Accretion Signatures and State Classification

An accretion state is an operational pattern in spectrum, variability, luminosity, and often outflow behavior. It is not a direct photograph of a disk–corona geometry. State classification is valuable because the same source traces repeatable transitions, but the thresholds depend on energy band, detector response, timing interval, and component model. This page builds a data-space classification before discussing physical interpretations; observational status is current through 2026-08-18.

Required background. Probability and inference for gravity supplies likelihoods, latent classes, uncertainty propagation, and selection effects.

Helpful background. Black-Hole Geometry supplies the strong-field scales without fixing an accretion state; Relativistic Matter and Compact Objects supplies plasma and radiation closures; Gravitational-Wave Astronomy supplies the separate compact-binary inference chain.

A state is a vector of observables

For a specified detector band and timing range, a useful state vector is

$$\mathbf x= \left(f_{\rm disk},\Gamma,r_{\rm rms},\nu_{\rm QPO},A_{\rm QPO},H,L/L_{\rm Edd}\right).$$

Here $f_{\rm disk}$ is the fitted thermal-disk fraction in a declared band, $\Gamma$ is a continuum photon index, $r_{\rm rms}$ is integrated fractional root-mean-square variability over a declared frequency interval, $\nu_{\rm QPO}$ and $A_{\rm QPO}$ describe any quasi-periodic peak, and $H$ is a hardness ratio with explicitly named numerator and denominator bands. Luminosity requires distance, mass, absorption, bolometric correction, and an isotropy assumption.

The integrated fractional variance is obtained from a noise-subtracted power spectrum,

$$r_{\rm rms}^2=\int_{\nu_1}^{\nu_2}P_{\rm frac}(\nu)\,d\nu.$$

Changing $\nu_1$, $\nu_2$, time resolution, segment length, dead-time correction, or Poisson-noise estimate changes the reported number. Likewise, a disk fraction is not portable between energy bands: a cool disk may dominate bolometric power while contributing little within a hard detector band.

Remillard and McClintock 2006, § 4.2 and Table 2 defines widely used RXTE-era thermal, hard, and steep-power-law states by simultaneous spectral and timing criteria. Its thermal state requires all three of the following: a disk fraction $f_{\rm disk}\gt0.75$ of the unabsorbed 2–20 keV flux; continuum fractional rms $r_{\rm rms}\lt0.075$ integrated over 0.1–10 Hz; and no 0.1–30 Hz QPO with fractional rms amplitude above $0.005$. The timing quantities use a broad detector band, approximately 2–30 keV for the RXTE PCA. A hard state combines a hard continuum, small disk fraction, and strong broad-band variability. These cuts are reproducible definitions for that analysis system, not constants of nature.

Phenomenology and nonunique geometry

The main patterns are summarized without identifying any one of them with a unique inner flow:

Phenomenological regime	Common spectral–timing pattern	Frequently used physical interpretation	Important degeneracy
Thermal dominant or soft	Strong multitemperature thermal component, weak rapid variability	Optically thick disk near the compact object with a weak high-energy tail	Atmosphere hardening, inner stress, warm Comptonization, absorption
Hard	Hard Comptonized continuum, strong band-limited noise, compact radio jet often present	Hot inner flow or corona plus a cooler disk	Disk truncation versus coronal heating, reflection, inclination
Steep power law or very high	Steep energetic tail, strong luminosity, QPOs may occur	Energetic nonthermal or hybrid corona near a bright disk	Pair content, seed photons, reflection, geometry
Intermediate	Rapidly changing spectrum, timing, and outflow	Transition among disk, corona, magnetic flux, and jet configurations	Classification boundary and nonstationarity
Quiescent	Very low luminosity, often hard spectrum	Radiatively inefficient inflow with strong mass loss or jet contribution	Horizon rate, electron heating, nonthermal particles

The table is deliberately asymmetric: the left columns classify measurements, while the physical column lists hypotheses. Done, Gierliński, and Kubota 2007, §§ 4–6 and 9 shows how disk, Comptonization, reflection, and variability evolve across black-hole binary states, while also exposing the source-model assumptions.

An accretion state does not identify the central object by itself. Neutron-star binaries and other accretors can show related spectral and timing regimes. The black-hole interpretation comes from dynamics, compactness, absence or presence of surface-sensitive phenomena, and consistency across methods. Conversely, a dynamically established black-hole binary does not make every state label a measurement of inner radius or spin.

Transitions, hysteresis, and jets

During an outburst, a black-hole X-ray binary often rises through a hard state, crosses intermediate states, reaches a soft state, and later returns to the hard state at a lower luminosity. A hardness–intensity diagram can therefore trace a loop rather than a single curve. The state at time $t$ depends on history, magnetic flux, disk surface density, irradiation, evaporation or condensation, and perhaps the outer mass-supply trajectory—not only the instantaneous $L/L_{\rm Edd}$.

This hysteresis falsifies a universal one-parameter classification by luminosity. It also makes transition sampling a selection issue: irregular observations can miss short intermediate states, while trigger policies oversample bright or unusual epochs. Comparisons across sources need a common energy band, timing range, mass and distance treatment, and outburst completeness model.

Radio behavior supplies an additional but not infallible coordinate. Compact, partially self-absorbed jets commonly accompany hard states; discrete ejecta can appear near transitions; persistent core radio emission is often weaker in soft states. Fender, Belloni, and Gallo 2004, §§ 2–4 and Fig. 7 organizes this empirical disk–jet coupling. Radio nondetection is not automatically jet absence because distance, frequency, cadence, optical depth, sensitivity, and beaming enter.

Classifying sources in a specified dataset

A reproducible worked example can use one named outburst from the HEASARC RXTE final archive data release, with the exact PCA and HEXTE products, response or CALDB version, background model, dead-time treatment, and observation identifiers recorded. Good-time intervals, elevation and pointing cuts, active detector units, energy channels, pile-up or telemetry exclusions, burst and dip removal, timing segment length, Fourier normalization, and QPO search range define the selected sample.

The forward model is evaluated in count space. A minimal spectral likelihood includes absorption, a thermal disk component, a Comptonized continuum, and reflection or line structure when demanded by residuals, all folded through the response. The timing analysis propagates counting noise, dead time, red-noise leakage, gaps, segment-to-segment nonstationarity, and trials in a QPO search. Distance, mass, inclination, absorption, calibration, and cross-normalization should be nuisance parameters or explicitly bounded external inputs.

State assignment can then be performed in two transparent ways. A rule-based classifier applies preregistered thresholds to posterior distributions of the observables. A probabilistic classifier treats the state as a latent class or continuous trajectory and reports class probabilities. Either approach should distinguish statistical uncertainty from systematic and model dependence. Absorption and response affect hardness; continuum decomposition affects $f_{\rm disk}$ and $\Gamma$; dead time and noise subtraction affect $r_{\rm rms}$; segment and trials choices affect QPO significance; inclination and distance affect physical interpretation.

The reproduction path is to rebuild hardness–intensity and rms–hardness tracks from the archived products, then repeat them with alternative but defensible energy bands, continuum decompositions, and state boundaries. A physical claim survives only if it is not created by the historical label. Source code, software environment, observation list, response files, and machine-readable derived products are part of that boundary.

Common pitfalls

Using luminosity as the state. The same luminosity can occur on the rising hard branch, soft branch, or declining transition. History and spectral–timing behavior matter.

Comparing hardness ratios with different bands. A numerical hardness is meaningful only with its two energy bands, response, absorption treatment, and source frame.

Turning a component fit into a unique geometry. A disk plus power-law fit is a phenomenological decomposition. Coronal geometry, disk truncation, atmosphere, reflection, and absorption require further observables.

Freezing the class before propagating uncertainty. A point estimate just across a threshold does not imply certain membership. Report the probability or sensitivity of the classification to the measurement and model choices.

Classify a thermal-state example

In the RXTE-era convention above, a source has disk fraction $f_{\rm disk}=0.82$ in unabsorbed 2–20 keV flux, continuum fractional rms $r_{\rm rms}=0.03$ over 0.1–10 Hz, and no 0.1–30 Hz QPO above the $0.5\%$ fractional rms threshold. Assume the timing band and data sensitivity are adequate to apply those cuts. Does it meet the thermal-state criteria? What additional information is needed before interpreting it as a disk reaching the ISCO?

Solution

Yes. The disk contributes more than $75\%$, the integrated rms is below the thermal-state limit, and no QPO violates the amplitude criterion. It is therefore classified as thermal dominant under those declared bands, timing intervals, component definitions, and thresholds.

That classification does not establish the inner boundary. Interpreting a fitted thermal radius as the ISCO additionally needs the compact-object mass, distance, disk inclination, alignment, atmosphere hardening, absorption, inner-stress assumption, thickness and luminosity range, returning radiation, calibration, and a test for Comptonization or wind contamination. The state is a necessary data-quality and regime selection for some disk models, not the spin result itself.

References

• Done, Chris, Marek Gierliński, and Aya Kubota. “Modelling the Behaviour of Accretion Flows in X-Ray Binaries: Everything You Always Wanted to Know about Accretion but Were Afraid to Ask.” Astronomy and Astrophysics Review 15 (2007): 1–66. DOI.
• Fender, Rob P., Tomaso M. Belloni, and Elena Gallo. “Towards a Unified Model for Black Hole X-Ray Binary Jets.” Monthly Notices of the Royal Astronomical Society 355 (2004): 1105–1118. DOI.
• Remillard, Ronald A., and Jeffrey E. McClintock. “X-Ray Properties of Black-Hole Binaries.” Annual Review of Astronomy and Astrophysics 44 (2006): 49–92. DOI.