Pulsar braking indices revisited

Using the standard equation for the slowdown of a neutron star, we derive a formula for the braking index via integration rather than the conventional differentiation. The new formula negates the need to measure the second time derivative of the rotation frequency, ν¨ . We show that the method gives similar braking indices for PSR B1509−58 and the Crab pulsar to those already in the literature. We point out that our method is useful for obtaining the braking indices of moderate-aged pulsars without the need for long, phase-connected timing solutions. We applied the method to 20 pulsars and discuss the implications of the results. We find that virtually all the derived braking indices are dominated by the effects of (unseen) glitches, the recovery from which corrupts the value of ν˙ . However, any real, large, positive braking index has implications for magnetic field decay and offers support to recent models of pulsar evolution.     

Toward an Understanding of the Periastron Puzzle of PSR B1259-63

Efforts are made to understand the timing behaviors (e.g., the jumps in the projected pulsar semimajor axis at the periastron passages) observed in the 13-year monitoring of PSR B1259-63. Planet-like objects are suggested to orbit around the Be star, which may gravitationally perturb the (probably low mass) pulsar when it passes through periastron. An accretion disk should exist outside the pulsar's light cylinder, which creates a spindown torque on the pulsar due to the propeller effect. The observed negative braking index and the discrepant timing residuals close to periastron could be related to the existence of a disk with a varying accretion rate. A speculation is presented that the accretion rate may increase on a long timescale in order to explain the negative braking index.     

A new look at pulsar statistics — Birthrate and evidence for injection

We make a statistical analysis of the periodsP and period-derivativesP of pulsars using a model independent theory of pulsar flow in theP-P diagram. Using the available sample ofP andP values, we estimate the current of pulsars flowing unidirectionally along theP-axis, which is related to the pulsar birthrate. Because of radio luminosity selection effects, the observed pulsar sample is biased towards lowP and highP. We allow for this by weighting each pulsar by a suitable scale factor. We obtain the number of pulsars in our galaxy to be 6.05_−2.80 ^+3.32 × 10⁵ and the birthrate to be 0.048_−0.011 ^+0.014 pulsars yr⁻¹ galaxy⁻¹. The quoted errors refer to 95 per cent confidence limits corresponding to fluctuations arising from sampling, but make no allowance for other systematic and random errors which could be substantial. The birthrate estimated here is consistent with the supernova rate. We further conclude that a large majority of pulsars make their first appearance at periods greater than 0.5 s. This ‘injection’, which runs counter to present thinking, is probably connected with the physics of pulsar radio emission. Using a variant of our theory, where we compute the current as a function of pulsar ‘age’ (1/2P/P), we find support for the dipole braking model of pulsar evolution upto 6 × 10⁶ yr of age. We estimate the mean pulsar braking index to be 3.7_−0.8 ^+0.8.     

Shapiro effect as a possible cause of the low-frequency pulsar timing noise in globular clusters

A prolonged timing of millisecond pulsars has revealed low-frequency uncorrelated (infrared) noise, presumably of astrophysical origin, in the pulse arrival time (PAT) residuals for some of them. Currently available pulsar timing methods allow the statistical parameters of this noise to be reliably measured by decomposing the PAT residual function into orthogonal Fourier harmonics. In most cases, pulsars in globular clusters show a low-frequency modulation of their rotational phase and spin rate. The relativistic time delay of the pulsar signal in the curved spacetime of randomly distributed and moving globular cluster stars (the Shapiro effect) is suggested as a possible cause of this modulation. Extremely important (from an astrophysical point of view) information about the structure of the globular cluster core, which is inaccessible to study by other observational methods, could be obtained by analyzing the spectral parameters of the low-frequency noise caused by the Shapiro effect and attributable to the random passages of stars near the line of sight to the pulsar. Given the smallness of the aberration corrections that arise from the nonstationarity of the gravitational field of the randomly distributed ensemble of stars under consideration, a formula is derived for the Shapiro effect for a pulsar in a globular cluster. The derived formula is used to calculate the autocorrelation function of the low-frequency pulsar noise, the slope of its power spectrum, and the behavior of the σ_z statistic that characterizes the spectral properties of this noise in the form of a time function. The Shapiro effect under discussion is shown to manifest itself for large impact parameters as a low-frequency noise of the pulsar spin rate with a spectral index of n = −1.8 that depends weakly on the specific model distribution of stars in the globular cluster. For small impact parameters, the spectral index of the noise is n = −1.5.     

Radio spectra of pulsars

The results of flux pulsar radioemission measurements at meter wavelengths, made at Pushchino Radio Astronomical Observatory of the Lebedev Physical Institute, are presented. Flux densities at 102, 85, 61 and 39 MHz have been measured for 85, 29, 37 and 23 pulsars correspondingly. Some of them were performed at all frequencies simultaneously. On the basis of these data and high frequencies data obtained by other authors, spectra of 52 pulsars were plotted. In practically all investigated pulsars we have detected a turn-over frequency at which the flux density of pulsar radioemission attained its maximum. Its mean value isv ^m =130±80 MHz. Averaged on many pulsars, the spectral index is negative in the 39–61 MHz frequency range and passes through zero at frequencies of about 100 MHz, becoming positive in the 100–400 MHz frequency range. It was noticed that the spectral index in the 100–400 MHz interval depends upon such pulsar periods as α₁₀₀₋=0.7logp+0.9. Using the spectra, more precise radio luminosities of pulsars have been computed.     

Non-monotonous character of single radio pulsar spin-down

Our paper is dedicated to the problem of anomalous values of braking indices n _obs and spin frequency second derivatives [(n)\ddot]\ddot \nu of isolated radio pulsars. Observations of these objects for over 40 years have shown that in addition to the complex short-term irregular component in the evolution of the pulsars’ frequency, secular values of its second derivative are orders of magnitude greater than the predicted theoretical ones, and in a good half of cases—they are even negative. We earlier attributed this behavior of secular values of the second derivative to the presence of a cyclic component in the secular evolution of ν(t), with a characteristic recurrence time of thousands to tens of thousand years. We continue to develop this hypothesis based on a more detailed statistical analysis of the characteristics of 297 isolated radio pulsars: we analyze the model of these objects spin-down, consisting of two components, monotonic and cyclic, and determine their parameters. We demonstrate that the monotonic spin-down component is described by the classical magnetodipolar power law with an braking index of about 3, while the large amplitude of the cyclic component causes a significant variation of the observed spin-down rate ([(n)\dot] )(\dot \nu ) (with respect to magnetodipolar one), and fully determines the anomalous values of [(n)\ddot]\ddot \nu and n _obs. An important consequence of the existence of a cyclic component of the pulsar rotational variations is the difference between their characteristic ages and respective secular values (by about 0.5–5 times). This allows to explainthe observed discrepancy of the characteristic and physical ages of some objects, as well as very large, up to 10⁸ years, characteristic ages of some old pulsars. The paper argues that the cyclic component of the observed spin-down is due to the long-term precession of neutron stars around their magnetic axes, which, in particular, may be driven by the anomalous braking torque. In the model of purely magnetodipolar braking this torque is a consequence of emission in the near field zone.     

Recent glitches detected in the Crab pulsar

From 2000 to 2010, monitoring of radio emission from the Crab pulsar at Xinjiang Observatory detected a total of nine glitches. The occurrence of glitches appears to be a random process as described by previous researches. A persistent change in pulse frequency and pulse frequency derivative after each glitch was found. There is no obvious correlation between glitch sizes and the time since last glitch. For these glitches Δν _p and D[(n)\dot]_p\Delta\dot{\nu}_{p} span two orders of magnitude. The pulsar suffered the largest frequency jump ever seen on MJD 53067.1. The size of the glitch is ∼6.8×10⁻⁶ Hz, ∼3.5 times that of the glitch occurred in 1989 glitch, with a very large permanent changes in frequency and pulse frequency derivative and followed by a decay with time constant ∼21 days. The braking index presents significant changes. We attribute this variation to a varying particle wind strength which may be caused by glitch activities. We discuss the properties of detected glitches in Crab pulsar and compare them with glitches in the Vela pulsar.     

The Crab Nebula: Interpretation of Chandra observations

We interpret the observed X-ray morphology of the central part of the Crab Nebula (torus + jets) in terms of the standard theory by Kennel and Coroniti (1984). The only new element is the inclusion of anisotropy in the energy flux from the pulsar in the theory. In the standard theory of relativistic winds, the Lorentz factor of the particles in front of the shock that terminates the pulsar relativistic wind depends on the polar angle as γ = γ₀ + γ _m sin² θ, where γ₀∼200 and γ_m∼4.5×10⁶. The plasma flow in the wind is isotropic. After the passage of the pulsar wind through the shock, the flow becomes subsonic with a roughly constant (over the plerion volume) pressure P=1/3;n∈ where n is the plasma particle density and ∈ is the mean particle energy. Since ∈∼γmc ², a low-density region filled with the most energetic electrons is formed near the equator. A bright torus of synchrotron radiation develops here. Jet-like regions are formed along the pulsar rotation axis, where the particle density is almost four orders of magnitude higher than that in the equatorial plane, because the particle energy there is four orders of magnitude lower. The energy of these particles is too low to produce detectable synchrotron radiation. However, these quasijets become comparable in brightness to the torus if additional particle acceleration takes place in the plerion. We also present the results of our study of the hydrodynamic interaction between an anisotropic wind and the interstellar medium. We compare the calculated and observed distributions of the volume emissivity of X-ray radiation.     

Constraining the relative inclinations of the planets B and C of the millisecond pulsar PSR B1257+12

We investigate on the relative inclination of the planets B and C orbiting the pulsar PSR B1257+12. First, we show that the third Kepler’s law does represent an adequate model for the orbital periods P of the planets, because other Newtonian and Einsteinian corrections are orders of magnitude smaller than the accuracy in measuring P _B/C. Then, on the basis of available timing data, we determine the ratio sin i _C/ sin i _B = 0.92±0.05 of the orbital inclinations i _B and i _C independently of the pulsar’s mass M. It turns out that coplanarity of the orbits of B and C would imply a violation of the equivalence principle. Adopting a pulsar mass range 1 ≲ M ≲ 3, in solar masses (supported by present-day theoretical and observational bounds for pulsar’s masses), both face-on and edge-on orbital configurations for the orbits of the two planets are ruled out; the acceptable inclinations for B span the range 36 deg ≲ i _B ≲ 66 deg, with a corresponding relative inclination range 6 deg ≲ (i _C − i _B) ≲ 13 deg.     

Volume Filling Factors of the DIG in M 31

The volume filling factor f _v of the diffuse ionized gas in the bright emission ring of M 31 is derived from radio continuumobservations. The dependence of f _v on the local mean electron density n _e is a power law, f _v(n _e) = a n _e ^-bwith a = 0.011± 0.003 and b = -1.2± 0.3, where n _e is in cm^-3. The same power law was recently found for the DIG in the solar neighbourhood from pulsar data.     

Radio-to-TeV γ-ray emission from PSR B1259–63

We discuss the implications of the recent X-ray and TeV γ-ray observations of the PSR B1259–63 system (a young rotation powered pulsar orbiting a Be star) for the theoretical models of interaction of pulsar and stellar winds. We show that previously considered models have problems to account for the observed behaviour of the system. We develop a model in which the broad band emission from the binary system is produced in result of collisions of GeV–TeV energy protons accelerated by the pulsar wind and interacting with the stellar disk. In this model the high energy γ-rays are produced in the decays of secondary neutral pions, while radio and X-ray emission are synchrotron and inverse Compton emission produced by low-energy (≤100 MeV) electrons from the decays of secondary charged π ^± mesons. This model can explain not only the observed energy spectra, but also the correlations between TeV, X-ray and radio emission components.      

Processing and Analysis of X-ray Timing Data for Crab Pulsartwo

The X-ray timing data for the Crab pulsar obtained by the Chinese X-ray pulsar navigation test satellite are processed and analyzed. The method to build the integrated and standard X-ray pulse profiles of the Crab pulsar by using the X-ray pulsar observation data and the satellite orbit data is described. The principle and algorithm for determining the pulsar's pulse time of arrival (toa) in the frequency domain are briefly introduced. The pulsar's pulse time of arrival is calculated by using the timing data of 50 min integration for each set of observational data. By the comparison between the observed Crab pulsar's pulse time of arrival at the solar system barycenter and that predicted with the Crab pulsar ephemeris, it is found that the timing accuracy is about 14 μs after the systematic error is removed by a quadratic polynomial fitting.     

Hard X-ray emission from the SNR G337.2+0.1

We report hard X-ray emission of the non-thermal supernova remnant G337.2+0.1. The source presents centrally filled and diffuse X-ray emission. A spectral study confirms that the column density of the central part of the object is about N _H∼5.9(±1.5)×10²² cm⁻² and its X-ray spectrum is well represented by a single power-law with a photon index Γ=0.96±0.56. Detailed spectral analysis indicates that the outer region is highly absorbed and quite softer than the inner region. Characteristics already observed in other well-known X-ray plerions. Based on the gathered information, we confirm the SNR nature of G337.2+0.1, and suggest that the central region of the source is a pulsar wind nebula (PWN), originated by an energetic though yet undetected pulsar.     

Timing irregularities of PSR J1705–1906

Timing analysis of PSR J1705–1906 using data from Nanshan 25-m and Parkes 64-m radio telescopes, which span over fourteen years, shows that the pulsar exhibits significant proper motion, and rotation instability. We updated the astrometry parameters and the spin parameters of the pulsar. In order to minimize the effect of timing irregularities on measuring its position, we employ the Cholesky method to analyse the timing noise. We obtain the proper motion of \(-77(3)\) mas?yr^?1 in right ascension and \(-38(29)\) mas?yr^?1 in declination. The power spectrum of timing noise is analyzed for the first time, which gives the spectral exponent \(\alpha =-5.2\) for the power-law model indicating that the fluctuations in spin frequency and spin-down rate dominate the red noise. We detect two small glitches from this pulsar with fractional jump in spin frequency of \(\Delta \nu /\nu \sim 2.9 \times 10^{-10}\) around MJD 55199 and \(\Delta \nu /\nu \sim 2.7\times 10^{-10}\) around MJD 55953. Investigations of pulse profile at different time segments suggest no significant changes in the pulse profiles around the two glitches.     

Two-frequency timing of the pulsar B1937+21 in Kalyazin and Kashima in 1997–2002

We present the results from our timing of the millisecond pulsar B1937+21, performed jointly since 1997 on two radio telescopes: the RT-64 in Kalyazin (Russia) at a frequency of 0.6GHz and RT-34 in Kashima (Japan) at a frequency of 2.15 GHz. The rms value of the pulse time of arrival (TOA) residuals for the pulsar at the barycenter of the Solar system is 1.8 μs (the relative variation is ≈10^?14 over the observing period). The TOA residuals are shown to be dominated by white phase noise, which allows this pulsar to be used as an independent time scale keeper. The upper limit for the gravitational background energy density Ω_gh² at frequencies ≈6.5 × 10^?9 Hz is estimated to be no higher than 10^?6. Based on the long-term timing of the pulsar, we have improved its parameters and accurately determined the dispersion measure and its time variation over the period 1984–2002, which was, on average, ?0.00114(3) pc cm^?3 yr^?1.     

Two decades of pulsar timing of Vela

Pulsar timing at the Mt Pleasant observatory has focused on Vela, which can be tracked for 18 hours of the day. These nearly continuous timing records extend over 24 years allowing a greater insight into details of timing noise, micro glitches and other more exotic effects. In particular we report the glitch parameters of the 2004 event, along with the reconfirmation that the spin up for the Vela pulsar occurs instantaneously to the accuracy of the data. This places a lower limit of about 30 seconds for the acceleration of the pulsar to the new rotational frequency. We also confirm of the low braking index for Vela, and the continued fall in the DM for this pulsar.     

Open cluster ASCC21 as a probable birthplace of the neutron star Geminga

We analyze the encounters of the neutron star (pulsar) Geminga with open star clusters in the OB association Ori OB1a through the integration of epicyclic orbits into the past by taking into account the errors in the data. The open cluster ASCC21 is shown to be the most probable birthplace of either a single progenitor star for the Geminga pulsar or a binary progenitor system that subsequently broke up. Monte Carlo simulations of Geminga-ASCC21 encounters with the pulsar radial velocity V _r = ?100±50 km s^?1 have shown that close encounters could occur between them within ≤10 pc at about t = ?0.52 Myr. In addition, the trajectory of the neutron star Geminga passes at a distance of ≈25 pc from the center of the compact OB association λ Ori at about t = ?0.39 Myr, which is close to the age of the pulsar estimated from its timing.     

Arrival-time analysis for a millisecond pulsar

Arrival times from a fast, quiet pulsar can be used to obtain accurate determinations of pulsar parameters. In the case of the millisecond pulsar, PSR 1937 + 214, the remarkably small rms residual to the timing fit indicates that precise measurements of position, proper motion and perhaps even trigonometric parallax will be possible (Backer 1984). The variances in these parameters, however, will depend strongly on the nature of the underlying noise spectrum. We demonstrate that for very red spectrai.e. those dominated by low-frequency noise, the uncertainties can be larger than the present estimates (based on a white-noise model) and can even grow with the observation period. The possibility of improved parameter estimation through prewhitening’ the data and the application of these results to other pulsar observations are briefly discussed. The post-fit rms residual of PSR 1937 + 214 may be used to limit the energy density of a gravitational radiation background at periods of a few months to years. However, fitting the pulsar position and pulse-emission times filters out significant amounts of residual power, especially for observation periods of less than three years. Consequently the present upper bound on the energy density of gravitational waves Ω_g <3 × 10^-4 R _Μs ² , though already more stringent than any other available, is not as restrictive as had been previously estimated. The present limit is insufficient to exclude scenarios which use primordial cosmic strings for galaxy formation, but should improve rapidly with time. On leave from Raman Research Institute, Bangalore 560080, India.     

Evidence for a binary companion to the central compact object 1E 1207.4-5209

Unique among neutron stars, 1E 1207.4-5209 is an X-ray pulsar with a spin period of 424 ms that contains at least two strong absorption features in its energy spectrum. This neutron star is positionally coincident with the supernova remnant PKS 1209-51/52 and has been identified as a member of the growing class of radio-quiet compact central objects in supernova remnants. From previous observations with Chandra and XMM-Newton, it has been found that the 1E 1207.4-5209 is not spinning down monotonically as is common for young, isolated pulsars. The spin frequency history requires either strong, frequent glitches, the presence of a fall-back disk, or a binary companion. Here, we report on a sequence of seven XMM-Newton observations of 1E 1207.4-5209 performed during a 40 day window between 2005 June 22 and July 31. Due to unanticipated variance in the phase measurements during the observation period that was beyond the statistical uncertainties, we could not identify a unique phase-coherent timing solution. The three most probable timing solutions give frequency time derivatives of +0.9, ?2.6, and +1.6×10^?12 Hz s^?1 (listed in descending order of significance). We conclude that the local frequency derivative during our XMM-Newton observing campaign differs from the long-term spin-down rate by more than an order of magnitude. This measurement effectively rules out glitch models for 1E 1207.4-5209. If the long-term spin frequency variations are caused by timing noise, the strength of the timing noise in 1E 1207.4-5209 is much stronger than in other pulsars with similar period derivatives. Therefore, it is highly unlikely that the spin variations are caused by the same physical process that causes timing noise in other isolated pulsars. The most plausible scenario for the observed spin irregularities is the presence of a binary companion to 1E 1207.4-5209. We identified a family of orbital solutions that are consistent with our phase-connected timing solution, archival frequency measurements, and constraints on the companions mass imposed by deep IR and optical observations.     

Open clusters IC 4665 and Cr 359 and a probable birthplace of the pulsar PSR B1929+10

Based on the epicyclic approximation, we have simulated the motion of the young open star clusters IC 4665 and Collinder 359. The separation between the cluster centers is shown to have been minimal 7 Myr ago, 36 pc. We have established a close evolutionary connection between IC 4665 and the Scorpius-Centaurus association — the separation between the centers of these structures was ≈200 pc 15 Myr ago. In addition, the center of IC 4665 at this time was near two well-known regions of coronal gas: the Local Bubble and the North Polar Spur. The star HIP 86768 is shown to be one of the candidates for a binary (in the past) with the pulsar PSR B1929+10. At the model radial velocity of the pulsar V _r = 2 ± 50 km s^?1, a close encounter of this pair occurs in the vicinity of IC 4665 at a time of ?1.1 Myr. At the same time, using currently available data for the pulsar B1929+10 at its model radial velocity V _r = 200 ± 50 km s^?1, we show that the hypothesis of Hoogerwerf et al. (2001) about the breakup of the ζ Oph-B1929+10 binary in the vicinity of Upper Scorpius (US) about 0.9 Myr ago is more plausible.