A Sample of Low-energy Bursts from FRB 121102

We present 41 bursts from the first repeating fast radio burst (FRB) discovered (FRB 121102). A deep search has allowed us to probe unprecedentedly low burst energies during two consecutive observations (separated by one day) using the Arecibo telescope at 1.4 GHz. The bursts are generally detected in less than one-third of the 580 MHz observing bandwidth, demonstrating that narrowband FRB signals may be more common than previously thought. We show that the bursts are likely faint versions of previously reported multi-component bursts. There is a striking lack of bursts detected below 1.35 GHz and simultaneous Very Large Array observations at 3 GHz did not detect any of the 41 bursts, but did detect one that was not seen with Arecibo, suggesting preferred radio emission frequencies that vary with epoch. A power-law approximation of the cumulative distribution of burst energies yields an index -1.8 +/- 0.3, which is much steeper than the previously reported value of similar to -0.7. The discrepancy may be evidence for a more complex energy distribution. We place constraints on the possibility that the associated persistent radio source is generated by the emission of many faint bursts (similar to 700 ms(-1)). We do not see a connection between burst fluence and wait time. The distribution of wait times follows a log-normal distribution centered around similar to 200 s; however, some bursts have wait times below 1 s and as short as 26 ms, which is consistent with previous reports of a bimodal distribution. We caution against exclusively integrating over the full observing band during FRB searches, because this can lower signal to noise.