Multi-Messenger Dark Matter Constraints from Combined Pulsar Timing and Shadow Observations

This idea creates a novel synthesis between two seemingly unrelated observational approaches. While Li et al. (2025) propose using gravitational waves from binary black holes to constrain dark matter profiles, and Röder et al. (2023) compare black hole shadows across different metrics, neither exploits the complementary nature of these constraints. We'd develop a joint analysis framework that combines SKA pulsar timing array data (sensitive to dark matter's dynamical effects) with EHT shadow measurements (sensitive to spacetime geometry). The key innovation is that certain dark matter profiles might produce subtle shadow distortions that are degenerate with other parameters, but would create unique gravitational wave signatures that break these degeneracies. This multi-messenger approach could provide unprecedented constraints on the dark matter density profile around Sgr A*, potentially distinguishing between different dark matter models that current methods cannot resolve.

References:

1. Probing the spacetime and accretion model for the Galactic Center: Comparison of Kerr and dilaton black hole shadows. J. Röder, A. Cruz-Osorio, C. Fromm, Y. Mizuno, Z. Younsi, L. Rezzolla (2023).
2. Detectability of dark matter density distribution via gravitational waves from binary black holes in the Galactic Center. Zhijin Li, Xiao Guo, Zhoujian Cao, Yun-Long Zhang (2025). Physical Review D.