Unveiling a 36 Billion Solar Mass Black Hole at the Centre of the Cosmic Horseshoe Gravitational Lens

Supermassive black holes (SMBHs) are found at the centre of every massive galaxy, with their masses tightly connected to their host galaxies through a co-evolution over cosmic time. For massive ellipticals, the SMBH mass ($M_\text{BH}$) strongly correlates with the central stellar velocity dispersion ($\sigma_e$), via the $M_\text{BH}-\sigma_e$ relation. However, SMBH mass measurements have traditionally relied on central stellar dynamics in nearby galaxies ($z < 0.1$), limiting our ability to explore the SMBHs across cosmic time. In this work, we present a self-consistent analysis combining 2D stellar dynamics and lens modelling of the Cosmic Horseshoe gravitational lens system ($z = 0.44$), one of the most massive galaxies ever observed. Using integral-field spectroscopic data from MUSE and high-resolution imaging from HST, we model the radial arc and stellar kinematics, constraining the galaxy's central mass distribution and SMBH mass. Bayesian model comparison yields a $5\sigma$ detection of an ultramassive black hole (UMBH) with $\log_{10}(M_\text{BH}/M_{\odot}) = 10.56^{+0.07}_{-0.08} \pm (0.12)^\text{sys}$, consistent across various systematic tests. Our findings place the Cosmic Horseshoe $\sim$$1.5\sigma$ above the $M_\text{BH}-\sigma_e$ relation, supporting an emerging trend observed in BGCs and other massive galaxies. This suggests a steeper $M_\text{BH}-\sigma_e$ relationship at the highest masses, potentially driven by a different co-evolution of SMBHs and their host galaxies. Future surveys will uncover more radial arcs, enabling the detection of SMBHs over a broader redshift and mass range. These discoveries will further refine our understanding of the $M_\text{BH}-\sigma_e$ relation and its evolution across cosmic time.