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The Donor of the Black-Hole X-Ray Binary MAXI J1820+070

We estimate the parameters of the donor of the accreting black-hole binary MAXI J1820+070. The measured values of the binary period, rotational and radial velocities and constraints on the orbital inclination imply the donor is a subgiant with the mass of $M_2\approx 0.49^{+0.10}_{-0.10}M_\odot$ and the radius of $R_2\approx 1.19^{+0.08}_{-0.08}R_\odot$. We re-analyze the previously obtained optical spectrum from the Gran Telescopio Canarias, and found it yields a strict lower limit on the effective temperature of $T>4200$ K. We compile optical and infrared fluxes observed during the quiescence of this system. From the minima $r$ and $i$-band fluxes found in Pan-STARSS1 Data Release 2 pre-discovery imaging and for a distance of $D\approx3$ kpc, reddening of $E(B$--$V)=0.23$ and $R_2\approx{1.11R_\odot}$, we find $T\lesssim4230$ K, very close to the above lower limit. For a larger distance, the temperature can be higher, up to about 4500 K (corresponding to a K5 spectral type, preferred by previous studies) at $D=3.5$ kpc, allowed by the Gaia parallax. We perform evolutionary calculations for the binary system and compare them to the observational constraints. Our model fitting the above temperature and radius constraints at $D\approx 3$ kpc has the mass of $0.4M_\odot$, $T\approx4200$ K and solar metallicity. Two alternative models require $D\gtrsim 3.3$--3.4 kpc at $0.4 M_\odot$, $T\approx4500$ K and half solar metallicity, and $0.5M_\odot$, $T\approx4300$ K and solar metallicity. These models yield mass transfer rates of $\sim\!\!10^{-10}M_\odot$/yr, compatible with those based on the estimated accreted mass of $\approx\!2\times 10^{25}$ g and the time between the 2018 discovery and the 1934 historical outburst.