Brown dwarf around "the Black Widow" (2007)

Yes, it's a bit old but it deserves attention.
It seems not the case of SWIFT J1756.9-2508 pulsar where secondary was once likely stellar and then turned into an exotic planet-sized object.
This object may have started its "life" as brown dwarf. Mass is around 22 times that of Jupiter and a very puffed radius (3 Jupiter radii).
Orbital period is very short of course: 9.17 hours. Assuming host pulsar's mass around 1.4 Mso, the average separation is close to 0.0115 AUs (=2.48 Solar radii).
It is not a white dwarf and orbits around a notable millisecond pulsar, nicknamed the "Black Widow": QX Sagittae.

Quote :

Furthermore, if the secondary in PSR B1957+20 was a ∼ 0.025 M⊙ white dwarf, one would expect a radius of ∼ 0.1 R⊙ - again in contrast with the value of ∼0.3 R⊙ which we have determined from our modelling.

Paper The light curve of the companion to PSR B1957+20

SIMBAD note:

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essential notes:

Millisecond pulsar with brown dwarf companion EQ J195936+204814

Apologies for unburying this old post but this seems the only one specifically mentioning black widow pulsars in general. Update for a recent (2020) discovery in a globular cluster, where this kind of weird objects seems rather frequent.

Discovery and timing of pulsars in the globular cluster M13 with FAST

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We report the discovery of a binary millisecond pulsar (namely PSR J1641+3627F or M13F) in the globular cluster M13 (NGC 6205) and timing solutions of M13A to F using observations made with the Five-hundred-metre Aperture Spherical radio Telescope (FAST). PSR J1641+3627F has a spin period of 3.00 ms and an orbital period of 1.4 days. The most likely companion mass is 0.16 M_Sol. M13A to E all have short spin periods and small period derivatives. We also confirm that the binary millisecond pulsar PSR J1641+3627E (also M13E) is a black widow with a companion mass around 0.02 M_Sol. We find that all the binary systems have low eccentricities compared to those typical for globular cluster pulsars and that they decrease with distance from the cluster core. This is consistent with what is expected as this cluster has a very low encounter rate per binary.

Emphasis mine. 0.02 M_Sol is about 21 M_Jup, well below hydrogen burning limit.

I think this topic should be renamed as Black Widow Pulsar Systems because there is a significant number of these weird objects around and several updates are required in the thread. The latest one:

FAST Globular Cluster Pulsar Survey: Twenty-four Pulsars Discovered in 15 Globular Clusters

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We present the discovery of 24 pulsars in 15 globular clusters (GCs) using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). These include the first pulsar discoveries in M2, M10, and M14. Most of the new systems are either confirmed or likely members of binary systems. M53C and NGC 6517H and I are the only three pulsars confirmed to be isolated. M14A is a black widow pulsar with an orbital period of 5.5 hr and a minimum companion mass of 0.016 M_Sol. M14E is an eclipsing binary pulsar with an orbital period of 20.3 hr. With the other 8 discoveries that have been reported elsewhere, in total 32 GC pulsars have been discovered by FAST so far. In addition, We detected M3A twice. This was enough to determine that it is a black widow pulsar with an orbital period of 3.3 hr and a minimum companion mass of 0.0125 M_Sol.

Both masses well within planetary domain. Same for IGR J17494-3030, XTE J0929-314, the former hosting a 0.014 to 0.02 M_Sol secondary, though regarded as white dwarf, the latter a 0.0083 M_Sol companion, that is 8.7 M_Jup. We are in the field of exotic objects.

It is also about time for SWIFT J1756.9−2508 to be reclassed among "exotic exoplanets" (nice pun) along with NGC 6440 X-2, same for 4U 1626-67 (or KZ TrA) and several other very low-mass X-ray binaries. The number of BW systems is likely going to increase as past discovery papers back to 2000 and back further too are considered...

New BW system and some older detections:

Intermediate long X-ray bursts from the ultra-compact binary candidate SLX 1737-282

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Aims: The low persistent X-ray burster source SLX 1737-282 is classified as an ultra-compact binary candidate. We compare the data on SLX 1737-282 with the other similar objects and attempt to derive constraints on the physical processes responsible for the formation of intermediate long bursts. Methods: Up to now only three intermediate long bursts, all with duration between ~15-30 minutes, have been recorded for SLX 1737-282. The properties of two intermediate long X-ray bursts observed by INTEGRAL from SLX 1737-282 are investigated. The broadband spectrum of the persistent emission in the 3-100 keV energy band is studied with the INTEGRAL data. Results: The persistent emission is measured to be < 1% Eddington luminosity. From the photospheric radius expansion observed during the bursts we derive the source distance at 7.3 kpc. The observed intermediate long burst properties from SLX 1737-282 are consistent with helium ignition at the column depth of 7-8 x 10E-9 g cm-2 and a burst energy release of 1E41 erg. The apparent recurrence time of ~80 days between the intermediate long bursts from SLX 1737-282 suggests a regime of unstable burning of a thick, pure helium layer slowly accreted from a helium donor star.

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Assuming an inclination angle of the binary system between the mean value of 60° to a maximum value of ∼85° the donor star has to be between 0.005 and 0.03 M_Sol

The Likely Orbital Period of the Ultracompact Low-mass X-ray Binary 2S 0918-549

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We report the discovery of the likely orbital period of the ultracompact low-mass X-ray binary (LMXB) 2S 0918-549. Using time-resolved optical photometry carried out with the 8 m Gemini South Telescope, we obtained a 2.4 hr long, Sloan r' light curve of 2S 0918-549 and found a periodic, sinusoidal modulation at 17.4 ± 0.1 minutes with a semiamplitude of 0.015 ± 0.002 mag, which we identify as the binary period. In addition to 4U 0513-40 in the globular cluster NGC 1851 and the Galactic disk source 4U 1543-624, 2S 0918-549 is the third member of the ultracompact LMXBs that have orbital periods around 18 minutes. Our result verifies the suggestion that 2S 0918-549 is an ultracompact binary based on its X-ray and optical spectroscopic properties. Given that the donor in 2S 0918-549 has been suggested to be either a C-O or He white dwarf, its likely mass and radius are around 0.024-0.029 M sun and 0.03-0.032 R sun, respectively, for the former case and 0.034-0.039 Msun and 0.033-0.035 R sun for the latter case. If the optical modulation arises from X-ray heating of the mass donor, its sinusoidal shape suggests that the binary has a low inclination angle, probably around 10°.

Optical detection of the black widow binary PSR J2052+1219

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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 the system parameters obtained from the radio data. As a result, we independently estimate the distance to the system of 3.94(16) kpc, which agrees with the dispersion measure distance. The companion star size is 0.12-0.15 Rsun, close to filling its Roche lobe. It has a surface temperature difference of about 3000 K between the side facing the pulsar and the back side. We summarise characteristics of all black widow systems studied in the optical and compare them with the PSR J2052+1219 parameters derived from our observations.

Eight Millisecond Pulsars Discovered in the Arecibo PALFA Survey

Among these PSR J1928+1245 hosts a companion with minimum mass of 9.4-11 M_Jup.

Finally a study on a well-known low-mass X-ray binary, SAX J1808.4-3658, with a substellar secondary and possibly a circumbinary 8 M_Jup planet too:

Radio pulse search and X-Ray monitoring of SAX J1808.4-3658: What Causes its Orbital Evolution

Quote :

Finally we attempted to fit the data with a Keplerian orbital delay curve that could represent the effect of orbital motion caused by a third body in an eccentric orbit. We find this can fit the data (with χ 2 = 1.1 for 1 dof) if the third body has a mass of about 8 Jupiter masses and is in a relatively wide (≈ 5 AU*) orbit with an eccentricity of about 0.7 and an orbital period of about 17.4 years.

(*) Actually farther away, about 7.6 AUs assuming a 1.4 M_Sol neutron star with a 0.055 M_Sol secondary.

Same for another system, XB 1916–053, with a likely brown dwarf (ca. 60 M_Jup or less) tertiary with an orbital period of 24 years.

Signature of the presence of a third body orbiting around XB 1916-053

Quote :

Context. The ultra-compact dipping source XB 1916-053 has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M⊙). The orbital period derivative of the source was estimated to be 1.5(3) × 10-11 s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002.
Aims: The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadratic term or a different scenario has to be considered.
Methods: We obtained 27 delays associated with the dip arrival times from data covering 37 years and used different models to fit the time delays with respect to a constant period model.
Results: We find that the quadratic form alone does not fit the data. The data are well fitted using a sinusoidal term plus a quadratic function or, alternatively, with a series of sinusoidal terms that can be associated with a modulation of the dip arrival times due to the presence of a third body that has an elliptical orbit. We infer that for a conservative mass transfer scenario the modulation of the delays can be explained by invoking the presence of a third body with mass between 0.10-0.14 M⊙, orbital period around the X-ray binary system of close to 51 yr and an eccentricity of 0.28 ± 0.15. In a non-conservative mass transfer scenario we estimate that the fraction of matter yielded by the degenerate companion star and accreted onto the neutron star is β = 0.08, the neutron star mass is ≥2.2 M⊙, and the companion star mass is 0.028 M⊙. In this case, we explain the sinusoidal modulation of the delays by invoking the presence of a third body with orbital period of 26 yr and mass of 0.055 M⊙.
Conclusions: From the analysis of the delays associated with the dip arrival times, we find that both in a conservative and non-conservative mass transfer scenario we have to invoke the presence of a third body to explain the observed sinusoidal modulation. We propose that XB 1916-053 forms a hierarchical triple system.

Another weird object

The Orbital Period of the Ultracompact Low-Mass X-Ray Binary 4U 1543-624

Quote :

We report the discovery of the orbital period of the ultracompact low-mass X-ray binary (LMXB) 4U 1543-624 using time-resolved optical photometry taken with the 6.5-m Clay (Magellan II) telescope in Chile. The light curve in the Sloan r' band clearly shows a periodic, sinusoidal modulation at 18.2+-0.1 min with a fractional semiamplitude of 8%, which we identify as the binary period. This is the second shortest orbital period among all the known LMXBs, and it verifies the earlier suggestion of 4U 1543-624 as an ultracompact binary based on X-ray spectroscopic properties. The sinusoidal shape of the optical modulation suggests that it arises from X-ray heating of the mass donor in a relatively low-inclination binary, although it could also be a superhump oscillation in which case the orbital period is slightly shorter. If the donor is a C-O white dwarf as previously suggested, its likely mass and radius are around 0.03 M_sun and 0.03 R_sun, respectively. For conservative mass transfer onto a neutron star and driven by gravitational radiation, this implies an X-ray luminosity of 6.5X10^36 erg/s and a source distance of 7 kpc. We also discuss optical photometry of another LMXB, the candidate ultracompact binary 4U 1822-000. We detected significant optical variability on a time scale of about 90 min, but it is not yet clear whether this was due to a periodic modulation.

A planetary-mass WD with ultra-short orbital period. Helium WD model is invoked but the mass seems very low, more compatible with a photoevaporated former stellar core. Exotic helium planet? But density is extreme (1,500 g/cc).

Quote :

Finally a study on a well-known low-mass X-ray binary, SAX J1808.4-3658, with a substellar secondary and possibly a circumbinary 8 MJup planet too

If you read the paper just a little further,

Quote :

We can test this scenario by looking at the pulse frequency derivative of SAX J1808.4−3658 since the pulsar would be accelerated along the orbit... Since we know from previous observations that SAX J1808.4−3658 is spinning down at a relatively constant rate of  ̇νs ≈10−15 Hz s−1 we can confidently exclude this scenario.

Sirius_Alpha wrote:

Quote :

Finally a study on a well-known low-mass X-ray binary, SAX J1808.4-3658, with a substellar secondary and possibly a circumbinary 8 MJup planet too

If you read the paper just a little further,

Quote :

We can test this scenario by looking at the pulse frequency derivative of SAX J1808.4−3658 since the pulsar would be accelerated along the orbit... Since we know from previous observations that SAX J1808.4−3658 is spinning down at a relatively constant rate of  ̇νs ≈10−15 Hz s−1 we can confidently exclude this scenario.

Indeed the planet hypothesis was a possibility, not probable (though I keep on hoping that an exotic planetary system is there). By the way there is the close, substellar companion: that one is real. The XB 1916-053 case seems more likely and deals with a circumbinary brown dwarf or even massive planet if the lower mass limit of 28 M_Jup is considered.

Apologies for repeating but I'd like to emphasize this unnoticed system:

Signature of the presence of a third body orbiting around XB 1916-053

Quote :

Context. The ultra-compact dipping source XB 1916-053 has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M⊙). The orbital period derivative of the source was estimated to be 1.5(3) × 10-11 s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002.
Aims: The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadratic term or a different scenario has to be considered.
Methods: We obtained 27 delays associated with the dip arrival times from data covering 37 years and used different models to fit the time delays with respect to a constant period model.
Results: We find that the quadratic form alone does not fit the data. The data are well fitted using a sinusoidal term plus a quadratic function or, alternatively, with a series of sinusoidal terms that can be associated with a modulation of the dip arrival times due to the presence of a third body that has an elliptical orbit. We infer that for a conservative mass transfer scenario the modulation of the delays can be explained by invoking the presence of a third body with mass between 0.10-0.14 M⊙, orbital period around the X-ray binary system of close to 51 yr and an eccentricity of 0.28 ± 0.15. In a non-conservative mass transfer scenario we estimate that the fraction of matter yielded by the degenerate companion star and accreted onto the neutron star is β = 0.08, the neutron star mass is ≥2.2 M⊙, and the companion star mass is 0.028 M⊙. In this case, we explain the sinusoidal modulation of the delays by invoking the presence of a third body with orbital period of 26 yr and mass of 0.055 M⊙.
Conclusions: From the analysis of the delays associated with the dip arrival times, we find that both in a conservative and non-conservative mass transfer scenario we have to invoke the presence of a third body to explain the observed sinusoidal modulation. We propose that XB 1916-053 forms a hierarchical triple system.

Circumbinary brown dwarf (or even planet) in a really exotic system.

Edasich wrote:

Another weird object

The Orbital Period of the Ultracompact Low-Mass X-Ray Binary 4U 1543-624

Quote :

We report the discovery of the orbital period of the ultracompact low-mass X-ray binary (LMXB) 4U 1543-624 using time-resolved optical photometry taken with the 6.5-m Clay (Magellan II) telescope in Chile. The light curve in the Sloan r' band clearly shows a periodic, sinusoidal modulation at 18.2+-0.1 min with a fractional semiamplitude of 8%, which we identify as the binary period. This is the second shortest orbital period among all the known LMXBs, and it verifies the earlier suggestion of 4U 1543-624 as an ultracompact binary based on X-ray spectroscopic properties. The sinusoidal shape of the optical modulation suggests that it arises from X-ray heating of the mass donor in a relatively low-inclination binary, although it could also be a superhump oscillation in which case the orbital period is slightly shorter. If the donor is a C-O white dwarf as previously suggested, its likely mass and radius are around 0.03 M_sun and 0.03 R_sun, respectively. For conservative mass transfer onto a neutron star and driven by gravitational radiation, this implies an X-ray luminosity of 6.5X10^36 erg/s and a source distance of 7 kpc. We also discuss optical photometry of another LMXB, the candidate ultracompact binary 4U 1822-000. We detected significant optical variability on a time scale of about 90 min, but it is not yet clear whether this was due to a periodic modulation.

A planetary-mass WD with ultra-short orbital period. Helium WD model is invoked but the mass seems very low, more compatible with a photoevaporated former stellar core. Exotic helium planet? But density is extreme (1,500 g/cc).

I hadn't considered the "quark planet" hypothesis...

Searching For Strange Quark Planets

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Strange quark matter (SQM) may be the true ground state of matter. According to this SQM hypothesis, the observed neutron stars actually should all be strange quark stars. But distinguishing between neutron stars and strange quark stars by means of obser- vations is extremely difficult. It is interesting to note that under the SQM hypothesis, less massive objects such as strange quark planets and strange dwarfs can also stably exist. The extremely high density and small radius of strange quark planets give us some new perspectives to identify SQM objects and to test the SQM hypothesis. First, the tidal disruption radius of strange quark planets is much smaller than normal planets, so, very close-in exoplanets can be safely identified as candidates of SQM objects. Second, gravitational waves (GW) from mergers of strange quark star-strange quark planet systems are strong enough to be detected by ground-based GW detectors. As a result, GW observation will be a powerful tool to probe SQM stars. At the same time, the tidal deformability of SQM planets can be measured to further strengthen the result.

"Ultra-dense planets" are indeed assumed.

New BW system in NGC 6712 cluster

An Eclipsing Black Widow Pulsar in NGC 6712

Quote :

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_⊙ and exhibits eclipsing of the pulsar signal. Though the distance to PSR J1853-0842A predicted from its dispersion measure (155.125±0.004 cm^-3 pc) and Galactic free electron density models are about 30\% smaller than that of NGC 6712 obtained from interstellar reddening measurements, this is likely due to limited knowledge about the spiral arms and Scutum stellar cloud in this direction. Follow-up timing observations spanning 445 days allow us to localize the pulsar's position to be 0.14 core radii from the center of NGC 6712 and measure a negative spin-down rate for this pulsar of −2.39(2)×10^-21ss^-1. The latter cannot be explained without the acceleration of the GC and decisively supports the association between PSR J1853-0842A and NGC 6712. Considering the maximum GC acceleration, Galactic acceleration, and Shklovskii effect, we place an upper limit on the intrinsic spin-down rate to be 1.11×10^-20 s s^-1. From an analysis of the eclipsing observations, we estimate the electron density of the eclipse region to be about 1.88×10⁶cm^-3. We also place an upper limit of the accretion rate from the companion is about 3.05×10^-13 M_⊙ yr^-1 which is comparable with some other BWs.

Plus another system

Unusual Emission Variations Near the Eclipse of A Black Widow PSR J1720-0533

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We report on an unusually bright observation of PSR J1720−0533 using the Five-hundred-meter Aperture Spherical radio Telescope (FAST). The pulsar is in a black widow system that was discovered by the Commensal Radio Astronomy FAST Survey (CRAFTS). By coincidence, a bright scintillation maximum was simultaneous with the eclipse in our observation which allowed for precise measurements of flux density variations, as well as dispersion measure (DM) and polarization. We found that there are quasi-periodic pulse emission variations with a modulation period of ∼ 22 s during the ingress of the eclipse, which could be caused by plasma lensing. No such periodic modulation was found during the egress of the eclipse. The linear polarization of the pulsar disappears before the eclipse, even before there is a visually obvious change in DM. We also found that the pulse scattering maybe play an important role in the eclipse of PSR J1720-0533.

Quote :

PSR J1720-0533 is a pulsar in the Galactic field which was newly discovered by the Commensal Radio Astronomy FAST Survey [...] with a 3.26 ms spin period, a 3.16 hr orbital period and a ∼0.034 M_Sun companion.

Two New Black Widow Millisecond Pulsars In M28

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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 5.82hour orbit and PSR J1824−2452N (M28N) is a 3.35-ms pulsar in a 4.76hour orbit. Both pulsars have dispersion measures near 119.30pccm−3 and have low mass companion stars (∼0.01−0.03M⊙), 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 phase of MeerKAT's globular cluster census (within the TRAPUM Large Survey Project). These faint discoveries demonstrate the advantages of MeerKAT's survey sensitivity over previous searches and we expect to find additional pulsars in continued searches of this cluster.

I have the impression that this is the main way to have "planets" (or something very close to that) forming in globular clusters.

A new Black Widow system

Measuring the mass of the black widow PSR J1555-2908

Quote :

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 for a given binary configuration. This method is applied to optical spectra of the newly discovered black widow PSR J1555-2908. By modelling the optical spectroscopy alongside optical photometry, we find that the radial velocity of the companion star is km s (errors quoted at 95% confidence interval), as well as a binary inclination of >75°. Combined with -ray pulsation timing information, this gives a neutron star mass of 1.67 M_Sol and a companion mass of 0.060 M_Sol, placing PSR J1555-2908 at the observed upper limit of what is considered a black widow system.

A new BW pulsar with undermassive secondary in NGC 6440 cluster.

Discoveries and Timing of Pulsars in NGC 6440

Quote :

Using the MeerKAT radio telescope, a series of observations have been conducted to time the known pulsars and search for new pulsars in the globular cluster NGC 6440. As a result, two pulsars have been discovered, NGC 6440G and NGC 6440H, one of which is isolated and the other a non-eclipsing (at frequencies above 962 MHz) "Black Widow", with a very low mass companion (Mc > 0.006 M⊙). It joins the other binary pulsars discovered so far in this cluster which all have low companion masses (Mc < 0.30 M⊙). We present the results of long-term timing solutions obtained using data from both Green Bank and MeerKAT telescopes for these two new pulsars and an analysis of the pulsars NGC 6440C and NGC 6440D. For the isolated pulsar NGC 6440C, we searched for planets using a Markov Chain Monte Carlo technique. We find evidence for significant unmodelled variations but they cannot be well modelled as planets nor as part of a power-law red-noise process. Studies of the eclipses of the "Redback" pulsar NGC 6440D at two different frequency bands reveal a frequency dependence with longer and asymmetric eclipses at lower frequencies (962-1283 MHz).

I definitely remember hints that there might be a planet around NGC 6440C from a long way back, so good to see some follow-up on this object, pity it seems that the planet hypothesis doesn't seem to work.

New Black Widow pulsar systems with very low-mass secondary withing planetary domain

XMM-Newton and NuSTAR observations of the compact millisecond pulsar binary PSR J1653-0158

Quote :

We have presented the first joint XMM-Newton and NuSTAR analysis of the millisecond pulsar (MSP) binary PSR J1653-0158. The 75-minute orbital period inferred from optical and gamma-ray observations together with the 1.97-ms pulsation in the gamma-rays indicate that this system is the most compact Black Widow MSP system known to date. The orbital period was not detected in the XMM-Newton and NuSTAR data, probably due to insufficient photon counts obtained in the observations. Fitting the joint X-ray spectrum of PSR J1653-0158 with a power law gives a photon index Γ=1.71±0.09. The X-ray luminosity of the source in the (0.2-40) keV band is deduced to be 1.18×10³¹erg s^-1, for an adopted distance of 0.84 kpc. We have shown that the broad-band X-ray spectrum can be explained by synchrotron radiation from electrons accelerated in the intra-binary shock, and the gamma-rays detected in the Fermi data are curvature radiations from electrons and positrons in the pulsar magnetosphere. Our kinematic analysis of the Tidarren* systems PSR J1653-0158 and PSR J1311-3430 indicates that the two Tidarren systems are likely to have originated in the Galactic Disk.

(*) It is interesting to notice terms borrowed from Arachnology to describe Black Widow pulsar systems...

It deals with an ablating/photoevaporating object:

Quote :

The deduced mass of ∼ 0.014 M_Sol (Nieder et al. 2020) of the companion is above the critical mass limit ∼ 0.006 M_Sol for dynamically stable mass transfer (see e.g. Kiel & Taam 2013). With continuous ablation by the energetic particles and evaporation by the radiation from the MSP, the companion star may lose all its mass completely, leaving only an isolated MSP in the system.

Formation of black widows through ultra-compact X-ray binaries with He star companions

Quote :

Black widows (BWs) are a type of eclipsing millisecond pulsars (MSPs) with companion masses ≲0.05M⊙, 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 companion masses M₂ ≲ 0.01M⊙, whereas another with M₂ ∼ 0.01-0.05M⊙. However, the origin of the former is still highly uncertain. In this paper, we investigated the formation of BWs with M2 ≲0.01M⊙ through ultra-compact X-ray binaries (UCXBs) with He star companions, in which a neutron star (NS) accretes material from a He star through Roche-lobe overflow. By considering different He star masses and evaporation efficiencies with the stellar evolution code Modules for Experiments in Stellar Astrophysics (MESA), we evolved a series of NS+He star systems that can undergo UCXB stage. We found that this channel can explain the formation of BWs with M2 ≲0.01M⊙ within the Hubble time, especially three widely studied BWs, i.e. PSRs J1719-1438, J2322-2650 and J1311-3430. We also found that X-ray irradiation feedback does not affect the evolutionary tracks of evaporation process. Our simulations indicate that the origin of BWs with M2 ≲0.01M⊙ is different with another sub-type of BWs, and that the UCXB channel with He star companions are the potential progenitors of isolated MSPs. In addition, the present work suggests that the BWs with M2 ≲0.01M⊙ may not be produced by redback systems.

A 62-minute orbital period black widow binary in a wide hierarchical triple

Quote :

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 of state. Here, we report observations of ZTF J1406+1222, a wide hierarchical triple hosting a 62-minute orbital period black widow candidate whose optical flux varies by a factor of more than 10. ZTF J1406+1222 pushes the boundaries of evolutionary models, falling below the 80 minute minimum orbital period of hydrogen-rich systems. The wide tertiary companion is a rare low metallicity cool subdwarf star, and the system has a Galactic halo orbit consistent with passing near the Galactic center, making it a probe of formation channels, neutron star kick physics, and binary evolution.

Interesting update on PSR J2051-0827 (aka LY Aquarii), one of the earliest Black Widow-type systems discovered.

Multi-colour optical light curves of the companion star to the millisecond pulsar PSR J2051-0827

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We present simultaneous, multi-colour optical light curves of the companion star to the black-widow pulsar PSR J2051-0827, obtained approximately 10 years 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 timescales 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_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<k₂<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.

Substellar mass confirmed along with strong analogy with brown dwarfs (despite they still call it "companion star") and extreme thermal contrast between dayside and nightside too.

PSR J0952-0607: The Fastest and Heaviest Known Galactic Neutron Star
https://arxiv.org/abs/2207.05124

Companion mass: 34 M_Jup

An Optical Study of the Black Widow Population

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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 neutron star mass. The substellar companions are substantially degenerate, with average densities 15−30× Solar, but are inflated above their zero temperature radii. We find evidence that the most extreme recycled BW pulsars have both large >0.8M⊙ accreted mass and low <108G magnetic fields. Examining a set of heavy BWs, we infer that neutron star masses larger than 2.19M⊙ (1σ confidence) or 2.08M⊙ (3σ confidence) are required; these bounds exclude all but the stiffest equations of state in standard tabulations.

Systems described with substellar degenerates: PSR J0023+0923 (0.018 M_Sol, 0.1 R_Sol), J0636+5128 (0.01 M_Sol, 0.095 R_Sol), J0952−0607 (0.032 M_Sol), J1301+0833 (0.036 M_Sol), J1311−3430 (0.012 M_Sol), J1653−0158 (0.014 M_Sol), J1810+1744 (0.064 M_Sol), J1959+2048 (0.024 M_Sol, 0.1 R_Sol), J2052+1219 (0.041 M_Sol).

The Green Bank North Celestial Cap Survey. VII. 12 New Pulsar Timing Solutions
https://arxiv.org/abs/2212.03926

Substellar companions to following neutron stars: PSR J0742+4110 (0.06 M_Sol), PSR J1221-0633 (0.01 M_Sol) and PSR J1317-0157 (0.02 M_Sol).

A black widow population dissection through HiPERCAM multi-band light curve modelling

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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 for PSR J1641+8049, as well as attain a significant increase in signal-to-noise and cadence compared with previous publications for the remaining 5 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, but also a puzzling positive correlation between the orbital inclination and the irradiation temperature of the companion. 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.

True masses of a few BW systems, all within planetary/substellar domain, some dense objects, other poorly dense (c. 2.8 g/cc).

More BW-type systems

Discovery and Timing of Millisecond Pulsars with the Arecibo 327 MHz Drift-Scan Survey
https://arxiv.org/abs/2306.10156

One object of interest:

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PSR J1630+3550 (hereafter J1630) is an MSP in a 7.6 hour binary orbit. Assuming a pulsar mass of 1.4 M⊙, an orbital inclination angle of i = 90° would imply a minimum companion mass of 0.0098 M⊙ and a median mass (i.e. i = 60°) of 0.0113 M⊙.The low mass of the companion and the tight orbit indicate that this is a black widow pulsar.

Companions in other systems yield typically stellar mass.

Optical Identification of the Shortest-Period Spider Pulsar System M71E
https://arxiv.org/abs/2306.14949

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M71E is a spider pulsar (i.e., a millisecond pulsar with a tight binary companion) with the shortest known orbital period of P=53.3 min discovered by Pan et al. (2023). Their favored evolutionary model suggests that it bridges between two types of spider pulsars, namely, it descended from a "redback" and will become a "black widow". Using Hubble Space Telescope (HST) archival imaging data, we report the first optical identification of its companion COM-M71E. The HST and pulsar timing coordinates are in excellent agreement (within ~10 mas). If M71E is associated with the globular cluster M71, our measured brightness of COM-M71E (m_F606W ~ 25.3) is broadly consistent with the expectation from Pan et al. (2023)'s preferred binary evolutionary model of a stripped dwarf companion.

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Pan23’s analysis favors a stripped dwarf companion with Mc=0.047−0.097M⊙,estimated by imposing mass-radius relations for brown dwarfs/low-mass dwarfs (Burrowsetal.1993) and restricting its radius within the Roche lobe radius(Eggleton1983).

The black widow pulsar J1641+8049 in the optical, radio and X-rays
https://arxiv.org/abs/2311.08688

Companion mass about 0.046 M_Sol (=48.2 M_Jup).