An analytical phase-space model for tidal caustics

TL;DR

This paper introduces an analytical phase-space model for tidal shells around galaxies, enabling the estimation of gravitational forces and mass distribution from observational data, under simplifying assumptions.

Contribution

The authors develop a simple analytical model for tidal shells that links observable features to the host galaxy's gravitational potential, improving mass estimation methods.

Findings

The model accurately describes shell density and phase-space distribution.

Shell appearance on the sky suffices to validate model assumptions.

Combining images with velocity data constrains the gravitational force.

Abstract

The class of tidal features around galaxies known variously as "shells" or "umbrellas" comprises debris that has arisen from high-mass-ratio mergers with low impact parameter; the nearly radial orbits of the debris give rise to a unique morphology, a universal density profile, and a tight correlation between positions and velocities of the material. As such they are accessible to analytical treatment, and can provide a relatively clean system for probing the gravitational potential of the host galaxy. In this work we present a simple analytical model that describes the density profile, phase-space distribution, and geometry of a shell, and whose parameters are directly related to physical characteristics of the interacting galaxies. The model makes three assumptions: that their orbit is radial, that the potential of the host is spherical at the shell radii, and that the satellite galaxy had a Maxwellian velocity distribution. We quantify the error introduced by the first two assumptions and show that selecting shells by their appearance on the sky is a sufficient basis to assume that these simplifications are valid. We further demonstrate that (1) given only an image of a shell, the radial gravitational force at the shell edge and the phase-space density of the satellite are jointly constrained, (2) that combining the image with measurements of either point line-of-sight velocities or integrated spectra will yield an independent estimate of the gravitational force at a shell, and (3) that an independent measurement of this force is obtained for each shell observed around a given galaxy, potentially enabling a determination of the galactic mass distribution.