Clustering in the 1.2 Jy IRAS Galaxy Redshift Survey I: The Redshift and Real Space Correlation Functions

We present analyses of the two-point correlation function derived from an all-sky redshift survey of 5313 galaxies extracted from the Infrared Astronomical Satellite (IRAS) database. The redshift space correlation function \xi(s) is well described by a power law, $\xi(s) = (s/4.53h^{-1}{\rm Mpc})^{-1.28}$, on scales \simlt 20\mpc; on larger scales \xi(s) drops below the extension of this power law. We examine the effect of redshift space distortions on the correlation function and compute the full two dimensional correlation function \xi(r_p,\pi). From this, we derive the real space correlation function, which is well described by $\xi(r) = (r/3.76h^{-1}{\rm Mpc})^{-1.66}$ on scales \simlt 20\mpc. The derived correlation functions are found to be consistent with previous determinations in the literature, and seem to show more power on large scales than predicted by the standard Cold Dark Matter (CDM) model. Comparison of the derived \xi(r) with the correlation function of optical galaxies implies an optical to IRAS bias ratio of $b_O/b_I = 1.38\pm 0.12$ on a scale of $\sim 8$\mpc . The variances in cubical cells inferred from \xi(s) appear discrepant with the previously reported results of Efstathiou et al. (1990).