A Radio-selected Population of Dark, Long Gamma-ray Bursts: Comparison to the Long Gamma-ray Burst Population and Implications for Host Dust Distributions

We present cm-band and mm-band afterglow observations of five long-duration $\gamma$-ray bursts (GRBs; GRB 130131A, 130420B, 130609A, 131229A, 140713A) with dust-obscured optical afterglow emission, known as "dark" GRBs. We detect the radio afterglow of two of the dark GRBs (GRB 130131A and 140713A), along with a tentative detection of a third (GRB 131229A) with the Karl G. Jansky Very Large Array (VLA). Supplemented by three additional VLA-detected dark GRBs from the literature, we present uniform modeling of their broadband afterglows. We derive high line-of-sight dust extinctions of $A_{V, \rm GRB} \gtrsim 2.2 - 10.6~{\rm mag}$. Additionally, we model the host galaxies of the six bursts in our sample, and derive host galaxy dust extinctions of $A_{V, \rm Host} \approx 0.3-4.7~{\rm mag}$. Across all tested $\gamma$-ray (fluence and duration) and afterglow properties (energy scales, geometries and circumburst densities), we find dark GRBs to be representative of more typical unobscured long GRBs, except in fluence, for which observational biases and inconsistent classification may influence the dark GRB distribution. Additionally, we find that $A_{V, \rm GRB}$ is not related to a uniform distribution of dust throughout the host, nor to the extremely local environment of the burst, indicating that a larger scale patchy dust distribution is the cause of the high line-of-sight extinction. Since radio observations are invaluable to revealing heavily dust-obscured GRBs, we make predictions for the detection of radio emission from host star formation with the next generation VLA.