# Nonaxisymmetric models of galaxy velocity maps

## TL;DR

This paper introduces a nonaxisymmetric radial ellipse model (REM) for galaxy velocity maps, highlighting degeneracies in traditional axisymmetric models and discussing implications for understanding galactic dynamics.

## Contribution

The paper proposes the REM, a nonaxisymmetric radial velocity model, and compares its effectiveness with existing models in fitting galaxy velocity data.

## Key findings

- REM fits residuals similar to RDM, capturing nonradial motions
- RTRM yields smallest residuals but cannot distinguish motion types in nonaxisymmetric systems
- Nonaxisymmetry introduces degeneracy between rotational and radial velocities

## Abstract

Galaxy velocity maps often show the typical pattern of a rotating disk, consistent with the dynamical model where emitters rotate in circular orbits around the galactic center. The simplest template used to fit these maps consists in the rotating disk model (RDM) where the amplitude of circular velocities is fixed by the observed velocity profile along the kinematic axis. A more sophisticated template is the rotating tilted-ring model (RTRM) that takes into account the presence of warps and allows a radius-dependent orientation of the kinematic axis. In both cases, axisymmetry is assumed and residuals between the observed and the model velocity fields are interpreted as noncircular motions. We show that if a galaxy is not axisymmetric, there is an intrinsic degeneracy between a rotational and a radial velocity field. We then introduce a new galaxy template, the radial ellipse model (REM), that is not axisymmetric and has a purely radial velocity field with an amplitude that is correlated with the major axis of the ellipse. We show that best fits to the observed two-dimensional velocity fields of 28 galaxies extracted from the THINGS sample with both the REM and the RDM give residuals with similar amplitudes, where the REM residuals trace nonradial motions. Best fits obtained with the RTRM, because of its larger number of free parameters, give the smallest residuals: however, we argue that this does not necessarily imply that the RTRM gives the most accurate representation of a galaxy velocity field. Instead, we show that this method is not able to disentangle between circular and radial motions for the case of nonaxisymmetric systems. Finally, we consider the physical motivation of the REM, and discuss how the interpretation of galactic dynamics changes if one assumes that the main component of a galaxy velocity field is modeled as a RDM/RTRM or as a REM.