Growth of black holes at the centre of early-type galaxies in MOND: constraints on cosmology and galaxy bias with harmonic-space power spectra

The formation of supermassive black holes (SMBHs) in early-type galaxies (ETGs) is a key challenge for galaxy formation theories. Using the monolithic collapse models of ETGs formed in Milgromian Dynamics (MOND) from Eappen et al. (2022, MNRAS, 516, 1081. https://doi.org/10.1093/mnras/stac2229. arXiv: 2209.00024 [astro-ph.GA].), we investigate the conditions necessary to form SMBHs in MOND and test whether these systems adhere to observed SMBH-galaxy scaling relations. We analyse the evolution of the gravitational potential and gas inflow rates in the model relics with a total stellar mass ranging from 0.1 × 10 ¹¹ M _☉ to 0.7 × 10 ¹¹ M _☉. The gravitational potential exhibits a rapid deepening during the initial galaxy formation phase, accompanied by high gas inflow rates. These conditions suggest efficient central gas accumulation capable of fuelling SMBH formation. We further examine the M _BH − σ relation by assuming that a fraction of the central stellar mass contributes to black hole formation. Black hole masses derived from 10%–100% of the central mass are comparable with the observed relation, particularly at higher central velocity dispersions (σ > 200 km/s). This highlights the necessity of substantial inner mass collapse to produce SMBHs consistent with observations. Our results demonstrate that MOND dynamics, through the rapid evolution of the gravitational potential and sustained gas inflows, provide a favourable environment for SMBH formation in ETGs. These findings support the hypothesis that MOND can naturally account for the observed SMBH-galaxy scaling relations without invoking cold dark matter, emphasising the importance of early gas dynamics in determining final SMBH properties.