Magnetic White Dwarfs

Nearly half a century ago, Kemp et al. (1970) detected circularly polarized light from the white dwarf GJ 742 proving that the star harboured a magnetic field. Since then hundreds of magnetic white dwarfs have been identified via spectropolarimetry (e.g. Friedrich et al. 1996; Vennes et al. 2003; Kawka et al. 2007) or detection of Zee- man splitting (e.g. Hagen et al. 1987; Reimers et al. 1996; Kleinman et al. 2013). Wide-area spectroscopic surveys have played a pivotal role in these searches, with SDSS in particular being responsible for the discovery of the majority of known magnetic white dwarfs (G¨ansicke et al., 2002; Schmidt et al., 2003; K¨ulebi et al., 2009; Kleinman et al., 2013; Kepler et al., 2015). The actual fraction of white dwarfs with magnetic fields is hard to estimate because of the lack of a well defined, ho- mogeneous, large spectroscopic sample of white dwarfs. Magnitude limited censuses suggest that 3₋4 per cent of all white dwarfs harbour strong (& 2 MG) magnetic fields (Liebert et al., 2003; Kepler et al., 2013). However, since hotter white dwarfs are visible at larger distances, magnitude limited samples are inevitably biased to- wards hotter systems. In contrast, the fraction of magnetic white dwarfs in a volume limited sample should reflect more accurately the true incidence of these objects. Kawka et al. (2007) closely examined the local sample of white dwarfs and found 10 to 30 per cent of the objects to be magnetic. But again sever biases may effect this statistics as the local sample is not representative of the entire white dwarfs population (Hollands et al., 2015).

origin of the magnetic field. Several scenarios have been put forward:

• Fossil field left over from the evolution of magnetic, peculiar Ap and Bp stars (Angel et al., 1981; Wickramasinghe & Ferrario, 2000). As these stars evolve off of the main sequence the magnetic flux is conserved and the contraction of the stellar radius can amplify the surface field by a factor_∼40,000. This single star formation channel can successfully explains the observed field strengths, but the low space density of Ap and Bp stars is not sufficient to account for the incidence of magnetic white dwarfs (Kawka & Vennes, 2004).

• Common envelope magnetic dynamo during binary evolution. In binary sys- tems, the evolution and consequent expansion of one of the two stars may lead to a common envelope phase (Webbink, 1984). Within this envelope the stars lose angular momentum and spiral inward towards each other. Eventually the common envelope is ejected leaving behind a close binary or a single star re- sulting from a merger. Tout et al. (2008) suggested that within the common envelope a magnetic dynamo may be generated and the resulting magnetic field may survive after the expulsion of the envelope remaining bound to the newly formed white dwarf. This formation mechanism could generate mag- netic fields _≥ 1 MG. Furthermore empirical evidence seems to suggest that magnetic white dwarfs have, on average, higher masses than non-magnetic ones (Liebert, 1988). Indeed the binary formation scenario proposed by Tout et al. (2008) would generate more massive white dwarfs.

On the other hand, recent work by Hollands et al. (2015) showed that a sig- nificant number of cool DZ white dwarfs harbour magnetic fields. Assuming a binary formation scenario it is hard to justify the presence of accreted plan- etary material in the magnetic white dwarf’s atmosphere.

• Magnetic dynamo generated during planetary engulfment. Some studies have suggested that a similar scenario to the common envelope one may occur if during its evolution, the white dwarf progenitor engulfs a giant gaseous planet or a brown dwarf. In this case the magnetic dynamo would be generated within the expanded shells of the star as the low-mass companion spirals inward (Farihi et al., 2011b; Nordhaus et al., 2011). This formation mechanism would not justify the higher average mass of magnetic white dwarfs, but it would explain the high incidence of magnetic fields in cool DZs (Hollands et al., 2015)

Some magnetic white dwarfs also exhibit period brightness variability. The origin of this variability is still matter of debate, but the most likely causes are stellar

rotation combined with localized magnetic dichroism (Brinkworth et al., 2013) or, in the case on convective white dwarfs (i.eTeff <14,000K for DAs), the presence of

star-spots (Lawrie et al., 2013). The period of these brightness modulation should, therefore, correspond to the rotation period of the white dwarf. The rotation period can provide valuable informations on the history of the white dwarf and, most impor- tantly it can help distinguish between different evolutionary scenarios (Brinkworth et al., 2013; Lawrie et al., 2013). For example, single stars evolutionary channel should produce white dwarfs with relatively low rotation rates while white dwarfs resulting from mergers in binary systems should be very fast rotators.

Inspecting the SDSS spectra available for our 26 Stripe 82 variable candidates, we identify two magnetic white dwarfs: SDSS J2218₋0000 and SDSS J0321₋0050. The Zeeman splitting of Hα in SDSS J0321₋0050 is very weak (Fig. 7.12). In fact, this star was previously classified as a non-magnetic DA (Eisenstein et al., 2006; Kleinman et al., 2013; Gentile Fusillo et al., 2015). Following Reid et al. (2001), we estimate the average surface magnetic field strength,Bs, according to the equation:

Bs/MG = ∆(1/λ)

46.686 , (7.1)

where ∆(1/λ) is the inverse wavelength separation in cm−1 _{between the components}

of a Zeeman triplet (Reid et al., 2001); and findBs = 1.36_±0.04 MG. In contrast, SDSS J2218₋0000 was already identified as a magnetic white dwarf and has a field sufficiently strong to smear out most of the Balmer lines (Bs_≃ 225 MG, Schmidt et al. 2003; K¨ulebi et al. 2009)