New insight into the physical essence of pulsar glitch☆
Introduction
The observed pulsar rotation periods often show that some young pulsars experience one or more glitches, which correspond to sudden jumps of rotation frequency () and its derivative () of pulsars. It is assumed that glitches could caused by an abrupt transfer of angular momentum from the interior superfluid to the crust of pulsars, however the origin of which remains not well understood yet, partly because the jump processes of most glitches are not well time-resolved. These events offer an opportunity investigating the interior structure of pulsars. The regular pulse signals could be occasionally shortened by glitches at typical amplitude of . These glitches are usually accompanied by a spin-down effect at a much larger rate Lyne et al. (2000); Yuan, 2010a, Yuan, 2010b; Zou (2004); Yuan (2017); Zou (2008). Some pulsars, such as PSRs J1722-3632, J1852-0635 undergo giant glitches of approximately regular size with Espinoza et al. (2011); Dang (2020); Wang (2012); Liu (2019). However, some of the youngest pulsars such as the Crab have smaller glitches with Ge (2020). The archetypal glitch neutron star is the Vela pulsar, which has exhibited a regular sequence of similarly sized glitches since the first observed event in 1969. The Pulsar glitch Catalog maintained by Jodrell Bank Center for Astrophysics suggests that 555 glitches have been observed from 190 pulsars, so far, and more than 120 glitches among them detected in eight of the glitch pulsars are great glitches with . Besides such macro glitches, some micro-glitches with jump amplitudes less than are detected. Observations with Nanshan Radio telescope show that the observational features of glitches are varied and their post-glitch behaviors show different decayKou (2018). The spin-down state change and mode change could be associated with glitch activity, which triggers the magnetic field decay and the plasma fluctuation Kou (2018); Gao (2021); Yan (2021); Fu (2020); Deng (2020); Wen, 2016, Wen, et al., 2020a, Wen, 2020b.
The most important observational statistics of pulsar glitch phenomena up to date are given as follows:
(1) There is a rough tendency for both the jump amplitude and the frequency of glitches to decrease with the pulse period as the pulsar ages Lyne et al. (2000). From Table 2 of Lyne et al.,(2000)Lyne et al. (2000), we can see that the most pulsars glitches have been detected with periods no longer than 0.7 s except for PSR B0525+21 (J0528+2200). Another example would be PSR J1814-1744 that has a long period of 3.9759 s for which a total of 7 glitches have been observed. Recently, Eya et al. (2019)Eya (2019) analyzed the glitch sizes and inter-glitch time intervals statistically in a sample of 168 pulsars with a total of 483 glitches.
(2) The glitch phenomenon is concentrated in a population of young pulsars with strong magnetic fields Lyne et al. (2000); Gao (2021); Yan (2021). The younger the pulsars, the larger frequency and the amplitude of the glitch becomes. The stronger the strong magnetic fields of the pulsar, the more frequenter the glitch occurred, and the greater the amplitude of glitch is Kou (2018).
(3) About a slow pulsar glitch, it is usually observed as a sudden change with very short timescale. However, a slow glitch with a timescale of several days was observed in 2005 (e.g.,Eya (2019)).
(4) Middleditch et al., (2006)Middleditch et al. (2006) discovered that the young pulsar PSR J0573-6910 in the Large Magellanic Cloud (LMC) underwent glitches with amplitude change roughly proportional to the time separation between two successive glitches after ten years of observation to monitor the radio pulsar period. Although no this rule has been found for most pulsars,the monitor of this young pulsar is the most complete. In a word, the above observational facts cannot be explained by any of current glitch models.
The consensus view about pulsar glitch is that these events are a manifestation of the presence of superfluid components inside the starRuderman (1969). This idea was first put forward by Anderson et al. (1975)Anderson and Itoh (1975). Several theoretical models of pulsar glitch are given as follows:
(1) The starquake model
One mechanism for explaining glitches in young pulsars is that they are caused by starquakes, a sudden rearrangement of the pulsar crust Pines et al. (1972); Takatsuka and Tamagaki (1997); Baym and Pines (1971). However, this model can not produce enough energy release to account for the largest glitches, such as those of the Vela pulsar. Negi (2006) proposed a starquake model and then constructed neutron star sequences and explained glitches for the Crab and the Vela pulsars Negi (2011).
(2) Oscillation model of the neutron star core
Glitches are likely to excite oscillation modes of the star, making them an interesting candidate source for gravitational wave emissionEichler and Shaisultanov (2010); Van Eysden (2014). In this model, a glitch may appear every several years with energy release erg. Zhang. (2015)Zhang (2015) investigated a physical model of pulsars as gravitational shielding and oscillating neutron stars. His results showed that the process by which periodically oscillating X-rays are emitted from hot spots on the inner edge of the accretion disk remains a mystery Keer and Jones (2015) discussed a model for neutron star oscillations following a starquake, and made upper estimates of the amplitude of the oscillations and the corresponding gravitational wave emission.
(3) A creep model of vortex filament by an action of shell-superfluid coupling
Pulsar glitches could be caused by the motion of superfluid vortex lines, and these lines tend to be pinned to nuclei pf stellar crust and sudden, large-scale creep of these lines from one pinning site to another can be responsible for glitches (e.g., Alpar et al. (1981); Andersson et al. (2003); Anderson and Itoh (1975); Link, Epstein, Lattimer, 1999, Link, Epstein, Baym, 1993). In this model, the key idea is that the roots of the superfluid vortices slide randomly in the inner shell, and occasionally they are pinned to the heavy nucleus. This model has been now regarded as the mainstream model by most researchers (e.g.,Link et al. (1993); Haskell and Melatos. (2015)). However, it is difficult for this model to explain huge glitches of the Vela pulsar. In addition, in this model there are too many free parameters, which are rather difficult to be determined to explain a series of observational facts of neutron star glitches.
(4) A model considering the effect of neutron superfluid vortex filament and proton superconducting flux tube
In order to study the relationship between the neutron star magnetic field evolution, crust movement, and glitches, Ruderman et al. (1998)Ruderman et al. (1998) proposed a magnetic tube model for pulsar glitch. Their results showed that spinning superfluid neutrons in the core of a neutron star interacted strongly with coexisting superconducting protons. In view of the fact that the spin axis of a pulsar does not coincide with its magnetic axis, the two-component model (i.e., neutron superfluid vorticestangled with proton superconducting magnetic flux tube) predicted the procession of spin axis of the star with a periods of few seconds Espinoza et al. (2011); Link (2003); Rezania (2003). This model has been seriously doubted Link (2003), because it’s difficult to explain the observed glitches.
Mastrano et al. (2005)Mastrano. and Melatos. (2005) investigated Kelvin-Helmholtz instability and circulation transfer at an isotropic-anisotropic superfluid interface in a neutron star. However, further explanations of many observed pulsar glitches are needed for their theory. A series of studies concerning on the glitches of the Vela pulsar have been conducted by some authors Mastrano. and Melatos. (2005); Chamel (2014). They considered the coupling of the crust withthe superfluid inside the star, although they did not investigate the mechanism by which pulsars produce glitches. Piekarewicz et al. (2014)Piekarewicz et al. (2014) believed that the Vela pulsar glitch phenomenon can be explained by the properties of nuclear matter in the inner crust of neutron stars. They have not yet discussed how to explain the series of glitches observed in pulsars and their statistical properties.
Magnetars are mostly young pulsars powered by the decay of their conspicuous magnetic field rather than the loss of their rotational energy Deng (2021); Wang (2020); Gao, 2019a, Gao, 2019b, Gao, 2017a. Ordinarily with respect to a rotation-powered pulsar with a similar characteristic age, glitches in magnetars should be smaller compared to what is observed, as such, there could be a contribution of magnetospheric activity to their glitch sizes. There could be a change in external braking torque accompanied by the glitch activity. As the dipole magnetic field strength increases, the pulsar’s braking index decreases due to an increasing braking torque and vice versa Eya (2019). A change in braking torque affects the magnetic field structure, which in turn affects the inclination angle. If this effect results from fluctuations in particle density outflow in the magnetosphere, fluctuation in the inclination angle should lead to changes in magnetic field structure, further leading to radiative changes accompanying a glitch Gao (2017b); Liu, Liu, 2017a, Liu, Liu, 2018a, Liu, Liu, 2018b, Liu, Liu, 2020. However, the physical causes for the pulsar glitches are still not well-known and it is one of the most difficult puzzling topics in pulsar researches.
Here, we propose a new physical mechanism for generating glitches, which is completely different from the existing known models. The reminder of thus paper is organized as follows. In Section 2, we study the anisotropic superfluid vortex motion in neutron star interiors. In Section 3, we summarize our researches and discuss the cooling and heating problem in neutron star interiors. In Section 4, we present our model and analyze the glitch properties. Some discussions and conclusions are given in Section 5.
Section snippets
The anisotropic superfluid vortex motion in neutron star interiors
There are two types of superfluid with different properties between the thin crust and the interior of a neutron star. When the density is , the superfluid is isotropic. The binding energy (i.e., the energy gap) of the cooper pairs for the state can reach MeV. The total spin of the Cooper pair is zero and there is no net magnetic moment.
When the internal temperature of a neutron star decreases to below K, the neutron fluid will change from the
Our researches on neutron stars
We proposed a theory Peng (1982)that the neutrino radiation by neutron superfluid vortices of neutron stars is a decisive factor for spin down of pulsars with longer periods ( s) and the rate of spin down, , is proportional to , which was repeatedly supported by statistical works of pulsars from some papers Malov, 1985, Malov, 1987, Malov, 2001. This theory is also confirmed by the recent observed () diagram of pulsars (ATNF Pulsar Catalogue, 2021 see Fig. 1), (we can see the link
Our model and the properties of pulsar glitches
In 2006, we proposed a phase oscillation model between normal neutron fluid and neutron superfluid vortex state to explain pulsar glitches, especially to explain large glitches in very young pulsars Zou (2008). Based on Eq. (18), we improve the above original model to reinterpret the pulsar glitch phenomena.
Conclusions
Based on our previous work, we proposed a new oscillation model to explain glitch phenomena for young pulsars. According to our model, the pulsar glitches are a repeat phenomena due to oscillating from the anisotropic neutron superfluid phase to the phase, and then to the phase (many repeated glitches with quasi-period). During the oscillation, the vortex quantum number of the neutron superfluid is gradually reduced, and the heating rate in the phase also gets lower and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was supported in part by the NSFC under grants 11965010, 11565020, and the Natural Science Foundation of Hainan Province under grants 2019RC239, 118MS071, 114,012 and the Counterpart Foundation of Sanya under grant 2016PT43, 2019PT76, the Special Foundation of Science and Technology Cooperation for Advanced Academy and Regional of Sanya under grant 2016YD28, the Scientific Research Starting Foundation for 515 Talented Project of Hainan Tropical Ocean University under grant RHDRC201701.
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This work was supported in part by the National NSFC under grants 11965010 and 11565020, and the foundation for high-level talents program of Hainan basic and applied basic research program (natural science) under grant 2019RC239, and the Natural Science Foundation of Hainan Province under grant 118MS071, 114012 and the Counterpart Foundation of Sanya under grant 2016PT43, 2019PT76, the Special Foundation of Science and Technology Cooperation for Advanced Academy and Regional ofSanya under grant 2016YD28, the Scientific Research Starting Foundation for 515 Talented Project of Hainan Tropical Ocean University under grant RHDRC201701.