---
title: "Binary mass transfer and common envelopes"
description: "Follow gas through the Roche passage, account for mass and angular momentum, and test a conditional common-envelope energy endpoint."
canonical_url: "https://sandboxphysics.com/stories/binary-mass-transfer/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/binary-mass-transfer/"
last_modified: "2026-11-04"
---

AC29

# Binary mass transfer and common envelopes

Sandbox Physics · 2026-11-03

Follow a parcel between two stars. Learn why the orbit and donor’s available space change together, then compare a historical period trend with the limits of an envelope-energy budget.

1. L1

   ## [When one star spills onto another](https://sandboxphysics.com/stories/binary-mass-transfer/when-a-star-spills/)

   A donor can spill through the narrow passage between two stars. Whether the overflow eases depends on how both the star and its Roche lobe respond.

2. L1

   ## [Finding the passage between two stars](https://sandboxphysics.com/stories/binary-mass-transfer/the-passage-at-l1/)

   Locate the inner saddle from gravity and rotation, build its Roche volume, and distinguish a volume radius from the distance to the opening.

3. L2

   ## [Why exchanging mass can widen an orbit](https://sandboxphysics.com/stories/binary-mass-transfer/exchanging-mass-changing-orbits/)

   Derive the circular orbital response to mass exchange, then let escaping matter carry different specific angular momentum and compare widening with shrinkage.

4. L3

   ## [When mass transfer feeds its own overflow](https://sandboxphysics.com/stories/binary-mass-transfer/when-transfer-feeds-itself/)

   Compare local stellar and Roche-lobe responses, retain a radius-fit sign failure, then derive a conditional envelope-energy endpoint from a native giant.

5. L3

   ## [A changing period in Beta Lyrae](https://sandboxphysics.com/stories/binary-mass-transfer/beta-lyrae-period-growth/)

   Fetch fixed primary sources and recompute a historical conditional transfer rate from fitted masses and period growth, then test loss and envelope assumptions.

6. L4

   ## [Where common-envelope energy goes](https://sandboxphysics.com/stories/binary-mass-transfer/where-common-envelope-energy-goes/)

   Read Lau 2025 v2 through Figs 6–8 and Appendices A/B, following radiation, unbound mass, energy drift and resolution limits.

[Drag the donor surface and follow the stream](https://sandboxphysics.com/labs/lagrange-channels/?analysis=mass-transfer)

## Sources and calculation scope

1. [Eggleton (1983), Approximations to the radii of Roche lobes](https://articles.adsabs.harvard.edu/pdf/1983ApJ...268..368E)

   Both pages, equations 1–3 and the independently integrated column of Table 1. The fit describes volume radius, not the distance to the inner saddle. Original PDF remains upstream.

2. [Soberman, Phinney & van den Heuvel (1997), astro-ph/9703016v1](https://arxiv.org/abs/astro-ph/9703016v1)

   Sections 2–3, angular-momentum loss channels, response exponents and AppendixA. Translate the paper’s donor/accretor names before using its mass-ratio convention.

3. [MESA 25.12.1, jdot\_ml\_check; commit 4a68bfbce0f6930c3f861d0611e914f02569a899](https://docs.mesastar.org/en/25.12.1/test_suite/jdot_ml_check.html)

   The native inlist and run\_binary\_extras.f90 give an analytic mixed-loss reference. Our ODE checks the mathematics; we did not compile or pass the MESA evolutionary test. Native code is LGPL3-or-later and is not copied into this Lab.

4. [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.

5. [Harmanec & Scholz (1993), A&A279,131–147](https://articles.adsabs.harvard.edu/pdf/1993A%26A...279..131H)

   Printed p139, equation 5 and the RV ephemeris discussion. The small quadratic coefficient must be checked on the scanned page. This historical RV analysis is not a new eclipse-time fit.

6. [Mennickent & Djurašević (2013), arXiv1303.5812v1](https://arxiv.org/abs/1303.5812v1)

   Table 1 fitted masses and section 4’s adopted 12.9-day/19-second-per-year calculation. The disc light-curve fit, evolutionary fit and covariance are not reproduced.

7. [Thoul & Chidester (2022), MESA Summer School; Zenodo 7082536](https://zenodo.org/records/7082536)

   CC BY 4.0. Exact lab3\_4M\_solutions/LOGS\_cheb\_case1/profile1.data from r22.05.1. Our gravity/core-cut aggregates and envelope figure are adaptations with attribution; not a new MESA run or total-age measurement.

8. [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.

9. [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.