Photometric properties and luminosity function of nearby massive
  early-type galaxies
  We perform photometric analyses for a bright early-type galaxy (ETG) sample
with 2949 galaxies ($M_{\rm r}<-22.5$ mag) in the redshift range of 0.05 to
0.15, drawn from the SDSS DR7 with morphological classification from Galaxy Zoo
1. We measure the Petrosian and isophotal magnitudes, as well as the
corresponding half-light radius for each galaxy. We find that for brightest
galaxies ($M_{\rm r}<-23$ mag), our Petrosian magnitudes, and isophotal
magnitudes to 25 ${\rm mag/arcsec^2}$ and 1\% of the sky brightness are on
average 0.16 mag, 0.20 mag, and 0.26 mag brighter than the SDSS Petrosian
values, respectively. In the first case the underestimations are caused by
overestimations in the sky background by the SDSS PHOTO algorithm, while the
latter two are also due to deeper photometry. Similarly, the typical half-light
radii ($r_{50}$) measured by the SDSS algorithm are smaller than our
measurements. As a result, the bright-end of the $r$-band luminosity function
is found to decline more slowly than previous works. Our measured luminosity
densities at the bright end are more than one order of magnitude higher than
those of Blanton et al. (2003), and the stellar mass densities at $M_{\ast}\sim
5\times10^{11} M_{\odot}$ and $M_{\ast}\sim 10^{12} M_{\odot}$ are a few tenths
and a factor of few higher than those of Bernardi et al. (2010). These results
may significantly alleviate the tension in the assembly of massive galaxies
between observations and predictions of the hierarchical structure formation
model.
