The discrete change in spin-down rate between the on and off states suggests a switching behaviour in the pulsar magnetosphere. While explanation for the phenomenon remains inconclusive, conventional treatments typically involve referring each emission state to different condition in the magnetosphere in such a way that a plasma-filled magnetosphere is related to the emission-on state and a sudden depletion of charge particles is responsible for the decrease in the spin-down rate during the emission-off state (Contopoulos 2005; Kramer et al. 2006; Beskin & Nokhrina 2007; Li et al. 2012). Kramer et al. (2006) and Beskin & Nokhrina (2007) suggest that energy loss of PSR B1931 + 24 is due only to the rotating dipole during the emission-off state where there is no current flowing, whereas current loss is responsible for the energy loss during the emission-on state. In this scenario, pulses are undetectable due to decrease in the plasma density in the emitting region to a magnetospheric state so that the pulse intensity of the pulsar decreases when it jumps to that state and resumes to its normal intensity when it returns to its initial state. While the approach has revealed unprecedented information about the pulsars, it implicitly treats the two emission states as independent entities with presumed vacuum condition for the emission-off state. Our investigation is based on a magnetospheric model that synthesizes the corotating magnetosphere model and the vacuum model (Melrose & Yuen 2014, 2016), in which multiple quasi-stable magnetospheric states are described by the parameter y such that the charge filling fraction of a state corresponds to a y value and a change in the charge filling fraction corresponds to a change of state which is signified by a change in y. The presence of plasma in the corotating magnetosphere model implies a global current flow that closes at the stellar surface within the polar cap region. By considering a simple framework for the spin-down torque as induced by the component of the global current that crosses the magnetic fields at the stellar surface, we show that discrete changes in the spin-down rates may be attributed to changes in the pulsar torque caused by variations in the global current flow when jumping takes place between different magnetospheric states in the pulsar magnetosphere. Using this idealized model, characteristics of intermittent pulsars are studied by jointly considering the two emission states based on the parameters y and α, the obliquity angle between the magnetic and rotation axes, through the ratio of the respective spin-down rate whose changes are described by the ratio of the corresponding spin-down torque in the two states. The yet unidentified links between intermittent and ordinary pulsars imply that, in addition to the parameters already under detailed examination in the literature, there may exist unknown factors that are distinctly related to intermittency and likely to be pulsar-specific. An obvious example is the large differences in the emission-on and -off cycles which range from days (Kramer et al. 2006) to years (Camilo et al. 2012). Since the correlation between these parameters and intermittency is still unclear, before including such factors, it is useful to explore the implications of the idealized model.
Citation: Melrose & Yuen 2014
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