# SDSS Luminosity Function

Much of my work over the past couple of years has focused on the luminosity function of galaxies in the SDSS. Blanton et al. (2001) published a luminosity function and the relationship of luminosity to other properties for a small amount of commissioning data. However, since then we have aquired much more data, and in addition we have improved our analysis. Most significantly, we have fit for luminosity evolution in the luminosity function. Blanton et al. (2003d) present the results of this analysis. All of its bitmapped figures may be downloaded, and we present a short description of the major results here. A separate paper (Blanton et al. 2003c) and web page present the relationships between luminosity and other properties.

We have recently looked at the luminosity function down to much lower luminosities. See the low-redshift catalog description for these results.

The sample this is drawn from looks like this in redshift space (limiting ourselves to the Equator for this figure):

Figure 1: Pie diagram of the Celestial Equation (plus or minus 5 degrees) from the SDSS Main sample of galaxies.

It turns out that in order to understand the luminosity function with the SDSS spectroscopic sample one needs to account for evolution within the sample. Blanton et al. (2003d) fit a nonparametric model accounting for evolution and flux uncertainties. The model is expressed as a sum of Gaussian basis functions. For the r-band we obtain the function (with best fit Schechter parameters listed):

Figure 2: Luminosity function of SDSS galaxies. Smooth line is the best fit to the data, with 1 sigma statistical errors shown as the grey region. Note that the errors are highly correlated. The Gaussians shown as light grey lines are the components of the best fit model. The dashed line is a Schechter function (with parameters listed). Do not use the Schechter function fit outside the range of absolute magnitudes shown here.

For the other bands we find:

Figure 3: Similar to Figure 2, for the other SDSS bands.

How do these results compare to other determinations of the luminosity density? Consider the luminosity density as a function of wavelength:

Figure 4: Luminosity density and its evolution as a function of wavelength. Black dots are from Blanton et al. 2003., blue dot is from Norberg et al 2002, magenta line is the Baldry et al. 2002 average spectrum, and the red and green points are 2MASS data from Cole et al. 2002 and Kochank et al 2002 respectively. The bottom panel shows the simple luminosity function evolution fits of Blanton et al. 2003 from the SDSS (compared to the prediction of the very simple instantaneous burst prediction).

The top panel shows the luminosity density, the bottom shows estimates of its evolution. The big black dots are from Blanton et al. (2003d), the magenta line is the cosmic spectrum from Glazebrook et al. (2003d), the blue dot is from the 2dFGRS results of Norberg et al. (2002), and the near infrared points are all from 2MASS.

Values of the luminosity function from the fit in each band are available in the following files:

Each line of each file is:

```[absolute magnitude] [phi] [sigma phi]
```
Remember the absolute magnitudes are band-shifted to 0.1 (with h=1). "phi" is in units of number per h-3 Mpc3 per mag.

MOST IMPORTANTLY, THE ERROR BARS ARE NOT INDEPENDENT. NOT EVEN CLOSE. The points at which these files sample the fit luminosity function are very closely spaced, so there is no way the errors are independent. The uncertainties in luminosity for each galaxy are about 0.05 mag, so that is the minimum magnitude difference between independent samples. However, since the uncertainties are dominated by large-scale structure, not numbers, the best approach is to assume the whole curve can be shifted up and down together (ie. the error bars are FULLY covariant). Note that both these aspects of the covariance matrix affect all luminosity function measurements; it is not a consequence of our method. Finally, I should note that for almost all purposes, the statistical error bars are completely irrelevant anyway. They are much smaller than any errors you expect from photometric and spectroscopic systematic effects (slight surface brightness incompleteness, definition of "galaxy flux", deblending issues) not to mention internal dust extinction in the galaxies. Thus, when comparing to theory it would be totally inappropriate to rely on chi^2 from these errors --- such a chi^2 will always be very high even for very successful theories.

Snail Mail: Michael Blanton; Email: blanton at nyu.edu