Stellar labels for hot stars from low-resolution spectra I. The HOTPAYNE method and results for 330 000 stars from LAMOST DR6

We set out to determine stellar labels from low-resolution survey spectra of hot stars, specifically OBA stars with T-eff greater than or similar to 7500 K. This fills a gap in the scientific analysis of large spectroscopic stellar surveys such as LAMOST, which offers spectra for millions of stars at R similar to 1800 and covers 3800 angstrom <= lambda <= 9000 angstrom. We first explore the theoretical information content of such spectra to determine stellar labels via the Cramer-Rao bound. We show that in the limit of perfect model spectra and observed spectra with signal-to-noise ratio similar to 50-100, precise estimates are possible for a wide range of stellar labels: not only the effective temperature, T-eff, surface gravity, log g, and projected rotation velocity, vsin i, but also the micro-turbulence velocity, v(mic), helium abundance, N-He/N-tot, and the elemental abundances [C/H], [N/H], [O/H], [Si/H], [S/H], and [Fe/H]. Our analysis illustrates that the temperature regime of T-eff similar to 9500 K is challenging as the dominant Balmer and Paschen line strengths vary little with T-eff. We implement the simultaneous fitting of these 11 stellar labels to LAMOST hot-star spectra using the PAYNE approach, drawing on Kurucz's ATLAS12/SYNTHE local thermodynamic equilibrium spectra as the underlying models. We then obtain stellar parameter estimates for a sample of about 330 000 hot stars with LAMOST spectra, an increase by about two orders of magnitude in sample size. Among them, about 260 000 have good Gaia parallaxes (omega/sigma(omega) > 5), and their luminosities imply that greater than or similar to 95% of them are luminous stars, mostly on the main sequence; the rest are evolved lower luminosity stars, such as hot subdwarfs and white dwarfs. We show that the fidelity of the results, particularly for the abundance estimates, is limited by the systematics of the underlying models as they do not account for nonlocal thermodynamic equilibrium effects. Finally, we show the detailed distribution of vsin i of stars with 8000-15 000 K, illustrating that it extends to a sharp cutoff at the critical rotation velocity, v(crit), across a wide range of temperatures.