Application of Data Compression Methods to the Redshift-space distortions of the PSCz galaxy catalogue

We apply a spherical harmonic analysis to the Point Source Redshift Survey (PSCz), to compute the real-space galaxy power spectrum and the degree of redshift distortion caused by peculiar velocities. We employ new parameter eigenvector and hierarchical data compression techniques, allowing a much larger number of harmonic modes to be included, and correspondingly smaller error bars. Using 4644 harmonic modes, compressed to 2278, we find that the IRAS redshift-space distortion parameter is $\beta =0.39\pm 0.12$ and the amplitude of galaxy clustering on a scale of $k=0.1\text{Mpch}$ is $\Delta_{\rm gal}(0.1)=0.42 \pm 0.02$. Combining these we find the amplitude of mass perturbations is ${\mathrm{\Delta }}_m(0.1)=(0.16\pm 0.04){\mathrm{\Omega }}_m^{-0.6}$. A preliminary model fitting analysis combining the PSCz amplitudes with the CMB and abundance of clusters yields the cosmological matter density parameter $\Omega_m=0.16\pm 0.03$,theamplitudeofprimordialperturbations$Q=(8.4\pm 3.8) \times 10^{-5}$,andtheIRASbiasparameter$b=0.84\pm 0.28$.