Accretion with two-phase gas supply and its application in black hole X-ray binaries

TL;DR

Black hole X-ray binaries exhibit hard, soft, and intermediate spectral states whose inner-flow geometry remains debated. The authors introduce a generalized two-phase accretion model in which cold gas feeds a disc and hot gas feeds a corona, and they unify corona condensation and disc evaporation within a semi-analytical framework complemented by Monte Carlo spectral synthesis. The key finding is that the inner accretion geometry and emergent spectrum depend on the total accretion rate $\dot{m}$ and the cold/hot gas fraction, featuring a critical corona-accretion limit $\dot{m}_{\rm cor,ini,max}$ that governs state transitions and a hardness–intensity diagram that captures the diversity of spectra at intermediate $\dot{m}$. The model successfully reproduces the Cygnus X-1 hardness–intensity correlation for $\alpha$ in $[0.25,0.35]$, while highlighting that luminous hard states in LMXBs may require additional coronal heating mechanisms. Overall, the work provides a unified physical framework linking gas supply composition to BHXRB spectral states and offers testable predictions for future observations.

Abstract

Accretion in black hole X-ray binaries is commonly believed to be supplied by the Roche lobe overflow or the stellar wind. The former is thought to form a geometrically thin disc while the diffuse wind could form a geometrically thick hot accretion flow. In this paper, we instead consider a more generalised case, i.e., accretion with both cold and hot gas supplies, which feed a disc and a corona respectively. We investigate the interaction of disc and corona by analysing the energy coupling and matter exchange, i.e. corona condensation/disc evaporation, with a semi-analytical method. It is found that the accretion geometry in the radial direction and the resultant emission spectrum depend strongly on both the total gas supply rate and the ratio of cold and hot gases. For gas supply rates of a few percent of the Eddington value, diverse geometries and spectral shapes are possible, depending on the fraction of cold gas supply. This provides an interpretation for the various spectra observed in intermediate states. However, at higher accretion rates, regardless of the form of the feeding gas, the inner accretion flow is always disc-dominated, implying an inevitable transition to the soft state, while at very low gas supply rates, hard state spectrum dominated by the hot flow is expected. We also present the predicted hardness-intensity correlation of Cygnus X-1, and constrain the value of the viscosity parameter of the accretion flow to the range of 0.25--0.35 by comparing our results with MAXI observations.

Figures (6)

• Figure 1: The highest possible values of initial accretion rate in the corona, $\dot{m}_{\rm cor,ini,max}$, with $\dot{m}$ ranging from $0.01$ to $0.05$.
• Figure 2: The predicted hardness-intensity diagram with hardness defined as the ratio of photon counts between 4-10 keV and 2-4 keV bands and intensity (in arbitrary unit) the sum of the two bands. Different symbols correspond to different total accretion rate, $\dot{m}$, and different points with the same symbol have different initial corona accretion rate, $\dot{m}_{\rm cor,ini}$. The solid line marks an 'upper track' where $\dot{m}_{\rm cor,ini}$ always takes the highest possible value (see Fig. \ref{['fig:mc_max']}). The dashed line instead marks a 'lower track' where $\dot{m}_{\rm cor,ini}$ takes the lowest value allowed by evaporation beyond $R_{\rm out} = 500 R_{\rm S}$, which can be as high as $\sim 0.01$meyer2000bliu2002liu2022.
• Figure 3: Panel (a): the accretion rates in the corona ($\dot{m}_{\rm cor}$) and the disc ($\dot{m}_{\rm disc}$), as functions of radius. Panel (b): radial distributions of the electron temperature in the corona, $T_{\rm e}$. Panel (c): radial distributions of the advection fraction, $f$. Panel (d): the emergent spectra calculated from Monte Carlo simulations. In all panels different lines correspond to different total accretion rates, $\dot{m}$. Initial accretion rate in the disc at $R_{\rm out}$ is fixed at $\dot{m}_{\rm disc,ini} = 0.001$.
• Figure 4: Panel (a): the accretion rates in the corona ($\dot{m}_{\rm cor}$) and the disc ($\dot{m}_{\rm disc}$), as functions of radius. Panel (b): radial distributions of the electron temperature in the corona, $T_{\rm e}$. Panel (c): radial distributions of the advection fraction, $f$. Panel (d): the emergent spectra calculated from Monte Carlo simulations. In all panels different lines correspond to different initial disc accretion rates at $R_{\rm out}$, $\dot{m}_{\rm disc,ini}$. The total accretion rate is fixed at $\dot{m} = 0.01$.
• Figure 5: Panel (a): the accretion rates in the corona ($\dot{m}_{\rm cor}$) and the disc ($\dot{m}_{\rm disc}$), as functions of radius. Panel (b): the emergent spectra calculated from Monte Carlo simulations. In both panels, different lines correspond to different outermost radii of the accretion flow, $R_{\rm out}$, where our calculations start. The line with $R_{\rm out} = 500 R_{\rm S}$ is calculated with $\dot{m} = 0.03$ and $\dot{m}_{\rm disc,ini} = 0.001$, and its disc accretion rates at $r = 300$ and $r = 100$ are used respectively as initial disc accretion rates ($\dot{m}_{\rm disc,ini}$) for the results with $R_{\rm out} = 300 R_{\rm S}$ and $R_{\rm out} = 100 R_{\rm S}$.