Light Curve Models of Convective Common Envelopes

TL;DR

This work addresses how convection and radiation modify the light curves of common-envelope (CE) events, focusing on convective CEs where orbital energy is carried to the surface and potentially radiated rather than used to unbind the envelope ($t_{\rm conv}$ vs $t_{\rm inspiral}$; $E_{\rm bind}$). Using $M_\star=1-6\,M_\odot$ stellar models from MESA and a grid of companion mass ratios, the authors compute the inspiral energy budget and compare the drag luminosity $L_{\rm drag}$ to the maximum convective luminosity $L_{\rm max,conv}$ to distinguish self-regulated versus ejection phases. They adopt a two-phase CE light-curve model: a self-regulated phase with drag-luminosity–driven brightening and an ejection phase with a recombination-powered plateau, described by the two-zone envelope and a recombination front at $T_{\rm ion}=5000$ K, yielding a plateau luminosity $L_{\rm bol}=8\pi\sigma_{\rm SB} T_{\rm ion}^4 v_{\rm exp}^2 \left[t_i t \left(1+\frac{t_i^2}{3 t_a^2}\right) - \frac{t^4}{3 t_a^2}\right]$. By applying Rubin/LSST filter responses, they forecast detectability out to roughly $8$ Mpc at a rate of about $0.3$ events per day, providing a concrete observational test of CE physics and informing search strategies for convective CE transients. The study demonstrates that convection can prolong CE visibility and imprint distinctive signatures on light curves, enabling empirical discrimination of CE energy transport mechanisms with upcoming Rubin observations.

Abstract

Common envelopes are thought to be the main method for producing tight binaries in the universe as the orbital period shrinks by several orders of magnitude during this phase. Despite their importance for various evolutionary channels, direct detections are rare, and thus observational constraints on common envelope physics are often inferred from post-CE populations. Population constraints suggest that the CE phase must be highly inefficient at using orbital energy to drive envelope ejection for low-mass systems and highly efficient for high-mass systems. Such a dichotomy has been explained by an interplay between convection, radiation and orbital decay. If convective transport to the surface occurs faster than the orbit decays, the CE self-regulates and radiatively cools. Once the orbit shrinks such that convective transport is slow compared to orbital decay, a burst occurs as the release of orbital energy can be far in excess of that required to unbind the envelope. With the anticipation of first light for the Rubin Observatory, we calculate light curve models for convective common envelopes and provide the time evolution of apparent magnitudes for the Rubin filters. Convection imparts a distinct signature in the light curves and lengthens the timescales during which they are observable. Given Rubin limiting magnitudes, convective CEs should be detectable out to distances of ~8 Mpc at a rate of ~0.3 per day and provide an intriguing observational test of common envelope physics.

Figures (6)

• Figure 1: Above are the inspiral and convective timescales for primary stars of 1 and 6 $\textup{M}_\odot$. The convective timescales define the time, on the y-axis, required for convection in the primary to carry energy from point $r$, on the x-axis, out to the surface ($R_\star$). These are shown as black lines for the 1 (thin) and 6 (thick) $\textup{M}_\odot$ primaries. The inspiral timescales define the time required for the companion to inspiral from its current radius to the center of the primary star. The five companions of the 1 $\textup{M}_\odot$ primary (0.02, 0.05, 0.08, 0.1, and 0.2 $\textup{M}_\odot$) and the five companion masses of the 6 $\textup{M}_\odot$ primary (0.12, 0.3, 0.48, 0.6 and 0.89 $\textup{M}_\odot$) are shown above using differing lines styles and colors. The location where each companion shreds for each companion is marked with an "$\times$" (1 $\textup{M}_\odot$ primary) or a "$\blacktriangle$" (6 $\textup{M}_\odot$ primary).
• Figure 2: The maximum amount of luminosity convection can carry out of the primary stars are shown via thin (1 $\textup{M}_\odot$) and thick (6 $\textup{M}_\odot$) solid black lines labeled $L_{\rm max, conv}$. The drag luminosities produced during each CE are shown with the varying dashed and coloured lines consistent with Figure \ref{['fig:timescales']}. The radial limits where the companions are destroyed via tidal disruption are marked by an "$\times$" (1 $\textup{M}_\odot$ primary) or a "$\blacktriangle$" (6 $\textup{M}_\odot$ primary).
• Figure 3: Illustrated above are the inspiral and binding energies for two primary masses (1 and 6 $\textup{M}_\odot$), with position along the radius of the primary on the x-axis in centimeters and energy in ergs on the y-axis. The binding energies for both are shown in thin (1 $\textup{M}_\odot$) and thick (6 $\textup{M}_\odot$) solid black lines, and represent the minimum energy required to unbind that portion of the primary's envelope at every point along its radius as a function of position. The companion's inspiral energies, shown in the varying colors and line patterns of Figures \ref{['fig:timescales']} and \ref{['fig:draglums']}, all intersect with the binding energy limits before reaching their shredding radii, illustrated via an "$\times$" (1 $\textup{M}_\odot$) or a "$\blacktriangle$" (6 $\textup{M}_\odot$). Therefore, all the companions shown unbind the primary's envelope and are expected to form close binary pairs.
• Figure 4: Time evolution of the predicted light curves for convective common envelopes are shown from top to bottom, then left to right, for primary masses of 1, 2, 3, 4, 5, and 6 ${\rm M}_\odot$. For each primary, five CE light curves for different mass ratios are displayed with various colors and line styles. The 1 $\textup{M}_\odot$ primary plot includes grey boxes representing times where apparent magnitudes were calculated (see Section \ref{['sec:obs approx']} for more detail). For each CE, we choose six of these times by uniformly sampling the corresponding light curve between its maximum value and 1.1 times its minimum value in log-space. The seventh point is taken after the envelope is ejected and represents an upper limit on the magnitude if the natal white dwarf were visible one year post-CE expulsion (depicted by upper limit triangle symbols above).
• Figure 5: Apparent AB magnitudes for the 1 $\textup{M}_\odot$ primary with the smallest mass ratio system (${\rm q}=0.02$; top left) and the largest mass ratio system (${\rm q}=0.2$; top right) and the 6 $\textup{M}_\odot$ primary with the smallest mass ratio system (${\rm q}=0.02$; bottom left) and the largest mass ratio system (${\rm q}=0.15$; bottom right). Each plot shows three of the six Rubin filters, namely, u, r, and y. The semi-transparent, horizontal lines on each plot display the limiting magnitudes for the instrument, where the colors are consistent with each filter. Magnitudes are shown for two distances: 100 kpc (triangles) and 8000 kpc (circles). The points illustrated are those sampled from various epochs in the light curves as described in Section \ref{['sec:obs approx']} and shown in Fig. \ref{['fig:lightcurves']}. The last evolutionary point represents an upper limit assuming the natal white dwarf is visible.