Procedimiento para la utilización de la identidad y la imagen como soporte del

Many of the observational targets discussed in this thesis are close, detached white dwarfs + M-dwarf binaries. In order to form such a binary, the initially more massive star (the primary) must evolve into a white dwarf. While shedding its envelope, it is thought that

the binary experiences anα common envelope event as described before, causing the orbit

to shrink significantly and resulting in a close white dwarf binary. Because phases after the main-sequence last a relatively short amount of time, the secondary star is still on the main-sequence and will not have evolved significantly during the primary star’s evolution. Even a small difference in ZAMS masses can therefore give rise to a white dwarf + main-

1950 1960 1970 1980 1990 2000 2010 2020 earliest reference in Ritter & Kolb catalogue

0 50 100 150 200 n u m b e r o f e c lip s in g b in a ri e s CV WD+MS WD+WD

Figure 1.12: Number of known eclipsing detached and semi-detached white dwarf + main-sequence

star binaries and eclipsing double white dwarf binaries (WD+MS, CV and WD+WD respectively). Data from Ritter & Kolb catalogue, edition 7.22, June 2014 (Ritter & Kolb, 2003).

sequence star (WD+MS) binary.

In particular, this thesis focuses on eclipsing white dwarf binaries, the numbers of which have increased dramatically in recent years, mainly due to large surveys such as the Sloan Digital Sky Survey (SDSS; York et al., 2000) and the Catalina Sky Survey (CSS; Drake et al., 2009). Fig. 1.12 shows the cumulative number of three subsets of known eclipsing white dwarf binaries from the Ritter & Kolb catalogue (Ritter & Kolb, 2003). In most binaries found so far in this eclipsing subset, the secondary star is a low-mass M- dwarf (dM) and typical orbital periods are between 2 hours and 2 days, with the majority closer to the lower boundary. The dominance of M-dwarf secondary stars, as well as the prevalence of short-period binaries, are partly due to observational selection effects. Stars with significantly earlier spectral types such as A, G and K stars are much brighter, and therefore more likely to outshine a white dwarf companion, making it more difficult to find such binaries, although some are known (Vennes et al., 1998; Burleigh & Barstow, 1999, 2000).

Although not the largest group, the detached binaries have the advantage of being simple systems because there are no varying elements in these binaries. Let us consider the light curves produced by an eclipsing WD+dM binary as seen from Earth. In these binaries, the orbital inclinationiis close to 90◦_{, so that the binary is viewed almost exactly}

edge-on. Orbital phase φ = 0 is defined at time T0, as the moment at which the line of

sight from Earth aligns with the line connecting the stellar centres while the white dwarf

is farthest away from the observer and the M-dwarf is closest. Half an orbital periodPorb

later the white dwarf is closest to the observer, and the orbital phase is equal toφ = 0.5,

etc.

In the simplest case, the white dwarf dominates the flux, and the M-dwarf is hardly visible. The resulting light curve will be flat at all orbital phases except for those during

which the white dwarf moves behind the M-dwarf and is being eclipsed. This is illustrated in the top panel of Fig. 1.13, where such a light curve is generated from a simple model.

When the M-dwarf is close to filling its Roche lobe, the star itself becomes distorted because it follows the gravitational equipotential surfaces (see 1.11). It takes on a droplet shape and therefore the star’s projected surface area is larger when viewed from the side than when viewed from the front or back. As the binary stars orbit their common centre of mass, the variable fraction of surface area visible produces a modulation in the light curve with a period equal to half the orbital period. This so-called ellipsoidal modulation is illustrated in the middle panel of Fig. 1.13. Modelling a light curve of a binary that shows

such a modulation of the M-dwarf can help determine the orbital periodPorb of the binary,

as well as the radius of the M-dwarf relative to the semi-major axis of the binary: RdM/a.

However, if the binary is not eclipsing, one should be careful not to confuse ellipsoidal modulation with the so-called reflection effect.

The reflection effect occurs when the white dwarf is sufficiently hot and the orbital distance between the stars is small enough for the side of the M-dwarf facing the white dwarf to be strongly irradiated. The atmosphere of the M-dwarf reprocesses the photons and emits them at slightly redder wavelengths. This produces the reflection effect in the light curve, but note that technically speaking it is not reflection but reprocessing of the light that causes the observed effect. When the irradiated face of the M-dwarf is visible to the observer, the flux increases and when the cool back of the M-dwarf turns towards the observer the flux decreases, as is illustrated in the bottom panel of Fig. 1.13. This type of modulation occurs on the orbital period.

A given binary may exhibit either ellipsoidal modulation or the reflection effect, or both. Both the ellipsoidal modulation and the reflection effect are more pronounced in

binaries with high orbital inclinations i, and may therefore be used to find such eclipsing

binaries (Parsons et al., 2013b, 2015).