The Star Formation Rate-Radius Connection: Data and Implications for Wind Strength and Halo Concentration

This paper is one in a series that explores the importance of radius as a second parameter in galaxy evolution. The topic investigated here is the relationship between star formation rate (SFR) and galaxy radius (Re) for main-sequence star-forming galaxies. The key observational result is that, over a wide range of stellar mass and redshift in both CANDELS and SDSS, there is little correlation between SFR and Re at fixed stellar mass. The Kennicutt-Schmidt law, or any similar density-related star formation law, then implies that smaller galaxies must have lower gas fractions than larger galaxies (at fixed M∗), and this is supported by observations of gas in local star-forming galaxies. We investigate the implications by adopting the equilibrium "bathtub"model: the ISM gas mass is assumed to be constant over time, and the net SFR is the difference between the accretion rate of gas onto the galaxy from the halo and the outflow rate due to winds. To match the observed null correlation between SFR and radius, the bathtub model requires that smaller galaxies at fixed mass have weaker galactic winds. Our hypothesis is that galaxies are a two-parameter family whose properties are set mainly by halo mass and concentration. These determine the radius and gas accretion rate, which in turn predict how wind strength needs to vary with Re to keep the SFR constant.