Stellar forensics — II. Millisecond pulsar binaries

We use the grid of models described in Paper I to analyse those millisecond pulsar binaries whose secondaries have been studied optically. In particular, we find cooling ages for these binary systems that range from < 1 to ∼ 15 Gyr. Comparison of cooling ages and characteristic spin-down ages allows us to constrain the initial spin periods and spin-up histories for individual systems, showing that at least some millisecond pulsars had sub-Eddington accretion rates and long magnetic field decay times.     

An empirical model for the polarization of pulsar radio emission

We present an empirical model for single pulses of radio emission from pulsars based on Gaussian probability distributions for relevant variables. The radiation at a specific pulse phase is represented as the superposition of radiation in two (approximately) orthogonally polarized modes (OPMs) from one or more subsources in the emission region of the pulsar. For each subsource, the polarization states are drawn randomly from statistical distributions, with the mean and the variance on the Poincaré sphere as free parameters. The intensity of one OPM is chosen from a lognormal distribution, and the intensity of the other OPM is assumed to be partially correlated, with the degree of correlation also chosen from a Gaussian distribution. The model is used to construct simulated data described in the same format as real data: distributions of the polarization of pulses on the Poincaré sphere and histograms of the intensity and other parameters. We concentrate on the interpretation of data for specific phases of PSR B0329+54 for which the OPMs are not orthogonal, with one well defined and the other spread out around an annulus on the Poincaré sphere at some phases. The results support the assumption that the radiation emerges in two OPMs with closely correlated intensities, and that in a statistical fraction of pulses one OPM is invisible.     

A new technique for timing the double pulsar system

In 2004, McLaughlin et al. discovered a phenomenon in the radio emission of PSR J0737−3039B (B) that resembles drifting subpulses. The repeat rate of the subpulses is equal to the spin frequency of PSR J0737−3039A (A); this led to the suggestion that they are caused by incidence upon B's magnetosphere of electromagnetic radiation from A. Here, we describe a geometrical model which predicts the delay of B's subpulses relative to A's radio pulses. We show that measuring these delays is equivalent to tracking A's rotation from the point of view of a hypothetical observer located near B. This has three main astrophysical applications: (i) to determine the sense of rotation of A relative to its orbital plane, (ii) to estimate where in B's magnetosphere the radio subpulses are modulated and (iii) to provide an independent estimate of the mass ratio of A and B. The latter might improve existing tests of gravitational theories using this system.     

A deep search for pulsar wind nebulae using pulsar gating

Using the Australia Telescope Compact Array (ATCA) we have imaged the fields around five promising pulsar candidates to search for radio pulsar wind nebulae (PWNe). We have used the ATCA in its pulsar-gating mode; this enables an image to be formed containing only off-pulse visibilities, thereby dramatically improving the sensitivity to any underlying PWN. Data from the Molonglo Observatory Synthesis Telescope were also used to provide sensitivity on larger spatial scales. This survey found a faint new PWN around PSR B0906−49; here we report on non-detections of PWNe towards PSRs B1046−58, B1055−52, B1610−50 and J1105−6107. Our radio observations of the field around PSR B1055−52 argue against previous claims of an extended X-ray and radio PWN associated with the pulsar. If these pulsars power unseen, compact radio PWNe, upper limits on the radio flux indicate that a fraction of less than 10⁻⁶ of their spin-down energy is used to power this emission. Alternatively, PSRs B1046−58 and B1610−50 may have relativistic winds similar to other young pulsars and the unseen PWN may be resolved and fainter than our surface brightness sensitivity threshold. We can then determine upper limits on the local interstellar medium (ISM) density of 2.2×10⁻³ and 1×10⁻² cm⁻³, respectively. Furthermore, we derive the spatial velocities of these pulsars to be ∼450 km s⁻¹ and thus rule out the association of PSR B1610−50 with supernova remnant (SNR) G332.4+00.1 (Kes 32). Strong limits on the ratio of unpulsed to pulsed emission are also determined for three pulsars.     

Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

Age constraints in the double pulsar system J0737–3039

We investigate the age constraints that can be placed on the double pulsar system using models for the spin-down of the first-born 22.7-ms Pulsar A and the 2.77-s Pulsar B with characteristic ages of 210 and 50 Myr, respectively. Standard models assuming dipolar spin-down of both pulsars suggest that the time since the formation of Pulsar B is ∼50 Myr, that is, close to Pulsar B's characteristic age. However, adopting models which account for the impact of Pulsar A's relativistic wind on Pulsar B's spin-down, we find that the formation of Pulsar B took place either 80 or 180 Myr ago, depending on the interaction mechanism. Formation 80 Myr ago, closer to Pulsar B's characteristic age, would result in the contribution from J0737−3039 to the inferred coalescence rates for double neutron star binaries increasing by 40 per cent. The 180 Myr age is closer to Pulsar A's characteristic age and would be consistent with the most recent estimates of the coalescence rate. The new age constraints do not significantly impact recent estimates of the kick velocity, tilt angle between pre- and post-supernova orbital planes or pre-supernova mass of Pulsar B's progenitor.     

Discovery of a highly dispersed pulsar at l=304°

We report the discovery of a pulsar with a Galactic longitude of 304° and a dispersion measure (DM) of 875 cm⁻³ pc. PSR J1302−63 has the second largest DM of any known pulsar. It is also relatively weak, with a flux density of only 0.2 mJy at 1500 MHz. This is the 13th pulsar with a DM greater than 400 cm⁻³ pc located more than 50° from the Galactic Centre. It provides further evidence for a significant pulsar population and enhanced electron densities within the major spiral arms.     

Spectral Constraints for Millisecond Pulsars Due to General Relativistic Frame Dragging

We develop a numerical code for simulating the magnetospheres of millisecond pulsars, which are expected to have unscreened electric potentials due to the lack of magnetic pair production. We incorporate General Relativistic (GR) expressions for the electric field and charge density and include curvature radiation (CR) due to primary electrons accelerated above the stellar surface, whereas inverse Compton scattering (ICS) of thermal X-ray photons by these electrons are neglected as a second-order effect. We apply the model to PSR J0437-4715, a prime candidate for testing the GR-Electrodynamic theory, and find that the curvature radiation spectrum cuts off at energies below 15 GeV, which are well below the threshold of the H.E.S.S. telescope, whereas Classical Electrodynamics predict a much higher cutoff near 100 GeV, which should be visible for H.E.S.S., if standard assumed Classical Electrodynamics apply. GR theory also predicts a relatively narrow pulse (2φ _L ∼ 0.2 phase width) centered on the magnetic axis, which sets the beaming solid angle to ∼0.5 sr per polar cap (PC) for a magnetic inclination angle of 35^∘ relative to the spin axis, given an observer which sweeps close to the magnetic axis. We also find that EGRET observations above 100 MeV of this pulsar constrain the polar magnetic field strength to B _pc < 4× 10⁸ G for a pulsar radius of 10 km and moment of inertia of 10⁴⁵ g cm². The field strength constraint becomes even tighter for a larger radius and moment of inertia. Furthermore, a reanalysis of the full EGRET data set of this pulsar, assuming the predicted pulse shape and position, should lead to even tighter constraints on neutron star and GR parameters, up to the point where the GR-derived potential and polar cap current may be questioned.     

Discovery of three new pulsars in a 610-MHz pulsar survey with the GMRT

We report on the discovery of three new pulsars in the first blind survey of the north Galactic plane  (45° < l < 135°; | b | < 1°)  with the Giant Meterwave Radio telescope (GMRT) at an intermediate frequency of 610 MHz. The survey covered 106 deg² with a sensitivity of roughly 1 mJy to long-period pulsars (pulsars with period longer than 1 s). The three new pulsars have periods of 318, 933 and 1056 ms. Their timing parameters and flux densities, obtained in follow-up observations with the Lovell Telescope at Jodrell Bank and the GMRT, are presented. We also report on pulse nulling behaviour in one of the newly discovered pulsars, PSR J2208+5500.     

Giant radio pulses from the millisecond pulsar PSR B1937+21 at 327 MHz

Seven giant radio pulses were recorded from the millisecond pulsar PSR B1937+21 during ≈8.1 min observation by the Ooty Radio Telescope (ORT) at 326.5 MHz. Although sparse, these observations support most of the giant pulse behaviour reported at higher radio frequencies (430 to 2380 MHz). Within the main component of the integrated profile, they are emitted only in a narrow (≲47 μs) window of pulse phase, close to its peak. This has important implications for doing super-high precision timing of PSR B1937+21 at low radio frequencies.     

A data analysis approach for detecting gravitational waves from PSR 0437–4715

A search for gravitational waves from the millisecond pulsar PSR 0437-4715 has been initiated using the bar detector NIOBE which is located at the University of Western Australia. We present a detailed report on the data analysis algorithm, called phase plane rotation , which will be used in this search. A discussion of the actual implementation of the algorithm is presented. The data analysis algorithm mentioned above has the advantage that it requires minimal changes to the already-existing data acquisition facility of NIOBE but, at the same time, it is as efficient as optimal filtering in detecting a signal. This search involves a very long coherent integration of the bar output which may stretch over a few years. With some planned improvements in the detector, a three-year integration should be able to put an upper limit of h  ∼ 10⁻²⁶ on the signal amplitude.     

Cooling curves and initial models for low-mass white dwarfs (<0.25 M⊙) with helium cores

We present a detailed calculation of the evolution of low-mass (<0.25 M_⊙) helium white dwarfs. These white dwarfs (the optical companions to binary millisecond pulsars) are formed via long-term, low-mass binary evolution. After detachment from the Roche lobe, the hot helium cores have a rather thick hydrogen layer with mass between 0.01 and 0.06 M_⊙. As a result of mixing between the core and outer envelope, the surface hydrogen content ( X _surf) is 0.5–0.35 , depending on the initial value of the heavy element Z and the initial secondary mass. We found that the majority of our computed models experience one or two hydrogen shell flashes. We found that the mass of the helium dwarf in which the hydrogen shell flash occurs depends on the chemical composition. The minimum helium white dwarf mass in which a hydrogen flash takes place is 0.213 M_⊙ ( Z =0.003), 0.198 M_⊙ ( Z =0.01), 0.192 M_⊙ ( Z =0.02) or 0.183 M_⊙ ( Z =0.03). The duration of the flashes (independent of chemical composition) is between a few ×10⁶ and a few ×10⁷ yr. In several flashes the white dwarf radius will increase so much that it forces the model to fill its Roche lobe again. Our calculations show that the cooling history of the helium white dwarf depends dramatically on the thickness of the hydrogen layer. We show that the transition from a cooling white dwarf with a temporarily stable hydrogen-burning shell to a cooling white dwarf in which almost all residual hydrogen is lost in a few thermal flashes (via Roche lobe overflow) occurs between 0.183 and 0.213 M_⊙ (depending on the heavy element value).     

A timing formula for main-sequence star binary pulsars

In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, owing to the anisotropic 1/ r ³ nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit, which leads to an evolution of the longitude of periastron and the projected semi-major axis, which is non-linear in time.   In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula that account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259–63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045–7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure.   Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045–7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron. A lower limit of 20° for the inclination of the B star with respect to the orbital plane is derived.     

The effect of pulse profile evolution on pulsar dispersion measure

In an earlier paper, based on simultaneous multifrequency observations with the Giant Metrewave Radio Telescope (GMRT), we reported the variation of pulsar dispersion measures (DMs) with frequency. A few different explanations are possible for such frequency dependence, and a possible candidate is the effect of pulse shape evolution on the DM estimation technique. In this paper we describe extensive simulations we have done to investigate the effect of pulse profile evolution on pulsar DM estimates. We find that it is only for asymmetric pulse shapes that the DM estimate is significantly affected due to profile evolution with frequency. Using multifrequency data sets from our earlier observations, we have carried out systematic analyses of PSR B0329+54 and PSR B1642−03. Both these pulsars have central core-dominated emission which does not show significant asymmetric profile evolution with frequency. Even so, we find that the estimated DM shows significant variation with frequency for these pulsars. We also report results from new, simultaneous multifrequency observations of PSR B1133+16 carried out using the GMRT in phased array mode. This pulsar has an asymmetric pulse profile with significant evolution with frequency. We show that in such a case, amplitude of the observed DM variations can be attributed to profile evolution with frequency. We suggest that genuine DM variations with frequency could arise due to propagation effects through the interstellar medium and/or the pulsar magnetosphere.