A redshift survey of IRAS galaxies. V. The acceleration on the local group

We calculate the acceleration on the Local Group from a full-sky redshift survey of 5288 galaxies detected by the Infrared Astronomical Satellite (IRAS). The median redshift of the sample is ≈4500 km s^-1; however, there is useful information on the acceleration to ≈ 20,000 km s^-1. We develop a formalism to compute the distribution function of the IRAS acceleration for a given power spectrum of initial perturbations, which includes the effects of shot noise, the finite window through which the acceleration is measured, and nonlinear effects on small scales. This distribution is very broad, which means that a value of βs Ξ Ω^0.6/h calculated by simply taking the ratio of the cosmic microwave background (CMB) dipole to the IRAS acceleration will be uncertain by a factor of 2 or more. The computed acceleration on the Local Group points 18°-28° from the direction of the Local Group peculiar velocity vector, depending on the model used for the velocity field, and the window through which the acceleration is measured. The convergence of the acceleration vector on large scales depends strongly on the correction made for the motion of the Local Group, an effect first recognized by Kaiser. This limits our ability to rule out contributions to the acceleration on large scales, although the data are consistent with the acceleration being due mostly to galaxies within 4000 km s^-1 of the Local Group. The data suggest that the CMB dipole is indeed due to the motion of the Local Group, that this motion is gravitationally induced, and that the distribution of IRAS galaxies on large scales is related to that of dark matter by a simple linear biasing model. The fact that IRAS galaxies underestimate the density of rich cluster cores affects the acceleration calculation at only the 10% level. A maximum-likelihood fit of different power spectra to the growth of the acceleration allows us to solve for β. The quantity β is constrained to lie between 0.4 and 0.85 (1 σ), and is rather insensitive to the power spectrum assumed. Our data favor cold dark matter over a baryon dark matter isocurvature model. Similarly, a power-law power spectrum cannot have a break on scales below 1800 km s^-1. These results are consistent with measurements of the dipole moment of optically selected galaxies; there is no need for strong relative biasing between IRAS and optically selected galaxies. We test the power of our techniques with the aid of N-body simulations.