On the effects of radiation on mass transfer in binary stars

TL;DR

The study analyzes how radiation pressure alters mass transfer through the L1 point in massive binaries by formulating a 1D nozzle model from 3D time-steady radiation–hydrodynamics under flux-limited diffusion and invoking the von Zeipel relation. It unveils two key MT regimes: for sub-Eddington donors, MT rates can be exponentially boosted as $Γ_{\rm Edd}$ approaches unity, and for donors with a super-Eddington subsurface layer, the photon-tiring constraint near L1 is relaxed, enabling MT rates near $10^{-2}\,M_\odot\,\mathrm{yr}^{-1}$ prior to Roche-lobe overflow. The authors derive analytic and algebraic MT-rate expressions for limiting cases and demonstrate numerical solutions with a realistic EOS that agree with traditional prescriptions within factors similar to inter-model scatter. They also develop a framework for super-Eddington MT boost and apply it to a 30$M_\odot$ donor in a BH binary, illustrating conditions under which such boosts could influence LBV-like eruptions and pre-overflow evolution. Overall, the work highlights two radiation-driven channels that can substantially modify binary evolution and motivates multidimensional simulations to validate these regimes.

Abstract

Mass transfer (MT) in binary systems is a common evolutionary process that can significantly affect the structure, evolution, and final fate of both stars. In modeling MT hydrodynamics, it is usually assumed that the critical point of the flow, where the velocity exceeds the local sound speed, coincides with the inner Lagrange point (L1). However, in massive donors where radiative pressure dominates over gas pressure and the Eddington factor $Γ_\text{Edd}$ can approach or exceed unity, radiation-gas coupling can shift the critical point away from L1, altering the MT rate ($\dot{M}_\text{d}$). We investigate the effects of radiation on MT using time-steady radiative hydrodynamic equations and the von Zeipel theorem. We derive analytical expressions that closely approximate $\dot{M}_\text{d}$, algebraic solutions for simplified cases, and numerical results using a realistic equation of state. Two main differences emerge relative to traditional prescriptions for $\dot{M}_\text{d}$. First, for Roche-lobe-underfilling donors with $Γ_\text{Edd} \lesssim 1$, radiative momentum exchange leads to an exponential increase of $\dot{M}_\text{d}$ as a function of $1-Γ_\text{Edd}$. We provide a simple modification of existing prescriptions that captures this effect. Second, the photon tiring limit for super-Eddington outflows is much less restrictive near L1 than in spherical stars. We suggest that donors with super-Eddington, convectively inefficient subsurface layers can drive MT with $-\dot{M}_\text{d} \gtrsim 10^{-2}\,\text{M}_\odot\,\text{yr}^{-1}$ even before Roche-lobe overflow. We characterize the conditions for this new mode of super-Eddington-boosted MT and discuss its implications for binary evolution, including potential links to nonterminal outbursts of Luminous Blue Variables.

Figures (8)

• Figure 1: Cartoon illustrating the idea of the super-Eddington mass-transfer boost.
• Figure 2: Comparison of density $\rho$, temperature $T$, and velocity $v$ profiles for a $30 \rm{M}_\odot$ low-metallicity star undergoing thermal time-scale MT cehula2023, small-$v$ case (Section \ref{['sec:small_v']}), and adiabatic case (Section \ref{['sec:adiabatic']}). We also show the underlying MESA hydrostatic density and temperature profiles and the value of convective velocity $v_{\rm conv}$. The profiles are shown as functions of radius $r$ going from the inner boundary at $R_0$ (that corresponds to $x_0$), to the outer boundary at $R_{\rm L}$ (the L1 point at $x_1$). The critical velocity $v_{\rm crit}$, indicated by dotted lines, is reached at the critical point, L1. With the top $x$ axis we indicate the distance to the critical point in units of pressure scale heights $\Delta N_{H_P}$.
• Figure 3: Comparison of the dependencies of the donor's MT rate $-\dot{M}_{\rm d}$ on $R_0$ for the same cases and donor star as in Fig. \ref{['fig:prof-comp-m7']}. We also show the analytical estimate $\dot{M}_{\rm an,thick}$ (equation \ref{['eq:dotM_an,thick']}). The outer fixed boundary at $R_L$ is indicated as well as the distance between $R_0$ and $R_{\rm{L}}$ in units of pressure scale heights $\Delta N_{H_P}$.
• Figure 4: Comparison of different MT prescriptions throughout the evolution of originally $30 \rm{M}_\odot$ low-metallicity donor undergoing thermal time-scale MT (Section \ref{['sec:30Msun']}, marchant2021). First panel: the small-$v$ case (Section \ref{['sec:small_v']}) for three different values of the distances between the inner and outer boundary in units of pressure scale heights $\Delta N_{H_P}$ vs. the analytical estimate $\dot{M}_{\rm an,thick}$ (equation \ref{['eq:dotM_an,thick']}). Second panel: the MT prescription introduced by kolb1990, $\dot{M}_{\rm KR}$ vs. the analytical estimate $\dot{M}_{\rm an,thick}$. Third panel: the MT prescription introduced by marchant2021, $\dot{M}_{\rm M}$, vs. the analytical estimate $\dot{M}_{\rm an,thick,tot}$ (equation \ref{['eq:dotM_an,thick,tot']}). Fourth panel: Comparison of the two analytical prescriptions $\dot{M}_{\rm an,thick,tot}$ vs. $\dot{M}_{\rm an,thick}$, throughout the evolution.
• Figure 5: Comparison of our analytical MT prescription $\dot{M}_{\rm an,thin}$ and $\dot{M}_{\rm an,thick}$ with the optically thin prescription introduced by jackson2017, $\dot{M}_{\rm J},$ and the optically thick prescription introduced by kolb1990, $\dot{M}_{\rm KR}$. We also show the Eddington factors $\Gamma_{\rm tot} = L/L_\text{Edd}$ and $\Gamma_{\rm Edd}$ (equation \ref{['eq:Gamma_Edd']}). The case shown is for an isolated originally $40 \rm{M}_\odot$ low-metallicity star in the supergiant stage.