Accuracy and precision of triaxial orbit models – II. Viewing angles, shape, and orbital structure

Abstract

We explore the potential of our novel triaxial modeling machinery in recovering the viewing angles, the shape and the orbit distribution of galaxies by using a high-resolution N-body merger simulation. Our modelling technique includes several recent advancements. (i) Our new triaxial deprojection algorithm SHAPE3D is able to significantly shrink the range of possible orientations of a triaxial galaxy and therefore to constrain its shape relying only on photometric information. It also allows to probe degeneracies, i.e. to recover different deprojections at the same assumed orientation. With this method we can constrain the intrinsic shape of the N-body simulation, i.e. the axis ratios p = b/a and q = c/a, with Δp and Δq ≲ 0.1 using only photometric information. The typical accuracy of the viewing angles reconstruction is 15-20○. (ii) Our new triaxial Schwarzschild code SMART exploits the full kinematic information contained in the entire non-parametric line-of-sight velocity distributions (LOSVDs) along with a 5D orbital sampling in phase space. (iii) We use a new generalised information criterion AICp to optimise the smoothing and to select the best-fit model, avoiding potential biases in purely χ2-based approaches. With our deprojected densities, we recover the correct orbital structure and anisotropy parameter β with Δβ≲ 0.1. These results are valid regardless of the tested orientation of the simulation and suggest that even despite the known intrinsic photometric and kinematic degeneracies the above described advanced methods make it possible to recover the shape and the orbital structure of triaxial bodies with unprecedented accuracy.

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.…”

“…This simulation of an ETG major merger includes two equal-mass SMBHs with a total black hole mass of 1.7 × 10 10 M e , and the two progenitor galaxies are set up by using a spherically symmetric Dehnen density potential (Dehnen 1993) with an initial inner stellar density slope of ρ ∝ r −3/2 . In a series of recent papers (Neureiter et al 2021(Neureiter et al , 2023de Nicola et al 2022a) we have modeled this simulation in great detail in order to test our triaxial modeling code. This N-body simulation was designed to explain another core galaxy (NGC 1600), which is only slightly different from NGC 5419 in terms of its stellar mass and black hole mass.…”

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).…”

“…Various dynamical modeling methods have been developed, based on velocity moments or on orbits, or even on particles (Schwarzschild 1979;Syer & Tremaine 1996;Gebhardt et al 2000;Siopis & Kandrup 2000;Thomas et al 2004;de Lorenzi et al 2007;Cappellari 2008;van den Bosch et al 2008;Napolitano et al 2011;Rusli et al 2013a;Thomas et al 2014;Mehrgan et al 2019;Cappellari 2020;Jethwa et al 2020;Vasiliev & Valluri 2020;Quenneville et al 2021Quenneville et al , 2022. The widely used Schwarzschild orbit superposition method in particular has recently seen several important advancements (de Nicola et al 2020;Liepold et al 2020;Lipka & Thomas 2021;Neureiter et al 2021;Thomas & Lipka 2022;de Nicola et al 2022;Neureither et al 2023).…”

“…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).…”