The far-UV Interstellar Radiation Field in Galactic Disks: Numerical and Analytic Models

The intensity of the far-ultraviolet (FUV; 6-13.6 eV) interstellar radiation field (ISRF) in galaxies determines the thermal and chemical evolution of the neutral interstellar gas and is key for interpreting extragalactic observations and for theories of star-formation. We run a series of galactic disk models and derive the FUV ISRF intensity as a function of the dust-to-gas ratio, star-formation rate density, gas density, scale radius, and observer position. We develop an analytic formula for the median FUV ISRF flux. We identify two dimensionless parameters in the problem: (1) the dimensionless galactic radius, $X$, which measures the radial extent of FUV sources (OB stellar associations) in the disk; (2) the opacity over the inter-source distance, $\tau_{\star}$, which measures the importance of dust absorption. These parameters encapsulate the dependence on all of the physical parameters. We find that there exists a critical $\tau_{\star}$, or equivalently a critical dust-to-gas ratio, $Z_{d,{\rm crit}}' \approx 0.01-0.1$ the Milky Way value, at which the ISRF changes behavior. For $Z'_d>Z_{d,{\rm crit}}'$ the ISRF is limited by dust absorption. With decreasing $Z'_d$, the ISRF intensity increases as more sources contribute to the flux. For $Z'_d < Z_{d,{\rm crit}}'$ the ISRF saturates as the disk becomes optically thin. We find that the ISRF per star-formation rate density in low metallicity systems, such as dwarf and high redshift galaxies, is higher by up to a factor of 3-6 compared to their Milky-Way counterparts. We discuss implications to the potential mechanisms that regulate star-formation in low metallicity galaxies.