SMART: A new implementation of Schwarzschild’s Orbit Superposition technique for triaxial galaxies and its application to an N-body merger simulation

Abstract

We present SMART, a new 3D implementation of the Schwarzschild Method and its application to a triaxial N-body merger simulation. SMART fits full line-of-sight velocity distributions (LOSVDs) to determine the viewing angles, black hole, stellar and dark matter (DM) masses and the stellar orbit distribution of galaxies. Our model uses a 5D orbital starting space to ensure a representative set of stellar trajectories adaptable to the integrals-of-motion space and it is designed to deal with non-parametric stellar and DM densities. SMART’s efficiency is demonstrated by application to a realistic N-body merger simulation including supermassive black holes which we model from five different projections. When providing the true viewing angles, 3D stellar luminosity profile and normalized DM halo, we can (i) reproduce the intrinsic velocity moments and anisotropy profile with a precision of $\sim 1\%$ and (ii) recover the black hole mass, stellar mass-to-light ratio and DM normalization to better than a few percent accuracy. This precision is smaller than the currently discussed differences between initial-stellar-mass functions and scatter in black hole scaling relations. Further tests with toy models suggest that the recovery of the anisotropy in triaxial galaxies is almost unique when the potential is known and full LOSVDs are fitted. We show that orbit models even allow the reconstruction of full intrinsic velocity distributions, which contain more information than the classical anisotropy parameter. Surprisingly, the orbit library for the analysed N-body simulation’s gravitational potential contains orbits with net rotation around the intermediate axis that is stable over some Gyrs.

Dynamical modelling of the twisted galaxy PGC 046832

“…One caveat however is that the recovery of the light fraction in different orbits may not be fully determined by the data (see e.g. Neureiter et al 2021). In this Section we associate orbital features with stellar population parameters.…”

A novel approach to optimize the regularization and evaluation of dynamical models using a model selection framework

“…The main reasons for picking up Schwarzschild models are: (i) This technique is very general and allows to model any kind of galaxy without apriori assumptions upon the orbital structure; (ii) The method is observationally not restricted to moments of the velocity distribution of the stars but instead can deal with the full information contained in the line-of-sight velocity distributions (e.g. Thomas et al 2004;Mehrgan et al 2019;Vasiliev & Valluri 2020;Neureiter et al 2021).…”

“…Several different implementations of the Schwarzschild Method with varying degrees of symmetry have been described (e.g. Rix et al 1997;Cretton et al 1999;Siopis & Kandrup 2000;Häfner et al 2000;Gebhardt et al 2000Gebhardt et al , 2003Valluri et al 2004;Thomas et al 2004;Vasiliev & Athanassoula 2015;Vasiliev & Valluri 2020;Neureiter et al 2021), but the main steps of the method are rather general. Very briefly: If an assumed gravitational potential is given, one needs to compute tens of thousands of representative orbits in the available phase space.…”

“…For simple, linear models this would imply a negative number of degrees of freedom of the resulting 𝜒 2 distribution (Press et al 1992) and the solution of the 𝜒 2 -minimization is non-unique (cf. Valluri et al 2004;Magorrian 2006;Neureiter et al 2021). Under the assumption that a model is generally detailed enough to deal with all the structure in the data, one would consequently expect that every data set is perfectly fitted due to the models comparatively huge number of free parameters, resulting in a 𝜒 2 → 0.…”

The dynamical structure of broken power-law and double power-law models for dark matter haloes

“…In order to investigate the structure and evolution of selfgravitating systems such as galaxies, clusters, and dark matter haloes, a characterisation of their structure in full 6D phase space is of paramount importance. Thanks to the improving observational data, novel modelling techniques, and increasing computational power, we now have various advanced dynamical modelling tools at our disposal (e.g., Bovy 2015;Vasiliev 2019;Vasiliev & Valluri 2020;Neureiter et al 2021). Nevertheless, relatively simple spherically symmetric models remain useful and important.…”