Modeling the effects of star formation histories on H$\alpha$ and ultraviolet fluxes in nearby dwarf galaxies

Abstract

We consider the effects of non-constant star formation histories (SFHs) on $\text{H}\alpha$ and GALEX far-ultraviolet (FUV) star formation rate (SFR) indicators. Under the assumption of a fully populated Chabrier initial mass function (IMF), we compare the distribution of $\text{H}\alpha$-to-FUV flux ratios from ~1500 simple, periodic model SFHs with observations of 185 galaxies from the $\textit{Spitzer}$ Local Volume Legacy survey. We find a set of SFH models that are well matched to the data, such that more massive galaxies are best characterized by nearly constant SFHs, while low-mass systems experience burst amplitudes of ~30 (i.e., an increase in the SFR by a factor of 30 over the SFR during the inter-burst period), burst durations of tens of Myr, and periods of ~250 Myr; these SFHs are broadly consistent with the increased stochastic star formation expected in systems with lower SFRs. We analyze the predicted temporal evolution of galaxy stellar mass, R-band surface brightness, $\text{H}\alpha$-derived SFR, and blue luminosity, and find that they provide a reasonable match to observed flux distributions. We find that our model SFHs are generally able to reproduce both the observed systematic decline and increased scatter in $\text{H}\alpha$-to-FUV ratios toward low-mass systems, without invoking other physical mechanisms. We also compare our predictions with those from the Integrated Galactic IMF theory with a constant SFR. We find that while both predict a systematic decline in the observed ratios, only the time variable SFH models are capable of producing the observed population of low-mass galaxies $\big(M_{*} \lesssim 10^{7} M_{\odot}\big)$ with normal $\text{H}\alpha$-to-FUV ratios. These results demonstrate that a variable IMF alone has difficulty explaining the observed scatter in the $\text{H}\alpha$-to-FUV ratios. We conclude by considering the limitations of the model SFHs and discuss the use of additional empirical constraints to improve future SFH modeling efforts.