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

TL;DR

SMART is a novel 3D Schwarzschild orbit superposition method that accurately models triaxial galaxies and recovers key properties like black hole mass and dark matter content from N-body simulations.

Contribution

It introduces a new implementation of the Schwarzschild method with a 5D orbital space, capable of fitting full LOSVDs and handling non-parametric densities in triaxial galaxies.

Findings

Achieves ~1% precision in velocity moments and anisotropy profiles.

Recovers black hole and dark matter parameters within a few percent.

Reconstructs full intrinsic velocity distributions, revealing stable orbit rotations.

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 ~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.