Measuring the 3D clustering of undetected galaxies through cross correlation of their cumulative flux fluctuations from multiple spectral lines

Abstract

We discuss a method for detecting the emission from high redshiftgalaxies by cross correlating flux fluctuations from multiple spectrallines. If one can fit and subtract away the continuum emission with asmooth function of frequency, the remaining signal containsfluctuations of flux with frequency and angle from line emittinggalaxies. Over a particular small range of observed frequencies,these fluctuations will originate from sources corresponding to aseries of different redshifts, one for each emission line. It ispossible to statistically isolate the fluctuations at a particularredshift by cross correlating emission originating from the sameredshift, but in different emission lines. This technique will allowdetection of clustering fluctuations from the faintest galaxies whichindividually cannot be detected, but which contribute substantially tothe total signal due to their large numbers. We describe thesefluctuations quantitatively through the line cross power spectrum. Asan example of a particular application of this technique, we calculatethe signal-to-noise ratio for a measurement of the cross powerspectrum of the OI(63 μm) and OIII(52 μm) fine structure lineswith the proposed Space Infrared Telescope for Cosmology andAstrophysics (SPICA). We find that the cross power spectrum can bemeasured beyond a redshift of z = 8. Such observations couldconstrain the evolution of the metallicity, bias, and duty cycle offaint galaxies at high redshifts and may also be sensitive to thereionization history through its effect on the minimum mass ofgalaxies. As another example of this technique, we calculate thesignal-to-noise ratio for the cross power spectrum of CO line emissionmeasured with a large ground based telescope like the Cornell CaltechAtacama Telescope (CCAT) and 21-cm radiation originating from hydrogenin galaxies after reionization with an interferometer similar in scaleto the Murchison Widefield Array (MWA), but optimized forpost-reionization redshifts.