The Baryonic Tully-Fisher Relationship for S$^4$G Galaxies and the
  "Condensed" Baryon Fraction of Galaxies
  We combine data from the Spitzer Survey for Stellar Structure in Galaxies
(S$^4$G), a recently calibrated empirical stellar mass estimator from Eskew et
al., and an extensive database of HI spectral line profiles to examine the
baryonic Tully-Fisher (BTF) relation. We find 1) that the BTF has lower scatter
than the classic Tully-Fisher (TF) relation and is better described as a linear
relationship, confirming similar previous results, 2) that the inclusion of a
radial scale in the BTF decreases the scatter but only modestly, as seen
previously for the TF relation, and 3) that the slope of the BTF, which we find
to be $3.5\pm 0.2$ ($\Delta$ log $M_{baryon}/\Delta$ log $v_c$), implies that
on average a nearly constant fraction ($\sim 0.4$) of all baryons expected to
be in a halo are "condensed" onto the central region of rotationally supported
galaxies. The condensed baryon fraction, $M_{baryon}/M_{total}$, is, to our
measurement precision, nearly independent of galaxy circular velocity (our
sample spans circular velocities, $v_c$, between 60 and 250 km s$^{-1}$, but is
extended to $v_c\sim 10$ km s$^{-1}$ using data from the literature). The
observed galaxy-to-galaxy scatter in this fraction is generally $\le$ a factor
of 2 despite fairly liberal selection criteria. These results imply that
cooling and heating processes, such as cold vs. hot accretion, mass loss due to
stellar winds, and AGN driven feedback, to the degree that they affect the
global galactic properties involved in the BTF, are independent of halo mass
for galaxies with $10 < v_c < 250$ km/s and typically introduce no more than a
factor of two range in the resulting $M_{baryon}/M_{total}$. Recent simulations
by Aumer et al. of a small sample of disk galaxies are in excellent agreement
with our data, suggesting that current simulations are capable of reproducing
the global properties of individual disk galaxies.
