1209.2478 (Shuang-Nan Zhang et al.)

Why do the braking indices of pulsars span over more than 100 millions?    [PDF]

Shuang-Nan Zhang, Yi Xie

Here we report that the observed braking indices of the 366 pulsars in the sample of Hobbs et al. (2012) span from about $-10^8$ to about $+10^8$ and are significantly correlated with their characteristic ages. Using the model of magnetic field evolution we developed previously (Zhang & Xie 2012) based on the same data, we derived an analytical expression of the braking index, which agrees with all the observed statistical properties of the braking indices of the pulsars in the sample of Hobbs et al. (2012). Our model is, however, incompatible to the previous interpretation that the magnetic field growth is responsible for the observed small values of braking indices ($<3$) of "baby" pulsars with characteristic ages of less than $2\times 10^3$ yr. We find that the "instantaneous" braking index of a pulsar may be different from the "averaged" braking index obtained from fitting the data over a certain time span. The close match between our model predicted "instantaneous" braking indices and the observed "averaged" braking indices suggests that the time spans used previously are usually smaller than or comparable to their magnetic field oscillation periods. Our model can be tested with the existing data, by calculating the braking index as a function of the time span for each pulsar. In doing do, one can obtain for each pulsar all the parameters in our magnetic field evolution model, and may be able to improve the sensitivity of using pulsars to detect gravitational waves.

View original: http://arxiv.org/abs/1209.2478