Dusty galaxies and the degeneracy between their dust distributions and
  the attenuation formula
  Do spatial distributions of dust grains in galaxies have typical forms, as do
spatial distributions of stars? We investigate whether or not the distributions
resemble uniform foreground screens, as commonly assumed by the high-redshift
galaxy community. We use rest-frame infrared, ultraviolet, and H$\alpha$ line
luminosities of dust-poor and dusty galaxies at z ~ 0 and z ~ 1 to compare
measured H$\alpha$ escape fractions with those predicted by the Calzetti
attenuation formula. The predictions, based on UV escape fractions,
overestimate the measured H$\alpha$ escape fractions for all samples. The
interpretation of this result for dust-poor z ~ 0 galaxies is that regions with
ionizing stars have more dust than regions with nonionizing UV-emitting stars.
Dust distributions for these galaxies are nonuniform. The interpretation of the
overestimates for dusty galaxies at both redshifts is less clear. If the
attenuation formula is inapplicable to these galaxies, perhaps the
disagreements are unphysical; perhaps dust distributions in these galaxies are
uniform. If the attenuation formula does apply, then dusty galaxies have
nonuniform dust distributions; the distributions are more uniform than they are
in dust-poor galaxies. A broad range of H$\alpha$ escape fractions at a given
UV escape fraction for z ~ 1 dusty galaxies, if real, indicates diverse dust
morphologies and the implausibility of the screen assumption.
