The Black Widow Pulsar: A Star Evaporating Its Own Companion

The anatomy of a black widow system

A black widow is a binary with two wildly mismatched members. The primary is a recycled millisecond pulsar: a neutron star of roughly 1.4–2.4 solar masses compressed into a 10–12 km sphere, spinning between about 200 and 700 times a second, with a comparatively weak surface magnetic field of ~10⁸–10⁹ gauss. The secondary is barely a star at all — typically 0.01 to 0.05 solar masses, which is 10 to 50 Jupiter masses, well below the ~0.075 M☉ hydrogen-burning limit. It survives as a bloated, partially degenerate remnant, not a functioning star.

The two are absurdly close. For PSR B1957+20, with an orbital period of 9.17 hours and a total mass near 1.7 M☉, Kepler's third law gives a separation of about 1.8 million kilometres — roughly 2.6 solar radii, or five Earth–Moon distances. Put another way, the entire orbit spans only about five solar radii, so the whole binary would sit comfortably inside a red giant. The companion fills perhaps 80–90 per cent of its Roche lobe, which at this separation is only about 0.2 million kilometres in radius (~0.3 R☉), so it is a distended teardrop rather than a sphere.

Tides circularised the orbit and locked the companion's rotation long ago, which is the key geometric fact: one hemisphere permanently faces the pulsar. Everything distinctive about black widows — the day/night temperature split, the once-per-orbit optical light curve, the phase-dependent radio eclipses — follows from a tidally locked object held under a fire hose of relativistic particles for hundreds of millions of years.

Recycling: the victim built its own killer

Neutron stars are born spinning at perhaps tens of milliseconds and spin down to periods of order a second over tens of millions of years. To find one turning in 1.6 ms, something must have spun it back up. The recycling scenario, proposed independently by M. Ali Alpar, Andrew Cheng, Malvin Ruderman and Jacob Shaham and by V. Radhakrishnan and G. Srinivasan in 1982, says the pulsar was fed. When the companion evolved and overflowed its Roche lobe, matter spiralled through an accretion disc onto the neutron star, and each gram delivered angular momentum roughly equal to √(GMR) at the magnetospheric radius.

The budget is easy to check. A neutron star's moment of inertia is I ≈ 10⁴⁵ g cm², so spinning it to 1.6 ms requires an angular momentum J = 2πI/P ≈ 4×10⁴⁸ g cm² s⁻¹. With a specific angular momentum near 2×10¹⁶ cm² s⁻¹, that needs only about 0.1 solar masses of accreted material. This is why the fastest pulsars are also the ones with stripped, lightweight companions, and why the accreting phase — visible today as a low-mass X-ray binary — is called the progenitor stage.

The link is no longer theoretical. PSR J1023+0038, discovered by Anne Archibald and collaborators in 2009, switched in 2013 from a radio millisecond pulsar into an accretion-disc-dominated X-ray source; IGR J18245−2452 in the globular cluster M28 went the other way that same year. These transitional millisecond pulsars caught recycling mid-handover. Once accretion stops for good, the pulsar's wind switches on and begins to destroy the star that fed it.

The energy budget: why the day side glows

A pulsar's power comes from its slowing rotation: Ė = 4π²IṖ/P³. For PSR B1957+20, with P = 1.607 ms and Ṗ ≈ 1.7×10⁻²⁰ s s⁻¹, that is Ė ≈ 10³⁵ erg s⁻¹, some 30 times the Sun's bolometric luminosity — but almost none of it emerges as ordinary starlight. Most leaves as a magnetised wind of electron–positron pairs moving at close to the speed of light, produced by pair cascades in the pulsar magnetosphere, plus a few per cent as pulsed gamma rays.

Spread over a sphere at the companion's distance, that flux is Ė/4πa² ≈ 4×10¹¹ erg cm⁻² s⁻¹, roughly 300,000 times the solar constant at Earth. If a surface absorbs it and reradiates locally, its equilibrium temperature is (F/σ)^1/4 ≈ 9,000 K. Observation matches: the day side of B1957+20's companion runs near 8,000 K while its night side sits around 2,900 K — a single object with a 5,000 K difference between hemispheres. In PSR J1311−3430 the irradiated face exceeds 10,000 K.

Does that heating actually unbind gas? The companion's gravitational binding energy is roughly GM²/R ≈ 10⁴⁶ erg. The companion intercepts a fraction (R/2a)² ≈ 1.5×10⁻³ of the wind, about 2×10³² erg s⁻¹, which over a gigayear is ~7×10⁴⁸ erg — several hundred times the binding energy. So even at one per cent efficiency the pulsar can strip its companion, at an implied rate of order 10⁻¹⁰ M☉ yr⁻¹ and a stripping time of ~10⁸ years. Efficiency, not energy, is the bottleneck.

Radio eclipses: reading the ablated plasma

The ablated gas does not vanish quietly. It fills a large volume around the companion and blots out the radio pulses whenever it lies along the line of sight. For PSR B1957+20 at 430 MHz the pulses disappear for about 50 minutes, roughly 10 per cent of the orbit. Crucially this is far too long to be a geometric eclipse: the eclipsing region is several times wider than the companion's Roche lobe, so what is blocking the beam is escaping plasma, not the star.

The plasma announces itself in the timing. Radio pulses passing through ionised gas are delayed by Δt = 4.15 ms × DM × ν_GHz⁻², where the dispersion measure DM is the integrated electron column. At ingress and egress, black widows show excess DM of ~10⁻³–10⁻² pc cm⁻³ — electron columns of order 10¹⁵–10¹⁶ cm⁻², and pulse delays of tens to hundreds of microseconds that swing with orbital phase. Since the effect scales as ν⁻² and the eclipses run longer at lower frequency, observers dissect the outflow by watching one system from 300 MHz to 3 GHz.

What actually removes the signal is still argued. Pure dispersion cannot do it; free–free absorption would require implausibly high densities; the leading candidates are cyclotron–synchrotron absorption in a magnetised plasma (Christopher Thompson and colleagues, 1994), induced Compton scattering, and scattering out of the beam. Faraday rotation and circular-polarisation measurements at ingress and egress with FAST and MeerKAT imply magnetic fields of order ten gauss threading the outflow, which supports the magnetised-absorption picture. Notably, the pulsar's gamma rays are never eclipsed — plasma is transparent at GeV energies — which is itself proof that the obscuration is a plasma effect rather than a solid body passing in front.

How they are found, and how their masses are weighed

PSR B1957+20 was discovered in 1988 by Andrew Fruchter, Daniel Stinebring and Joseph Taylor with the 305 m Arecibo telescope; Shrinivas Kulkarni and Jeff Hester found its Hα bow shock the same year, showing the pulsar ploughing supersonically through the interstellar medium. For two decades it stayed nearly unique. The population exploded after NASA launched the Fermi Gamma-ray Space Telescope in June 2008: its Large Area Telescope delivered hundreds of unassociated point sources, and radio follow-up with Green Bank, Parkes, the GMRT, LOFAR and MeerKAT converted them into millisecond pulsars. More than 60 spiders are now known in the Galactic field, plus dozens in globular clusters such as 47 Tucanae and Terzan 5.

Some were found in the gamma rays alone. PSR J1311−3430 (Holger Pletsch et al., Science, 2012) was the first millisecond pulsar detected in a blind gamma-ray search, and has a 93.8-minute orbit around a helium-dominated speck of ~0.01 M☉. PSR J1653−0158, dug out of Fermi data by the Einstein@Home volunteer computing project in 2020, has a 75-minute orbit — the shortest known for any rotation-powered pulsar binary.

Masses combine two measurements: pulsar timing fixes the mass function, while the companion's irradiated light curve constrains the inclination and its radial-velocity amplitude gives the mass ratio. Applying this at Keck with LRIS, Roger Romani and collaborators reported in 2022 that PSR J0952−0607, a 707 Hz pulsar found by Cees Bassa's team in a 2017 LOFAR survey, weighs 2.35 ± 0.17 M☉ — among the heaviest neutron stars measured, and a direct constraint on the dense-matter equation of state and the Tolman–Oppenheimer–Volkoff limit. The record spin, 716 Hz, belongs to another eclipsing system, PSR J1748−2446ad in Terzan 5.

Where the picture breaks: systematics, look-alikes, and misconceptions

The mass measurements are the most fragile part. They assume the companion is heated symmetrically about the substellar point and radiates like a stellar atmosphere. Real spiders violate this: several show hot spots displaced from the substellar point and light-curve minima that shift with wavelength, plausibly because the wind is channelled by the companion's own magnetic field or reprocessed at an intrabinary shock. Marten van Kerkwijk, René Breton and Kulkarni obtained 2.40 ± 0.12 M☉ for B1957+20 in 2011 while warning that systematics dominate; asymmetric-heating models have since shifted such values by tenths of a solar mass. A quoted black widow mass is a model output, not a direct weighing.

Timing is equally messy. Black widow orbital periods wander quasi-cyclically on decade timescales, in both directions, generally attributed to the Applegate mechanism — magnetic activity redistributing angular momentum inside the tidally locked companion and changing its quadrupole moment. That makes these systems poor clocks and complicates their use in pulsar timing arrays.

Three confusions are common. First, black widow eclipses are not geometric eclipses like those of an ordinary eclipsing binary — they are frequency-dependent plasma absorption, and the blocked region dwarfs the star. Second, these are not accreting systems: unlike a cataclysmic variable or an LMXB there is no disc, and the energy source is rotation, not infall. Third, redbacks (a name coined by Mallory Roberts around 2011, after the Australian relative of the widow spider) are not simply bigger black widows: their 0.1–0.4 M☉ companions are non-degenerate, their intrabinary shocks usually wrap around the pulsar rather than the companion, and they are the systems that flip into accretion states.

Open questions: can a pulsar finish the job?

The headline unresolved question is whether ablation ever runs to completion and leaves an isolated millisecond pulsar. About a fifth to a quarter of millisecond pulsars in the Galactic field have no companion at all, and full evaporation is the natural explanation — but nobody has caught the transition. The physics cuts both ways: an isotropic wind tends to widen the orbit (a ∝ 1/M_total), diluting the irradiation, while a degenerate companion expands as it is lightened (R ∝ M^−1/3), keeping it exposed. Which wins depends on how much angular momentum the escaping gas carries — unmeasured in any system.

Suggestive endpoints exist: PSR J1719−1438, reported by Matthew Bailes and colleagues in 2011, orbits a roughly Jupiter-mass companion every 2.2 hours at a density that earned it the nickname diamond planet — plausibly a white dwarf stripped almost to nothing.

Two further problems stay open. First, the coupling: how spin-down power actually reaches the surface. Direct GeV photons, the pair wind and shock-reprocessed X-rays all contribute, and the inferred 10–30 per cent heating efficiencies are hard to derive from first principles. Second, the eclipse mechanism, which leaves mass-loss rates spanning 10⁻¹² to 10⁻⁹ M☉ yr⁻¹ because the outflow velocity is unconstrained. The Vera C. Rubin Observatory, the Square Kilometre Array and continued Fermi-driven searches are the likeliest tools to settle both.

Black widows compared with their relatives among binary neutron stars

System	Companion mass	Orbital period	Defining signature
Black widow	~0.01–0.05 M☉, bloated and semi-degenerate	~1.2–10 hours	Radio eclipses over ~10% of the orbit; huge day/night temperature contrast
Redback	~0.1–0.4 M☉, non-degenerate main-sequence-like	~4–20 hours	Longer, deeper eclipses; some switch to accretion states
Transitional MSP (e.g. PSR J1023+0038)	~0.2 M☉	4.75 hours	Observed to flip between radio pulsar and accretion-disc X-ray binary
Classic recycled MSP + white dwarf	0.15–0.4 M☉ helium white dwarf	days to years	Clean, circular, uneclipsed orbit; the quiet end state of recycling
Low-mass X-ray binary (LMXB)	~0.1–1 M☉ donor filling its Roche lobe	hours to days	Active accretion disc, X-ray bright, no radio pulses — the ancestor stage