The results from a systematic study of eleven 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, Edot. A logarithmic linear fit between the two parameters yields log r = (0.57 +- 0.22) log Edot -22.3 +- 8.0 with a correlation coefficient of 0.82, where the units of r and Edot are pc and ergs s^-1, respectively. The value obtained for the Edot 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.
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