PSR J0737-3039B Research Articles

Simulation of the orbit and spin period evolution of the double pulsars PSR J0737-3039 from their birth to coalescence induced by gravitational wave radiation

The complete orbital and spin period evolutions of the double neutron star (NS) system PSR J0737–3039 are simulated from birth to coalescence, which include the two observed radio pulsars classified as primary NS PSR J0737–3039A and companion NS PSR J0737–3039B. By employing the characteristic age of PSR J0737–3039B to constrain the true age of the double pulsar system, the initial orbital period and initial binary separation are obtained as 2.89 h and 1.44 × 106 km, respectively, and the coalescence age or the lifetime from the birth to merger of PSR J0737–3039 is obtained to be 1.38 × 108 yr. At the last minute of coalescence, corresponding to the gravitational wave frequency changing from 20 Hz to 1180 Hz, we present the binary separation of PSR J0737–3039 to be from 442 km to 30 km, while the spin periods of PSR J0737–3039A and PSR J0737–3039B are 27.10 ms and 4.63 s, respectively. From the standard radio pulsar emission model, before the system merged, the primary NS could still be observed by a radio telescope, but the companion NS had crossed the death line in the pulsar magnetic-field versus period (B – P) diagram at which point it is usually considered to cease life as a pulsar. This is the first time that the whole life evolutionary simulation of the orbit and spin periods for a double NS system is presented, which provides useful information for observing a primary NS at the coalescence stage.

The Classifications of Double Neutron Stars and their Correlations with the Binary Orbital Parameters

The statistical distribution of the total mass of 14 double neutron star (DNS) systems (out of 18 pairs observed) is found to be very narrow, with the average and standard deviation as 2.65 ± 0.03 M⊙. For the seven pairs of DNSs with the precisely measured masses of the recycled NSs (first formed) and their non-recycled companions (second formed), their masses are homogeneously distributed as 1.38 ± 0.02 M⊙ and 1.29 ± 0.02 M⊙, respectively. It is shown by the Anderson–Darling and Mann–Whitney–Wilcoxon tests that the first-born NSs share a same distribution, which should be formed by the supernova explosion; however, the second-formed NSs have the different statistical origins, which can be ascribed to three formation mechanisms after the further investigations of their orbital parameters and mass values, for instance, supernova explosion (e.g., PSR B1913+16), electron capture (e.g., PSR J0737-3039B), and ultra-stripped cores in close-orbit systems (e.g., PSR J1411+2551). In addition, by means of Fisher’s discriminant method, through simulation of the two groups of DNS samples that originated from electron-capture supernova and core-collapse supernova, we obtained the linear discriminant equation (e = −4.5Porb(day) + 1.1) between the eccentricity and orbital period, which can divide the DNSs into two groups involved in NS formed by electron-capture supernova (core-collapse supernova) without (with) kick.

Rapidly Rising Optical Transients from the Birth of Binary Neutron Stars

Abstract We study optical counterparts of a new-born pulsar in a double neutron star system like PSR J0737-3039A/B. This system is believed to have ejected a small amount of mass of  ( 0.1 M ⊙ ) at the second core-collapse supernova. We argue that the initial spin of the new-born pulsar can be determined by the orbital period at the time when the second supernova occurs. The spin angular momentum of the progenitor is expected to be similar to that of the He-burning core, which is tidally synchronized with the orbital motion, and then the second remnant may be born as a millisecond pulsar. If the dipole magnetic field strength of the nascent pulsar is comparable with that inferred from the current spin-down rate of PSR J0737-3039B, the initial spin-down luminosity is comparable to the luminosity of super-luminous supernovae. We consider thermal emission arising from the supernova ejecta driven by the relativistic wind from such a new-born pulsar. The resulting optical light curves have a rise time of ∼10 days and a peak luminosity of ∼1044 erg s−1. The optical emission may last for a month to several months, due to the reprocessing of X-rays and UV photons via photoelectric absorption. These features are broadly consistent with those of the rapidly rising optical transients. The high spin-down luminosity and small ejecta mass are favorable for the progenitor of the repeating fast radio burst, FRB 121102. We discuss a possible connection between new-born double pulsars and fast radio bursts.

A Statistical Study on Double Neutron Star Masses

By statistically analyzing the masses of twelve double neutron star (DNS) systems, it is concluded that the weighted mean value of DNS masses is (1.339±0.042) M⊙, where the weighted mean masses of the primary and companion stars are respectively (1.439±0.036) M⊙ and (1.239±0.020) M⊙. The mean value of the masses of primary stars is higher than that of companion stars, which indicates that the primary star may increase its mass by accretion, or the mass of its progenitor star is higher. Therefore, the physical process of supernova explosion through which the high-mass stars become NSs can be investigated hereby. Also it is found that the total masses of the DNSs span a narrow range of 2.5∼2.8M⊙, implying that the companion stars might impact on the mass formation of DNSs. Moreover, the mass ratios of the DNSs (primaries to companions) approximate 1 (slightly larger than 1), indicating that the masses of the progenitors of primary stars are approximately equal to the masses of the progenitors of companion stars. By analyzing the distribution of the 12 DNSs in the surface magnetic field strength versus spin period (B-Ps) diagram, it is found that the surface magnetic field strength in the primary stars of the DNSs is ∼ 1010 Gs, and the spin period is ∼ 50ms; while the two pulsars, i.e. PSR J1906+0746 and PSR J0737-3039B, are located in the region of normal pulsars in the B-Ps diagram, their surface magnetic field strength is ∼ 1012 Gs, suggesting that they might not be accelerated through accretion.

Similarity of PSR J1906+0746 to PSR J0737–3039: a Candidate of a New Double Pulsar System?

Abstract PSR J1906+0746 is a nonrecycled strong magnetic field neutron star (NS), sharing the properties of the secondary-formed NS PSR J0737–3039B in the double pulsar system PSR J0737–3039AB. By comparing the orbital parameters of PSR J1906+0746 with those of PSR J0737–3039AB, we conclude that both systems have a similar origin and evolution history, involving an e-capture process for forming the second-born NS, like in the case of PSR J0737–3039B. We expect the companion of PSR J1906+0746 to be a long-lived recycled pulsar with radio beams that currently cannot be observed from Earth. We suggest possible ways to detect its presence. To compare PSR J1906+0746 with PSR J0737–3039, we also present the mass distribution of eight pairs of double NSs and find that in double NSs the mass of the recycled pulsar is usually larger than that of the nonrecycled one, which may be the result of accretion.

Cooling of neutron stars and hybrid stars with a stiff hadronic EoS

Within the "nuclear medium cooling" scenario of neutron stars all reliably known temperature - age data, including those of the central compact objects in the supernova remnants of Cassiopeia A and XMMU-J1732, can be comfortably explained by a set of cooling curves obtained by variation of the star mass within the range of typical observed masses. The recent measurements of the high masses of the pulsars PSR J1614-2230 and PSR J0348-0432 on the one hand, and of the low masses for PSR J0737-3039B and the companion of PSR J1756-2251 on the other, provide independent proof for the existence of neutron stars with masses in a broad range from $\sim 1.2$ to 2 $M_\odot$. The values $M>2 M_{\odot}$ call for sufficiently stiff equations of state for neutron star matter. We investigate the response of the set of neutron star cooling curves to a stiffening of the nuclear equation of state so that maximum masses of about $2.4 M_\odot$ would be accessible and to a deconfinement phase transition from such stiff nuclear matter in the outer core to color superconducting quark matter in the inner core. Without readjustment of cooling inputs the mass range required to cover all cooling data for the stiff DD2 equation of state should include masses of $2.426 M_\odot$ for describing the fast cooling of CasA while the existence of a quark matter core accelerates the cooling so that CasA cooling data are described with a hybrid star of mass $1.674 M_\odot$.

Implications of PSR J0737-3039B for the Galactic NS-NS binary merger rate

The Double Pulsar (PSR J0737-3039) is the only neutron star-neutron star (NS-NS) binary in which both NSs have been detectable as radio pulsars. The Double Pulsar has been assumed to dominate the Galactic NS-NS binary merger rate R_g among all known systems, solely based on the properties of the first-born, recycled pulsar (PSR J0737-3039A, or A) with an assumption for the beaming correction factor of 6. In this work, we carefully correct observational biases for the second-born, non-recycled pulsar (PSR J0737-0737B, or B) and estimate the contribution from the Double Pulsar on R_g using constraints available from both A and B. Observational constraints from the B pulsar favour a small beaming correction factor for A (~2), which is consistent with a bipolar model. Considering known NS-NS binaries with the best observational constraints, including both A and B, we obtain R_g=21_{-14}^{+28} per Myr at 95 per cent confidence from our reference model. We expect the detection rate of gravitational waves from NS-NS inspirals for the advanced ground-based gravitational-wave detectors is to be 8^{+10}_{-5} per yr at 95 per cent confidence. Within several years, gravitational-wave detections relevant to NS-NS inspirals will provide us useful information to improve pulsar population models.

Revisiting the border between Newtonian mechanics and General Relativity: The periastron advance

The problem of periastron advance, which is the basis of one of the three classical tests of relativity theory, is revised with respect to both Newtonian mechanics and General Relativity and updated in the light of recent astronomical measurements of binary pulsars. We show that in Newtonian mechanics the addition of a corrective term to Newton’s law of gravitation, consistent with the principles of Newtonian mechanics, leads to the same formula of periastron advance as that used in General Relativity, which proves to be valid in all astronomical cases known, even in the cases of binary pulsars such as PSR B1913+16, PSR J1141-6545 and the so-called double pulsar PSR J0737-3039A and PSR J0737-3039B, which are considered as natural relativity laboratories. Thus, among the relativistic phenomena, the periastron advance is one that can be also understood in Newtonian terms by means of an ad hoc assumption.

ULTRA-STRIPPED TYPE Ic SUPERNOVAE FROM CLOSE BINARY EVOLUTION

Recent discoveries of weak and fast optical transients raise the question of their origin. We investigate the minimum ejecta mass associated with core-collapse supernovae (SNe) of Type Ic. We show that mass transfer from a helium star to a compact companion can produce an ultra-stripped core which undergoes iron core collapse and leads to an extremely fast and faint SN Ic. In this Letter, a detailed example is presented in which the pre-SN stellar mass is barely above the Chandrasekhar limit, resulting in the ejection of only ~0.05-0.20 M_sun of material and the formation of a low-mass neutron star. We compute synthetic light curves of this case and demonstrate that SN 2005ek could be explained by our model. We estimate that the fraction of such ultra-stripped to all SNe could be as high as 0.001-0.01. Finally, we argue that the second explosion in some double neutron star systems (for example, the double pulsar PSR J0737-3039B) was likely associated with an ultra-stripped SN Ic.

FERMILAT PULSED DETECTION OF PSR J0737–3039A IN THE DOUBLE PULSAR SYSTEM

We report the Fermi Large Area Telescope discovery of gamma-ray pulsations from the 22.7 ms pulsar A in the double pulsar system J0737-3039A/B. This is the first mildly recycled millisecond pulsar (MSP) detected in the GeV domain. The 2.7 s companion object PSR J0737-3039B is not detected in gamma rays. PSR J0737-3039A is a faint gamma-ray emitter, so that its spectral properties are only weakly constrained; however, its measured efficiency is typical of other MSPs. The two peaks of the gamma-ray light curve are separated by roughly half a rotation and are well offset from the radio and X-ray emission, suggesting that the GeV radiation originates in a distinct part of the magnetosphere from the other types of emission. From the modeling of the radio and the gamma-ray emission profiles and the analysis of radio polarization data, we constrain the magnetic inclination $\alpha$ and the viewing angle $\zeta$ to be close to 90$^\circ$, which is consistent with independent studies of the radio emission from PSR J0737-3039A. A small misalignment angle between the pulsar's spin axis and the system's orbital axis is therefore favored, supporting the hypothesis that pulsar B was formed in a nearly symmetric supernova explosion as has been discussed in the literature already.

RADIUS CONSTRAINT OF THE RECYCLED DOUBLE PULSAR PSR J0737-3039

We investigate the radius of the recycled pulsar in double pulsar system PSR J0737-3039. In the standard accretion spin-up model, the recycled pulsar spin up continues until arriving at a minimum spin period, or so-called "equilibrium period", which is related to the stellar magnetic field, the accretion rate and radius. The generic spin-down age may give realistic estimates for normal pulsar PSR J0737-3039B, since its present spin period is much longer than the one at birth. In this paper, we estimate the radius of millisecond pulsar (MSP) PSR J0737-3039A by assuming its true age is same as the spin-down age of its companion PSR J0737-3039B. We find that the radius of recycled pulsar PSR J0737-3039A ranges approximately from 12 to 38 km, and it should be far from the composition of strange quark matters, as shown in the mass-radius diagram.

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity II

This paper presents a new family of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ nm=2.5×1017 kg m−3. By this model we obtain the mass of the Crab pulsar, M Crab, 1.36M ⊙ and radius 13.21 km, constraining the moment of inertia > 1.61×1038 kg m2 for the conservative estimate of Crab nebula mass 2M ⊙. And M Crab=1.96M ⊙ with radius R Crab=14.38 km constraining the moment of inertia > 3.04×1038 kg m2 for the newest estimate of Crab nebula mass, 4.6M ⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I A =1.4285×1038 kg m2 and I B =1.3647×1038 kg m2 respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M G(max)=4.7487M ⊙ with radius $R_{M_{\max}}=15.24~\mathrm{km}$ , surface redshift 0.9878, charge 7.47×1020 C, and central density 4.31ρ nm.

A family of well behaved charge analogues of Durgapal’s perfect fluid exact solution in general relativity

This paper presents a new family of interior solutions of Einstein–Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of charge distribution. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a star is maximized with all degree of suitability by assuming the surface density equal to normal nuclear density, ρ nm=2.5×1017 kg m−3. By this model we obtain the mass of the Crab pulsar, M Crab, 1.36M ⊙ and radius 13.21 km, constraining the moment of inertia > 1.61×1038 kg m2 for the conservative estimate of Crab nebula mass 2M ⊙. And M Crab=1.96M ⊙ with radius R Crab=14.38 km constraining the moment of inertia > 3.04×1038 kg m2 for the newest estimate of Crab nebula mass, 4.6M ⊙. These results are quite well in agreement with the possible values of mass and radius of Crab pulsar. Besides this, our model yields moments of inertia for PSR J0737-3039A and PSR J0737-3039B, I A =1.4285×1038 kg m2 and I B =1.3647×1038 kg m2 respectively. It has been observed that under well behaved conditions this class of solutions gives us the overall maximum gravitational mass of super dense object, M G(max)=4.7487M ⊙ with radius \(R_{M_{\max}}=15.24~\mathrm{km}\), surface redshift 0.9878, charge 7.47×1020 C, and central density 4.31ρ nm.

A new well behaved class of charge analogue of Adler’s relativistic exact solution

The paper presents a new class of parametric interior solutions of Einstein-Maxwell field equations in general relativity for a static spherically symmetric distribution of a charged perfect fluid with a particular form of electric field intensity. This solution gives us wide range of parameter, K, for which the solution is well behaved hence, suitable for modeling of superdense star. For this solution the gravitational mass of a superdense object is maximized with all degree of suitability by assuming the surface density of the star equal to the normal nuclear density 2.5E17 kg/m3. By this model we obtain the mass of the Crab pulsar 1.401 Solar mass and the radius 12.98 km constraining the moment of inertia parameter greater than 1.61 for the conservative estimate of Crab nebula mass 2 Solar mass and 2.0156 Solar mass with radius 14.07 km constraining the moment of inertia parameter greater than 3.04 for the newest estimate of Crab nebula mass 4.6 Solar mass which are quite well in agreement with the possible values of mass and radius of Crab pulsar.Besides this, our model yields the moments of inertia for PSR J0737-3039A and PSR J0737-3039B are 1.4624E38 kgm2 and 1.2689E38 kgm2 respectively. It has been observed that under well behaved conditions this class of parametric solution gives us the maximum gravitational mass of causal superdense object 2.8020 Solar mass with radius 14.49 km, surface redshift 0.4319, charge 4.67E20 C, and central density 2.68 times nuclear density.

Magnetospheric interactions and emission properties in the double pulsar system

Our ability to observe both pulsars in the double-pulsar system, PSR J0737–3039A/B, combined with its short binary period and almost edge-on orbit, provides an unique opportunity to study pulsar magnetospheric interactions and the pulse emission mechanism. Pulses from J0737–3039A (A) are eclipsed by the magnetosphere of PSR J0737–3039B (B) which is believed to be highly distorted by the relativistic wind from A. In addition, pulses from B are modulated at the A rotational period, revealing an interaction between radiation from A and the B pulse emission mechanism. Relativistic geodetic precession of the spin axes of the two pulsars is expected. Surprisingly, no precessional effects have been observed in A, but secular changes in the B pulse profile and orbital modulation are seen. Finally, based on polarisation observations, we discuss the inclination of A’s magnetic axis relative to its spin axis.

Constraining the gravitational binding energy of PSR J0737-3039B using terrestrial nuclear data

We show that the gravitational binding energy of a neutron star of a given mass is correlated with the slope of the nuclear symmetry energy at 1-2 times nuclear saturation density for equations of state without significant softening (i.e., those that predict maximum masses $M_{\rm max} > 1.44M_{\odot}$ in line with the largest accurately measured neutron star mass). Applying recent laboratory constraints on the slope of the symmetry energy to this correlation we extract a constraint on the baryon mass of the lower mass member of the double pulsar binary system, PSR J0737-3039B. We compare with independent constraints derived from modeling the progenitor star of J0737-3039B up to and through its collapse under the assumption that it formed in an electron capture supernova. The two sets of constraints are consistent only if $L \lesssim$ 70 MeV.

PSR J0737−3039: Interacting Pulsars in X‐Rays1

We present the results of a ~230 ks long X-ray observation of the relativistic double-pulsar system PSR J0737–3039 obtained with the XMM-Newton satellite in 2006 October. We confirm the detection in X-rays of pulsed emission from PSR J0737–3039A (PSR A), mostly ascribed to a soft nonthermal power-law component (Γ ~ 3.3) with a 0.2-3 keV luminosity of ~1.9 × 1030 erg s−1 (assuming a distance of 500 pc). For the first time, pulsed X-ray emission from PSR J0737–3039B (PSR B) is also detected in part of the orbit. This emission, consistent with thermal radiation with temperature kBT 30 eV and a bolometric luminosity of ~1032 erg s−1, is likely powered by heating of PSR B's surface caused by PSR A's wind. A hotter (~130 eV) and fainter (~5 × 1029 erg s−1) thermal component, probably originating from backfalling particles heating polar caps of either PSR A or PSR B, is also required by the data. No signs of X-ray emission from a bow shock between PSR A's wind and the interstellar medium or PSR B's magnetosphere are present. The upper limit on the luminosity of such a shock component (~1029 erg s−1) constrains the wind magnetization parameter σM of PSR A to values greater than 1.

Changes in radio emission from PSR J0737–3039B

The double pulsar system, J0737–3039, provides a unique probe of a pulsar magnetosphere due to its edge-on viewing geometry, a tight orbit and a significant rate of advance of the angle of periastron. In this paper, we report on the changes in radio emission from the long period pulsar in this system, J0737–3039B, over a period of 9 months. Observations of this system with Giant Metrewave Radio Telescope (GMRT) show that the duration of the first bright phase of the pulsar centered at 210° orbital longitude from the ascending node is shrinking. These observations will be useful to constrain the proposed models for this system.

Long-Term Variations in the Pulse Emission from PSR J0737-3039B

Analysis of 20 months of observations at the Parkes radio telescope shows secular changes in the pulsed emission from J0737-3039B, the 2.77 s pulsar of the double-pulsar system. Pulse profiles are becoming single-peaked in both bright phases of the orbital modulation, although there is no clear variation in overall pulse width. The shape of the orbital modulation is also varying systematically, with both bright phases shrinking in longitude by ~7° yr-1. However, the combined span of the two bright phases is relatively constant, and together they are shifting to higher longitudes at a rate of ~3° yr-1. We discuss the possible contributions of geodetic precession and periastron advance to the observed variations.

The Double Pulsar System J0737-3039: Modulation of A by B at Eclipse

We have investigated the eclipse of the 23 ms pulsar, PSR J0737-3039A, by its 2.8 s companion PSR J0737-3039B in the recently discovered double pulsar system using data taken with the Green Bank Telescope at 820 MHz. We find that the pulsed flux density at eclipse is strongly modulated with the periodicity of the 2.8 s pulsar. The eclipse occurs earlier and is deeper at those rotational phases of B when its magnetic axis is aligned with the line of sight than at phases when its magnetic axis is at right angles to the line of sight. This is consistent with the eclipse of A being due to synchrotron absorption by the shock-heated plasma surrounding B, the asymmetry arising from the higher plasma densities expected in the B magnetosphere's polar cusps.