Cross-checking SMBH mass estimates in NGC 6958 – I. Stellar dynamics from adaptive optics-assisted MUSE observations

Abstract

Supermassive black hole masses (MBH) can dynamically be estimated with various methods and using different kinematic tracers. Different methods have only been cross-checked for a small number of galaxies and often show discrepancies. To understand these discrepancies, detailed cross-comparisons of additional galaxies are needed. We present the first part of our cross-comparison between stellar- and gas-based MBH estimates in the nearby fast-rotating early-type galaxy NGC 6958. The measurements presented here are based on ground-layer adaptive optics-assisted Multi-Unit Spectroscopic Explorer (MUSE) science verification data at around 0${^{\prime\prime}_{.}}$6 spatial resolution. The spatial resolution is a key ingredient for the measurement and we provide a Gaussian parametrisation of the adaptive optics-assisted point spread function (PSF) for various wavelengths. From the MUSE data, we extracted the stellar kinematics and constructed dynamical models. Using an axisymmetric Schwarzschild technique, we measured an MBH of $(3.6^{+2.7}_{-2.4}) \times 10^8\,$M⊙ at 3σ significance taking kinematical and dynamical systematics (e.g. radially-varying mass-to-light ratio) into account. We also added a dark halo, but our data does not allow to constrain the dark matter fraction. Adding dark matter with an abundance matching prior results in a 25 per cent more massive black hole. Jeans anisotropic models return MBH of $(4.6^{+2.5}_{-2.7}) \times 10^8\, \mathrm{M}_{\odot }$ and $(8.6^{+0.8}_{-0.8}) \times 10^8\, \mathrm{M}_{\odot }$ at 3σ confidence for spherical and cylindrical alignment of the velocity ellipsoid, respectively. In a follow-up study, we will compare the stellar-based MBH with those from cold and warm gas tracers, which will provide additional constraints for the MBH for NGC 6958, and insights into assumptions that lead to potential systematic uncertainty.

Testing the robustness of DYNAMITE triaxial Schwarzschild modelling: The effects of correcting the orbit mirroring

“…Our investigation suggests that this inconsistency is not driven by the incorrect mirroring bug, but by other systematics, e.g. radially varying versus constant mass-to-light ratio (Thater et al 2017(Thater et al , 2019(Thater et al , 2022, the inclusion of dark matter into the models (Gebhardt & Thomas 2009;Rusli et al 2013;Thater et al 2022) or other assumptions of the modelling techniques. Furthermore, the incorrect mirroring bug is not present in the Leiden version of the axisymmetric Schwarzschild code that was used to derive several black hole mass measurements (e.g., Krajnović et al 2009Krajnović et al , 2018Thater et al 2017, and the axisymmetric measurement in den Brok et al 2021 .…”

“…In the past two decades, the Schwarzschild method has been applied to multiple galaxies, initially in axisymmetric geometry and more recently also in triaxial geometry, to study their internal stellar structure (e.g., Thomas et al 2007;Cappellari et al 2007;van de Ven et al 2008;Feldmeier-Krause et al 2017;Poci et al 2019;Jin et al 2020;Santucci et al 2022;Pilawa et al 2022), to determine their dark matter (DM) content (e.g., Thomas et al 2007;Cappellari et al 2013;Poci et al 2016;Santucci et al 2022), to weigh their central massive black holes (e.g., van der Marel et al 1998;Verolme et al 2002;Gebhardt et al 2003;Valluri et al 2004;Gebhardt & Thomas 2009;Krajnović et al 2009;Walsh et al 2012;Rusli et al 2013;Thater et al 2017;Krajnović et al 2018;Ahn et al 2018;Thater et al 2019;Mehrgan et al 2019;Liepold et al 2020;den Brok et al 2021;Roberts et al 2021;Thater et al 2022;Pilawa et al 2022) and to identify accreted galactic components (e.g., Zhu et al 2020;Poci et al 2021;Zhu et al 2022). Independent implementations of the triaxial Schwarzschild method include van den Bosch et al (2008), Vasiliev & Valluri (2020) and Neureiter et al (2021).…”

On the robustness of triaxial Schwarzschild modelling: The effects of correcting the orbit mirroring

“…Our investigation suggests that this inconsistency is not driven by the incorrect mirroring bug, but by other systematics, e.g. radially varying versus constant mass-to-light ratio (Thater et al 2017(Thater et al , 2019(Thater et al , 2022, the inclusion of dark matter into the models (Gebhardt & Thomas 2009;Rusli et al 2013;Thater et al 2022) or other assumptions of the modelling techniques. In the following three rows, the left panels are for models with incorrect mirroring, the right panels are for models with correct mirroring.…”

“…In the past two decades, the Schwarzschild method has been applied to multiple galaxies, initially in axisymmetric geometry and more recently also in triaxial geometry, to study their internal stellar structure (e.g., Thomas et al 2007;Cappellari et al 2007;van de Ven et al 2008;Feldmeier-Krause et al 2017;Poci et al 2019;Jin et al 2020;Santucci et al 2022;Pilawa et al 2022), to determine their dark matter (DM) content (e.g., Thomas et al 2007;Cappellari et al 2012;Poci et al 2016;Santucci et al 2022), to weigh their central massive black holes (e.g., van der Marel et al 1998;Verolme et al 2002;Gebhardt et al 2003;Valluri et al 2004;Gebhardt & Thomas 2009;Krajnović et al 2009;Walsh et al 2012;Rusli et al 2013;Thater et al 2017;Krajnović et al 2018;Ahn et al 2018;Thater et al 2019;Liepold et al 2020;den Brok et al 2021;Roberts et al 2021;Thater et al 2022;Pilawa et al 2022) and to identify accreted galactic components (e.g., Zhu et al 2020;Poci et al 2021;Zhu et al 2022). Independent implementations of the triaxial Schwarzschild method include van den Bosch et al (2008), Vasiliev & Valluri (2020 and Neureiter et al (2021).…”

Orbit-superposition Dynamical Modeling of Barred Galaxies

“…Constraining the Schwarzschild models to fit photometric and kinematic observational data was started by Pfenniger (1984) and Richstone & Tremaine (1984, 1985. Currently, there are several commonly used implementations of the Schwarzschild's orbit-superposition method in different geometries, including those for spherical systems (Richstone & Tremaine 1985;Breddels et al 2013;Kowalczyk et al 2017), axisymmetric systems (Cretton et al 1999;Gebhardt et al 2000;Valluri et al 2004;Cappellari et al 2006;Thomas et al 2007;Saglia et al 2016;Thater et al 2019;2022a), and triaxial systems (van den Bosch et al 2008;Jin et al 2019;Neureiter et al 2021). In particular, the van den Bosch et al (2008) triaxial orbitsuperposition code (hereafter VdB08) has been widely used in measuring the central supermassive BH mass (e.g., van den Bosch & de Zeeuw 2010; Walsh et al 2012;Seth et al 2014;Walsh et al 2015;Feldmeier-Krause et al 2017;Ahn et al 2018;Quenneville et al 2022), probing the underlying luminous and dark mass distribution and stellar orbit distribution for large sample of galaxies across the Hubble types from CALIFA (Zhu et al 2018), MaNGA (Jin et al 2020), and SAMI (Santucci et al 2022), and studying formation history of galaxies by tagging orbits with stellar population properties (Poci et al 2019;Zhu et al 2020;Poci et al 2021;Zhu et al 2022).…”