An Analytic Scale-dependent Dark Matter Profile and the Baryonic Tully-Fisher Relation

TL;DR

This paper introduces an analytic, scale-dependent dark matter model with self-interactions that successfully fits rotation curves of many low-mass galaxies and reproduces the baryonic Tully-Fisher relation, addressing challenges faced by cold dark matter models.

Contribution

The paper presents a novel analytic dark matter profile with scale-dependent properties that can fit a wide range of galaxy rotation curves and reproduce the baryonic Tully-Fisher relation.

Findings

Successfully models rotation curves of 116 out of 175 galaxies.

Reproduces the baryonic Tully-Fisher relation with a power-law index close to 4.

Fails to reproduce the canonical Tully-Fisher relation.

Abstract

In this work we use the recently introduced concept of self-interacting dark matter with scale-dependent equation of state, and we provide an analytic model of dark matter that can produce viable rotation curves even for low-surface-brightness galaxies, irregular galaxies, low-luminosity spirals and dwarf galaxies, all known to challenge the cold dark matter description. The radius dependent effective equation of state of the self-interacting dark matter model we shall introduce is assumed to be an isothermal equation of state of the form $P(r)=K(r)\left(\frac{\rho(r)}{\rho_{\star}}\right)$, where the energy density will have the form $\rho(r)=\frac{\rho_0}{\left( 1+\frac{r^2}{\alpha^2}\right)^{5/2}}$, while the entropy function $K(r)$ is $K(r)=\frac{K_0}{\left( 1+\frac{r^2}{\alpha^2}\right)^{1/2}}$. The resulting model is confronted in detail with the SPARC galaxy data and 175 galaxies are used and tested. It proves that the analytic model can successfully produce the rotation curves of 116 galaxies, most of which are small mass spirals, irregular galaxies, low-surface-brightness and low-luminosity spirals and dwarf galaxies. On the other hand, 59 galaxies cannot be successfully described by our analytic model. We tested statistically the correlation between the parameter $K_0$ of the entropy function corresponding to the viable galaxies, and the flat rotation velocity $V_{flat}$ and the maximum rotation velocity $V_{max}$ of the galaxies from the SPARC data. We also examined the baryon mass $M_b$-$K_0$ relation and the luminosity $L$-$K_0$ relation. We have been able to produce the baryonic Tully-Fisher relation for the viable galaxies, directly from the correlation $K_0$-$M_b$ and $K_0$-$V_{flat}$, with the resulting relation being $M_b\sim V_{flat}^{4.026 \pm 0.371}$, however we failed to produce the canonical Tully-Fisher relation.