Radio efficiency of pulsars

Abstract: We investigate radio emission efficiency $\xi$ of pulsars and report a near linear inverse correlation between $\xi$ and the spindown power $\dot E$, as well as a near linear correlation between $\xi$ and pulsar age $\tau$. This is a consequence of very weak, if any, dependences of radio luminosity $L$ on pulsar period $P$ and period derivative $\dot{P}$, in contrast to X-ray or $\gamma$-ray emission luminosities. The analysis of radio fluxes suggests that these correlations are not due to a selection effect, but are intrinsic to the pulsar radio emission physics. We have found that, although with a large variance, the radio luminosity of pulsars is $\left<L\right>\approx 10^{29} \,{\rm erg/s}$, regardless of the position in the $P-\dot P$ diagram. Within such a picture, a model-independent statement can be made that the death line of radio pulsars corresponds to an upper limit in the efficiency of radio emission. If we introduce the maximum value for a radio efficiency into Monte Carlo-based population syntheses we can reproduce the observed sample using the random luminosity model. The Kolmogorov-Smirnov test on a synthetic flux distribution shows high probability of reproducing the observed distribution. Our results suggests that the plasma responsible for generating radio emission is produced under similar conditions regardless of pulsar age, dipolar magnetic field strength, and spin-down rate. The magnetic fields near the pulsar surface are likely dominated by crust-anchored magnetic anomalies, which do not significantly differ among pulsars, leading to similar conditions for generating electron-positron pairs necessary to power radio emission.