Z. Igo, A. Merloni, A. Georgakakis, J. Buchner, R. Arcodia, M. Salvato, J. Aird, K. Nandra, B. Trakhtenbrot, P. G. Boorman, J. Comparat, G. Lamer, B. Laloux, M. Kluge, W. Roster, E. Bulbul, F. Balzer, T. Dwelly, W. N. Brandt, R. Seppi, S. Morrison, E. Kyritsis, J. Gelfand, S. F. Anderson, D. P. Schneider

Combining deep, wide-area X-ray surveys with multi-wavelength catalogues provides insights into rare, highly-accreting AGN and low-mass galaxies at low redshift, the latter potentially representing local analogues of the first galaxies in the early Universe. We use the four-pass eROSITA All Sky Survey to select the largest catalogue of X-ray AGN in a highly complete sample of low-redshift galaxies, including low-mass (logM*/Msol<10) ones. We probe their distribution of specific accretion rates, $λ$_SAR, and the cumulative AGN fraction above varying $λ$_SAR thresholds. Our parent sample consists of ~5.35 million galaxies selected from the Legacy Survey DR10 with z-band fluxes brighter than 20 mag and redshifts 0.03<z<0.2. We place particular emphasis on the detailed characterisation of our sample, including estimating unbiased physical galaxy properties and rigorous cleaning and validation of the X-ray aperture photometry and host-galaxy associations. We identify 874 X-ray AGN in low-mass galaxies, most of them newly discovered as X-ray emitters. Thanks to a Bayesian framework that makes use of the X-ray information from all parent sample galaxies, we constrain the specific accretion rate distribution, p(log$λ$_SAR | M*, z), across a wide range of $λ$_SAR and uncover second-order mass-dependent effects. We detect a break at high $λ$_SAR, possibly indicating Eddington-limited, self-regulated black hole growth. Integrating p(log$λ$_SAR | M*, z) above $λ$_SAR>10^-3, we find a cumulative AGN fraction of ~1% for low-mass galaxies, placing a firm lower limit on the black hole occupation fraction in this regime. Overall, our specific accretion rate distributions, sampling down to the as-of-yet unexplored low-mass regime, highlight a more nuanced, mass-dependent view of AGN growth and accretion history that must be taken into account in future modelling.