Pulsar Glitch Models Research Articles

Rotating self-gravitating Bose-Einstein condensates with a crust: A model for pulsar glitches

We develop a minimal self-gravitating model for pulsar glitches by introducing a solid-crust potential in the three-dimensional Gross-Pitaevskii-Poisson equation, which we have used earlier to study gravitationally bound Bose-Einstein condensates, i.e., bosonic stars. In the absence of the crust potential, we show that, if we rotate such a bosonic star, it is threaded by vortices. We then show, via extensive direct numerical simulations, that the interaction of these vortices with the crust potential yields (a) stick-slip dynamics and (b) dynamical glitches. We demonstrate that, if enough momentum is transferred to the crust from the bosonic star, then the vortices are expelled from the star, and the crust's angular momentum ${J}_{c}$ exhibits features that may be interpreted as glitches. From the time series of ${J}_{c}$, we compute the cumulative probability distribution functions (CPDFs) of event sizes, event durations, and waiting times, which are consistent with the previous work. We show that these CPDFs have signatures of self-organized criticality, which are similar to those seen in observations of pulsar glitches and are consistent with previous work.

The impact of superconductivity and the Hall effect in models of magnetised neutron stars

AbstractEquilibrium configurations of the internal magnetic field of a pulsar play a key role in modelling astrophysical phenomena from glitches to gravitational wave emission. In this paper, we present a numerical scheme for solving the Grad–Shafranov equation and calculating equilibrium configurations of pulsars, accounting for superconductivity in the core of the neutron star, and for the Hall effect in the crust of the star. Our numerical code uses a finite difference method in which the source term appearing in the Grad–Shafranov equation, which is used to model the magnetic equilibrium is non-linear. We obtain solutions by linearising the source and applying an under-relaxation scheme at each step of computation to improve the solver’s convergence. We have developed our code in both C++ and Python, and our numerical algorithm can further be adapted to solve any non-linear PDEs appearing in other areas of computational astrophysics. We produce mixed toroidal–poloidal field configurations, and extend the portion of parameter space that can be investigated with respect to previous studies. We find that in even in the more extreme cases, the magnetic energy in the toroidal component does not exceed approximately 5% of the total. We also find that if the core of the star is superconducting, the toroidal component is entirely confined to the crust of the star, which has important implications for pulsar glitch models which rely on the presence of a strong toroidal field region in the core of the star, where superfluid vortices pin to superconducting fluxtubes.

Bayesian estimate of the superfluid moments of inertia from the 2016 glitch in the Vela pulsar

Context. The observation of the first pulse-to-pulse glitch in the Vela pulsar opens a new window among theoretical speculations on the internal dynamics of neutron stars as it allows us for testing models to factor in the circumstances of the first moments of a glitch. Several works in the literature have already considered the observational and physical parameters of the star by employing a minimal model with three rigidly rotating components. Aims. We improve the analytical study of the minimal three-component model for pulsar glitches by solving it with generic initial conditions for the two initial lags of their superfluid components. The purpose is to use this solution to fit the data of the 2016 Vela glitch by employing a Bayesian approach and to obtain a probability distribution for the physical parameters of the model and for observational parameters, such as the glitch rise time and the relaxation timescale. Methods. The fit is achieved through Bayesian inference. Due to the presence of an increase in the timing residuals near the glitch time, an extra magnetospheric component was added to the three-component model to deal with this phenomenon. A physically reasonable, non-informative prior was set on the different parameters of the model, so that the posterior distribution could be compared with state-of-the-art information obtained from microphysical calculations. By considering a model with a tightened prior on the moment of inertia fractions and by comparing it with the original model by means of Bayesian model selection, we studied the possibility of a crust-limited superfluid reservoir. Results. We obtained the posterior distribution for the moment of inertia fractions of the superfluid components, the coupling parameters, and the initial velocity lags between the components. An analysis of the inferred posterior also confirmed the presence of an overshoot in that glitch and set an upper limit of ∼6 s on the glitch rise timescale. The comparison between the two models with different priors on the moment of inertia fractions appears to indicate a need for a core participation in the glitch phenomenon, regardless of the uncertain strength of the entrainment coupling.

Modelling Pulsar Glitches: The Hydrodynamics of Superfluid Vortex Avalanches in Neutron Stars

AbstractThe dynamics of quantised vorticity in neutron star interiors is at the heart of most pulsar glitch models. However, the large number of vortices (up to ≈1013) involved in a glitch and the huge disparity in scales between the femtometre scale of vortex cores and the kilometre scale of the star makes quantum dynamical simulations of the problem computationally intractable. In this paper, we take a first step towards developing a mean field prescription to include the dynamics of vortices in large-scale hydrodynamical simulations of superfluid neutron stars. We consider a one-dimensional setup and show that vortex accumulation and differential rotation in the neutron superfluid lead to propagating waves, or ‘avalanches’, as solutions for the equations of motion for the superfluid velocities. We introduce an additional variable, the fraction of free vortices, and test different prescriptions for its advection with the superfluid flow. We find that the new terms lead to solutions with a linear component in the rise of a glitch, and that, in specific setups, they can give rise to glitch precursors and even to decreases in frequency, or ‘anti-glitches’.

Superfluid Density of Neutrons in the Inner Crust of Neutron Stars: New Life for Pulsar Glitch Models.

Calculations of the effects of band structure on the neutron superfluid density in the crust of neutron stars made under the assumption that the effects of pairing are small [N. Chamel, Phys. Rev. C 85, 035801 (2012)PRVCAN0556-2813] lead to moments of inertia of superfluid neutrons so small that the crust alone is insufficient to account for the magnitude of neutron star glitches. Inspired by earlier work on ultracold atomic gases in an optical lattice, we investigate fermions with attractive interactions in a periodic lattice in the mean-field approximation. The effects of band structure are suppressed when the pairing gap is of order or greater than the strength of the lattice potential. By applying the results to the inner crust of neutron stars, we conclude that the reduction of the neutron superfluid density is considerably less than previously estimated and, consequently, it is premature to rule out models of glitches based on neutron superfluidity in the crust.

Properties and observability of glitches and anti-glitches in accreting pulsars

Several glitches have been observed in young, isolated radio pulsars, while a clear detection in accretion-powered X-ray pulsars is still lacking. We use the Pizzochero snowplow model for pulsar glitches as well as starquake models to determine for the first time the expected properties of glitches in accreting pulsars and their observability. Since some accreting pulsars show accretion-induced long-term spin-up, we also investigate the possibility that anti-glitches occur in these stars. We find that glitches caused by quakes in a slow accreting neutron star are very rare and their detection extremely unlikely. On the contrary, glitches and anti-glitches caused by a transfer of angular momentum between the superfluid neutron vortices and the non-superfluid component may take place in accreting pulsars more often. We calculate the maximum jump in angular velocity of an anti-glitch and we find that it is expected to be about 1E-5 - 1E-4 rad/s. We also note that since accreting pulsars usually have rotational angular velocities lower than those of isolated glitching pulsars, both glitches and anti-glitches are expected to have long rise and recovery timescales compared to isolated glitching pulsars, with glitches and anti-glitches appearing as a simple step in angular velocity. Among accreting pulsars, we find that GX 1+4 is the best candidate for the detection of glitches with currently operating X-ray instruments and future missions such as the proposed Large Observatory for X-ray Timing (LOFT).

Efficacy of crustal superfluid neutrons in pulsar glitch models

In order to assess the ability of purely crust-driven glitch models to match the observed glitch activity in the Vela pulsar, we conduct a systematic analysis of the dependence of the fractional moment of inertia of the inner crustal neutrons on the stiffness of the nuclear symmetry energy at saturation density $L$. We take into account both crustal entrainment and the fact that only a fraction $Y_{\rm g}$ of the core neutrons may couple to the crust on the glitch-rise timescale. We use a set of consistently-generated crust and core compositions and equations-of-state which are fit to results of low-density pure neutron matter calculations. When entrainment is included at the level suggested by recent microscopic calculations and the core is fully coupled to the crust, the model is only able to account for the Vela glitch activity for a 1.4$M_{\odot}$ star if the equation of state is particularly stiff $L>100$ MeV. However, an uncertainty of about 10\% in the crust-core transition density and pressure allows for the Vela glitch activity to be marginally accounted for in the range $L\approx30-60$MeV consistent with a range of experimental results. Alternatively, only a small amount of core neutrons need be involved. If less than 50\% of the core neutrons are coupled to the crust during the glitch, we can also account for the Vela glitch activity using crustal neutrons alone for EOSs consistent with the inferred range of $L$. We also explore the possibility of Vela being a high-mass neutron star, and of crustal entrainment being reduced or enhanced relative to its currently predicted values.

LONG-TERM TIMING AND GLITCH CHARACTERISTICS OF ANOMALOUS X-RAY PULSAR 1RXS J170849.0–400910

We present the results of our detailed timing studies of an anomalous X-ray pulsar, 1RXS J170849.0-400910, using Rossi X-ray Timing Explorer (RXTE) observations spanning over ~6 yr from 2005 until the end of RXTE mission. We constructed the long-term spin characteristics of the source and investigated time and energy dependence of pulse profile and pulsed count rates. We find that pulse profile and pulsed count rates in the 2-10 keV band do not show any significant variations in ~6 yr. 1RXS J170849.0-400910 has been the most frequently glitching anomalous X-ray pulsar: three spin-up glitches and three candidate glitches were observed prior to 2005. Our extensive search for glitches later in the timeline resulted in no unambiguous glitches though we identified two glitch candidates (with Delta(nu)/nu ~10^{-6}) in two data gaps: a strong candidate around MJD 55532 and another one around MJD 54819, which is slightly less robust. We discuss our results in the context of pulsar glitch models and expectancy of glitches within the vortex unpinning model.

Applying the "snowplow" model for pulsar glitches to constrain nuclear symmetry energy

Glitches in pulsars are occasional, sudden increases in their rotation frequency as the pulsar otherwise steadily spins down. A broad class of glitch models suppose the sudden spin-ups are due to angular momentum transfer between some of the crustal superfluid neutrons and the rigid crust plus anything that couples to it on timescales shorter than the superfluid-crust coupling time. Using a set of neutron star equations of state (EOS) which span the experimentally constrained range of asymmetric nuclear matter properties, and estimates of the strength of the coupling between the crust and the core superfluid neutrons, we calculate the moment of inertia (MoI) of crustal superfluid neutrons involved in storing angular momentum in the glitch process. Following the recent, microscopically based "snowplow" model for glitches, we restrict the calculation to just those superfluid neutron vortices that are strongly pinned to the crustal lattice, a region which corresponds to an equatorial annulus of the inner crust. We compare calculations to observational estimates of the average rate of angular momentum transfer between superfluid neutrons and the rest of the star in the Vela pulsar, and also the relative acceleration of the crust post-glitch estimated from the 2002 Vela glitch. We found that to match the observations of the glitch sizes and recovery from Vela glitches, a value of L 50 MeV for the density slope of the symmetry energy at saturation density is required and the coupling between core superfluid neutrons and crust is relatively weak.

INVESTIGATING SUPERCONDUCTIVITY IN NEUTRON STAR INTERIORS WITH GLITCH MODELS

The high density interior of a neutron star is expected to contain superconducting protons and superfluid neutrons. Theoretical estimates suggest that the protons will form a type II superconductor in which the stellar magnetic field is carried by flux tubes. The strong interaction between the flux tubes and the neutron rotational vortices could lead to strong 'pinning', i.e. vortex motion could be impeded. This has important implications especially for pulsar glitch models as it would lead to a large part of the vorticity of the star being decoupled from the 'normal' component, to which the electromagnetic emission is locked. In this paper we explore the consequences of strong pinning in the core on the 'snowplow' model for pulsar glitches (Pizzochero 2011), making use of realistic equations of state and relativistic background models for the neutron star. We find that in general a large fraction of pinned vorticity in the core is not compatible with observations of giant glitches in the Vela pulsar. The conclusion is thus that either most of the core is in a type I superconducting state or that the interaction between vortices and flux tubes is weaker than previously assumed.

The effect of realistic equations of state and general relativity on the ‘snowplough’ model for pulsar glitches

Many pulsars are observed to "glitch", i.e. show sudden jumps in their rotational frequency $\nu$, some of which can be as large as $\Delta \nu/\nu\approx 10^{-6}-10^{-5}$ in a subset of pulsars known as giant glitchers. Recently Pizzochero (2011) has shown that an analytic model based on realistic values for the pinning forces in the crust and for the angular momentum transfer in the star can describe the average properties of giant glitches, such as the inter-glitch waiting time, the step in frequency and that in frequency derivative. In this paper we extend the model (originally developed in Newtonian gravity and for a polytropic equation of state) to realistic backgrounds obtained by integrating the relativistic equations of stellar structure and using physically motivated equations of state to describe matter in the neutron star. We find that this more detailed treatment still reproduces the main features of giant glitches in the Vela pulsar and allows us to set constraints on the equation of state. In particular we find that stiffer equations of state are favoured and that it is unlikely that the Vela pulsar has a high mass (larger than $M\approx 1.5 M_\odot$).

Vortex-lattice interaction in Pulsar Glitches

In this proceeding we present a quantitative model to study the pinning interaction between a neutron vortex and the nuclear lattice in the inner crust of a neutron star, which is formed by nuclear clusters immersed in a superfluid neutron gas. This is one of the most important quantities in the vortex model for pulsar glitches, where the sudden variations of the rotation velocity observed in some neutron stars are explained in terms of pinning-depinning processes between vortices and the nuclear lattice. The study has been done through an actual counting of the number of pinning sites between the vortex and the nuclear lattice. Moreover, it has been recognized that the vortices can have a generic orientation with respect to the lattice and thus the simple pinned-unpinned scenario (that is characteristic of the aligned case and has been assumed in previous qualitative models) is not acceptable for a realistic calculation. The forces that we have found are more than two orders of magnitude smaller than those calculated so far in the literature, and of the same order as what suggested to explain real Vela-like glitches. They can thus be applied to quantitative models for the vortex dynamics, in order to better simulate and understand these remarkable astrophysical phenomena.

A VERY LARGE GLITCH IN PSR B2334+61

Seven years of pulse time-of-arrival measurements have been collected from observations of the young pulsar PSR B2334+61 using the Nanshan radio telescope of Urumqi Observatory. A phase-connected solution has been obtained over the whole data span, 2002 August to 2009 August. This includes a very large glitch that occurred between 2005 August 26 and September 8 (MJDs 53608 and 53621). The relative increase in rotational frequency for this glitch, $\Delta\nu_{g}/\nu~\sim~20.5\times10^{-6}$, is the largest ever seen. Although accounting for less than 1\% of the glitch, there were two well-defined exponential decay terms with time constants of 21 and 147 days respectively. There was also a large long-term increase in the spindown rate with $\Delta\dot\nu_p/\dot\nu \sim 0.011$ at the time of the glitch. A highly significant oscillation with a period of close to one year is seen in the post-glitch residuals. It is very unlikely that this can be accounted for by a pulsar position error or proper motion -- it appears to result from effects interior to the neutron star. Implications of these results for pulsar glitch models are discussed.

The dynamics of pulsar glitches: contrasting phenomenology with numerical evolutions

In this paper we consider a simple two-fluid model for pulsar glitches. We derive the basic equations that govern the spin evolution of the system from two-fluid hydrodynamics, accounting for the vortex mediated mutual friction force that determines the glitch rise. This leads to a simple "bulk" model that can be used to describe the main properties of a glitch event resulting from vortex unpinning. In order to model the long term relaxation following the glitch our model would require additional assumptions regarding the repinning of vortices, an issue that we only touch upon briefly. Instead, we focus on comparing the phenomenological model to results obtained from time-evolutions of the linearised two-fluid equations, i.e. a "hydrodynamic" model for glitches. This allows us to study, for the first time, dynamics that was "averaged" in the bulk model, i.e. consider the various neutron star oscillation modes that are excited during a glitch. The hydro-results are of some relevance for efforts to detect gravitational waves from glitching pulsars, although the conclusions drawn from our rather simple model are pessimistic as far as the detectability of these events is concerned.

Search for Thermal Afterglow from PSR 0656+14

Thermal afterglow caused by transient energy releases in neutron stars could alter the X-ray pulse shape of pulsars by heating a portion of the crust so that more thermal X-rays are emitted at a particular phase. We developed a method to look for such changes in X-ray pulsars. We put a typical lower limit of 3.9 × 1031 ergs s-1 (1.4 × 1035 ergs in a 1 hr exposure) on the average excess X-ray luminosity required to see thermal afterglow from ROSAT data of PSR 0656+14 consisting of three separate observations lasting 3-5 hr. The lower limit obtained allows us to constrain the glitch parameters and the equation of state for neutron stars. In particular, a differentiation could be made between the vortex unpinning model and the starquake model for pulsar glitches if a search for thermal afterglow were performed contemporaneously with glitch observations.

Pinning and Threading of Quantized Vortices in the Pulsar Crust Superfluid

view Abstract Citations (120) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Pinning and Threading of Quantized Vortices in the Pulsar Crust Superfluid Alpar, M. Ali Abstract A neutron superfluid coexists with a lattice of nuclear clusters in the inner crust of a pulsar. Quantized vortices in this superfluid are pinned to the nuclear clusters in the innermost part of this region, while threading between nuclear clusters in outer layers. As a pulsar slows down, outer layers of the crust superfluid will be free to expel vortices while the pinning layer constrains the relaxation of the superfluid rotation throughout the crust and vortex movements through the core of the star. This picture should modify pulsar glitch models that depend on release of pinned vortices. Subject headings: dense matter - pulsars - stars: neutron Publication: The Astrophysical Journal Pub Date: April 1977 DOI: 10.1086/155183 Bibcode: 1977ApJ...213..527A full text sources ADS |