Mass Ejection Driven by Sudden Energy Deposition in Stellar Envelopes

Abstract

A number of stellar astrophysical phenomena, such as tidal novae and planetary engulfment, involve sudden injection of sub-binding energy in a thin layer within the star, leading to mass ejection of the stellar envelope. We use a 1D hydrodynamical model to survey the stellar response and mass loss for various amounts ($E_{\mathrm{dep}}$) and locations of the energy deposition. We find that the total mass ejection has a nontrivial dependence on $E_{\mathrm{dep}}$ due to the varying strengths of mass ejection events, which are associated with density/pressure waves breaking out from the stellar surface. The rapid occurrence of multiple breakouts may present a unique observational signature for sudden envelope heating events in stars.

Figures (6)

• Figure 1: Ejected mass as a function of the dimensionless energy deposition, $\epsilon=E_\mathrm{dep} R_\ast / (GM_\ast^2)$ for the deposition radius $\tilde{r}_\mathrm{dep}=0.7$. The solid line with circular points represents the total ejected mass, while the dashed line with triangular points depicts only the mass ejected from the first breakout (measured at $t=2.5t_\mathrm{dyn}$). The separation between the two lines indicates the presence of multiple mass breakout events. Our fiducial resolution has $N_\mathrm{cells}=3000$ (maroon). The dots of different color depicts results at different resolutions. Also included is a dotted line of spectral slope $3.2$, representing the scaling of the mass loss in the first breakout with $\epsilon$.
• Figure 2: Evolution of the radii of the outermost mass shells as a function of $t$ for energy injection $\epsilon=0.005, 0.01, 0.032, 0.05$ (left to right, top to bottom), all with $\tilde{r}_\mathrm{dep}=0.7$. The evolution is shown up to $t=20 t_\mathrm{dyn}$ to concentrate on the behavior of the second breakout, even though all simulations were run until at least $t=45 t_\mathrm{dyn}$. All cells with external mass $\Delta M \leq 10^{-2} M_\ast$ are shown, but the cells at half logarithmic steps in $\Delta M$ are represented with thicker lines for ease of reference. In each plot, the thick blue dash-dotted line represents the transition from bound to unbound material, such that all mass external to the cell is considered ejected.
• Figure 3: Same as Figure \ref{['radiusev']} for $\epsilon=3.2\times10^{-2}$ and $\tilde{r}_\mathrm{dep}=0.8$. In this case, waves close to the unbound layer prevent a quasi-steady state from forming at $t \lesssim 45 t_\mathrm{dyn}$, and an accurate determination of the ejected mass requires long-term integration.
• Figure 4: Profiles of radius, radial velocity, density, and specific internal energy (top to bottom) as a function of the external mass at time steps $t=0.2, 2.2, 3.6, 8.0, 45.0 t_\mathrm{dyn}$ (yellow, orange, red, purple, black) for our fiducial run with $\epsilon=10^{-2}$ and $\tilde{r}_\mathrm{dep}=0.7$. The specific time steps are chosen to highlight the key stages in the time evolution of the system. In order, they are: (i) the initial generation of the ingoing and outgoing density waves; (ii) the rebound of the initially ingoing wave after the initially outgoing wave has ejected material; (iii) the generation of the shock of the second breakout as material that failed to eject during the first breakout crashes back down onto the stellar surface; (iv) the escape of the second breakout and beginning of pulsations in the remnant star; (v) the weakening of remnant oscillations in the underdense region. Bound material is represented by solid lines, while unbound material is represented by dotted lines.
• Figure 5: Ejected mass as a function of $\epsilon$ for $\tilde{r}_\mathrm{dep}=0.6, 0.7, 0.8$ (bright to dark in increasing $\tilde{r}_\mathrm{dep}$). As in Figure \ref{['massej']}, the total mass ejected (solid line, circular points) is distinguished from the mass ejected by the first breakout alone (dashed line, triangular points), and the first breakout is described by a power law of spectral slope 3.2.