2010ApJ...709..507B

The results from a systematic study of 11 pulsar wind nebulae with a torus structure observed with the Chandra X-ray Observatory are presented. A significant observational correlation is found between the radius of the tori, r, and the spin-down luminosity of the pulsars, {dot}E. A logarithmic linear fit between the two parameters yields log r = (0.57±0.22) log {dot}E -22.3 ±8.0 with a correlation coefficient of 0.82, where the units of r and {dot}E are pc and ergs/s, respectively. The value obtained for the {dot}E dependency of r is consistent with a square-root law, which is theoretically expected. This is the first observational evidence of this dependency, and provides a useful tool to estimate the spin-down energies of pulsars without direct detections of pulsation. Applications of this dependency to some other samples are also shown.