofísica, Universidad de La Laguna, E-38206 La Laguna, Spain 16 Astrobiology Center, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 17 National Astronomical Observatory of Japan, NINS, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 18 JST, PRESTO, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan 19 Center for Astronomy and Astrophysics, TU Berlin, Hardenbergstr. 36, D-10623 Berlin, Germany 20 Astronomical Institute, Czech Academy of Sciences, Fričova 298, 25165, Ondr ejov, Czech Republic 21 Las Cumbres Observatory, 6740 Cortona Dr., Ste. 102, Goleta, CA 93117, USA 22 Thüringer Landessternwarte Tautenburg, Sternwarte 5, D-07778 Tautenberg, Germany 23 Leiden Observatory, University of Leiden, P.O. Box 9513, 2300 RA, Leiden, The Netherlands 24 Department of Astronomy and McDonald Observatory, University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA 25 Institut für Physik, Karl-Franzens Universität Graz, Universitätsplatz 5/II, NAWI, Austria 26 Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 125, DK-8000 Aarhus C, Denmark Received 2021 September 8; revised 2022 January 17; accepted 2022 February 28; published 2022 April 20 Abstract πMen hosts a transiting planet detected by the Transiting Exoplanet Survey Satellite space mission and an outer planet in a 5.7 yr orbit discovered by radial velocity (RV)surveys. We studied this system using new RV measurements taken with the HARPS spectrograph on ESO’s 3.6 m telescope, as well as archival data. We constrain the stellar RV semiamplitude due to the transiting planet, πMen c, as K c =1.21 ±0.12 m s −1 , resulting in a planet mass of M c =3.63 ±0.38 M ⊕ . A planet radius of R c =2.145 ±0.015 R ⊕ yields a bulk density of ρ c =2.03 ±0.22 g cm −3 . The precisely determined density of this planet and the brightness of the host star make πMen c an excellent laboratory for internal structure and atmospheric characterization studies. Our HARPS RV measurements also reveal compelling evidence for a third body, πMen d, with a minimum mass M d sin i d =13.38 ±1.35 M ⊕ orbiting with a period of P orb,d =125 days on an eccentric orbit (e d =0.22).A simple dynamical analysis indicates that the orbit of πMen d is stable on timescales of at least 20 Myr. Given the mutual inclination between the outer gaseous giant and the inner rocky planet and the presence of a third body at 125 days, πMen is an important planetary system for dynamical and formation studies. Unified Astronomy Thesaurus concepts: Exoplanet systems (484) Supporting material: machine-readable table 1. Introduction The bright (V=5.65; Table 1)G0 dwarf star πMen has been the target of exoplanet studies for over 20 yr. Jones et al. (2002) reported long-period (P orb,b ≈2100 days)radial velocity (RV) variations that were consistent with the presence of a substellar companion (πMen b)with a minimum mass of ≈10 M Jup in a highly eccentric (e b ≈0.6)orbit. The star was later found by NASA’s Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014)to host a small planet (R c ≈2R ⊕ )in a 6.27 day orbit (πMen c; Gandolfiet al. 2018; Huang et al. 2018). Due to the brightness of the host star, this planet is a prime candidate The Astronomical Journal, 163:223 (17pp), 2022 May https://doi.org/10.3847/1538-3881/ac5dcb © 2022. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s)and the title of the work, journal citation and DOI. 1 for atmospheric characterization studies (García Muñoz et al. 2020,2021). Accurate planetary masses and radii are important for exoplanet studies. True planet masses are needed for understanding the architecture of exoplanets and for dynamical studies. Accurate bulk densities are essential for constraining the internal composition of the planet. In the case of πMen c, the measured RV amplitude (and thus mass)was based on archival data taken with the HARPS spectrograph. The observing strategy consisted of sparse observations spread over a relatively long time and thus was not geared to detect small, short-period planets. The corresponding error in the mass, ≈20%, made it difficult to distinguish between interior models consisting mostly of water, or having a significant fraction (≈50%)of silicates (Gandolfiet al. 2018). The πMen system has received heightened interest because astrometric studies have determined the orbital inclination of the outer planet. Xuan & Wyatt (2020), De Rosa et al. (2020), and Damasso et al. (2020)combined the long time series of RV measurements for this star with Hipparcos and Gaia astrometric measurements to determine an orbital inclination of i b ≈50°. Not only does this pin down the true planet mass as M b ≈14 M Jup , but, more importantly, it establishes that the inner and outer planetary orbits are misaligned. πMen joins υ Andromedae (McArthur et al. 2010), Kepler-108 (Mills & Fabrycky 2017), and possibly 14 Her (Bardalez Gagliuffiet al. 2021)as stars hosting planets with large mutually inclined orbits. The πMen system is thus important for constraining planet formation theories and studying the dynamical evolution of planetary systems. In order to measure a more precise mass for πMen c, we included observations of the host star as part of our ESO HARPS large program of spectroscopic follow-up of transiting planet candidates found by TESS. The purpose of these RV measurements was twofold. First, we wished to improve on the error in the planet mass to constrain better compositional models. An accurate mass is also needed to estimate the atmospheric pressure scale height needed for planning observations to detect atmospheric features. Second, we wished to study the architecture of this system by searching for additional planetary companions. This is especially important given the recent discovery of the mutual inclination of the orbits between the inner and outer planets. πMen was also intensively observed by the newly commissioned ESPRESSO spectrograph on the ESO’s Very Large Telescope, which yielded a Kamplitude of 1.5 ±0.2 m s −1 for the inner transiting planet πMen c (Damasso et al. 2020). This result offered us a chance to compare the performance of two state-of-the-art spectrographs designed for precise RV work, one a venerable instrument, HARPS (Mayor et al. 2003), mounted on a 3.6 m telescope and in use for almost 20 yr, and a more modern one, ESPRESSO, mounted on an 8.2 m telescope (Pepe et al. 2014). The star is bright, so high signal-to-noise ratio (S/N)data can be obtained on both instruments with relatively short exposure times. In the future, considerable telescope resources will be invested in the RV follow-up of transiting small planets found by the PLATO mission (Rauer et al. 2014), so it is useful to compare the performance of both instruments using contemporaneous observations on the same target. In this work, we adopted the most recent stellar parameters derived by Damasso et al. (2020). The only exception is the stellar radius. For the sake of completeness, they are listed in Table 1, along with the equatorial coordinates, V-band magnitude, parallax, distance, and proper motion of the star. 2. The Radial Velocity Data Our RV data consist of archival and new measurements from our ESO’s HARPS large follow-up program. A total of 77 RV measurements come from the UCLES spectrograph mounted on the 3.9 m telescope of the Anglo Australian Telescope (AAT). These can be found in Butler et al. (2006)or in Gandolfiet al. (2018). R. Wittenmyer kindly provided us with the more recent measurements used by Huang et al. (2018). Archival HARPS data consisting of 145 RV measurements (51 nightly averaged)were also taken from the public archive of the European Southern Observatory (ESO). We also included 275 RV measurements (37 nightly averaged)taken with the ESPRESSO spectrograph (Damasso et al. 2020). The new data for πMen were taken as part of our ESO observing programs 0101.C-0829, 1102.C-0923, and 106.21TJ.001 (PI: Gandolfi)and during technical nights Table 1 Equatorial Coordinates, Proper Motion, Parallax, Distance, V-band Magnitude, and Fundamental Parameters of πMen Parameter Value Source Equatorial coordinates and V-band magnitude R.A. (hh:mm:ss, J2000)05:37:09.885 Gaia Collaboration et al. (2018) R.A. (dd:mm:ss, J2000)−80:28:08.831 Gaia Collaboration et al. (2018) V5.65 ±0.01 Mermilliod (1987) Proper motion, parallax, and distance m d acos (mas yr −1 )311.187 ±0.127 Gaia Collaboration et al. (2018) μ δ (mas yr −1 )1048.845 ±0.136 Gaia Collaboration et al. (2018) Parallax (mas)54.7052 ±0.0671 Gaia Collaboration et al. (2018) Distance (pc)18.280 ±0.022 Gaia Collaboration et al. (2018) Fundamental parameters Star mass M å (M e )1.07 ±0.04 Damasso et al. (2020) Star radius R å (R e )1.190 ±0.004 Csizmadia et al. (2021, submitted) Effective remperature T eff (K)5998 ±62 Damasso et al. (2020) Iron abundance [Fe/H](dex)0.09 ±0.04 Damasso et al. (2020) Projected rotational velocity vsin i å (km s −1 )3.34 ±0.07 Damasso et al. (2020) Age (Gyr)- + 3 .92 0.98 1.03 Damasso et al. (2020) 2 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. (program IDs 60.A-9700 and 60.A-9709)on HARPS. These consisted of 413 RV measurements 27 spanning 2018 September to 2020 December (hereafter “HARPS-Large”data set). The star is bright, so we typically took several observations per night. Exposure times were 150–300 s, resulting in a median S/ Nof∼250 pixel –1 at 550 nm. If one considers only nightly averages, our program resulted in 177 new measurements taken at different epochs. In 2015 June the HARPS fiber bundle was upgraded (Lo Curto et al. 2015). This results in a zero-point offset between the data taken before and after the upgrade. We therefore treated the complete data as four independent sets with different zero-point offsets: UCLES, ESPRESSO, and HARPS before (HARPS-PRE)and after the fiber upgrade (HARPS-POST; this set also includes HARPS-Large). We extracted the HARPS spectra using the Data Reduction Software (DRS; Lovis & Pepe 2007). There are a number of reduction pipelines available for the calculation of RVs: the DRS, which uses the cross-correlation method with a digital mask (Pepe et al. 2002), the HARPS Template-Enhanced Radial velocity Re-analysis Application (HARPS-TERRA, Anglada-Escudé & Butler 2012), and the SpEctrum Radial Velocity AnaLyser (SERVAL)pipeline (Zechmeister et al. 2018). For our final analysis we used the RVs calculated with HARPS-TERRA, as this produced a final rms scatter that was about 4% lower than the other two methods. We emphasize, however, that all reduction programs produced consistent orbital parameters that were well within the uncertainties. Briefly, HARPS-TERRA performs a least-squares matching of each observed spectrum to a high-S/N template spectrum produced by co-adding all the observations of the target star after they have all been placed on the same wavelength scale and corrected for Earth’s barycentric motion. The RV for each spectrum is calculated with respect to this master template. πMen is a high-proper-motion star. The RV data span 17 yr, so it is important to remove the secular acceleration. The star has a systemic RV of 10.7317 ±0.0003 km s −1 (as derived from the analysis of the HARPS-POST DRS RVs), a parallax of 54.705 ±0.067 mas, and proper motion of 311.187 ± 0.127 mas yr −1 and 1048.845 ±0.136 mas yr −1 in R.A. and decl., respectively (Gaia Collaboration et al. 2018, see also Table 1). This results in a secular acceleration of ∼0.48 ms −1 yr −1 . This was removed for all RVs except for those processed with HARPS-TERRA, which already accounts for the secular acceleration in its pipeline. Table 2lists the data sets used in our RV analysis. We reiterate that the “HARPS-POST”data contain both the 17 archival HARPS measurements after the upgrade and those from our large program. The “HARPS-Large”is a subset of this that only contains our new 404 useful measurements from the large program. The standard deviation listed is the rms scatter of the data sets after the removal of all periodic signals (see below). Table 3lists the new RV measurements from our ESO large programs. 3. Periodogram Analysis of the RV Data We first performed a frequency (periodogram)analysis on the RV data in order to confirm that the signal of the transiting planet πMen c is indeed present in the data. Furthermore, identifying all significant signals in the data and modeling these is important for deriving a precise RV amplitude for the transiting planet. To find weak periodic signals, we first had to remove the large variations due to the outer planet. Since the UCLES measurements increase the time base of the measurements needed to refine the parameters of the outer planet, we included these in spite of them having poorer RV precision. An initial orbital solution was performed using the general nonlinear least-squares fitting program Gaussfit(Jefferys et al. 1987). All orbital parameters were allowed to vary, including the zero-point offset of each individual data set. The orbit parameters listed in Table 4represent the final ones from our Table 2 The RV Data Sets Data Set Time Span (yr)Measurements (Nightly)σ(ms −1 ) UCLES 1988.04–2015.9 77 5.88 HARPS-PRE 2004.0–2015.0 31 2.72 HARPS-POST (Archival)2015.8–2016.2 9 0.83 HARPS-POST (Large)2018.7–2020.2 177 1.40 ESPRESSO 2018.7–2019.2 37 0.95 Table 3 RV Measurements and Activity Indicators from the ESO HARPS-Large Programs BJD TDB RV σ RV BIS FWHM S-index σ S‐index (days)(ms −1 )(ms −1 )(ms −1 )(km s −1 ) 2,458,383.896397 10994.6 0.4 8.974 7.6796 0.153485 0.000362 2,458,383.899499 10994.5 0.4 9.763 7.6807 0.153990 0.000368 2,458,384.814003 10998.8 0.4 9.695 7.6768 0.153351 0.000338 2,458,384.817116 11000.3 0.4 8.031 7.6791 0.153506 0.000362 2,458,385.813365 11003.3 0.4 8.265 7.6798 0.153090 0.000287 2,458,385.816513 11003.4 0.4 8.884 7.6788 0.153815 0.000288 2,458,385.898502 11003.7 0.3 8.891 7.6788 0.152502 0.000327 (This table is available in its entirety in machine-readable form.) 27 We excluded seven measurements taken on 2018 November 27 and 28 (UT), which are affected by a poor wavelength solution (see Nielsen et al. 2020). We also rejected two spectra taken on 2019 December 5 (UT), due to a failure of the telescope guiding system. This gives 404 useful HARPS spectra. 3 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. joint fit(see below), which are entirely consistent with the Gaussfitresults. The orbital fit for πMen b is shown in Figure 1. The UCLES measurements have an rms scatter more than twice that of the HARPS data and will be excluded from the subsequent analyses. The generalized Lomb–Scargle (GLS)periodogram (Zechmeister & Kürster 2009)of the residual HARPS-Large RV data, after removing the orbital frequency of planet b (f 1 =4.79 ×10 −4 day −1 ), is shown in the top panel of Figure 2. We only used the HARPS-Large data for this analysis for two reasons. First, it provides a much simpler sampling window. Including the early HARPS-PRE data results in a very complex window with many more alias peaks. Second, the HARPS-PRE data start approximately 10 yr earlier and have much sparser sampling. This means that any underlying long-term stellar variability, which will be difficult to model, can boost power into an alias frequency, thus masking the true one that is present. The highest peak occurs at a frequency of f 2 =0.008 day −1 (P=125 days), although one can see significant power at the orbital frequency of the transiting planet (f 3 =0.16 day −1 , P=6.27 days). Removing f 2 increases the power seen at orbital frequency of the transiting planet (middle panel of Figure 2). The final residuals (bottom panel)result in no additional significant peaks. A peak is seen at f=1.56 ×10 −3 (P=640 days), but this has low significance with an estimated falsealarm probability (FAP)≈2%, which we do not consider significant. We assessed the statistical significance of the new ∼125 day period via the bootstrap randomization process, where the RV values were randomly shuffled, keeping the time stamps fixed (Murdoch et al. 1993). In 300,000 realizations of the bootstrap there was no instance where the random data periodogram showed power higher than the real data. This implies an FAP =3.3 ×10 −6 . It is highly unlikely that this peak is due to random noise. 4. The Nature of the 125 Day Period Before we can adequately model the 125 day signal in our analysis, it is important to establish its nature. If it is planetary in origin, it would be an important new member of the πMen system; however, it can also arise from stellar activity. Table 4 Orbital Parameters for πMen b and c Parameter πMen b πMen c Orbital period P orb (days)2088.33 ±0.34 6.267852 ±0.000016 Time of inf. conj./first transit T 0 (BJD TDB –2,450,000 days)6540.34 ±0.75 8519.8068 ±0.0003 Orbit eccentricity e0.6396 ±0.0009 0 (fixed) Argument of periastron of stellar orbit ω å (deg)331.03 ±0.25 90 (fixed) Radial velocity semiamplitude variation K(ms −1 )192.99 ±0.38 1.21 ±0.12 Planetary minimum mass M p ×sin i p 9.82 ±0.24 M Jup 3.63 ±0.38 M ⊕ True a planetary mass M p 12.6 ±2.0 M Jup 3.63 ±0.38 M ⊕ Note. a Using i b = - + 5 1.2 9.8 14.1 for πMen b (Xuan & Wyatt 2020)and i c =87°.05±0°.15 for πMen c (Damasso et al. 2020). Figure 1. Top: the RV time series from UCLES (brown squares), HARPS-PRE (red circles), and HARPS-POST (blue triangles). For clarity we do not plot the ESPRESSO measurements, as these are contemporaneous with the HARPS-POST data. The curve is the Keplerian orbital solution for πMen b. Bottom: the residuals after subtracting the orbit of πMen b. 4 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. Important criteria for establishing the planetary nature of an RV signal are that it is long-lived and coherent and that it is not present in any activity indicators. 4.1. Coherence of the 125 Day Period There are several ways to test whether the 125 day period in the RV data is coherent and stable. One can examine the evolution of the power in the standard Lomb–Scargle (LS) periodogram as a function of the number of measurements (Hatzes 2016)or the evolution of the FAP (Trifonov et al. 2018). Alternatively, one can use the Stacked-Bayesian GLS periodogram (Mortier & Collier Cameron 2017)to assess the stability of a signal. However, it can be difficult to assess the stability of a signal merely by looking at the stacked periodogram. The pathology of the sampling often can make a signal appear unstable for a time when in fact it is not, or vice versa. We therefore chose to use the growth of the LS power and compare it to what is expected from a simulated signal with the appropriate noise added. This provides a somewhat more “quantitative”assessment of the stability. We first isolated the 125 day signal by removing the contribution of the outer and transiting planets. The blue circles in Figure 3show the growth of the LS power (P)of the 125 day signal as a function of the number (N)of RV measurements (we will refer to this as the P–Nrelationship)using the Figure 2. Top: the GLS periodogram of the HARPS-Large RV measurements after removing the motion of the outer planet (orbital frequency, f 1 =4.79 ×10 −4 day −1 ). Middle: the GLS periodogram of the RV residuals after removing the contribution of the dominant peak at f 2 =0.008 day −1 . Bottom: the GLS periodogram of the final RV residuals after removing the orbital frequency of the transiting planet, f 3 =0.16 day −1 . Figure 3. Growth of the LS power of the 125 day period attributed to a third body in the system as a function of the number of RV measurements for the real data (HARPS-Large and ESPRESSO; blue circles)and simulations (red triangles). 5 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. HARPS-Large and ESPRESSO data. We then compared this to expectations (red triangles)using an orbital fit to the 125 day RV variations (see below)sampled like the data and with the appropriate random noise added (σ=1.5 m s −1 ). The error bars indicate the standard deviation in the power using simulated data with 10 different realizations of the noise. The evolution of the power of the 125 day period largely follows the simulated data in that there is a monotonic increase in the power as a function of number of data points, although the slope in the power evolution of the real data is slightly shallower than the simulated data. Overall, the behavior of the P–Nrelationship seems to indicate that the 125 day period is stable and coherent. 4.2. Activity Indicators Stellar activity can also create periodic RV signals that can mimic a planet, and this can be revealed by a periodogram analysis of activity indicators. If an RV signal is absent in all activity indicators, then we can be more confident that it is the barycentric motion of the host star due to the presence of a companion. We have three activity indicators at our disposal: the FWHM and bisector inverse slope (BIS)of the crosscorrelation function, and the Ca II S-index measurement (see Baliunas et al. 1995). HARPS-TERRA also delivers indices on the Balmer Hαand Na D lines. However, a period analysis of these data showed a dominant period at 1 yr, possibly an indication of telluric contamination. We therefore excluded these from our analysis. Figure 4shows the GLS periodograms for the three activity indicators extracted from HARPS-Large data. All have the highest peak at low frequencies that seem to be unrelated to the frequency found in the RV time series. The only exception is the BIS, which shows a secondary peak near 0.008 day −1 (see Section 4.2.1 for a more detailed discussion of the bisector variations). Table 5lists the dominant periodic signals found in the activity indicators and the FAP determined via 200,000 realizations of a bootstrap. Figure 5shows the fit to the time series of each activity indicator using the period of the dominant peak found in the corresponding periodogram. We investigated whether additional signals could be hidden in the activity indicators. Prewhitening, i.e., the subsequent fitting and removal of dominant frequencies in the periodogram of the time series and its residuals, is a powerful tool for finding weak, underlying signals in data. For instance, prewhitening of the Hαindex measurements for GL 581 was able to isolate variations with the same period as the purported planet GL 581 d (Hatzes 2016), thus supporting the claim of activity as the origin for the 66 day RV period (Robertson et al. 2014). The GLS periodograms of the residuals of the activity indicators, after removing the appropriate sine fits to the dominant frequency in the data, are shown in Figure 6. The S-index and FWHM residuals do not show any significant 28 peaks at 0.008 day −1 . The S-index only shows a weak one that is the fifth-highest peak in the frequency range. In the amplitude spectrum it appears to be less than twice the mean height of the surrounding noise peaks, an indication that it is not significant (see Kuschnig et al. 1997). The peak in the BIS residuals at 0.008 day −1 is the highest peak in the frequency range considered (Figure 6). We assessed the significance of this peak via a bootstrap. The FAP that noise can produce a peak exactly coincident at this frequency is about 7%, which we do not consider statistically significant. Note that a nearby peak has comparable power. 4.2.1. The Bisector Variations The bisector is the only activity indicator that shows possible variations at the 125 day RV period. Both the raw and residual Figure 4. The GLS periodograms of the activity indicators extracted from the HARPS-Large data set. From top to bottom: S-index, FWHM, and BIS. The vertical dashed line marks the orbital frequency of the 125 days detected in the RVs. Table 5 Periods in Activity Indicators and Their False-alarm Probabilities Indicator Period (days)FAP S-Index 456 ±9<5×10 −6 FWHM 184 ±2<5×10 −6 BIS 757 ±64 0.0025 28 We considered a signal to be significant if its FAP <0.1%. 6 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. BIS variations show an isolated and modestly strong peak at the period (frequency)of interest. Since the bisector variations may be the only indicator to cast doubt on a planet hypothesis for the RV period, and given the importance of establishing that the 125 day period is planetary in nature, this merits a critical evaluation of the reality of these. The periodogram of the raw bisector measurements (Figure 4, bottom panel)shows a peak coincident with the 125 day period (f=0.008 day −1 ). Without any a priori information, this has an FAP ∼30%. However, this FAP represents the probability that noise can create a peak at least this high over a broad frequency range. As pointed out by Scargle (1982), for a known signal (i.e., 125 days)we need to consider the probability that noise can create a peak with the observed power or higher exactly at this frequency. If z represents the unnormalized power, then FAP ∼e −z . In this case the FAP is rather low at FAP =0.13%. This value is consistent with the FAP obtained with a bootstrap analysis. In spite of this low FAP, we are confident that this signal is not significant for several reasons. First, the bisector data are quite noisy. A sine fit to these using the 125 day period results in an amplitude of 0.33 m s −1 or 2.5 times smaller than the rms scatter (σ=0.83 m s −1 )about the fit. In spite of this, the 125 day signal should have been detected at much higher significance owing to the large number of measurements. As a test, we took a 125 day sine function with an amplitude of 0.33 m s −1 and added random noise with the rms scatter of the measurements. The periodogram of the simulated data showed power consistent with an FAP that was more than 1000 times lower than was seen for the real data. A Figure 5. The time series of the S-index (top), FWHM (middle), and BIS (bottom)measurements extracted from the HARPS-Large data set. The red curves are sine fits using the period of the dominant peak in each periodogram (Table 5). Figure 6. GLS periodogram of the activity indicators after removal of the dominant signal in each (Table 5). The vertical dashed line is the frequency of the 125 day period seen in the RV data. 7 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. true signal should have shown a much higher power (i.e., lower FAP)than is observed. Second, the prewhitened analysis provides unconvincing support that the bisector variations are intrinsic to the star. Our analysis of the residuals showed an FAP ∼7%. Since we were focused on the 125 day signal, we initially only considered the frequency range out to 0.025 day −1 (Figure 6, bottom panel).If we extend the analysis to higher frequencies, we find that the highest peak in the residuals occurs at 20 days (f=0.05 day −1 ). Removing this signal weakens the peak at 125 days further such that its FAP increases to ∼50%. Third, we examined whether any phase variations of the bisectors can be related to the 125 day signal. Figure 7shows the orbital fit to the 125 day RV variations. This fit is presented and discussed in detail in Section 5.1. The points show the binned (bin size ≈0.05 in phase)residual BIS measurements, after removing the dominant signal, phased to the same period. There is no hint of sinusoidal variations in the BIS that could account for the observed 125 day RV signal. This strongly indicates that the signal found in the periodogram is due to noise, consistent with the large FAP we derived. Finally, it is worth noting that the case of 51 Peg highlights the pitfalls of relying only on bisector measurements to refute a planet hypothesis. Gray & Hatzes (1997)found bisector variations in 51 Peg that were coincident with the orbital period of the planet. The formal FAP for this signal was 0.3% and thus seemed to be significant. Subsequently, higher-quality bisector measurements were found to be constant (Hatzes et al. 1998). In spite of the low FAP, the previous variations were in fact due to noise. Since the bisector signal at 125 days in πMen is not supported by other activity indicators, we conclude that these do not provide convincing enough evidence to refute a planet hypothesis for the RV signal. 4.3. The Rotational Period In the full time series we found no significant peaks that may be indicative of stellar rotation. This is expected given that rotational modulation from activity may not be coherent over the long time span of our data. However, our time series did have long stretches when closely spaced measurements were made spanning 10–20 days. We searched for evidence of rotational modulation in these subsets and found only one instance, at the end of the S-index time series, which may show variations due to rotational modulation. Figure 8shows a 16 day time span of S-index measurements showing sine-like variations with a period of 18.7 ±0.8 days. Damasso et al. (2020)measured a projected rotational velocity of the star of vsin i=3.34 ±0.07 km s −1 , which agrees with the value of 3.3 ±0.5 km s −1 found by Gandolfi et al. (2018). Csizmadia et al. (2021, submitted)measured a stellar radius of R å =1.190 ±0.004 R e , which results in a maximum rotation period of P rot =18.0 ±0.4 days, consistent with the value from the S-index variations and that inferred by Damasso et al. (2020). Interestingly, the 20 day period found in the bisector measurements is close to this value. Given the low significance of the bisector signal, we are uncertain that it is truly related to stellar rotation. 5. Keplerian Motion for the 125 Day Period The most likely explanation for the 125 day period is that it stems from the presence of a third companion that we refer to as πMen d. Here we determine the orbital parameters and investigate the stability of the system. 5.1. Orbital Solution A preliminary Keplerian fit to the 125 day period using the residuals after removing the contributions of the inner and outer planets indicates an eccentric orbit (e∼0.2). We performed a joint fit for all three Keplerian signals using the code pyaneti (Barragán et al. 2019), which employs a Bayesian approach combined with Markov Chain Monte Carlo sampling to estimate the planetary parameters. We derived the best-fitting orbital solution for πMen b from the UCLES, HARPS-PRE, HARPS-POST, and ESPRESSO data and used only the HARPS-POST and ESPRESSO data sets to determine the Figure 7. The phase-binned BIS measurements using the ≈125 day period found in the RVs. The red curve represents an orbital solution to the 125 day period (see Section 5.1). 8 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. parameters of πMen c and d. We imposed uniform uninformative priors for all the fitted parameters, except for the orbital period and time of first transit of πMen c, for which we adopted Gaussian priors from Damasso et al. (2020). A circular orbit for the inner transiting planet was assumed, but we fitted the eccentricity for πMen b and d. We accounted for the RV offsets between the different instruments/setups and fitted for jitter terms to account for both instrumental noise not included in the nominal uncertainties and RV variation induced by stellar activity. A parameter space with 500 Markov chains was explored to generate a posterior distribution of 250,000 independent points for each model parameter. The inferred parameters are given in Tables 4and 6. They are defined as the median and 68% region of the credible interval of the posterior distributions for each fitted parameter. πMen d has a minimum mass of M d sini d =13.38 ± 1.35 M ⊕ and an orbit that is modestly eccentric (e=0.220 ± 0.079). Interestingly, the angle of periastron passage, ω,is comparable to that of the outer planet. The phase curve of the orbit is shown in Figure 9, and the time series, focusing on just the time span of the HARPS-Large RVs, is shown in Figure 10. We found that the difference between the Bayesian information criterion of the three-planet (b, c, and d)and two-planet (b and c)models is ΔBIC =−73, providing very strong evidence for the existence of a third Doppler signal in the data. After removing the contribution of the orbital motions of all planetary signals, the HARPS data have an rms scatter of σ HARPS‐Post =1.40 m s −1 , and the ESPRESSO data have σ ESPRESSO =0.95 m s −1 . Both are about a factor of three larger than the nominal measurement errors, which are typically better than 0.5 m s −1 . 5.2. Orbital Stability For the 125 day RV variations to be due to a planet, it must lie on a stable orbit. A detailed dynamical investigation is beyond the scope of this paper. Instead, we performed a preliminary analysis to assess whether a stable orbit is at least feasible. For this dynamical study we employed Rebound (Rein & Liu 2012)and drew samples from the posterior distributions of our three-planet orbital solutions, while the inclination of πMen b was drawn from i b =50°±5°according to previous studies (Damasso et al. 2020; De Rosa et al. 2020; Xuan & Wyatt 2020). Since we can only derive the minimum mass 29 (M d sin i d )of πMen d, we allowed for an orbital inclination between 20°and 90°. The left and middle panels of Figure 11 show the stability probability as a function of the eccentricity, period, and mass of planet d for our simulation. For the period range of 110–130 days the orbit of planet d is stable, although there are isolated regions where it is unstable. The planet must have a mass <20 M ⊕ for stability. For our orbital solution (Table 6)this implies an orbital inclination i d >40°. The right panel of Figure 11 shows the stability probability in the mass versus mutual inclination plane. In general, orbits are more likely to be unstable for high mutual inclinations and a low-mass planet, or high mass even for relatively low mutual inclinations. Due to limited computational resources, our simulations only covered a time span of 20 Myr, a small fraction of the estimated stellar age of ≈3.3 Gyr (Damasso et al. 2020). Clearly, a numerical simulation is called for, covering a much larger fraction of the stellar life. For such a simulation covering a longer time span it would be important to obtain more accurate orbital parameters in order to restrict the parameter space of the simulations. Figure 8. S-index measurements over 16 consecutive nights. The curve represents the sine fit with a period of 18.7 days. Table 6 Orbital Parameters for πMen d Parameter Value Orbital period P orb,d (days)- + 1 24.64 0.5 2 0.4 8 Time of inferior conjunction T 0,d (BJD TDB –2,450,000 days)- + 7 595.46 6.39 6.90 Eccentricity e d 0.220 ±0.079 Argument of periastron of stellar orbit ω å,d (deg)- + 3 23 73 25 Radial velocity semiamplitude variation K d (ms −1 )1.68 ±0.17 Planetary minimum mass M d ×sin i d (M ⊕ )13.38 ±1.35 29 The orbital inclination of the outer planet comes from astrometry, and that of the inner planet comes from the transit light curve. 9 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. “red”noise component, most likely attributable to a variable contribution of stellar jitter. One cannot always rely on a few more RV measurements to improve the error on the K amplitude. In the case of πMen c, improving the mass measurement to better than 5% would require more than 1000 RV measurements if one were to adhere to the same observing strategy and sampling of our study. This is 50% more than the number estimated based on the trend shown at the start of the measurements. Clearly, if one is only interested in deriving the mass of the transiting planet, it is more effective to obtain a large number of RV measurements for πMen over a much shorter time span, preferably over a single orbital period. Even then, a considerable number of observations will be required to find and remove additional signals due to stellar rotation or other planets that also can have a large influence on the K amplitude of the transiting planet. This is demonstrated by the ESPRESSO data. Damasso et al. (2020)found a K c -amplitude 20% higher than our value for the same data set, most likely by not including the Keplerian motion of the third planet. Considerably more RV measurements were required to be certain of the presence of the 125 day signal. It is clear that the precise mass determinations of small planets will come at a very steep price even for bright targets. Second, πMen seems to be a relatively inactive star, at least at the timescales of the transiting planet’s orbital period. It is also a bright star, which results in high-S/N data acquired in short exposure times. In spite of this, the resulting rms scatter for the RV measurements is ≈1.5 m s −1 even after removing all periodic signals. This is a factor of 2–3 larger than the measurement errors, even when using the premier instruments in the world for RV measurements. Regardless of the effort taken to minimize instrumental and photon noise, the noise floor will be set by the intrinsic variability of the star. We will be hard-pressed to find stars that are “RV quieter”than about 1ms −1 , and most stars will have an intrinsic jitter higher than this. For bright targets with high stellar jitter, telescope size will not necessarily matter. The RV confirmation of small transiting planets will require an inordinate amount of telescope resources. πMen has shown us that for bright targets with high intrinsic jitter, using a larger-aperture telescope does not always result in higher-precision measurements. PLATO is expected to produce a large number of small transiting planets, which will severely stress the available telescope resources. Instruments on 2–3 m class telescopes that provide an RV measurement precision of 3–5ms −1 can clearly play an important role in the PLATO era. The lack in measurement precision can be compensated with the shear number of measurements that can be invested on one target. A simple simulation shows that with ∼150 RV measurements over nine consecutive nights one can recover the Kamplitude of πMen c (4σresult)with a modest measurement precision of 3 m s −1 . Bringing more 2–3 m class telescopes to the upcoming PLATO follow-up effort could play an important role in the success of the mission. This work was supported by the KESPRINT collaboration, an international consortium devoted to the characterization and research of exoplanets discovered with space-based missions (www.kesprint.science). S.G., M.P., S.C., A.P.H., K.W.F.L., M.E., and H.R. acknowledge support by DFG grants PA525/ 18-1, PA525/19-1, PA525/20-1, HA 3279/12-1, and RA 714/14-1 within the DFG Schwerpunkt SPP 1992, “Exploring the Diversity of Extrasolar Planets.”L.M.S. and D.G. gratefully acknowledge financial support from the CRT foundation under grant No. 2018.2323 “Gaseous or rocky? Unveiling the nature of small worlds.”J.K. gratefully acknowledges the support of the Swedish National Space Agency (SNSA; DNR 202000104). P.G.B. acknowledges the financial support by NAWI Graz. We thank Matthias Hoeft and Alexander Drabent for use of the computer of the Tautenburg radio group for our dynamical study. Software: pyaneti (Barragán et al. 2019), DRS (Lovis & Pepe 2007), HARPS-TERRA (Anglada-Escudé & Butler 2012), Gaussfit(Jefferys et al. 1987). ORCID iDs Artie P. Hatzes https://orcid.org/0000-0002-3404-8358 Davide Gandolfihttps://orcid.org/0000-0001-8627-9628 Judith Korth https://orcid.org/0000-0002-0076-6239 Florian Rodler https://orcid.org/0000-0003-0650-5723 Silvia Sabotta https://orcid.org/0000-0001-9078-5574 Massimiliano Esposito https://orcid.org/0000-00026893-4534 Oscar Barragán https://orcid.org/0000-0003-0563-0493 Vincent Van Eylen https://orcid.org/0000-0001-5542-8870 John H. Livingston https://orcid.org/0000-0002-4881-3620 Luisa Maria Serrano https://orcid.org/0000-00019211-3691 Rafael Luque https://orcid.org/0000-0002-4671-2957 Seth Redfield https://orcid.org/0000-0003-3786-3486 Carina M. Persson https://orcid.org/0000-0003-1257-5146 Enric Palle https://orcid.org/0000-0003-0987-1593 Grzegorz Nowak https://orcid.org/0000-0002-7031-7754 Norio Narita https://orcid.org/0000-0001-8511-2981 Savita Mathur https://orcid.org/0000-0002-0129-0316 Petr Kabáth https://orcid.org/0000-0002-1623-5352 Marshall C. Johnson https://orcid.org/0000-00025099-8185 Sascha Grziwa https://orcid.org/0000-0003-3370-4058 Malcolm Fridlund https://orcid.org/0000-0003-2180-9936 Michael Endl https://orcid.org/0000-0002-7714-6310 Hans J. Deeg https://orcid.org/0000-0003-0047-4241 Szilard Csizmadia https://orcid.org/0000-0001-6803-9698 William D. Cochran https://orcid.org/0000-00019662-3496 Priyanka Chaturvedi https://orcid.org/0000-00021887-1192 Ilaria Carleo https://orcid.org/0000-0002-0810-3747 Juan Cabrera https://orcid.org/0000-0001-6653-5487 Paul G. Beck https://orcid.org/0000-0003-4745-2242 Simon Albrecht https://orcid.org/0000-0003-1762-8235 References Anglada-Escudé, G., & Butler, R. P. 2012, ApJS,200, 15 Baliunas, S. L., Donahue, R. A., Soon, W. H., et al. 1995, ApJ,438, 269 Bardalez Gagliuffi, D. C., Faherty, J. K., Li, Y., et al. 2021, ApJL,922, L43 Barragán, O., Gandolfi, D., & Antoniciello, G. 2019, MNRAS,482, 1017 Butler, R. P., Wright, J. T., Marcy, G. W., et al. 2006, ApJ,646, 505 Damasso, M., Sozzetti, A., Lovis, C., et al. 2020, A&A,642, A31 De Rosa, R. J., Dawson, R., & Nielsen, E. L. 2020, A&A,640, A73 Fulton, B. J., & Petigura, E. A. 2018, AJ,156, 264 Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ,154, 109 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2018, A&A,616, A1 16 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al. Gandolfi, D., Barragán, O., Livingston, J. H., et al. 2018, A&A,619, L10 García Muñoz, A., Fossati, L., Youngblood, A., et al. 2021, ApJL,907, L36 García Muñoz, A., Youngblood, A., Fossati, L., et al. 2020, ApJL,888, L21 Ginzburg, S., Schlichting, H. E., & Sari, R. 2018, MNRAS,476, 759 Gray, D. F., & Hatzes, A. P. 1997, ApJ,490, 412 Gupta, A., & Schlichting, H. E. 2019, MNRAS,487, 24 Hatzes, A. P. 2016, A&A,585, A144 Hatzes, A. P., Cochran, W. D., & Bakker, E. J. 1998, Natur,391, 154 Hatzes, A. P., Cochran, W. D., Endl, M., et al. 2015, A&A,580, A31 Hatzes, A. P., Cochran, W. D., McArthur, B., et al. 2000, ApJL,544, L145 Hatzes, A. P., Dvorak, R., Wuchterl, G., et al. 2010, A&A,520, A93 Huang, C. X., Burt, J., Vanderburg, A., et al. 2018, ApJL,868, L39 Huber, D., White, T. R., Metcalfe, T. S., et al. 2022, AJ,163, 79 Jefferys, W. H., Fitzpatrick, M. J., & McArthur, B. E. 1987, CeMec,41, 39 Jones, H. R. A., Paul Butler, R., Tinney, C. G., et al. 2002, MNRAS,333, 871 Kuschnig, R., Weiss, W. W., Gruber, R., Bely, P. Y., & Jenkner, H. 1997, A&A, 328, 544 Lo Curto, G., Pepe, F., Avila, G., et al. 2015, Msngr, 162, 9 Lopez, E. D., & Fortney, J. J. 2014, ApJ,792, 1 Lovis, C., & Pepe, F. 2007, A&A,468, 1115 Mawet, D., Hirsch, L., Lee, E. J., et al. 2019, AJ,157, 33 Mayor, M., Pepe, F., Queloz, D., et al. 2003, Msngr, 114, 20 McArthur, B. E., Benedict, G. F., Barnes, R., et al. 2010, ApJ,715, 1203 Mermilliod, J.-C. 1987, A&AS, 71, 413 Mills, S. M., & Fabrycky, D. C. 2017, AJ,153, 45 Mortier, A., & Collier Cameron, A. 2017, A&A,601, A110 Murdoch, K. A., Hearnshaw, J. B., & Clark, M. 1993, ApJ,413, 349 Nielsen, L. D., Gandolfi, D., Armstrong, D. J., et al. 2020, MNRAS,492, 5399 Owen, J. E., & Wu, Y. 2017, ApJ,847, 29 Pepe, F., Mayor, M., Rupprecht, G., et al. 2002, Msngr, 110, 9 Pepe, F., Molaro, P., Cristiani, S., et al. 2014, AN,335, 8 Rauer, H., Catala, C., Aerts, C., et al. 2014, ExA,38, 249 Reichert, K., Reffert, S., Stock, S., Trifonov, T., & Quirrenbach, A. 2019, A&A,625, A22 Rein, H., & Liu, S. F. 2012, A&A,537, A128 Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, Proc. SPIE,9143, 914320 Robertson, P., Mahadevan, S., Endl, M., & Roy, A. 2014, Sci,345, 440 Scargle, J. D. 1982, ApJ,263, 835 Schmitt, J. H. M. M., & Mittag, M. 2017, A&A,600, A120 Trifonov, T., Kürster, M., Zechmeister, M., et al. 2018, A&A,609, A117 Van Eylen, V., Agentoft, C., Lundkvist, M. S., et al. 2018, MNRAS,479, 4786 Xuan, J. W., & Wyatt, M. C. 2020, MNRAS,497, 2096 Zechmeister, M., & Kürster, M. 2009, A&A,496, 577 Zechmeister, M., Reiners, A., Amado, P. J., et al. 2018, A&A,609, A12 Zeng, L., Sasselov, D. D., & Jacobsen, S. B. 2016, ApJ,819, 127 17 The Astronomical Journal, 163:223 (17pp), 2022 May Hatzes et al.