ExoMol line lists VII: The rotation-vibration spectrum of phosphine up to 1500 K

A comprehensive hot line list is calculated for $^{31}$PH$_3$ in its ground electronic state. This line list, called SAlTY, contains almost 16.8 billion transitions between 7.5 million energy levels and it is suitable for simulating spectra up to temperatures of 1500~K. It covers wavelengths longer than 1~$\mu$m and includes all transitions to upper states with energies below $hc \cdot 18\,000$~cm$^{-1}$ and rotational excitation up to $J=46$. The line list is computed by variational solution of the Schr\"odinger equation for the rotation-vibration motion employing the nuclear-motion program TROVE. A previously reported {\it ab initio} dipole moment surface is used as well as an updated `spectroscopic' potential energy surface (PES), obtained by refining an existing \textit{ab initio} surface through least-squares fitting to the experimentally derived energies. Detailed comparisons with other available sources of phosphine transitions confirms SAlTY's accuracy and illustrates the incompleteness of previous experimental and theoretical compilations for temperatures above 300 K. Atmospheric models are expected to severely underestimate the abundance of phosphine in disequilibrium environments, and it is predicted that phosphine will be detectable in the upper troposphere of many substellar objects. This list is suitable for modelling atmospheres of many astrophysical environments, namely carbon stars, Y dwarfs, T dwarfs, hot Jupiters and solar system gas giant planets. It is available in full as supplementary data to the article and at \url{www.exomol.com}.