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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 $3.5\pm 0.2$ ($Δ$ log $M_{baryon}/Δ$ 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.