Superfluid Neutron Vortices Research Articles

Vortex creep heating in neutron stars

Recent observations of old warm neutron stars suggest the presence of a heating source in these stars, requiring a paradigm beyond the standard neutron-star cooling theory. In this work, we study the scenario where this heating is caused by the friction associated with the creep motion of neutron superfluid vortex lines in the crust. As it turns out, the heating luminosity in this scenario is proportional to the time derivative of the angular velocity of the pulsar rotation, and the proportionality constant J has an approximately universal value for all neutron stars. This J parameter can be determined from the temperature observation of old neutron stars because the heating luminosity is balanced with the photon emission at late times. We study the latest data of neutron star temperature observation and find that these data indeed give similar values of J, in favor of the assumption that the frictional motion of vortex lines heats these neutron stars. These values turn out to be consistent with the theoretical calculations of the vortex-nuclear interaction.

Superfluid Rivers in Spinning-down Neutron Stars

We study the motion of neutron superfluid vortices in a spinning-down neutron star, assuming axisymmetry of the flow and ignoring the motion of vortices about the rotation axis. We find that the vortex array, if initially rectilinear, is soon substantially deformed as the star spins down; vortices are swept outward by the Magnus force, accumulating in regions of the inner crust where they pin, accompanied by significant bending of the vortex array. As the star spins down to below a spin rate of ∼20 Hz (twice the spin rate of the Vela pulsar), the Magnus and pinning forces gradually compress the vortex array into dense sheets that follow spherical shells. In some cases, the vortex array bends on itself and reconnects, forming one or more tori of vortex rings that contain superfluid “rivers” with significant angular momentum. Vortex sheets are likely to form near the base of the inner crust in the regime of nuclear pasta.

Vortex creep heating vs. dark matter heating in neutron stars

Dark matter particles captured in neutron stars deposit their energy as heat. This DM heating effect can be observed only if it dominates over other internal heating effects in neutron stars. In this work, as an example of such an internal heating source, we consider the frictional heating caused by the creep motion of neutron superfluid vortex lines in the neutron star crust. The luminosity of this heating effect is controlled by the strength of the interaction between the vortex lines and nuclei in the crust, which can be estimated from the many-body calculation of a high-density nuclear system as well as through the temperature observation of old neutron stars. We show that both the temperature observation and theoretical calculation suggest that the vortex creep heating dominates over the DM heating. The vortex-nuclei interaction must be smaller than the estimated values by several orders of magnitude to overturn this.

Revisiting neutron starquakes caused by spin-down

Context. Pulsars show a steady decrease in their rotational frequency, occasionally interrupted by sudden spin-ups called glitches, whose physical origin is still a mystery. One suggested explanation for at least the small glitches are starquakes, that is, failures of the solid neutron star crust, in which the progressive reduction in the centrifugal force deforms the star, stressing the solid until it breaks. This produces a spin-up, dissipating energy inside the star. Aims. We explore this suggestion by analyzing a mostly analytical model in order to understand the possible consequences of starquakes, particularly whether they can explain at least the small glitches. Methods. We analyze the deformations and strains produced by the decreasing centrifugal force, modeling the neutron star with a fluid core and a solid crust, each with uniform density and with the core possibly denser than the crust, as a simple approximation to the strong density gradient present in real neutron stars. Results. The deformation of a star with very different densities in the core and crust is qualitatively different from the previously studied case of equal densities. The former more closely resembles the behavior of a fluid star, in which the core-crust interface is a surface of constant gravitational plus centrifugal potential. Conclusions. Regardless of the uncertain breaking strain, the glitch activity in this model is several orders of magnitude smaller than observed, even if only small glitches are considered. For a large breaking strain, suggested by simulations, glitches due to starquakes could be roughly of the correct size but much less frequent than observed glitches. The energy released in each such glitch is much larger than in the standard model of angular momentum transfer from a faster rotating superfluid in the inner crust. On the other hand, we cannot rule out that the heating produced by small starquakes could trigger glitches by allowing neutron superfluid vortices to move. We also confirm that stresses in the neutron star crust can in principle support an ellipticity much larger than some observational upper limits from pulsar timing and continuous gravitational wave searches.

New insight into the physical essence of pulsar glitch

Based on the oscillation between the B phase and A phase of 3P2 neutron superfluid in neutron stars, we propose a new glitch model for young pulsars. According to our model, the glitch is explained as a repeat phenomena from the quasi period 3P2 neutron superfluid B phase, to A phase, then to B phase (many repeated glitches with quasi-period). With the repeating of the phase transition, the vortex quantum number of 3P2 neutron superfluid vortices is gradually reduced, and the heating rate ε(B) in B phase also gets lower and lower. After a number of glitches, the time intervals between successive glitches will gradually become longer, and the glitch amplitude decreases. When the heating rate ε(B) of an old neutron star becomes lower than the cooling rate of the direct Urca, which can happen in a super-strongmagnetic field, the B phase of the 3P2 neutron superfluid vortices is no longer returned to the A phase state and the phase oscillation of the system is stopped immediately. The slowing glitch phenomenon of some older pulsars is a natural result of our theory, which means that very old pulsars will no longer present the glitch. Our model will be tested in future pulsar glitch observations.

Vortices penetrating two-flavor quark-hadron continuity

Alice and Boojums are both representative characters created by Lewis Carroll. We show that they possibly meet in cores of rotating neutron stars. Recent studies of quark-hadron continuity suggest that neutron superfluid matter can connect smoothly to two-flavor symmetric quark matter at high densities. We study how this can be maintained in the presence of the vortices. In the neutron matter, quantized superfluid vortices arise. In the two-flavor dense quark matter, vortices carrying color magnetic fluxes together with fractionally quantized superfluid circulations appear as the most stable configuration, and we call these as the non-Abelian Alice strings. We show that three integer neutron superfluid vortices and three non-Abelian Alice strings of different color magnetic fluxes with total color flux canceled out are joined at a junction called a Boojum.

Angular momentum conservation and core superfluid dynamics for the pulsar J1734‐3333

AbstractPulsars emit pulsed radiation at well‐defined frequencies. In the canonical model, a pulsar is assumed to be a rotating, highly magnetized sphere made mostly of neutrons that has a magnetic dipole misaligned with respect to its rotation axis, which would be responsible for the emission of the observed pulses. The measurement of the pulse frequency and its first two derivatives allows the calculation of the braking index, n. One limitation of the canonical model is that, for all pulsars, it yields n = 3, a result that does not correspond to observational values of n. In order to contribute to the solution of this problem, we proposed a model for pulsars' rotation frequency decay assuming that the star's total moment of inertia would vary with time due to mass motions inside the core. As a result, we found that the pulsar J1734‐3333 has total angular momentum practically conserved, a phenomenon that we explain by relating the motion of neutron superfluid vortices in the core to torques associated with radiation emission.

Vortex pinning in the superfluid core of neutron stars and the rise of pulsar glitches

ABSTRACT Timing of the Crab and Vela pulsars has recently revealed very peculiar evolutions of their spin frequency during the early stage of a glitch. We show that these differences can be interpreted from the interactions between neutron superfluid vortices and proton fluxoids in the core of these neutron stars. In particular, pinning of individual vortices to fluxoids is found to have a dramatic impact on the mutual friction between the neutron superfluid and the rest of the star. The number of fluxoids attached to vortices turns out to be a key parameter governing the global dynamics of the star. These results may have implications for the interpretation of other astrophysical phenomena such as pulsar-free precession or the r-mode instability.

A hybrid model for pulsar's spin‐down evolution

AbstractBy considering the combined effects of both the standard magnetic dipole model and the composite neutron superfluid vortex model on pulsar's spin‐down, we study the evolution of pulsar's spin‐down on the P − diagram. The evolution path of each pulsar is dictated by a particular mechanism in our hybrid model within different parameter spaces. The valley of each curve is the most possible place for a neutron star (NS) to be observed as this is the place corresponding to the minimum value of the evolution speed (i.e., the time derivative ). In other words, pulsars would distribute around these valleys on the P − diagram. The suppressed region in the lower‐right part of the diagram can be explained by neutrino cyclotron emission from the 1S0 neutron superfluid vortexes in NSs.

Glitches in neutron stars with magnetically decoupled core

The magnetically decoupled core model was proposed earlier as a way to solve the problem of inconsistency between the neutron star long-period precession and superfluid vortex pinning which is the base of most theories of pulsar glitches. It was assumed that the pinning takes place in the region of the neutron star core which, being magnetically decoupled, can rotate relative to the crust. In present work some aspects of the glitch spin-up stage in the framework of the proposed model are discussed. Estimated spin-up time-scales are compared with observational data. According to the estimations the Crab pulsar is likely posses a magnetically decoupling core region, while the results for the Vela pulsar is more controversial.

A possible way to reconcile long-period precession with vortex pinning in neutron stars

ABSTRACT We propose a possible way to solve the problem of inconsistency between the neutron star long-period precession and superfluid vortex pinning, which is the basis of the most successful theories of pulsar glitches. We assume that the pinning takes place in the region of the neutron star core, which, being magnetically decoupled, can rotate relative to the crust. In the framework of a simple three-component model we show that these two phenomena can coexist in the same pulsar. Some constraints on the formally introduced interaction coefficients following from observation data are formulated.

Relating braking indices of young pulsars to the dynamics of superfluid cores

Pulsars are stars that emit electromagnetic radiation in well-defined time intervals. The frequency of such pulses decays with time as is quantified by the braking index (n). In the canonical model n = 3 for all pulsars, but observational data show that n ≠ 3, indicating a limitation of the model. In this work we present a new approach to study the frequency decay of the rotation of a pulsar, based on an adaptation of the canonical one. We consider the pulsar a star that rotates in vacuum and has a strong magnetic field but, differently from the canonical model, we assume that its moment of inertia changes in time due to a uniform variation of a displacement parameter in time. We found that the braking index results smaller than the canonical value as a consequence of an increase in the star's displacement parameter, whose variation is small enough to allow plausible physical considerations that can be applied to a more complex model for pulsars in the future. In particular, this variation is of the order of neutron vortices' creep in rotating superfluids. When applied to pulsar data our model yielded values for the stars' braking indices close to the observational ones. The application of this approach to a more complex star model, where pulsars are assumed to have superfluid interiors, is the next step in probing it. We hypothesize that the slow expansion of the displacement parameter might mimic the motion of core superfluid neutron vortices in realistic models.

Stability of interlinked neutron vortex and proton flux-tube arrays in a neutron star – II. Far-from-equilibrium dynamics

The equilibrium configurations of neutron superfluid vortices interacting with proton superconductor flux tubes in a rotating, harmonic trap are non-trivial in general, when the magnetorotational symmetry is broken. A non-zero angle $\theta$ between the magnetic and rotation axes leads to tangled vorticity due to competition between vortex-vortex repulsion and vortex-flux-tube pinning. Here we investigate the far-from-equilibrium behaviour of the vortices, as the trap decelerates, by solving the time-dependent, stochastic, Gross-Pitaevskii equation numerically in three dimensions. The numerical simulations reveal new vortex behaviours. Key geometrical attributes of the evolving vortex tangle are characterised, as is the degree to which pinning impedes the deceleration of the neutron condensate as a function of $\eta$, the pinning strength, and $\theta$. The simulated system is a partial analogue of the outer core of a decelerating neutron star, albeit in a very different parameter regime.

Towards laboratory detection of topological vortices in superfluid phases of QCD

Topological defects arise in a variety of systems, e.g. vortices in superfluid helium to cosmic strings in the early universe. There is an indirect evidence of neutron superfluid vortices from the glitches in pulsars. One also expects that the topological defects may arise in various high baryon density phases of quantum chromodynamics (QCD), e.g. superfluid topological vortices in the color flavor locked (CFL) phase. Though vastly different in energy/length scales, there are universal features in the formation of all these defects. Utilizing this universality, we investigate the possibility of detecting these topological superfluid vortices in laboratory experiments, namely heavy-ion collisions (HICs). Using hydrodynamic simulations, we show that vortices can qualitatively affect the power spectrum of flow fluctuations. This can give an unambiguous signal for superfluid transition resulting in vortices, allowing for the check of defect formation theories in a relativistic quantum field theory system, and the detection of superfluid phases of QCD. Detection of nucleonic superfluid vortices in low energy HICs will give opportunity for laboratory controlled study of their properties, providing crucial inputs for the physics of pulsars.

Stability of interlinked neutron vortex and proton flux tube arrays in a neutron star: equilibrium configurations

Three-dimensional, Gross-Pitaevskii equation (GPE) simulations are presented of the interaction between neutron superfluid vortices and proton superconductor flux tubes in a rotating, harmonic trap, representing an idealised model of the outer core of a neutron star. Low-energy states of the neutron condensate are calculated by evolving the GPE in imaginary time in the presence of a prescribed, static, rectilinear flux tube array. The calculations are carried out as a function of the angle between the global magnetic and rotation axes, and the amplitude and sign of the current-current and density couplings between the neutron and proton condensates. It is found that the system is frustrated by the competition between vortex-vortex repulsion and vortex-flux-tube attraction (pinning), leading to the formation of vortex tangles and "glassy" behaviour characterized by multiple metastable states spaced closely in energy. The dimensionless parameters in the simulations are ordered as one expects in a neutron star, but the dynamic range is many orders of magnitude smaller than in reality, so caution must be exercised when assessing the astrophysical implications. Nevertheless the results suggest that tangled vorticity may be endemic in neutron star outer cores.

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).

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.

Vortex structure of neutron stars with triplet neutron superfluidity

The vortex structure of the “npe” phase of neutron stars with a 3P2 superfluid neutron condensate of Cooper pairs is discussed. It is shown that, as the star rotates, superfluid neutron vortex filaments described by a unitary ordering parameter develop in the “npe” phase. The entrainment of superconducting protons by the rotating superfluid neutrons is examined. The entrainment effect leads to the appearance of clusters of proton vortices around each neutron vortex and generates a magnetic field on the order of 1012 G. 3P2 neutron vortex filaments combine with quark semi-superfluid vortex filaments at the boundary of the “npe” and “CFL” phases. At the boundary of the “Aen” and “npe” phases, they combine with 1S0 neutron vortex filaments. In this way, a unified vortex structure is formed. The existence of this structure and its collective elastic oscillations explain the observed oscillations in the angular rotation velocity of pulsars.

Do superfluid instabilities prevent neutron star precession?

We discuss short wavelength (inertial wave) instabilities present in the standard two-fluid neutron star model when there is sufficient relative flow along the superfluid neutron vortex array. We demonstrate that these instabilities may be triggered in precessing neutron stars, since the angular velocity vectors of the neutron and proton fluids are misaligned during precession. Our results suggest that the standard (Eulerian) slow precession that results for weak drag between the vortices and the charged fluid (protons and electrons) is not seriously affected by the instability. In contrast, the fast precession, which results when vortices are strongly coupled to the charged component, is generally unstable. The presence of this instability renders the standard (solid body) rotation model for free precession inconsistent and makes unsafe conclusions that have recently been drawn regarding neutron star interiors based on observations of precession in radio pulsars.

Vortex structure of neutron stars with CFL quark cores

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields of nonabelian semi-superfluid vortex filaments in color superconducting cores of neutron stars containing a diquark CFL condensate. The interaction of the diquark CFL condensate with the magnetic and gluomagnetic gauge fields is taken into account. The asymptotic values of the energies of these filaments are determined from the quantization conditions. It is shown that a lattice of semi-superfluid vortex filaments with a minimal quantum of circulation develops in the quark superconducting core during rotation of the star. The magnetic field in the core of this vortex is on the order of 1018 G. A cluster of proton vortices, which develops in the hadron phase surrounding every superfluid neutron vortex owing to an entrainment effect, creates new semi-superfluid vortex filaments with a minimal quantum of circulation in the quark superconducting core.