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Register a new userMaximum Likelihood Random Galaxy Catalogues and Luminosity Function Estimation
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Shaun Cole
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We present a new algorithm to generate a random (unclustered) version of an magnitude limited observational galaxy redshift catalogue. It takes into account both galaxy evolution and the perturbing effects of large scale structure. The key to the algorithm is a maximum likelihood (ML) method for jointly estimating both the luminosity function (LF) and the overdensity as a function of redshift. The random catalogue algorithm then works by cloning each galaxy in the original catalogue, with the number of clones determined by the ML solution. Each of these cloned galaxies is then assigned a random redshift uniformly distributed over the accessible survey volume, taking account of the survey magnitude limit(s) and, optionally, both luminosity and number density evolution. The resulting random catalogues, which can be employed in traditional estimates of galaxy clustering, make fuller use of the information available in the original catalogue and hence are superior to simply fitting a functional form to the observed redshift distribution. They are particularly well suited to studies of the dependence of galaxy clustering on galaxy properties as each galaxy in the random catalogue has the same list of attributes as measured for the galaxies in the genuine catalogue. The derivation of the joint overdensity and LF estimator reveals the limit in which the ML estimate reduces to the standard 1/Vmax LF estimate, namely when one makes the prior assumption that the are no fluctuations in the radial overdensity. The new ML estimator can be viewed as a generalization of the 1/Vmax estimate in which Vmax is replaced by a density corrected Vdc,max.
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Whitbourn & Shanks (2014) have reported evidence for a local void underdense by ~15% extending to 150-300h-1Mpc around our position in the Southern Galactic Cap (SGC). Assuming a local luminosity function they modelled K- and r-limited number counts and redshift distributions in the 6dFGS/2MASS and SDSS redshift surveys and derived normalised n(z) ratios relative to the standard homogeneous cosmological model. Here we test further these results using maximum likelihood techniques that solve for the galaxy density distributions and the galaxy luminosity function simultaneously. We confirm the results from the previous analysis in terms of the number density distributions, indicating that our detection of the Local Hole in the SGC is robust to the assumption of either our previous, or newly estimated, luminosity functions. However, there are discrepancies with previously published K and r band luminosity functions. In particular the r-band luminosity function has a steeper faint end slope than the r0.1 results of Blanton et al. (2003) but is consistent with the r0.1 results of Montero-Dorta & Prada (2009); Loveday et al. (2012).
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