# Reconstructing the velocity dispersion profiles from the line-of-sight kinematic data in disc galaxies

## TL;DR

This paper introduces a new method for reconstructing stellar velocity ellipsoids in disc galaxies without parametrizing dispersion profiles, relying only on the assumption of a constant ratio of vertical to radial velocity dispersions, and demonstrates its application to multiple galaxy types.

## Contribution

The authors develop a novel, less assumption-dependent method for SVE reconstruction and successfully apply it to several galaxies, including lenticular and Sab types, expanding the applicability of kinematic analysis.

## Key findings

- Successful SVE reconstruction for intermediate inclination galaxies.
- Determined variable $\sigma_z/\sigma_R$ ratios in NGC 1167.
- Provided constraints on $\sigma_R$ using asymmetric drift equation.

## Abstract

We present a modification of the method for reconstructing the stellar velocity ellipsoid (SVE) in disc galaxies. Our version does not need any parametrization of the velocity dispersion profiles and uses only one assumption that the ratio $\sigma_z/\sigma_R$ remains constant along the profile or along several pieces of the profile. The method was tested on two galaxies from the sample of other authors and for the first time was applied to three lenticular galaxies NGC~1167, NGC~3245 and NGC~4150 as well as to one Sab galaxy NGC~338. We found that for galaxies with a high inclination ($i >55-60^\circ$) it is difficult or rather impossible to extract the information about SVE while for galaxies at an intermediate inclination the procedure of extracting is successful. For NGC~1167 we managed to reconstruct SVE, provided that the value of $\sigma_z/\sigma_R$ is piecewise constant. We found $\sigma_z/\sigma_R=0.7$ for the inner parts of the disc and $\sigma_z/\sigma_R=0.3$ for the outskirts. We also obtained a rigid constrain on the value of the radial velocity dispersion $\sigma_R$ for highly inclined galaxies and tested the result using the asymmetric drift equation, provided that the gas rotation curve is available.