Thermal-Radiative Winds in Accretion Discs

• Thermal-radiative winds are outflows driven by intense irradiation that heats a disc’s atmosphere, enabling thermal expansion to counteract gravity and boost acceleration via radiation pressure and atomic forces.
• They are modeled using integrated hydrodynamics, photoionization, and radiative transfer techniques, which refine traditional Compton-heated approaches by accounting for effective gravity and nuanced heating/cooling balances.
• Observational diagnostics including Fe K absorption lines, velocity profiles, and polarimetry constrain wind geometry, density, and feedback effects on accretion disc evolution in systems like X-ray binaries and AGN.

Thermal-radiative winds are outflows produced when irradiation from a compact accretor heats gas in an outer disc atmosphere to temperatures at which thermal expansion can overcome gravity, while radiation pressure and atomic radiative forces can further assist acceleration. In X-ray binaries, these winds are typically equatorial, are most evident in luminous disc-dominated states, and are now modeled as a coupled problem in hydrodynamics, photoionization, and radiative transfer rather than as a purely hydrodynamic flow with approximate heating and cooling. Across the recent literature, the term encompasses both classical Compton-heated thermal winds and regimes in which electron scattering, bound-free opacity, and line driving materially modify launch radii, velocity structure, observability, and feedback on the disc itself (Done et al., 2016, Tomaru et al., 2019).

1. Physical basis and launch criteria

The canonical thermal component is set by irradiation of the disc atmosphere. The relevant ionization and thermal state are commonly expressed through the ionization parameter

$\xi = \frac{L_X}{n_H r^2},$

and, in pressure form,

$$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$

The characteristic temperature is the Compton temperature $T_{\rm IC}$, and the associated Compton radius is

$R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$

Beyond this scale, or more specifically from radii of order $0.1\,R_{\rm IC}$ to $0.2\,R_{\rm IC}$ in the standard thermal-wind framework, gas heated to $T_{\rm IC}$ can escape if its sound speed exceeds the local escape speed (Done et al., 2016, Avakyan et al., 2023).

At higher luminosities, radiation pressure ceases to be a perturbation. In the binary-wind literature this produces the “thermal-radiative” regime: thermal expansion still initiates the outflow, but electron scattering and atomic radiative forces reduce the effective gravity and allow launch from smaller radii. A widely used correction writes the effective gravity as

$$g_{\rm eff} = \frac{GM}{R^2}\left(1-\frac{L}{L_{\rm Edd}}\right),$$

with a corresponding reduction in the effective Compton radius,

$$R_{IC,\text{eff}} \approx R_{IC}\left(1-\frac{L}{0.71L_{Edd}}\right).$$

In this regime the wind can become substantially stronger and, near Eddington, even optically thick (Done et al., 2016).

The same physical framework also emphasizes geometry. These winds are generally concentrated toward the disc plane, so absorption signatures are preferentially seen in high-inclination systems. In luminous neutron-star and black-hole binaries, an irradiated inner atmosphere can also shadow the outer disc, so the launch region is determined not only by $T_{\rm IC}$ and $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$0 but by how much of the outer disc actually sees the ionizing continuum (Tomaru et al., 2019).

2. Thermal equilibrium curves, heating and cooling, and SED dependence

A defining development in the subject is the replacement of analytic heating/cooling fits by rates computed from photoionization codes. In the ZEUS-based 2.5D calculations of Higginbottom and Proga, previous analytic prescriptions (“Blondin equations”) were contrasted with CLOUDY-derived rates tabulated in $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$1 space. The hydrodynamic energy equation was solved with an explicit radiative source term,

$$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$2

so the shape of the thermal equilibrium curve directly controlled acceleration and stability (Higginbottom et al., 2016).

The resulting equilibrium structure is materially more complex than the classic single unstable segment between cold and hot stable branches. For the CLOUDY rates, the curve contains an intermediate stable zone at $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$3 K, and the upper stable branch begins at $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$4 K rather than $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$5 K. The unstable region is therefore narrower and relocated. In dynamical terms, less energy is deposited while gas crosses the unstable regime, acceleration is less efficient, and the presence of an intermediate stable zone inhibits rapid launch close to the disc surface. The outflow is then initiated at larger radii and develops a denser, slower structure (Higginbottom et al., 2016).

This sensitivity to microphysics generalizes beyond any one spectral state. Using XSTAR-coupled hydrodynamics, Dyda and collaborators showed that thermally driven winds depend strongly on the detailed spectral energy distribution rather than on a single Compton temperature. In their 1D spherical calculations, winds evolve along the radiative equilibrium curve until adiabatic cooling causes departure from radiative equilibrium; if heating is very rapid in a thermally unstable regime, the corresponding column density is low. They also found a two stage acceleration of the wind when there are two thermally unstable regions and the flux is relatively high. The efficiency of radiative energy transfer depends particularly on the relative flux of soft X-rays, implying that full photoionization calculations are required not only for synthetic spectra but for the flow dynamics themselves (Dyda et al., 2016).

A plausible implication is that “thermal-radiative” denotes not a single launch mechanism but a family of irradiation-regulated outflows in which the equilibrium curve, the irradiating SED, and optical-depth effects jointly determine whether the wind resembles a slow thermal expansion, a radiation-assisted equatorial wind, or a multi-stage accelerated flow.

3. Hydrodynamic and radiation-hydrodynamic structure in X-ray binaries

In purely thermal calculations with realistic heating and cooling, the flow can be massive yet slow. The CLOUDY-based ZEUS models found a wind that is much denser and slower than flows obtained with approximate analytical rates: the mass-loss rate is a factor of two higher and the characteristic velocities are a factor of three lower. In the extended domain, the mass-loss rate reaches $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$6, while the observable dense gas has characteristic speeds below $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$7 and the overall maximum speed is $$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$8. The flow is unsteady, turbulent in the inner regions, and shows a density step associated with the intermediate stable zone on the equilibrium curve (Higginbottom et al., 2016).

These low velocities are not generic once radiation forces are included self-consistently. In radiation-hydrodynamic simulations for H 1743-322, the radiative acceleration was written as

$$\Xi = \frac{P_{\rm rad}}{P_{\rm gas}} = \frac{\mathcal{F}}{c\,P_{\rm gas}}.$$9

where the force multiplier $T_{\rm IC}$0 includes electron scattering, bound-free opacity, and line driving. At $T_{\rm IC}$1, the multiplier is $T_{\rm IC}$2, so the effective radiative force can exceed gravity even at sub-Eddington luminosity. In this model, the predicted Fe XXV and Fe XXVI line velocities at high inclination match the observed $T_{\rm IC}$3 and $T_{\rm IC}$4, whereas thermal-only simulations are too slow and produce excessive high-inclination columns (Tomaru et al., 2019).

A comparable conclusion emerges in the neutron-star system GX 13+1. There, a radiation hydrodynamic calculation coupled to CLOUDY and then to the MONACO Monte Carlo transfer code reproduced the observed Fe XXV and Fe XXVI line profiles with a thermal-radiative wind alone. The wind is very strong because the system has a very large disc and is very luminous, and the line profiles are dominated by saturation and velocity structure rather than by column alone. The simulated Fe XXVI absorption peaks near $T_{\rm IC}$5 and Fe XXV near $T_{\rm IC}$6; Chandra third-order data rule out isotropic turbulence at the level of the radial velocity of $T_{\rm IC}$7, while the upper limit to additional turbulence is at the level of the azimuthal velocity of $T_{\rm IC}$8 (Tomaru et al., 2020).

These results make the distinction between thermal and thermal-radiative winds concrete. Pure heating can supply very large mass fluxes, but realistic radiative forces appear necessary when the observed absorber is both dense and moderately fast.

4. Observational diagnostics: absorption lines, velocity structure, and polarization

The principal empirical diagnostics are highly ionized Fe K absorption lines, their equivalent widths, and their velocity structure. In the optically thin limit of the CLOUDY-based thermal models, the simulated columns and ionization parameters are consistent with those observed in low-mass X-ray binaries, with hydrogen columns $T_{\rm IC}$9 and $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$0, and the equivalent widths of Fe K$R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$1 absorption indicate detectability at moderate-to-high inclination. The central difficulty is kinematic: the observable dense gas is much slower than the $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$2 blue shifts commonly inferred in X-ray binaries (Higginbottom et al., 2016).

Velocity structure is therefore the key discriminant among launch mechanisms. Monte Carlo transfer calculations based on radiation-hydrodynamic models of H 1743-322 showed that thermal-radiative winds produce a static or slightly inflowing Compton atmosphere at small radii, followed by acceleration and then an outflow plateau at a few hundred $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$3. Magnetic winds, by contrast, are faster at smaller radii and do not predict the same inner static zone. The existence of such static atmospheres in small disc systems was argued to rule out self-similar magnetic fields from the entire disc as the origin of the absorption features. The same work identified XRISM as the instrument capable of separating static and outflowing components through its higher spectral resolution (Tomaru et al., 2019).

Polarimetry adds an orthogonal diagnostic. For the black-hole binary 4U 1630-472, Monte Carlo calculations with MONACO showed that an optically thin(ish) thermal-radiative disc wind polarises scattered light in a direction orthogonal to that predicted from a standard optically thick disc, and reduces about $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$4 rather than enhancing the predicted polarisation of the total emission. At high inclination, the expected total polarisation with wind is $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$5, whereas IXPE measured $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$6 in the disc-dominated soft state. The wind therefore cannot explain the unexpectedly high observed polarisation; if the state-dependent $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$7 change is genuinely due to the presence or absence of wind, the total polarisation direction must be orthogonal to the disc plane rather than parallel as expected from optically thick material (Tomaru et al., 2023).

Taken together, line profiles, line saturation, and polarization imply that the thermal-radiative wind problem is observationally overconstrained: density, ionization, kinematics, and scattering geometry must all be reproduced simultaneously.

5. Disc evolution, state transitions, and feedback on accretion

Thermal-radiative winds are not only spectral features but sinks of mass and angular momentum. In the classical X-ray binary framework, the wind mass-loss rate can exceed the inner accretion rate by factors of $R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$8–$R_{\rm IC} = \frac{GM \mu m_p}{k T_{\rm IC}}.$9 in systems where $0.1\,R_{\rm IC}$0, and the cumulative mass loss is

$0.1\,R_{\rm IC}$1

Wind scattering also enhances outer-disc irradiation, raising the effective irradiation constant $0.1\,R_{\rm IC}$2 and helping to keep large discs hot. This explains the existence of persistently bright systems with large discs such as Cyg X-2, 1E 1740.7-2942, or GRS 1758-258, and produces plateau light curves in long-$0.1\,R_{\rm IC}$3 systems like GRO J1655-40. At the same time, wind mass loss alone is not a major driver for outburst dynamics up to luminosities $0.1\,R_{\rm IC}$4–$0.1\,R_{\rm IC}$5; magnetic winds were identified as more promising for the generically fast decays of black-hole X-ray binary outbursts (Dubus et al., 2019).

Time-dependent disc calculations sharpen this point. Using an upgraded version of FREDDI, Avakyan and collaborators evolved a non-stationary irradiated disc with a thermal wind launched only from the ionised part of the disc. The governing equation was

$0.1\,R_{\rm IC}$6

with $0.1\,R_{\rm IC}$7. In these simulations, neglecting the wind causes the viscosity parameter $0.1\,R_{\rm IC}$8 inferred from outburst decays to be overestimated by factors of $0.1\,R_{\rm IC}$9–$0.2\,R_{\rm IC}$0, and in extreme cases by as much as $0.2\,R_{\rm IC}$1. For the 2002 outburst of 4U 1543-47, the best-fit value changes from $0.2\,R_{\rm IC}$2 without wind to $0.2\,R_{\rm IC}$3 with wind, while the wind mass-loss rate is of order the accretion rate at the outburst peak. The wind shuts off when the hot disc shrinks inside $0.2\,R_{\rm IC}$4, about $0.2\,R_{\rm IC}$5 days after peak (Avakyan et al., 2023).

The possibility of wind-regulated state change was already implicit in the ZEUS/CLOUDY models, where $0.2\,R_{\rm IC}$6 was identified as large enough to destabilize the disc. This suggests that the most important consequence of thermal-radiative winds may lie less in producing the highest observed blue shifts than in re-partitioning mass and angular momentum across the disc on outburst timescales (Higginbottom et al., 2016).

6. Magnetic competition and extensions beyond sub-Eddington X-ray binaries

A persistent controversy concerns whether magnetic fields augment or suppress thermal-radiative outflows. Axisymmetric ideal-MHD simulations with Athena++ showed that adding a strong poloidal magnetic field to a thermally driven Compton-heated wind does not necessarily boost the outflow. In low plasma beta regions, the field lines reshape the streamlines into a geometry that is less conducive to gas-pressure acceleration; the thermal wind is then suppressed, with wind velocities and mass flux densities reduced by factors of $0.2\,R_{\rm IC}$7–$0.2\,R_{\rm IC}$8 in steady regions, and the kinetic luminosity also reduced. Magneto-centrifugal launching is present but weak near $0.2\,R_{\rm IC}$9, so successful magnetothermal models for fast, dense outflows must be launched well inside the Compton radius (Waters et al., 2018).

The same thermal-radiative logic extends to more luminous and more geometrically complex accretors. In ultraluminous X-ray sources, photoionization calculations for thick-disc, radiation-pressure-driven winds found that the winds are generally in thermally stable equilibrium, but that long-term variations in accretion rate and inclination can affect both appearance and stability. Harder ULX states are associated with higher wind velocity and ionization parameter, and the trends can explain the observed correlation between spectral residuals around $T_{\rm IC}$0 keV and spectral state (Pinto et al., 2019). A complementary outer-disc analysis showed that irradiation from the photosphere of an optically thick inner outflow can trigger additional thermally driven mass loss from the outer disc; for Eddington-scaled accretion rates $T_{\rm IC}$1, almost all neutron star and black hole ULXs in a simulated population should be able to drive powerful outflows from their outer discs. Since several observed ULXs remain persistently accreting, anisotropic irradiation was proposed as the natural resolution (Middleton et al., 2021).

In active galactic nuclei, thermal-radiative winds also appear in at least two distinct guises. On parsec and sub-parsec scales around low-luminosity AGN, slowly rotating hot flows irradiated by X-rays can drive thermally dominated winds with mass fluxes $T_{\rm IC}$2, powers $T_{\rm IC}$3, and wind-generation efficiencies $T_{\rm IC}$4 between $T_{\rm IC}$5 and $T_{\rm IC}$6 (Bu et al., 2018). Much closer to the black hole, two-dimensional simulations of a $T_{\rm IC}$7 K corona above a thin disc found supersonic outflows once the disc luminosity is sufficiently high; at $T_{\rm IC}$8, the maximum speed reaches $T_{\rm IC}$9, and the mass outflow rate measured at $$g_{\rm eff} = \frac{GM}{R^2}\left(1-\frac{L}{L_{\rm Edd}}\right),$$0 Schwarzschild radii obeys $$g_{\rm eff} = \frac{GM}{R^2}\left(1-\frac{L}{L_{\rm Edd}}\right),$$1 (Yang et al., 2018).

A broader historical analogue exists in massive-star winds. In late-type O dwarfs with the weak-wind phenomenon, a two-component model found that cool radiatively driven clumps survive inside a coronal ambient medium until conduction destroys them at $$g_{\rm eff} = \frac{GM}{R^2}\left(1-\frac{L}{L_{\rm Edd}}\right),$$2, after which the flow becomes a pure coronal wind with terminal velocity $$g_{\rm eff} = \frac{GM}{R^2}\left(1-\frac{L}{L_{\rm Edd}}\right),$$3. This is not an accretion-disc wind, but it shows that a radiative-to-thermal transition can also organize outflows in stellar atmospheres (Lucy, 2012).

Thermal-radiative winds therefore span a continuum of irradiation-driven outflows. In sub-Eddington X-ray binaries they are most tightly constrained and most fully modeled; in ULXs and AGN they become embedded in thicker geometries, stronger radiation fields, and more complicated screening. The central unresolved issue is not whether irradiation can drive winds, but under what microphysical and geometrical conditions thermal expansion alone suffices, when radiation forces become decisive, and when magnetic stresses merely supplement—or instead suppress—the resulting outflow.