an explanation for the period gap, there is a significant scientific drawback: thus far there has been no observational evidence for a discontinuous change in spin-down rate due to magnetic braking between late-type field stars that are fully convective and those that have a radiative core (Andronov et al., 2003; King & Schenker, 2002).
There are, in fact, a number of severe disagreements between the predictions of the stan- dard model and observational evidence. The response to these failings has been the proposal of several modifications/alternatives (King & Kolb, 1995; Kolb et al., 1998; Patterson, 1998; Kolb & Baraffe, 1999; King et al., 2002; King & Schenker, 2002; Andronov et al., 2003; Barker & Kolb, 2003), none of which have been completely successful in matching all the features ob- served in the current CV period distribution.
(1) The predicted period minimum is ≈ 65 min, whilst the observed value is ≈
80 min (Kolb & Baraffe, 1999; Paczy ´nski, 1971).
thought to occur whenτM˙ =τKH(Paczy´nski, 1971; King, 1988). This is the point in the evolu-
tion of a binary where the consequence of mass loss has resulted in the transition of the donor star from a main sequence star to a degenerate, brown dwarf. As mass loss continues, the BD responds by expanding adiabatically, as the binary separation increases to compensate for the mass transfer. Roche lobe contact is maintained by the expanding BD, and the system evolves towards longer periods.
The actual period Pminat which CVs ‘bounce’ depends on the ratioτ= tKH/tM˙. Ifτis
small, then Pminis short. Thus Pminis sensitive to the orbital angular momentum loss rate which
determines the rate of mass transfer−M˙2and also, to the interior structure of the donor.
Paczy´nski was the first to point out that Pmin ≈ 80 min, if gravitational wave radiation
drives the mass transfer. Since then, stellar models with different input physics have been em- ployed to verify a quantitative agreement between the observed and calculated Pmin. However
a number of calculations have thrown a spanner in the works: Kolb & Ritter (1992); Howell et al. (1997); Kolb & Baraffe (1999) notoriously give Pminat≈ 65 min instead of the observed
≈80 min.
(2) Population synthesis models show that there should be a significant accumu- lation of systems near the period minimum, (Paczy ´nski & Sienkiewicz, 1983; Paczy ´nski, 1971) and that 99% of CVs should have orbital periods below the period gap (Howell et al., 1997; Kolb, 1993), whilst the period distribution plot shows similar numbers of CVs above and below the period gap.
The probability of finding a system within a given period range is proportional to the time taken to evolve through this region, N(P)∝1/|P|˙ (King & Schenker, 2002).
Since ˙P = 0 at Pmin, then N(P) must clearly have a significant maximum. Thus com-
pared to the rapid evolution above the period gap, where high mass transfer rates are driven by magnetic braking, there should be large accumulation of systems, corresponding to the slow velocity in period space, driven by a lower mass transfer rates attributed to gravitational wave radiation, which would increase the probability of detection (de Kool, 1992; de Kool & Ritter, 1993; Kolb, 1993; Kolb & Baraffe, 1999).
Figure 2.1: The evolution of the orbital period Porbof a system with the mass transfer rate – ˙M. Also
shown are the percentages of systems believed to populate particular stages of the evolution. 99% of systems are theorised to exist below the period gap. Modified from Howell et al. (2001)
Unfortunately observational evidence for the presence of a large population of systems with low mass transfer rates has thus far remained elusive.
Figure 2.1 provides an illustrative support to the discussion. The plot shown shows the percentages of CVs theorised to populated different stages of CV evolution. According to the standard theory 1% of systems are believed to exist above the gap, while 99% have periods below the gap, 70% of all systems should be post period minimum systems. Figure 2.2 from Barker & Kolb (2003) compares the observed orbital period distribution (top panel) to the the- orised distribution (bottom panel) for systems below the period gap. The predicted change of mass transfer rate due to gravitational radiation has also been plotted (middle panel). Note the large accumulation in systems ‘spike’ that is expected to exist at the period minimum of 65 min in the theoretical distribution, which is absent from the observed sample which has a minimum at 80 min.
(3) Population synthesis also suggests that the space density of CVs should range from 10−5 −10−4pc−3 (Politano, 1996; de Kool, 1992), whereas the number derived from observations is 10−6 −10−5pc−3 (Downes, 1986; Ringwald, 1996; Pretorius et al., 2007b; Araujo-Betancor et al., 2005a; Aungwerojwit et al., 2006).
Figure 2.2: Top panel: the observed period distribution of CVs with periods less than 116 min (Ritter
& Kolb, 1998). Middle panel: calculated evolutionary track in the orbital period versus mass rate ˙M plane for CVs that evolve under the influence of angular momentum loss via gravitational radiation. The systems reach a period minimum of ∼65 min. Lower panel: period distribution expected from evolutionary trace in middle panel. As shown in Barker & Kolb (2003).
If the standard model is correct, then the vast number of systems below the period gap would infer a high space density. Unfortunately, current observations have so far identified only 1-10% of the predicted CV population (G¨ansicke et al., 2002b).
Possible causes of all these discrepancies have been attributed to the uncertainties in CV evolution (King, 1988; Schenker & King, 2002; Andronov et al., 2003; Barker & Kolb, 2003; Taam et al., 2003) as well as observational selection effects, (Downes, 1986; Ringwald, 1996; G¨ansicke, 2005).