The power spectra of IRAS galaxies and of Abell clusters

This work measures the power spectra of IRAS galaxies and of Abell clusters by analyzing the 2 Jy IRAS redshift survey and two redshift samples of Abell clusters. In terms of the variance {DELTA}^2^(k), we find that the {DELTA}^2^(k) of IRAS galaxies obeys a power law {DELTA}^2^(k) is proportional to k^1.3^ up to the largest possible wavelength λ = 2π/k ~ 100 h^-1^ Mpc which the survey is able to explore. The {DELTA}^2^(k) of Abell clusters has the same slope as that of IRAS galaxies for λ < 100 h^-1^ Mpc but has an amplitude about 10 times higher, which supports the "linear" biasing mechanism as the origin of rich clusters. At larger wavelengths, the variance of Abell clusters falls more rapidly than the power law. Under the "linear" biasing assumption, the {DELTA}^2^(k) of IRAS galaxies is well expressed by {DELTA}^2^(k) = (k/0.3)^1.3^/[1 t (k/0.025)^-2.7^], where k is in h Mpc^-1^. The fitting formula is taken to be scale-invariant at large wavelengths, which is supported by the recent C0BE DMR observation as well as inflation theories. Assuming a biasing factor of 1.5 for IRAS galaxies, we find the Sachs-Wolfe effect with the above variance can correctly produce the temperature quadrupole Q = 6 x 10^6^ observed in the COBE experiment.