Parametrizing the Stellar Haloes of Galaxies
  We study the stellar haloes of galaxies out to 70-100 kpc as a function of
stellar mass and galaxy type by stacking aligned $r$ and $g$ band images from a
sample of 45508 galaxies from SDSS DR9 in the redshift range
$0.06\,\le\,z\,\le\,0.1$ and in the mass range $10^{10.0} M_{\odot} < M_{*} <
10^{11.4} M_{\odot}$r. We derive surface brightness profiles to a depth of
almost $\mu_r \sim 32 \,\mathrm{mag\,arcsec}^{-2}$. We find that the
ellipticity of the stellar halo is a function of galaxy stellar mass and that
the haloes of high concentration ($C > 2.6$) galaxies are more elliptical than
those of low concentration ($C < 2.6$) galaxies. The $g$-$r$ colour profile of
high concentration galaxies reveals that the $g$-$r$ colour of the stellar
population in the stellar halo is bluer than in the main galaxy, and the colour
of the stellar halo is redder for higher mass galaxies. We further demonstrate
that the full two-dimensional surface intensity distribution of our galaxy
stacks can only be fit through multi-component S\'{e}rsic models. Using the
fraction of light in the outer component of the models as a proxy for the
fraction of accreted stellar light, we show that this fraction is a function of
stellar mass and galaxy type. For high concentration galaxies, the fraction of
accreted stellar light rises from $30\%$ to $70\%$ for galaxies in the stellar
mass range from $10^{10.0} M_{\odot}$ to $10^{11.4} M_{\odot}$. The fraction of
accreted light is much smaller in low concentration systems, increasing from
$2\%$ to $25\%$ over the same mass range. This work provides important
constraints for the theoretical understanding of the formation of stellar
haloes of galaxies.
