Crustal entrainment and pulsar glitches

Gapless Neutron Superfluidity Can Explain the Late Time Cooling of Transiently Accreting Neutron Stars

The current interpretation of the observed late time cooling of transiently accreting neutron stars in low-mass x-ray binaries during quiescence requires the suppression of neutron superfluidity in their crust at variance with recent ab initio many-body calculations of dense matter. Focusing on the two emblematic sources KS 1731-260 and MXB 1659-29, we show that their thermal evolution can be naturally explained by considering the existence of a neutron superflow driven by the pinning of quantized vortices. Under such circumstances, we find that the neutron superfluid can be in a gapless state in which the specific heat is dramatically increased compared to that in the classical BCS state assumed so far, thus delaying the thermal relaxation of the crust. We perform neutron-star cooling simulations taking into account gapless superfluidity, and we obtain excellent fits to the data, thus reconciling astrophysical observations with microscopic theories. The imprint of gapless superfluidity on other observable phenomena is briefly discussed.

Pulsar glitches from quantum vortex networks

Neutron stars or pulsars are very rapidly rotating compact stars with extremely high density. One of the unsolved long-standing problems of these enigmatic celestial bodies is the origin of pulsars' glitches, i.e., the sudden rapid deceleration in the rotation speed of neutron stars. Although many glitch events have been reported, there is no consensus on the microscopic mechanism responsible for them. One of the important characterizations of the glitches is the scaling law P ( E ) ∼ E - α of the probability distribution for a glitch with energy E. Here, we reanalyse the accumulated up-to-date observation data to obtain the exponent α ≈ 0.88 for the scaling law, and propose a simple microscopic model that naturally deduces this scaling law without any free parameters. Our model explains the appearance of these glitches in terms of the presence of quantum vortex networks arising at the interface of two different kinds of superfluids in the core of neutron stars; a p-wave neutron superfluid in the inner core which interfaces with the s-wave neutron superfluid in the outer core, where each integer vortex in the s-wave superfluid connects to two half-quantized vortices in the p-wave superfluid through structures called "boojums".

Rapid spin changes around a magnetar fast radio burst

Magnetars are neutron stars with extremely high magnetic fields (≳1014 gauss) that exhibit various X-ray phenomena such as sporadic subsecond bursts, long-term persistent flux enhancements and variable rotation-period derivative1,2. In 2020, a fast radio burst (FRB), akin to cosmological millisecond-duration radio bursts, was detected from the Galactic magnetar SGR 1935+2154 (refs. 3-5), confirming the long-suspected association between some FRBs and magnetars. However, the mechanism for FRB generation in magnetars remains unclear. Here we report the X-ray observation of two glitches in SGR 1935+2154 within a time interval of approximately nine hours, bracketing an FRB that occurred on 14 October 20226,7. Each glitch involved a significant increase in the magnetar's spin frequency, being among the largest abrupt changes in neutron-star rotation8-10 observed so far. Between the glitches, the magnetar exhibited a rapid spin-down phase, accompanied by an increase and subsequent decline in its persistent X-ray emission and burst rate. We postulate that a strong, ephemeral, magnetospheric wind11 provides the torque that rapidly slows the star's rotation. The trigger for the first glitch couples the star's crust to its magnetosphere, enhances the various X-ray signals and spawns the wind that alters magnetospheric conditions that might produce the FRB.

Pulsar glitches: observations and physical interpretation

The interpretation of pulsar rotational glitches, the sudden increase in spin frequency of neutron stars, is a half-century-old challenge. The common view is that glitches are driven by the dynamics of the stellar interior, and connect in particular to the interactions between a large-scale neutron superfluid and the other stellar components. This thesis is corroborated by observational data of glitches and the post-glitch response seen in pulsars' rotation, which often involves very long timescales, from months to years. As such, glitch observables combined with consistent models incorporating the rich physics of neutron stars-from the lattice structure of their crust to the equation of state for matter beyond nuclear densities-can be very powerful at placing limits on, and reduce uncertainties of, the internal properties. This review summarises glitch observations, current data, and recent analyses, and connects them to the underlying mechanisms and microphysical parameters in the context of the most advanced theoretical glitch models to date.

Unified Equation of State for Neutron Stars Based on the Gogny Interaction

The effective Gogny interactions of the D1 family were established by D. Gogny more than forty years ago with the aim to describe simultaneously the mean field and the pairing field corresponding to the nuclear interaction. The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree–Fock–Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS’s based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner–Seitz approximation in the Variational Wigner–Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known.

A Superfluid Perspective on Neutron Star Dynamics

As mature neutron stars are cold (on the relevant temperature scale), one has to carefully consider the state of matter in their interior. The outer kilometre or so is expected to freeze to form an elastic crust of increasingly neutron-rich nuclei, coexisting with a superfluid neutron component, while the star’s fluid core contains a mixed superfluid/superconductor. The dynamics of the star depend heavily on the parameters associated with the different phases. The presence of superfluidity brings new degrees of freedom—in essence we are dealing with a complex multi-fluid system—and additional features: bulk rotation is supported by a dense array of quantised vortices, which introduce dissipation via mutual friction, and the motion of the superfluid is affected by the so-called entrainment effect. This brief survey provides an introduction to—along with a commentary on our current understanding of—these dynamical aspects, paying particular attention to the role of entrainment, and outlines the impact of superfluidity on neutron-star seismology.

Statistical Estimates of the Pulsar Glitch Activity

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

Return of the Big Glitcher: NICER timing and glitches of PSR J0537-6910

PSR J0537-6910, also known as the Big Glitcher, is the most prolific glitching pulsar known, and its spin-induced pulsations are only detectable in X-ray. We present results from analysis of 2.7 years of NICER timing observations, from 2017 August to 2020 April. We obtain a rotation phase-connected timing model for the entire timespan, which overlaps with the third observing run of LIGO/Virgo, thus enabling the most sensitive gravitational wave searches of this potentially strong gravitational wave-emitting pulsar. We find that the short-term braking index between glitches decreases towards a value of 7 or lower at longer times since the preceding glitch. By combining NICER and RXTE data, we measure a long-term braking index n = -1.25 ± 0.01. Our analysis reveals 8 new glitches, the first detected since 2011, near the end of RXTE, with a total NICER and RXTE glitch activity of 8.88 × 10-7 yr-1. The new glitches follow the seemingly unique time-to-next-glitch-glitch-size correlation established previously using RXTE data, with a slope of 5 d μHz-1. For one glitch around which NICER observes two days on either side, we search for but do not see clear evidence of spectral nor pulse profile changes that may be associated with the glitch.

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.

Pinning down the superfluid and measuring masses using pulsar glitches

Pulsars are known for their superb timing precision, although glitches can interrupt the regular timing behavior when the stars are young. These glitches are thought to be caused by interactions between normal and superfluid matter in the crust of the star. However, glitching pulsars such as Vela have been shown to require a superfluid reservoir that greatly exceeds that available in the crust. We examine a model in which glitches tap the superfluid in the core. We test a variety of theoretical superfluid models against the most recent glitch data and find that only one model can successfully explain up to 45 years of observational data. We develop a new technique for combining radio and x-ray data to measure pulsar masses, thereby demonstrating how current and future telescopes can probe fundamental physics such as superfluidity near nuclear saturation.

Towards a metallurgy of neutron star crusts

In the standard picture of the crust of a neutron star, matter there is simple: a body-centered-cubic lattice of nuclei immersed in an essentially uniform electron gas. We show that, at densities above that for neutron drip (∼ 4 × 1 0(11)  g cm(-3) or roughly one-thousandth of nuclear matter density), the interstitial neutrons give rise to an attractive interaction between nuclei that renders the lattice unstable. We argue that the likely equilibrium structure is similar to that in displacive ferroelectric materials such as BaTiO3. As a consequence, the properties of matter in the inner crust are expected to be much richer than previously appreciated, and we mention possible consequences for observable neutron star properties.

Strength of the vortex-pinning interaction from real-time dynamics

We present an efficient and general method to compute vortex-pinning interactions--which arise in neutron stars, superconductors, and trapped cold atoms--at arbitrary separations using real-time dynamics. This method overcomes uncertainties associated with matter redistribution by the vortex position and the related choice of ensemble that plague the typical approach of comparing energy differences between stationary pinned and unpinned configurations: uncertainties that prevent agreement in the literature on the sign and magnitude of the vortex-nucleus interaction in the crust of neutron stars. We demonstrate and validate the method with Gross-Pitaevskii-like equations for the unitary Fermi gas, and demonstrate how the technique of adiabatic state preparation with time-dependent simulation can be used to calculate vortex-pinning interactions in fermionic systems such as the vortex-nucleus interaction in the crust of neutron stars.