We present predictions of centimeter and millimeter radio emission from reverse shocks in the early afterglows of gamma-ray bursts with the goal of determining their detectability with current and future radio facilities. Using a range of GRB propert
ies, such as peak optical brightness and time, isotropic equivalent gamma-ray energy and redshift, we simulate radio light curves in a framework generalized for any circumburst medium structure and including a parametrization of the shell thickness regime that is more realistic than the simple assumption of thick- or thin-shell approximations. Building on earlier work by Mundell et al. (2007) and Melandri et al. (2010) in which the typical frequency of the reverse shock was suggested to lie at radio, rather than optical wavelengths at early times, we show that the brightest and most distinct reverse-shock radio signatures are detectable up to 0.1 -- 1 day after the burst, emphasizing the need for rapid radio follow-up. Detection is easier for bursts with later optical peaks, high isotropic energies, lower circumburst medium densities, and at observing frequencies that are less prone to synchrotron self-absorption effects - typically above a few GHz. Given recent detections of polarized prompt gamma-ray and optical reverse-shock emission, we suggest that detection of polarized radio/mm emission will unambiguously confirm the presence of low-frequency reverse shocks at early time.
We use a parent sample of 118 gamma-ray burst (GRB) afterglows, with known redshift and host galaxy extinction, to separate afterglows with and without signatures of dominant reverse-shock emission and to determine which physical conditions lead to a
prominent reverse-shock emission. We identify 10 GRBs with reverse shock signatures - GRBs 990123, 021004, 021211, 060908, 061126, 080319B, 081007, 090102, 090424 and 130427A. By modeling their optical afterglows with reverse and forward shock analytic light curves and using Monte Carlo simulations, we estimate the parameter space of the physical quantities describing the ejecta and circumburst medium. We find that physical properties cover a wide parameter space and do not seem to cluster around any preferential values. Comparing the rest-frame optical, X-ray and high-energy properties of the larger sample of non-RS-dominated GRBs, we show that the early-time ($<$ 1ks) optical spectral luminosity, X-ray afterglow luminosity and $gamma$-ray energy output of our reverse-shock dominated sample do not differ significantly from the general population at early times. However, the GRBs with dominant reverse shock emission have fainter than average optical forward-shock emission at late time ($>$ 10 ks). We find that GRBs with an identifiable reverse shock component show high magnetization parameter $R_{mathrm{B}} = varepsilon_{rm B,r}/varepsilon_{rm B,f} sim 2 - 10^4$. Our results are in agreement with the mildly magnetized baryonic jet model of GRBs.
