Truncated Disk Simulations
Hot coronae and truncated thin disks in simulations of accreting stellar-mass black holes
Executive Summary
This project studies how a cold, truncated thin disk and a hot X-ray-emitting corona can emerge naturally in simulations of accreting stellar-mass black holes. We used two-dimensional hydrodynamical simulations with radiative cooling to model accretion flows in X-ray binaries, varying the mass accretion rate across the range relevant for hard-state systems. The simulations show that as the accretion rate increases, the corona contracts and the inner edge of the thin disk moves closer to the black hole.
Black hole X-ray binaries cycle between hard and soft spectral states. In the hard state, observations are commonly interpreted with a geometry in which a hot corona coexists with a colder thin disk whose inner edge is truncated away from the event horizon. The physics that forms the corona, sets the truncation radius, and drives the hard-to-soft transition is still debated.
This work addresses that problem with numerical simulations designed to follow the collapse of a hot accretion flow when radiative cooling becomes dynamically important.
Scientific Motivation
In X-ray binaries, the hard state is associated with a hard power-law X-ray spectrum and is usually modeled with a hot corona or radiatively inefficient accretion flow inside a truncated thin disk. As the source brightens, the thin disk is expected to move inward and the system transitions toward the soft state.
The central questions are:
- How does a hot corona form and survive around a stellar-mass black hole?
- What controls the inner radius of the thin disk?
- Does the disk truncation radius decrease as the accretion rate increases?
Numerical Experiment
We performed two-dimensional hydrodynamical simulations of accretion onto a $10 M_\odot$ black hole using the PLUTO code. This was a team effort including Ivan Almeida, Artur Vemado, Pedro Motta, and Javier Garcia. The simulations approximate Schwarzschild gravity with a pseudo-Newtonian potential and include radiative losses from bremsstrahlung, synchrotron emission, synchrotron self-Compton cooling, and optically thick cooling in dense regions.
The initial condition is a hot torus. After a burn-in phase, radiative cooling is enabled and the flow is allowed to evolve. We varied the accretion rate over $0.02 \leq \dot{M}/\dot{M}_{\rm Edd} \leq 0.35$, covering the regime where hard-state X-ray binaries are expected to transition between radiatively inefficient and thin-disk-dominated accretion.
Main Results
For $\dot{M}/\dot{M}_{\rm Edd} \geq 0.06$, the simulations form a cold thin disk embedded inside a hot corona. The disk is dense and geometrically thin, while the corona remains hot, with typical electron temperatures of $10^{9}$-$10^{10}$ K.
At the lowest simulated accretion rate, $\dot{M}/\dot{M}_{\rm Edd} = 0.02$, the thin disk disappears and the flow remains hot and geometrically thick. This constrains the critical accretion rate for the disk to disappear to roughly $0.02 < \dot{M}_{\rm crit}/\dot{M}_{\rm Edd} \lesssim 0.06$.
The trends are consistent with the standard picture of state transitions: increasing accretion rate leads to stronger cooling, a smaller corona, and a thin disk whose inner edge approaches the black hole.
Observational Relevance
The simulations provide a physical mechanism for the hard-state geometry inferred in X-ray binaries. They predict that the disk inner radius should anticorrelate with accretion rate and luminosity, matching the qualitative behavior expected from observations of systems such as GX 339-4.
The work also suggests that a compact corona can persist even at luminosities typical of softer states, potentially contributing to the hard X-ray tail observed in some systems.