An e-MERLIN & EVN radio counterpart to the ultraluminous X-ray source M82 X-1

Ultra-luminous X-ray sources (ULXs) are X-ray bright (L$_{\rm X-ray} >$3$\times$10$^{39}$erg s$^{-1}$) extra-galactic objects that are powered by either neutron stars, or stellar or intermediate-mass black holes (IMBHs) but few have been detected in the radio waveband. In the nearby galaxy M82, the brightest ULX - M82 X$-$1, is thought to be associated with an IMBH but to date does not have a radio counterpart. We present deep wide-band reprocessed e-MERLIN images observed in 2015 May with an r.m.s. sensitivity of 7$\mu$Jy beam$^{-1}$ and report the discovery of a new radio source with an integrated flux of S$_{\rm \nu=4.88\,GHz}$ = 174$\pm$15$\mu$Jy, which is spatially co-incident with the Chandra X-ray position of M82 X$-$1. This source is not detected in archival MERLIN/e-MERLIN observations in the last three decades. A search for intra-observation variability in the 2015 e-MERLIN data was inconclusive, but a comparison with 1.5 GHz e-MERLIN observations taken a week prior yielded no detection. We also detect the source at the same position with milliarcsecond angular resolution in EVN+e-MERLIN data from 2021 March at 53$\pm$10$\mu$Jy. The radio source position is ICRF J2000 RA: 09$^{h}$55$^{m}$50.1172$^{s}$, Dec: +69$^{\circ}$40'46.606" ($\pm$1.5 mas). These radio fluxes are consistent with other radio-detected ULXs on the radio:X-ray plane and points towards a stellar/intermediate-mass black hole. The black hole mass inferred by the `fundamental plane of black hole activity' is 2650 M$_{\odot}$, but this value remains highly uncertain.