We present the first measurement of the gravitational quadrupole moment of the companion star of a spider pulsar, namely the black widow PSR J2051$-$0827. To this end we have re-analysed radio timing data using a new model which is able to account for periastron precession caused by tidal and centrifugal deformations of the star as well as by general relativity. The model allows for a time-varying component of the quadrupole moment, thus self-consistently accounting for the ill-understood orbital period variations observed in these systems. Our analysis results in the first detection of orbital precession in a spider system at $\dotω = -68.6_{-0.5}^{+0.9}$ deg/yr and the most accurate determination of orbital eccentricity for PSR J2051$-$0827 with $e = (4.2 \pm 0.1) \times 10^{-5}$. We show that the variable quadrupole component is about 100 times smaller than the average quadrupole moment $\bar{Q} = -2.2_{-1}^{+0.6} \times 10^{41}$ kg.m$^2$. We discuss how accurate modelling of high precision optical light curves of the companion star will allow its apsidal motion constant to be derived from our results.
The companions of evaporating binary pulsars (black widows and related systems) show optical emission suggesting strong heating. In a number of cases large observed temperatures and asymmetries are inconsistent with direct radiative heating for the observed pulsar spindown power and expected distance. Here we describe a heating model in which the pulsar wind sets up an intrabinary shock (IBS) against the companion wind and magnetic field, and a portion of the shock particles duct along this field to the companion magnetic poles. We show that a variety of heating patterns, and improved fits to …
We present the discovery of a new optical/X-ray source likely associated with the Fermi $γ$-ray source 4FGL J1408.6-2917. Its high-amplitude periodic optical variability, large spectroscopic radial velocity semi-amplitude, evidence for optical emission lines and flaring, and X-ray properties together imply the source is probably a new black widow millisecond pulsar binary. We compile the properties of the 41 confirmed and suspected field black widows, finding a median secondary mass of $0.027\pm0.003\,M_{\odot}$. Considered jointly with the more massive redback millisecond pulsar binaries, we …
The low mass companions of evaporating binary pulsars (black widows and their ilk) are strongly heated on the side facing the pulsar. However in high-quality photometric and spectroscopic data the heating pattern does not match that expected for direct pulsar illumination. Here we explore heating mediated by an intra-binary shock (IBS). We develop a simple analytic model and implement it in the popular `ICARUS' light curve code. The model is parameterized by the wind momentum ratio beta and velocity v_Rel v_orb and assumes that the reprocessed pulsar wind emits prompt particles or radiation to…
Black widows are close binary systems in which a millisecond pulsar is orbited by a companion a few per cent the mass of the sun. It has been suggested that the pulsar's rotationally powered $γ$-ray luminosity gradually evaporates the companion, eventually leaving behind an isolated millisecond pulsar. The evaporation efficiency is determined by the temperature $T_{\rm ch}\propto F^{2/3}$ to which the outflow is heated by the flux $F$ on a dynamical time-scale. Evaporation is most efficient for companions that fill their Roche lobes. In this case, the outflow is dominated by a cap around the L…
We present a model for atmospheric wind circulation in binary millisecond pulsar (MSP) companions, showing how the optical light curve (LC) and radial velocities (RV) are sensitive to the wind flow, causing LC orbital phase shifts and asymmetries, as observed for several `spider' MSP. Velocity widths of spectral lines offer additional opportunities for measuring surface wind speed. As examples, we fit optical data for a black widow pulsar J1959+2048 and a redback pulsar J2215+5135; the wind heating models (WH) are statistically strongly preferred over direct heating (DH) for both objects, alth…
The 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 sub-category 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 i…
I obtained time-series photometry of the compact binary candidate for the Fermi source 4FGL J0935.3+0901. Superposed on the 2.44 hr orbital modulation are day-to-day variations and frequent flaring as seen in several redback and black widow millisecond pulsars (MSPs). The short orbital period favors a black widow. While the modulation of $\leq 1$ mag is smaller than that of most black widows, it could indicate a low orbital inclination. Although a published optical spectrum shows strong emission lines, the light curve evinces pulsar heating of the companion star rather than accretion-disk emis…
Black widows are millisecond pulsars with low-mass companions, a few per cent the mass of the sun, on orbits of several hours. These companions are presumably the remnants of main sequence stars that lost their mass through a combination of Roche-lobe overflow and ablation by the host pulsar's high-energy radiation. While ablation itself is too weak to significantly reduce the mass of the companion star, the ablated wind couples to its magnetic field, removes orbital angular momentum, and thus maintains stable Roche-lobe overflow. We use the MESA stellar evolution code, complemented by analyti…
Multi-wavelength observations of the black-widow binary system 2FGL J2339.6-0532 are reported. The Fermi gamma-ray source 2FGL J2339.6-0532 was recently categorized as a black widow in which a recycled millisecond pulsar (MSP) is evaporating up the companion star with its powerful pulsar wind. Our optical observations show clear sinusoidal light curves due to the asymmetric temperature distribution of the companion star. Assuming a simple geometry, we constrained the range of the inclination angle of the binary system to 52$^{\circ}$ < i < 59$^{\circ}$, which enables us to discuss the interact…
Black widows and redbacks are binary systems consisting of a millisecond pulsar in a close binary with a companion having matter driven off of its surface by the pulsar wind. X-rays due to an intra-binary shock have been observed from many of these systems, as well as orbital variations in the optical emission from the companion due to heating and tidal distortion. We have been systematically studying these systems in radio, optical and X-rays. Here we will present an overview of X-ray and optical studies of these systems, including new XMM-Newton and NuStar data obtained from several of them,…
Binary systems composed of a recycled millisecond pulsar and a stellar companion in close orbit could be excellent sites to diagnose pulsar winds. In such systems, the pulsar outflow irradiates and heats up the companion atmosphere, which can lead to the observation of strong day/night modulations in temperature. We demonstrate with particle shower simulations that the particle energy of the wind affects the heating depth in the atmosphere: the wind heat can be deposited above or below the photosphere, leading to different signatures in the observed spectra. We apply our method to four specifi…
We report our discovery of orbitally modulated $γ$-ray emission from the black widow system PSR J1311-3430. We analyze the \textit{Fermi} Large Area Telescope data during the offpulse phase interval of the pulsar, and find the orbital modulation signal at a $\sim$3$σ$ confidence level. Further spectral analysis shows no significant differences for the spectra obtained during the bright and faint orbital phase ranges. A simple sinusoid-like function can describe the modulation. Given these properties, we suggest that the intrabinary $γ$-ray emission arises from the region close to the companion…
We collect new and archival optical observations of nine "black-widow" millisecond pulsar binaries. New measurements include direct imaging with the Keck, Gemini-S, MDM, and LCO 2~m telescopes. This is supplemented by synthesized colors from Keck long-slit spectra. Four black-widow optical companions are presented here for the first time. Together these data provide multicolor photometry covering a large fraction of the orbital phase. We fit these light curves with a direct (photon) heating model using a version of the ICARUS light-curve modeling code. The fits provide distance and fill-factor…
We report on the determination of the astrometric, spin and orbital parameters for PSR J1953+1846A, a "black widow" binary millisecond pulsar in the globular cluster M71. By using the accurate position and orbital parameters obtained from radio timing, we identified the optical companion in ACS/Hubble Space Telescope images. It turns out to be a faint (m_F606W>=24, m_F814W>=23) and variable star located at only ~0.06" from the pulsar timing position. The light curve shows a maximum at the pulsar inferior conjunction and a minimum at the pulsar superior conjunction, thus confirming the associat…
The optical study of the heated substellar companions of `Black Widow' (BW) millisecond pulsars (MSP) provides unique information on the MSP particle and radiation output and on the neutron star mass. Here we present analysis of optical photometry and spectroscopy of a set of relatively bright BWs, many newly discovered in association with Fermi $γ$-ray sources. Interpreting the optical data requires sophisticated models of the companion heating. We provide a uniform analysis, selecting the preferred heating model and reporting on the companion masses and radii, the pulsar heating power and ne…
We report on radio timing observations of the black widow binary pulsar J0610$-$2100 and optical observations of its binary companion. The radio timing observations extend the timing baseline to 16yr and reveal a marginal detection of the orbital period derivative, but they show no significant evidence of orbital variations such as those seen in other black widow pulsars. Furthermore, no eclipses are seen in the observations at observing frequencies ranging from 310 to 2700MHz. The optical VRI light curves were modulated with the orbital period, reaching maximum brightness of $V=26.8$, $R=25.4…
We present optical time-resolved multi-band photometry of the black widow binary millisecond pulsar J2052+1219 using direct-imaging observations with the 2.1m telescope of Observatorio Astronomico Nacional San Pedro Martir, Mexico (OAN-SPM). The observations revealed a variable optical source whose position and periodicity P = 2.752h coincide with the pulsar coordinates and the orbital period obtained from radio timing. This allowed us to identify it with the binary companion of the pulsar. We reproduce light curves of the source modelling the companion heating by the pulsar and accounting for…
Recently, several eclipsing millisecond pulsars have been shown to experience strong and apparent weak lensing from the outflow of their ionized companions. Lensing can be a powerful probe of the ionized plasma, with the strongest lenses potentially resolving emission regions of pulsars. Understanding lensing in the `laboratory-like' conditions of an eclipsing pulsar may be analogously applied to fast radio bursts, many of which reside in dense, magnetized environments. We examined variable dispersion measure (DM), absorption, scattering, and flux density in the original Black Widow pulsar PSR…
Black widows are extreme millisecond pulsar binaries where the pulsar wind ablates their low-mass companion stars. Their optical 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 multi-band observations obtained with the HIPERCAM instrument at the 10.4-m GTC telescope for six of these systems. The combination of this five-band 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 fo…
We report on a series of spectroscopic observations of PSR J1311-3430, an extreme black-widow gamma-ray pulsar with a helium-star companion. In a previous study we estimated the neutron star mass as M_NS= 2.68+/-0.14M_Sun (statistical error), based on limited spectroscopy and a basic (direct heating) light curve model; however, much larger model-dependent systematics dominate the mass uncertainty. Our new spectroscopy reveals a range of complex source behavior. The variable He I companion wind emission lines can dominate broad-band photometry, especially in red filters or near minimum brightne…
We report the discovery of PSR J1555-2908, a 1.79 ms radio and gamma-ray pulsar in a 5.6 hr binary system with a minimum companion mass of 0.052 $M_\odot$. This fast and energetic ($\dot E = 3 \times 10^{35}$ erg/s) millisecond pulsar was first detected as a gamma-ray point source in Fermi LAT sky survey observations. Guided by a steep spectrum radio point source in the Fermi error region, we performed a search at 820 MHz with the Green Bank Telescope that first discovered the pulsations. The initial radio pulse timing observations provided enough information to seed a search for gamma-ray pul…
X-ray studies of the Black Widow Pulsar PSR B1957+20
我们报告的黑寡妇脉冲星，PSR B1957+20的钱德拉观测。通过对该脉冲星的深空观测，发现了脉冲星X射线辐射具有二元相位依赖性的证据。二元相分辨光谱分析揭示了PSR B 1957 +20的非热X射线发射，证实了以前的研究结果。这表明X射线主要是由于双星内的冲击发射造成的，当脉冲星风与伴星的烧蚀物质相互作用时，这种冲击发射最强。在我们的研究中确定的几何形状的峰值发射。非热X射线尾谱的边缘软化可能表明在终止激波处注入的粒子主要由同步辐射冷却控制。
The GMRT High-Resolution Southern Sky Survey for pulsars and transients -- VII: Timing of Spider MSP J1242-4712, A Bridge Between Redback and Black Widow Pulsars
The 559 Hz black-widow pulsar PSR J1555-2908, originally discovered in radio, is also a bright gamma-ray pulsar. Timing its pulsations using 12 yr of Fermi-LAT gamma-ray data reveals long-term variations in its spin frequency that are much larger than is observed from other millisecond pulsars. While this variability in the pulsar rotation rate could be intrinsic "timing noise", here we consider an alternative explanation: the variations arise from the presence of a very-low-mass third object in a wide multi-year orbit around the neutron star and its low-mass companion. With current data, this…
The wealth of detections of millisecond pulsars (MSPs) in $γ$-rays by {\em Fermi} has spurred searches for these objects among the several unidentified $γ$-ray sources. Interesting targets are a sub-class of binary MSPs, dubbed "Black Widows" (BWs) and "Redbacks" (RBs), which are in orbit with low-mass non-degenerate companions fully or partially ablated by irradiation from the MSP wind. These systems can be easily missed in radio pulsar surveys owing to the eclipse of the radio signal by the intra-binary plasma from the ablated companion star photosphere, making them better targets for multi-…
Black widows (BWs) are a type of eclipsing millisecond pulsars (MSPs) with companion masses $M_2$ $\lesssim 0.05\,\rm M_\odot$, which can be used to study the accretion history and the radiation of pulsars, as well as the origin of isolated MSPs. Recent observations indicate that there are two sub-types of BWs. One is the BWs with $M_2$ $\sim$ $0.01-0.05\,\rm M_\odot$, whereas another with $M_2$ $\lesssim 0.01\,\rm M_\odot$. However, the origin of the latter is still highly uncertain. In this paper, we investigated the formation of BWs with $M_2$ $\lesssim 0.01\,\rm M_\odot$ through ultra-comp…
Over a dozen millisecond pulsars are ablating low-mass companions in close binary systems. In the original "black widow", the 8-hour orbital period eclipsing pulsar PSR J1959+2048 (PSR B1957+20), high energy emission originating from the pulsar is irradiating and may eventually destroy a low-mass companion. These systems are not only physical laboratories that reveal the dramatic result of exposing a close companion star to the relativistic energy output of a pulsar, but are also believed to harbour some of the most massive neutron stars, allowing for robust tests of the neutron star equation …
Accurate measurements of the masses of neutron stars are necessary to test binary evolution models, and to constrain the neutron star equation of state. In pulsar binaries with no measurable post-Keplerian parameters, this requires an accurate estimate of the binary system's inclination and the radial velocity of the companion star by other means than pulsar timing. In this paper, we present the results of a new method for measuring this radial velocity using the binary synthesis code Icarus. This method relies on constructing a model spectrum of a tidally distorted, irradiated star as viewed …
We report on an unusually bright observation of PSR J2051$-$0827 recorded during a regular monitoring campaign of black-widow pulsar systems with the Effelsberg 100-m telescope. Through fortunate coincidence, a particularly bright scintillation maximum is simultaneous with the eclipse by the companion, enabling precise measurements of variations in the flux density, dispersion measure (DM), and scattering strength throughout the eclipse. The flux density is highly variable throughout the eclipse, with a peak 1.7 times the average away from the eclipse, and yet does not significantly decrease o…
We report the discovery of two Black Widow millisecond pulsars in the globular cluster M28 with the MeerKAT telescope. PSR J1824$-$2452M (M28M) is a 4.78-ms pulsar in a $5.82\,$hour orbit and PSR J1824$-$2452N (M28N) is a 3.35-ms pulsar in a $4.76\,$hour orbit. Both pulsars have dispersion measures near $119.30\,$pc$\,$cm$^{-3}$ and have low mass companion stars ($\sim$$0.01-0.03\,$M$_\odot$), which do not cause strong radio eclipses or orbital variations. Including these systems, there are now five known black widow pulsars in M28. The pulsar searches were conducted as a part of an initial ph…
We study the timing stability of three black widow pulsars, both in terms of their long-term spin evolution and their shorter-term orbital stability. The erratic timing behaviour and radio eclipses of the first two black widow pulsar systems discovered (PSRs B1957+20 and J2051$-$0827) was assumed to be representative for this class of pulsars. With several new black widow systems added to this population in the last decade, there are now several systems known that do not show these typical orbital variations or radio eclipses. We present timing solutions using 7$-$8 yrs of observations from fo…
In this paper we report on $\sim10$ years of observations of PSR J2051$-$0827, at radio frequencies in the range 110--4032 MHz. We investigate the eclipse phenomena of this black widow pulsar using model fits of increased dispersion and scattering of the pulsed radio emission as it traverses the eclipse medium. These model fits reveal variability in dispersion features on timescales as short as the orbital period, and previously unknown trends on timescales of months--years. No clear patterns are found between the low-frequency eclipse widths, orbital period variations and trends in the intra-…
In regions with strongly varying electron density, radio emission can be magnified significantly by plasma lensing. In the presence of magnetic fields, magnification in time and frequency will be different for two circular polarizations. We show how these effects can be used to measure or constrain the magnetic field parallel to the line of sight, $B_\parallel$, as well as its spatial structure, $σ_{B_\parallel}$, in the lensing region. In addition, we discuss how generalized Faraday rotation can constrain the strength of the perpendicular field, $B_\perp$. We attempt to make such measurements…
Redbacks (RBs) and black widows (BWs) are two peculiar classes of eclipsing millisecond pulsars (MSPs). The accretion-induced collapse (AIC) of an oxygen/neon/magnesium composition white dwarf to a neutron star has been suggested as one possible formation pathway for those two classes of MSPs. However, it is difficult to produce all known MSPs with the traditional AIC scenario. In this study by using the MESA stellar evolution code, we investigate the detailed pre-AIC evolution of magnetized white dwarf binaries with the magnetic confinement model where the high magnetic field strength of the …
We report the discovery of the first radio pulsar associated with NGC 6712, an eclipsing black widow (BW) pulsar, J1853$-$0842A, found by high-sensitivity searches using the Five-hundred-meter Aperture Spherical radio Telescope. This 2.15 ms pulsar is in a 3.56 hr compact circular orbit with a very low mass companion likely of mass 0.018 to 0.036 $M_{\rm \odot}$ and exhibits eclipsing of the pulsar signal. Though the distance to PSR J1853$-$0842A predicted from its dispersion measure ($155.125 \pm 0.004$ cm$^{-3}$ pc) and Galactic free electron density models are about 30\% smaller than that o…
A large number of new black widow and redback energetic millisecond pulsars with irradiated stellar companions have been discovered through radio searches of unidentified \emph{Fermi} sources. We construct a 3D emission model of these systems to predict the high-energy emission components from particles accelerated to several TeV in the intrabinary shocks, and its predicted modulation at the binary orbital period. Synchrotron emission is expected at X-ray energies and such modulated emission has already been detected by \emph{Chandra} and \emph{XMM-Newton} in some systems. Synchrotron and inve…
We present the results of detailed X-ray analysis of two black-widow pulsars (BWPs), J1446-4701 and J1311-3430. PSR J1446-4701 is a BWP with orbital parameters near the median values of the sample of known BWPs. Its X-ray emission detected by $XMM-Newton$ is well characterized by a soft power-law (PL) spectrum (photon index $Γ\approx 3$), and it shows no significant orbital modulations. In view of a lack of radio eclipses and an optical non-detection, the system most likely has a low orbital inclination. PSR J1311-3430 is an extreme BWP with a very compact orbit and the lowest minimum mass com…
In the past five years, approximately one third of the 65 pulsars discovered by radio observations of Fermi unassociated sources are black widow pulsars (BWPs). BWPs are binary millisecond pulsars with companion masses ranging from 0.01-0.1 solar masses which often exhibit radio eclipses. The bloated companions in BWP systems exert small torques on the system causing the orbit to change on small but measurable time scales. Because adding parameters to a timing model reduces sensitivity to a gravitational wave (GW) signal, the need to fit many orbital frequency derivatives to the timing data is…
Black widow and redback systems are compact binaries in which a millisecond pulsar heats and may even ablate its low-mass companion by its intense wind of relativistic particles and radiation. In such systems, an intrabinary shock can form as a site of particle acceleration and associated non-thermal emission. We model the X-ray and gamma-ray synchrotron and inverse-Compton spectral components for select spider binaries, including diffusion, convection and radiative energy losses in an axially-symmetric, steady-state approach. Our new multi-zone code simultaneously yields energy-dependent ligh…
We have observed and analysed the eclipses of the black widow pulsar J1810+1744 at low radio frequencies. Using LOw-Frequency ARray (LOFAR) and Westerbork Synthesis Radio Telescope observations between 2011--2015 we have measured variations in flux density, dispersion measure and scattering around eclipses. High-time-resolution, simultaneous beamformed and interferometric imaging LOFAR observations show concurrent disappearance of pulsations and total flux from the source during the eclipses, with a $3σ$ upper limit of 36 mJy ($<10\%$ of the pulsar's averaged out-of-eclipse flux density). The …
