Predicting the Braking Indices of Nulling and Intermittent Pulsars

The braking index is an important factor when examining the pulsar braking mechanism. Measuring braking indices requires measuring the pulsar period and its first and second derivatives. Among them, the second derivative is easily contaminated by timing noise and an unresolved glitch effect. The absence of data bounding a given transition into (or out of) a radio-on phase is another disadvantage in measuring the second derivatives of intermittent pulsars, as was recently demonstrated by Young and coworkers. But, the observed period first derivatives, in the on and off states of the intermittent pulsars, give us a possible way to predict their braking indices even though they are hard to observe. In this paper, we will give a simple and useful method to study the braking indices of intermittent pulsars. As an application of our method, we will calculate the possible braking indices of three intermittent pulsars and one nulling pulsar, namely, PSR B1931 + 24, PSR J1841 0500, PSR J1832 + 0029 and PSR B0823 + 26, under three different magnetospheric conditions, which include polar cap size variation, charge density variation and the combination of the above two cases. We have found that all the braking indices we predicted are almost within the observed domain It is concluded that, in a relatively short observation period, in which the variation of the braking index can be ignored, we can accurately predict the braking indices of intermittent pulsars, under a specific magnetosphere model, by using the observed on and off state period first derivatives.