Ed continues, and does case A, B and C mass transfer.
Conservatively, mostly.
For conservative mass transfer, mass and orbital angular momentum are conserved.
If you let mass leave the system, as it often does, and carry away some specific angular momentum, as it will, then things get more complicated.
So: M = M1 + M2 is constant
generally M1 >= M2
q = M2/M1
Jorb = M1M2 √ (G a/M1 M2) is constant
semi-major axis changes a/ai = (M01M02/M1M2)2
Since is is conservative, dM2/dt = - dM1/dt
and (1/a)da/dt = -2dM1/dt (1/M1 - 1/M2)
start mass transfer from more massive to less massive, orbital period shrinks,
when masses are equal hit orbital minumum at equal masses, if those are reached, then orbital period starts increasing again
Case A mass transfer: primary fills Roche Lobe during hydrogen burning - orbital period less than about 1.5 days (for canonical q ~ 0.5)
Case B mass transer: primary fills Roche Lobe on Hertzsprung gap - operates for wide range of orbital periods
Case C mass transfer: primary fills Rochel Lobe after helium burning loop on giant branch ~ operates for orbital periods > 97 days (again q = 0.5)
During these phases we also get mass loss from wind, which may generally exit the system without going through Roche flow.
Also get spin-orbit coupling.
Stellar timescales, in solar units.
Nuclear time scale ~ 1010 M/L years ~ 1010 M-2.5 years
thermal time scale ~ GM2/RL ~ 3.1*107 M-2 years
dynamical time scale ~ 50 mins √(1/ρ)
Notes on this are available on the wiki - scroll down to dates of talk and look for notes on right - we'll get pdf versions...
So, if evolution is not conservative, it is of course liberal.
Or do we mean progressive?
Anyway, things get complicated.
For small q may get outflow through outer lagrange points, so excreted carrying away angular momentum
or donor star may have convective envelope (cf red giant) - goes to γ=5/3 and radius increases as M-1/3 - so get runaway mass transfer
- hence Common Envelope Evolution?
Need system big enough that donor gets high up on RGB
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How can a giant branch star do anything conservatively? We're still picking bits of those out of our meteorites...
A single giant branch star, of which there are a number, or one which is in a wide enough binary, emits a quasi-spherical wind with all those good dust grains and dredged up junk.
A giant branch star in a close enough binary, with high enough a mass companion, has, as a first approximation, all the slow wind outflow go through the inner lagrange point onto an accretion disk onto the secondary - which as a first approximation implies no mass is lost to infinity - so conservative mass transfer.
As a second approximation, some mass is lost to infinity; and more generally, there are cases, especially for rapid or fast mass loss, and for extreme mass ratios, where the companion cannot accommodate the flow and some goes out through the outer lagrange point, or through jets, and is very much not conservative.
And then there are magnetic fields...
We hate magnetic fields...
Except when we don't.
Is this an equilibrium Giant branch star, or do He flashes and what-not neatly squirt everything through the lagrange point just like the steady state system?
Also, how do you get slow wind close to a star (with or without a close companion)?
equilibrium giant branch stars tend to have slow steady winds, at the onset of shell burning the binding energy of the envelope becomes very low and it is in some sense just lifting off the star - the wind is "slow" in the sense that its speed at the surface is close to the escape velocity, and hence its speed at infinite is near zero - much smaller than the surface speed.
At flashes you (sometimes) get more rapid pulsating mass loss, it gets complicated. The flash driven mass loss may overwhelm the "channel" through the lagrange point and lead to non-conservative mass loss
for hotter star - supergiants and flashing stars - the wind may also be "fast" in which case it just blows past the lagrange points instead of flowing along equipotential surfaces