  We use principal component analysis (PCA) to estimate stellar masses, mean
stellar ages, star formation histories (SFHs), dust extinctions and stellar
velocity dispersions for ~290,000 galaxies with stellar masses greater than
$10^{11}Msun and redshifts in the range 0.4<z<0.7 from the Baryon Oscillation
Spectroscopic Survey (BOSS). We find the fraction of galaxies with active star
formation first declines with increasing stellar mass, but then flattens above
a stellar mass of 10^{11.5}Msun at z~0.6. This is in striking contrast to
z~0.1, where the fraction of galaxies with active star formation declines
monotonically with stellar mass. At stellar masses of 10^{12}Msun, therefore,
the evolution in the fraction of star-forming galaxies from z~0.6 to the
present-day reaches a factor of ~10. When we stack the spectra of the most
massive, star-forming galaxies at z~0.6, we find that half of their [OIII]
emission is produced by AGNs. The black holes in these galaxies are accreting
on average at ~0.01 the Eddington rate. To obtain these results, we use the
stellar population synthesis models of Bruzual & Charlot (2003) to generate a
library of model spectra with a broad range of SFHs, metallicities, dust
extinctions and stellar velocity dispersions. The PCA is run on this library to
identify its principal components over the rest-frame wavelength range
3700-5500A. We demonstrate that linear combinations of these components can
recover information equivalent to traditional spectral indices such as the
4000A break strength and HdA, with greatly improved S/N. This method is able to
recover physical parameters such as stellar mass-to-light ratio, mean stellar
age, velocity dispersion and dust extinction from the relatively low S/N BOSS
spectra. We examine the sensitivity of our stellar mass estimates to the input
parameters in our model library and the different stellar population synthesis
models.
