Binary Millisecond Pulsars Research Articles

Revisiting the Intrabinary Shock Model for Millisecond Pulsar Binaries: Radiative Losses and Long‐Term Variability

Revisiting the Intrabinary Shock Model for Millisecond Pulsar Binaries: Radiative Losses and Long‐Term Variability

A 350 MHz Green Bank Telescope Survey of Unassociated Fermi LAT Sources: Discovery and Timing of 10 Millisecond Pulsars

We have searched for radio pulsations toward 49 Fermi Large Area Telescope (LAT) 1FGL Catalog γ-ray sources using the Green Bank Telescope at 350 MHz. We detected 18 millisecond pulsars (MSPs) in blind searches of the data; 10 of these were discoveries unique to our survey. 16 are binaries, with eight having short orbital periods P B < 1 day. No radio pulsations from young pulsars were detected, although three targets are coincident with apparently radio-quiet γ-ray pulsars discovered in LAT data. Here, we give an overview of the survey and present radio and γ-ray timing results for the 10 MSPs discovered. These include the only isolated MSP discovered in our survey and six short-P B binary MSPs. Of these, three have very-low-mass companions (M c ≪ 0.1 M ⊙) and hence belong to the class of black widow pulsars. Two have more massive, nondegenerate companions with extensive radio eclipses and orbitally modulated X-ray emission consistent with the redback class. Significant γ-ray pulsations have been detected from nine of the discoveries. This survey and similar efforts suggest that the majority of Galactic γ-ray sources at high Galactic latitudes are either MSPs or relatively nearby nonrecycled pulsars, with the latter having on average a much smaller radio/γ-ray beaming ratio as compared to MSPs. It also confirms that past surveys suffered from an observational bias against finding short-P B MSP systems.

A targeted radio pulsar survey of redback candidates with MeerKAT

ABSTRACT Redbacks are millisecond pulsar binaries with low-mass, irradiated companions. These systems have a rich phenomenology that can be used to probe binary evolution models, pulsar wind physics, and the neutron star mass distribution. A number of high-confidence redback candidates have been identified through searches for variable optical and X-ray sources within the localization regions of unidentified but pulsar-like Fermi-LAT gamma-ray sources. However, these candidates remain unconfirmed until pulsations are detected. As part of the TRAPUM project, we searched for radio pulsations from six of these redback candidates with MeerKAT. We discovered three new radio millisecond pulsars, PSRs J0838−2827, J0955−3947, and J2333−5526, confirming their redback nature. PSR J0838−2827 remained undetected for 2 yr after our discovery despite repeated observations, likely due to evaporated material absorbing the radio emission for long periods of time. While, to our knowledge, this system has not undergone a transition to an accreting state, the disappearance, likely caused by extreme eclipses, illustrates the transient nature of spider pulsars and the heavy selection bias in uncovering their radio population. Radio timing enabled the detection of gamma-ray pulsations from all three pulsars, from which we obtained 15-yr timing solutions. All of these sources exhibit complex orbital period variations consistent with gravitational quadrupole moment variations in the companion stars. These timing solutions also constrain the binary mass ratios, allowing us to narrow down the pulsar masses. We find that PSR J2333−5526 may have a neutron star mass in excess of 2 M⊙.

Discoveries and timing of pulsars in M62

ABSTRACT Using MeerKAT, we have discovered three new millisecond pulsars (MSPs) in the bulge globular cluster M62: M62H, M62I, and M62J. All three are in binary systems, which means all ten known pulsars in the cluster are in binaries. M62H has a planetary-mass companion with a median mass Mc, med ∼ 3 MJ and a mean density of ρ ∼ 11 g cm−3. M62I has an orbital period of 0.51 d and a Mc, med ∼ 0.15 M⊙. Neither of these low-mass systems exhibit eclipses. M62J has only been detected in the two Ultra High Frequency band (816 MHz) observations with a flux density S816 = 0.08 mJy. The non-detection in the L-band (1284 MHz) indicates it has a relatively steep spectrum (β &amp;lt; −3.1). We also present 23-yr-long timing solutions obtained using data from the Parkes ‘Murriyang’, Effelsberg, and MeerKAT telescopes for the six previously known pulsars. For all these pulsars, we measured the second spin-period derivatives and the rate of change of orbital period caused by the gravitational field of the cluster, and their proper motions. From these measurements, we conclude that the pulsars’ maximum accelerations are consistent with the maximum cluster acceleration assuming a core-collapsed mass distribution. Studies of the eclipses of the redback M62B and the black widow M62E at four and two different frequency bands, respectively, reveal a frequency dependence with longer and asymmetric eclipses at lower frequencies. The presence of only binary MSPs in this cluster challenges models which suggest that the MSP population of core-collapsed clusters should be dominated by isolated MSPs.

A pulsar in a binary with a compact object in the mass gap between neutron stars and black holes.

Some compact objects observed in gravitational wave events have masses in the gap between known neutron stars (NSs) and black holes (BHs). The nature of these mass gap objects is unknown, as is the formation of their host binary systems. We report pulsar timing observations made with the Karoo Array Telescope (MeerKAT) of PSR J0514-4002E, an eccentric binary millisecond pulsar in the globular cluster NGC 1851. We found a total binary mass of 3.887 ± 0.004 solar masses (M⊙), and multiwavelength observations show that the pulsar's binary companion is also a compact object. The companion's mass (2.09 to 2.71 M⊙, 95% confidence interval) is in the mass gap, indicating either a very massive NS or a low-mass BH. We propose that the companion formed in a merger between two earlier NSs.

MeerKAT Pulsar Timing Array parallaxes and proper motions

Abstract We have determined positions, proper motions, and parallaxes of 77 millisecond pulsars (MSPs) from ∼3 years of MeerKAT radio telescope observations. Our timing and noise analyses enable us to measure 35 significant parallaxes (12 of them for the first time) and 69 significant proper motions. Eight pulsars near the ecliptic have an accurate proper motion in ecliptic longitude only. PSR J0955−6150 has a good upper limit on its very small proper motion (&amp;lt;0.4 mas yr−1). We used pulsars with accurate parallaxes to study the MSP velocities. This yields 39 MSP transverse velocities, and combined with MSPs in the literature (excluding those in Globular Clusters) we analyse 66 MSPs in total. We find that MSPs have, on average, much lower velocities than normal pulsars, with a mean transverse velocity of only 78(8) km s−1 (MSPs) compared with 246(21) km s−1 (normal pulsars). We found no statistical differences between the velocity distributions of isolated and binary millisecond pulsars. From Galactocentric cylindrical velocities of the MSPs, we derive 3-D velocity dispersions of σρ, σφ, σz = 63(11), 48(8), 19(3) km s−1. We measure a mean asymmetric drift with amplitude 38(11) km s−1, consistent with expectation for MSPs, given their velocity dispersions and ages. The MSP velocity distribution is consistent with binary evolution models that predict very few MSPs with velocities &amp;gt;300 km s−1 and a mild anticorrelation of transverse velocity with orbital period.

The Green Bank North Celestial Cap Survey. VIII. 21 New Pulsar Timing Solutions

We present timing solutions for 21 pulsars discovered in 350 MHz surveys using the Green Bank Telescope (GBT). All were discovered in the Green Bank North Celestial Cap pulsar survey, with the exception of PSR J0957−0619, which was found in the GBT 350 MHz Drift-scan pulsar survey. The majority of our timing observations were made with the GBT at 820 MHz. With a spin period of 37 ms and a 528 days orbit, PSR J0032+6946 joins a small group of five other mildly recycled wide binary pulsars, for which the duration of recycling through accretion is limited by the length of the companion’s giant phase. PSRs J0141+6303 and J1327+3423 are new disrupted recycled pulsars. We incorporate Arecibo observations from the NANOGrav pulsar timing array into our analysis of the latter. We also observed PSR J1327+3423 with the Long Wavelength Array, and our data suggest a frequency-dependent dispersion measure. PSR J0957−0619 was discovered as a rotating radio transient, but is a nulling pulsar at 820 MHz. PSR J1239+3239 is a new millisecond pulsar (MSP) in a 4 days orbit with a low-mass companion. Four of our pulsars already have published timing solutions, which we update in this work: the recycled wide binary PSR J0214+5222, the noneclipsing black widow PSR J0636+5128, the disrupted recycled pulsar J1434+7257, and the eclipsing binary MSP J1816+4510, which is in an 8.7 hr orbit with a redback-mass companion.

Improving Distances to Binary Millisecond Pulsars with Gaia

Pulsar distances are notoriously difficult to measure, and play an important role in many fundamental physics experiments, such as pulsar timing arrays. Here, we perform a cross-match between International PTA pulsars (IPTA) and Gaia's Data Release 2 (DR2) and Data Release 3 (DR3). We then combine the IPTA pulsar’s parallax with its binary companion’s parallax, found in Gaia, to improve the distance measurement to the binary. We find seven cross-matched IPTA pulsars in Gaia DR2, and when using Gaia DR3 we find six IPTA pulsar cross-matches but with seven Gaia objects. Moving from Gaia DR2 to Gaia DR3, we find that the Gaia parallaxes for the successfully cross-matched pulsars improved by 53%, and pulsar distances improved by 29%. Finally, we find that binary companions with a <3.0σ detection are unreliable associations, setting a high bar for successful cross-matches.

Convective dynamos of black widow companions

ABSTRACT Black widows and redbacks are binary millisecond pulsars with close low-mass companions that are irradiated and gradually ablated by the pulsar’s high-energy luminosity Lirr. These binaries evolve primarily through magnetic braking, which extracts orbital angular momentum and pushes the companion to overflow its Roche lobe. Here, we use the stellar evolution code mesa to examine how the irradiation modifies the companion’s structure. Strong Lirr inhibits convection to the extent that otherwise fully convective stars become almost fully radiative. By computing the convective velocities and assuming a dynamo mechanism, we find that the thin convective envelopes of such strongly irradiated companions ($L_{\rm irr}\gtrsim 3\, {\rm L}_\odot$) generate much weaker magnetic fields than previously thought – halting binary evolution. With our improved magnetic braking model, we explain most observed black widow and redback companions as remnants of main-sequence stars. We also apply our model (with Lirr) to evolved companions that overflow their Roche lobe close to the end of their main-sequence phase. The evolutionary tracks of such companions bifurcate, explaining the shortest period systems (which are potential gravitational wave sources) as well as the longest period ones (which are the progenitors of common pulsar–white dwarf binaries). The variety of black widow structures and evolutionary trajectories may be utilized to calibrate the dependence of magnetic braking on the size of the convective layer and on the existence of a radiative–convective boundary, with implications for single stars as well as other binaries, such as cataclysmic variables and AM Canum Venaticorum stars.

A Gaia view of the optical and X-ray luminosities of compact binary millisecond pulsars

ABSTRACT In this paper, we study compact binary millisecond pulsars with low- and very low-mass companion stars (spiders) in the Galactic field, using data from the latest Gaia data release (DR3). We infer the parallax distances of the optical counterparts to spiders, which we use to estimate optical and X-ray luminosities. We compare the parallax distances to those derived from radio pulse dispersion measures and find that they have systematically larger values, by 40 per cent on average. We also test the correlation between X-ray and spin-down luminosities, finding that most redbacks have a spin-down to X-ray luminosity conversion efficiency of ∼0.1 per cent, indicating a contribution from the intrabinary shock. On the other hand, most black widows have an efficiency of ∼0.01 per cent, similar to the majority of the pulsar population. Finally, we find that the bolometric optical luminosity significantly correlates with the orbital period, with a large scatter due to different irradiated stellar temperatures and binary properties. We interpret this correlation as the effect of the increasing size of the Roche Lobe radius with the orbital period. With this newly found correlation, an estimate of the optical magnitude can be obtained from the orbital period and a distance estimate.

Quantifying irradiation in spider pulsars: the extreme case of PSR J1622−0315

ABSTRACT We present the first multiband optical light curves of PSR J1622−0315, among the most compact known redback binary millisecond pulsars, with an orbital period $P_\mathrm{orb}=3.9 \, \text{h}$. We find a flux modulation with two maxima per orbital cycle and a peak-to-peak amplitude ${\simeq} 0.3 \, \text{mag}$, which we attribute to the ellipsoidal shape of the tidally distorted companion star. The optical colours imply a late-F to early-G spectral-type companion and do not show any detectable temperature changes along the orbit. This suggests that the irradiation of the star’s inner face by the pulsar wind is unexpectedly missing despite its short orbital period. To interpret these results, we introduce a new parameter fsd, defined as the ratio between the pulsar wind flux intercepted by the companion star and the companion intrinsic flux. This flux ratio fsd, which depends on the spin-down luminosity of the pulsar, the base temperature of the companion and the orbital period, can be used to quantify the effect of the pulsar wind on the companion star and turns out to be the most important factor in determining whether the companion is irradiated or not. We find that the transition between these two regimes occurs at fsd ≃ 2–4 and that the value for PSR J1622−0315 is fsd = 0.7, placing it firmly in the non-irradiated regime.

Green Bank Telescope Discovery of the Redback Binary Millisecond Pulsar PSR J0212+5321

We report the discovery of a 2.11 ms binary millisecond pulsar during a targeted search of the redback optical candidate coincident with the γ-ray source 3FGL J0212.5+5320 using the Robert C. Byrd Green Bank Telescope (GBT) with the Breakthrough Listen backend at L band. Over a seven month period, five pointings were made near inferior conjunction of the pulsar in its 20.9 hr orbit, resulting in two detections, lasting 12 and 42 minutes. The pulsar dispersion measure (DM) of 25.7 pc cm−3 corresponds to a distance of 1.15 kpc in the NE2001 Galactic electron density model, consistent with the Gaia parallax distance of 1.16 ± 0.03 kpc for the companion star. We suspect the pulsar experiences wide orbital eclipses, similar to other redbacks, as well as scintillation and DM delays caused by its interaction with its companion and surroundings. Although the pulsar was only detected over ≈3.7% of the orbit, its measured acceleration is consistent with published binary parameters from optical radial velocity spectroscopy and light-curve modeling of the companion star, and it provides a more precise mass ratio and a projected semimajor axis for the pulsar orbit. We also obtained a refined optical photometric orbit ephemeris, and observed variability of the tidally distorted companion over 7 yr. A hard X-ray light curve from NuSTAR shows expected orbit-modulated emission from the intrabinary shock. The pulsar parameters and photometric ephemeris greatly restrict the parameter space required to search for a coherent timing solution including pulsar spin-down rate, either using Fermi γ-rays or further radio pulse detections.

Optical spectral observations of three binary millisecond pulsars

ABSTRACT We present the results of optical spectroscopy of stellar companions to three binary millisecond pulsars, PSRs J0621+2514, J2317+1439, and J2302+4442, obtained with the Gran Telescopio Canarias. The spectrum of the J0621+2514 companion shows a blue continuum and prominent Balmer absorption lines. The latter are also resolved in the spectrum of the J2317+1439 companion, showing that both are DA-type white dwarfs. No spectral features are detected for the J2302+4442 companion; however, its broad-band magnitudes and the spectral shape of the continuum emission imply that this is also a DA-type white dwarf. Based on the spectral analyses, we conclude that the companions of J0621+2514 and J2317+1439 are relatively hot, with effective temperatures Teff = 8600 ± 200 and 9600 ± 2000 K, respectively, while the J2302+4442 companion is significantly cooler, Teff&amp;lt;6000 K. We also estimated the distance to J0621+2514 of 1.1 ± 0.3 kpc and argue that its companion and the companion of J2317+1439 are He-core white dwarfs providing constraints on their cooling ages of $\lesssim$2 Gyr.

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.

PSR J1910–5959A: A rare gravitational laboratory for testing white dwarf models

Context. PSR J1910−5959A is a binary millisecond pulsar in a 0.837 day circular orbit around a helium white dwarf (HeWD) companion. The position of this pulsar is 6.3 arcmin (∼74 core radii) away from the optical centre of the globular cluster (GC) NGC 6752. Given the large offset, the association of the pulsar with the GC has been debated. Aims. We aim to obtain precise measurements of the masses of the stars in the system along with secular orbital parameters, which will help identify if the system belongs to the GC. Methods. We have made use of archival Parkes 64 m ‘Murriyang’ telescope data and carried out observations with the MeerKAT telescope with different backends and receivers over the last two decades. Pulse times of arrival were obtained from these using standard pulsar data reduction techniques and analysed using state-of-the-art Bayesian pulsar timing techniques. We also performed an analysis of the pulsar’s total intensity and polarisation profile to understand the interstellar scattering along the line of sight, and we determined the pulsar’s geometry by fitting the rotating vector model to the polarisation data. Results. We obtain precise measurements of several post-Keplerian parameters: the range, r = 0.202(6) T⊙, and shape, s = 0.999823(4), of the Shapiro delay, from which we infer: the orbital inclination to be 88.9−0.14+0.15 deg; the masses of the pulsar and the companion to be 1.55(7) M⊙ and 0.202(6) M⊙, respectively; a secular change in the orbital period Ṗb = −53−6.0+7.4 × 10−15 s s−1 that proves the GC association; and a secular change in the projected semi-major axis of the pulsar, ẋ = −40.7−8.2+7.3 × 10−16 s s−1, likely caused by the spin–orbit interaction from a misaligned HeWD spin, at odds with the likely isolated binary evolution of the system. We also discuss some theoretical models for the structure and evolution of white dwarfs in neutron star–white dwarf binaries, using PSR J1910−5959A’s companion as a test bed. Conclusions. PSR J1910−5959A is a rare system for which several parameters of both the pulsar and the HeWD companion can be accurately measured. As such, it is a test bed for discriminating between alternative models of HeWD structure and cooling.

Magnetic Inclination Evolution of Accreting Neutron Stars in Intermediate/Low-mass X-Ray Binaries

The magnetic inclination angle χ, namely the angle between the spin and magnetic axes of a neutron star, plays a vital role in its observational characteristics. However, there are few systematic investigations of its long-term evolution, especially for accreting NSs in binary systems. Applying the model of Biryukov & Abolmasov and the binary evolution code MESA, we simultaneously simulate the evolution of the accretion rate, spin period, magnetic field, and magnetic inclination angle of accreting NSs in intermediate/low X-ray binaries. We show that the evolution of χ depends not only on the initial parameters of the binary systems, but also on the mass transfer history and the efficiency of pulsar loss. Based on the calculated results we present the characteristic distribution of χ for various types of systems including ultracompact X-ray binaries, binary millisecond pulsars, and ultraluminous X-ray sources, and discuss their possible observational implications.

Thefalse widowlink between neutron star X-ray binaries and spider pulsars

ABSTRACTThe discovery of transitional millisecond pulsars (tMSPs) provided conclusive proof that neutron star (NS) low-mass X-ray binaries (LMXBs) comprise part of the evolutionary pathway towards binary millisecond pulsars (MSPs). Redback and black widow ‘spider’ pulsars are a subcategory of binary MSPs that ‘devour’ their companions through ablation – the process through which material is lifted from the stellar surface by a pulsar wind. In addition to reducing the companion star’s mass, ablation introduces observable characteristics like extended, energy-dependent, and asymmetric eclipse profiles in systems observed at a sufficiently high inclination. Here, we present a detailed study and comparison of the X-ray eclipses of two NS LMXBs: Swift J1858.6 − 0814 and EXO 0748 − 676. Some of the X-ray eclipse characteristics observed in these two LMXBs are similar to the radio eclipse characteristics of eclipsing redback and black widow pulsars, suggesting that they may also host ablated companion stars. X-ray irradiation or a pulsar wind could drive the ablation. We conduct orbital phase-resolved spectroscopy for both LMXBs to map the column density, ionization, and covering fraction of the material outflow. From this, we infer the presence of highly ionized and clumpy ablated material around the companion star in both systems. We term LMXBs undergoing ablation, false widows, and speculate that they may be the progenitors of redback pulsars under the assumption that ablation begins in the LMXB stage. Therefore, the false widows could provide a link between LMXBs and spider pulsars. The detection of radio pulsations during non-accreting states can support this hypothesis.

A black widow population dissection through HiPERCAM multiband light-curve modelling

ABSTRACT Black widows are extreme millisecond pulsar binaries where the pulsar wind ablates their low-mass companion stars. In the optical range, their light curves vary periodically due to the high irradiation and tidal distortion of the companion, which allows us to infer the binary parameters. We present simultaneous multiband observations obtained with the HIPERCAM instrument at the 10.4-m GTC telescope for six of these systems. The combination of this five-band (us,gs, rs, is, zs) fast photometer with the world’s largest optical telescope enables us to inspect the light curve range near minima. We present the first light curve for PSR J1641+8049, as well as attain a significant increase in signal to noise and cadence compared with previous publications for the remaining five targets: PSR J0023+0923, PSR J0251+2606, PSR J0636+5129, PSR J0952−0607, and PSR J1544+4937. We report on the results of the light-curve modelling with the Icarus code for all six systems, which reveals some of the hottest and densest companion stars known. We compare the parameters derived with the limited but steadily growing black widow population for which optical modelling is available. We find some expected correlations, such as that between the companion star mean density and the orbital period of the system, which can be attributed to the high number of Roche-lobe filling companions. On the other hand, the positive correlation between the orbital inclination and the irradiation temperature of the companion is puzzling. We propose such a correlation would arise if pulsars with magnetic axis orthogonal to their spin axis are capable of irradiating their companions to a higher degree.

Binding energy produced within the framework of the accretion of millisecond pulsars

The role and implication of binding energy through the accretion-induced collapse (AIC) of accreting white dwarfs (WDs) for the production of millisecond pulsars (MSPs) are investigated. The binding energy model is examined due to the dynamic process in closed binary systems, and the possible mass of the companion sufficient to induce their orbital parameters is investigated. The deterministic nature of this interaction has a strong sensitivity to the equation of state of the binary systems (where the compactness of a neutron star is proportional to the amount of binding energy) associated with their initial conditions. This behavior mimics the commonly assumed mass and amount of accreted matter under the instantaneous mass loss (). As a result, this indicates an increase in the MSP's gravitational mass due to angular momentum losses. The outcome of such a system is then a circular binary MSP in which the companion is a low-mass WD, thus distinguishing the binary formation scenarios. In addition, the results of this work could provide constraints on the expected mass and binding energy of a neutron star based on the accretion rate.

Searches for Shapiro delay in seven binary pulsars using the MeerKAT telescope

ABSTRACT Precision timing of millisecond pulsars (MSPs) in binary systems enables observers to detect the relativistic Shapiro delay induced by space–time curvature. When favourably aligned, this enables constraints to be placed on the component masses and system orientation. Here, we present the results of timing campaigns on seven binary MSPs observed with the 64-antenna MeerKAT radio telescope that show evidence of Shapiro delay: PSRs J0101−6422, J1101−6424, J1125−6014, J1514−4946, J1614−2230, J1732−5049, and J1909−3744. Evidence for Shapiro delay was found in all of the systems, and for three the orientations and data quality enabled strong constraints on their orbital inclinations and component masses. For PSRs J1125−6014, J1614−2230, and J1909−3744, we determined pulsar masses to be $M_{\rm p} = 1.68\pm 0.17$, $1.94\pm 0.03$, and $1.45 \pm 0.03 \, {\rm M_{\odot }}$, and companion masses to be $M_{\rm c} = 0.33\pm 0.02$, $0.495\pm 0.005$, and $0.205 \pm 0.003 \, {\rm M_{\odot }}$, respectively. This provides the first independent confirmation of PSR J1614−2230’s mass, one of the highest known. The Shapiro delays measured for PSRs J0101−6422, J1101−6424, J1514−4946, and J1732−5049 were only weak, and could not provide interesting component mass limits. Despite a large number of MSPs being routinely timed, relatively few have accurate masses via Shapiro delays. We use simulations to show that this is expected, and provide a formula for observers to assess how accurately a pulsar mass can be determined. We also discuss the observed correlation between pulsar companion masses and spin period, and the anticorrelation between recycled pulsar mass and their companion masses.