Abstract
The number of sudden spin-ups in radio pulsars known as pulsar glitches has increased over the years. Though a consensus has not been reached with regards to the actual cause of the phenomenon, the electromagnetic braking torque on the crust quantified via the magnitude of pulsar spin frequency first derivative, \(\dot{\nu } \) is a key factor in mechanisms put across toward the understanding of the underlying principles involved. The glitch size has been used to establish a quantity used to constrain the mean possible change in pulsar spin frequency \((\nu ) \) per year due to a glitch known as the ‘glitch activity’. Traditionally, the glitch activity parameter \(A_{g} \) is calculated from the cumulative glitch sizes in a pulsar at a certain observational time span. In this analysis, we test the possibility of quantifying the \(A_{g} \) with the pulsars main spin frequency derivatives (i.e. \(\dot{\nu } \) and \(\ddot{\nu } \)). In this approach, the ratio of the frequency derivatives, i.e. \(|\ddot{\nu }|/\dot{\nu }^{2} \) is seen to constrains the glitch activity in radio pulsars. The glitch size is found to be independent of the magnitude of the ratio, however, based on the recorded glitch events, the lower end of \(|\ddot{\nu }|/\dot{\nu }^{2} \) distribution appear to have more glitches. The minimum inter-glitch time interval in the ensemble of pulsars scale with the ratio as \(t_{g} \sim 3.35(|\ddot{\nu }|/\dot{\nu }^{2})^{0.23} \). The \(A_{g} \) quantified in this analysis supports the idea of neutron star inner-crust superfluid being the reservoir of momentum transferred during glitches. It suggests that the moment of inertia of the inner-crust to be at most 10% of the entire neutron star moment of inertia.
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Data Availability
The pulsar glitch data is from (Espinoza et al. 2011) and the Jodrell Bank Observatory (JBO) pulsar glitch catalogue, which is readily available at http://www.jb.man.ac.uk/pulsar/glitches.html and references therein. The pulsar spin parameters are from the Australia Telescope National Facility (ATNF) pulsar catalogue, which is readily available at http://www.atnf.csiro.au/people/pulsar/psrcat and references therein.
Notes
Age as used here is the assumed spin-down time (\(\tau _{c} = \frac{\nu }{2\dot{\nu }} \)) of pulsar known as the characteristic age.
Other higher terms of frequency derivatives are neglected.
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Acknowledgements
We wish to thank the anonymous reviewer whose suggestions led to a salient result unimagined to us. That is the possibility of constraining the FMI with FDR. We are grateful to you.
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I.O. Eya is the Principal Investigator and the corresponding author. He and other authors contributed in the interpretation of the results and in writing of the paper.
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Eya, I.O., Alhassan, J.A., Iyida, E.U. et al. On the pulsar spin frequency derivatives and the glitch activity. Astrophys Space Sci 367, 28 (2022). https://doi.org/10.1007/s10509-022-04059-0
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DOI: https://doi.org/10.1007/s10509-022-04059-0