Super-giant pulses from the Crab pulsar : Energy distribution and occurrence rate

We present statistical analysis of a fluence limited sample of over 1100 giant pulses from the Crab pulsar, with fluence > 130 Jy ms at ~1330 MHz. These were detected in ~260 hours of observation with the National Centre for Radio Astrophysics (NCRA)-15m radio telescope. We find that the pulse energy distribution follows a power law with index $\alpha\approx$-3 at least up to a fluence of ~5 Jy s. The power law index agrees well with that found for lower energy pulses in the range 3-30 Jy ms. The fluence distribution of the Crab pulsar hence appears to follow a single power law over ~3 orders of magnitude in fluence. We do not see any evidence for the flattening at high fluences reported by earlier studies. We also find that at these fluence levels, the rate of giant-pulse emission varies by as much as a factor of ~5 on time-scales of a few days, although the power law index of the pulse-energy distribution remains unchanged. The slope of the fluence distribution for Crab giant pulses is similar to that recently determined for the repeating FRB 121102. We also find an anti-correlation between the pulse fluence and the pulse width, so that more energetic pulses are preferentially shorter.