Unbiased TGAS$\times$LAMOST distances and the role of binarity
  Spectrophotometric distances to stars observed by large spectroscopic surveys
offer a crucial complement to parallax distances that remain very important
also after the future Gaia data releases. Here we present a probabilistic
approach to modeling spectroscopic information for a subset of 4,000 main
sequence stars with good parallaxes ($\sigma_\varpi/\varpi<0.1$) from the
LAMOST $\times$ TGAS $\times$ 2MASS cross-match, yielding a precise
spectroscopic distance estimator with uncertainties of $\sim$6% for single
stars. Unlike previous approaches to this problem, we explicitly account for
the individual parallax uncertainties in the model building and fully
incorporate the fraction of near-equal binaries of main sequence stars, which
would lead to biased distance estimates if neglected. Using this model, we
estimate the distance for all (150,000) main sequence stars from LAMOST Data
Release 5, without parallax information. As an application, we compute their
orbital actions, where our more precise distances result in 5 times smaller
action uncertainties. This illustrates how future studies of the Milky Way's
orbital structure can benefit from using our model. For the fainter and more
distant stars of most current spectroscopic surveys, an approach such as the
one presented in this work will deliver better distances than Gaia Data Release
2.
