Spin Period Derivative Research Articles

An X-Ray and Radio View of the 2022 Reactivation of the Magnetar SGR J1935+2154

Recently, the Galactic magnetar SGR J1935+2154 has garnered attention due to its emission of an extremely luminous radio burst, reminiscent of fast radio bursts (FRBs). SGR J1935+2154 is one of the most active magnetars, displaying flaring events nearly every year, including outbursts as well as short and intermediate bursts. Here, we present our results on the properties of the persistent and bursting X-ray emission from SGR J1935+2154 during the initial weeks following its outburst on 2022 October 10. The source was observed with XMM-Newton and NuSTAR (quasi-)simultaneously during two epochs, separated by ∼5 days. The persistent emission spectrum is well described by an absorbed blackbody plus power-law model up to an energy of ∼25 keV. No significant changes were observed in the blackbody temperature (kT BB ∼ 0.4 keV) and emitting radius (R BB ∼ 1.9 km) between the two epochs. However, we observed a slight variation in the power-law parameters. Moreover, we detected X-ray pulsations in all the data sets and derived a spin-period derivative of Ṗ=5.52(5)×10−11 s s−1. This is 3.8 times larger than the value measured after the first recorded outburst in 2014. Additionally, we performed quasi-simultaneous radio observations using three 25–32 m class radio telescopes for a total of 92.5 hr to search for FRB-like radio bursts and pulsed emission. However, our analysis did not reveal any radio bursts or periodic emission.

The Effect of Irradiation on the Spin of Millisecond Pulsars

A millisecond pulsar (MSP) is an old neutron star (NS) that has accreted material from its companion star, causing it to spin up, which is known as the recycling scenario. During the mass transfer phase, the system manifests itself as an X-ray binary. PSR J1402+13 is an MSP with a spin period of 5.89 ms and a spin period derivative of . These properties make it a notable object within the pulsar population, as MSPs typically exhibit low spin period derivatives. In this paper, we aim to explain how an MSP can possess a high spin period derivative by binary evolution. By utilizing the stellar evolution code MESA, we examine the effects of irradiation on the companion star and the propeller effect on the NS during binary evolution. We demonstrate that irradiation can modify the spin period and mass of an MSP, resulting in a higher spin period derivative. These results suggest that the irradiation effect may serve as a key factor in explaining MSPs with high spin period derivatives.

Binary neutron star populations in the Milky Way

ABSTRACT Galactic binary neutron stars (BNSs) are a unique laboratory to probe the evolution of BNSs and their progenitors. Here, we use a new version of the population synthesis code sevn to evolve the population of Galactic BNSs, by modelling the spin up and down of pulsars self-consistently. We analyse the merger rate $\mathcal {R}_{\rm MW}$, orbital period Porb, eccentricity e, spin period P, and spin period derivative $\dot{P}$ of the BNS population. Values of the common envelope parameter α = 1−3 and an accurate model of the Milky Way star formation history best reproduce the BNS merger rate in our Galaxy ($\mathcal {R}_{\rm MW}\approx {}30$ Myr−1). We apply radio-selection effects to our simulated BNSs and compare them to the observed population. Using a Dirichlet process Gaussian mixture method, we evaluate the four-dimensional likelihood in the $(P_{\rm orb}, e, P, \dot{P})$ space, by comparing our radio-selected simulated pulsars against Galactic BNSs. Our analysis favours an uniform initial distribution for both the magnetic field (1010−13 G) and the spin period (10−100 ms). The implementation of radio selection effects is critical to match not only the spin period and period derivative, but also the orbital period and eccentricity of Galactic BNSs. According to our fiducial model, the Square Kilometre Array will detect ∼20 new BNSs in the Milky Way.

Discovery and Timing Analysis of New Pulsars in Globular Cluster NGC 5024: New Observations from FAST

The most distant globular cluster (GC) with known pulsars is NGC 5024 (M53). In this paper, we report the discovery of a new binary millisecond pulsar, PSR J1312+1810E (M53E), and present the new timing solutions for M53B–E based on 22 observations from the Five-hundred-meter Aperture Spherical radio Telescope (FAST). These discoveries and timing work benefit from FAST’s high sensitivity. We find that M53C is the only isolated millisecond pulsar known in this distant GC, with a spin period of 12.53 ms and spin period derivative of 5.26 × 10−20 s s−1. Our results reveal orbital periods of 47.7, 5.8, and 2.4 days for M53B, D, and E, respectively. The companions, with masses of 0.25, 0.27, and 0.18 M ⊙, respectively, are likely to be white dwarf stars; if they are extended objects, they do not eclipse the pulsars. We find no X-ray counterparts for these millisecond pulsars in archival Chandra images in the band of 0.3–8 keV. The characteristics of this pulsar population are similar to the population of millisecond pulsars in the Galactic disk, as expected from the low stellar density of M53.

X-ray pulsar HD 49798: a contracting white dwarf with a debris disk?

HD 49798/RX J0648.0C4418 is a peculiar binary including a hot subdwarf of O spectral type and a compact companion in a 1.55 day orbit. Based on the steady spin period derivative Ṗ = (−2.17 ± 0.01) × 10−15 s s−1 , the compact object was thought to be a contracting young white dwarf (WD). However, the X-ray luminosity produced by the wind accretion of the massive WD is one order of magnitude smaller than the observed value. In this work, we propose an alternative model to account for the observed X-ray luminosity. If the WD were surrounded by a debris disk, the accretion from the debris disk could produce the observed X-ray luminosity and X-ray pulses. Based on the time-varying accretion rate model, the current mass of the debris disk is constrained to 3.9 × 10−6 M⊙. The accretion torque exerted by such a debris disk can only influence the spin evolution of the WD in the early stages, and its affect is obviously smaller than that caused by the contraction of the WD in the current stage. According to accretion theory, the magnetic field of the WD is constrained to ∼(0.7−7) × 104 G. The calculated conventional polar cap radius of the WD is larger than the observed emitting-zone radius, which probably originates from the existence of strong and small-scale local magnetic field in the polar cap surface. We expect that further multiband observations of this source could help us to confirm or rule out the existence of a debris disk.

NICER Study of Pulsed Thermal X-Rays from Calvera: A Neutron Star Born in the Galactic Halo?

Abstract Calvera (1RXS J141256.0+792204) is an isolated neutron star detected only through its thermal X-ray emission. Its location at high Galactic latitude (b = +37°) is unusual if Calvera is a relatively young pulsar, as suggested by its spin period (59 ms) and period derivative (3.2 × 10−15 s s−1). Using the Neutron Star Interior Composition Explorer, we obtained a phase-connected timing solution spanning four years, which allowed us to measure the second derivative of the frequency ν ̈ = − 2.5 × 10 − 23 Hz s−2 and to reveal timing noise consistent with that of normal radio pulsars. A magnetized hydrogen atmosphere model, covering the entire star surface, provides a good description of the phase-resolved spectra and energy-dependent pulsed fraction. However, we found that a temperature map more anisotropic than that produced by a dipole field is required, with a hotter zone concentrated toward the poles. By adding two small polar caps, we found that the surface effective temperature and that of the caps are ∼0.1 and ∼0.36 keV, respectively. The inferred distance is ∼3.3 kpc. We confirmed the presence of an absorption line at 0.7 keV associated with the emission from the whole star surface, difficult to interpret as a cyclotron feature and more likely originating from atomic transitions. We searched for pulsed γ-ray emission by folding seven years of Fermi-LAT data using the X-ray ephemeris, but no evidence for pulsations was found. Our results favor the hypothesis that Calvera is a normal rotation-powered pulsar, with the only peculiarity of being born at a large height above the Galactic disk.

On the Mass and Magnetic Field of the Neutron Star in the Ultraluminous X-Ray Source NGC 300 ULX1

The accreting compact objects in most of ultraluminous X-ray sources (ULXs) are likely to be neutron stars rather than black holes as suggested by the recent detection of periodic pulsations from some of these sources located in neighboring galaxies and one ULX that has hitherto been discovered in our own galaxy. As a member of the ULX family, NGC 300 ULX1 is a new pulsating ULX (PULX) spinning up at substantially high rates compared with other PULXs. In this paper, we infer the strength of the magnetic field on the surface of the neutron star from the energy of the cyclotron absorption line detected in the pulsed X-ray spectrum of NGC 300 ULX1 and estimate the plausible ranges for the neutron-star mass and beaming fraction using the observed spin period and period derivative of the pulsar and the measured X-ray flux of the source. Our analysis favors proton cyclotron resonance scattering as a viable mechanism to account for both the observed cyclotron energy and high spin-up rates provided that the absorption line is generated close to the surface of the neutron star.

IKT 16 aka PSR J0058–7218: discovery of a 22 ms energetic rotation-powered pulsar in the Small Magellanic Cloud

ABSTRACT We report here on the discovery with XMM–Newton of pulsations at 22 ms from the central compact source associated with IKT 16, a supernova remnant in the Small Magellanic Cloud (SMC). The measured spin period and spin period derivative correspond to 21.7661076(2) ms and 2.9(3) × 10−14 s s−1, respectively. Assuming standard spin-down by magnetic dipole radiation, the spin-down power corresponds to 1.1 × 1038 erg s−1 implying a Crab-like pulsar. This makes it the most energetic pulsar discovered in the SMC so far and a close analogue of PSR J0537–6910, a Crab-like pulsar in the Large Magellanic Cloud. The characteristic age of the pulsar is 12 kyr. Having for the first time a period measure for this source, we also searched for the signal in archival data collected in radio with the Parkes telescope and in γ-rays with the Fermi/LAT, but no evidence for pulsation was found in these energy bands.

An improved spin-down rate for the proposed white dwarf pulsar AR scorpii

ABSTRACT We analyse rapid-cadence, multiwavelength photometry of AR Scorpii from three observatories, covering five observing seasons. We measure the arrival times of the system’s beat pulses and use them to compute an updated ephemeris. The white dwarf spin-down rate is estimated with an uncertainty of only 4 per cent. These results confirm, beyond any doubt, that the white dwarf’s spin period is increasing at the rate consistent with by that of Stiller et al. (2018). We study the evolution of the beat pulse’s colour index across the orbit. The colour of the primary pulse maxima varies significantly across the orbit, with the peaks being bluer after superior conjunction than in the first half of the orbit. Specifically, at orbital phase 0.5, the colour index of the primary pulse shows a very sharp discontinuity towards bluer indices. This supports the Potter & Buckley (2018b) synchrotron emission model where the two emitting poles differ significantly in colour. However, no corresponding jump in the colour of the secondary pulses is seen. Furthermore, our analysis reveals that the arrival times of the pulses can differ by as much as 6 s in simultaneous u and r photometry, depending on the binary orbital phase. If left uncorrected, this wavelength-dependent timing offset could lead to erroneous measurements of the spin-period derivative, particularly with heterogeneous data sets.

Long-term variations of X-ray pulse profiles for the Crab pulsar: data analysis and modeling

The pulse profiles of the Crab pulsar (as well as some other pulsars) vary with time. They can lead to a major source of intrinsic timing noise, which lacks a detailed physical model. The phase separation $\\Delta$ between the first left peak (P1) and the second right peak (P2) is a key parameter that shows the variations of pulse profiles for the Crab pulsar.It was found that the evolution of $\\Delta$ has a tendency with increasing rates of $0.82^{\\circ}\\pm0.25^{\\circ}$, $0.80^{\\circ}\\pm0.54^{\\circ}$, and $0.77^{\\circ}\\pm0.28^{\\circ}$ per century for the 2-6, 6-15, and 15-60 keV bands, respectively. Furthermore, the flux ratios (P2/P1) of X-ray pulse profiles in the three bands were calculated, and the derived flux ratios were consistent with the radio and X-ray measurements of the sl Insight-HXMT.In addition to discovering the physical origin of the pulse changes, the high-SNR X-ray pulse profiles were simulated in the annular gap model, and two model parameters (e.g., the maximum emission heights of the two peaks) were observed to slightly affect the variations of peak separation. We fitted the long-term variations of emission heights of the two peaks and discovered that the emission heights showed increasing tendencies with time. Variations of these emission heights induced a characteristic period derivative, and a complete formula for both the magnetic dipole radiation and wind-particle-induced variations of the moment of inertia was used for the pulsars spin-down to obtain the variation rate $\\dot{\\alpha}$ of the magnetic inclination angle, which was $-1.60^{\\circ}$ per century.Intrinsic timing noise is observed to be mainly induced by the variations of pulse profiles, which might correlate with a characteristic spin period derivative arising from the fluctuations of the emission regions. This work will lay a foundation for understanding the origin of intrinsic timing noise and making high-precision timing models in the future.

On the peculiar torque reversals and the X-ray luminosity history of the accretion-powered X-ray pulsar 4U 1626–67

ABSTRACT The X-ray luminosity (Lx) and the rotational properties of 4U 1626–67 have been measured at regular intervals during the last four decades. It has been recorded that the source underwent torque reversals twice. We have tried to understand whether these eccentrical sign-switches of the spin period derivative ($\dot{P}$) of 4U 1626–67 could be accounted for with the existing torque models. We have found that the observed source properties are better estimated with the distances close to the lower limit of the previously predicted distance range (5−13 kpc). Furthermore, assuming an inclined rotator, we have considered the partial accretion/ejection from the inner disc radius that leads to different Lx–$\dot{P}$ profiles than the aligned rotator cases. We have concluded that the oblique rotator assumption with the inclination angle χ ∼ (10°−30°) brings at least equally best fitting to the observed Lx and $\dot{P}$ of 4U 1626–67. More importantly, the estimated change of the mass accretion rate, which causes the change in observed Lx of 4U 1626–67 is much less than that is found in an aligned rotator case. In other words, without the need for a substantial modification of mass accretion rate from the companion star, the range of the observed Lx could be explained naturally with an inclined magnetic axis and rotation axis of the neutron star.

An X-ray and optical study of the outbursting behaviour of the SMC Be X-ray binary SXP 91.1

ABSTRACT In this paper we report on the optical and X-ray behaviour of the Be X-ray binary, SXP 91.1, during a recent type I outburst. We monitored the outburst using the Neil Gehrels Swift Observatory. These data were supported by optical data from the Southern African Large Telescope and the Optical Gravitational Lensing Experiment (OGLE) to show the circumstellar disc activity. Matter from this disc accretes on to the neutron star, giving rise to the X-ray outburst as seen in the synchronous evolution of the optical and X-ray light curves. Using data taken with OGLE we show that the circumstellar disc has exhibited stable behaviour over two decades. A positive correlation is seen between the colour and magnitude from the OGLE and massive compact halo object observations, which indicates that the disc is orientated at relatively low-inclination angles. From the OGLE and Swift data, we demonstrate that the system has shown relative phase offsets that have persisted for many years. The spin period derivative is seen to be at maximum spin-up at phases when the mass accretion rate is at maximum. We show that the neutron star in SXP 91.1 is an unusual member of its class in the sense that it has had a consistent spin period derivative over many years, with the average spin-up rate being one of the highest for known Small Magellanic Cloud pulsars. The most recent measurements of the spin-up rate reveal higher values than the global trend, which is attributed to the recent mass accretion event leading to the current outburst.

Evolution of high‐mass X‐ray binaries in the small magellanic cloud

To understand the progenitor of rotation‐powered pulsars, we compare them with accreting High‐Mass X‐ray binary pulsars, (hereafter X‐ray pulsars), in the small magellanic cloud. The diagram of spin period vs. period derivative shows that isolated neutron stars could be evolved from X‐ray pulsars. The pulsars with long spin period might spin up to 0.001–1 s. The binary orbit is disrupted by a third body in the universe, and the binaries are detached. Therefore, some of the pulsars become isolated neutron stars.

LOFAR Discovery of a 23.5 s Radio Pulsar

We present the discovery of PSR J0250+5854, a radio pulsar with a spin period of 23.5 s. This is the slowest-spinning radio pulsar known. PSR J0250+5854 was discovered by the LOFAR Tied-Array All-Sky Survey (LOTAAS), an all-Northern-sky survey for pulsars and fast transients at a central observing frequency of 135 MHz. We subsequently detected pulsations from the pulsar in the interferometric images of the LOFAR Two-metre Sky Survey, allowing for sub-arcsecond localization. This, along with a pre-discovery detection 2 years prior, allowed us to measure the spin-period derivative to be $\dot{P}=2.7 \times 10^{-14}$ s s$^{-1}$. The observed spin period derivative of PSR J0250+5854 indicates a surface magnetic field strength, characteristic age and spin-down luminosity of $2.6 \times 10^{13}$G, $13.7$ Myr and $8.2 \times 10^{28}$ erg s$^{-1}$ respectively, for a dipolar magnetic field configuration. This also places the pulsar beyond the conventional pulsar death line, where radio emission is expected to cease. The spin period of PSR J0250+5854 is similar to those of the high-energy-emitting magnetars and X-ray dim isolated neutron stars (XDINSs). However, the pulsar was not detected by the Swift/XRT in the energy band of 0.3-10 keV, placing a bolometric luminosity limit of $1.5 \times 10^{32}$ erg s$^{-1}$ for an assumed $N_{\rm H}=1.35\times10^{21}$ cm$^{-2}$ and a temperature of 85 eV (typical of XDINSs). We discuss the implications of the discovery for models of the pulsar death line as well as the prospect of finding more similarly long-period pulsars, including the advantages provided by LOTAAS for this.

Is PSR J0250+5854 at the Hall Attractor Stage?

In this note we propose that recently discovered radio pulsar J0250+5854 with 23.5 sec spin period is presently at the Hall attractor stage. This can explain low temperature and absence of magnetar-like activity of this source together with its spin period and period derivative. We present results of calculations of the evolution of this source in a simple model of magnetic field decay. The neutron star could start its evolution as a magnetar with initial field $\sim 10^{14}-10^{15}$ G for realistic range of parameter $Q$ describing crust imperfections. Future measurements of surface temperature and age of this neutron star might help to probe this hypothesis.

PALFA Discovery of a Highly Relativistic Double Neutron Star Binary

Abstract We report the discovery and initial follow-up of a double neutron star (DNS) system, PSR J1946+2052, with the Arecibo L-Band Feed Array pulsar (PALFA) survey. PSR J1946+2052 is a 17 ms pulsar in a 1.88 hr, eccentric (e = 0.06) orbit with a ≳1.2 M ⊙ companion. We have used the Jansky Very Large Array to localize PSR J1946+2052 to a precision of 0.″09 using a new phase binning mode. We have searched multiwavelength catalogs for coincident sources but did not find any counterparts. The improved position enabled a measurement of the spin period derivative of the pulsar ( P ˙ = 9 ± 2 × 10 − 19 ); the small inferred magnetic field strength at the surface (B S = 4 × 109 G) indicates that this pulsar has been recycled. This and the orbital eccentricity lead to the conclusion that PSR J1946+2052 is in a DNS system. Among all known radio pulsars in DNS systems, PSR J1946+2052 has the shortest orbital period and the shortest estimated merger timescale, 46 Myr; at that time it will display the largest spin effects on gravitational-wave waveforms of any such system discovered to date. We have measured the advance of periastron passage for this system, ω ˙ = 25.6 ± 0.3 deg yr − 1 , implying a total system mass of only 2.50 ± 0.04 M ⊙, so it is among the lowest-mass DNS systems. This total mass measurement combined with the minimum companion mass constrains the pulsar mass to ≲1.3 M ⊙.

A Comprehensive Library of X-Ray Pulsars in the Small Magellanic Cloud: Time Evolution of Their Luminosities and Spin Periods

AbstractWe have collected and analyzed the complete archive ofXMM-Newton(116),Chandra(151), andRXTE(952) observations of the Small Magellanic Cloud (SMC), spanning 1997–2014. The resulting observational library provides a comprehensive view of the physical, temporal, and statistical properties of the SMC pulsar population across the luminosity range oferg s−1. From a sample of 65 pulsars we report ∼1654 individual pulsar detections, yielding ∼1260 pulse-period measurements. Our pipeline generates a suite of products for each pulsar detection: spin period, flux, event list, high time-resolution light curve, pulse profile, periodogram, and spectrum. Combining all three satellites, we generated complete histories of the spin periods, pulse amplitudes, pulsed fractions, and X-ray luminosities. Some pulsars show variations in pulse period due to the combination of orbital motion and accretion torques. Long-term spin-up/spin-down trends are seen in 12/11 pulsars, respectively, pointing to sustained transfer of mass and angular momentum to the neutron star on decadal timescales. Of the sample, 30 pulsars have a relatively very small spin period derivative and may be close to equilibrium spin. The distributions of pulse detection and flux as functions of spin period provide interesting findings: mapping boundaries of accretion-driven X-ray luminosity and showing that fast pulsars (P < 10 s) are rarely detected, which as of yet are more prone to giant outbursts. Accompanying this paper is an initial public release of the library so that it can be used by other researchers. We intend the library to be useful in driving improved models of neutron star magnetospheres and accretion physics.

FORMATION OF THE DOUBLE NEUTRON STAR SYSTEM PSR J1930–1852

ABSTRACT The spin period (185 ms) and period derivative ( 1.8 × 10 − 17 s s − 1 ?> ) of the recently discovered double neutron star (DNS) system PSR J1930–1852 indicate that the pulsar was mildly recycled through the process of Roche-lobe overflow. This system has the longest orbital period (45 days) of the known DNS systems, and can be formed from a helium star-NS binary if the initial mass of the helium star was ≲ 4.0 M ⊙ ; ?> otherwise, the helium star would never fill its Roche-lobe. At the moment of the supernova explosion, the mass of the helium star was ≲ 3.0 M ⊙ ?> . We find that the probability distribution of the velocity kick imparted to the new-born neutron star has a maximum at about 30 km s − 1 ?> (and a tail up to 260 km s − 1 ?> ), indicating that this NS probably received a low kick velocity at birth.

Einstein@HomeDISCOVERY OF A PALFA MILLISECOND PULSAR IN AN ECCENTRIC BINARY ORBIT

We report the discovery of the millisecond pulsar (MSP) PSR J1950+2414 ($P=4.3$ ms) in a binary system with an eccentric ($e=0.08$) 22-day orbit in Pulsar ALFA survey observations with the Arecibo telescope. Its companion star has a median mass of 0.3 $M_\odot$ and is most likely a white dwarf. Fully recycled MSPs like this one are thought to be old neutron stars spun-up by mass transfer from a companion star. This process should circularize the orbit, as is observed for the vast majority of binary MSPs, which predominantly have orbital eccentricities $e < 0.001$. However, four recently discovered binary MSPs have orbits with $0.027 < e < 0.44$; PSR J1950+2414 is the fifth such system to be discovered. The upper limits for its intrinsic spin period derivative and inferred surface magnetic field strength are comparable to those of the general MSP population. The large eccentricities are incompatible with the predictions of the standard recycling scenario: something unusual happened during their evolution. Proposed scenarios are a) initial evolution of the pulsar in a triple system which became dynamically unstable, b) origin in an exchange encounter in an environment with high stellar density, c) rotationally delayed accretion-induced collapse of a super-Chandrasekhar white dwarf, and d) dynamical interaction of the binary with a circumbinary disk. We compare the properties of all five known eccentric MSPs with the predictions of these formation channels. Future measurements of the masses and proper motion might allow us to firmly exclude some of the proposed formation scenarios.

A possible cyclotron resonance scattering feature near 0.7 keV in X1822-371

Context. The source X1822-371 is a low-mass X-ray binary system (LMXB) viewed at a high inclination angle. It hosts a neutron star with a spin period of ~0.59 s, and recently, the spin period derivative was estimated to be (−2.43 ± 0.05) × 10-12 s/s.