Orbital periods in systems containing white dwarfs (‘WDs’) can be extremely short, especially if both of the stars are H-exhausted objects. The best examples of this are WD+WD binaries with periods of 7 and 9 minutes. Such systems almost certainly involve one or more phases of mass transfer. But what will be the minimum allowed orbital periods when at least one of the stars is still H-rich? Take BD+WD binaries, for instance (BD- Brown dwarf). Thats what, Rappaport and colleagues answered in their recently published paper on Arxiv.
They have used radius-mass relations, R(M) displayed in fig 1, in conjunction with function:
to derive the minimum allowed orbital period vs. the body’s mass. The results are shown in fig 2 below.
As we can see, there is a general trend of decreasing minimum orbital periods, Pmin from 620 min (10.3 hr) for Saturn-mass objects (red circle in Fig. 4), to 430 min (7.2 hr) for Jupiters (orange circle), to 104 min (1.7 hr) for objects on the boundary between super-Jupiters and brown dwarfs (blue circle), all the way down to 37 min (0.62 hr) for the coldest and most massive brown dwarfs (purple circle), respectively. These values are summarized in Table 1 below.
Their work also aimed, towards distinguishing brown dwarfs from planets that are found transiting the host white dwarf without recourse to near infrared or radial velocity measurements. For objects with orbital periods ≲ 100 minutes they concluded that we are observing a brown dwarf (or second WD) rather than a gas-giant planet.
Reference: S. Rappaport, A. Vanderburg, J. Schwab, L. Nelson, “Minimum Orbital Periods of H-Rich Bodies”, Arxiv, pp. 1-10, 2021. https://arxiv.org/abs/2104.12083
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