Continuum emission from within the plunging region of black hole discs

The thermal continuum emission observed from accreting black holes across X-ray bands has the potential to be leveraged as a powerful probe of the mass and spin of the central black hole. The vast majority of existing ``continuum fitting'' models neglect emission sourced at and within the innermost stable circular orbit (ISCO) of the black hole. Numerical simulations, however, find non-zero emission sourced from these regions. In this work we extend existing techniques by including the emission sourced from within the plunging region, utilising new analytical models which reproduce the properties of numerical accretion simulations. We show that in general the neglected intra-ISCO emission produces a hot-and-small quasi-blackbody component, but can also produce a weak power-law tail for more extreme parameter regions. A similar hot-and-small blackbody component has been added in by hand in an ad-hoc manner to previous analyses of X-ray binary spectra. We show that the X-ray spectrum of MAXI J1820+070 in a soft-state outburst is extremely well described by a full Kerr black hole disc, while conventional models which neglect intra-ISCO emission are unable to reproduce the data. We believe this represents the first robust detection of intra-ISCO emission in the literature, and allows additional constraints to be placed on the MAXI J1820+070 black hole spin which must be low $a_\bullet < 0.5$ to allow a detectable intra-ISCO region. Emission from within the ISCO is the dominant emission component in the MAXI J1820+070 spectrum between $6$ and $10$ keV, highlighting the necessity of including this region. Our continuum fitting model is made publicly available.