Probing Hernquist dark matter with black hole shadows: A comprehensive study of various accretions

Abstract

The shadow of a black hole is critically dependent on the surrounding accreting matter. We investigate the observational signatures of a Schwarzschild black hole embedded in a Hernquist dark matter (DM) halo under three distinct accretion scenarios: a geometrically thin disk, a static spherical flow, and an infalling spherical flow. For the thin disk model, we find that direct emission dominates the total observed intensity, while the size and brightness of the lensing and photon rings serve as sensitive probes of the Hernquist DM parameters. Under spherical accretion, the Hernquist DM halo significantly enlarges the photon sphere. This results in an observable shadow that is approximately $2\%$ to $30\%$ larger than in the vacuum case, though this increase in size is accompanied by a considerable decrease in overall image brightness. Furthermore, the Doppler de-boosting effect in the infalling scenario produces a markedly darker image than its static counterpart. Our results demonstrate that the size and brightness profile of a black hole shadow provide a powerful observational tool to probe and constrain the distribution of dark matter in galactic centers.

Figures (12)

• Figure 1: The metric function $f(r)$ as a function of the radial coordinate $r/M$ for different Hernquist DM halo parameters. The horizontal line represents $f(r)=0$. A close-up of the area close to the event horizon is shown in the inset. In contrast to the Schwarzschild case (black line), it is clear that the zero-crossing point, which determines the event horizon radius $r_h$, spreads outward as the halo parameters $\rho_c$ and $r_s$ grow.
• Figure 2: The effective potential $V_{\text{ph}}$ as a function of the radius $r/M$ for the Schwarzschild-Hernquist black holes with varying Hernquist DM parameters. We set $M=1$ here. The peak of each curve corresponds to the photon sphere radius $r_{ph}$, which determines the critical impact parameter $b_p$. Three different physical regions of the photon trajectories are distinguished by the critical value: scattering to infinity (Region 1, $b>b_p$), critical unstable orbit (Region 2, $b=b_p$) and capture (Region 3, $b<b_p$).
• Figure 3: The behaviour of light trajectories under various $\rho_c$ and $r_s$ in the polar coordinate system $(r,\varphi)$. The solid black disk and the green dashed circle indicates the event horizon and the photon shpere, respectively. The yellow lines correspond to scattered rays $(b>b_p)$, the blue lines to captured light $(b<b_p)$ and the red one means the critical unstable orbit $(b=b_p)$.
• Figure 4: The number of orbits $n$ as a function of the impact parameter $b$ is shown for various Hernquist DM parameters $\rho_c$ and $r_s$. Based on the number of plane intersections, the horizontal lines at $n=0.75$ and $n=1.25$ indicate three different observational zones: direct emission ($n<3/4$), the lensing ring ($3/4<n<5/4$) and the photon ring ($n>5/4$). The divergence of the curves corresponds to the critical impact parameter $b_p$.
• Figure 5: Photon behaviour as a function of impact parameter $b$ in the Schwarzschild-Hernquist black hole. The blue lines represent trajectories contributing to direct emission ($n<3/4$), yellow lines constitute the lensing ring ($3/4<n<5/4$), and red lines mean the photon ring ($n>5/4$). The black disk and the green dashed circle indicates the event horizon and the photon shpere $r_p$, respectively.