Evolution of CVs: the initial stages

The early evolution starts with the two stars on the ZAMS, where the more massive star (primary star with mass M₁) evolves off the MS first, towards the RG phase. If, during the RG phase, the primary fills its Roche lobe, then material from the envelope starts to be transferred to the companion (secondary star with massM₂). The mass transfer continues if the primary (donor) expands faster than its Roche lobe. For low_MÛ_{1mass transfer is stable,} meaning that the secondary is able to accrete (a fraction of) the transferred matter. However, if_MÛ_{1 increases, eventually the accretion luminosity may exceed the Eddington luminosity} limit and the secondary is not able to accrete the material at the rate that is deposited. It results that the secondary is engulfed by material lost from the primary, and the system will enter a common envelope phase. The details of this stage remain poorly understood.

The classical prescription of the common envelope is based on the conservation of energy, so that the envelope is expelled extracting a fractionαof the difference of orbital energy between the initial and final configuration of the binary (Webbink, 1984; Tutukov &

Figure 1.11: Schematic representation of the evolution resulting in the formation of a white dwarf (WD) plus main sequence (MS) post common envelope binary. HG stands for Hertzsprung gap and GB for giant branch. Figure taken from Willems & Kolb (2004). Yungelson, 1979; van den Heuvel, 1976; Paczyński, 1967):

E_bind =α∆E_orb. (1.13)

The orbital separation needs to be highly reduced such that the envelope is ejected. However, this prescription fails to reconstruct the common envelope phase of double white dwarfs since it requires a physically unrealistic high (or even negative) efficiency, meaning that following the first common envelope the orbit shrunk significantly, that there would not be enough space for the secondary star to evolve and to produce a core as massive as the primary white dwarf (Nelemans et al., 2000). As a consequence, an alternative prescription was proposed based on conservation of angular momentum, J, in which the amount by which the binary’s orbital separation decreases depends on the fraction of the mass of the envelope,m_env(Nelemans et al., 2000; Nelemans & Tout, 2005):

∆J J =γ

m_env

M₁+M₂ . (1.14)

The physics of the common envelope phase are not fully understood (e.g Toonen & Nelemans, 2013), basically because the duration of this phase is believed to be very short (.103yr, challenging the observations) and accordingly difficult to model dynami-

cally. The components emerging from the common envelope phase comprise the remnant of the primary, a He or CO white dwarf (depending on the mass and evolutionary state of

Figure 1.12: SED of SDSS1238-0339, a cataclysmic variable that has evolved beyond the period minimum (see text for details). Dots show the J HK magnitudes, L4 stands for a L4-brown dwarf. Figure taken from Aviles et al. (2010).

the progenitor), and it is usually assumed in binary population synthesis studies that the secondary remains unaffected, and is still on the MS. Figure 1.11 shows the evolution of a 1.2-Mprimary plus a 0.8-M secondary, which were initially separated by a distance of '181 R and shrink dramatically to '6 R through the common envelope. The result of ejecting the envelope leaves a detached system composed by a compact stellar remnant white dwarf in a much tighter orbit with its companion, a Post Common Envelope Binary (PCEB). The PCEB population is dominated by systems with low-mass MS-companions and according to population synthesis studies (Yungelson, 2005) about one third of them never evolve further in the Hubble time. If following the common envelope the orbital separation of the binary is a few solar radii and the mass of the companion is lower than∼1.4M, gravitational radiation and magnetic braking bring the stars together and the secondary will eventually overflow its Roche lobe. This new configuration is a semi-detached system called as cataclysmic variable, in which the white dwarf is accreting from the low-mass MS companion.

Therefore, the Spectral Energy Distribution (SED) of a CV is composed by three components (plus one): the white dwarf which is hot and its emission dominates mainly in the ultraviolet, declining towards the optical; the companion which is cooler and contributes flux in optical towards near Infrared (IR), and the accretion disc, identified by its clearly

double peaked emission lines. If the disc is bright, it can contaminate the flux of the white dwarf and the secondary, and it results very difficult to disentangle the three components. Sometimes, there is additional flux from a fourth component corresponding to a hot spot produced by the shock of the accreting material from the secondary to the disc. Figure 1.12 shows an example of the SED of a CV whose evolution was driven beyond the period minimum (which is the shortest period that CVs can reach and will be explained in more details later).

As explained in Section 1.2.1, the stability of the mass transfer in CVs depends upon the mass ratioq. For systems withq > 1, the mass transfer increases to rates at which the accreted material can steadily burn on the the white dwarf surface, providing a potential pathway for Supernovae type Ia (SNIa). This evolutionary channel will be explained in more detail in Section 1.2.6. Alternatively, for systems with q < 1 the mass transfer can only occur if the systems lose angular momentum. I will now explain the evolution of this latter case.