Title: The Connection between Molecular Gas and Star Formation in Extended Ultraviolet (XUV) 
Disk Galaxies

Abstract:
Star formation beyond the optical radius in galaxies allows us to test empirical relations in 
extreme conditions with low gas density and low molecular fraction. Previous studies discovered 
galaxies with extended ultraviolet (XUV) disks, which often contain star forming regions with 
lower Halpha-to-far-UV (FUV) flux ratios compared to inner disk star forming regions. However, 
most previous studies lack molecular gas, which is the component of the interstellar medium 
out of which stars form. We used the IRAM 30m telescope to measure a deep upper limit for 
the molecular hydrogen surface density (Sigma_H2) in one star forming region at 3.4 times the 
optical radius in the XUV disk of NGC 4625. We compared this Sigma_H2 measurement, as 
well as published Sigma_H2 measurements for six star forming regions in the XUV disk of NGC 
6946, to star formation rate surface densities derived from Halpha, FUV, and 24 micron data. 
We found that star forming regions in the XUV disks of NGC 4625 and NGC 6946 are consistent 
with the same molecular-hydrogen Kennicutt-Schmidt law that applies within the optical radius. 
Deeper data may enable us to use the presence or absence of molecular gas as an evolutionary 
probe to break the degeneracy between age and stochasticity as the explanation for the low 
Halpha-to-FUV flux ratios in XUV disks.