Roche lobe

Fig. 5.22. Roche-lobe geometry. Adapted from Iben (1991).

EMPIRICAL DETERMINATION OF THE GRAVITY-DARKENING EXPONENT FOR THE SECONDARY COMPONENTS FILLING THE ROCHE LOBE IN SEMI-DETACHED CLOSE BINARY SYSTEMS... 

Thus, by assigning 0(a = 1 to the early-type main-sequence primaries in semi-detached systems, similar practical analysis as done in the previous work of Kitamura and Nakamura (1986) has been carried out to determine empirical values of the exponent for the secondaries of those systems which fill the critical Roche lobe. 

Figure 1. Carbon abundance as a function of mass for both components of a close binary system at the onset of mass transfer. The region from Mx=0 to Mr=Mgi=8.1 Mo corresponds to the originally less massive component (gainer), whereas the carbon distribution of the loser is plotted from 8.1 Mo (surface) to 17.1 M (center). The first occurrence of hydrogen depleted layers (Xat<0.7) and the end of the Roche Lobe Overflow are indicated.

We note, however, the following possible difficulty with the original "hibernation" scenario. If the secondary s atmosphere is isothermal (due to irradiation by the WD), then it can be expected that the mass transfer rate will be reduced by a factor 10-100 depending on Aa/H, where Aa is the change in the separation and H is the (constant) scaleheight (Livio and Shara 1987). If, however, the secondary s atmosphere is con-vective, then M (aR)3, where AR is the distance by which the Roche lobe is overfilled. In such a case, an increase in the separation by Aa/a io-l+ will result in a decrease in I by at most a factor 2 (Edwards and Pringle 1987). Thus, it is not clear at all whether an increased separation can produce a significant decrease in M. 

Empirical Determination of the Gravity-Darkening Exponent for the Secondary Components Filling the Roche Lobe in Semi-Detached Close Binary Systems... 

The thermal time scale mass transfer is initiated by the shrinkage of the orbit as a consequence of angular momentum conservation, as long as Md > Mwd- the Roche lobe filling main sequence star is squeezed into a continuously shrinking volume. The stellar radius can fall much below the zero-age main sequence mass-radius relation. Consequently, orbital periods can be achieved which are smaller by a factor / than periods corresponding to unperturbed main sequence stars filling their Roche lobes. For conser-... 

An alternative channel for the formation of sdB stars considers the ultimate fate of binary systems which are so evolved as to comprise two white dwarfs in a close binary orbit. This predicates a binary system which has passed through several stages of mass transfer (whether common-envelope or stable Roche-lobe overflow) to leave these remnants. 

Upon contact, the less massive white dwarf will have a larger radius (Sect. 13) and will fill its Roche lobe first. Upon transferring a small amount of mass, the white dwarf radius will increase at a rate faster than the binary orbit will widen, and at a rate much faster than matter can be accreted by the companion. This leads to a runaway (or dynamical) disruption of the less massive white dwarf which will form a hot disk in Keplerian orbit around the other more massive white dwarf. Simulations of the process show that the disruption of the white dwarf will take only a few orbits, PQrb 3 m at the time of contact [57,58,59]. 

Early models suggest at least two phases of mass transfer necessary to explain the very low surface hydrogen abundances e.g. [J27]. The current best model for the evolution of v Sgr [9] is that it began as a f 0+3 Mq, f 50 d binary in which the envelope was blown to infinity, with little change of orbit, as the more massive star approached both Roche Lobe overflow and the Cepheid instability strip simultaneously. 

Roche lobe One ofthe two pear-shaped regions that surround each of a pair of bi-... 

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