Prospects of using quasar for cosmology. LOI Code: Pol-NCB-6

Prospects of using quasar for cosmology LOI Code: Pol-NCB-6 B. Czerny, V. K. Jaiswal, A. Mandal, S. Panda, F. Pozo Nunez 1. Center for Theoretical Physics, Warsaw, Poland 2. International Gemini Observatory/NSF NOIRLab, La Serena, Chile 3.Astroinformatics, Heidelberg Institute for Theoretical Studies, Heidelberg, Germany 1. Introduction Quasars are the brightest persistent objects in the Universe, seen from large cosmological distances (redshifts up to 10). Together with their fainter cousins – Active Galactic Nuclei (AGN) – located in the local Universe they create a potentially interesting tool to study the expansion of the Universe. They show no strong trends in the metallicity despite the broad redshift range which may pose a problem for other probes. AGN are not standard candles, but they can be standardized – knowing their physical properties we can establish the distance for each individual object, if we have the required data at our disposal. A number of methods was developed to use quasars for cosmology. Some of the methods do not require extra calibrations and can be used directly to measure the Hubble constant. The currently developed methods based of that type include: ■ Strong quasar lensing [1] ■ Water maser [2] ■ Emission line time delay combined with interferometry [3] ■ Continuum time delays Contact: Bożena Czerny Center for Theoretical Physics PAN [email protected] REFERENCES [1] Birrer, S. et al., 2025, arXiv:2506.03023 [2] Barua, S., Ramakrishnan, V., Desai, S., 2025, ApSS, 370, 62 [3] Li, Y.-R. Et al., 2025, ApJ, 988, 42 [4] Hönig, S. F. et al., 2017, MNRAS, 464, 1693 [5] Watson, D. et al., 2011, ??? [6] Haas, M. et al. 2011, ??? [7] Czerny, B, et al., 2023, A&A675, A163 [8] Cao, S, et al., 2024, MNRAS 528, 6444 [9] Collier, S.J. et al., 1988, ApJ, 500, 162 [10] Cackett, E.M. et al., 2007, MNRAS, 380, 669 Two other methods (emission line time delays and UV/X-ray luminosity ratio) do not give the Hubble constant as they require calibration of the method or a combination with other methods. Dust continuum method may eventually be calibrated without external calibration, at the basis of the dust sublimation temperature [4]. LSST will bring the detection of about 10 million AGN from the Main Survey (MS) and about 4000 AGN from the Deep Drilling Field (DDF). In our work we concentrated on the prospects of using the light echo measurements of AGN. 3. Two reprocesors The reprocessing takes place both in the accretion disk and in the surrounding Broad Line Region (BLR). BLR size in turn is determined by our theory [12,13]: assumption that emission lines like Hbeta form in the wind pushed by the radiation pressure acting on dusty disk atmosphere Thus size is related to the dust sublimation temperature (1500 K) and the source luminosity. We used a 3-D structure of the region from the model, and the emitted spectrum from radiative transfer computations (not just lines, but also continuum is produced in those clouds, [14]). 4. Results for NGC 5548 We were able to model the spectrum and the details of the time delay measurements available in the literature for the object NGC 5548 [15,16]. NGC 5548 5. Prospects for continuum time delay measurement from LSST The method can be only applied to DDF, as the MS does not have the high enough cadence. We performed some tests for continuum time delay based on uniform cadence ref. [19] and for likely DDF cadence [18]. The results from uniform cadence were too optimistic but even with expected cadence there are prospects to measure the continuum time delay for sources containing the black hole mass above 2 x 108 Msun. We can estimate the fraction of AGN suitable for continuum reverberation mapping at the basis of the [17] who estimated the stellar mass in three of the DDFs. Assuming the black hole mass to stellar mass of 1%, we conclude that 84% of the black hole masses in detected quasars with be higher than the limit from [18]. Measuring the continuum time delays to 3000 objects and assuming 50% error in an individual measurement we would be able to estimate the Hubble constant with accuracy 0.9 %, if no systematic effects bias our measurements. We can also try to decrease the individual measurement error using the methodology using a combined spectral/time delay fit we tested for NGC 5548 which gave 10 % error. REFERENCES - continuation [11] Jaiswal, V.K. et al., 2025, A&A (in press), arXiv:2410.03597 [12] Czerny, B,. Hryniewicz, K., 2011, A&A, 525, L8 [13] Naddaf, M.H., Czerny, B., Szczerba, R., 2021, ApJ, 920, 30 [14] Korista, K.T., Goad, M.R., 2001, ApJ, 553, 695 [15] Mehdipour, M. et al. 2015, A&A, 575, A22 [16] Fausnaugh, M. M. et al. 2016, ApJ, 821, 56 [17] Zou, F. et al., 2022, ApJS, 262, 15 [18] Pozo Nunez, F. et al., 2024, Res. Notes AAS 8 47 [19] Pozo Nunez F.et al., 2023, MNRAS, 522, 2002 2. Continuum time delays - method This is the method which allows directly to measure the Hubble constant, without additional calibration. Determination of the Hubble constant is still under vigorous discussion since there seems to be a tension between the methods based on Early Universe measurements (Cosmic Microwave Background) and Late Universe measurements (distances in redshift from zero to 10). A number of methods were developed so far with the aim to get a Hubble constant proposed a long time ago [9,10] but it was finally successfully used by our team [11]. Current best results for H0 based on AGN: 71.6+3.9-3.3 km-1s-1Mpc-1(TDCOSMO 2025) [1] 73.9+3.0-3.0 km-1s-1Mpc-1(MCP 2025) [2] 69+12-10 km-1s-1Mpc-1(SARM 2025) [3] The method basically relies on measurement of the light echo from the variable compact source irradiating the AGN surrounding. The theory is connecting the time delay between various spectral bands with the object absolute luminosity (brighter sources are larger). The idea based on just a continuum time delay from the accretion disk was not working [9,10] since the delays were too long. But recently there were better observations covering the delays at various wavelengths and these delays showed a specific features clearly suggesting the atomic features. So our model is based on two reprocessors. Current best results H0 from our method: 66.9+10.6-2.1 km-1s-1Mpc-1(NGC 5548) [11] 2. Line emission delay expected from LSST This method was proposed for the use in cosmology by [5] and [6]. The technique required to use the line contamination to the LSST bands which depends on the chosen line and the source redshift. We performed simulations of such lag recovery for the MS and DDF field, for expected cadence [7]. The examples of the time delay recovery is illustrated below. The results even from the MS are satisfactory for bright AGN. The determination of the time delay allows for direct tests of the nonlinear part of the Universe expansion. We performed cosmological tests at the basis of the time delays currently measured in Halpha, Hbeta, Mg II and CIV lines [8[. The constraints are not strong and roughly consistent with the standard ΛCDM model since the data were not uniform, and the largest sample contained only just over 100 time delay measurements. With hugely improved statistics the constraints should be significant. Probability density