Multigroup Radiation Diffusion with Compton Scattering on a Moving Mesh: Implementation in RICH and Application to Tidal Disruption Events

The gist: This paper extends a multigroup flux-limited diffusion module in the moving-mesh RHD code rich to include Compton scattering with an exact thermal Compton kernel, applying it to a three-dimensional simulation of a tidal disruption event (TDE) to identify where inverse Compton scattering dominates the energy exchange and its impact on dynamics.

Introduction and Motivation

Compton scattering exchanges energy between radiation and hot gas and changes the spectrum in high-energy astrophysical systems such as tidal disruption events (TDEs) Because it couples all photon energies and can act faster than the hydrodynamic time step, many radiation-hydrodynamics (RHD) simulations omit its spectral redistribution or treat its energy exchange in the gray approximation The thermal Compton kernel couples all photon energies and depends on the gas temperature Many RHD simulations instead use a gray energy-exchange term with a single radiation temperature or photon number Full-kernel treatments, needed when individual scatterings produce large energy shifts, have been developed for deterministic transport and for Monte Carlo transport Implicit methods avoid this restriction by linearizing the temperature dependence of the coupling within the time step

Semi-Implicit Treatment of Compton Scattering

The authors extend the derivation of implicit equations (Fleck & Cummings 1971) to include the temperature dependence of the Compton scattering cross section They define a heat capacity ratio cv ≡ ∂um/∂Ur = cv / (4aRT3/4) The time-discretized gas energy equation is then solved by linearizing the Compton integrand C[σs; I, I] using a generalized Fleck factor f This leads to the semi-implicit transport equation (Eq. 2.17), where the terms proportional to U n r in Eq. (2.17) form the emission source

Multigroup Diffusion Equation

The monochromatic equations are reduced to the flux-limited diffusion (FLD) approximation, which is extended here to include Compton scattering and bulk material motion The evolution equation for the total gas energy density Em accounts for both radiative energy and momentum exchange The resulting equation for the group radiation energy density Eg is given by Eq. (4.4), which includes terms describing diffusion, compression, and Doppler effects

Compton Scattering Coefficients

The group-averaged Compton scattering cross section is defined as σs(g → g′; ρ, T) = νg / Bg Z g dν Bν / ν Z g' dν' × σs(ν → ν′; ρ, T) (5.2) The macroscopic scattering coefficients are obtained by multiplying the microscopic cross sections by the local electron number density Detailed balance is enforced pairwise at the local gas temperature to correct for approximations in the group operator

Equilibration Verification

The scheme was tested in a spatially uniform, one-cell configuration where the evolution is governed entirely by Compton scattering and absorption–emission coupling The rich solutions agree with independent ODE solutions and published results for both equilibrium temperature and time-dependent evolution The scheme remains stable for time steps that do not resolve the Compton equilibration timescale in the configurations considered

Tidal Disruption Event Simulation

In a three-dimensional simulation of the disruption of a 0.5 M⊙ star by a 106 M⊙ black hole, inverse Compton scattering dominates the coupling between the gas and the radiation near the nozzle shock Outside the X-ray thermalization radii, its instantaneous X-ray production rate during the flash is comparable to or larger than the escaping X-ray luminosity This suggests that Compton scattering may contribute substantially to the X-ray emission from TDEs

Conclusion

The authors have extended the multigroup FLD module of the moving-mesh RHD code rich to include Compton scattering with the exact thermal Compton kernel, deriving a semi-implicit scheme for the TRT equation In the three-dimensional TDE simulation, Compton scattering is locally important near the black hole and in regions where it dominates energy exchange The gas near the nozzle shock is much hotter than the Compton temperature, so Compton scattering cools it and shifts the radiation to higher photon energies The net Compton X-ray power outside the X-ray thermalization radii is comparable to or larger than the X-ray luminosity during the flash. The scheme remains stable for time steps that do not resolve the Compton equilibration timescale in the configurations considered. The group Compton operator conserves the total photon number by construction and is corrected pairwise to satisfy detailed balance In equilibration problems, the rich solutions agree with independent ODE solutions and published results without absorption and emission the radiation relaxes to the Bose–Einstein spectrum that conserves the initial energy and photon number. The scheme remains stable for time steps that do not resolve the Compton equilibration timescale in the configurations considered at reduced accuracy in the temperature evolution.

How it works

The authors extend the multigroup FLD module of rich to include Compton scattering with an exact thermal Compton kernel, using group coefficients computed with mace They derive a semi-implicit scheme for the TRT equation in which the temperature dependence of the Compton kernel enters a generalized Fleck factor The time-discretized gas energy equation is then solved by linearizing the Compton integrand C[σs; I, I] using a generalized Fleck factor f

Numerical Scheme Details

The multigroup equations form a linear system M⃗ E⃗ n+1 = ⃗b (6.1) The matrix M⃗ of Eq. (6.1) has a block-sparse structure The rich code solves Eq. (6.1) using an MPI-parallel, Jacobi-preconditioned BiCGSTAB method The addition of Compton scattering modifies the matrix structure and coefficients, but does not change the implementation in rich

Stability Safeguards

The temperature dependence of the Compton operator can produce a negative or weak effective coupling in the generalized Fleck factor With the Compton coupling coefficient κC of Eq. (4.8), they apply a safeguard whenever f 0.1 κP When this condition is satisfied, they suppress induced Compton scattering for that cell and time step by setting the group occupation number ng of Eq. (4.6) to zero when constructing the Compton matrices They additionally cap the occupation number entering the induced-scattering factors at ng = 100

Application to TDEs

The simulation follows the disruption of a star of mass M⋆ = 0.5 M⊙ by a black hole of mass MBH = 106 M⊙ with penetration factor β = rt/rp = 1 The X-ray luminosity (soft and hard), L ph X, rises rapidly and reaches ≈ 10 42 erg s−1 at 0.

1. Improved spectral redistribution modeling for astrophysical systems allows AI to accurately predict X-ray emission from tidal disruption events by accounting for Compton scattering, which adds X-ray energy much faster than thermal emission.

2. AI systems can now simulate the dynamics of TDEs with higher fidelity by incorporating a semi-implicit scheme that conserves photon number and satisfies detailed balance during radiation transport.

3. The improved numerical scheme enables AI to handle time steps that do not resolve the Compton equilibration timescale, making simulations more robust even when explicit treatments are unstable for short timescales.

4. AI can perform diagnostics on astrophysical flows by calculating local rates like Erad = X g' Eg' , Cg = c X g' Sg'gEg' to determine where Compton scattering dominates coupling, as shown in Figure 10.

5. The system can now quantify the Compton coupling fraction as fC, which is defined as QC / (QC + Qabs), to distinguish between energy exchange mechanisms and identify regions where Compton scattering dominates the energy exchange between the radiation and the gas.

6. AI can predict spectral evolution by using "group-averaged Compton scattering cross section sigma s(g -> g'; ρ, T) = νg Bg / Z g dν Bν / ν Z g' dν' × σ s(ν -> ν'; ρ, T) ν' - ν γg'".

Compton scattering exchanges energy between radiation and hot gas and changes the spectrum in high-energy astrophysical systems such as tidal disruption events (TDEs). Because it couples all photon energies and can act faster than the hydrodynamic time step, many radiation-hydrodynamics (RHD) simulations omit its spectral redistribution or treat its energy exchange in the gray approximation. We extend the multigroup flux-limited diffusion module of the moving-mesh RHD code RICH to include Compton scattering with the exact thermal Compton kernel. In our semi-implicit scheme for the thermal radiative transfer equation, the temperature dependence of the kernel enters a generalized Fleck factor, and the group Compton operator conserves photon number and satisfies detailed balance. In equilibration tests, the scheme agrees with independent solutions, relaxes without absorption and emission to a Bose-Einstein spectrum, and remains stable for time steps that do not resolve the Compton equilibration timescale. We apply it to a three-dimensional simulation of the disruption of a 0.5,M star by a 10 6,M black hole. We find that during the X-ray flash, inverse Compton scattering dominates the coupling between the gas and the radiation near the nozzle shock, where it adds X-ray energy much faster than thermal emission and may affect the dynamics. Outside the X-ray thermalization radii, its instantaneous X-ray production rate during the flash is comparable to or larger than the escaping X-ray luminosity, so it may contribute substantially to the X-ray emission from TDEs.