--- title: "Where common-envelope energy goes" description: "Read Lau 2025 v2 through Figs 6–8 and Appendices A/B, following radiation, unbound mass, energy drift and resolution limits." canonical_url: "https://sandboxphysics.com/stories/binary-mass-transfer/where-common-envelope-energy-goes/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/binary-mass-transfer/where-common-envelope-energy-goes/" last_modified: "2026-11-03" --- [Binary mass transfer and common envelopes](https://sandboxphysics.com/stories/binary-mass-transfer/) AC29 · L4 # Where common-envelope energy goes Sandbox Physics · 2026-11-03 Energy released by a shrinking orbit need not remain in gas long enough to eject the envelope. Radiation can redistribute heat first, changing the escaped mass substantially while leaving the early post-plunge separation relatively similar. This fixed-paper guide follows those distinct outputs and their numerical evidence. ## Before you begin Read the energy-endpoint chapter. Kinetic energy, gravity and heat are enough to begin; no radiation-hydrodynamics programming is required. Open the complete HTML revision dated 2 July 2025 alongside this guide. ## Can the deposited heat do work in time? A companion moving through a giant’s envelope compresses gas and drives shocks. Retained heat can raise pressure and make gas expand. If radiation moves that energy elsewhere first, the pressure driving the same parcel weakens. Two calculations with similar orbital-energy release can therefore leave different gas distributions and ejected masses. This is a question left open by a scalar energy endpoint. An efficiency parameter summarizes how much release pays a chosen cost. It does not follow which layer receives the energy, when heat becomes pressure work, or how energy leaves. Find that route through the calculation before focusing on a final number. Reading: Ivanova et al. (2013), Common envelope evolution; arXiv:1209.4302v2 · Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 ## Fix the paper and its initial star We read Lau and collaborators’ arXiv2503.20506v2, comparing a twelve-solar-mass red supergiant with a three-solar-mass point companion. The three main cases are adiabatic, radiative diffusion, and radiative diffusion with extra central heating. Production resolution uses two million SPH particles. Read section 2 before comparing curves. These are not higher-resolution versions of the interactive school giant. The paper starts from a nonrotating donor with a constructed flat-entropy envelope, without driving its pre-existing equilibrium convection; a softened point mass replaces the inner structure. Our separate fifteen-solar-mass school snapshot differs in both mass and structure. Sharing the name red supergiant does not turn them into one evolutionary sequence. The heated case has a specific control purpose: it helps maintain central density and entropy. The authors do not simply label it the most realistic default. Initial convective transport is suppressed while heating is added near the center, so its thermal consistency needs discussion. Central heating, convection and surface cooling must together define an interpretable thermal initial state. Reading: Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 · Jared Goldberg (2025), MESA School Leuven Friday model ## Place Figures 6 and 7 beside each other Figure 6 shows the envelope fraction counted as unbound; Figure 7 shows the separation between the two compact centers. Match colors first, then distinguish the rapid plunge from the later slow inspiral. The last plotted frame may still belong to an evolving slow phase. Solid curves in Figure 6 use positive mechanical specific energy. Dashed curves additionally count gas and radiation internal energy. These definitions must be compared consistently. $$ e_{\rm k}+e_{\rm p}>0,\qquad\hbox{or}\qquad e_{\rm k}+e_{\rm p}+e_{\rm gas}+e_{\rm rad}>0 $$ A parcel can pass the second test before internal energy becomes outward mechanical motion. Subsequent cooling or pressure work can alter its fate. Reported late-time examples give about 20.8% unbound in the adiabatic case, 11.0% in the radiative case, and 8.9% with radiative heating. “Roughly halved” captures a scale, but actual comparisons still need the same time and energy criterion; it is not an exact ratio valid at every point. Against this substantial mass difference, separation evolution is more similar during the initial post-plunge interval. How much heat gas retains and where the gas resides are different outputs from where the binary has shrunk at that stage. The comparison motivates following gas and orbit through a slower nonadiabatic phase. Reading: Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 ## Use Figure 8 to locate efficient energy transport Figure 8 places density, local diffusion time, mechanical specific energy, opacity and hydrogen ionization in matching spatial slices. Choose one evolutionary column. Then ask where gas is dense, where the radiation-energy gradient is steep, and where radiation can redistribute energy before the gas moves appreciably. $$ t_{\rm diff}={\kappa\rho\over c\lambda_{\rm FLD}}\left({E_{\rm rad}\over|\nabla E_{\rm rad}|}\right)^2 $$ This is the paper’s local radiation-energy transport time. The flux limiter $lambda_{ m FLD}$ is not the binding-energy lambda of the preceding chapter. In optically thick material, repeated interactions provide a diffusion picture. In thin regions the flux limiter prevents transport beyond the free-streaming scale, but does not restore a fully directional radiation field. Where gas pressure dominates, the radiation-energy transport time is not automatically the thermal-adjustment time of all the gas. The partial-ionization and opacity maps are striking, but read the equation of state in section 2.3: these runs omit energy released by atomic and molecular recombination. They can discuss optical depth around ionization zones without becoming recombination-powered ejection calculations. One caption detail deserves a note in this fixed revision. Figure 8 places $e_{ m kp}>0$ beside “bound material,” inconsistent with section 3.2’s positive-mechanical-energy unbound definition. We use the body’s energy definition here. The label inconsistency alone does not establish that the simulation code selected material backward. Record it as a question about this fixed caption, and follow the physical definition in the text. Reading: Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 ## Appendix A: ask separately about energy and angular momentum Turn to Appendix A and Figure 9. By about eight years the radiative cases report total-energy drifts of 10.7% and 6.9%; the explicitly injected heating has been accounted for separately in the latter. Most drift accumulates after plunge-in and is associated with an implicit radiation solver that does not conserve energy exactly. Angular momentum is much better preserved, within about 0.020% and 0.022%. Keep both facts. Good conservation of one global quantity does not clear another equation. Nor is energy drift a universal percentage error for every observable that can simply be subtracted from unbound mass. Its physical effect depends on where and when the discrepancy enters. The interactive energy equation can have a near-machine-precision residual because it checks one algebraic equality. The paper solves coupled gas, gravity and radiation. Ranking these two calculations by their decimal residuals would erase the difference between the questions they actually solve. Reading: Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 ## Appendix B: which results survive ten times fewer particles? Appendix B compares production runs with ten times fewer particles. Begin with separation in Figure 10. Trends remain similar for roughly the first one to two years after plunge-in. A pronounced late drop in the radiative case near 8.5 years is absent at lower resolution. The authors retain stochastic turbulence or a numerical artifact as possibilities; this feature cannot establish a unique long-term orbital fate. Figure 11 then compares unbound mass. Intermittent late plumes increase resolution differences, but both resolutions preserve the qualitative contrast: sustained post-plunge ejection is stronger without radiative diffusion. Different outputs and time intervals therefore carry different numerical evidence. That is more informative than calling every late detail converged or rejecting every result together. A useful reading conclusion names the scope: under this initial state, equation of state and transport approximation, radiation changes the gas’s ability to retain heat and expand. Earlier separation comparisons and later fine structure have different support. Other masses, rotation, convective initial conditions and recombination release call for additional controlled comparisons. Reading: Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782 ## Exercises and explanations 1. Why can an internal-energy-inclusive unbound criterion count more mass without proving that all of it has permanently escaped? Read the explanation Internal energy may still become pressure work or be redistributed by radiation. Counting it includes a potential resource, whereas positive mechanical energy asks a different question. Later transport and dynamics determine long-term escape. 2. Does angular-momentum drift of about two parts in ten thousand make a roughly ten-percent energy drift negligible? Read the explanation No. The ledgers test different equations and error pathways. Good angular-momentum conservation does not remove errors in radiation exchange or diffusion, nor independently validate the unbound mass. 3. If the late separation drop disappears at lower resolution, must the entire radiative-ejection contrast be discarded? Read the explanation No. Leave the late feature unresolved while assessing other outputs separately. Earlier separation trends and the ejection difference seen at both resolutions retain their own limited evidence. State conclusions by observable and evolutionary interval. ## Try the prediction ### [Give the scalar endpoint its proper role](https://sandboxphysics.com/labs/lagrange-channels/?analysis=mass-transfer) 1. Vary the energy fraction in the compact-pair preset. List its inputs, outputs and missing gas variables. 2. Compare Figures 6 and 7 of the fixed paper at the same stage. Why cannot one endpoint separation replace both curves? 3. Read Appendices A/B and write one sentence each for a supported physical tendency, an uncertain late feature, and an omitted energy source. [Previous: A changing period in Beta Lyrae](https://sandboxphysics.com/stories/binary-mass-transfer/beta-lyrae-period-growth/) ## Sources and calculation scope 1. [Ivanova et al. (2013), Common envelope evolution; arXiv:1209.4302v2](https://arxiv.org/abs/1209.4302v2) Energy formalism, sources/sinks, timescales and core/remnant boundary discussions. The scalar endpoint does not predict the flow or an ejection morphology. 2. [Jared Goldberg (2025), MESA School Leuven Friday model](https://vincentvanlaer.github.io/mesa-school-labs/friday/morning-session/) CC BY-SA 4.0; repository commit ade5bca00e5caae97ac0b6f880f1de7ccead1553, work\_minimini3/ALPHA\_TEST\_LOGS/LOGS\_mlt2mesh1time1/profile8.data. Derived structure aggregates retain these terms. This 15-solar-mass model is distinct from the frontier paper’s 12-solar-mass donor. 3. [Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782](https://arxiv.org/html/2503.20506v2) Fixed revision 2 July 2025: sections 2–4, Figs 6–8 and Appendices A/B. Radiative versus adiabatic 12+3-solar-mass setup, energy/J drifts and tenfold particle-resolution comparison; no recombination-energy release. We do not reproduce the fluid calculation or republish its imagery.