Envelope Inflation and outflow Driven by Energy Deposition in Massive Stars

TL;DR

This work addresses how impulsive energy deposition within the envelopes of evolved massive stars drives outflows, using a 1D hydrodynamic framework with a $70\,M_\u0012$ star modeled in MESA. By placing energy near the radius where envelope binding energy equals the gravitational energy of a hypothetical companion ($R_{\rm crit} \approx 23.21\,R_\u0012$) and depositing it over a narrow region and sustained period, the authors compare hydrostatic and hydrodynamic responses, exploring different $E_{\rm dep}$ and heating widths. They find a threshold-like behavior: hydrostatic models inflate the envelope without ejecting mass, while dynamic models generate outflows whose mass loss, energetics, and duration depend on both $E_{\rm dep}$ and the spatial extent of heating; broader heating regions yield more massive, sustained outflows, whereas higher $E_{\rm dep}$ produce more impulsive ejections with larger energy fractions carried away. The results illuminate the generic hydrodynamic envelope response to impulsive energy input in massive stars and lay groundwork for connecting such processes to eruptive phenomena, while acknowledging that these idealized simulations do not aim to reproduce LBV or pre-SN outbursts in detail. Future work will extend to a broader set of stellar masses and evolutionary stages to map out the thresholds and potential observational signatures of such envelope-driven outflows.

Abstract

Evolved massive stars are known to undergo outflow with high mass ejections, resulting in the loss of a substantial portion of their envelopes. One proposed mechanism driving these events is the release or deposition of energy within the stellar envelope. We use a one-dimensional hydrodynamical code to investigate the resulting outflow and stellar response to energy deposition at specific regions inside a $\rm 70 \, M_{\odot}$ star. We compare hydrostatic and hydrodynamic models and test for different energies and widths of the depositing region. We find that due to the deposited energy, the envelope expands significantly, and under certain conditions, such as assuming a uniform electron scattering opacity, this energy input becomes sufficient to unbind material from the outer envelope. This, in turn, leads to the formation of an outflow. We find that higher deposited energy triggers a strong outflow and results in a somewhat hotter and less expanded envelope due to the rapid loss of energy through expelled material. This driving mechanism leads to sudden envelope expansion and the formation of strong outflows in our models, highlighting the generic hydrodynamic response of massive star envelopes to impulsive energy input.

Figures (4)

• Figure 1: The binding energy and gravitational energy of our model are shown as functions of the stellar radius ($R$). In this setup, the primary star has a ZAMS mass of 70 $\rm M_{\odot}$, while the companion is treated as a point mass. The point of intersection, where both energies become equal, occurs at a critical radius of $R_{\rm crit} =$ 23.21 $\rm R_{\odot}$, corresponding to an energy of $4.22 \times 10^{48}$ erg.
• Figure 2: Schematic diagram of a $70\,\rm M_{\odot}$ star. (a) Stable pre-deposition stage; the stellar parameters are listed in Table \ref{['T1']}. (b) Hydrostatic response (Case 1): the envelope expands after energy deposition, with the deposition shell indicated. (c) Hydrodynamic response: outflows are launched near radius $R_{\rm out} \simeq \rm 58.1\,\rm R_{\odot}$ and propagate outward to $\sim 10^{4}\,\rm R_{\odot}$.
• Figure 3: Panel (a) shows the hydrostatic, while panel (b) shows hydrodynamic response of the stellar envelope to energy deposition.
• Figure 4: Panel (a): Mass-loss rate profiles, calculated using $\dot{M}(r) = 4\pi r^2 \rho (r) v (r)$, at $t = 0$, 0.4, 0.8, and 1.2 years for Case 2A, and Case 2B. Here the solid lines correspond to Case 2A (section \ref{['3.2']}), for the width of the heating region of 0.5 $\rm R_{\odot}$, while the dashed region corresponds to Case 2B, where the width of the heating 0.8 $\rm R_{\odot}$ (section \ref{['3.3']}). Panel (b): Mass-loss rate profiles, calculated using $\dot{M}(r) = 4\pi r^2 \rho (r) v (r)$, at $t = 0$, 0.4, 0.8, and 1.2 years for Case 2C for heating region 0.5 $\rm R_{\odot}$ (section \ref{['3.4']}).