Evolution Of Pulsars Research Articles

On the overall properties of young neutron stars: an application to the Crab pulsar

In this brief report, we present a model that complements the well-established canonical model for the spin evolution of rotation-powered pulsars, which is typically used to estimate ages, spin-down luminosity, and surface magnetic fields of middle-aged pulsars. We analytically explore the growth of the magnetic field during a pulsar’s early history, a period shortly after supernova explosion from which the neutron star forms, encompassing the hypercritical phase and subsequent reemergence of the magnetic field. We analyze the impact of such growth on the early dynamics of the pulsar. Investigations into a pulsar’s magnetic evolution are not new, and we expand the knowledge in this area by examining the evolutionary implications in a scenario governed by growth functions. The proposed growth functions, calibrated with data from the Crab pulsar, exhibit satisfactory physical behaviors.

Formation of long-period radio pulsars

Abstract This study investigates the influence of different braking mechanisms on the formation of three long-period radio pulsars (PSRs J0250 + 5854, J2251-3711, and J0901-4046): plasma-filled magnetosphere in combination with magnetic field decay, fall-back disc, and r-mode instability. These braking mechanisms can also affect the thermal evolution of pulsars. By comparing the model-predicted values with observational data such as spin periods, period derivatives, and upper limits of the bolometric luminosity of these pulsars, we find that these three braking mechanisms can reasonably explain the spin period and the period derivative within a certain range of parameters for these sources. The model-predicted bolometric luminosity associated with magnetic field dissipation exceeds the upper limit for PSR J0901-4046 but falls below the upper limits for PSR J0250 + 5854 and PSR J2251-3711. The model-predicted bolometric luminosity within the fall-back disc model exceeds the observed results, whereas the luminosity within the r-mode instability falls below the observed upper limit for these three pulsars. However, a conflict arises when we consider the pulsar radio activity and the accretion phases within the fall-back disc model simultaneously. By combining data from radio and X-ray observations, along with precise measurements of surface thermal emissions, we can enhance our understanding of the braking mechanisms involved in the formation of long-period radio pulsars or constrain key model parameters. Finding more long-period pulsars in the future and conducting multi-band observations will enhance our understanding of the formation and nature of long-period radio pulsars.

On the Nature of Long Period Radio Pulsar GPM J1839-10: Death Line and Pulse Width

Recently another long period radio pulsar GPM J1839−10 has been reported, similar to GLEAM-X J162759.5−523504.3. Previously, the energy budget and rotational evolution of long period radio pulsars had been considered. This time, the death line and pulse width for neutron star and white dwarf pulsars are investigated. The pulse width is included as the second criterion for neutron star and white dwarf pulsars. It is found that: (1) PSR J0250+5854 and PSR J0901−4046 etc. should be normal radio pulsars. They have narrow pulse width and they lie near the radio emission death line. (2) The two long period radio pulsars GLEAM-X J162759.5−523504.3 and GPM J1839−10 are unlikely to be normal radio pulsars. Their possible pulse width is relatively large. They lie far below the fiducial death line on the diagram. (3) GLEAM-X J162759.5−523504.3 and GPM J1839−10 may be magnetars or white dwarf radio pulsars. At present, there are many parameters and uncertainties in both of these possibilities.

Spin Equilibrium of Rapidly Spinning Neutron Stars via Transient Accretion

The concept of spin equilibrium due to an interaction between the stellar magnetosphere and a thin, Keplerian accretion disk, and a well-known formula of the corresponding equilibrium spin frequency, provide a key understanding of spin evolution and the distribution of rapidly spinning neutron stars, viz., millisecond pulsars. However, this concept and formula are for stable accretion, but the mass transfer to most accreting millisecond pulsars is transient and the accretion rate evolves by orders of magnitude during an outburst. In this short and focussed review, we briefly discuss a relatively new concept of the spin equilibrium condition and a new formula for the equilibrium spin frequency for transiently accreting millisecond pulsars. We also review a new method to estimate this equilibrium spin frequency for observed transiently accreting millisecond pulsars, even when a pulsar has not yet attained the spin equilibrium. These will be crucial to probe the spin evolution and distribution of millisecond pulsars, and should also be applicable to all magnetic stars transiently accreting via a thin, Keplerian accretion disk.

Influences of dynamical disruptions on the evolution of pulsars in globular clusters

ABSTRACT By comparing the physical properties of pulsars hosted by core-collapsed (CCed) and non-core-collapsed (non-CCed) globular clusters (GCs), we find that pulsars in CCed GCs rotate significantly slower than their counterparts in non-CCed GCs. Additionally, radio luminosities at 1.4 GHz in CCed GCs are higher. These findings are consistent with the scenario that dynamical interactions in GCs can interrupt angular momentum transfer processes and surface magnetic field decay during the recycling phase. Our results suggest that such effects in CCed GCs are stronger due to more frequent disruptions of compact binaries. This is further supported by the observation that both estimated disruption rates and the fraction of isolated pulsars are predominantly higher in CCed GCs.

Long-period Pulsars as Possible Outcomes of Supernova Fallback Accretion

For about half a century, the radio pulsar population was observed to spin in the ∼0.002–12 s range, with different pulsar classes having a spin-period evolution that differs substantially depending on their magnetic fields or past accretion history. The recent detection of several slowly rotating pulsars has reopened the long-standing question of the exact physics, and observational biases, driving the upper bound of the period range of the pulsar population. In this work, we perform a parameter study of the spin-period evolution of pulsars interacting with supernova fallback matter and specifically look at the fallback accretion disk scenario. Depending on the initial conditions at formation, this evolution can differ substantially from the typical dipolar spin-down, resulting in pulsars that show spin periods longer than their coeval peers. By using general assumptions for the pulsar spin period and magnetic field at birth, initial fallback accretion rates, and including magnetic field decay, we find that very long spin periods (≳100 s) can be reached in the presence of strong, magnetar-like magnetic fields (≳1014 G) and moderate initial fallback accretion rates (∼1022−1027 g s−1). In addition, we study the cases of two recently discovered periodic radio sources, the pulsar PSR J0901–4046 (P = 75.9 s) and the radio transient GLEAM-X J162759.5–523504.3 (P = 1091 s), in light of our model. We conclude that the supernova fallback scenario could represent a viable channel to produce a population of long-period isolated pulsars that only recent observation campaigns are starting to unveil.

Tests of gravitational scalar polarization and constraints of chameleon f(R) gravity from comprehensive analysis of binary pulsars

Chameleon $f(R)$ gravity is equivalent to a class of scalar-tensor theories of gravity with chameleon screening mechanism allowing the theory to satisfy local tests of gravity. Within the framework of chameleon $f(R)$, we study the impact of the chameleon mechanism on the orbital evolution of binary pulsars, and calculate in detail the post-Keplerian (PK) effects (periastron advance, Einstein delay, Shapiro delay, orbital period decay and eccentricity decay) of binary orbit. The differences in PK effects between general relativity (GR) and chameleon $f(R)$ are elegantly quantified by a combination of star's compactness and theory parameter. We use the mass-radius relation to break the degeneracy between these two parameters, thus allowing us to constrain the theory. We simulate the temporal evolution of the orbital period and eccentricity of neutron star (NS) - white dwarf (WD) binaries, and the results indicate that the orbital evolution is typically faster than in GR due to the emission of dipole radiation in chameleon $f(R)$. We use the observables of PK parameters from the three NS-WD binary pulsars to place constraints on chameleon $f(R)$ and possible deviations from GR by performing Monte-Carlo simulations. We find that PSR J1738$+$0333 is the most constraining test of chameleon $f(R)$ in these systems. Our results show no solid evidence of the existence of helicity-0 or helicity-1 polarization states inducing dipole radiation, exclude significant strong-field deviations and confirm that GR is still valid for strong-field asymmetric systems.

Timing and evolution of PSR B0950+08

ABSTRACT We present timing solutions of PSR B0950+08, using 14 years of observations from the Nanshan 26-m Radio Telescope of Xinjiang Astronomical Observatory. The braking index of PSR B0950+08 varies from –367 392 to 168 883, which shows an oscillation with large amplitude (∼105) and uncertainty. Considering the variation of braking indices and the most probable kinematic age of PSR B0950+08, a model with long-term magnetic field decay modulated by short-term oscillations is proposed to explain the timing data. With this magnetic field decay model, we discuss the spin and thermal evolution of PSR B0950+08. The uncertainties of its age are also considered. The results show that three-component oscillations are the more reasonable for the spin-frequency derivative distributions of PSR B0950+08, and the initial spin period of PSR B0950+08 must be shorter than $97\rm \ ms$ when the age is equal to the lower bound of its kinematic age. The standard cooling model could explain the surface temperature of PSR B0950+08 with its most probable kinematic age. Vortex creep heating with a long-term magnetic field decay could maintain a relatively high temperature at the later stages of evolution and explain the thermal emission data of old and warm pulsars. Coupling with the long-term magnetic field decay, an explanation of the temperature of PSR B0950+08 with roto-chemical heating needs an implausibly short initial rotation period ($P_0 \lesssim 17\rm { ms}$). The spin and thermal evolution of pulsars should be studied simultaneously. Future timing, ultraviolet or X-ray observations are essential for studying the evolution and interior properties of pulsars.

Magnetic angle evolution in accreting neutron stars

ABSTRACT The rotation of a magnetized accreting neutron star (NS) in a binary system is described by its spin period and two angles: spin inclination α with respect to the orbital momentum and magnetic angle χ between the spin and the magnetic moment. Magnetospheric accretion spins the NS up and adjusts its rotation axis, decreasing α to nearly perfect alignment. Its effect upon the magnetic angle is more subtle and relatively unstudied. In this work, we model the magnetic angle evolution of a rigid spherical accreting NS. We find that the torque spinning the NS up may affect the magnetic angle while both α and χ significantly deviate from zero, and the spin-up torque varies with the phase of the spin period. As the rotation axis of the NS is being aligned with the spin-up torque, the magnetic axis becomes misaligned with the rotation axis. Under favourable conditions, magnetic angle may increase by Δχ ∼ 15°−20°. This orthogonalization may be an important factor in the evolution of millisecond pulsars, as it partially compensates the χ decrease potentially caused by pulsar torques. If the direction of the spin-up torque changes randomly with time, as in wind-fed high-mass X-ray binaries, both the rotation axis of the NS and its magnetic axis become involved in a non-linear random-walk evolution. The ultimate attractor of this process is a bimodal distribution in χ peaking at χ = 0° and χ = 90°.

Long-term Coherent Timing of the Accreting Millisecond Pulsar IGR J17062–6143

Abstract We report on a coherent timing analysis of the 163 Hz accreting millisecond X-ray pulsar IGR J17062–6143. Using data collected with the Neutron Star Interior Composition Explorer and XMM-Newton, we investigated the pulsar evolution over a time span of four years. We obtained a unique phase-coherent timing solution for the stellar spin, finding the source to be spinning up at a rate of (3.77 ± 0.09) × 10−15 Hz s−1. We further find that the 0.4–6 keV pulse fraction varies gradually between 0.5% and 2.5% following a sinusoidal oscillation with a 1210 ± 40 day period. Finally, we supplemented this analysis with an archival Rossi X-ray Timing Explorer observation and obtained a phase-coherent model for the binary orbit spanning 12 yr, yielding an orbital period-derivative measurement of (8.4 ± 2.0) × 10−12 s s−1. This large orbital period derivative is inconsistent with a binary evolution that is dominated by gravitational wave emission and is suggestive of highly nonconservative mass transfer in the binary system.

Modelling neutron star–black hole binaries: future pulsar surveys and gravitational wave detectors

ABSTRACT Binaries comprised of a neutron star (NS) and a black hole (BH) have so far eluded observations as pulsars and with gravitational waves (GWs). We model the formation and evolution of these NS+BH binaries – including pulsar evolution – using the binary population synthesis code COMPAS. We predict the presence of a total of 50–2000 binaries containing a pulsar and a BH (PSR+BHs) in the Galactic field. We find the population observable by the next generation of radio telescopes, represented by the SKA and MeerKAT, current (LIGO/Virgo) and future (LISA) GW detectors. We conclude that the SKA will observe 1–80 PSR+BHs, with 0–4 binaries containing millisecond pulsars. MeerKAT is expected to observe 0–40 PSR+BH systems. Future radio detections of NS+BHs will constrain uncertain binary evolution processes such as BH natal kicks. We show that systems in which the NS formed first (NSBH) can be distinguished from those where the BH formed first (BHNS) by their pulsar and binary properties. We find 40 per cent of the LIGO/Virgo observed NS+BHs from a Milky Way like field population will have a chirp mass ≥3.0 M⊙. We estimate the spin distributions of NS+BHs with two models for the spins of BHs. The remnants of BHNS mergers will have a spin of ∼0.4, whilst NSBH merger remnants can have a spin of ∼0.6 or ∼0.9 depending on the model for BH spins. We estimate that approximately 25–1400 PSR+BHs will be radio alive whilst emitting GWs in the LISA frequency band, raising the possibility of joint observation by the SKA and LISA.

Orthogonal pulsars as a key test for pulsar evolution

ABSTRACT At present, there is no direct information about evolution of inclination angle χ between magnetic and rotational axes in radio pulsars. As to theoretical models of pulsar evolution, they predict both the alignment, i.e. evolution of inclination angle χ to 0°, and its counter-alignment, i.e. evolution to 90°. In this paper, we demonstrate that the statistics of interpulse pulsars can give us the key test to solve the alignment/counter-alignment problem as the number of orthogonal interpulse pulsars (χ ≈ 90°) drastically depends on the evolution trajectory.

Timing of young radio pulsars – II. Braking indices and their interpretation

ABSTRACT In Paper I of this series, we detected a significant value of the braking index (n) for 19 young, high-$\dot{E}$ radio pulsars using ∼10 yr of timing observations from the 64-m Parkes radio telescope. Here, we investigate this result in more detail using a Bayesian pulsar timing framework to model timing noise and to perform selection to distinguish between models containing exponential glitch recovery and braking index signatures. We show that consistent values of n are maintained with the addition of substantial archival data, even in the presence of glitches. We provide strong arguments that our measurements are unlikely due to exponential recovery signals from unseen glitches even though glitches play a key role in the evolution of a pulsar’s spin frequency. We conclude that, at least over decadal time-scales, the value of n can be significantly larger than the canonical 3 and discuss the implications for the evolution of pulsars.

Discovery of a retrogradely rotating neutron star in the X-ray pulsar GX 301–2

ABSTRACT We report on the analysis of the spin evolution of a slow X-ray pulsar GX 301–2 along the orbit using long-term monitoring by Fermi/Gamma-ray Burst Monitor. Based on the observationally confirmed accretion scenario and an analytical model for the accretion of angular momentum, we demonstrate that in this system, the neutron star spins retrogradely, that is, in a direction opposite to the orbital motion. This first-of-a-kind discovery of such a system proves the principal possibility of retrograde rotation in accreting systems with suitable accretion torque, and might have profound consequences for our understanding of the spin evolution of X-ray pulsars, estimates of their initial spin periods, and the ultimate result of their evolution.

Predictive and Characterized Pulsar Evolution From its Optical Pulsation

The measured and predicted variables of pulsar PSR B1937+21 were explored from the energetics obtained from the previous observation made. The target parameters such as the brightness, luminosities, and optical efficiency. A series of observations were analysed to determine the individual values of the parameters chosen. Within the extended area of optical pulsation, the values were plotted to determine the relation of it to synchrotron emission. The results were presented graphically to see whether PSR B1937+21 will remain consistent with the expected pulsar model. The researcher suggests that simulation and correlation of previous observation made together with a new one to explore the cause of optical pulsation from mass transfer and spectral evolution.

On the Rapid Orbital Expansion in the Compact Low-mass X-Ray Binary 2A 1822–371

Abstract The neutron star (NS) low-mass X-ray binary 2A 1822−371 has an orbital period of 5.57 hr. Mass transfer in such short-period binaries is thought to be driven by magnetic braking with orbital shrinking. However, 2A 1822−371 shows a very rapid orbital expansion, implying that mass transfer occurs rapidly in this system. The accretion rate of the NS is observationally estimated to be higher than the Eddington limit, which is also hard to explain by the standard magnetic braking mechanism. In this work, we construct a model to account for the peculiar properties of 2A 1822−371. We assume that the donor star possesses a relatively strong magnetic field, which is coupled with the stellar winds excited by the X-ray radiation from the NS. This would generate efficient angular momentum loss, leading to a high mass transfer rate and hence orbital expansion. We provide possible evolutionary tracks of 2A 1822−371 and study how the input parameters affect the results. The observational implications of the irradiation-driven mass loss are also briefly discussed in the context of evolution of low-mass X-ray binaries and millisecond pulsars.

Light curve analysis of a transitional millisecond pulsar PSR J1023+0038 with Kepler K2 mission

PSR J1023+0038 has been known as a transitional pulsar-low-mass-X-ray binary (LMXB) system, which provides crucial information in understanding the evolution of pulsars in binary systems. We report analysis of 80-day continuous optical light curve of PSR J1023+0038 with the Kepler observations during K2 mission. The light curve was observed from May to August 2017, where the system appeared to be in its LMXB state. At ∼30 minutes time resolution, the data were fitted with a Gaussian window function, which generated a smoothed light curve with 100, 000 from 3545 raw data input. The time at the maxima and minima of the light curve was measured and compared with the orbit ephemeris predicted from a quadratic polynomial function published by previous work. We found that at MJD ∼57935 there appeared to be a constant delay of ∼1.06 hr added to the orbit, which then gradually recovered to the expected period at MJD ∼57965. Possible causes have been proposed to explain such delay includes a third body involvement or hot spots on the star.

Multi-frequency Scatter-broadening Evolution of Pulsars. II. Scatter-broadening of Nearby Pulsars

Abstract We present multi-frequency scatter-broadening evolution of 29 pulsars observed with the LOw Frequency ARray (LOFAR) and Long Wavelength Array (LWA). We conducted new observations using LOFAR Low Band Antennae as well as utilized the archival data from LOFAR and LWA. This study has increased the total of all multi-frequency or wide-band scattering measurements up to a dispersion measure (DM) of 150 pc cm−3 by 60%. The scatter-broadening timescale (τ sc) measurements at different frequencies are often combined by scaling them to a common reference frequency of 1 GHz. Using our data, we show that the τ sc–DM variations are best fitted for reference frequencies close to 200–300 MHz, and scaling to higher or lower frequencies results in significantly more scatter in data. We suggest that this effect might indicate a frequency dependence of the scatter-broadening scaling index (α). However, a selection bias due to our chosen observing frequencies cannot be ruled out with the current data set. Our data did not favor any particular model of the DM–τ sc relations, and we do not see a statistically significant break at the low-DM range in this relation. The turbulence spectral index (β) is found to be steeper than what is expected from a Kolmogorov spectrum. This indicates that the local ISM turbulence may have a low wavenumber cutoff or the presence of large-scale inhomogeneities in the line of sight to some of the reported pulsars.

The Exotic Zoo of Millisecond Pulsars in Globular Clusters: a multi-wavelength study

This work is focused on the study of millisecond pulsars in globular cluster by using multi-wavelength observations. Radio observations have been used to search for and timing the pulsars. An alternative method to search for very faint pulsars is first presented and then successfully applied to observations of stellar system Terzan 5, leading to the discovery of three new pulsars. The update of the timing solutions of 9 pulsars in M28 is then presented. The timing solutions now cover a data span of 10 years and provide spin, astrometric and orbital properties for all the systems. For the case of the eccentric binaries M28C and M28D, post-Keplerian corrections to the orbit have been measured in order to derive the masses of the binary components. The measurement of the pulsar proper motions allowed to constrain the cluster motion as a whole and its orbit around the Galaxy. Finally, the pulsar spin and orbital period derivatives have been used to measure their accelerations induced by the cluster potential field. Optical observations have been used to search for millisecond pulsar optical counterparts. Six new companion stars have been discovered. In particular, four companions turned out to be He white dwarfs. One companion turned out to be a faint and non-degenerate object, strongly affected by heating of the stellar side exposed to the pulsar flux. Finally, one companion is a main-sequence star which shows Hα emission likely due to a low-level mass transfer. Furthermore, we identified the companion star to a transient low-mass X-ray binary. This companion turned out to be a sub-giant branch star and therefore this system is likely in a very early phase of the mass accretion stage. Conclusion are drawn in the final chapter, where the evolution of millisecond pulsars is discussed and possible future developments are suggested.

Search for a radio pulsar in the remnant of supernova 1987A

We have observed the remnant of supernova SN~1987A (SNR~1987A), located in the Large Magellanic Cloud (LMC), to search for periodic and/or transient radio emission with the Parkes 64\,m-diameter radio telescope. We found no evidence of a radio pulsar in our periodicity search and derived 8$\sigma$ upper bounds on the flux density of any such source of $31\,\mu$Jy at 1.4~GHz and $21\,\mu$Jy at 3~GHz. Four candidate transient events were detected with greater than $7\sigma$ significance, with dispersion measures (DMs) in the range 150 to 840\,cm$^{-3}\,$pc. For two of them, we found a second pulse at slightly lower significance. However, we cannot at present conclude that any of these are associated with a pulsar in SNR~1987A. As a check on the system, we also observed PSR~B0540$-$69, a young pulsar which also lies in the LMC. We found eight giant pulses at the DM of this pulsar. We discuss the implications of these results for models of the supernova remnant, neutron star formation and pulsar evolution.