Disentangling gammabeta: the 4thorder velocity moments based on spherical Jeans analysis
Abstract
Distinguishing a core and a cusp within dark matter halos is complexified by the existence of massanisotropy degeneracy, where various combinations of velocity anisotropy ($\beta$) and inner density slope ($\gamma$) yield similar observational signatures. We construct a dynamical model that incorporates the 4thorder velocity moments to alleviate this challenge. The inclusion of the 4thorder velocity moments enables stars' lineofsight velocity distribution (LOSVD) to be flexible. This flexible LOSVD can cover from a thintailed to a heavytailed distribution that is inaccessible if only the 2ndorder moments are considered. We test our dynamical model using mock galaxies and find that a ratio of the global lineofsight velocity dispersion of the mock galaxy to the velocity error measurement $\sigma_{\mathrm{los,global}} / \Delta v_{\mathrm{los}} \gtrsim 4$ is required to avoid obtaining systematically biased results. This bias arises from the strong dependency of the 4thorder moments on the LOSVD tails, and not even increasing the sample size to $10^4$ stars can mitigate this effect. In that velocity ratio, $\beta$ is recovered within $\sim 1 \sigma$ even when the sample size is only 500 stars, regardless of the recovery of the other parameters. However, the estimation of $\gamma$ varies, depending on the degree to which LOSVDs deviate from Gaussianity. Because of the more significant change in its LOSVDs, a cored dark halo is more likely to be identified than a cusp.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.12671
 arXiv:
 arXiv:2404.12671
 Bibcode:
 2024arXiv240412671D
 Keywords:

 Astrophysics  Astrophysics of Galaxies;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 19 pages, 14 figures, submitted to ApJ