We present a comprehensive analysis of the relationship between star formation rate surface density , \Sigma _ { SFR } , and gas surface density , \Sigma _ { gas } , at sub–kpc resolution in a sample of 18 nearby galaxies .
We use high resolution H i data from THINGS , CO data from HERACLES and BIMA SONG , 24 µm data from the Spitzer Space Telescope , and UV data from GALEX .
We target 7 spiral galaxies and 11 late-type/dwarf galaxies and investigate how the star formation law differs between the H _ { 2 } -dominated centers of spiral galaxies , their H i -dominated outskirts and the H i -rich late-type/dwarf galaxies .
We find that a Schmidt-type power law with index N = 1.0 \pm 0.2 relates \Sigma _ { SFR } and \Sigma _ { H 2 } across our sample of spiral galaxies , i.e. , that H _ { 2 } forms stars at a constant efficiency in spirals .
The average molecular gas depletion time is \sim 2 \cdot 10 ^ { 9 } years .
The range of \Sigma _ { H 2 } over which we measure this relation is \sim 3 - 50 M _ { \odot } pc ^ { -2 } , significantly lower than in starburst environments .
We find the same results when performing a pixel-by-pixel analysis , averaging in radial bins , or when varying the star formation tracer used .
We interpret the linear relation and constant depletion time as evidence that stars are forming in GMCs with approximately uniform properties and that \Sigma _ { H 2 } may be more a measure of the filling fraction of giant molecular clouds than changing conditions in the molecular gas .
The relationship between total gas surface density ( \Sigma _ { gas } ) and \Sigma _ { SFR } varies dramatically among and within spiral galaxies .
Most galaxies show little or no correlation between \Sigma _ { HI } and \Sigma _ { SFR } .
As a result , the star formation efficiency ( SFE ) , \Sigma _ { SFR } / \Sigma _ { gas } , varies strongly across our sample and within individual galaxies .
We show that this variation is systematic and consistent with the SFE being set by local environmental factors : in spirals the SFE is a clear function of radius , while the dwarf galaxies in our sample display SFEs similar to those found in the outer optical disks of the spirals .
We attribute the similarity to common environments ( low-density , low-metallicity , H i -dominated ) and argue that shear ( which is typically absent in dwarfs ) can not drive the SFE .
In addition to a molecular Schmidt law , the other general feature of our sample is a sharp saturation of H i surface densities at \Sigma _ { HI } \approx 9 M _ { \odot } pc ^ { -2 } in both the spiral and dwarf galaxies .
In the case of the spirals , we observe gas in excess of this limit to be molecular .