Braking Indices Of Pulsars Research Articles

Spatio-spectral-temporal modelling of two young pulsar wind nebulae

Abstract Recent observations of a few young pulsar wind nebulae (PWNe) have revealed their morphologies in some detail. Given the availability of spatio-spectral-temporal data, we use our multi-zone (1D) leptonic emission code to model the PWNe associated with G29.7−0.3 (Kes 75) and G21.5−0.9 (G21.5) and obtain (by-eye) constraints on additional model parameters compared to spectral-only modelling. Kes 75 is a Galactic composite supernova remnant (SNR) with an embedded pulsar, PSR J1846−0258. X-ray studies reveal rapid expansion of Kes 75 over the past two decades. PWN G21.5 is also a composite SNR, powered by PSR J1833−1034. For Kes 75, we study a sudden plasma bulk speed increase that may be due to the magnetar-like outbursts of the central pulsar. An increase of a few percent in this speed does not result in any significant change in the model outputs. For G21.5, we investigate different diffusion coefficients and pulsar spin-down braking indices. We can reproduce the broadband spectra and X-ray surface brightness profiles for both PWNe, and the expansion rate, flux over different epochs, and X-ray photon index vs epoch and central radius for Kes 75 quite well. The latter three features are also investigated for G21.5. Despite obtaining reasonable fits overall, some discrepancies remain, pointing to further model revision. We find similar values to overlapping parameters between our 1D code and those of an independent 0D dynamical code (tide). Future work will incorporate spatial data from various energy wavebands to improve model constraints.

Pulsar timing anomalies: a window into baryon number violation

We investigate the influence of a specific class of slow Baryon Number Violation (BNV)—one that induces quasi-equilibrium evolution — on pulsar spin characteristics. This work reveals how BNV can potentially alter observable parameters, including spin-down rates, the second derivative of spin frequency, and braking indices of pulsars. Moreover, we demonstrate that BNV could lead to anomalies in pulsar timing, along with a wide array of braking indices, both positive and negative. In addition, we examine the possibility of pulsar spin-up due to BNV, which may result in a novel mechanism for the revival of “dead” pulsars. We conclude by assessing the sensitivity required for future pulsar timing efforts to detect such BNV effects, thus highlighting the potential for pulsars to serve as laboratories for testing fundamental physics.

Estimation of the Pulsar Braking Index Using the Evolution of the Rotational Kinetic Energy Loss Rate. Testing on the Crab Pulsar

Estimation of the Pulsar Braking Index Using the Evolution of the Rotational Kinetic Energy Loss Rate. Testing on the Crab Pulsar

Correction to: Apparent dispersion in pulsar braking index measurements caused by timing noise

Correction to: Apparent dispersion in pulsar braking index measurements caused by timing noise

Confronting the Neutron Star Population with Inverse Cascades

The origin and evolution of magnetic fields of neutron stars from birth have long been a source of debate. Here, motivated by recent simulations of the Hall cascade with magnetic helicity, we invoke a model where the large-scale magnetic field of neutron stars grows as a product of small-scale turbulence through an inverse cascade. We apply this model to a simulated population of neutron stars at birth and show how this model can account for the evolution of such objects across the diagram, explaining both pulsar and magnetar observations. Under the assumption that small-scale turbulence is responsible for large-scale magnetic fields, we place a lower limit on the spherical harmonic degree of the energy-carrying magnetic eddies of ≈40. Our results favor the presence of a highly resistive pasta layer at the base of the neutron star crust. We further discuss the implications of this paradigm on direct observables, such as the nominal age and braking index of pulsars.

Imprint of magnetic obliquity in apparent spin-down of radio pulsars

ABSTRACT Numerical simulations predict that the spin-down rate of a single rotation-powered neutron star depends on the angle α between its spin and magnetic axes as $P\dot{P} \propto \mu ^2 (k_0 + k_1\sin ^2\alpha)$, where P is the star spin period, μ is its magnetic moment, while k0 ∼ k1 ∼ 1. Here, we describe a simple observational test for this prediction based on the comparison of spin-down rates of 50 nearly orthogonal (with α close to 90 deg) and 27 nearly aligned (with α close to 0 deg) pulsars. We found, that the apparent pulsar spin-down is consistent with the theory if assumed, that magnetic moments of orthogonal rotators are systematically larger than those of aligned ones for ∼0.15...0.2 dex. Also, as a by-product of the analysis, we provide yet another constraint on the average braking index of radio pulsars as 1 ≤ n ≤ 4 with formal significance not worse than 99 per cent.

Apparent dispersion in pulsar braking index measurements caused by timing noise

ABSTRACT Stochastic temporal wandering of the spin frequency ν of a rotation-powered pulsar (i.e. the achromatic component of timing noise unrelated to interstellar propagation) affects the accuracy with which the secular braking torque can be measured. Observational studies confirm that pulsars with anomalous braking indices $\vert n \vert = \vert \nu \ddot{\nu } / \dot{\nu }^2 \vert \gg 1$ exhibit elevated levels of timing noise, where an overdot symbolizes a derivative with respect to time. Here it is shown, through analytic calculations and Monte Carlo simulations involving synthetic data and modern Bayesian timing techniques, that the variance 〈n2〉 of the measured n scales with the square of the timing noise amplitude $\sigma _{\ddot{\nu }}$ . The anomalous regime 〈n2〉 ≫ 1 corresponds to $\sigma _{\ddot{\nu }}^2 \gg 10^{-60} (\gamma _{\ddot{\nu }}/10^{-6} \, {\rm s^{-1}})^2 (\dot{\nu } / 10^{-14} \, {\rm Hz \, s^{-1}})^4 (\nu / 1 \, {\rm Hz})^{-2} (T_{\rm obs} / 10^8 \, {\rm s}) \, {\rm Hz}^2{\rm s}^{-5 }$ , where $\gamma _{\ddot{\nu }}$ is a stellar damping time-scale, and Tobs is the total observing time. When the inequality in the earlier condition is reversed, n is dominated by the secular braking torque, and timing measurements return n ∼ 3, if the secular braking torque is electromagnetic. The variance 〈n2〉 is greater, when the stochastic process driving spin fluctuations differs from the red noise model (e.g. power-law spectral density) assumed in the timing solution.

Probing the Internal Physics of Neutron Stars through the Observed Braking Indices and Magnetic Tilt Angles of Several Young Pulsars

The braking indices of pulsars may contain important information about the internal physics of neutron stars (NSs), such as neutron superfluidity and internal magnetic fields. As a subsequent paper of Cheng et al., we perform the same analysis as that done in the previous paper to other young pulsars with a steady braking index, n. Combining the timing data of these pulsars with the theory of magnetic field decay, and using their measured magnetic tilt angles, we can set constraints on the number of precession cycles, ξ, which represents the interactions between superfluid neutrons and other particles in the NS interior. For the pulsars considered in this paper, the results show that ξ is within the range of a few ×103 to a few ×106. Interestingly, for the Crab and Vela pulsars, the constraints on ξ obtained with our method are generally consistent with that derived from modeling of the glitch rise behaviors of the two pulsars. Furthermore, we find that the internal magnetic fields of pulsar with n < 3 may be dominated by the toroidal components. Our results may not only help to understand the interactions between the superfluid neutrons and other particles in the interior of NSs but also be important for the study of continuous gravitational waves from pulsars.

Effects of Spin Properties on Braking Indices of 208 Glitching Pulsars

Pulsars are stars that emit electromagnetic radiation in a definite time interval. Detailed study of the long-term timing observations of pulsars indicate that the predictable smooth spin- down of pulsars is predisposed to discrete fluctuations known as glitch. The rotation frequency of pulsars decays with time as quantified by the braking index (<i>n</i>). The braking indices have been known to have no consequence on the quantities like obliquity angle evolution or complex high-order multipole structure but on the spin properties of the pulsars. In the canonical model of the theory of braking indices, <i>n</i> = 3 for all pulsars, but observational information has shown that <i>n</i> ≠ 3, indicating that the canonical model requires reconsideration. Using the Australian Telescope National Facility (ATNF) pulsar catalogue, we selected 208 pulsars with 670 glitches and used the distributions of the spin properties to statistically investigate their effects on the braking indices. We computed the braking indices of these pulsars using the theoretical method and observed that the braking index is much smaller for very young pulsars (10⁴-10⁷) which have been observed to show more glitch activity than their old, stable counterparts. A simple regression analysis of our data show that spin properties of pulsar are more than 65% correlated with the magnitude of pulsar braking index. The implications of the spin properties on braking indices on long timescales are discussed.

The influence of deceleration and internal structure on the braking index of pulsars: Simplest model for the star

AbstractPulsars are rotating neutron stars whose electromagnetic radiation is observed to pulsate and, despite the extremely stable rates, the frequencies of the pulses decay with time, as quantified by the braking index (n). It is extremely difficult to obtain this index from observations due to different factors. Theoretically, in the canonical model for neutron stars, one finds n = 3, but observational data shows that n is less than three. In this work, the canonical model is modified, incorporating the influence of the deceleration of the neutron star. As the star's rotation decelerates, the deformation of the star due to the centrifugal force decreases thereby reducing its moment of inertia. Consequently, the star decelerates less, reducing the braking index. In this work, the star is modeled as a very hard, compressible spherical shell filled with neutrons and protons superfluid that do not interacts with the shell. Using this toy model as a first approach, the braking index is found as a function of rotation, yielding a theoretical braking index closer to the one derived from observational data.

Pulsars in supernova remnants

ABSTRACT A comparative analysis of the properties of 60 pulsars located in supernova remnants (SNRs) was carried out. We found that (1) anomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs) are characterized by longer periods and higher values of period derivatives, (2) the remainder of the pulsars in this sample have shorter periods compared to the bulk of radio pulsars, (3) rotation of their neutron stars is braking faster, (4) this braking seems unlikely to be solely a result of the loss of angular momentum through magnetic dipole radiation. Using the measured and the estimated braking indices of individual pulsars, we calculated their birth periods. We found that (1) AXPs/SGRs are formed with periods of order of several seconds at the time of birth, (2) the remainder of the pulsars show the wide distribution of initial periods from 13 to 1300 ms with no predominance of millisecond values. Estimates of angles β between the rotation axis and the magnetic moment of the neutron stars are obtained. We found that the distribution of these angles is very close to the uniform distribution. This suggests that pulsars are born with arbitrary values of β. We found that the radio luminosities of pulsars observed inside their SNRs are, on average, one order of magnitude less than the average for neutron stars outside their SNRs. While we note that our data set of pulsars within SNRs of 60 is rather small our findings suggest that these pulsars do not show a decrease in their radio luminosity during their evolution.

Could acceleration of a pulsar affect braking index?

In the coming era of multi-messenger astrophysics, pulsars might be one of the most possible electromagnetic counterparts of the gravitational wave. The braking indices, which are related closely to the electromagnetic radiation of pulsars, are shown to be larger for the pulsars with companion. It motivates us to set up a modified spin-down equation for accelerated pulsars. In this model, we attempt to figure out whether acceleration of a pulsar can cause a larger braking index.

The influence of superfluid core cooling in the braking index of Pulsars.

Pulsars are stars from which electromagnetic radiation is observed to pulsate in well-defined time intervals as the star rotates and the emission of eletromagnetic signal is located in a place different from the rotation center. The frequencies of the pulses decay with time, quantified by the braking index (n). In the canonical model n = 3, in general, for all pulsars, but observational data shows that n is lower than 3. In this work a new model is presented, based on a modification of the canonical one incorporating the influence of neutron and proton density that appear in the superfluid core and, as the star cools down, the density of the superfluid core increases making the star to shrink with time and temperature, making the inertia moment to decrease. The difference ot this model from the canonical one is that the star moment of inertia decreases with time (what would accelerate the rotation of the star) what makes the star to not slow down as fast as it should without this process.

Unifying neutron star sub-populations in the supernova fallback accretion model

We employ the supernova fallback disk model to simulate the spin evolution of isolated young neutron stars (NSs). We consider the submergence of the NS magnetic fields during the supercritical accretion stage and its succeeding reemergence. It is shown that the evolution of the spin periods and the magnetic fields in this model is able to account for the relatively weak magnetic fields of central compact objects and the measured braking indices of young pulsars. For a range of initial parameters, evolutionary links can be established among various kinds of NS sub-populations including magnetars, central compact objects and young pulsars. Thus, the diversity of young NSs could be unified in the framework of the supernova fallback accretion model.

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.

Possible Evolution of the Pulsar Braking Index from Larger than Three to About One

Abstract The coupled evolution of pulsar rotation and inclination angle in the wind braking model is calculated. The oblique pulsar tends to align. The pulsar alignment affects its spin-down behavior. As a pulsar evolves from the magneto-dipole radiation dominated case to the particle wind dominated case, the braking index first increases and then decreases. In the early time, the braking index may be larger than three. During the following long time, the braking index is always smaller than three. The minimum braking index is about one. This can explain the existence of a high braking index larger than three and a low braking index simultaneously. The pulsar braking index is expected to evolve from larger than three to about one. The general trend is for the pulsar braking index to evolve from the Crab-like case to the Vela-like case.

Braking Indices of Pulsars Obtained in the Presence of an Effective Force

The theoretical calculation of braking indices of pulsars is still an open problem. In this work we present a study on this issue which adapts the model that assumes that pulsars are rotating magnetic dipoles by introducing a compensating component in the energy conservation equation of the system. Such component relates to an effective force that varies with the first power of the tangential velocity of the pulsar’s crust. We tested the proposed model using data available.

A Model for the Braking Indices of Pulsars

Stars known as pulsars are generally modeled as magnetized spheres made of neutrons with high rotation frequency. It is known that such stars are spinning down and this braking is measured by a parameter, n, known as braking index. For the canonical model such parameter should have a single value for all pulsars: n = 3. However, from observations it is known that n diverges from 3. In this work, differently from the canonical model, we have hypothesized the existence of a variation of the moment of inertia of the star through a time-varying radius. Using energy conservation we find the values for the variation of the radius of our pulsar sample. Our results indicate that it may be reasonable to consider that the radius of pulsars can be changing with time.

GRAVITATIONAL WAVES FROM PULSARS AND THEIR BRAKING INDICES: THE ROLE OF A TIME DEPENDENT MAGNETIC ELLIPTICITY

ABSTRACT We study the role of time dependent magnetic ellipticities ( ) on the calculation of the braking index of pulsars. Moreover, we study the consequences of such a on the amplitude of gravitational waves (GWs) generated by pulsars with measured braking indices. We show that, since the ellipticity generated by the magnetic dipole is extremely small, the corresponding amplitude of GWs is much smaller than the amplitude obtained via the spindown limit.

Assessing the effects of timing irregularities on radio pulsars anomalous braking indices

We investigate the statistical effects of non-discrete timing irregularities on observed radio pulsar braking indices using correlations between the second derivative of the measured anomalous frequency (̈νobs) and some parameters that have been widely used to quantify pulsar timing fluctuations (the timing activity parameter (A), the amount of timing fluctuations absorbed by the cubic term (σR23) and a measure of pulsar rotational stability (σz)) in a large sample of 366 Jodrell Bank Observatory radio pulsars. The result demonstrates that anomalous braking indices are largely artifacts produced by aggregations of fluctuations that occur within or outside the pulsar system. For a subsample of 223 normal radio pulsars whose observed timing activity appeared consistent with instabilities in rotation of the underlying neutron stars (or timing noise) over timescales of ∼ 10 – 40 yr, |̈νobs| strongly correlates (with correlation coefficient |r| ∼ 0.80 – 0.90) with the pulsar timing activity parameters and spin-down properties. On the other hand, no meaningful correlations (r < 0.3) were found between ̈νobs and the timing activity diagnostics and spin-down parameters in the remaining 143 objects, whose timing activity appears significantly dominated by white noise fluctuations. The current result can be better understood if the timing noise in isolated pulsars originates from intrinsic spin-down processes of the underlying neutron stars, but white noise fluctuations largely arise from processes external to the pulsar system.