An Exploration of the Paradigm for the 2–3 Hour Period Gap in Cataclysmic Variables

Abstract

We critically examine the basic paradigm for the origin of the 2-3 hr period gap in cataclysmic variables (CVs), i.e., binary systems in which a white dwarf accretes from a relatively unevolved, low-mass donor star. The observed orbital period distribution for ∼ 300 CVs shows that these systems typically have orbital periods, P orb , in the range of ∼ 80 min to ∼ 8 hr, but a distinct dearth of systems with 2 ∼ < P orb (hr) ∼ < 3. This latter feature of the period distribution is often referred to as the "period gap". The conventional explanation for the period gap involves a thermal bloating of the donor star for P orb ∼ > 3 hr due to mass transfer rates which are enhanced over those which could be driven by gravitational radiation (GR) losses alone (e.g., magnetic braking). If for some reason the supplemental angular momentum losses become substantially reduced when P orb decreases below ∼ 3 hr, the donor star will relax thermally and shrink inside of its Roche lobe. This leads to a cessation of mass transfer until GR losses can bring the system into Roche-lobe contact again at P orb ∼ 2 hr.We carry out an extensive population synthesis study of CVs starting from ∼ 3 × 10 6 primordial binaries, and evolving some ∼ 2 × 10 4 surviving systems through their CV phase. In particular we study current-epoch distributions of CVs in theṀ −P orb , R 2 −P orb , M 2 −P orb , q−P orb , T ef f −P orb , and L 2 −P orb planes, whereṀ is the mass transfer rate, q is the mass ratio M 2 /M 1 , and M 2 , R 2 , T ef f , and L 2 are the donor star mass, radius, effective temperature, and luminosity, respectively. This work presents a new perspective on theoretical studies of the long-term evolution of CVs. In particular, we show that if the current paradigm is correct, the secondary masses in CVs just above the period gap should be as much as ∼ 50% lower than would be inferred if one assumes a main-sequence radius-mass relation for the donor star. We quantify the M 2 − P orb relations expected from models wherein the donor stars are thermally bloated. Finally, we propose specific observations, involving the determination of secondary masses in CVs, that would allow for a definitive test of the currently accepted model (i.e., interrupted thermal bloating) for the period gap in CVs.

Dynamical masses of a nova-like variable on the edge of the period gap

“…These authors also point out the possibility that the WD temperature might not be a good tracer of the medium-term mass transfer rate. The time-averaged mass transfer rate of IP Peg is also inconsistent with the results of the population synthesis study by Howell et al (2001). It is therefore clear that more direct measurements of masses and temperatures of WDs in the 3 − 4 h orbital period regime are needed.…”

“…9 also shows that the secondary star in IP Peg is underluminous for its mass. The spectral types measured for HS 0220+0603 and IP Peg are also much later than predicted by Howell et al (2001) (cf. the effective temperature-orbital period distribution for CVs in their fig.…”

“…In the case of detached white dwarf/main sequence (WDMS) binaries a drop in the fraction of post-common envelope binaries (PCEBs) relative to wide binaries is observed at a mass of ∼ > 0.25 M , which is an independent observation in support of the disrupted magnetic braking mechanism invoked to reproduce the observed orbital period gap in CVs (Schreiber et al 2010). On the other hand, in the population synthesis study of CVs by Howell et al (2001) their zero-age main sequence models have a fully convective configuration at a mass of ∼ 0.34 M , while the semi-empirical donor star sequence for CVs of Knigge (2006) suggests a (fully convective) donor mass of 0.2 M at the upper edge of the period gap. These authors warn against the lack of fundamental input in the form of accurate masses, especially in the 3-4 h orbital period range.…”

White Dwarf Colors in Low Accretion Rate Binaries

“…Figure 1 shows the color and magnitude we predict for quiescent CV binaries using standard CV evolution to relate the companion mass to Ṁ [2,3]. The data shown for comparison are members of the globular cluster M4 as determined by proper motion studies with HST [4].…”

Spectroscopy From the Hubble Space Telescope Cosmic Origins Spectrograph of the Southern Nova-Like Bb Doradus in an Intermediate State

“…The system then reappears as active and continues to evolve, reducing its period. The majority of CVs in our galaxy should have already evolved to a minimum period near 80 minutes and now have degenerate brown dwarf-like secondaries (Howell et al 2001;Goliasch & Nelson 2016). However, some discrepancies have arisen between the observations and the standard model, prompting suggestions of additional (or alternative) theoretical scenarios (see, e.g., Knigge et al 2011 and references therein for a review of the problem).…”