Radio Properties of Rotating Radio Transients: Single Pulse Spectral and Wait Time Analyses

Rotating radio transients (RRATs) are a sub-class of pulsars characterized by sporadic emission and thus can generally only be studied by analysis of their single-pulses. Here we present a single-pulse analysis using 11 years of timing data at 1400~MHz of three RRATs, PSRs~J1819$-$1458, J1317$-$5759, and J1913$+$1330. We perform a spectral analysis on the single-pulses of these RRATs for the first time, finding their mean spectral indices to be $-1.1 \pm 0.1$, $-0.6 \pm 0.1$, and $-1.2 \pm 0.2$ respectively, within the known range of pulsar spectral indices. We find no evidence for narrowband features as seen for FRB~121102. However, we find the spread of single-pulse spectral indices for these RRATs (ranging from $-7$ to $+4$) to be larger than has been seen in other pulsars, with the exception of the Crab pulsar. We also analyze the time between detected pulses, or wait-time, and find that the pulses are not random and cluster around wait-times of a few pulse periods as well as $\sim 25$ pulse periods for PSRs~J1819$-$1458 and J1317$-$5759. Additionally we find that there is no correlation between the wait-time and pulse flux density. Finally we find that the distribution of the pulse energy for PSRs~J1317$-$5759 and J1913$+$1330 are log-normal, while that of PSR~J1819$-$1458 is log-normal with possible evidence of an additional power-law component.