How covariant is the galaxy luminosity function?

Monthly Notices of the Royal Astronomical Society (Impact Factor: 5.11). 05/2012; 426(1). DOI: 10.1111/j.1365-2966.2012.21745.x
Source: arXiv

ABSTRACT We investigate the error properties of certain galaxy luminosity function
(GLF) estimators. Using a cluster expansion of the density field, we show how,
for both volume and flux limited samples, the GLF estimates are covariant. The
covariance matrix can be decomposed into three pieces: a diagonal term arising
from Poisson noise; a sample variance term arising from large-scale structure
in the survey volume; an occupancy covariance term arising due to galaxies of
different luminosities inhabiting the same cluster. To evaluate the theory one
needs: the mass function and bias of clusters, and the conditional luminosity
function (CLF). We use a semi-analytic model (SAM) galaxy catalogue from the
Millennium run N-body simulation and the CLF of Yang et al. (2003) to explore
these effects. The GLF estimates from the SAM and the CLF qualitatively
reproduce results from the 2dFGRS. We also measure the luminosity dependence of
clustering in the SAM and find reasonable agreement with 2dFGRS results for
bright galaxies. However, for fainter galaxies, L<L*, the SAM overpredicts the
relative bias by ~10-20%. We use the SAM data to estimate the errors in the GLF
estimates for a volume limited survey of volume V~0.13 [Gpc/h]^3. We find that
different luminosity bins are highly correlated: for L<L* the correlation
coefficient is r>0.5. Our theory is in good agreement with these measurements.
These strong correlations can be attributed to sample variance. For a
flux-limited survey of similar volume, the estimates are only slightly less
correlated. We explore the importance of these effects for GLF model parameter
estimation. We show that neglecting to take into account the bin-to-bin
covariances can lead to significant systematic errors in best-fit parameters.

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