Rotating black holes in the Hernquist galactic halo and its accretion disk luminosity

TL;DR

This work investigates rotating black holes embedded in Hernquist-type dark matter halos and their thin-disk electromagnetic signatures. It constructs rotating solutions from static Cardoso BHs using the Newman–Janis algorithm and applies the steady-state Novikov–Thorne model to predict $F(r)$, $T(r)$, and $L( u)$ for various spins $a$ and halo compactness $C$. The results show that the dark matter halo modestly affects disk observables, and for astrophysical high spins the rotating Cardoso BH remains largely indistinguishable from a Kerr black hole, limiting observational tests based on disk spectra. Consequently, disk emission is not a reliable discriminator of Kerr vs rotating Cardoso BHs in Hernquist halos at large $a$, informing interpretations of accretion signatures in DM environments.

Abstract

Static, spherically symmetric black holes immersed in a dark matter halo with a Hernquist-type density profile have been derived by Cardoso et. al. in Ref. \redcite{Cardoso:2021wlq}. Using the Newman-Janis algorithm, we construct the metric for a stationary and axially symmetric rotating black hole in this environment. Then, we obtain the electromagnetic properties of thin accretion disks around such rotating black holes by utilizing the steady-state Novikov-Thorne model, and study the effects of spin parameter and halo compactness parameter on the disk properties. Finally, by comparison the results of the rotating Cardoso black hole with that of Kerr black hole in the absence of dark matter, we find that the presence of dark matter can not significantly affect the disk properties and thus for astrophysical black holes with large spin parameter, the distinction of rotating Cardoso black holes becomes more difficult than the Kerr black hole.

Figures (4)

• Figure 1: The behavior of horizons as a function of $r$ for different values of ${\cal C}$ and rotation parameter $a=0.5M_{\rm BH}$ (left panel), and $a=0.95M_{\rm BH}$ (right panel), respectively. The solid curve corresponds to the Kerr BH without dark matter.
• Figure 2: The energy flux $F(r)$ from a disk (left panel) and the disk temperature $T(r)$ (right panel) around a rotating Cardoso BH with the mass accretion rate $\dot{M}=2\times10^{-6}M_{\odot}\rm yr^{-1}$, for different values of $M$ and $a_0$ with $a=0.5M_{\rm BH}$. In each panel the solid curve corresponds to the Kerr BH without dark matter.
• Figure 3: The emission spectrum $\nu L(\nu)$ of the accretion disk around a rotating Cardoso BH with mass accretion rate $\dot{M}\sim10^{18}\rm g$$\rm s^{-1}$ and inclination $\gamma=0^{\circ}$, for different values of $M$ and $a_0$ with $a=0.5M_{\rm BH}$. The solid curve represents the disk spectrum for the Kerr BH without dark matter.
• Figure 4: The behavior of the ISCO radius as a function of the spin parameter in rotating Cardoso BH with $M=10 M_{BH}$ and $a_0=100 M_{BH}$ and in the Kerr BH for co-rotating orbits.