Stacking Quasars

I heard an interesting talk today by J. Xavier Prochaska, from Santa Cruz. The abstract is below. The basic idea was that we can co-add quasar spectra to get a cleaner signal of opacity (due to lyman absorption) and thus the mean free path as a function of redshift. We should totally do this with BOSS.

~~~
"Direct Measurement of the IGM Opacity to H I Ionizing Photons"
Paper: http://arxiv.org/abs/0910.0009
We present a new method to directly measure the opacity from HI Lyman limit (LL) absorption k_LL along quasar sightlines by the intergalactic medium (IGM). The approach analyzes the average (``stacked'') spectrum of an ensemble of quasars at a common redshift to infer the mean free path (MFP) to ionizing radiation. We apply this technique to 1800 quasars at z=3.50-4.34 drawn from the Sloan Digital Sky Survey (SDSS), giving the most precise measurements on k_LL at any redshift. From z=3.6 to 4.3, the opacity increases steadily as expected and is well parameterized by MFP = (48.4 +/- 2.1) - (38.0 +/- 5.3)*(z-3.6) h^-1 Mpc (proper distance). The relatively high MFP values indicate that the incidence of systems which dominate k_LL evolves less strongly at z>3 than that of the Lya forest. We infer a mean free path three times higher than some previous estimates, a result which has important implications for the photo-ionization rate derived from the emissivity of star forming galaxies and quasars. Finally, our analysis reveals a previously unreported, systematic bias in the SDSS quasar sample related to the survey's color targeting criteria. This bias potentially affects all z~3 IGM studies using the SDSS database.

A Likely Result

In SDSS-III, the BOSS project is targeting 160,000 quasars (QSOs) at redshifts between 2.2 and 3.5. A color-color plot of spectroscopically confirmed QSOs (green) and stars (red). You can see that the quasars and stars have regions of overlap in the color space, and are therefore difficult to distinguish from each other.

David Schlegel suggested using a likelihood estimator to select quasars from stars. The basic idea is to have a templates of "quasar objects" and "all other objects" we would expect to see in the Sloan data set. We then take a "test object," one which we are trying to determine if it is a quasar or not, and compute a likelihood between it and the two templates. The likelihood of a test object (i) is for a set of template data (j) with color filters (f) is defined as follows:

where x is the flux of an object in the template data and mu is the flux of your test object and sigma if the error in your test object flux measurement.

I computed this likelihood with a set of test object where I knew if they were quasars or not. Below is a plot of the above likelihood computed on the test objects with a "quasar template" and a "everything else template." I am plotting the likelihood of the test objects with everything else (on the x axis) versus with quasars (on the y axis). Because I know what these test objects are, I can color the quasars (green) and the stars (blue). You can see that I get a clear separation in likelihood-likelihood space of these populations, where the quasars fall along a higher likelihood for quasars and the stars fall along a higher likelihood for everything else: