A Study On The Braking Index And State Switching Mechanism Of Intermittent Pulsars

The discoveries of the intermittent pulsars bring both challenge and opportunity to the studies of the pulsar spin-down mechanism, magnetosphere configuration and emission mechanism. In this thesis, on the base of emission characteristics and spin-down features of the intermittent pulsars, we will focus on predicting their braking index in "on" state (radio emission is detected) and in "off" state (no emission is detected), and study their "on" and "off" state switching mechanism. The following briefly describes the main research work.The second chapter introduces a method to calculate the braking index of the intermittent pulsars on the base of pulsar wind braking model. The braking index is an important factor when examining the rotational energy losing and spin-down mechanism of pulsars. Measuring braking index requires measuring the pulsar spin period and its first and second derivatives. Among them the second derivative is easily contaminated by timing noise and an unresolved glitch effect-sudden jumps in spin frequency. 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, and that causes the failure of the braking index measurement of the intermittent pulsars. However, the observed period first derivatives in the "on" (radio-loud) and "off" (radio-quite) states of the intermittent pulsars give us a possible way to predict their braking indices even though they are hard to observe. 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 magneto-spheric cases 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 and they also met with the spin-down behavior and energy losing mechanism of these pulsars. This indicates the plausibility of our approach in predicting the braking index of intermittent pulsars only by the observed period first derivatives in the "on" and "off" state.Knowing the second braking index is as important as the braking index (the first braking index). The second braking index requires the measurement of period third derivative, in addition to the period second derivative. But, the failure of the measurement of the first braking index of the intermittent pulsars indicates that, at present, it is almost impossible to measure the second braking index. However, studying the second braking index under a model still make a sense. In the third chapter, by developing the method of calculating the first braking index in chapter 2, we put forward a method to calculate the second braking index of the intermittent pulsars. Similarly, in this chapter, we will calculate the second braking indices of these pulsars by only using the measured spin frequency first derivatives in the "on" and "off" states, under three different magnetospheric configuration changes, which include polar cap size, charge density and the combination of the above two cases. We have noted that our results are within the plausible range and meet with the spin-down behavior and energy losing mechanism of these pulsar. Moreover, It is also noted that our model and results are almost in agreement with the predictions of simple spin-down law. These results indicate that the methods to calculate the first and second braking index are consistent. This implies that our model may have a potential application to the study of the braking index (n,m) of intermittent pulsars.This chapter discusses the possible state switching mechanism of intermittent pulsars. Although the pulsar wind braking model seems to explain the different spin-down rate in the "on" and "off" state of intermittent pulsars, but it has a disadvantage to account for the state switching features of the intermittent pulsars due to the absence of particle acceleration mechanism in it. In general, without considering the particle acceleration mechanism in pulsar magnetosphere, it is hard to explain the observed radio emission features of pulsars. In order to match the observation, the vacuum gap particle acceleration mechanism is considered in the "on" state. The difference of the spin-down rate between "on" and "off" state is presumed as the variation of the relativistic particle flow in gap region with and without the particle acceleration mechanism. Then, the difference of the energy loss rate between "on" and "off" phases is attributed to the energy flux taken away by the accelerated particles in the vacuum gap region in "on" state. Under the possibility that the accelerated particle’s charge density equals to Goldreich-Julian charge density (ρGJ), the gap parameters of the four pulsars are studied. Results show that the gap potential, its height and the curvature radius of the magnetic field line almost met with the requirements of polar cap theory, and well match with the emission features and the P - P distributions of these pulsars. This not only indicates that the method we used is appropriate, but also shows that the charge density of the accelerated particles can have ρGJ-The obtained gap height and potential drops of these pulsars showed that the variations of these parameters around their maximum value can account for the state switching features of the intermittent pulsars.