Galactic disks, infall, and the global value of Omega

The thinness and coldness of galactic disks can be used to set stringent limits on the current rate of infall of satellite systems onto spiral galaxies. After reviewing the literature concerning numerical results, we develop analytical arguments which confirm and considerably extend prior work. For infalling satellites on isotropically oriented circular orbits, we show that, due to scattering, the thermal energy gain of the disk exceeds the satellite energy loss from dynamical friction by a factor of 1. 6, with 25% deposited in z motion and 75% in planar motions. This factor almost compensates for the frictional loss to the halo, with halo-to-disk loss rates being approximately 2. 87rρₕ_ (r) /SIGMAd_ (r). For our chosen Galactic model this corresponds to 62% of the energy deposited in the spherical component at the solar radius. While satellite infall will thicken disks by perturbing the stellar orbits, it will cause adiabatic contraction too. If there is gas infall, this makes the disk thinner by settling down in the galactic plane. However, the first effect dominates, the ratio between stellar heating and gas cooling being 0. 11 (vᵣot/σₙormal_) ²^~7 for equal masses added in stars and gas. Applying these arguments to current models for our Galaxy, we find that no more than 4% of its mass inside the solar radius can have accreted within the last 5 billion years, or else its scale height and its Toomre Q-parameter would exceed observed values. We find that tidal stripping of infalling dwarfs is not a large effect unless core radii significantly exceed 1 kpc. In standard cold dark matter-dominated models for the growth of structure with OMEGAₜot_ = 1, the mass accreted in dark matter lumps rises faster than t²/3^ and would exceed 28% in the last 5 Gyr. If our Galaxy is typical (and the prevalence of spiral structure indicates that this is so), then such models for the growth of structure may be ruled out. There is no such difficulty in open universes, since accretion declines after a time t₁/2_= H^-1^₀piOMEGA₀_/ (1 - OMEGA³/2^, nor is there a problem if OMEGA = 1 in the form of radiation, LAMBDA, or a hot component which would not accrete. Heating from satellite infall may account for a substantial fraction of the increase of velocity dispersion and scale height with age that is observed in our Galaxy. In addition, since the satellite infall events are discrete, the age-velocity dispersion relation should reflect this, and the velocity distribution will have a non-Gaussian tail, which will contribute to a thick disk.