Full spectrum fitting with photometry in pPXF: stellar population versus dynamical masses, non-parametric star formation history and metallicity for 3200 LEGA-C galaxies at redshift z~0.8

I introduce some improvements to the pPXF method, which measures the stellar and gas kinematics, star formation history (SFH) and chemical composition of galaxies. I describe the new optimization algorithm that pPXF uses and the changes I made to fit both spectra and photometry simultaneously. I apply the updated pPXF method to a sample of 3200 galaxies at redshift $0.6<z<1$ (median $z=0.76$, stellar mass $M_\ast>3\times10^{10}$ M$_\odot$), using spectroscopy from the LEGA-C survey (DR3) and 28-bands photometry from two different sources. I compare the masses from new JAM dynamical models with the pPXF stellar population $M_\ast$ and show the latter are more reliable than previous estimates. I use three different stellar population synthesis (SPS) models in pPXF and both photometric sources. I confirm the main trend of the galaxies' global ages and metallicity $[M/H]$ with stellar velocity dispersion $\sigma_\ast$ (or central density), but I also find that $[M/H]$ depends on age at fixed $\sigma_\ast$. The SFHs reveal a sharp transition from star formation to quenching for galaxies with $\lg(\sigma_\ast/\mathrm{km\, s^{-1}})>2.3$, or average mass density within 1 kpc $\lg(\Sigma_1^{\rm JAM}/\mathrm{M_\odot kpc^{-2}})>9.9$, or with $[M/H]>-0.1$, or with Sersic index $\lg n_{\rm Ser}>0.5$. However, the transition is smoother as a function of $M_\ast$. These results are consistent for two SPS models and both photometric sources, but they differ significantly from the third SPS model, which demonstrates the importance of comparing model assumptions. The pPXF software is available from https://pypi.org/project/ppxf/.