How dark matter changes the appearance of rotating black holes: from shadow to photon ring ✦
Using backward ray tracing, the optical appearance of rotating black holes surrounded by dark matter was investigated. Two spacetime metrics were compared: one for the Einasto (regular) profile and one for the cored NFW profile; the Kerr metric served as a reference. The event horizon, shadow, gravitational lensing, and synthetic images from a semi-analytical accretion model were analyzed. Diagnostic criteria were introduced: comparison of images and visibility curves, including matching with data for M87* and Sgr A*. For the Einasto model, deviations from the Kerr case are minimal. In contrast, cored NFW leads to significant brightness redistribution: centroid shift of the image, ring asymmetry, increased radius, and altered visibility amplitude. The detected systematic effects are degenerate with spin and inclination—these factors can mimic each other. This result is important for future radiation transfer simulations in such environments.
Context
Observations of central objects in galaxies, such as M87* and Sgr A*, have shown that the visible image of a black hole is shaped not only by the event horizon but also by plasma motion in the accretion disk and gravitational lensing in the strong field. Although dark matter dominates galaxy masses, its direct influence near the horizon has traditionally been considered negligible. However, theoretical models allow constructing metrics of black holes immersed in realistic dark matter density profiles, opening the possibility of searching for its signatures on event horizon scales.
Methods
To construct images, adaptive ray tracing was used in reverse: photons were emitted from the observer's point, and their trajectories were computed in the given spacetime until they intersected the equatorial plane or were captured by the horizon. Geometries of rotating black holes were built as effective extensions of static solutions with Einasto and cored-NFW profiles. For each model, the shadow boundary, lensing bands, transfer maps, and synthetic images were computed based on a semi-analytical optically thin disk model. This approach allows a direct comparison of the role of spacetime curvature without the complexities of full magnetohydrodynamics.
Results
At moderate parameters (spin χ=0.95, inclination 70°), the Einasto model is virtually indistinguishable from Kerr: effective image diameter, centroid shift, and asymmetry agree within fractions of a percent. Meanwhile, cored-NFW shows noticeable differences: the centroid shifts by 5.13M versus 3.65M for Kerr, left-right asymmetry increases from 0.19 to 0.32, and the peak of the radial brightness profile shifts outward from 6.64M to 10.78M. When converted to angular scales using the masses and distances to M87* and Sgr A*, the characteristic angular size of the bright ring for cored-NFW (40.96 μas for M87* and 51.74 μas for Sgr A*) turns out to be close to the EHT reference values (42±3 and 51.8±2.3 μas, respectively), whereas Kerr and Einasto give smaller values (~25.2 and 31.9 μas). These numbers are not a fit to the data, but show that the environment's influence can be significant on observational scales.
Implications
The main conclusion is the existence of a degeneracy between dark matter parameters, spin, and orbital inclination. Changes in the distribution of the dark halo can mimic effects traditionally attributed to black hole spin or accretion flow geometry. This raises the question of how unambiguously current methods can separate the contributions of the central object and its environment. For future tests of gravity theories and dark matter models, accounting for such systematic uncertainties is critical, which is especially relevant in the context of data from active galactic nuclei.
Future development
In the future, it is planned to replace the semi-analytical emission model with full-fledged transport calculations within general relativity including magnetic fields (GRRMHD), as well as to incorporate polarization and scattering effects for Sgr A*. Joint analysis of metric parameters and the dark matter profile using Monte Carlo methods on realistic EHT data will either constrain the properties of dark matter or set upper limits on its influence at horizon scales. Galactic centers are becoming a natural laboratory for testing fundamental physics.
Impact
The results impact several areas: interpretation of black hole images in strong gravitational fields, indirect searches for dark matter via gravitational signatures, and tests of general relativity under conditions where environmental effects become substantial.
Next steps
The next steps include implementing full radiation transport with magnetohydrodynamics of the accretion flow and adapting the method for analyzing polarimetric EHT data, which will allow direct comparison of models with observations of redshift and Doppler boosting.
Key open problems
This work is directly connected to the unsolved problem of the nature of dark matter and testing the hypothesis that it may consist of unknown particles that form characteristic density profiles around supermassive black holes. Furthermore, it touches on the fundamental question of the uniqueness of the Kerr solution for astrophysical black holes and the need to go beyond the standard model in strong gravitational fields.
🎯 Although dark matter makes up about 85% of all galaxy mass, its direct gravitational influence on the scales of a black hole horizon billions of times more massive than the Sun is only a small fraction. Nevertheless, as simulations show, this is enough to change the apparent size of the bright ring by tens of percent.
Key numbers
- Centroid shift (Kerr): 3.65 M
- Centroid shift (cored-NFW): 5.13 M
- Peak diameter (Kerr): 6.644 M
- Peak diameter (cored-NFW): 10.779 M
- Peak angular scale (M87*) for cored-NFW: 40.96 μas