Roche equipotential [@TaurisvandenHeuvel+2023]

This is some black magic mathmathmatic reasoning
Co-rotating binaries with have a tidal bulge that can be `easily’ calculated
also love the seemingly kinda personal rant about how the RL diagram is actually wrong, then provides a diagram which is way less intuitive

Mass transfer Galore

Mass transfer through $L_{1}$ does not majority effect angular momentum, however, transfer through $L_{2}$ does, causing a shrinkage in separation, and typically mergers
Different ways of modeling the transfer, depending on how you treat angular momentum with respect to the transfer
Orbit widens if the donor is less massive then accretor, and shrinks if the donor is more

Mass transfer onto NS and BH are limited by the Eddington Limit
However, mass transferred off of the donor is at the rate of the evolution of its envelope. (thermal-timescale)
mass transfer off of the donor is much greater (2 to 4 orders of magnitude) then the maximum accretion rate thus, the bulk of the mass will be “blown away”
if more than half of the total mass of the binary system is lost in a SN, the system will become unbounded
What on earth is a applegate mechanism
and what is gravitational quadrupole coupling
^^ im pretty sure its just when the oblateness of the star various from some convection stuff, which causes the period to variation causing period variations

Depends on the response of the star losing mass as well as the RL
more likely to detect it if the mass transfer is stable
orbit always expands for $q < 1$ and always shrinks when $q = 1.28$
Depends on whether the donor contracts or swells upon starting to transfer mass
Donors with radiative envelopes (Case A RLO) or slightly convective envelopes (early Case B RLO) will typically either shrink or stay the same radius

Grav interaction will cause Tidal Bulges to form
If rotation of the stars is not synced with orbital motion, the movement of the bulges will cause friction, thus dissipating the KE of the star.
If the orbit is eccentric, the effect is greater in magnitude
This leads to the orbit becoming perfectly circular
Happens faster in systems with closer separations
Tempature can heavily effect orbtial eccentrictiy based on convection rates

Trigged by unstable runaway mass transfer
companion star is engulfed in the envelope of the donor
the companion moving through this envelope causing friction, thus reducing angular moment, thus shrinking orbit
In some cases the envelope is ejected, and if it isnt, it leads to merger
Likely progenitor of some planetary nebulae
Very hard to predict due to unstable nature
Onset is caused by runaway RLO, Darwin instability, or the expansion of the accreting star

Whether not the envelope will be ejected is dependent on how good the system is at converting the GPE into KE, this added KE can then eject the envelope
This can be described as the efficiency $α_{CE}$ of converting orbital energy $Δ E_{or b}$
$E_{bin d} = α_{CE} Δ E_{or b}$
Ability to eject a CE depends heavily on the evolutionary status of the donor at the onset of CE
Separation post CE ejection is about 100-1000x smaller than at Onset
$E_{bin d} \equiv - \frac{G M _{d o n or} M _{e n v}}{λ R _{d o n or}}$
$λ$ various heavily on stealer mass and evolutionary status
For low max systems the envelopes of the donors are typically ejected, as $∣ E_{bin d} ∣$ is typically quite small
Many HMXBs with NSs will not survive CE and hence DNS mergers are rare, although these do theoretically form Thorne-Zytkov objects