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, OBA stars with effective temperature (Teff) higher than 7500K. 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=1800. We first explore the theoretical information content of such spectra for determining stellar labels, via the Cram\'er-Rao bound. We show that in the limit of perfect model spectra and observed spectra with S/N of 100, precise estimates are possible for a wide range of stellar labels: not only the effective temperature Teff, surface gravity logg, and projected rotation velocity vsini, but also the micro-turbulence velocity, Helium abundance 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 around 9500K is challenging, as the dominant Balmer and Paschen line strength vary little with Teff. 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 LTE 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 (S/N>5), and more than 95 percent of them are luminous stars, mostly on the main sequence; the rest reflects lower luminosity evolved stars, such as hot subdwarfs and white dwarfs. We show that the fidelity of the abundance estimates is limited by the systematics of the underlying models, as they do not account for NLTE effects. Finally, we show the detailed distribution of vsini of stars with 8000-15,000K, illustrating that it extends to a sharp cut-off at the critical rotation velocity, across a wide range of temperatures.