Observational Signatures of Accretion Disks around a Schwarzschild Black Hole in a Hernquist Dark Matter Halo

Abstract

We investigate how a Hernquist type dark matter (DM) halo, parametrized by its core radius $r_{s}$ and central density $ρ_{s}$, influences both the gravitational wave (GW) emission from timelike periodic orbits and the electromagnetic appearance of a thin accretion disk around a Schwarzschild black hole (BH). By analyzing the effective potential for timelike geodesics, we show that the DM halo shifts the marginally bound orbit (MBO) and the innermost stable circular orbit (ISCO) outward, reflecting its modification of the spacetime geometry and the energy-angular momentum structure of particle motion. Employing a semi-analytical method, we compute orbital trajectories and the associated GW waveforms, revealing that the DM halo alters the characteristic zoom-whirl dynamics and induces measurable changes in waveform morphology. Furthermore, we generate direct and secondary images of the accretion disk across various observer inclinations and find that increasing $r_{s}$ or $ρ_{s}$ results in cooler, dimmer disks with modified flux distributions. Our results demonstrate that the presence of a DM halo imprints distinct signatures in both gravitational and electromagnetic observables, offering a multimessenger pathway to probe DM environments near BHs.

Figures (5)

• Figure 1: The effective potential $V_{\mathrm{eff}}$ for different values of the Hernquist halo parameter and angular momentum $L$. Left: $r_{\mathrm{s}}=0.2$, $L=3.8$; Middle: $\rho_{\mathrm{s}}=0.4$, $L=3.8$; Right: $r_{\mathrm{s}}=0.3$, $\rho_{\mathrm{s}}=0.4$.
• Figure 2: Left: The radius of the marginally bound orbit ($r_{\mathrm{MBO}}$) as a function of the dark matter halo core radius $r_{\mathrm{s}}$ for several values of the central density $\rho_{\mathrm{s}}$. Right: The corresponding angular momentum ($L_{\mathrm{MBO}}$) versus $r_{\mathrm{s}}$, with the same set of $\rho_{\mathrm{s}}$ values.
• Figure 3: The ISCO radius $r_{\mathrm{ISCO}}$, the angular momentum $L_{\mathrm{ISCO}}$, and the energy $E_{\mathrm{ISCO}}$ as functions of the Hernquist halo scale radius $r_{\mathrm{s}}$, for different values of the central density $\rho_{\mathrm{s}}$.
• Figure 4: The allowed parameter space of the energy and the orbital angular momentum for the bound orbits around the Schwarzschild BH embedded in a Hernquist dark matter halo with different values of the parameters. Left: $r_{\mathrm{s}}=0.2$; Right: $\rho_{\mathrm{s}}=0.4$.
• Figure 5: Top panel: The dependence of the rational number $q$ on the energy $E$ for periodic orbits around a Schwarzschild black hole embedded in a Hernquist dark matter halo. The left panel shows the results for varying central density $\rho_{\mathrm{s}}$ (with fixed scale radius $r_{\mathrm{s}} = 0.2$), while the right panel displays the dependence on the scale radius $r_{\mathrm{s}}$ (with fixed central density $\rho_{\mathrm{s}} = 0.4$). In both cases, the orbital angular momentum is set to $L = \frac{1}{2}(L_{\rm MBO} + L_{\rm ISCO})$. Bottom panel: The rational number $q$ as a function of the orbital angular momentum $L$, with particle energy fixed as $E = 0.96$. Different curves correspond to distinct combinations of the halo parameters $\rho_{\mathrm{s}}$ and $r_{\mathrm{s}}$.