Single magnetic white dwarfs with Balmer emission lines: A small class with consistent physical characteristics as possible signposts for close-in planetary companions
Boris T. Gaensicke, Pablo Rodriguez-Gil, Nicola P. Gentile Fusillo, Keith Inight, Matthias R. Schreiber, Anna F. Pala, Pier-Emmanuel Tremblay
MMNRAS , 1–12 (2019) Preprint 28 September 2020 Compiled using MNRAS L A TEX style file v3.0
Single magnetic white dwarfs with Balmer emission lines:A small class with consistent physical characteristics aspossible signposts for close-in planetary companions
Boris T. G¨ansicke (cid:63) , Pablo Rodr´ıguez-Gil , , Nicola P. Gentile Fusillo ,Keith Inight , Matthias R. Schreiber , , Anna F. Pala , Pier-Emmanuel Tremblay Department of Physics, University of Warwick, Coventry, CV4 7AL, UK Instituto de Astrof´ısica de Canarias, 38205 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain European Southern Observatory, Karl Schwarzschild Straße 2, Garching, 85748, Germany Departamento de F´ısica, Universidad T´ecnica Federico Santa Mar´ıa, Av. Espa˜na 1680, Valpara´ıso, Chile Millennium Nucleus for Planet formation, NPF, Valpara´ıso, Chile
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We report the identification of SDSS J121929.45+471522.8 as the third apparentlyisolated magnetic ( B (cid:39) . ± . MG) white dwarf exhibiting Zeeman-split Balmeremission lines. The star shows coherent variability at optical wavelengths with anamplitude of (cid:39) . mag and a period of 15.26 h, which we interpret as the spin periodof the white dwarf. Modelling the spectral energy distribution and Gaia parallax, wederive a white dwarf temperature of ± K, a mass of . ± .
022 M (cid:12) , anda cooling age of . ± . Gyr, as well as an upper limit on the temperature of asub-stellar or giant planet companion of (cid:39)
K. The physical properties of this whitedwarf match very closely those of the other two magnetic white dwarfs showing Balmeremission lines: GD356 and SDSS J125230.93 − Key words: stars: abundances – white dwarfs – planetary systems – stars: individual:SDSS J121929.45+471522.8
White dwarfs are the remnants of stars born with initialmasses (cid:46) −
10 M (cid:12) (e.g. Smartt et al. 2009; Cummings et al.2019). Whereas the possibility that some of these stellar rem-nants possess strong magnetic fields was explored alreadyby Blackett (1947), the observational confirmation occurredonly much later (Kemp et al. 1970). It is now firmly estab-lished that a small fraction, − per cent of single whitedwarfs exhibit magnetic fields of B (cid:38) MG (Hollands et al.2015; Ferrario et al. 2015; Kawka 2020), and there is evi-dence that weaker fields are equally or possibly even morecommon (Landstreet & Bagnulo 2019b,a; Bagnulo & Land-street 2019). The origin of magnetic fields in white dwarfs is (cid:63)
E-mail: [email protected] still debated, with working hypotheses including fossil fields(Angel et al. 1981; Braithwaite & Spruit 2004), binary in-teractions either in the form of a common envelope (Toutet al. 2008, but see Belloni & Schreiber 2020 for a discussionof a number of serious problems in that scenario) or mergers(Garc´ıa-Berro et al. 2012), or processes internal to the whitedwarf (Isern et al. 2017).In the vast majority of magnetic white dwarfs, the pres-ence of the field is established via the detection of Zeeman-split absorption lines of the atmospheric constituents: hydro-gen (Angel et al. 1974), helium (Jordan et al. 1998), carbon(Schmidt et al. 1999), and other metals (Kawka & Vennes2011).One exception to this rule has been the maverick whitedwarf GD356, exhibiting Balmer emission lines Zeeman-split in a field of B (cid:39) MG (Greenstein & McCarthy © a r X i v : . [ a s t r o - ph . S R ] S e p G¨ansicke et al. (cid:39) min, in-terpreted as the spin period of the white dwarf (Brinkworthet al. 2004), which is moderately rapid for a single whitedwarf (Hermes et al. 2017a).Left with none of the conventional models providing asatisfactory explanation for the Balmer emission lines, Liet al. (1998) suggested that a conductive planet, or planetcore in a close orbit around GD356 would result in the gener-ation of electric currents that could heat the regions near themagnetic poles of the white dwarf – akin to the Jupiter-Ioconfiguration (Goldreich & Lynden-Bell 1969). Wickramas-inghe et al. (2010) revisited the unipolar inductor model,arguing that such a planet was unlikely to have survivedthe giant branch evolution of the progenitor of GD356. In-stead, these authors proposed that GD356 is the product ofa double-white dwarf merger and the putative planet formedfrom the metal-rich debris disc left over by this merger(Garc´ıa-Berro et al. 2007) – a rare event, explaining the (atthe time) unmatched properties of GD356.In the light of the rapidly growing evidence for plan-etesimals and planets around white dwarfs (Becklin et al.2005; G¨ansicke et al. 2006; Farihi et al. 2009; Vanderburget al. 2015; Manser et al. 2019; G¨ansicke et al. 2019), Ve-ras & Wolszczan (2019) studied the survivability of conduc-tive planetary cores, and found that a significant parameterspace of white dwarf plus planet configurations exists, lend-ing support to the unipolar inductor model.GD356 remained a fascinating but lonely system for 35years, until Reding et al. (2020) announced the discoveryof SDSS J125230.93 − − B (cid:39) MG), single white dwarf exhibiting Zeeman-split Balmer emission lines with an exceptionally short ro-tation period of 317 s – making it the fastest spinning whitedwarf.We report the identification of a third magnetic ( B (cid:39) . MG), single white dwarf with Zeeman-split Balmeremission lines, SDSS J121929.45+471522.8. We also discussthe physical properties and possible nature of this emergingnew class of white dwarfs and their possible link to closeplanetary companions.
The first spectrum of SDSS J121929.45+471522.8(SDSS J1219+4715 henceforth) was obtained on 2004April 21 with the SDSS spectrograph on the 2.5-m SDSStelescope (Fig. 1; York et al. 2000; Adelman-McCarthy et al.2006), using an exposure time of 2520 s. The SDSS spectrumcovers the wavelength range − ˚A at a spectralresolution of R = λ / δλ (cid:39) . Szkody et al. (2006) noticeda weak H α emission line in this spectrum and classified SDSS J1219+4715 as a candidate cataclysmic variable(CV), i.e. a short-period interacting binary containing awhite dwarf and a low-mass star. The authors argued morespecifically that the optical spectrum is likely dominated bythe hot accretion disc of a CV with a relatively high masstransfer rate. This hypothesis was ruled out by Pala et al.(2020) based on the Gaia parallax (Gaia Collaborationet al. 2018), putting the system firmly at a distance of d = . ± . pc (Bailer-Jones et al. 2018). Pala et al.(2020) noted that the wavelength of the emission featureis (cid:39) ˚A, noticeably blue-ward of H α , and tentativelyexplained it by contamination from the nearby largeSeyfert 2 galaxy M 106.To clarify the nature of SDSS J1219+4715, we obtainedone spectrum on 2020 April 21 using the SPectrograph forthe Rapid Acquisition of Transients (SPRAT, Piascik et al.2014) on the robotic Liverpool Telescope (LT, Steele et al.2004). These data cover the wavelength range (cid:39) − ˚Awith a dispersion of 4.6 ˚A per pixel, resulting in R (cid:39) at 6000 ˚A. The exposure time was 1800 s. The SPRAT ob-servations were processed by an automated pipeline whichcorrects for bias, dark and flatfield effects, performs thesky subtraction and extracts the spectrum, and derives thewavelength and flux calibration. Cosmic rays were manu-ally cleaned from the reduced spectrum. Despite the lowresolution, the LT spectrum (Fig. 1) confirmed the emis-sion line near H α noticed previously in the SDSS spectrum(Szkody et al. 2006). The wavelength of the emission featureis (cid:39) ˚A, also blue-ward of H α , and within uncertaintiesidentical to that in the SDSS spectrum. Interpreting thisline as Doppler-shifted H α emission would imply a velocityof (cid:39) km s − , extremely high for any kind of close whitedwarf binary. Moreover, it would be rather unlikely that ourLT spectrum sampled the same orbital phase as the SDSSspectrum obtained 16 years earlier. Closer inspection of theLT spectrum suggested that additional structure was presentnear H β .Intrigued by the features in the LT spectrum, we ac-quired higher resolution spectroscopy with the Optical Sys-tem for Imaging and low-Intermediate-Resolution IntegratedSpectroscopy (OSIRIS; S´anchez et al. 2012) on the 10.4-m Gran Telescopio Canarias (GTC). The observations werecarried out as 600 s exposures in the period April 24 to 2020June 29. We obtained a total of two and four spectra usingthe R2500V and R2500R grisms, respectively, which provide R (cid:39) with the 1-arcsec slit. The wavelengths coveredwere − ˚A and − ˚A for the R2500V andR2500R grisms, respectively.The GTC spectra were reduced using iraf . After de-biasing and flat-fielding, we performed cosmic-ray removalwith the L.A.Cosmic package (van Dokkum 2001). Optimalextraction of the spectral trace (Horne 1986) was subse-quently done with the starlink / pamela reduction package(Marsh 1989). We used spectra of HgAr+Ne+Xe arc lampsobtained at the beginning of the nights for wavelength cali-bration, which was performed with molly . iraf is distributed by the National Optical Astronomy Obser-vatories. molly is available at http://deneb.astro.warwick.ac.uk/phsaap/software MNRAS000
The first spectrum of SDSS J121929.45+471522.8(SDSS J1219+4715 henceforth) was obtained on 2004April 21 with the SDSS spectrograph on the 2.5-m SDSStelescope (Fig. 1; York et al. 2000; Adelman-McCarthy et al.2006), using an exposure time of 2520 s. The SDSS spectrumcovers the wavelength range − ˚A at a spectralresolution of R = λ / δλ (cid:39) . Szkody et al. (2006) noticeda weak H α emission line in this spectrum and classified SDSS J1219+4715 as a candidate cataclysmic variable(CV), i.e. a short-period interacting binary containing awhite dwarf and a low-mass star. The authors argued morespecifically that the optical spectrum is likely dominated bythe hot accretion disc of a CV with a relatively high masstransfer rate. This hypothesis was ruled out by Pala et al.(2020) based on the Gaia parallax (Gaia Collaborationet al. 2018), putting the system firmly at a distance of d = . ± . pc (Bailer-Jones et al. 2018). Pala et al.(2020) noted that the wavelength of the emission featureis (cid:39) ˚A, noticeably blue-ward of H α , and tentativelyexplained it by contamination from the nearby largeSeyfert 2 galaxy M 106.To clarify the nature of SDSS J1219+4715, we obtainedone spectrum on 2020 April 21 using the SPectrograph forthe Rapid Acquisition of Transients (SPRAT, Piascik et al.2014) on the robotic Liverpool Telescope (LT, Steele et al.2004). These data cover the wavelength range (cid:39) − ˚Awith a dispersion of 4.6 ˚A per pixel, resulting in R (cid:39) at 6000 ˚A. The exposure time was 1800 s. The SPRAT ob-servations were processed by an automated pipeline whichcorrects for bias, dark and flatfield effects, performs thesky subtraction and extracts the spectrum, and derives thewavelength and flux calibration. Cosmic rays were manu-ally cleaned from the reduced spectrum. Despite the lowresolution, the LT spectrum (Fig. 1) confirmed the emis-sion line near H α noticed previously in the SDSS spectrum(Szkody et al. 2006). The wavelength of the emission featureis (cid:39) ˚A, also blue-ward of H α , and within uncertaintiesidentical to that in the SDSS spectrum. Interpreting thisline as Doppler-shifted H α emission would imply a velocityof (cid:39) km s − , extremely high for any kind of close whitedwarf binary. Moreover, it would be rather unlikely that ourLT spectrum sampled the same orbital phase as the SDSSspectrum obtained 16 years earlier. Closer inspection of theLT spectrum suggested that additional structure was presentnear H β .Intrigued by the features in the LT spectrum, we ac-quired higher resolution spectroscopy with the Optical Sys-tem for Imaging and low-Intermediate-Resolution IntegratedSpectroscopy (OSIRIS; S´anchez et al. 2012) on the 10.4-m Gran Telescopio Canarias (GTC). The observations werecarried out as 600 s exposures in the period April 24 to 2020June 29. We obtained a total of two and four spectra usingthe R2500V and R2500R grisms, respectively, which provide R (cid:39) with the 1-arcsec slit. The wavelengths coveredwere − ˚A and − ˚A for the R2500V andR2500R grisms, respectively.The GTC spectra were reduced using iraf . After de-biasing and flat-fielding, we performed cosmic-ray removalwith the L.A.Cosmic package (van Dokkum 2001). Optimalextraction of the spectral trace (Horne 1986) was subse-quently done with the starlink / pamela reduction package(Marsh 1989). We used spectra of HgAr+Ne+Xe arc lampsobtained at the beginning of the nights for wavelength cali-bration, which was performed with molly . iraf is distributed by the National Optical Astronomy Obser-vatories. molly is available at http://deneb.astro.warwick.ac.uk/phsaap/software MNRAS000 , 1–12 (2019) ingle magnetic white dwarfs with Balmer emission lines Figure 1.
Spectroscopy of SDSS J1219+4715. The SDSS spec-trum (April 2004) revealed weak H α emission, which was con-firmed with the LT in April 2020. Higher resolution spectra ob-tained with the GTC between April and June 2020 show theZeeman-split emission lines of H α and H β . The GTC spectroscopy reveals that the emission de-tected previously in the SDSS and LT data is the π compo-nent of Zeeman-split H α emission, flanked to the blue andred by the associated σ − , + components (Fig. 1, 2). Multiplesharp emission features are also detected near H β , unam-biguously identifying SDSS J1219+4715 as a magnetic whitedwarf. Given that many magnetic white dwarfs exhibit photomet-ric variability (Hermes et al. 2017b), we obtained sparsephotometry with the robotic LT from 2020 May 19 to2020 July 6. We used the Bessel B -band filter which pro-vides high throughput over the range (cid:39) − ˚A,covering the higher Balmer lines where photometric vari-ability might be expected. We used the default detec-tor binning of × and obtained groups of three 80-s exposures separated by at least two hours. We col-lected a total of 174 images over 38 individual nights. TheLT data are provided in a reduced (bias-corrected andflat-fielded) format, and we extracted the photometry ofSDSS J1219+4715 using the pipeline described in G¨ansickeet al. (2004) relative to Gaia DR2 1545014673992066048( G BP = . ), a spectroscopically confirmed G-type star(LAMOST J121936.84+471554.8, Luo et al. 2015, 2019).The photometry revealed SDSS J1219+4715 to be variablewith an amplitude of (cid:39) . mag.We complemented our LT observations with the g -and r -band photometry provided by Data Release 3 of theZwicky Transient Facility (ZTF, Masci et al. 2019), adding263 observations spanning 2018 April 9 throughout 2019 De-cember 29. The GTC spectra of SDSS J1219+4715 clearly resolve threecomponents of the H α emission line (Fig. 2, right panel),which can be identified as the σ − , π , and σ + triplet of H α within the linear regime of the Zeeman effect, i.e. where theexternal field removes the energy degeneracy with respectto the magnetic quantum number m l . However, the differ-ent widths of the three components imply that H α emis-sion originates within an environment with a field strength B where the Zeeman effect transitions into the quadraticregime, removing also the energy degeneracy with respectto the orbital angular momentum l , splitting H α into 15transitions (of which two have degenerate energies, henceonly 14 components can be observationally be detected,Henry & O’Connell 1985). The GTC spectra reveal a com-plex structure of multiple sharp emission features of H β (Fig. 2, left panel), which transitions into the quadratic Zee-man regime at lower fields compared to H α . We over-plot inFig. 2 the wavelengths of the individual H α and H β transi-tions (Friedrich et al. 1996) as a function of B and find thatthe H α emission arises in a field of (cid:39) . MG. Whereas asmentioned above, H α still largely appears as a linear Zee-man triplet, we do detect the → transition which issplit off the other π components.The Zeeman components of H α and H β shift rapidly asa function of changing B -field, hence any substantial spreadin the B -field across the region in which the emission linesarise would smear them out in wavelength. The sharpness ofthe H α π components and of the H β emission lines implies ahomogeneous field within the emitting region. We indicatein Fig. 2 the locations of the individual Zeeman componentsfor B = . MG (green ticks) and B = . MG (blue ticks),and conclude that the H α and H β emission lines arise withina field of B (cid:39) . ± . MG. For a dipolar field structure onthe white dwarf, the field near the magnetic equator is afactor two lower than the polar field (Achilleos et al. 1992),which implies that the emission lines form in a relativelysmall region(s), most likely near the magnetic pole(s). Thisis very similar to the situation in GD356, where Greenstein& McCarthy (1985) measured B = ± . MG in the emit-ting region and Ferrario et al. (1997a) estimated that thisregion covers about ten per cent of the white dwarf sur-face. Similarly, Reding et al. (2020) derived B = . ± . MGfrom the emission lines in SDSS J1252 − H α emission(Section 3.4), we do not detect photospheric absorption linesfrom the white dwarf. At a field strength of (cid:39) . MG, thesplitting of the three Zeeman components would by far ex-ceed the pressure-broadening of the Balmer lines, in particu-lar for a white dwarf as cool as SDSS J1215+4715, and hencethe photospheric Balmer lines are usually easily visible (seee.g. fig. 9 of Greenstein & McCarthy 1985 and fig. A12 ofTremblay et al. 2020). Most likely, the photospheric absorp-tion lines are filled in by the emission lines and possibly somesmall amount of continuum flux originating from the sameregion – which in SDSS J1215+4715 remains visible through-out the spin cycle. We note that in SDSS J1252 − MNRAS , 1–12 (2019)
G¨ansicke et al.
Figure 2.
Normalised and averaged GTC spectra of SDSS J1219+4715, centred on H β (left) and H α (right). Shown in grey are thewavelengths of the individual Balmer line components as a function of field strength, which is given on the right-hand-side axis. The fieldstrength in SDSS J1219+4715 is near the transition between linear and quadratic Zeeman splitting for H α , and in the quadratic regimefor H β . The tick marks below the spectrum indicate the locations of the Balmer transitions in a field of 17.5 MG (green) and 19.5 MG(blue), illustrating that the spread in field strength within the region where the emission lines form is small, B (cid:39) . ± . MG. emitting region is self-eclipsed by the white dwarf for partsof the spin cycle, when the emission lines disappear and thephotospheric Balmer absorption lines become visible (Red-ing et al. 2020).
The standard technique to measure the atmospheric pa-rameters, effective temperature ( T eff ) and surface gravity( log g ), of hydrogen-atmosphere white dwarfs from mod-eling their Stark-broadened Balmer absorption lines (e.g.Bergeron et al. 1992; Finley et al. 1997) is problematic inmagnetic white dwarfs, as the simultaneous effect of electricand magnetic fields on the energy levels of hydrogen cannotyet be satisfactorily computed (Jordan 1992; Friedrich et al.1994). In the case of the three magnetic white dwarfs dis-cussed here, a spectroscopic analysis of their atmospheric pa-rameters is further complicated by the fact that the Balmeremission lines partially or fully fill in the photospheric ab-sorption lines.Nonetheless, at the moderate magnetic field strengthsfound at these white dwarfs, the overall spectral energy dis-tribution of a star should not be significantly affected and,given an accurate distance measurement, T eff and log g canbe reliably determined from broad-band photometry alone(e.g. Koester et al. 1979) when also making use of the well-established mass-radius relation of white dwarfs (Panei et al.2000; Tremblay et al. 2017; Parsons et al. 2017; Joyce et al.2018; Chandra et al. 2020). Gentile Fusillo et al. (2019)adopted this method to estimate atmospheric parameters forGD356, SDSS J1252 − Gaia photometry and astrometry, and non-magnetic whitedwarf model atmospheres. In the temperature range of thesethree stars, non-magnetic white dwarfs with hydrogen-richatmospheres develop convection zones. The effect of mag-netic fields on convection has been discussed at length forsolar-like stars (e.g. Weiss 1966; Chaplin et al. 2011). In thecontext of white dwarfs, it has been argued both on the-oretical (Tremblay et al. 2015) and observational grounds (Gentile Fusillo et al. 2018) that the presence of fields in ex-cess of B (cid:39) − kG suppresses convection, which resultsin an altered temperature structure within the atmospherecompared to weakly- or non-magnetic white dwarfs. For thefields considered here ( B (cid:39) − MG, Table 1), convectionwill be fully suppressed.We have therefore re-derived the atmospheric parame-ters of the three stars fitting non-magnetic, purely radiativemodel spectra computed by enforcing a convective flux ofzero when solving for the atmospheric stratification (Gen-tile Fusillo et al. 2018). We retrieved
GALEX ( nuv , Mar-tin et al. 2005), SDSS ( ugriz , Albareti et al. 2017) andPanSTARRS ( grizy , Chambers et al. 2016) photometry forGD356, SDSS J1252 − Gaia parallaxes and correctedfor reddening using E ( B − V ) values from the 3D STructuringby Inversion the Local Interstellar Medium (STILISM) red-dening map (Lallement et al. 2018). We used a χ minimisa-tion routine to find the best fitting models and determinedthe T eff and log g of the three white dwarfs. As part of thisprocedure, we noted a marked discrepancy between the ob-served and predicted photometry in the SDSS- u band. Thisfilter covers the wavelength range − ˚A and is there-fore very sensitive to flux changes in the Balmer jump, whichare likely to arise from two separate effects. On the one hand,the presence of a magnetic field likely affects the profile ofthe Balmer jump in a way our models cannot reproduce. Onthe other hand, it is likely that the region responsible forthe emission lines contributes also some small level of con-tinuum flux associated with the bound-free opacity of hy-drogen, κ bf . As κ bf ∝ λ up to the ionisation threshold of theconsidered energy level, this continuum emission is expectedto contribute in particular at wavelengths blue-wards of theBalmer jump. We therefore decided to exclude the SDSS- u band photometry in our final fits.The atmospheric parameters are reported in Table 1,along with the corresponding white dwarf masses and cool-ing ages, which we calculated using evolutionary models MNRAS000
GALEX ( nuv , Mar-tin et al. 2005), SDSS ( ugriz , Albareti et al. 2017) andPanSTARRS ( grizy , Chambers et al. 2016) photometry forGD356, SDSS J1252 − Gaia parallaxes and correctedfor reddening using E ( B − V ) values from the 3D STructuringby Inversion the Local Interstellar Medium (STILISM) red-dening map (Lallement et al. 2018). We used a χ minimisa-tion routine to find the best fitting models and determinedthe T eff and log g of the three white dwarfs. As part of thisprocedure, we noted a marked discrepancy between the ob-served and predicted photometry in the SDSS- u band. Thisfilter covers the wavelength range − ˚A and is there-fore very sensitive to flux changes in the Balmer jump, whichare likely to arise from two separate effects. On the one hand,the presence of a magnetic field likely affects the profile ofthe Balmer jump in a way our models cannot reproduce. Onthe other hand, it is likely that the region responsible forthe emission lines contributes also some small level of con-tinuum flux associated with the bound-free opacity of hy-drogen, κ bf . As κ bf ∝ λ up to the ionisation threshold of theconsidered energy level, this continuum emission is expectedto contribute in particular at wavelengths blue-wards of theBalmer jump. We therefore decided to exclude the SDSS- u band photometry in our final fits.The atmospheric parameters are reported in Table 1,along with the corresponding white dwarf masses and cool-ing ages, which we calculated using evolutionary models MNRAS000 , 1–12 (2019) ingle magnetic white dwarfs with Balmer emission lines for thick hydrogen layers . We discuss the interpretation ofthe cooling ages in the context of the possible evolution-ary history of these stars further in Sect. 4.3. We note thatthe parameters derived here for SDSS J1252 − T eff = ± K, log g = . ± . ) differ somewhat from thoseof Reding et al. (2020) ( T eff = ± K, log g = . ± . ),who used convective atmosphere models, and did not makeuse of the GALEX nu v fluxes.We caution that there is one caveat to the white dwarfparameter determination: additional continuum flux associ-ated with the observed emission lines will affect the fits,most likely resulting (via the scaling factor) in slightlyoverestimated radii, and hence underestimated masses.SDSS J1252 − (cid:39) per cent peak-to-peak in a BG40 blue broadbandpass) and is also the only system where the emissionlines disappear for a part of the white dwarf spin cycle, sug-gesting that the emitting region is self-eclipsed behind thewhite dwarf. Taking nine per cent as a conservative upperlimit on the continuum flux contribution (some of the ob-served photometric variability may be associated with inho-mogeneous emission across the surface of the magnetic whitedwarfs), our white dwarf radii might be over-estimated bythree per cent, corresponding to masses under-estimated byup to (cid:39) .
028 M (cid:12) . We note that this is the most extremecase, adopting the largest amplitude observed among thethree stars and assuming that it is entirely related to ad-ditional emission in excess of the photospheric white dwarfflux. A quantitative assessment of this potential effect willbe extremely difficult as it will require high-quality, accu-rately flux-calibrated, spin-phase resolved spectroscopy, andphysically correct models for both the magnetic white dwarfphotosphere and the emission region.
There is no evidence for a stellar companion at optical wave-lengths. To place an upper limit on the presence of a substel-lar or planetary companion, we complemented the
GALEX ( nuv ), SDSS ( g riz ), and Pan-STARRS ( g riz y ) photometryused in Section 3.2 (where we exclude again the SDSS- u bandfor the reasons discussed above) with the WISE ( W , W )bands (Wright et al. 2010). The reconstructed spectral en-ergy distribution of SDSS J1219+4715 was fitted using amodel accounting for both the white dwarf flux and thatof a possible low-mass stellar or substellar companion.For the white dwarf, we used the best-fit radiative modelspectrum ( T eff , wd = K, log g = . , see Table 4.1). Forthe companion, we retrieved a grid of AMES-Cond 2000models (Allard et al. 2001; Baraffe et al. 2003) for browndwarfs from the Theoretical Spectra Web Server . The gridcovered the range T eff = − K in steps of
K for Z = Z (cid:12) and a surface gravity log g = . The latter was eval-uated considering WD 0806–661, a white dwarf with a simi- ∼ bergeron/CoolingModels. http://svo2.cab.inta-csic.es/theory/newov2/index.php?models=cond00 Wavelength [ m ] F l u x [ m J y ] White dwarf onlyWhite dwarf + brown dwarf
GALEX nuv
SDSS g SDSS r SDSS i SDSS z PanSTARRS g PanSTARRS r PanSTARRS i PanSTARRS z PanSTARRS yWISE WISE Figure 3.
Spectral energy distribution of SDSS J1219+4715showing the photometry obtained by the different surveys(coloured points). Shown in cyan is a composite model of thebestˆa ˘A¸Sfit white dwarf ( T eff , wd = K, log g = . , see Sec-tion 3.2) and a brown dwarf companion (blue) with effective tem-perature T eff , bd (cid:39) K, while the red curve shows the white dwarfonly. lar age to SDSS J1219+4715, which has a wide planet-masscompanion, M P = J (Luhman et al. 2011). We then as-sumed a typical radius for the given mass and age, R = . (cid:12) (see e.g. fig. 3 from Burrows et al. 2011).We performed the spectral fit using the Markov chainMonte Carlo (MCMC) implementation for Python, emcee (Foreman-Mackey et al. 2013), constraining the white dwarfand the companion to be located at the same distance.The best-fit model is shown in Fig. 5 (cyan) and impliesa brown dwarf companion (blue) with effective temperature T (cid:39) K. However, only accounting for the presence ofthe white dwarf (red) allows to adequately reproduce theobserved flux level in the
WISE filters. Our result thus rep-resents an upper limit on the effective temperature of a pos-sible companion to SDSS J1219+4715.
The combined LT and ZTF light curve of SDSS J1219+4715extends from 2018 March 25 to 2020 July 6, with a to-tal of 437 photometric epochs. We computed a discreteFourier transform of the photometry using the tsa contextwithin midas . The resulting amplitude spectrum (Fig. 4,left panel) shows a number of sharp signals spaced outby one-day aliases that are typical of single-site observa-tions. The strongest alias corresponds to a period of P = . ± . h, where the uncertainty was determinedfrom a sine fit to the data. We subjected the photometricdata to a bootstrap test (see Southworth et al. 2006, 2007)and found a 99.9 per cent likelihood that the strongest aliascorrectly identifies the underlying period. Pre-whitening thelight curve with that period and computing a new amplitudespectrum completely removes all significant signals (Fig. 4,left panel).The limits on the mass and luminosity of a companionto SDSS J1219+4715 (Section 3.3) rule out that the photo-metric modulation is associated with binarity, and the most MNRAS , 1–12 (2019)
G¨ansicke et al.
Figure 4.
Amplitude spectrum (left panel, computed from the combined ZTF and LT data) and the light curve of SDSS J1219+4715phase-folded on the 15.26-h period (right panel, LT data only). The red and blue tickmarks above the folded light curve indicate thephases of the H α and H β spectra obtained with the GTC, respectively. The amplitude spectrum (black) shows a complex pattern ofaliases, reflecting the window function of the combined ZTF and LT observations. Shown in light blue are the data pre-whitened witha sine wave of P = . h. No signal exceeding the significance threshold (blue dashed line) is detected after the window function isremoved. Figure 5.
Normalised GTC H α spectra of SDSS J1219+4715 ob-tained close to the photometric minimum (red) and maximum(black). The strength of the emission lines varies in anti-phasewith the broad-band photometry, however, the Zeeman compo-nents do not shift in wavelength. likely interpretation is that it reflects the spin period of thewhite dwarf.The phase-folded light curve of SDSS J1219+4715(Fig. 4, right panel) shows a symmetric parabola-shapedminimum that extends in phase, ∆ φ (cid:39) . . Whereas the ZTF g - and r -band data, because of their long baseline, are usefulin improving the accuracy of the spin period, their photo-metric precision is insufficient to assess any colour depen-dence of the modulation.We established a photometric ephemeris forSDSS J1219+4715 where phase zero corresponds tothe minimum brightness of the system, T ( HJD ) = . ( ) + . ( ) × E . (1) We determined the zero-point by fitting a parabola to thebroad minimum in the phase-folded light curve. Using thisephemeris, we computed the phases of the GTC spectra (seeFig. 4, left panel). While our spectroscopic sampling of thespin phase is limited, the data suggest that the strength ofthe emission lines varies in anti-phase with the photome-try, i.e. the H α emission is strongest during the photometricminimum (Fig. 5). We integrated the H α emission line fluxesafter subtracting the underlying continuum using a polyno-mial fit, and find that the strength of the H α emission linevaries from ( . ± . ) × − erg cm − s − near the photo-metric minimum ( φ = . ) to ( . ± . ) × − erg cm − s − near the photometric maximum ( φ = . ). Adopting anaverage H α flux of . × − erg cm − s − results in a lumi-nosity of L ( H α ) (cid:39) . × erg s − , which is almost iden-tical to the (cid:39) × erg s − reported by Greenstein &McCarthy (1985) for GD356. Also the emission-line fluxof H β varies in anti-phase with the photometric modu-lation, ( . ± . ) × − erg cm − s − at φ = . and ( . ± . . ) × − erg cm − s − at φ = . (the latter spec-trum being rather noisy as it was taken under poor con-ditions). We note that the same anti-phased behaviour be-tween the emission lines and the broad-band continuum wasobserved in SDSS J1252 − MNRAS000
Normalised GTC H α spectra of SDSS J1219+4715 ob-tained close to the photometric minimum (red) and maximum(black). The strength of the emission lines varies in anti-phasewith the broad-band photometry, however, the Zeeman compo-nents do not shift in wavelength. likely interpretation is that it reflects the spin period of thewhite dwarf.The phase-folded light curve of SDSS J1219+4715(Fig. 4, right panel) shows a symmetric parabola-shapedminimum that extends in phase, ∆ φ (cid:39) . . Whereas the ZTF g - and r -band data, because of their long baseline, are usefulin improving the accuracy of the spin period, their photo-metric precision is insufficient to assess any colour depen-dence of the modulation.We established a photometric ephemeris forSDSS J1219+4715 where phase zero corresponds tothe minimum brightness of the system, T ( HJD ) = . ( ) + . ( ) × E . (1) We determined the zero-point by fitting a parabola to thebroad minimum in the phase-folded light curve. Using thisephemeris, we computed the phases of the GTC spectra (seeFig. 4, left panel). While our spectroscopic sampling of thespin phase is limited, the data suggest that the strength ofthe emission lines varies in anti-phase with the photome-try, i.e. the H α emission is strongest during the photometricminimum (Fig. 5). We integrated the H α emission line fluxesafter subtracting the underlying continuum using a polyno-mial fit, and find that the strength of the H α emission linevaries from ( . ± . ) × − erg cm − s − near the photo-metric minimum ( φ = . ) to ( . ± . ) × − erg cm − s − near the photometric maximum ( φ = . ). Adopting anaverage H α flux of . × − erg cm − s − results in a lumi-nosity of L ( H α ) (cid:39) . × erg s − , which is almost iden-tical to the (cid:39) × erg s − reported by Greenstein &McCarthy (1985) for GD356. Also the emission-line fluxof H β varies in anti-phase with the photometric modu-lation, ( . ± . ) × − erg cm − s − at φ = . and ( . ± . . ) × − erg cm − s − at φ = . (the latter spec-trum being rather noisy as it was taken under poor con-ditions). We note that the same anti-phased behaviour be-tween the emission lines and the broad-band continuum wasobserved in SDSS J1252 − MNRAS000 , 1–12 (2019) ingle magnetic white dwarfs with Balmer emission lines in the photospheric spectrum due to the changing viewinggeometry of the magnetic field distribution. Accurate, si-multaneous spectroscopic (ideally spectropolarimetric) andphotometric observations will be required to disentangle thevariability intrinsic to the white dwarf and the associatedwith the emitting region. Inspection of the physical characteristics of GD356,SDSS J1252 − Gaia
Hertzsprung-Russell diagram(Fig. 6) shows they cluster closely in effective temperature( (cid:39) − K), mass ( (cid:39) . − .
73 M (cid:12) ), cooling age( (cid:39) . − . Gyr), and magnetic field strength ( (cid:39) − MG)when compared to the full parameter space occupied bywhite dwarfs. The tangential velocities of the three starsare (cid:39) − km s − , well within the range of white dwarfswith similar cooling ages (e.g. McCleery et al. 2020), consis-tent with thin disc membership, and not indicative of anymajor dynamical interactions in their past lives. A notice-able exception are their spin periods, which span over twoorders of magnitude. Non-magnetic single white dwarfs havetypical rotation periods of several tens of hours, with veryfew stars known to spin faster than (cid:39) h (Hermes et al.2017a). SDSS J1252 − H α line fluxes from the GTC average spectrum by sub-tracting the continuum via a polynomial fit. We then pro-duced a set of DA white dwarf models with log g = . andtemperatures ranging from 6000 K to 10 000 K, scaled themto a distance of 69.6 pc, and added Gaussian noise to emu-late the data quality of the GTC spectra. Finally, we addedthe observed emission-line fluxes to the (noisy) white dwarfmodels, and subjected them both to a visual inspection andan equivalent width measurement of the H α region. The con-clusion from this exercise was that the H α line fluxes seenin SDSS J1219+4715 would be detectable in white dwarfswith temperatures of up to (cid:39) K – corresponding to acooling age of (cid:39) Gyr, or (cid:39) % of the present cooling ageof SDSS J1219+4715. Assuming that the mechanism thatgenerates the emission lines is always active, there is hencea reasonably long period of time where they could be de-tected at slightly hotter effective temperatures, and a similarreasoning holds true for the other two systems. It thereforeappears somewhat coincidental that all three white dwarfsare found at ages which are clearly past the detection thresh- old – and there is no shortage of slightly hotter and youngermagnetic white dwarfs (Fig. 6).However, the question of observational selection effectsbecomes more problematic at lower temperatures – as thewhite dwarf luminosity decreases, it should be easier to de-tect emission lines of similar strength among cooler magneticwhite dwarfs. There is a substantial number of magneticwhite dwarfs with T eff (cid:46) K, and emission lines were de-tected in none of those (Ferrario et al. 2015; Hollands et al.2015, 2017; Landstreet & Bagnulo 2019b; McCleery et al.2020; Kawka 2020). It appears hence that the mechanismcausing the emission lines in the three stars discussed hereis no longer active among cooler magnetic white dwarfs.Thus, taking the clustering of these three stars at facevalue suggests that whatever the mechanism responsible forthe emission lines is, it becomes active at T eff (cid:39) K,and is relatively short-lived, (cid:39) . − Gyr. A quick com-parison of the rotational kinetic energy of the white dwarfswith the estimated luminosity of the emission lines rules outthat the emission process itself results in a sufficiently rapidspin-down of the white dwarf that might eventually stop themechanism. Within the unipolar inductor model involving aplanet in a close-in orbit, the limited life time of the planetdue to ohmic dissipation may provide a natural explanationfor this short duration (Li et al. 1998; Veras & Wolszczan2019). However, the late appearance of this effect along thewhite dwarf cooling track still remains a mystery.
The detection of photospheric emission lines from sin-gle white dwarfs is extremely rare, with the exceptionof extremely hot and young (pre-) white dwarfs (e.g.Werner 1991; Werner et al. 1991) and a number of helium-atmosphere white dwarfs with T eff (cid:39)
14 000 −
17 000
K (Kleinet al. 2020) – in both cases, the presence of the emissionlines is intrinsic to their atmospheric structures.To our knowledge, only the following seven cooler whitedwarfs display noticeable emission lines: the three magneticwhite dwarfs discussed here (optical Balmer lines, Table 1),one nearby white dwarf with weak, single-peaked H α emis-sion (Tremblay et al. 2020; McCleery et al. 2020) , onewhite dwarf accreting planetary debris (Ca ii H/K lines,PG 1225 − The sharp H α emission in WD J041246.85+754942.26 showedno radial velocity variation in observations obtained on three con-secutive nights, and the optical-to-infrared spectral energy distri-bution rules out a companion earlier than a T-type brown dwarf.At the moment, the origin of this emission line remains unex-plained, and the association with the stars discussed here un-clear. With T eff (cid:39) K, log g (cid:39) . , WD J0412+7549 lies closeto the three magnetic white dwarfs exhibiting Balmer line emis-sion, and one speculative hypothesis is that it might have a weakfield ( B (cid:46) kG). Additional observations of this white dwarfare encouraged.MNRAS , 1–12 (2019) G¨ansicke et al.
Table 1.
Stellar parameters of the three magnetic white dwarfs exhibiting Zeeman-split Balmer emission lines.Parameter GD356 SDSS J1252–0234 SDSS J1219+4715 ReferencesParallax (cid:36) [mas] 49.65 ± ± ± d [pc] 20.1 ± ± ± Gaia photometry G [mag] 14.9808 ± ± ± µ α [mas/yr] − ± ± − ± µ δ [mas/yr] − ± − ± − ± T eff [K] 7698 ±
74 7856 ±
101 7500 ±
148 3Surface gravity log g (cgs) 8.22 ± ± ± M wd [ M (cid:12) ] 0.733 ± ± ± τ cool [Myr] 1916 ±
144 1136 ±
95 1558 ±
124 3Magnetic field ∗ B [MG] 11 ± ± ± P [h] 1.9280 ± ± ± ∗ We report the measurements obtained from the emission lines, which correspond to the field strength in the emitting region. GaiaCollaboration et al. (2018); Bailer-Jones et al. (2018); this paper; Greenstein & McCarthy (1985); Reding et al. (2020); Brinkworthet al. (2004), we report the average and standard deviation of their two possible periods. G BP - G RP G a b s [ m a g ] M M M M K K K K K K K K L og B S [ M G ] Figure 6.
Hertzsprung-Russell diagram of the white dwarfswithin 100 pc (Gentile Fusillo et al. 2019), with those known tobe magnetic (Ferrario et al. 2015; Hollands et al. 2017; McCleeryet al. 2020) colour-coded by their field strength. The three mag-netic white dwarfs exhibiting Zeeman-split emission lines clus-ter extremely closely within the parameter space spanned by theoverall population of magnetic white dwarfs. White dwarf coolingtracks for a range of white dwarf masses are superimposed, withtemperatures along those tracks indicated as short vertical tickmarks. For comparison, the massive ( M wd (cid:39) . (cid:12) ), rapidly spin-ning ( P = s) and strongly magnetic ( B (cid:39) − MG) whitedwarf CL Oct which is discussed as a merger product (Barstowet al. 1995; Ferrario et al. 1997b; K¨ulebi et al. 2010), is shown asan orange star – clearly differing from the three stars discussedhere. magnetic field in GD356 is suppressing convection (Trem-blay et al. 2015; Gentile Fusillo et al. 2018), chromosphericactivity is unlikely.Sharp photospheric emission lines are indeed detectedamong a number of close binaries containing an accreting white dwarf. Examples include several AM CVn systems,ultra-short period binaries consisting of a cool white dwarfaccreting from an extremely low-mass degenerate donor(Marsh 1999; Kupfer et al. 2016), and detached white dwarfplus M-dwarf binaries, in which the white dwarf accretesfrom the stellar wind of its companion (Tappert et al. 2007,2011). One characteristic that all these systems have in com-mon is that they harbour ( (cid:46)
10 000
K) cool white dwarfsthat accrete at relatively low rates, and whereas no quanti-tative model has been developed, it appears likely that it isthe energy deposited by the accreted material that resultsin a temperature inversion in the white dwarf atmosphere,resulting in the observed emission lines.The system that bears most resemblance tothe three magnetic white dwarfs discussed here isSDSS J030308.35+005444.1, a short-period detachedbinary containing a ( (cid:46)
K) cool white dwarf plusan M-dwarf (Pyrzas et al. 2009). Parsons et al. (2013)detected Zeeman-split Balmer emission lines, derived a fieldstrength of (cid:39) MG, and argued that the emission linesare caused by accretion of wind captured by the whitedwarf and funnelled towards its magnetic pole(s). A keyfeature of accretion onto magnetic white dwarfs is that theshock-heated plasma near the white dwarf surface also emitscyclotron radiation (Visvanathan & Wickramasinghe 1979;Woelk & Beuermann 1992). At field strengths of ∼ MG,the cyclotron emission lines are located in the near-infrared,and are indeed detected in SDSS J030308.35+005444.1 asan infrared excess over the M-dwarf (Debes et al. 2012).Given their field strengths of − MG (Table 1), ac-cretion onto the three single magnetic white dwarfs withZeeman-split Balmer emission lines should equally resultin cyclotron emission, with an associated infrared excess –which is, however, detected in none of them. This stronglyargues against ongoing accretion as the cause for the ob-served emission lines. This extends the conclusions of Weis-skopf et al. (2007), who placed an upper limit on the X-rayluminosity of GD356 of L x ≤ × erg s − , and already ar-gued that the non-detection of an infrared excess at GD356is inconsistent with the possible presence of a hot corona as asource of the Balmer emission lines (see also Musielak et al.1995 for an earlier X-ray study of GD356 and Ferrario et al.1997a for an additional discussion arguing against ongoing MNRAS000
K) cool white dwarf plusan M-dwarf (Pyrzas et al. 2009). Parsons et al. (2013)detected Zeeman-split Balmer emission lines, derived a fieldstrength of (cid:39) MG, and argued that the emission linesare caused by accretion of wind captured by the whitedwarf and funnelled towards its magnetic pole(s). A keyfeature of accretion onto magnetic white dwarfs is that theshock-heated plasma near the white dwarf surface also emitscyclotron radiation (Visvanathan & Wickramasinghe 1979;Woelk & Beuermann 1992). At field strengths of ∼ MG,the cyclotron emission lines are located in the near-infrared,and are indeed detected in SDSS J030308.35+005444.1 asan infrared excess over the M-dwarf (Debes et al. 2012).Given their field strengths of − MG (Table 1), ac-cretion onto the three single magnetic white dwarfs withZeeman-split Balmer emission lines should equally resultin cyclotron emission, with an associated infrared excess –which is, however, detected in none of them. This stronglyargues against ongoing accretion as the cause for the ob-served emission lines. This extends the conclusions of Weis-skopf et al. (2007), who placed an upper limit on the X-rayluminosity of GD356 of L x ≤ × erg s − , and already ar-gued that the non-detection of an infrared excess at GD356is inconsistent with the possible presence of a hot corona as asource of the Balmer emission lines (see also Musielak et al.1995 for an earlier X-ray study of GD356 and Ferrario et al.1997a for an additional discussion arguing against ongoing MNRAS000 , 1–12 (2019) ingle magnetic white dwarfs with Balmer emission lines accretion). No X-ray observations of the other two stars dis-cussed here are available.With both chromospheric activity and accretion beingunlikely to be the cause for the Balmer emission lines in thesethree magnetic white dwarfs, the unipolar inductor model(Li et al. 1998; Wickramasinghe et al. 2010) remains cur-rently the only plausible explanation. This model requires aconductive planet or planet core in a close orbit around eachof the three stars, which, in the light of the detections of solidplanetesimals (Vanderburg et al. 2015; Manser et al. 2019;Vanderbosch et al. 2020) as well as giant planets (G¨ansickeet al. 2019), appears entirely feasible. The fact that all threestars discussed here are relatively nearby ( d (cid:46) pc) impliesthat such configurations of evolved planetary systems maynot be exceedingly rare. Wickramasinghe et al. (2010) and Reding et al. (2020) ar-gued that GD356 and SDSS J1252 − , < M wd > (cid:39) .
65 M (cid:12) (Giammichele et al. 2012; Hollandset al. 2018; Tremblay et al. 2020), and hence if produced bydouble-degenerate mergers, the progenitor binaries wouldhave contained two He-core white dwarfs. Detailed hydro-dynamical simulations of double-degenerate mergers showthat He-core mergers eject very little mass ( (cid:46) × − M (cid:12) ).This implies that the total masses of the double-degeneratesthat merged were very close to the masses measured for thethree magnetic white dwarfs, i.e. (cid:39) . − .
73 M (cid:12) .Inspecting the roster of double-degenerates with mea-sured masses for both components (Rebassa-Mansergaset al. 2017; Breedt et al. 2017; Napiwotzki et al. 2020) sug-gests that potential progenitor systems matching the top-end of the mass range spanned by the three magnetic sys-tems are known, but that they are rare – and their mergertime scales are typically exceeding a Hubble time (Geieret al. 2010). Given the large observational bias favouring theidentification of lower mass white dwarfs (because of theirlarger radii), the scarcity of progenitors is exacerbated. Wenote that progenitors containing one extremely low mass(ELM) white dwarf are even less likely, as the total massesof the known ELM binaries peak at (cid:39) (cid:12) (Brown et al.2016), and as ELM binaries are intrinsically rare (Kawkaet al. 2020). The average white dwarf mass in a magnitude-limited sample isslightly lower, < M wd > (cid:39) . (cid:12) , as lower mass white dwarfs arelarger and hence can be detected out to larger distances (Koesteret al. 1979; Bergeron et al. 1992, 2019; Tremblay et al. 2019). Exceptions exist, but are extremely rare (Brown et al. 2020).
One additional potential issue with invoking second-generation planets forming out of the ejected material isthat Garc´ıa-Berro et al. (2007) modelled a CO+He merger.It is not clear if a He+He merger would result in sufficientlymetal-rich ejecta to form a conductive, second-generationplanet.Assuming nevertheless a merger origin for these threemagnetic white dwarfs, the characteristics of the known pop-ulation of double-degenerates would suggest that a largernumber of similar systems with resulting masses for themerger product of (cid:39) . − . (cid:12) should exist – yet none hasbeen found so far. Moreover, it would appear very coinci-dental that these three stars share many of their properties,in particular their effective temperatures and cooling ages,as discussed in the previous section. A double-degeneratemerger will result in a re-heated and possibly strongly mag-netic white dwarf (Garc´ıa-Berro et al. 2012; Wegg & Phinney2012), such as it may be the case for CL Oct (see Fig. 6, Fer-rario et al. 1997b). If the Balmer line mechanism in such asystem is active, it should be detectable before it cools downto (cid:39) K (Section 4.1 and Fig. 6).We conclude that while a double-degenerate mergerorigin cannot be ruled out, the clustered properties ofthese three magnetic white dwarfs and the sufficiently dis-parate characteristics of the known double-degenerates ar-gue against it. One final note concerns the cooling ages cal-culated in Sect. 3.2. In the case of a double-degenerate evo-lution history, these would approximate the time since themerger event (Wegg & Phinney 2012; Temmink et al. 2020),but that would change none of our arguments regarding thetight clustering of the three stars in their physical propertiesoutlined above and in Sect. 4.1.
Our argument against double-degenerate mergers leaves uswith the question: how can some single white dwarfs reachvery short periods, such as SDSS J1252 − We have identified SDSS J1219+4715 as an additional mag-netic white dwarf exhibiting Zeeman-split Balmer emissionlines and photometric variability with a 15.26-h period,which we interpret as being related to the white dwarf ro-tation. The upper limit on the temperature of a possiblesubstellar or giant planet companion is (cid:39)
K. The emis-sion lines originate in a region with a fairly homogeneous
MNRAS , 1–12 (2019) G¨ansicke et al. field strength of B (cid:39) . ± . MG. Whereas the emis-sion lines vary in flux over the white dwarf spin phase bya factor approximately four, they always remain visible,indicating that the emitting region never fully disappearsbehind the limb of the white dwarf. With a temperatureof ± K, a mass of . ± .
022 M (cid:12) , and a cool-ing age of . ± . Gyr, SDSS J1219+4715 very closely re-sembles the other two members of this small class of stars:GD356 and SDSS J1252 − (cid:39) . Gyr, (b) lasts (cid:39) . − . Gyr, and (c) does not affect all magnetic whitedwarfs. Given the growing observational evidence for the ex-istence of planetesimals and planets in close orbits aroundwhite dwarfs, the unipolar inductor model developed forGD356 seems a plausible scenario that satisfies (b) and (c)above, however, the onset of the emission lines at advancedcooling ages remains unexplained. We encourage closer spec-troscopic scrutiny of the known magnetic white dwarfs withtemperatures − K to either detect additional exam-ples of this class of stars, or to place stringent upper limitson the presence of Balmer emission lines.
ACKNOWLEDGEMENTS
We thank Detlev Koester and Ken Shen for insight-ful discussions, and the referee S.O. Kepler for helpfulcomments. BTG was supported by the UK STFC grantST/T000406/1. PR-G acknowledges support from the StateResearch Agency (AEI) of the Spanish Ministry of Science,Innovation and Universities (MCIU), and the European Re-gional Development Fund (FEDER) under grant AYA2017–83383–P. The research leading to these results has receivedfunding from the European Research Council under the Eu-ropean Union’s Horizon 2020 research and innovation pro-gramme n. 677706 (WD3D). The use of the pamela and molly
DATA AVAILABILITY
All observational data used in this paper will be availablefrom the public data archives of the SDSS, LT, GTC, andZTF.
MNRAS000
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