Descripción de los recursos digitales que formarán parte del aula virtual

In CVs with q < 1, the masses of the companions are limited to masses lower than the Chandrasekhar mass limit. And since under a Roche lobe overflow assumption, the average density of the companion is a function of the orbital period (ρ ∝ P_orb−2), It results that the orbital periods in these CVs are shorter than ∼12 h. As explained above, the standard evolution of CVs is regulated by angular momentum losses, which reduce the orbit towards shorter periods, but it is also important to understand the response that the MS secondary has to its mass loss. Therefore, it is necessary to explain the mass-radius index, (ζ, M∝Rζ), which is tightly related with the contraction or expansion of the secondary in response to mass loss, Û R₂ R₂ =ζ Û M₂ M₂ (1.15)

If the mass loss timescale is longer than thermal timescale, τ_ML » τ_KH, then the secondary is in total equilibrium and the index can be obtained from the thermal equilibrium mass-radius relation of low mass MS stars, (M∼Rζ, withζ '0.8). If, in contrast, the mass loss timescale is shorter than thermal timescale,τ_ML«τ_KH, the response is adiabatic (ζ=-1/3 for low mass stars with significant convective envelopes, Paczyński 1965; Rappaport et al. 1982). The response of the secondary to mass loss is regulated by this index.

Period gap

The period gap is a strong feature in the period distribution of CVs with a dearth of systems in the rangeP_orb'2–3 h (green band in Figure 1.13 ), that can be explained by the cessation of magnetic braking. During the evolution driven by angular momentum losses (mainly magnetic braking for systems with P_{orb &} 3 h), the timescale at which the outer layers are removed from the secondary (hereafter mass loss timescaleτ_ML) is somewhat shorter than the timescale on which the companion can readjust its thermal equilibrium (thermal timescale τ_KH) by the rate of nuclear burning in its core. Hence, the CV is only a bit out of its thermal equilibrium (ζ ' 0.65). In other words, by the removing the envelope, the gravity decreases faster than the thermal pressure and therefore the secondary inflates. Indeed, it has been found that the secondaries in CVs withP_orb < 6 h are 20%–30% larger than MS stars of the same mass (Patterson et al., 2005; Knigge, 2006). During the evolution the mass-losing companion eventually reaches a stage at which it becomes fully convective (M₂'0.2–0.3 M,Knigge et al. 2011) and as a consequence the magnetic field topology of the secondary is highly modified, from large, open field lines atM₂ &0.2–0.3 Mto small closed field lines atM_2.0.2–0.3 M(Morin et al., 2010; Shulyak et al., 2017). Hence, it is thought that magnetic braking abruptly decreases, becoming very inefficient. The response of the secondary to this relaxation is to find again its thermal equilibrium, shrinking inside its Roche lobe, and stopping the mass transfer. At this stage, the orbital period of the CV is roughly 3 h, and the detached CV enters into the period gap, and the secondary recovers the mass-radius index of'0.8. From now on, the evolution is driven by the less effective gravitational wave radiation, which continues reducing the orbit and hence the size of the Roche lobe, until the secondary fills it again, and the mass transfer resumes at orbital periods of around 2 h. The re-emerging active CV contains a secondary in thermal equilibrium and therefore will be indistinguishable from a MS analogue (King & Kolb, 1995).

Period minimum

After the CV exits the period gap, the decreasing orbital period is limited to a minimum value (P_min), then the system bounces back towards longer orbital periods. Approaching P_min, the secondary is slowly running out of H in the core, progressively extinguishing the nuclear fusion. Therefore, the core evolves towards a state of non-relativistic electron degeneracy, i.e. the response of the secondary is to become adiabatic (ζ −→-1/3). The decreasing mass-radius index is responsible that the orbit stops shrinking and starts to widen. Let us look at the reason for this statement: in this regimeqis very small and therefore the Roche lobe can be approximated by Paczynski’s (1971) approximation given in equation 1.11, where_RÛ_{/Rcan be replaced by equation 1.15, resulting in:}

Figure 1.13: Period distribution of CVs with white dwarfs with no (or very weak) magnetic fields. The period gap ('2–3 h) and the period minimum ('80–86 min) are represented with green and blue bands, respectively. Data taken from Ritter & Kolb Catalogue Version 7.20.

Û a a = ζ− 1 3 _Û M_sec M_sec. (1.16)

It is clear that ifζ < 1/3 the orbit expands (_MÛ_{sec is negative). Therefore, it is not} expected to find CVs at periods shorter than P_min '65–70 min (Kolb & Baraffe, 1999; Howell et al., 2001), and the period distribution of a homogeneous sample of CVs from the

Sloan Digital Sky Survey (SDSS) shows a peak atP_min'80–86 min (Gänsicke et al., 2009). The observed period minimum is marked within a blue band in Figure 1.13.

While the rare kind of AM Canum Venaticorum (AM CVn) stars are not strictly CVs, they are usually included in the zoo of CVs. They have ultra-short orbital periods, between 10 and 65 minutes (see bottom panel in Figure 1.13). The lack of H in their spectra indicates that their donors are He-dominated, and different evolutionary pathways have been proposed for their origin which will be explained in more details in Section 1.2.6