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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 B1957+20 through an eclipse at the Arecibo Observatory at |$327\, {\rm MHz}$|⁠. We discovered clear evidence of the two regimes of lensing, strong, and apparent weak. We show that the flux density variations in the apparently weak lensing regime can be modelled directly from variations of DM, using geometric optics. The mean effective velocities in the ingress, |$(954\pm 99)\, {\rm km\, s^{-1}}$|⁠ , and egress |$(604\pm 47)\, {\rm km\, s^{-1}}$| cannot be explained by orbital motions alone, but are consistent with significant outflow velocity of material from the companion. We also show that geometric optics can predict when and where the lensing regime-change between weak and strong occurs, and argue that the apparent weak lensing is due to averaging many images. Our framework can be applied in any source with variable electron columns, measuring their relative velocities and distances. In other eclipsing pulsars, this provides a unique opportunity to measure companion outflow velocity, predict regions of weak and strong lensing, and in principle independently constrain orbital inclinations. [ABSTRACT FROM AUTHOR]

We present simultaneous, multicolour optical light curves of the companion star to the black-widow pulsar PSR J2051−0827, obtained approximately 10 yr apart using ULTRACAM and HiPERCAM, respectively. The ULTRACAM light curves confirm the previously reported asymmetry in which the leading hemisphere of the companion star appears to be brighter than the trailing hemisphere. The HiPERCAM light curves, however, do not show this asymmetry, demonstrating that whatever mechanism is responsible for it varies on time-scales of a decade or less. We fit the symmetrical HiPERCAM light curves with a direct-heating model to derive the system parameters, finding an orbital inclination of |$55.9^{+4.8}_{-4.1}$| degrees, in good agreement with radio-eclipse constraints. We find that approximately half of the pulsar's spin-down energy is converted to optical luminosity, resulting in temperatures ranging from approximately |$5150^{+190}_{-190}$|  K on the day side to |$2750^{+130}_{-150}$|  K on the night side of the companion star. The companion star is close to filling its Roche lobe (⁠|$f_{\rm RL} =0.88^{+0.02}_{-0.02}$|⁠) and has a mass of |$0.039^{+0.010}_{-0.011}$|  M⊙, giving a mean density of |$20.24^{+0.59}_{-0.44}$|  g cm−3 and an apsidal motion constant in the range 0.0036 < k 2 < 0.0047. The companion mass and mean density values are consistent with those of brown dwarfs, but the apsidal motion constant implies a significantly more centrally condensed internal structure than is typical for such objects. [ABSTRACT FROM AUTHOR]

Binaries harbouring millisecond pulsars (MSPs) enable a unique path to determine neutron star (NS) masses: radio pulsations reveal the motion of the NS, while that of the companion can be characterized through studies in the optical range. PSR J1012+5307 is an MSP in a 14.5-h orbit with a helium-core white dwarf (WD) companion. In this work we present the analysis of an optical spectroscopic campaign, where the companion star absorption features reveal one of the lightest known WDs. We determine a WD radial velocity semi-amplitude of |$K_2 = 218.9 \pm 2.2\, \rm km\, s^{-1}$|⁠ , which combined with that of the pulsar derived from the precise radio timing, yields a mass ratio of q  = 10.44 ± 0.11. We also attempt to infer the WD mass from observational constraints using new binary evolution models for extremely low-mass (ELM) WDs, but find that they cannot reproduce all observed parameters simultaneously. In particular, we cannot reconcile the radius predicted from binary evolution with the measurement from the photometric analysis (⁠|$R_{\rm WD}=0.047_{-0.002}^{+0.003}\, \mathrm{ R}_{\odot }$|⁠). Our limited understanding of ELM WD evolution, which results from binary interaction, therefore comes as the main factor limiting the precision with which we can measure the mass of the WD in this system. Our conservative WD mass estimate of |$M_{\rm WD} = 0.165 \pm 0.015\, \mathrm{ M}_{\rm \odot }$|⁠ , along with the mass ratio enables us to infer a pulsar mass of |$M_{\rm NS} = 1.72 \pm 0.16\, \mathrm{ M}_{\rm \odot }$|⁠. This value is clearly above the canonical |$\sim 1.4\, \mathrm{ M}_{\rm \odot }$|⁠ , therefore adding PSR J1012+5307 to the growing list of massive MSPs. [ABSTRACT FROM AUTHOR]

In the last few years, over 43 millisecond radio pulsars have been discovered by targeted searches of unidentified γ -ray sources found by the Fermi Gamma-Ray Space Telescope. A large fraction of these millisecond pulsarsare in compact binaries with low-mass companions. These systems often show eclipses of the pulsar signal andare commonly known as black widows and redbacks because the pulsar is gradually destroying its companion. In this paper, we report on the optical discovery of four strongly irradiated millisecond pulsar companions. All four sources show modulations of their color and luminosity at the known orbital periods from radio timing. Light curvemodeling of our exploratory data shows that the equilibrium temperature reached on the companion ’s dayside with respect to their nightside is consistent with about 10%–30% of the available spin-down energy from the pulsar being reprocessed to increase the companion's dayside temperature. This value compares well with the range observed inother irradiated pulsar binaries and offers insights about the energetics of the pulsarwind and the production of γ -ray emission. In addition, this provides a simple way of estimating the brightness of irradiated pulsar companions given the pulsar spin-down luminosity. Our analysis also suggests that two of the four new irradiated pulsar companionsare only partially filling their Roche lobe. Some of these sources are relatively bright and represent good targets forspectroscopic follow-up. These measurements could enable, among other things, mass determination of the neutronstars in these systems. [ABSTRACT FROM AUTHOR]

Most millisecond pulsars with low-mass companions are in systems with either helium-core white dwarfs or nondegenerate ("black widow" or "redback") stars. A candidate counterpart to PSR J1816+4510 was identified by Kaplan et al. whose properties were suggestive of both types of companions although identical to neither. We have assembled optical spectroscopy of the candidate companion and confirm that it is part of the binary system with a radial velocity amplitude of 343 ± 7 kms-1, implying a high pulsar mass, Mpsr sin3 i = 1.84 ± 0.11M☉, and a companion mass Mc sin3 i = 0.193 ± 0.012M☉, where i is the inclination of the orbit. The companion appears similar to proto-white dwarfs/sdB stars, with a gravity log10(g) = 4.9 ± 0.3, and effective temperature 16,000±500 K. The strongest lines in the spectrum are from hydrogen, but numerous lines from helium, calcium, silicon, and magnesium are present as well, with implied abundances of roughly 10 times solar (relative to hydrogen). As such, while from the spectrum the companion to PSR J1816+4510 is superficially most similar to a low-mass white dwarf, it has much lower gravity, is substantially larger, and shows substantial metals. Furthermore, it is able to produce ionized gas eclipses, which had previously been seen only for low-mass, non-degenerate companions in redback or black widow systems.We discuss the companion in relation to other sources, but find that we understand neither its nature nor its origins. Thus, the system is interesting for understanding unusual stellar products of binary evolution, as well as, independent of its nature, for determining neutron-star masses. [ABSTRACT FROM AUTHOR]

ABSTRACT PSR J1738+0333 is one of the four millisecond pulsars known to be orbited by a white dwarf companion bright enough for optical spectroscopy. Of these, it has the shortest orbital period, making it especially interesting for a range of astrophysical and gravity related questions. We present a spectroscopic and photometric study of the white dwarf companion and infer its radial-velocity curve, effective temperature, surface gravity and luminosity. We find that the white dwarf has properties consistent with those of low-mass white dwarfs with thick hydrogen envelopes, and use the corresponding mass-radius relation to infer its mass; M⊙. Combined with the mass ratio q= 8.1 ± 0.2 inferred from the radial velocities and the precise pulsar timing ephemeris, the neutron star mass is constrained to M⊙. Contrary to expectations, the latter is only slightly above the Chandrasekhar limit. We find that, even if the birth mass of the neutron star was only 1.20 M⊙, more than 60 per cent of the matter that left the surface of the white dwarf progenitor escaped the system. The accurate determination of the component masses transforms this system in a laboratory for fundamental physics by constraining the orbital decay predicted by general relativity. Currently, the agreement is within 1σ of the observed decay. Further radio timing observations will allow precise tests of white dwarf models, assuming the validity of general relativity. [ABSTRACT FROM AUTHOR]

Middle-aged, cooling neutron stars are observed both as relatively rapidly spinning radio pulsars and as more slowly spinning, strongly magnetized isolated neutron stars (INSs), which stand out by their thermal X-ray spectra. The difference between the two classes may be that the INSs initially had much stronger magnetic fields, which decayed. To test this, we used the Chandra X-ray Observatory to observe IRXS J072559.8-261229, a possible X-ray counterpart to PSR J0726-2612, which, with its 3.44 s period and 3 x 1013 G inferred magnetic field strength, is the nearest and least extincted among the possible slowly spinning, strong-field INS progenitors (it likely is in the Gould Belt, at ~1 kpc). We confirm the identification and find that the pulsar has a spectrum consistent with being purely thermal, with blackbody temperature kT = 87 ± 5 eV and radius Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed km at a distance of 1 kpc. We detect sinusoidal pulsations at twice the radio period with a semi-amplitude of 27% ± 5%. The properties of PSR J0726-2612 strongly resemble those of the INSs, except for its much shorter characteristic age of 200 kyr (instead of several Myr). We conclude that PSR J0726-2612 is indeed an example of a young INS, one that started with a magnetic field strength on the low end of those inferred for the INSs, and that, therefore, decayed by a relatively small amount. Our results suggest that the long-period, strong-field pulsars and the INSs are members of the same class, and open up new opportunities to understand the puzzling X-ray and optical emission of the INSs through radio observations of PSR J0726-2612. [ABSTRACT FROM AUTHOR]

We present high-speed, multicolour optical photometry of the anomalous X-ray pulsar 4U 0142+61, obtained with ULTRACAM on the 4.2-m William Herschel Telescope. We detect 4U 0142+61 at magnitudes of and , consistent with the magnitudes found recently by Hulleman et al. and hence confirming their discovery of both a spectral break in the optical and a lack of long-term optical variability. We also confirm the earlier discovery of Kern & Martin that 4U 0142+61 shows optical pulsations with an identical period (∼8.7 s) to the X-ray pulsations. The rms pulsed fraction in our data is per cent, 5–7 times greater than the 0.2–8 keV X-ray rms pulsed fraction. The optical and X-ray pulse profiles show similar morphologies and appear to be approximately in phase with each other, the former lagging the latter by only cycles. In conjunction with the constraints imposed by X-ray observations, the results presented here favour a magnetar interpretation for the anomalous X-ray pulsars. [ABSTRACT FROM AUTHOR]