Spin Frequency Derivative Research Articles

Pulsar Glitch Activities: The Spin Parameters Approach

Glitch activity refers to the mean increase in pulsar spin frequency per year due to rotational glitches. It is an important tool for studying super-nuclear matter using neutron star interiors as templates. Glitch events are typically observed in the spin frequency (ν) and frequency derivative ( ν̇ ) of pulsars. The rate of glitch recurrence decreases as the pulsar ages, and the activity parameter is usually measured by linear regression of cumulative glitches over a given period. This method is effective for pulsars with multiple regular glitch events. However, due to the scarcity of glitch events and the difficulty of monitoring all known pulsars, only a few have multiple records of glitch events. This limits the use of the activity parameter in studying neutron star interiors with multiple pulsars. In this study, we examined the relationship between the activity parameters and pulsar spin parameters (spin frequency, frequency derivative, and pulsar characteristic age). We found that a quadratic function provides a better fit for the relationship between activity parameters and spin parameters than the commonly used linear functions. Using this information, we were able to estimate the activity parameters of other pulsars that do not have records of glitches. Our analysis shows that the relationship between the estimated activity parameters and pulsar spin parameters is consistent with that of the observed activity parameters in the ensemble of pulsars.

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.

The thousand-pulsar-array programme on MeerKAT XIII: Timing, flux density, rotation measure and dispersion measure timeseries of 597 pulsars

Abstract We report here on the timing of 597 pulsars over the last four years with the MeerKAT telescope. We provide Times-of-Arrival, pulsar ephemeris files and per-epoch measurements of the flux density, dispersion measure (DM) and rotation measure (RM) for each pulsar. In addition we use a Gaussian process to model the timing residuals to measure the spin frequency derivative at each epoch. We also report the detection of 11 glitches in 9 individual pulsars. We find significant DM and RM variations in 87 and 76 pulsars respectively. We find that the DM variations scale approximately linearly with DM, which is broadly in agreement with models of the ionised interstellar medium. The observed RM variations seem largely independent of DM, which may suggest that the RM variations are dominated by variations in the interstellar magnetic field on the line of sight, rather than varying electron density. We also find that normal pulsars have around 5 times greater amplitude of DM variability compared to millisecond pulsars, and surmise that this is due to the known difference in their velocity distributions.

Algorithmic Pulsar Timer for Binaries

Pulsar timing is a powerful tool that, by accounting for every rotation of a pulsar, precisely measures the spin frequency, spin frequency derivatives, astrometric position, binary parameters when applicable, properties of the interstellar medium, and potentially general relativistic effects. Typically, this process demands fairly stringent scheduling requirements for monitoring observations as well as deep domain knowledge to “phase connect” the timing data. We present an algorithm that automates the pulsar-timing process for binary pulsars, whose timing solutions have an additional level of complexity, although the algorithm works for isolated pulsars as well. Using the statistical F-test and the quadratic dependence of the reduced χ 2 near a minimum, the global rotation count of a pulsar can be determined efficiently and systematically. We have used our algorithm to establish timing solutions for two newly discovered binary pulsars, PSRs J1748−2446aq and J1748−2446at, in the globular cluster Terzan 5, using ∼70 Green Bank Telescope observations from the last 13 yr.

Confirmation of the presence of a CRSF in the NICER spectrum of X 1822-371

Aims. X 1822-371 is an eclipsing binary system with a period close to 5.57 h and an orbital period derivative Ṗorb of 1.42(3) × 10−10 s s−1. The extremely high value of its Ṗorb is compatible with a super-Eddington mass transfer rate from the companion star and, consequently, an intrinsic luminosity at the Eddington limit. The source is also an X-ray pulsar, it shows a spin frequency of 1.69 Hz and is in a spin-up phase with a spin frequency derivative of 7.4 × 10−12 Hz s−1. Assuming a luminosity at the Eddington limit, a neutron star magnetic field strength of B = 8 × 1010 G is estimated. However, a direct measure of B could be obtained observing a CRSF in the energy spectrum. Analysis of XMM-Newton data suggested the presence of a cyclotron line at 0.73 keV, with an estimated magnetic field strength of B = (8.8 ± 0.3)×1010 G. Methods. Here we analyze the 0.3–50 keV broadband spectrum of X 1822-371 combining a 0.3–10 keV NICER spectrum and a 4.5–50 keV NuSTAR spectrum to investigate the presence of a cyclotron absorption line and the complex continuum emission spectrum. Results. The NICER spectrum confirms the presence of a cyclotron line at 0.66 keV. The continuum emission is modeled with a Comptonized component, a thermal component associated with the presence of an accretion disk truncated at the magnetospheric radius of 105 km and a reflection component from the disk blurred by relativistic effects. Conclusions. We confirm the presence of a cyclotron line at 0.66 keV inferring a NS magnetic field of B = (7.9 ± 0.5)×1010 G and suggesting that the Comptonized component originates in the accretion columns.

Improving the spin-down limits of the continuous gravitational waves emitted from rotating triaxial pulsars

The spin-down limit of the continuous gravitational wave strain from pulsars assumed to be triaxial stars rotating about a principal moment of inertia axis depends upon the value of the intrinsic spin frequency derivative of the pulsar, among other parameters. In order to get more accurate intrinsic spin frequency derivative values, dynamical effects contributing to the measured spin frequency derivative values must be estimated via more realistic approaches. In this work, we calculated improved values for the spin-down limit of the continuous gravitational wave strain (assuming that pulsars are triaxial stars rotating about a principal moment of inertia axis) for a set of 237 pulsars for which a targeted search for continuous gravitational waves was recently carried out by the LIGO-Virgo-KAGRA (LVK) Collaboration. We used ‘GalDynPsr’, a Python-based public package, to calculate more realistic values for the intrinsic spin frequency derivatives and, consequently, we get more realistic values of the spin-down limit. The realistic values that we obtain for the intrinsic spin frequency derivatives can also provide a valuable contribution to improving the sensitivity of searches for continuous gravitational waves from known pulsars.

Simultaneous 2.25/8.60 GHz Observations of the Magnetar XTE J1810-197

We did 194 epochs of simultaneous 2.25/8.60 GHz observations of XTE J1810−197 in 926 days shortly following its reactivation in 2018 with Shanghai Tian Ma Radio Telescope (TMRT). Although its integrated profiles changed with both time and frequency during this period, they could be classified into 12 types according to phase areas of active radiation components. After MJD 59015, XTE J1810−197 turned from the normal emission state into the spiky emission state that was manifesting as a series of bright narrow sub-pulse bursts at both 2.25 and 8.60 GHz. Due to its variable integrated profiles and unsteady rotations, we got the spin frequency ν and spin-frequency derivatives with the piecewise fitting method. In addition, its long-term declining trend of ν was also obtained as s−2 with the linear fitting method based on our observations spanning a comparatively longer period. We found its flux densities went through three stages: sharp decrease, stabilization, and day-to-day fluctuations in our dual-frequency observations. Although the flux density showed different stages, XTE J1810−197 showed a relatively flat spectrum (α > –1) in most observations. Assuming an ideal dipole magnetic field as some previous research works, we obtained the emission heights of XTE J1810−197 were about 7.5(9) × 104 km and 2.38(7) × 104 km at 2.25 and 8.60 GHz, respectively. We also found that its emission heights would decrease rapidly with the degree of magnetic field twisting.

Timing analysis of EXO 2030+375 during its 2021 giant outburst observed withInsight-HXMT

ABSTRACTWe report the evolution of the X-ray pulsations of EXO 2030+375 during its 2021 outburst using the observations from Insight-HXMT. Based on the accretion torque model, we study the correlation between the spin frequency derivatives and the luminosity. Pulsations can be detected in the energy band of 1–160 keV. The pulse profile evolves significantly with luminosity during the outburst, leading to that the whole outburst can be divided into several parts with different characteristics. The evolution of the pulse profile reveals the transition between the supercritical (fan-beam dominated) and the subcritical accretion (pencil-beam dominated) mode. From the accretion torque model and the critical luminosity model, based on a distance of 7.1 kpc, the inferred magnetic fields are (0.41 − 0.74) × 1012 and (3.48 − 3.96) × 1012 G, respectively, or based on a distance of 3.6 kpc, the estimated magnetic fields are (2.4 − 4.3) × 1013 and (0.98 − 1.11) × 1012 G, respectively. Two different sets of magnetic fields both support the presence of multipole magnetic fields of the neutron star.

Long-term photometric monitoring and spectroscopy of the white dwarf pulsar AR Scorpii

ABSTRACT AR Scorpii (AR Sco) is the only radio-pulsing white dwarf known to date. It shows a broad-band spectrum extending from radio to X-rays whose luminosity cannot be explained by thermal emission from the system components alone, and is instead explained through synchrotron emission powered by the spin-down of the white dwarf. We analysed NTT/ULTRACAM, TNT/ULTRASPEC, and GTC/HiPERCAM high-speed photometric data for AR Sco spanning almost seven years and obtained a precise estimate of the spin frequency derivative, now confirmed with 50-σ significance. Using archival photometry, we show that the spin-down rate of $P/\dot{P} = 5.6 \times 10^6$ yr has remained constant since 2005. As well as employing the method of pulse-arrival time fitting used for previous estimates, we also found a consistent value via traditional Fourier analysis for the first time. In addition, we obtained optical time-resolved spectra with WHT/ISIS and VLT/X-shooter. We performed modulated Doppler tomography for the first time for the system finding evidence of emission modulated on the orbital period. We have also estimated the projected rotational velocity of the M-dwarf as a function of orbital period and found that it must be close to Roche lobe filling. Our findings provide further constraints for modelling this unique system.

On the pulsar spin frequency derivatives and the glitch activity

The number of sudden spin-ups in radio pulsars known as pulsar glitches has increased over the years. Though a consensus has not been reached with regards to the actual cause of the phenomenon, the electromagnetic braking torque on the crust quantified via the magnitude of pulsar spin frequency first derivative, $ \dot{\nu} $ is a key factor in mechanisms put across toward the understanding of the underlying principles involved. The glitch size has been used to establish a quantity used to constrain the mean possible change in pulsar spin frequency $ (\nu) $ per year due to a glitch known as the `glitch activity'. Traditionally, the glitch activity parameter $ A_{g} $ is calculated from the cumulative glitch sizes in a pulsar at a certain observational time span. In this analysis, we test the possibility of of quantifying the $ A_{g} $ with the pulsars main spin frequency derivatives (i.e. $ \dot{\nu} $ and $\ddot{\nu} $). In this approach, the ratio of the frequency derivatives, i.e. $ |\ddot{\nu}|/\dot{\nu}^{2} $ is seen to constrains the glitch activity in radio pulsars. The glitch size is found to be independent of the magnitude of the ratio, however, based on the recorded glitch events, the lower end of $ |\ddot{\nu}|/\dot{\nu}^{2} $ distribution appear to have more glitches. The minimum inter-glitch time interval in the ensemble of pulsars scale with the ratio as $t_{g} \sim 3.35(|\ddot{\nu}|/\dot{\nu}^{2})^{0.23} $. The $ A_{g} $ quantified in this analysis supports the idea of neutron star inner-crust superfluid being the reservoir of momentum transferred during glitches. It suggests that the moment of inertia of the inner-crust to be at most 10 % of the entire neutron star moment of inertia.

Long term radio and X-ray evolution of the magnetar Swift J1818.0-1607

ABSTRACT We report on the the long term monitoring campaign of the seemingly youngest magnetar Swift J1818.0–1607 at radio and X-ray wavelengths over a span of one year. We obtained a coherent timing solution for the magnetar over the same time span. The frequency derivative of the magnetar shows systematic variation with the values oscillating about a mean value of −1.37 × 10−11 Hz s−1. The magnitude of the variation in the frequency derivative reduces with time before converging on the mean value. This corresponds to a characteristic age of ∼ 860 years, 2–4 times more than previously estimated. We were able to identify four states in the spin-frequency derivative that were quantified by the amount of modulation about the mean value and the transition between these states seem to be correlated with the change in the radio emission of the magnetar while no correlation is seen in the average radio profile variability on a shorter time-scale (days). The 0.5–12 keV X-ray flux shows a monotonic decrease that can be attributed to thermal emission from a hot spot on the surface of the neutron star that is reducing in size. Such decrease is consistent with what is seen in other magnetars. The potential correlation between the radio emission mode and the behaviour of the spin-down rate hints to a global change in the magnetopshere of the magnetar akin to the correlation seen in a subset of mode-changing radio pulsars and suggests a physical link between the two sub-populations.

Torque reversal and orbital profile of X-ray pulsar OAO 1657−415

ABSTRACT OAO 1657−415 is an atypical supergiant X-ray binary among wind- and disc-fed systems, showing alternate spin-up/spin-down intervals lasting of the order of tens of days. We study different torque states of OAO 1657−415 based on the spin history monitored by Fermi/Gamma-Ray Burst Monitor, together with fluxes from Swift/Burst Alert Telescope (BAT) and Monitor of All-sky X-ray Image/Gas Slit Camera. Its spin frequency derivatives are well correlated with Swift/BAT fluxes during rapid spin-up episodes, anticorrelated with Swift/BAT fluxes during rapid spin-down episodes, and not correlated in between. The orbital profile of spin-down episodes is reduced by a factor of 2 around orbital phases of 0.2 and 0.8 compared to that of spin-up episodes. The orbital hardness ratio profile of spin-down episodes is also lower than that of spin-up episodes around phases close to the mid-eclipse, implying that there is more material between the neutron star and the observer for spin-down episodes than for spin-up episodes around these phases. These results indicate that the torque state of the neutron star is connected with the material flow on orbital scale and support the retrograde/prograde disc accretion scenario for spin-down/spin-up torque reversal.

The dissipation of toroidal magnetic fields and spin‐down evolution of young and strongly magnetized pulsars

AbstractMagnetars are a kind of pulsars powered mainly by superhigh magnetic fields. They are popular sources with many unsolved issues in themselves but are also linked to various high‐energy phenomena, such as quasi periodic oscillations (QPOs), giant flares, fast radio bursts, and superluminous supernovae. In this work, we first review our recent works on the dissipation of toroidal magnetic fields in magnetars and rotationally powered pulsars and then review the spin‐down evolution of young and strongly magnetized pulsars, especially of magnetars. We present an interesting and important relation between the magnetization parameter and magnetic field in the magnetar crust. Finally, we introduce our two works in progress: to explain the magnetar “antiglitch” events in the thermal plastic flow model and to revisit the expression of braking index n, which is independent of the second derivative of spin frequency of a pulsar, and give some proposals for our future work.

Timing and emission variation of PSR J1733−3716

We present analysis of the timing noise in PSR J1733-3716, which combines data from Parkes 64-m radio telescope and nearly 15 years of timing data obtained from the Nanshan 25-m radio telescope. The variations in the spin frequency and frequency derivative are determined. The fluctuation in the spin frequency is obvious with an amplitude of 1.94(7)*10 -9 Hz. Variations of the integrated profile at 1369 MHz are detected with the changes occur in the relative peak intensity from the right profile component. From analysis of the single pulse data at 1382 MHz, we detect weak emission states that account for 63% of the whole data, and its duration distribution can be fitted with a power law. The pulsar also exhibits strong emission states, during which the emission shows multiple modes. This includes the normal mode, left mode and the right mode, with the time scales spanning between one and seventeen pulse periods. Such short term variability in pulses contributes to the variation of the integrated profile. Examination of the correlations between the spin parameters and the integrated profiles shows likelihood of a random distribution, which reveals that there is probably no obvious relationship between spin-down rate variations and changes of emission in this pulsar.

Updated Spin and Orbital Parameters and Energy Dependent Pulse Behaviors of the Accreting Millisecond X-Ray Pulsar IGR J17591–2342

Abstract We present our work in updating the spin and orbital parameters for the newly discovered accreting millisecond X-ray pulsar (AMXP) IGR J17591–2342 through pulsar timing and analyzing its energy dependent pulse behaviors. The data being analyzed were collected by Neutron Star Interior Composition ExploreR, which observed this AMXP from 2018 August to October. Using the pulse arrival time delay technique, more accurate spin and orbital parameters were evaluated. From the measured spin frequency derivative, it is estimated that the magnetic field of the neutron star in IGR J17591–2342 is approximately 4 × 108 G. Precise pulse profiles can be made using the updated spin and orbital parameters. The soft phase lag phenomenon that is usually seen in other AMXPs is also observed from ∼4 to 12 keV with a value of 0.06 cycles (1.14 μs). Additionally, the pulsed fractional amplitude increases from 1 to ∼5 keV and then decreases for higher energy bands. We found that these phenomena, as well as the energy spectrum, can be explained by the two-component model with a relatively strong blackbody component and an additional unpulsed disk blackbody component.

Tests of Conservation Laws in Post-Newtonian Gravity with Binary Pulsars

Abstract General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider nonconservative ones with a parameterized post-Newtonian parameter, ζ 2. A nonzero ζ 2 induces a self-acceleration for the center of mass of an eccentric binary pulsar system, which contributes to the second time derivative of the pulsar spin frequency, . In our work, using Will’s method, we provide an improved analysis with four well-timed, carefully chosen binary pulsars. In addition, we extend Will’s method and derive the effect of on the third time derivative of the spin frequency, . For PSR B1913+16, the constraint from is even tighter than that from . We combine multiple pulsars with Bayesian inference, and obtain the upper limit, at the 95% confidence level, assuming a flat prior in . It improves the existing bound by a factor of 3. Moreover, we propose an analytical timing formalism for . Our simulated times of arrival with simplified assumptions show the capability of binary pulsars in limiting ζ 2, and useful clues are extracted for real-data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737−3039A, can yield more constraining limits than .

Timing of the accreting millisecond pulsar IGR J17591–2342: evidence of spin-down during accretion

ABSTRACT We report on the phase-coherent timing analysis of the accreting millisecond X-ray pulsar IGR J17591–2342, using Neutron Star Interior Composition Explorer (NICER) data taken during the outburst of the source between 2018 August 15 and 2018 October 17. We obtain an updated orbital solution of the binary system. We investigate the evolution of the neutron star spin frequency during the outburst, reporting a refined estimate of the spin frequency and the first estimate of the spin frequency derivative ($\dot{\nu }\sim -7\times 10^{-14}$ Hz s−1), confirmed independently from the modelling of the fundamental frequency and its first harmonic. We further investigate the evolution of the X-ray pulse phases adopting a physical model that accounts for the accretion material torque as well as the magnetic threading of the accretion disc in regions where the Keplerian velocity is slower than the magnetosphere velocity. From this analysis we estimate the neutron star magnetic field Beq = 2.8(3) × 108 G. Finally, we investigate the pulse profile dependence on energy finding that the observed behaviour of the pulse fractional amplitude and lags as a function of energy is compatible with the down-scattering of hard X-ray photons in the disc or the neutron star surface.

Spin frequency evolution and pulse profile variations of the recently re-activated radio magnetar XTE J1810–197

Abstract After spending almost a decade in a radio-quiet state, the Anomalous X-ray Pulsar XTE J1810–197 turned back on in early 2018 December. We have observed this radio magnetar at 1.5 GHz with nearly daily cadence since the first detection of radio re-activation on 2018 December 8. In this paper, we report on the current timing properties of XTE J1810–197 and find that the magnitude of the spin frequency derivative has increased by a factor of 2.6 over our 48-d data set. We compare our results with the spin-down evolution reported during its previous active phase in the radio band. We also present total intensity pulse profiles at five different observing frequencies between 1.5 and 8.4 GHz, collected with the Lovell and the Effelsberg telescopes. The profile evolution in our data set is less erratic than what was reported during the previous active phase, and can be seen varying smoothly between observations. Profiles observed immediately after the outburst show the presence of at least five cycles of a very stable ∼50 ms periodicity in the main pulse component that lasts for at least tens of days. This remarkable structure is seen across the full range of observing frequencies.

High-precision pulsar timing and spin frequency second derivatives

We investigate the impact of intrinsic, kinematic and gravitational effects on high precision pulsar timing. We present an analytical derivation and a numerical computation of the impact of these effects on the first and second derivative of the pulsar spin frequency. In addition, in the presence of white noise, we derive an expression to determine the expected measurement uncertainty of a second derivative of the spin frequency for a given timing precision, observing cadence and timing baseline and find that it strongly depends on the latter ($\propto t^{-7/2}$). We show that for pulsars with significant proper motion, the spin frequency second derivative is dominated by a term dependent on the radial velocity of the pulsar. Considering the data sets from three Pulsar Timing Arrays, we find that for PSR J0437$-$4715 a detectable spin frequency second derivative will be present if the absolute value of the radial velocity exceeds 33 km s$^{-1}$. Similarly, at the current timing precision and cadence, continued timing observations of PSR J1909$-$3744 for about another eleven years, will allow the measurement of its frequency second derivative and determine the radial velocity with an accuracy better than 14 km s$^{-1}$. With the ever increasing timing precision and observing baselines, the impact of the, largely unknown, radial velocities of pulsars on high precision pulsar timing can not be neglected.

Correlation between the luminosity and spin-period changes during outbursts of 12 Be binary pulsars observed by the MAXI/GSC and the Fermi/GBM

Abstract To study observationally the spin-period changes of accreting pulsars caused by the accretion torque, the present work analyzes X-ray light curves of 12 Be binary pulsars obtained by the MAXI Gas-Slit Camera all-sky survey and their pulse periods measured by the Fermi Gamma-ray Burst Monitor pulsar project, both covering more than six years, from 2009 August to 2016 March. The 12 objects were selected because they are accompanied by clear optical identification and accurate measurements of surface magnetic fields. The luminosity L and the spin-frequency derivatives $\dot{\nu }$, measured during large outbursts with L ≳ 1 × 1037 erg s−1, were found to follow approximately the theoretical relations in the accretion torque models, represented by $\dot{\nu } \propto L^{\alpha }$ (α ≃ 1), and the coefficient of proportionality between $\dot{\nu }$ and Lα agrees, within a factor of ∼3, with that proposed by Ghosh and Lamb (1979b, ApJ, 234, 296). In the course of the present study, the orbital elements of several sources were refined.