AC29
Binary mass transfer and common envelopes
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.
L1
When one star spills onto another
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.
L1
Finding the passage between two stars
Locate the inner saddle from gravity and rotation, build its Roche volume, and distinguish a volume radius from the distance to the opening.
L2
Why exchanging mass can widen an orbit
Derive the circular orbital response to mass exchange, then let escaping matter carry different specific angular momentum and compare widening with shrinkage.
L3
When mass transfer feeds its own overflow
Compare local stellar and Roche-lobe responses, retain a radius-fit sign failure, then derive a conditional envelope-energy endpoint from a native giant.
L3
A changing period in Beta Lyrae
Fetch fixed primary sources and recompute a historical conditional transfer rate from fitted masses and period growth, then test loss and envelope assumptions.
L4
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
Sources and calculation scope
- Eggleton (1983), Approximations to the radii of Roche lobes
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.
- Soberman, Phinney & van den Heuvel (1997), 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.
- MESA 25.12.1, jdot_ml_check; commit 4a68bfbce0f6930c3f861d0611e914f02569a899
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.
- Ivanova et al. (2013), Common envelope evolution; arXiv:1209.4302v2
Energy formalism, sources/sinks, timescales and core/remnant boundary discussions. The scalar endpoint does not predict the flow or an ejection morphology.
- Harmanec & Scholz (1993), A&A279,131–147
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.
- Mennickent & Djurašević (2013), arXiv1303.5812v1
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.
- Thoul & Chidester (2022), MESA Summer School; Zenodo 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.
- Jared Goldberg (2025), MESA School Leuven Friday model
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.
- Lau et al. (2025), arXiv2503.20506v2; DOI10.1051/0004-6361/202554782
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.