arXiv subjects

Pierre Pizzochero

Publications and source records attributed to Pierre Pizzochero.

14 recordsLinked to original sources

arXiv2023

Insights into the physics of neutron star interiors from pulsar glitches

The presence of superfluid phases in the interior of a neutron star affects its dynamics, as neutrons can flow relative to the non-superfluid (normal) components of the star with little or no viscosity. A probe of superfluidity comes from pulsar glitches, sudden jumps in the observed rotational period of radio pulsars. Most models of glitches build on the idea that a superfluid component of the star is decoupled from the spin-down of the normal component, and its sudden recoupling leads to a glitch. This transition in the strength of the hydrodynamic coupling is explained in terms of quantum vortices (long-lived vortices that are naturally present in the neutron superfluid at the microscopic scale). After introducing some basic ideas, we derive (as a pedagogical exercise) the formal scheme shared by many glitch studies. Then, we apply these notions to present some recent advances and discuss how observations can help us to indirectly probe the internal physics of neutron stars.

astro-ph.HE↗

arXiv2022

Continuous gravitational wave emission from neutron stars with pinned superfluids in the core

We investigate the effect of a pinned superfluid component on the gravitational wave emission of a rotating neutron star. Pinning of superfluid vortices to the flux-tubes in the outer core (where the protons are likely to form a type-II superconductor) is a possible mechanism to sustain long-lived and non-axisymmetric neutron currents in the interior, that break the axial symmetry of the unperturbed hydrostatic configuration. We consider pinning-induced perturbations to a stationary corotating configuration, and determine upper limits on the strength of gravitational wave emission due to the pinning of vortices with a strong toroidal magnetic field of the kind predicted by recent magneto-hydrodynamic simulations of neutron star interiors. We estimate the contributions to gravitational wave emission from both the mass and current multipole generated by the pinned vorticity in the outer core, and find that the mass quadrupole can be large enough for gravitational waves to provide the dominant spindown torque in millisecond pulsars.

astro-ph.HE↗

arXiv2022

Two decades of X-ray observations of the isolated neutron star RX J1856.5-3754: detection of thermal and non-thermal hard X-rays and refined spin-down measurement

The soft X-ray pulsar RX J1856.5-3754 is the brightest member of a small class of thermally-emitting, radio-silent, isolated neutron stars. Its X-ray spectrum is almost indistinguishable from a blackbody with $kT^\infty\approx 60$ eV, but evidence of harder emission above $\sim 1$ keV has been recently found. We report on a spectral and timing analysis of RX J1856.5-3754 based on the large amount of data collected by XMM-Newton in 2002--2022, complemented by a dense monitoring campaign carried out by NICER in 2019. Through a phase-coherent timing analysis we obtained an improved value of the spin-down rate $\dot{\nu}=-6.042(4)\times10^{-16}$ Hz s$^{-1}$, reducing by more than one order magnitude the uncertainty of the previous measurement, and yielding a characteristic spin-down field of $1.47\times10^{13}$ G. We also detect two spectral components above $\sim1$ keV: a blackbody-like one with $kT^\infty=138\pm13$ eV and emitting radius $31_{-16}^{+8}$ m, and a power law with photon index $\Gamma=1.4_{-0.4}^{+0.5}$. The power-law 2--8\,keV flux, $(2.5_{-0.6}^{+0.7})\times10{-15}$ erg cm$^{-2}$ s$^{-1}$, corresponds to an efficiency of $10^{-3}$, in line with that seen in other pulsars. We also reveal a small difference between the $0.1$--$0.3$ keV and $0.3$--$1.2$ keV pulse profiles, as well as some evidence for a modulation above $1.2$ keV. These results show that, notwithstanding its simple spectrum, \eighteen still has a non-trivial thermal surface distribution and features non-thermal emission as seen in other pulsars with higher spin-down power.

astro-ph.HE↗

arXiv2021

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.

astro-ph.HE↗

arXiv2020

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

The observation of the first pulse-to-pulse glitch in the Vela pulsar opens a new window on the internal dynamics of neutron stars. We study the minimal three-component model for pulsar glitches by solving it with generic initial conditions. 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. 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 parameters of the model, so that the posterior distribution could be compared with 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. 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 $\sim 6\,$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.

astro-ph.HE↗

arXiv2020

A universal formula for the relativistic correction to the mutual friction coupling time-scale in neutron stars

Vortex-mediated mutual friction governs the coupling between the superfluid and normal components in neutron star interiors. By, for example, comparing precise timing observations of pulsar glitches with theoretical predictions it is possible to constrain the physics in the interior of the star, but to do so an accurate model of the mutual friction coupling in general relativity is needed. We derive such a model directly from Carter's multifluid formalism, and study the vortex structure and coupling time-scale between the components in a relativistic star. We calculate how general relativity modifies the shape and the density of the quantized vortices and show that, in the quasi-Schwarzschild coordinates, they can be approximated as straight lines for realistic neutron star configurations. Finally, we present a simple universal formula (given as a function of the stellar compactness alone) for the relativistic correction to the glitch rise-time, which is valid under the assumption that the superfluid reservoir is in a thin shell in the crust or in the outer core. This universal relation can be easily employed to correct, a posteriori, any Newtonian estimate for the coupling time-scale, without any additional computational expense.

astro-ph.HE↗

arXiv2020

Core and crust contributions in overshooting glitches: the Vela pulsar 2016 glitch

During the spin-up phase of a large pulsar glitch - a sudden decrease of the rotational period of a neutron star - the angular velocity of the star may overshoot, namely reach values greater than that observed for the new post-glitch equilibrium. These transient phenomena are expected on the basis of theoretical models for pulsar internal dynamics and their observation has the potential to provide an important diagnostic for glitch modelling. We present a simple criterion to assess the presence of an overshoot, based on the minimal analytical model that is able to reproduce an overshooting spin-up. We employ it to fit the data of the 2016 glitch of the Vela pulsar, obtaining estimates of the fractional moments of inertia of the internal superfluid components involved in the glitch, of the rise and decay timescales of the overshoot, and of the mutual friction parameters between the superfluid components and the normal one. We study the cases with and without strong entrainment in the crust: in the former, we find indication of a large inner core strongly coupled to the observable component and of a reservoir of angular momentum extending into the core to densities below nuclear saturation, while in the latter a large reservoir extending above nuclear saturation and a standard normal component without inner core are suggested.

astro-ph.HE↗

arXiv2020

The role of mass, equation of state and superfluid reservoir in large pulsar glitches

Observations of pulsar glitches may provide insights on the internal physics of neutron stars and recent studies show how it is in principle possible to constrain pulsar masses with timing observations. The reliability of these estimates depend on the current uncertainties about the structure of neutron stars and on our ability to model the dynamics of the superfluid neutrons in the internal layers. We assume a simplified model for the rotational dynamics of a neutron star and estimate an upper bound to the mass of 25 pulsars from their largest glitch and average activity: the aim is to understand to which extent the mass constraints are sensitive to the choice of the unknown structural properties of neutron stars, like the extension of the superfluid region and the equation of state. Reasonable values, within the range measured for neutron star masses, are obtained only if the superfluid domain extends for at least a small region inside the outer core, which is compatible with calculations of the neutron S-wave pairing gap. Moreover, the mass constraints stabilise when the superfluid domain extends to densities over nuclear saturation, irrespective of the equation of state tested.

astro-ph.HE↗

arXiv2020

Modelling strains and stresses in continuously stratified rotating neutron stars

We introduce a Newtonian model for the deformations of a compressible, autogravitating, and continuously stratified neutron star. The present framework can be applied to a number of astrophysical scenarios as it allows us to account for a great variety of loading forces. In this first analysis, the model is used to study the impact of a frozen adiabatic index in the estimate of rotation-induced deformations: we assume a polytropic equation of state for the matter at equilibrium but, since chemical reactions may be slow, the perturbations with respect to the unstressed configuration are modelled by using a different adiabatic index. We quantify the impact of a departure of the adiabatic index from its equilibrium value on the stressed stellar configuration and we find that a small perturbation can cause large variations both in displacements and strains. As a first practical application, we estimate the strain developed between two large glitches in the Vela pulsar showing that, starting from an initial unstressed configuration, it is not possible to reach the breaking threshold of the crust, namely to trigger a starquake. In this sense, the hypothesis that starquakes could trigger the unpinning of superfluid vortices is challenged and, for the quake to be a possible trigger, the solid crust must never fully relax after a glitch, making the sequence of starquakes in a neutron star an history-dependent process.

astro-ph.HE↗

arXiv2019

Incompressible analytical models for spinning-down pulsars

We study a class of Newtonian models for the deformations of non-magnetized neutron stars during their spin-down. The models have all an analytical solution, and thus allow to understand easily the dependence of the strain on the star's main physical quantities, such as radius, mass and crust thickness. In the first ``historical'' model the star is assumed to be comprised of a fluid core and an elastic crust with the same density. We compare the response of stars with different masses and equations of state to a decreasing centrifugal force, finding smaller deformations for heavier stars: the strain angle is peaked at the equator and turns out to be a decreasing function of the mass.We introduce a second, more refined, model in which the core and the crust have different densities and the gravitational potential of the deformed body is self-consistently accounted for. Also in this case the strain angle is a decreasing function of the stellar mass, but its maximum value is at the poles and is always larger than the corresponding one in the one-density model by a factor of two. Finally, within the present analytic approach, it is possible to estimate easily the impact of the Cowling approximation: neglecting the perturbations of the gravitational potential, the strain angle is 40\% of the one obtained with the complete model.

astro-ph.HE↗

arXiv2018

Constraints on pulsar masses from the maximum observed glitch

Pulsar glitches, sudden jumps in frequency in otherwise steadily spinning down radio pulsars, offer a unique glimpse into the superfluid interior of neutron stars. The exact trigger of these events remains, however, elusive and this has hampered attempts to use glitch observations to constrain fundamental physics. In this paper we propose a new method to measure the mass of glitching pulsars, using observations of the maximum glitch recorded in a star, together with state of the art microphysical models of the pinning interaction between superfluid vortices and ions in the crust. Studying systematically all the presently observed large glitchers, we find an inverse correlation between size of the maximum glitch and the pulsar mass. Our procedure will allow current and future observations of glitching pulsars to constrain not only the physics of glitch models but also the equation of state of dense matter in neutron star interiors.

astro-ph.HE↗

arXiv2017

Pulsar rotation with superfluid entrainment

Large pulsar glitches (like the ones detected in the Vela) are though to be a consequence of the superfluid component present in the interior of mature neutron stars. However strong entrainment challenges this picture. We study the impact of entrainment on the angular momentum that can be exchanged between the normal component and the superfluid during a glitch by means of a consistent global model. This allows to estimate the maximum angular momentum reservoir stored into the superfluid component of the star: the essential ingredient are newly calculated mesoscopic pinning forces that block the superfluid vorticity in the crust of the neutron star. This method can also provide a quantitative test for global models of rotating neutron stars, as well as for microphysical inputs present in literature (like entrainment parameters and pinning forces).

astro-ph.HE↗

arXiv2016

Axially symmetric equations for differential pulsar rotation with superfluid entrainment

In this article we present an analytical two-component model for pulsar rotational dynamics. Under the assumption of axial symmetry, implemented by a paraxial array of straight vortices that thread the entire neutron superfluid, we are able to project exactly the 3D hydrodynamical problem to a 1D cylindrical one. In the presence of density dependent entrainment the superfluid rotation is non-columnar: we circumvent this by using an auxiliary dynamical variable directly related to the areal density of vortices. The main result is a system of differential equations that take consistently into account the stratified spherical structure of the star, the dynamical effects of non-uniform entrainment, the differential rotation of the superfluid component and its coupling to the normal crust. These equations represent a mathematical framework in which to test quantitatively the macroscopic consequences of the presence of a stable vortex array, a working hypothesis widely used in glitch models. Even without solving the equations explicitly, we are able to draw some general quantitative conclusions; in particular, we show that the reservoir of angular momentum (corresponding to recent values of the pinning forces) is enough to reproduce the largest glitch observed in the Vela pulsar, provided its mass is not too large.

astro-ph.SR↗

arXiv2011

Modelling pulsar glitches with realistic pinning forces: a hydrodynamical approach

Although pulsars are one of the most stable clocks in the universe, many of them are observed to 'glitch', i.e. to suddenly increase their spin frequency (ν) with fractional increases that range from Δν/ν\approx 10^{-11} to 10^{-5}. In this paper we focus on the 'giant' glitches, i.e. glitches with fractional increases in the spin rate of the order of Δν/ν \approx 10^{-6}, that are observed in a sub class of pulsars including the Vela. We show that giant glitches can be modelled with a two-fluid hydrodynamical approach. The model is based on the formalism for superfluid neutron stars of Andersson and Comer (2006) and on the realistic pinning forces of Grill and Pizzochero (2011). We show that all stages of Vela glitches, from the rise to the post-glitch relaxation, can be reproduced with a set of physically reasonable parameters and that the sizes and waiting times between giant glitches in other pulsars are also consistent with our model.

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