Full spectrum fitting with photometry in ppxf: non-parametric star formation history, metallicity and the quenching boundary from 3200 LEGA-C galaxies at redshift z~0.8

I start by describing some updates to the pPXF method, which has been used to measure stellar and gas kinematics as well as the formation history (SFH) and chemical composition of galaxies. I outline the novel linearly-constrained least-squares optimization algorithm used by pPXF and I illustrate the changes I made to be able to include photometric measurements together with full-spectrum fitting in pPXF. Then I present an application of the revised pPXF method to the study of the non-parametric SFH and metallicity $[M/H]$ of a sample of 3200 galaxies at redshift $0.63\times10^{10}$ M$_\odot$, with spectroscopy from the LEGA-C survey and 28-bands photometry from two alternative catalogues. I extract and compare the stellar population using three independent stellar population synthesis (SPS) methods and both photometric catalogues. I find robust trends in the global light-weighted ages and $[M/H]$ consistent and of similar quality as those from nearby galaxy surveys, with the well-known main dependence on the galaxies' stellar velocity dispersion $\sigma_\ast$ (or alternative measures of central density). The recovered SFH indicate a sharp and strikingly clear boundary from star formation to quenching at $\lg(\sigma_\ast/km s^{-1})\approx2.3$, similar to what is invoked by some models. Equally clear quenching boundaries are seen at $[M/H]\approx-0.1$ and for a Sersic exponent $n_{\rm Ser}\approx0.5$. Results are consistent with two SPS methods and both photometric catalogues, but the third SPS method displays significant differences, highlighting the importance of comparing model assumptions. The pPXF software is available from https://pypi.org/project/ppxf/.