X-ray Binary

A binary that turned the sky X-ray bright

The first cosmic X-ray source other than the Sun was discovered in June 1962, when an Aerobee rocket carrying Geiger counters launched by a team led by Riccardo Giacconi was meant to look for solar X-rays reflected off the Moon. Instead, it found a bright, unrelated source in Scorpius — Sco X-1, now known to be a low-mass X-ray binary 9000 light-years away. Within a decade, the Uhuru satellite catalogued 339 X-ray sources, and the picture became clear: most extra-solar X-ray emission in the Milky Way comes from compact objects feeding off ordinary stars.

An X-ray binary is exactly that — a binary star system in which one component is a compact remnant (neutron star, stellar-mass black hole, or in rare cases a white dwarf) and the other is a non-degenerate star. Mass is transferred from the donor to the accretor either as a captured stellar wind or as Roche-lobe overflow through the inner Lagrangian point. The gas, carrying angular momentum, settles into an accretion disk, spirals inward, releases gravitational binding energy, and emits the bulk of that energy as X-ray photons because the temperature near the compact object reaches 10⁶–10⁸ K.

X-ray binaries are the workhorses of compact-object astrophysics. They were the first systems to confirm neutron-star surfaces (via thermonuclear bursts), the first to provide dynamical evidence of stellar-mass black holes (Cyg X-1), the cleanest probes of accretion-disk physics across spectral states, and a major source of progenitors for the merging compact binaries detected by LIGO.

HMXBs versus LMXBs

The two main classes are distinguished by the mass of the companion and the mode of mass transfer.

	HMXB	LMXB
Companion mass	~10–60 M☉ (O/B star)	≲ 1 M☉ (K/M dwarf, evolved)
Mass transfer mode	Stellar-wind capture	Roche-lobe overflow
Population age	10⁵–10⁷ yr	10⁸–10¹⁰ yr
Galactic location	Spiral arms, star-forming	Bulge & globular clusters
Compact object	NS (often Be/X-ray) or BH	NS or BH
Optical brightness	Companion dominates	X-ray-heated disk dominates
Orbital period	Days to ~100 days	Minutes to days
Examples	Cyg X-1, LMC X-3, Vela X-1, SS 433	Sco X-1, GX 339-4, A0620-00, V404 Cyg

HMXBs come with a flag: their X-ray emission is often pulsed, modulated by the rotating magnetic poles of the neutron-star accretor. Cen X-3, the first detected X-ray pulsar, has a 4.84-second pulse period and a 2.087-day orbital period. The pulse modulation immediately reveals that the compact object has a surface and a structured magnetic field — diagnostic features impossible for a black-hole accretor. LMXBs, in contrast, rarely pulse coherently because most low-mass NS accretors have weakly magnetised surfaces (B ~ 10⁸ G), the legacy of long mass-accretion-driven field decay.

Case study: Cygnus X-1

Cygnus X-1 was discovered in 1964 by Bowyer, Byram, Chubb and Friedman in an Aerobee rocket flight from White Sands. It is one of the persistently brightest X-ray sources in the sky, modulated at the 5.6-day orbital period of the system. Its optical counterpart is HDE 226868, an O9.7 supergiant of about 40 M☉, sitting at a Gaia DR3 parallax distance of about 2.22 kpc.

The dynamical case for a black hole rests on the radial-velocity curve of HDE 226868. The mass function

f(M) = (M_X sin i)³ / (M_X + M_O)² = P K_O³ / (2π G)

where P is the orbital period and K_O the radial-velocity semi-amplitude of the optical star, is a strict lower bound on the unseen object's mass. For Cyg X-1, P = 5.6 days, K_O ≈ 75 km/s, giving f(M) ≈ 0.25 M☉. The distance and orbital inclination then push M_X up dramatically. The 2021 reanalysis by Miller-Jones and collaborators, using radio parallax to nail the distance to 2.22 ± 0.18 kpc, gave

M_BH    = 21.2 ± 2.2 M☉
M_O     = 40.6 ± 7.7 M☉
i       = 27.5° ± 0.8°
distance = 2.22 ± 0.18 kpc

21 M☉ is far above the ~3 M☉ Tolman-Oppenheimer-Volkoff limit for neutron-star mass; nothing other than a black hole is permitted. The companion's wind feeds an accretion flow that, in the persistent low-hard state, peaks near 30 keV with a spectrum dominated by Comptonisation in a hot corona; in occasional soft-state excursions, the cool inner disk dominates and a power-law tail extends out beyond 500 keV.

Case study: Sco X-1

Sco X-1 is the brightest persistent extra-solar X-ray source. Discovered in 1962, it sits at a distance of 2.8 kpc and emits L_X ~ 2.3 × 10³⁸ erg/s — close to the Eddington limit for a 1.4 M☉ neutron star. The companion is a M-type subgiant of 0.4 M☉ in a 0.787-day orbit, transferring mass via Roche-lobe overflow. The system is a Z-source, the canonical class of bright LMXBs whose hardness-intensity track in colour-colour diagrams traces a Z-shaped pattern as the accretion rate sloshes near Eddington.

Sco X-1 is also a benchmark target for the LIGO continuous-wave search. Spinning, accreting neutron stars are predicted to develop persistent quadrupole moments — perhaps from r-mode instabilities or buried magnetic fields — that radiate gravitational waves at twice the spin frequency. Because the X-ray luminosity provides an independent measurement of the spin-up torque, Sco X-1 has the tightest "torque-balance" upper limit on continuous gravitational-wave strain from any known source.

Worked example: Cyg X-1 mass function

Suppose we observe the optical companion HDE 226868 with high-resolution spectroscopy and measure

P_orb = 5.5995 days = 4.838 × 10⁵ s
K_O   = 75 km/s    = 7.5 × 10⁶ cm/s

(K_O is the velocity amplitude of the optical star in its orbit around the system's centre of mass.) The mass function is

f(M) = P K_O³ / (2π G)

with G = 6.674 × 10⁻⁸ cm³ g⁻¹ s⁻². Plugging in:

f(M) = (4.838 × 10⁵)(7.5 × 10⁶)³ / (2π × 6.674 × 10⁻⁸)
     = (4.838 × 10⁵)(4.219 × 10²⁰) / (4.193 × 10⁻⁷)
     = 2.04 × 10²⁶ / 4.19 × 10⁻⁷
     = 4.87 × 10³² g
     = 0.245 M☉

This f(M) is the value the unseen object would have if the system were edge-on (sin i = 1) and the visible star were massless. Because f(M) = M_X³ sin³i / (M_X + M_O)², we need to invert with assumptions about M_O and i. Take M_O = 40 M☉ and sin i ≈ 0.46 (i ≈ 27°). Solving

0.245 = M_X³ (0.46)³ / (M_X + 40)²
      = 0.0973 M_X³ / (M_X + 40)²

iterating numerically (try M_X = 21 M☉):

0.0973 × 21³ / 61²  = 0.0973 × 9261 / 3721
                    = 0.242 M☉  ≈ f(M) ✓

21 M☉ reproduces the observed mass function and lies firmly above the neutron-star mass ceiling. This is the dynamical argument that promotes Cyg X-1 from "unidentified X-ray source" to "confirmed black-hole binary".

Spectral states and outburst cycles

Stellar-mass black hole XRBs spend most of their lives in deep quiescence, occasionally undergoing months-long outbursts driven by thermal-viscous instabilities in their accretion disk. During an outburst, the system traces a counter-clockwise loop in a hardness-intensity diagram (HID). The full outburst cycle has a textbook ladder:

(1) Quiescent state: very low Ṁ, hard power law, jet often present.
(2) Low/Hard state:  L_X ~ 10⁻³ to 10⁻¹ L_Edd, dominant Γ ~ 1.6 power law.
(3) Hard-to-soft transition: hot corona shrinks, disk pushes inward, jet quenches.
(4) High/Soft state: thermal disk dominates, L ~ L_Edd, no compact jet.
(5) Soft-to-hard transition: rebuilds corona, jet may switch back on.
(6) Decay back to quiescence.

The bridge between hard and soft states is also when the most spectacular discrete radio jet ejections are observed, e.g. in GRS 1915+105 and MAXI J1820+070. These transient ejections are how stellar-mass black holes contribute to the population of microquasars. Understanding what triggers state transitions, and how disk truncation correlates with corona geometry, is one of the most active areas of current XRB research; eROSITA, NICER, IXPE and Insight-HXMT are pouring data into the question.

Ultraluminous X-ray sources

Off-nuclear point sources in nearby galaxies with apparent isotropic luminosities above 10³⁹ erg/s are termed ultraluminous X-ray sources (ULXs). Because the Eddington luminosity for a 10 M☉ stellar-mass accretor is ~1.3 × 10³⁹ erg/s, ULXs at 10⁴⁰–10⁴¹ erg/s either host more massive accretors or radiate non-isotropically.

The breakthrough came in 2014 when Bachetti and collaborators detected coherent 1.37-second X-ray pulsations from M82 X-2 — the brightest ULX in the Cigar Galaxy at L_X ~ 1.8 × 10⁴⁰ erg/s. The pulsations are a smoking gun for a magnetised neutron star, putting the source at ~100 L_Edd_NS. NGC 5907 ULX-1 at L_X ~ 10⁴¹ (~500 L_Edd) and NGC 7793 P13 at ~5 × 10⁴⁰ followed. The mechanism appears to be magnetic confinement of the accretion column: above the surface a tall radiation-photosphere shell forms, and locally super-Eddington accretion is sustained while the column geometry beams the X-rays toward the observer. The cleanest implication is that the apparent luminosity overestimates the isotropic-equivalent rate by some factor of order 10.

Some ULXs may still host intermediate-mass black holes (IMBHs, 10²–10⁴ M☉). Hyperluminous X-ray sources (HLXs) at L_X > 10⁴¹ erg/s, like ESO 243-49 HLX-1 at ~10⁴² erg/s with state-transition behaviour mimicking stellar-mass BHs scaled up, remain the strongest candidates for genuine IMBHs.

Variants and extensions

• Be/X-ray binaries. A subclass of HMXB in which the companion is a Be star with an equatorial decretion disk. The neutron-star accretor flares up at periastron passage when it crosses the disk, producing transient X-ray outbursts. Roughly two-thirds of the Galactic HMXB population are Be/X.
• Microquasars. XRBs with resolved relativistic radio jets — scaled-down analogues of AGN. SS 433 (precessing 0.26 c jets), GRS 1915+105, and Cyg X-1 in its hard state are canonical. The connection to AGN unifies the "fundamental plane of black-hole activity" linking radio luminosity, X-ray luminosity, and mass.
• Symbiotic X-ray binaries. Wide binaries in which a neutron star or BH accretes from the wind of an M-giant companion. Long orbital periods (hundreds of days), low duty cycles, and rare X-ray outbursts when the wind density spikes.
• Eclipsing X-ray binaries. When the orbital plane is edge-on, the companion periodically blocks our view of the compact object. EXO 0748-676 and Hercules X-1 are textbook eclipsers; eclipses give clean measurements of orbital geometry and the size of the X-ray emitting region.
• Black-widow / redback pulsars. Recycled millisecond pulsars whose pulsar wind ablates the surface of a low-mass companion in a tight binary (orbital periods of hours). They are the bright LMXB end-state seen long after mass transfer has ended; they pulse in radio and γ-rays rather than X-rays.

Where X-ray binaries show up

• Cygnus X-1 (HMXB, BH). M_BH ≈ 21 M☉ + O9.7 supergiant at d = 2.22 kpc. The first dynamically-confirmed black hole; long-running benchmark for spin measurements via continuum fitting (a* > 0.95).
• Sco X-1 (LMXB, NS). Brightest persistent X-ray source in the sky, L_X ≈ 2.3 × 10³⁸ erg/s, 0.79-day orbit, ~2.8 kpc away. Z-source archetype.
• SS 433 (HMXB, BH or NS, microquasar). A 0.26 c precessing jet with a 162-day cone period; the only known X-ray binary with optical jet emission lines Doppler-shifted by ±50,000 km/s.
• GRS 1915+105 (LMXB, BH). 12.4 M☉ black hole + K-giant donor; the first Galactic superluminal source, with apparent jet motions of 1.25 c. State-transitions on timescales of seconds make it a benchmark variability source.
• M82 X-2 (ULX, NS). First confirmed ULX pulsar, P = 1.37 s, L_X ≈ 1.8 × 10⁴⁰ erg/s — ~100 × Eddington for a neutron star. Established the magnetic-column super-Eddington mechanism.

Common pitfalls

• Confusing the mass function with the mass. f(M) is a strict lower limit on the unseen mass only when the visible companion is massless and the orbit is edge-on. Realistic M_X values require independent constraints on M_companion and inclination; otherwise the inferred BH mass can be off by a factor of two.
• Assuming all X-ray pulsators are HMXBs. Accreting millisecond pulsars in LMXBs (e.g. SAX J1808.4-3658) also pulse, but in the kHz range. The slow-pulsar / fast-pulsar dichotomy maps onto magnetic-field strength rather than companion mass.
• Using the standard Eddington formula for accreting NS. The luminosity at which radiation pressure just balances gravity is helium-rich for NS surfaces (Y_He ≈ 0.27) and hydrogen for many HMXB winds. The accurate threshold depends on composition; published Eddington values for NS run 1.8–3.0 × 10³⁸ erg/s.
• Treating the disk as the only X-ray emitter. The hot corona and (in HMXBs) the wind shock contribute substantially to the keV-to-MeV continuum. Spectral fitting that neglects the corona drives the inferred disk temperature into the wrong regime.
• Forgetting kicks at compact-object birth. Supernova natal kicks of 100–500 km/s frequently disrupt the binary or shift it to high-eccentricity orbits. The fact that XRBs exist at all means kick magnitudes for many BH formations must be modest, an active constraint on supernova engine models.