Dynamical Confirmation of a Black Hole in MAXI J1820+070

We present time-resolved 10.4 m Gran Telescopio Canarias and 4.2 m William Herschel Telescope intermediate resolution spectroscopy of the X-ray transient MAXI J1820+070 (=ASASSN-18ey) obtained during its decline to the quiescent state. Cross-correlation of the 21 individual spectra against late-type templates reveals a sinusoidal velocity modulation with a period of 0.68549 +/- 0.00001 day and semi-amplitude of 417.7 +/- 3.9 km s(-1). We derive a mass function f(M) = 5.18 +/- 0.15 M-circle dot, dynamically confirming the black hole (BH) nature of the compact object. Our analysis of the stellar absorption features supports a K3-5 spectral classification for the donor star, which contributes approximate to 20% of the total flux at 5200-6800 angstrom. The photometric 0.703 +/- 0.003 day periodicity observed during outburst is 2.6% longer than the orbital period supporting the presence of a superhump modulation in the outburst light curves. In line with this interpretation, we constrain the binary mass ratio to be q similar or equal to 0.12. In addition, we observe a sharp increase in the H alpha emission line equivalent width during inferior conjunction of the donor star that we interpret as a grazing eclipse of the accretion disk and allows us to constrain the binary inclination to i greater than or similar to 69 degrees. On the other hand, the absence of X-ray eclipses during outburst imply i less than or similar to 77 degrees. These inclination limits, together with our dynamical solution, lead to a BH mass in the range 7-8 M-circle dot. We also measure a systemic velocity gamma = -21.6 +/- 2.3 km s(-1), which, combined with the Gaia second data release proper motion and parallax, implies a large peculiar velocity similar to 100 km s(-1).