Accuracy and precision of triaxial orbit models I: SMBH mass, stellar mass, and dark-matter halo

Abstract

We investigate the accuracy and precision of triaxial dynamical orbit models by fitting two dimensional mock observations of a realistic N-body merger simulation resembling a massive early-type galaxy with a supermassive black hole (SMBH). We show that we can reproduce the triaxial N-body merger remnant’s correct black hole mass, stellar mass-to-light ratio and total enclosed mass (inside the half-light radius) for several different tested orientations with an unprecedented accuracy of 5-10 per cent. Our dynamical models use the entire non-parametric line-of-sight velocity distribution (LOSVD) rather than parametric LOSVDs or velocity moments as constraints. Our results strongly suggest that state-of-the-art integral-field projected kinematic data contain only minor degeneracies with respect to the mass and anisotropy recovery. Moroever, this also demonstrates the strength of the Schwarzschild method in general. We achieve the proven high recovery accuracy and precision with our newly developed modeling machinery by combining several advancements: (i) our new semi-parametric deprojection code probes degeneracies and allows to constrain the viewing angles of a triaxial galaxy; (ii) our new orbit modeling code SMART uses a 5-dim orbital starting space to representatively sample in particular near-Keplerian orbits in galaxy centers; (iii) we use a generalised information criterion AICp to optimise the smoothing and to compare different mass models to avoid biases that occur in χ2-based models with varying model flexibilities.

The Isotropic Center of NGC 5419—A Core in Formation?

“…By taking the individual model's degrees of freedom m eff into account, bias in the evaluation of different mass models gets avoided. In Neureiter et al (2023) andde Nicola et al (2022a) we show that our triaxial models are able to recover the correct dynamical structure and mass composition of a realistic simulated ETG merger remnant with an accuracy at the 5%-10% level. SMART uses the density output from SHAPE3D to compute the corresponding stellar part of the gravitational potential by expansion into spherical harmonics.…”

Detailed Shapes of the Line-of-sight Velocity Distributions in Massive Early-type Galaxies from Nonparametric Spectral Models

“…Typically, the fit to the spectrum will remain very similar for most setups, but the recovered LOSVD, particularly at large projected velocities, may differ. While for many purposes the detailed shapes of the high-velocity tails of galaxy LOSVDs may not be important, they certainly are for accurate and precise dynamical modeling (de Nicola et al 2022;Neureiter et al 2023).…”

“…The ETGs are part of a larger sample of galaxies that have been previously analyzed for their photometric, kinematic, and dynamical properties using different instruments in previous publications (Rusli et al 2011(Rusli et al , 2013a(Rusli et al , 2013bThomas et al 2014;Mazzalay et al 2016;Erwin et al 2018). In subsequent publications, we will use the nonparametric LOSVDs from the present study to construct new Schwarzschild orbital dynamical models with stellar mass-to-light ratio gradients in order to investigate the IMF (including possible radial gradients) and the details of stellar orbital system and DM halos, including their triaxiality (K. Mehrgan et al 2023, in preparation;Neureiter et al 2023;Parikh et al 2023;J. Thomas et al 2023, in preparation).…”

“…For example, one of the most important methods, the Fourier correlation quotient (FCQ) method (Bender 1990), produces in principle nonparametric LOSVDs, and other codes for nonparametric LOSVD reconstructions have been developed as well (Gebhardt et al 2002;Pinkney et al 2003;Houghton et al 2006;Fabricius et al 2014;Falcón-Barroso & Martig 2021). Detailed knowledge about the LOSVD shapes is currently of particular importance because recent developments in Schwarzschild dynamical modeling have shown that a surprisingly high level of accuracy and precision can be reached given adequate kinematic data (Lipka & Thomas 2021;Neureiter et al 2021Neureiter et al , 2023de Nicola et al 2022). Pushing the limits of the kinematic information that we can extract from galactic spectra is therefore important to achieve mass measurements with a precision necessary, for example, to unlock the stellar initial mass function (IMF) of ETGs and to understand its seeming variation between ETGs (and probably also within individual galaxies), which is one of the most important missing puzzle pieces of galaxy formation (e.g., Rusli et al 2011;Spiniello et al 2011;Cappellari et al 2012;Parikh et al 2018).…”

The Fornax3D project: Environmental effects on the assembly of dynamically cold disks in Fornax cluster galaxies

“…There are a few methods widely used for modelling the IFU kinematic data of external galaxies, including the Jeans-Anisotripic-MGE (JAM) models (e.g., Cappellari 2008;Li et al 2017) , the particle-based Made-to-Measure (M2M) models (e.g., Syer & Tremaine 1996;de Lorenzi et al 2007;Long & Mao 2010Zhu et al 2014), and the orbit-superposition Schwarzschild method used in this work (Schwarzschild 1979). The Schwarzschild's orbit superposition method can be used in different geometries such as the spherical systems (Richstone & Tremaine 1985;Breddels et al 2013;Kowalczyk et al 2017), axisymmetric systems (Cretton & van den Bosch 1999;Gebhardt et al 2000;Valluri et al 2004;Cappellari et al 2006a;Thomas et al 2007;Saglia et al 2016), andtriaxial systems (van den Bosch et al 2008;Neureiter et al 2021). The orbit-superposition model reconstructs the backbone of galaxies without ad-hoc assumptions of the underlying distribution functions, it has been widely used to uncover galaxies' underlying dark matter distributions (e.g., Cappellari et al 2006b;Yang et al 2020), central black hole mass (e.g., van der Marel et al 1998;Cretton & van den Bosch 1999;Verolme et al 2002;Gebhardt et al 2003;Valluri et al 2004;Krajnović et al 2009;Ahn et al 2018;Thater et al 2022b), and internal stellar orbit distributions (e.g., Zhu et al 2018a,b;Jin et al 2020).…”