Rotation curves from baryonic infall - Dependence on disk-to-halo ratio, initial angular momentum, and core radius, and comparison with data

Using a simple analytic model of the response of dark matter halos to the dissipative infall of the luminous material to form an exponential disk, we explore the dependence of the final rotation curves on all the relevant parameters: the ratio F = M_b_/M of the dissipative baryonic mass M_b_ to the total galaxy mass M including dark matter; the ratio b/R of the disk exponential scale length b to the truncation radius R (beyond which infall can be neglected); the core radius r_core_ of the isothermal halo in the absence of dissipation; and the dimensionless angular momentum parameter λ = J|E|^1/2^G^-1^M^-5/2^ (where J and E are the total angular momentum and energy of the galaxy). We explore in particular the final rotation curves expected in the tidal torque theory of angular momentum, in which <λ> ~ 0.05. For λ = 0.05, we find the final rotation curve to be flat when the gravitational effect of the infalling baryonic material on the dark halo is included and if F ~ 0.05, the value suggested by nucleosynthesis constraints if the Hubble parameter H_0_ ~ 50 km s^-1^ Mpc^-1^. Also, the mass inside a "Holmberg" radius R_H_ = 4.5b is about half luminous and half dark as observations indicate. These results are quite insensitive to r_core_ provided it is sufficiently large, and are characteristic of any theory in which <λ> ~ F. The key results are that for F ~ 0.05 the dispersion in λ expected in the tidal torque theory, 0.02 <~ λ <~ 0.1, (a) leads to rotation curves for bright galaxies whose systematics are much like those of the galaxies for which H I data are available when consistent baryonic disk scale lengths are used throughout; and (b) the mass inside R_H_ shows a spread of values consistent with observations except possibly for the smallest galaxies, which may have suffered significant gas loss. With this range of λ-values, the distribution of outer rotation curve slopes for a given maximum rotation velocity is inconsistent with the data if F is substantially larger or smaller than 0.05, or if r_core_/R is substantially smaller than 0.2.