Mysterious, Variable, and Extremely Hot: White Dwarfs Showing Ultra-High Excitation Lines I. Photometric Variability
Nicole Reindl, Veronika Schaffenroth, Semih Filiz, Stephan Geier, Ingrid Pelisoli, S. O. Kepler
AAstronomy & Astrophysics manuscript no. UHE © ESO 2021February 10, 2021
Mysterious, Variable, and Extremely Hot:White Dwarfs Showing Ultra-High Excitation Lines
I. Photometric Variability
Nicole Reindl , Veronika Scha ff enroth , Semih Filiz , Stephan Geier , Ingrid Pelisoli , , and S. O. Kepler Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24 /
25, D-14476 Potsdam, [email protected] Department of Physics, University of Warwick, Coventry, CV4 7AL, UK Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-900 Porto-Alegre, RS, BrazilReceived 6 January 2021 / Accepted 3 February 2021
ABSTRACT
Context.
About 10% of all stars exhibit absorption lines of ultra-high excited (UHE) metals (e.g. O viii ) in their optical spectra whenentering the white dwarf cooling sequence. This is something that has never been observed in any other astrophysical object, andchallenges our understanding of the late stages of stellar evolution since decades. The recent discovery of a both spectroscopic andphotometric variable UHE white dwarf led to the speculation that the UHE lines might be created in a shock-heated circumstellarmagnetosphere.
Aims.
We aim to gain a better understanding of these mysterious objects by studying the photometric variability of the whole popula-tion of UHE white dwarfs, and white dwarfs showing only the He ii line problem, as both phenomena are believed to be connected. Methods.
We investigate (multi-band) light curves from several ground- and space-based surveys of all 16 currently known UHEwhite dwarfs (including one newly discovered) and eight white dwarfs that show only the He ii line problem. Results.
We find that 75 + − % of the UHE white dwarfs, and 75 + − % of the He ii line problem white dwarfs are significantly photo-metrically variable, with periods ranging from a 0.22 d to 2.93 d and amplitudes from a few tenth to a few hundredth mag. The highvariability rate is in stark contrast to the variability rate amongst normal hot white dwarfs (we find 9 + − %), marking UHE and He ii line problem white dwarfs as a new class of variable stars. The period distribution of our sample agrees with both the orbital perioddistribution of post-common envelope binaries and the rotational period distribution of magnetic white dwarfs if we assume that theobjects in our sample will spin-up as a consequence of further contraction. Conclusions.
We found further evidence that UHE and He ii line problem white dwarfs are indeed related, as concluded from theiroverlap in the Gaia HRD, similar photometric variability rates, light curve shapes and amplitudes, as well as period distributions. Thelack of increasing photometric amplitudes towards longer wavelengths, as well as the non-detection of optical emission lines arisingfrom the highly irradiated face of a hypothetical secondary in the optical spectra of our stars, makes it seem unlikely that an irradiatedlate type companion is the origin of the photometric variability. Instead, we believe that spots on the surfaces of these stars and / orgeometrical e ff ects of circumstellar material might be responsible. Key words. (Stars:) white dwarfs, Stars: variables: general, (Stars:) starspots, binaries: close
1. Introduction
White dwarfs are the end products of the vast majority ofall stars, with about 20% of them being H-deficient. Theyare observed over a huge temperature interval, ranging from250 000 K (Werner & Rauch 2015) down to 2 710 K (Gianninaset al. 2015). The early stages of white dwarf cooling occur veryrapidly. When a star enters the white dwarf cooling sequence, itcools down to 65,000 K within less than a million years, whilethe cooling phase down to 3 000 K takes several billions of years(Althaus et al. 2009; Renedo et al. 2010). Thus, although about37 000 white dwarfs have been spectroscopically confirmed tothis day (Kepler et al. 2019), only a tiny fraction (less than 1%)have e ff ective temperatures ( T e ff ) above 65,000 K.These extremely hot white dwarfs cover a large but sparselypopulated region in the Hertzsprung-Russell Diagram (HRD)and represent an important link in stellar evolution between the(post-)asymptotic giant branch (AGB) stars, and the bulk ofthe white dwarfs on the cooling sequence. Several intriguing physical processes take place during the early stages of whitedwarf cooling that mark those stars as important astronomicaltools even beyond stellar evolution studies. The intense extremeultraviolet (UV) flood radiated from a very hot white dwarf canevaporate giant planets. A fraction of the evaporated volatilesmay then be accreted, which could lead to the pollution ofthe white dwarf atmosphere (Gänsicke et al. 2019; Schreiberet al. 2019). Thus, detailed abundance analyses of hot whitedwarfs bear the potential of reconstructing the compositionof exosolar gaseous planets. Some white dwarfs in the T e ff interval 58 000 −
85 000 K were found to display high abun-dances of trans-iron group elements (atomic number Z > ffi cient radiative levitationof those elements (Chayer et al. 2005; Hoyer et al. 2017,2018; Löbling et al. 2020). These stars serve as importantstellar laboratories to derive atomic data for highly ionizedspecies of trans-iron elements (Rauch et al. 2012, 2014b,a,2015b,a, 2016, 2017a,b). Hot white dwarfs have also proven Article number, page 1 of 24 a r X i v : . [ a s t r o - ph . S R ] F e b & A proofs: manuscript no. UHE to be powerful tools for Galactic archaeology and cosmology.They are employed to check a dependency of fundamentalconstants, i.e., the fine structure constant α , with gravity,(Berengut et al. 2013; Bainbridge et al. 2017; Hu et al. 2020),to derive the age of the Galactic halo (Kalirai 2012; Kilicet al. 2019) or to derive the properties of weakly interactingparticles via the hot white dwarf luminosity function (Isernet al. 2008; Miller Bertolami 2014; Miller Bertolami et al. 2014).A particularly ba ffl ing phenomenon that takes place at thebeginning of the white dwarf cooling sequence is the presence of(partly very strong) absorption lines of ultra-high excited (UHE)metals (e.g. N VII , O
VIII ) in the optical spectra of the hottestwhite dwarfs. The occurrence of these obscure features requiresa dense environment with temperatures of the order 10 K, byfar exceeding the stellar e ff ective temperature. A photosphericorigin can therefore be ruled out. Since some of the UHE linesoften exhibit an asymmetric profile shape, it was first suggestedthat those lines might form in a hot, optically thick stellar wind(Werner et al. 1995). Another peculiarity of these objects is, thatall show the Balmer or He II line problem, meaning that theirBalmer / He II lines are unusually deep and broad and cannot befitted with any model. There are also white dwarfs showing onlythe Balmer / He II line problem, but no UHE lines. In case of theH-rich (DA-type) white dwarfs it was found that the Balmer lineproblem is to some extent due to the neglect of metal opacitiesin the models (Werner 1996). But there are also cases in whichthe Balmer line problem persist, even when sophisticated mod-els are used (Gianninas et al. 2011; Werner et al. 2018b, 2019).For the He-dominated (DO-type) white dwarfs showing the He II line problem, however, even by the addition of metal opacitiesto the models does not help to overcome this problem. Since theHe II line problem is – without exception – observed in everyUHE white dwarf, a link between these two phenomena seemsvery likely (Werner et al. 2004). It is thought, that the He II lineproblem objects are related to the UHE white dwarfs and that thesame process is operating in these stars, but failing to generatethe UHE features (Werner et al. 2014).The Balmer / He II line problem makes it also di ffi cult – if not im-possible – to derive accurate temperatures, gravities, and spec-troscopic masses. Some objects show weak He I lines, that allowto constrain their T e ff to some degree. High-resolution UV spec-troscopy is available only for three UHE white dwarfs, whichwere analyzed by Werner et al. (2018a). They found that the T e ff derived by exploiting several ionization balances of UV metallines, agree with what can be estimated from the He I / He II ion-ization equilibrium in the optical. In addition the study revealedthat in these object light metals (C, N, O, Si, P, and S) are foundat generally subsolar abundances and heavy elements from theiron group (Cr, Mn, Fe, Co, Ni) with solar or over solar abun-dances. This is not di ff erent from other hot white dwarfs andcan be understood as a result of gravitational settling and radia-tive levitation of elements. Werner et al. (2018a) discussed thepossibility that the UHE lines might form in a multicomponentradiatively driven wind that is frictionally heated. Such windsare expected to occur in a narrow strip in the T e ff -log g -diagram(Fig. 4 in Krtiˇcka & Kubát 2005), which indeed overlaps with theregion in which the UHE white dwarfs are observed (see Fig. 3in Reindl et al. 2014).While this strip could explain why the occurrence of UHE fea-tures is restricted to white dwarfs hotter than ≈
65 000 K, themodel does not explain why not all hot white dwarfs locatedin this region show this phenomenon. In addition, the friction-ally heated wind model, that assumes a spherically-symmetric wind, fails to explain the photometric and spectroscopic variabil-ity of the UHE white dwarf J01463 + + ≈ .
24 d). Interpreting this pe-riod as the rotational period of the star, they argue that the UHEfeatures are rotationally modulated and stem from a co-rotating,shock-heated, circumstellar magnetosphere. Furthermore, theysuggested that the cooler parts of the magnetosphere likely con-stitute an additional line forming region of the too-broad andtoo-deep He II lines (or Balmer lines in case of DAs). Whitedwarfs which lack the UHE lines and only show the Balmer / He II line problem could then be explained by having cooler magne-tospheres with temperatures not high enough to produce UHElines. Since this model requires the white dwarfs to be at leastweakly magnetic (meaning that they should have magnetic fieldstrengths above a few hundred to thousand Gauss), it could alsoexplain why only a fraction of the hottest white dwarfs showsUHE lines.The UHE phenomenon a ff ects about 10% of all stars in the uni-verse when entering the white dwarf cooling sequence, thus abetter understanding of these objects is highly desirable. Here,we aim to study the properties of the UHE white dwarfs, as wellas their relatives – white dwarfs showing only the He ii line prob-lem – as a whole. In particular, we desire to find out if the photo-metric and spectroscopic variability observed in J0146 + ff ects all UHE white dwarfs, and possibly alsothe He ii line problem white dwarfs. This article is the first partof a series of papers and introduces the sample of UHE and He II line problem white dwarfs and investigates their photometricvariability. In Sect. 2 we first present the sample and discuss thelocation of these stars in the Gaia HRD. Then we search for pho-tometric variability using light curves from various ground- andspace-based surveys (Sect. 3). The overall results of this studyare presented in Sect. 4. Finally, we will discuss our findings(Sect. 5) and give an outlook on how more progress can be made(Sect. 6).
2. The sample of UHE and He ii line problem whitedwarfs The first two UHE white dwarfs, the DO-type white dwarfsHS 0713 + + + + + − R ≈
18 500, ProgID 167.D-0407(A), PI: R. Napiwotzki), wedetect for the first time UHE lines around 3872, 4330, 4655,
Article number, page 2 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Table 1.
Names, spectral types, J2000 coordinates, observed Gaia eDR3 G band magnitudes, distances, Gaia extinction coe ffi cients, dereddenedGaia color indexes, and the absolute dereddened G band magnitudes of all known UHE white dwarfs and white dwarfs showing only the He IIline problem. Name Spectral RA DEC G d A G ( BP − RP ) M G type J2000 J2000 [mag] [pc] [mag] [mag] [mag]UHE white dwarfsSDSSJ003213.14 + ( a ) DOZ*V UHE 8.05472 16.07633 15.75 413 + − − ( b ) DOZ*V UHE 16.06273 -18.02916 15.74 398 + − + ( c ) DO*V UHE 26.65308 32.60403 15.54 331 + − + ( d , e ) DO*V UHE 30.36338 23.83134 16.97 476 + − + ( f ) DO*V UHE 43.51563 0.98173 17.41 764 + − − ( g, h ) DO UHE 76.57540 -24.06685 15.69 468 + − + ( e ,g, h ) DO*V UHE 109.26134 39.88989 16.56 654 + − + ( d , h ) DO*V UHE 112.83912 59.96028 16.09 426 + − + ( e ) DO UHE 116.85481 65.21699 15.73 332 + − + ( a ) DA UHE 135.09954 23.73146 18.74 2133 + − + ( i ) DOZ*V UHE 164.98336 40.72568 18.31 2499 + − + ( f ) DOZ*V UHE 183.84619 12.05022 18.14 1402 + − + ( a ) DA*V UHE 194.35026 42.34845 17.44 889 + − + ( f ) DO*V UHE 227.61031 61.11581 17.26 786 + − + ( d ) DO*V UHE 307.38544 7.01881 16.62 524 + − + ( d , i , h ) DAO*V UHE 319.57804 12.02558 16.44 523 + − + ( i ) DOZ*V UHE: 125.39562 17.65539 19.01 1173 + − + ( i ) DO UHE: 126.85192 58.98104 17.47 579 + − + ( i ) DOZ UHE: 146.84374 10.25657 18.00 898 + − + ( a ) DO*V UHE: 157.28044 25.66901 17.05 583 + − + ( j ) DOZ*V 199.35303 0.04380 16.01 321 + − + ( i ) DOZ*V 228.06540 6.86566 17.22 1019 + − + ( k ) DOZ*V 229.19388 73.86848 16.63 774 + − + ( f ) DO*V 238.48667 48.54126 18.61 1138 + − Notes. ( a ) Kepler et al. (2019) ( b ) This work ( c ) Reindl et al. (2019) ( d ) Dreizler et al. (1995) ( e ) Reindl et al. (2014) ( f ) Hügelmeyer et al. (2006) ( g ) Werneret al. (1995) ( h ) Werner et al. (2018a) ( i ) Werner et al. (2014) ( j ) Werner et al. (2004) ( k ) Dreizler & Heber (1998) I λ IV λ , T e ff =
90 000 K and C = .
003 (massfraction).Besides these 16 UHE white dwarfs, our sample includeseight more objects which show only the He II line problembut no clear sign of UHE lines. The prototype of this class ofstars is HE 1314 + + II line problem, respectively. For HS2027 + / STIS spectra are shown that were observed with theG430L and G750L gratings ( R ≈ R ≈ + + + + + Article number, page 3 of 24 & A proofs: manuscript no. UHE
Fig. 1.
Locations of the UHE white dwarfs (star symbols) and whitedwarfs showing only the He ii line problem (diamonds) in the GaiaHRD. Hot subdwarfs (triangles), SDSS white dwarfs (dots), as well aswhite dwarf-main sequence binaries (plus symbols) containing a veryhot ( T e ff ≥
50 000 K) white dwarf are also shown. The color codingindicates the e ff ective temperatures of the stars. and HE 1314 + / November2014 at the Calar Alto 3 . . + + . R ≈ − II line problem white dwarfsalong with their spectral types, J2000 coordinates, observed Gaiaearly DR3 G band magnitudes (Gaia Collaboration et al. 2016,2018), distances, d , Gaia extinction coe ffi cients, A G , the dered-dened Gaia color indexes, ( BP − RP ) , and the absolute dered-dened G band magnitudes. A spectral type DOZ UHE indicatesa He-rich white dwarf that shows photospheric metal lines inthe optical as well as UHE lines. A spectral subtype UHE: in-dicates an object with an uncertain identification of UHE lines.The distances have been calculated from the parallaxes (via 1 /π ),which we corrected for the zeropoint bias using the Python code provided by Lindegren et al. (2020) . Following Gentile Fusilloet al. (2019), we assume that the extinction coe ffi cient A G inthe Gaia G passband scales as 0 . × A V based on the nomi-nal wavelengths of the respective filters and the reddening ver-sus wavelength dependence employed by Schlafly & Finkbeiner(2011). Values for A V were obtained from the 3D dust map ofLallement et al. (2018) using the distance calculated from theGaia parallax of each object. Nine of our stars are located out-side of the Lallement et al. (2018) 3D dust map (that is starswith a distance from the Galactic plane of | z | (cid:38)
500 pc). Forthose we obtained A V from the 2D dust map of Schlafly &Finkbeiner (2011) and assumed that A G scales with a factor of1 − exp ( −| z | / ff erence in reddening obtained from thetwo methods varies by a factor of 0.65 to 2.24 for stars locatedwithin the 3D dust map ( −
500 pc < z <
500 pc). This demon-strates that an accurate determination is not easy. The color in-dies, ( BP − RP ) were calculated using Eq. 18 and 19 in GentileFusillo et al. (2019). The absolute Gaia magnitude in the G bandwas calculated via M G = G − A G + + × log(1 /π ), where π is the zero point corrected parallax in milli arcsec from the Gaiaearly DR3.In Fig. 1 we show the locations of the UHE white dwarfs (starsymbols) and white dwarfs showing only the He II line prob-lem (diamonds) that have parallaxes better than 20% in the GaiaHRD. Also shown are the locations of white dwarfs from theSDSS (dots) with Gaia parallaxes better than 5 % and a redden-ing smaller than E B − V < T e ff ≥
50 000 K) white dwarf primaryand have parallaxes better than 30 %.It can be seen that the UHE white dwarfs and white dwarfsshowing only the He II line problem overlap in a narrow re-gion ( − .
71 mag ≤ ( BP − RP ) ≤ − .
37 mag, and 7.19 mag ≤ M G ≤ .
43 mag). Both are located well below the hot sub-dwarf cloud and are just on top of the white dwarf banana . Italso becomes obvious, that the stars in our sample are amongstthe bluest objects. Most of the hot white dwarfs with an M-typecompanion are found at similar absolute magnitudes, but red-der colors. This is a consequence of the flux of the low masscompanion that significantly contributes to the flux in the opticalwavelength range. The only object from the sample of Rebassa-Mansergas et al. (2010) that directly lies on the white dwarfbanana is SDSS J033622.01-000146.7. For this object the latetype companion is not noticeable in the continuum flux (no in-creased flux at longer wavelengths) and also shows no absorptionlines from the secondary. Only the emission lines in the core ofthe Balmer series are seen, which originate from the close andhighly irradiated side of the cool companion. Two of our stars,the DA-type UHE white dwarf J1257 + + II line problem, are found at notice-ably redder colors ( − .
42 mag and − .
37 mag, respectively) thanthe rest of our sample. While J0827 + A g = .
32 mag, which mightbe underestimated by the 3D dust map, this is unlikely the casefor J1257 + A G = .
04 mag). Looking at the Gaia eDR3 https://gitlab.com/icc-ub/public/gaiadr3_zeropoint The term “white dwarf banana” was coined by Girven et al. (2011).Article number, page 4 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
RUWE (Renormalized Unit Weight Error) values of our stars,we find they all have a value close to one (indicating that thesingle-star model provides a good fit to the astrometric obser-vations), except for J1257 + + BP − RP = − .
58 mag (standard deviation σ = − .
08 mag), with the UHEwhite dwarfs being slightly bluer ( BP − RP = − .
60 mag, σ = − .
07 mag) than white dwarfs showing only the He II lineproblem ( BP − RP = − .
54 mag, σ = − .
08 mag). We alsofind that the mean dereddened absolute G band magnitude ofthe UHE white dwarfs with parallaxes better than 20% ( M G = .
76 mag, σ = − .
27 mag) is slightly brighter than that of whitedwarfs showing only the He II line problem ( M G = .
02 mag, σ = − .
56 mag).We note that 18 out of the 24 stars in our sample have a prob-ability of being a white dwarf (PWD) greater than 90% as de-fined by Gentile Fusillo et al. (2019). For the remaining objectsPWDs between 72% and 89% are found. The only object thatis not included in the catalog of Gentile Fusillo et al. (2019)is J0900 + − . ≤ M G ≤ .
3. Light curve analysis
The discovery of a photometric variability in the UHE whitedwarf J01463 + ii line problem white dwarfs. Here we want to investi-gate this possibility by searching for periodic signals in the lightcurves of these objects.For the analyses of the light curves we used the VARTOOLSprogram (Hartman & Bakos 2016) to perform a generalizedLomb-Scargle (LS) search (Zechmeister & Kürster 2009; Presset al. 1992) for periodic sinusoidal signals. We classify ob-jects that show a periodic signal with a false alarm probability(FAP) of log( FAP ) ≤ − − ≤ log( FAP ) < − FAP ) > − FAP ) ≤ − m ( t ) = A × sin (cid:32) π ( t − t ) P (cid:33) − B × cos (cid:32) π ( t − t ) P (cid:33) + m (1)to each light curve. By that we determine the peak-to-peak am-plitude of the light curve, which we define as the di ff erence be-tween the maximum and minimum of the fit. The same functionwas also used to estimate the uncertainties on the derived periodsby running a Di ff erential Evolution Markov Chain Monte Carlo (DEMCMC) routine (Ter Braak 2006) employing the -nonlinfitcommand. The number of accepted links was set to 10 000. Asinitial guesses we used the period obtained from the LS search,and for the remaining parameters the values from the killharmfit.In Table A.1 and Table A.2 we summarize the light curves usedin our analysis, data points of each light curve, mean magnitudein each band, the median value of each period and its uncer-tainty as calculated in the DEMCMC simulation, and amplitudesfor the UHE white dwarfs and white dwarfs showing only theHe II line problem, respectively. In the following we give now anoverview of the data sets used in our work (Sect. 3.1) and thenprovide notes on individual objects (Sect. 3.2). Light curves were obtained from various surveys as well as ourown observing campaign.
TESS
The Transiting Exoplanet Survey Satellite (TESS) scansthe sky with 26 segments and with a 27.4 day observing pe-riod per segment. TESS uses a red-optical bandpass covering thewavelength range from about 6000 to 10 000 Å and which is cen-tered on 7865 Å, like the traditional Cousins I-band. We down-loaded the target pixel files (TPF) of each object from MASTas FITS format. The FITS files are already processed based onthe Pre-Search Data Conditioning Pipeline (Jenkins et al. 2016)from where we have extracted the barycentric corrected dynami-cal Julian days ("BJD - 2457000", a time system that is correctedby leap seconds, see Eastmanet al. 2010) and the pre-searchData Conditioning Simple Aperture Photometry flux ("PDCSAPFLUX") for which long-term trends have been removed usingthe co-trending basis vectors. In this work, we used the PDClight curves and converted the fluxes to fractional variations fromthe mean (i.e. di ff erential intensity). Since TESS has a poor spa-tial resolution (one detector pixel corresponds to 21 arcsec on thesky) and our targets are faint, we carefully checked for blendswith close by stars using the tpfplotter code (Aller et al. 2020).In Fig. 2 we show the TPF plots for the UHE and He II lineproblem white dwarfs. The red circles represent Gaia sources,which are scaled by magnitude contrast against the target source.Also shown is the aperture mask used by the pipeline to extractthe photometry. In total, ten UHE, and two He II problem whitedwarfs were observed by TESS in the two-minute cadence mode. K2 In a series of sequential observing campaigns 20 fields,which were distributed around the ecliptic plane, were observedby the K2 mission (campaign duration ≈
80 d, Howell et al.2014). Throughout the mission K2 observed in two cadencemodes, long cadence ( ≈
30 min data-point cadence) and shortcadence ( ≈ + + Article number, page 5 of 24 & A proofs: manuscript no. UHE
Fig. 2.
From left to right and top to bottom: target pixel files(TPFs) of WD0101 − + + + + + + + + + Targets (EVEREST, Luger et al. 2016, 2018) pipelines. The datawere obtained from the MAST archive.
ATLAS
Since 2015 the Asteroid Terrestrial-impact Last AlertSystem (ATLAS, Tonry et al. 2018), surveys about 13,000 deg at least four times per night using two independent and fullyrobotic 0.5 m telescopes located at Haleakala and Mauna Loa inHawaii. It provides c- and o-band light curves (e ff ective wave-lengths 0 . µ m and 0 . µ m, respectively) which are taken withan exposure time of 30 s. Eight stars in our sample have ATLASlight curves. Catalina Sky Survey
The Catalina Sky Survey uses three 1 mclass telescopes to cover the sky between declination − <δ < + SDSS stripe 82
The SDSS Stripe 82 covers an area of 300 deg on the Celestial Equator, and has been repeatedly scanned in theu-, g-, r-, i-, and z-bands by the SDSS imaging survey (Abazajianet al. 2009). For J0254 + ZTF
The Zwicky Transient Facility (ZTF, Bellm et al. 2019;Masci et al. 2019) survey uses a 48-inch Schmidt telescope witha 47 deg field of view, which ensures that the ZTF can scanthe entire northern sky every night. We obtained data from theDR4 which were acquired between March 2018 and September2020, covering a time span of around 470 days. The photometryis provided in the g, r, and – less frequent – in the i-band, witha uniform exposure time of 30 s per observation. Most objects inour sample are covered by this survey, with 21 having at least 50data points in at least one band. BUSCA
For HS 0727 + ff erent bands namely U B , B B , R B , and I B . However, due to technical problems withBUSCA, we could not obtain data in the I B band. Instead of fil-ters, we used the intrinsic transmission curve given by the beamsplitters to avoid light loss. For the data reduction, IRAF’s aper-ture photometry package was utilized. + is a DO-type UHE white dwarf with the strongestUHE features. It was observed within CSS and ATLAS. The pe-riodograms of all light curves show the strongest signal around Article number, page 6 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Fig. 3.
Periodograms and phase-folded light curves of the UHE white dwarfs J0032 + + + P = . ff er signifi-cantly. In the first two rows on the left side of Fig. 3, we showthe periodogram and phase-folded light curve from the ATLASc-band, which predicts lowest FAP. The original periodogram isshown in gray and the whitened periodogram is shown in light-blue. No other significant signal is left after whitening the lightcurve for the 0.91 d periodicity. The black line on top of thephase-folded light curve (red) is a fit of a harmonic series usedto predict the peak-to-peak amplitude. WD0101 − This bright ( G = .
74 mag) DOZ-type UHEwhite dwarf was observed with TESS, CSS and ATLAS. Theperiodogram of the TESS light curve shows the strongest peakaround 2.32 d. This period is also confirmed by the CSS V bandand ATLAS c band light curves, respectively. The periodogramof the ATLAS o-band light curve predicts the strongest peak at1.747674 d, but another significant peak occurs at 2.31 d, close towhat is found in the ATLAS c, CSS V, and TESS band. We alsonote, that the 2.32 d periodicity is already clearly visible in the unfolded TESS light curve and is also reported by Heinze et al.(2018). The amplitudes of the ATLAS and CSS phase-foldedlight curves are consistent.
J0146 + is the only object for which rapid changes inthe EWs of the UHE features were observed thus far. Drakeet al. (2014) and Heinze et al. (2018) already reported a pho-tometric variability of P = . P = . P = . HS 0158 + was observed with CSS, ATLAS, ZTF, andTESS. In the TESS light curve, we detect the strongest signalaround 0.45 d. No other significant period is left after the first Article number, page 7 of 24 & A proofs: manuscript no. UHE
Fig. 4.
Like Fig. 3 for the UHE white dwarfs J0254 + + + + whitening cycle. In the periodograms calculated for the ATLASo-band (96 data points) and ZTF g-band (43 data points) no sig-nificant periodic signal can be detected. In all other light curveswe also find a significant period at P ≈ .
45 d. The periodfound by us is confirmed by Drake et al. (2014) who reported P = . P = . J0254 + was observed within CSS, ATLAS, ZTF, TESS,and is the only object in our sample included in the SDSS stripe82 survey. Becker et al. (2011), Drake et al. (2014), and Heinzeet al. (2018) report a period of about 2.17 d for this object, basedon SDSS stripe 82 (u, g, and r band), CSS V band, and ATLASo- and c band light curves, respectively. The periodograms of thelight curves of all surveys mentioned above predict the strongestperiodic signal at around 1.09 d. The amplitudes of the phase-folded light curves are always around 0.3 mag and do not dif-fer significantly amongst the di ff erent bands. The shapes of the phase-folded light curves are – just as for J0146 + FAP ) = − . < − HE 0504 − is one of the objects showing the strongestUHE features, and one of the brightest ( G = .
77 mag) starsin our sample. It was observed in the course of the CSS (69 datapoints) and the SSS (182 data points). The SSS light curve in-dicates that the star underwent a brightening of 0.4 mag from
MJD = MJD = V ≈ .
65 mag. Using only data obtained after
MJD = FAP ) = − . HS 0713 + is yet another example whose phase-foldedlight curves show extended, flat minima (second row right inFig. 4). The periodogram of the TESS light curve shows the Article number, page 8 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Fig. 5.
Like Fig. 3 for the UHE white dwarfs J1215 + + + − strongest periodic signal around P = .
78 d (first row right inFig. 4). No other significant signal is left in the periodogram af-ter whitening the light curve for this periodicity. The strongestperiodic signals in the CSS, and ZTF g- and r-band light curvesare also detected around 0.78 d. In the ATLAS c- and o-bandlight curve the strongest periodic signals are found at 1.379916 dand 0.304796 d, respectively. However, we also find in both peri-odograms periodic signals around 0.78 d above our FAP thresh-old. Heinze et al. (2018) report a period of P = . + . ± . HS 0727 + The periodogram of the TESS light curveshows the strongest periodic signal around P = .
22 d (penul-timate row right in Fig. 4). No other significant period is foundafter the first whitening cycle. The ≈ .
22 d period is also foundin the CSS, ATLAS c- and o-band, and ZTF g- and r-bandlight curves. Again, the minima of the phase-folded light curvesare broad and flat. The amplitudes are all around 0.13 mag anddo not di ff er significantly amongst the di ff erent bands. Drakeet al. (2014) gives a period of P = . P = . U B , B B , and R B band light curves (0 . ± .
014 mag, 0 . ± .
008 mag, and0 . ± .
011 mag, respectively) agree with each other as well aswith the amplitudes from the light curves from the other surveys.
Article number, page 9 of 24 & A proofs: manuscript no. UHE
Fig. 6.
Like Fig. 3 for the He ii line problem white dwarfs J0821 + + + + HS 0742 + is - like HE 0504 − FAP ) = − .
7. The phase-folded light curve has an amplitude of 0.01 mag only. Thus, thisstar is likely not variable.
J0900 + is a faint ( G = .
79 mag) DA-type UHE whitedwarf. Visual inspection of the K2 light curves processed by theEVEREST and K2SSF pipeline indicates that the data still suf-fer from systematic errors. Thus, we discard the K2 data of thisobject from our analysis. The star was also observed within theCSS (469 data points) and ZTF (only 44 data points in both theg- and r-band), however, no significant periodic signal can be de-tected in those light curves. The non-detection of a variability inthis object may be a consequence of the faintness of the star.
J1059+4043 is half a magnitude brighter ( G = .
34 mag) thanJ0900 + P = .
41 d. The phase-folded light curves have an amplitude of 0.08 mag and their shapes are roughly sinusoidal(bottom row right in Fig. 4 for the ZTF g band data). In the peri-odogram of CSS V-band light curve (315 data points) no signif-icant period can be found.
J1215+1203 : This faint ( G = .
17 mag) DO-type UHE whitedwarf was observed in the course of the CSS, and ZTF. The pe-riodograms of all these light curves show the strongest periodicsignal at P ≈ .
60 d. The shape of the phase-folded light curveis roughly sinusoidal (top row, left in Fig. 5).
J1257+4220 is a DA-type UHE white dwarf and was ob-served in the course of the CSS, ZTF, and ATLAS. While inthe CSS V-band and ATLAS o-band no significant periodic sig-nal can be detected, the ZTF light curves and ATLAS c-bandlight curves indicate the strongest periodic signal at P ≈ .
43 d.Heinze et al. (2018) classified J1257 + P = . Article number, page 10 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
J1510+6106 is a DO UHE white dwarf and two minute ca-dence light curves are available from four TESS sectors. Thereare no blends with other stars in the TESS aperture or a contam-ination by nearby bright stars (Fig. 2). In the periodogram of thecombined TESS light curve TESS light curve we find one signif-icant peak at 5.187747 d (log(
FAP ) = − . HS 2027+0651 is a DO UHE white dwarf that was observedwithin the ZTF. The periodogram of the ZTF g-band light curveindicates P ≈ .
29 d. The amplitude of the phase-folded lightcurve is 0.06 mag, and its minimum is again broad and flat(bottom left panel in Fig. 5).
HS 2115 − is a DAO-type UHE white dwarf with veryweak UHE lines. The periodogram of the ZTF r-band (Fig. 6)predicts the strongest signal around 1.32 d. The amplitude of thephase-folded light curve is 0.04 mag. ii line problemJ0821 + is the faintest object in our sample ( G = .
07 mag). In the periodogram (top row left in Fig. 6) of theK2 light curve processed by the EVEREST pipeline only onestrong signal can be found at P = . ≈ .
38 d period is also confirmed bythe K2 light curve processed by the K2SFF pipeline, though, weobtain a higher
FAP for the variability. Even though the targetis quite faint, we also find the ≈ .
38 d period in the CSS andZTF g-band light curves, however, in the latter it is not signifi-cant (log(
FAP ) = − . < J0827+5858 was observed 332 times in the course of the CSS( V = .
46 mag), about 200 times in both the ZTF g- and r-band.We do not find a significant periodic variability in any of thoselight curves.
J0947+1015 was observed 447 times in the course of the CSS( V ≈ .
07 mag), and 64 /
81 times the ZTF g / r band, respec-tively. The periodogram of the CSS light curve indicates a periodof 0.257938 d with an associated log( FAP ) = − .
6. The ampli-tude of the phase folded light curve is 0.10 mag. We classify thisstar as possibly variable.
J1029+2540
In the periodogram of the ZTF g-band light curvewe find the strongest periodic signal in the ZTF g-band around P = .
28 d (first row right in Fig. 6). This period is confirmed bythe CSS V-band and ZTF r-band.
Fig. 7.
Like Fig. 3 for the He ii line problem white dwarfsHS 1517 + + HE 1314+0018
In the TESS data of this fairly bright ( G = .
05 mag) star we find a significant period around 0 .
52 d. Theamplitude of the phase folded light curve is only 0.03%. Afterthe first whitening cycle no other significant peak remains in theperiodogram (penultimate row left of Fig. 6). The star was alsoobserved 368 times within the CSS, however, in this data set nosignificant periodic signal can be found.
J1512+0651
Was observed 103 /
119 times in the ZTF g / r band,and 365 times in the CSS V-band. In the periodogram of the ZTFr band we find the strongest signal at 0.226 d. In the ZTF g andCSS V band we also find the 0.226 period, however, at FAPsbelow our threshold. The amplitude of the phase-folded ZTF rband light curve is 0.06 mag. HS 1517+7403
In the periodograms of the ZTF g- and r-bandlight curves we find the strongest signals around 1.09 d, respec-tively. After the first whitening cycle, no other significant sig-nal remains. The star was also observed with TESS. The pe-riodogram of the TESS light curve predicts the strongest peakaround 8.78 d, however, another strong signal is detected at1.09 d confirming what is found from in the ZTF light curves.
Article number, page 11 of 24 & A proofs: manuscript no. UHE
Since in the ZTF periodograms we do not see a significant peakat around 8.78 d, we adopt 1.09 d as the photometric period of thestar. After whitening the TESS light curve for the 1.09 d period(including it harmonics and subharmonics), the signal at 8.78 ddisappears, however, other significant signals around 7 d, and 2 dremain. Since those signals are not detected in the ZTF peri-odograms, we conclude that they most likely originate from theother star(s) inside the aperture mask, or the two orders of mag-nitude brighter star right next to it (bottom row right in Fig. 2).
J1553+4832
This faint (G =
4. Overall results
We find that 12 out of the 16 UHE white dwarfs are significantlyphotometrically variable, meaning their light curves exhibit pe-riodic signals with a log(
FAP ) ≤ −
4. This leads to a variabilityrate of 75 + − %. Given the low-number statistics, the uncertain-ties were calculated assuming a binomial distribution and indi-cate the 68% confidence-level interval (see e.g. Burgasser et al.2003). For two objects, HE 0504 − + FAPs ) ≈ −
3. ForJ1510 + + G = .
79 mag). For the white dwarfs that show only theHe II line problem, we find a similar variability rate of 75 + − %,meaning that six out of the eight He II line problem white dwarfsare significantly photometrically variable. For J0827 + + II lineproblem phenomena are linked to the variability.But is the photometric variability indeed an intrinsic character-istic of these stars alone, or not rather something that is ob-served amongst all very hot white dwarfs? In order to test this,we obtained ZTF DR4 light curves of a comparison sampleand search for photometric variability in those light curves aswell. Our comparison sample consist of several very hot ( T e ff ≥
65 000 K) DO-type (55 in total, including 28 PG1159-typestars) white dwarfs from Dreizler & Werner (1996); Dreizler &Heber (1998); Hügelmeyer et al. (2005, 2006); Werner & Her-wig (2006); Reindl et al. (2014); Werner et al. (2014) and Reindlet al. (2018), as well as very hot ( T e ff ≥
65 000 K) DA-type(90 in total) white dwarfs from the samples of Gianninas et al.(2011) and Tremblay et al. (2019). We considered only ZTF lightcurves which have at least 50 data points (this value was found from our previous analysis to be approximately needed to de-tect periodic signals in the ZTF data). We find that amongst theH-deficient white dwarfs, only one of the 41 objects with su ffi -cient data points in the ZTF is significantly variable (variabilityrate: 2 + − %) . For the H-rich white dwarfs we find a higher vari-ability rate of 14 + − % (59 stars had at least 50 data points andeight turned out to be significantly variable). In Table A.3, welist all of the normal white dwarfs which we found to be variablebased on the ZTF data, including the mean magnitudes, derivedperiods, and amplitudes. The variability rate of all normal whitedwarfs together is then 9 + − % and in stark contrast to the com-bined variability rate of 67 + − % based on ZTF data for the UHEand He II line problem white dwarfs . Thus, we conclude that pe-riodic photometric variability is indeed a characteristic of UHEand He II line problem white dwarfs. The shapes of the light curves are quite diverse. Some objectsshow near perfect sinusoidal variations (e.g. HE 1314 + + + + + + + + + + + II line prob-lem), though, higher S / N light curves would be needed to con-firm this.
The amplitudes of the light curve variations range from a fewtenth to hundredth mag. For a given object, the amplitudes inthe di ff erent bands do not vary significantly. That means, wefind that the di ff erence in the amplitudes as measured in the dif-ferent bands, is smaller or equal than the standard deviation ofthe di ff erence between the observations and our mathematical fit(black lines in Fig. 3-Fig. 7). In particular, the SDSS stripe 82light curves of J0254 + + ff erence in the am-plitudes.We note that we do not trust the amplitudes of the TESS lightcurves. This is because the TESS mission was designed for starsbrighter than 15 mag, and all our targets are fainter than this. Sec-ond, the large pixel size implies that an accurate background sub-traction is very complicated, in particular in crowded fields. Themajority of the TESS light curves predicts amplitudes that arelarger than what is observed in the other bands. For example, theamplitude of the phase folded TESS light curve of J0254 + ≈ . We note that the ZTF data are not suitable to detect pulsations. Other-wise a higher variability rate could be expected for very hot H-deficientwhite dwarfs, as many of them are GW Vir pulsators. Amongst the UHE and He II line problem white dwarfs 21 objectshave at least 50 data points in at least one ZTF band, and 14 of themturned out to be variable based on the ZTF data.Article number, page 12 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability Fig. 8.
Distribution of the photometric periods of the variable UHE and He II line problem white dwarfs (blue, in purple the period distribution ofonly the UHE white dwarfs is shown). In the left their period distribution is compared to the orbital period distribution of PCE CSPNe (light green,the bold teal line indicates the period distribution of binary CSPNe that show an reflection e ff ect) and white dwarfs plus main sequence binaries(light yellow). In left panel a comparison with the rotational periods of normal white dwarfs (light green with dashed contours) and magnetic whitedwarfs are shown (bold yellow lines). The median period and standard deviation of each sample is indicated. ness of our targets and large TESS pixel size of 21 arcsec, whichoften leads to contamination from neighboring stars, also resultsin a large scatter in the TESS light curves. This in combinationwith the shorter duration of the TESS light curves compared tothose obtained from ground-based surveys like ZTF (about onemonth compared to more than two years), explains the larger un-certainties on the periods obtained from the TESS data. The photometric periods of the UHE white dwarfs range from0.22 to 2.32 d, with a median of 0.69 d and a standard devia-tion of 0.59 d. For the six photometrically variable white dwarfsshowing only the He II line problem, we find a very similar pe-riod range from 0.22 to 2.93 d, with a median of 0.45 d and astandard deviation of 0.95 d. Considering both classes togetherwe find a median of 0.56 d with a standard deviation of 0.73 d.The observed periods are consistent with typical white dwarf ro-tational rates (Kawaler 2004; Hermes et al. 2017a), but couldalso indicate post-common envelope (PCE) binaries (NebotGómez-Morán et al. 2011). It is therefore worth comparing theperiod distribution of those objects to the period distribution ofour sample in detail.In Fig. 8 we show in blue the combined period distribution ofthe UHE white dwarfs and white dwarfs showing only the He II line problem. In purple the period distribution of only the UHEwhite dwarfs is shown. In the left panel we compare their pe-riod distribution to the orbital period distribution of confirmedpost-common envelope (PCE) binary central stars of planetarynebulae (CSPNe, light green, Jones & Bo ffi n 2017; Bo ffi n &Jones 2019) and PCE white dwarf and main sequence binaries(light yellow) from the sample of Nebot Gómez-Morán et al.(2011). The bold teal line indicates the period distribution ofbinary CSPNe that show a reflection e ff ect. In the right panel we show a comparison with the rotational periods of pulsatingwhite dwarfs (light green with dashed contours, values takenfrom Kawaler 2004; Hermes et al. 2017a) and apparently sin-gle magnetic white dwarfs (bold yellow lines, values taken fromFerrario et al. 2015). We note that there are also a few longerperiod magnetic white dwarfs (Putney & Jordan 1995; Bergeronet al. 1997; Schmidt et al. 1999; Kawka & Vennes 2012) andPCE binary central stars (Miszalski et al. 2018a,b; Brown et al.2019), which we omit from Fig. 8 for better visibility. From thisfigure it already seems that the period distribution of our sam-ple resembles more the period distribution of PCE binaries thanthe rotational period distribution of white dwarfs. The medianrotational period of non-magnetic white dwarfs is 1.20 d, whilethe median period of our sample is half of that. The observedrotational periods of magnetic white dwarfs as determined frompolarimetry and photometry range from a few minutes, to hours,to days, over decades to centuries. The short spin period onesshow their peak near 0.1 d, a period much shorter than what weobserve for the UHE white dwarfs and white dwarfs showing theHe II line problem.In order to test the statistical significance of this impres-sion we performed two-sample Kolmogorov-Smirnov tests. Thistest allows to compare two samples and to check the equalityof their one-dimensional probability distributions without mak-ing specific distributional assumptions. The statistical analysisis based on a D-value that represents the maximum distance be-tween the empirical cumulative distribution function of the sam-ple and the cumulative distribution function of the reference dis-tribution. Based on the D-value, we then calculate the p-value,which is used to evaluate if the outcomes di ff er significantly. Itis a measure for the probability of obtaining test results at leastas extreme as the results actually observed, assuming that thenull hypothesis is correct. In our case the null hypothesis is thatthe two samples which are compared follow the same distribu-tion. A p-value of one indicates a perfect agreement with the nullhypothesis, while a p-value approaching zero rejects the null hy- Article number, page 13 of 24 & A proofs: manuscript no. UHE pothesis. We performed these tests for the various samples men-tioned above. First, we find that the period distributions of bothUHE white dwarfs, and white dwarfs showing only the He II lineproblem agree with each other ( p = . p = .
42) and PCE CSPNe ( p = . p = .
25 for only the binary CSPNeshowing a reflection e ff ect). No agreement is found with the ro-tational period distribution of magnetic ( p = . p = . M (cid:12) decreases from 0.017 R (cid:12) to 0.013 R (cid:12) while the star cools downfrom 80 000 K (typical T e ff for a UHE white dwarf) to 20 000 K(the majority of magnetic white dwarfs from Ferrario et al. 2015are reported to have temperatures below this value, as well asall of the non-magnetic white dwarfs from Kawaler 2004; Her-mes et al. 2017a). If we assume conservation of angular momen-tum, then the rotational period should decrease approximatelyby a factor of 0.5. Therefore, we repeated the statistical tests un-der the simplified assumption that all of the objects in our sam-ple will halve their periods as they cool down. By that we findthat there is no agreement with the rotational period distributionof non-magnetic white dwarfs ( p = . p = .
5. Discussion
We found that both UHE and He II line problem white dwarfsoverlap in a narrow region in the Gaia HRD. As expected, theylie on top of the white dwarf banana and are well separated fromthe hot subdwarf stars, and are much bluer than similarly hotwhite dwarfs with M dwarf companions. On average, UHE whitedwarfs are found to be slightly bluer and have slightly brighterabsolute G-band magnitudes than the white dwarfs showing onlythe He II line problem. This might suggest that white dwarfs withUHE lines could evolve into objects that show only the He II line problem. However, better constraints on the temperaturesof these stars as well as a larger sample would be needed to in-vestigate this possibility further.Our light curves studies revealed that the majority of both theUHE white dwarfs (75 + − %) and He II line problem white dwarfs(75 + − %) are photometrically variable. The fact that their photo-metric period distributions agree with each other, and that theirlight curves exhibit similar amplitudes and shapes, reinforcedthat both classes are indeed related. What remains to be dis-cussed is the cause of the photometric variability and how it islinked to the occurrence of the UHE features and He II line prob-lem.The photometric periods of all stars in our sample are well abovethe theoretical upper limit of 10 s predicted for non-radial g-mode pulsations that are frequently observed amongst PG 1159stars (most of them having periods below 3000 s, Quirion et al.2007; Córsico et al. 2019, 2020). Thus, we see two possible sce-narios that could instead account for the photometric variabilityin our stars – one is linked to close binaries, and the other onerelated to magnetic fields. n o r m a li z e d f l u x + o ff s e t u g r i z Fig. 9.
SDSS-ugriz light curves of J0254 + A = Because of the very good agreement of the period distribution ofour stars with that of PCE systems, an obvious assumption is thatour stars are close binaries. Then a variety of physical processescould lead to the observed periodic variability. We rule out thatthe objects in our sample are (over-)contact binaries, since thelight curves of such systems have extended maxima and narrow(sometimes V-shaped) photometric minima and also often twouneven minima (e.g., Miszalski et al. 2009; Drake et al. 2014).Also ellipsoidal deformation that occurs in a detached systemand in which one star is distorted due to the gravity of its com-panion, can be ruled out as main source for the photometric vari-ability. This is because the amplitudes of the light curve varia-tions caused by ellipsoidal deformation in systems that containa hot and compact white dwarf and an extended companion arealways much smaller than that from the so called irradiation ef-fect.An irradiation or reflection e ff ect, caused by the heated face(day-side) of a cooler companion whose rotational period is syn-chronized to the orbital period, appears as an attractive scenario.Irradiation binaries display sinusoidal light curve variations,however, when the system is seen under a high inclination an-gle, the light curves have extended and flat photometric minima,just what we find for seven objects in our sample (Sect. 4.2). Wellstudied examples which exhibit that latter kind of light curves arethe hot subdwarf plus M-dwarf binary HS 2333 + + ff ect system scenario. First,we would expect to find – at least for some objects – noticeabledi ff erences in the amplitudes observed in the di ff erent bands. Forexample in the very hot ( T e ff ≥
49 500 K) white dwarf plus lowmass main sequence star irradiation systems SDSSJ212531.92-010745.9, and the central stars of Abell 63, V477 Lyr, ESO330-9, PN HaTr 7, the ratio of the R-band to V-band amplitude ranges
Article number, page 14 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability a m p li t u d e o f r e f l e c t i o n e ff e c t u'g'r'i'z' Fig. 10.
Expected amplitude for J0254 + ff ect asa function of the temperature of the temperature of the heated side ofthe companion. The amplitude was calculated by the di ff erence in fluxof a white dwarf and a M-dwarf companion with the parameters de-rived in the light curve fit in phase 0 and phase 0.5 using a black bodyapproximation. from 1.13 to 1.38, (Shimansky et al. 2015; Afs , ar & Ibanoˇglu2008; Hillwig et al. 2017). WD1136 +
667 and NN Ser even dis-play r-band to g-band amplitude ratios of 1.44 and 1.67, respec-tively (this work, Brinkworth et al. 2006). An even larger di ff er-ences in the amplitudes by a factor of almost 2 are expected whenalso u-band photometry is available (De Marco et al. 2008). Thisshould be easily noticeable in the light curves of J0254 + + ff ect models forthe SDSS-ugriz light curves of J0254 + lcurve (for details, see Appendix A in Copperwheat et al. 2010),which was developed for white dwarfs plus M-dwarf systemsand has been used to fit detached or accreting white dwarfs plusM-dwarf and hot subdwarf plus M-dwarf systems showing asignificant reflection e ff ect (see Parsons et al. 2010; Scha ff en-roth et al. 2020, for more details). For that we assumed T e ff =
80 000 K for the white dwarf (Hügelmeyer et al. 2006) andtypical values for the masses and radii of white dwarfs plus M-dwarf systems ( q = . R = .
02 R (cid:12) , R = .
15 R (cid:12) , Parsonset al. 2010). To find a first good model we fitted the SDSS-r lightcurve by letting the inclination i , the temperature of the com-panion T , and the albedo of the companion vary. We found aperfectly fitting model for an inclination of i = . ◦ and a tem-perature of the companion of T = A = . A = . A = ff ect from blue to red is expected. The amplitude of the re-flection e ff ect is given by the di ff erence in the flux between phase0, where the white dwarf and the maximum projected area of thecool side of the companion is visible, and phase 0.5, where thewhite dwarf and the maximum projected area of the heated side of the companion is visible. Depending on the temperature of thewhite dwarf and the orbital separation of the system the compan-ion is heated up to around 10 000 −
20 000 K. As the white dwarfhas the maximum of the flux in the UV, the contribution of thecompanion increases from blue to red.To simulate this, we used the parameters that we derived in thelight curve fit and used a black body approximation to calculatethe amplitude of the reflection e ff ect as a function of the tem-perature of the heated side of the companion. As the period ofthe putative binary system is relatively long, we calculated am-plitudes up to 8000 K for the heated side of the companion. Thisis shown in Fig. 10. A significant increase of the amplitude fromSDSS-u (5%) to SDSS-z (40%) is predicted, which is not ob-served. From Fig. 10 it also becomes clear, that the amplitude inthe r band should be about twice of that in the g band. However,also none of the ten other objects, which show significant peri-odic variations in both ZTF bands, show an increased amplitudein the r band compared to the g band.The second drawback of the reflection e ff ect scenario is thatnone of our stars exhibits spectral features of a cool secondary(Fig. B.1 and Fig. B.2). As mentioned before, a late-type Mdwarf or a brown dwarf may easily be outshined by the still lumi-nous white dwarf, thus the non-detection of an increased contin-uum flux in the optical or lack of (molecular) absorption featuresfrom the companion cannot serve as killer argument. However,to our very best knowledge, without exception all PCE systemscontaining a very hot ( T e ff ≥
60 000 K) white dwarf primary (andeven those who outshine their cool companions in the optical),exhibit emission lines (e.g. the Balmer series or the CNO com-plex around 4650 Å) arising from the highly irradiated hemi-sphere of secondary. These emission lines are typically quitestrong and can therefore also be detected in low resolution (e.g.SDSS) spectra (Nagel et al. 2006; Nebot Gómez-Morán et al.2011). It is also well known that the emission lines appear anddisappear over the orbital cycle, reaching maximum strength atphotometric maximum. Thus, it may be possible, that when thesystems is observed close to the photometric minimum, that theemission lines are not detectable. But it is more than unlikelythat all spectra of the stars in our sample were taken at just thatphase.For a reflection e ff ect the amplitudes of the light curve variationsare expected to be correlated to the temperature of the day-sideof the irradiated companion. If we assume that all hypotheticalclose companions to our stars have the same temperature, thenthe amplitudes should correlate to L / P / , where L is the lumi-nosity of the white dwarf and P the orbital (photometric) period.This means that more luminous primaries at shorter orbital pe-riods are expected to cause a larger reflection e ff ect than lessluminous primaries at longer periods. However, using M G as aproxy for L , no correlation between M G / P / and the mean am-plitudes is found (Pearson correlation coe ffi cient: r = − . than 20% to check for this correlation. This serves as a thirdargument against our stars being reflection e ff ect binaries.Finally, we would like to note, that if the variability in all ourobjects would be indeed caused by close companions, it wouldimply an exceptionally high compact binary fraction amongst We only used objects with a relative uncertainty for the parallaxsmaller The inclination angle of the system also has an impact on the ampli-tudes, which would cause an additional scatter. However, it is unlikelythe inclinations are distributed in such a way that the correlation of theamplitude to M G / P / just vanishes. Article number, page 15 of 24 & A proofs: manuscript no. UHE
H-deficient stars of 30% . Amongst the immediate precursors ofDO-type white dwarfs, only one O(He) star and one luminousPG 1159 star are known to be radial velocity variable (Reindlet al. 2016). Another O(He)-type star, the central star of Pa 5shows a photometric variability of 1.12 d, which however, mightalso be attributed to spots on its surface (De Marco et al. 2015).Although no systematic search for close binaries amongst thesestars has been conducted yet, this would lead us to an estimatedclose binary fraction of 11.5% amongst H-deficient pre-whitedwarfs, i.e. a factor of 2.6 below what would be needed to ex-plain the variability in our stars via close binaries. The fraction of the hottest white dwarfs that show UHE linesor the He II line problem (about 10%) matches the fraction ofmagnetic white dwarfs (2-20% are reported, Liebert et al. 2003;Giammichele et al. 2012; Sion et al. 2014; Kepler et al. 2013,2015). In addition, we found that the period distribution ofour stars agrees with that of magnetic white dwarfs if we as-sume they will spin-up as a consequence of further contrac-tion. Proposing UHE white dwarfs are magnetic, Reindl et al.(2019) suggested that optically bright spots on the magneticpoles and / or geometrical e ff ects of a circumstellar magneto-sphere could be responsible for the photometric variability inJ0146 + ff ects of gravity and radiative lev-itation (Alecian & Stift 2017). If the radiative and gravitationalforces are of similar orders of magnitude, these structures areable to form and subsist (Wade & Neiner 2018). In fact, it wasfound by Reindl et al. (2014), that the DO-type UHE and He II line problem white dwarfs are located at this very region in the T e ff − log g diagram, where also the wind limit as predicted byUnglaub & Bues (2000) occurs. This further supports that grav-itational settling and radiation-driven mass loss hold balance inour stars, and that, thus, long-lived spots can be expected.Reindl et al. (2019) showed that the light curve ofJ0146 + T e ff =
80 000 K, log g = .
0, and included opacitiesof He and the iron-group elements (Ca, Sc, Ti, V, Cr, Mn, Fe,Co, and Ni), of which Fe was found to be the most abundanttrace element in UHE white dwarfs (Werner et al. 2018a). Iron-group elements were combined in a generic model atom, using astatistical approach, employing seven superlevels per ion linked
30% of all DO-type white dwarfs hotter than 65 000 K show UHElines or only the He II line problem. If we exclude those that classifyas PG 1159 stars ( C / He > .
02, number fraction) from the group ofnormal DO-type white dwarfs a percentage of 47% is obtained. Only ten O(He) stars and 16 PG 1159 pre-white dwarfs (log g < . Fig. 11.
The di ff erences in the fluxes of models with di ff erent metalcontents and a model containing only He (red). The upper panel inshows fluxes for di ff erent abundances of the iron-group elements, andthe lower panel shows a model that contains opacities of He, C, and O.The filter response functions of the Galex FUV, and NUV, as well as theSDSS u, g, r, i, and z bands are indicated. by superlines, together with an opacity sampling method (An-derson 1989; Rauch & Deetjen 2003). Ionization stages iv - vii augmented by a single ground-level stage viii were consideredand we assumed solar abundance ratios. The models were calcu-lated for a metallicity of 10 − , 10 − , and 10 − (mass fractions). Inaddition, we calculated a model including besides He also opac-ities of C, and O at typical abundance values of low-luminosityPG 1159 stars (mass fractions of 5 × − , and 1 × − , respec-tively). For the calculations we considered ionization stages iii - v and iii - vii for C and O, respectively, and a total of 404 non-LTElevels. Finally, also a pure He model was computed. After that,the model fluxes were convolved with filter response functionsof the Galex FUV, and NUV, as well as the SDSS u, g, r, i, and zbands to calculate synthetic magnitudes.In Fig. 11 the various synthetic spectra are shown, and the fil-ter response functions are indicated. The di ff erences in the re-sulting magnitudes relatively to our pure He model are listed inTable 2. We find that with an increasing abundance of the iron-group elements, the continuum flux becomes steeper towards theUV. Most of the bound-bound transitions are located at FUVwavelengths at this e ff ective temperature, which in turn causes aflattening of total flux in the FUV band (upper panel in Fig. 11).Comparing our pure He model to our model that contains also Cand O, we find that the continuum flux also increases from thenear IR until FUV (hence also producing optically bright spots). Article number, page 16 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Table 2.
Predicted di ff erences in the resulting magnitudes from syn-thetic spectra containing metals relative to a model containing only He.The di ff erent photometric bands and metal abundances adopted in thecalculations are listed. Model IG IG IG C, O10 − − − × − × − Band ∆ m ∆ m ∆ m ∆ m [mag] [mag] [mag] [mag]FUV 0.096 0.234 0.462 0.148NUV 0.239 0.381 0.624 0.182u 0.223 0.339 0.535 0.176g 0.037 0.133 0.296 0.089r 0.062 0.146 0.289 0.160i 0.040 0.117 0.247 0.103z 0.061 0.133 0.249 0.168However, since many strong bound-bound transitions of C and Oare located in the optical (especially in the SDSS g band, lowerpanel in Fig. 11), the behavior of the amplitude di ff erences variesquite a bit from our models with iron-group elements. This hasbeen shown for a Cen by Krtiˇcka et al. (2020b), where for exam-ple an enhancement in He, Si, or Fe not only predicts a di ff erentamplitude, respectively, but also the maxima of the light curvevariations are found to occur at di ff erent phases .We also note, that since spots cover only a part of the stellarsurface, the amplitudes listed in Table 2 can be seen merely asan upper limit of what could be expected observationally fromthe metal enhancement in the spot. Yet, it demonstrates thatchemical spots could indeed explain the relatively large ampli-tude variations we see in our stars. The only drawback is, thatfor all metals considered here, the predicted amplitude in the uband is always significantly larger than in the redder bands. Thisis not observed for the two stars in our sample for which wehave u band light curves. However, only time-resolved UV spec-troscopy combined with detailed light curve modeling will beable to shed light on which enhancement of elements could beresponsible for the observed light curve variability and if chem-ical spots are indeed the source of the variability.Besides a chemically inhomogeneous photosphere, stellarmagnetism can create another source of photometric variability.Munoz et al. (2020) recently hypothesize, that the photometricvariability observed in magnetic O-type stars is a consequenceof electron scattering in the obliquely rotating magnetosphere,which periodically occults the stellar disk. They presented the-oretical light curves for various inclinations, i , and magneticobliquity angles, β , mass-feeding rates, magnetic field strengths,terminal wind velocities, and smoothing lengths. Increasing thelatter four parameters, they find that the amplitude of the lightcurves variations should increase. For low inclination and obliq-uity angles, they find roughly sinusoidal light curve variations.When i + β > i = β = + i ≈ β ≈ + ff set model.
6. Conclusions
Our work revealed exceptionally high photometric variabilityrates amongst both UHE white dwarfs and white dwarfs thatshow only the He II line problem, marking them as a new classof variable stars. We found further evidence that both classesare indeed related, as concluded from their overlap in the GaiaHRD, similar photometric variability rates, light curves shapesand amplitudes, as well as period distributions. While an irra-diation e ff ect could explain their observed period distribution,and the shapes of their light curves, we believe that this scenariois unlikely. This is because we do not detect increasing ampli-tudes towards longer wavelengths in any object, nor do we seeemission lines arising from the strongly irradiated side of a hy-pothetical close binary. Instead, we hold on to the suggestion ofReindl et al. (2019) that the variability is caused by magneticspots and / or the co-rotating, circumstellar material.Further investigations are needed for a profound understand-ing of these special objects. A systematic search for radial ve-locity variations, as well as an IR excess in combination withdetailed light curve modeling will help to decide if the closebinary scenario can really be ruled out. On the other hand,the spots / magnetosphere scenario can be checked with spectro-polarimetric observations and time-resolved UV (that is wherephotospheric metals can be detected) spectroscopy, which in turncould reveal the magnetic field strengths and chemical spots, re-spectively. Last but not least, the discovery that the majority ofthe UHE and He II line problem white dwarfs are photometri-cally variable, provides an important observational constraint todetect more of these systems. Acknowledgements.
We thank Jiri Krtiˇcka, Thomas Kupfer, and JJ Hermesfor helpful comments. We thank Stefan Dreizler for providing us with theTWIN spectrum of HS1517 + Deutsche For-schungsgemeinschaft, DFG through grant GE 2506 / / T000406 /
1. IP was partially supported by the
Deutsche Forschungsgemein-schaft, DFG through grant GE2506 / / T001380 /
1. Some of the data pre-sented in this paper were obtained from the Mikulski Archive for Space Tele-scopes (MAST). This research has made use of NASA’s Astrophysics Data Sys-tem and the SIMBAD database, operated at CDS, Strasbourg, France. Basedon observations collected at the German-Spanish Astronomical Center, CalarAlto, jointly operated by the Max-Planck-Institut für Astronomie Heidelberg andthe Instituto de Astrofísica de Andalucía (CSIC). Based on data obtained fromthe ESO Science Archive Facility under request number nreindl / http://astro.uni-tuebingen.de/~TMAD ) and TIRO tool ( http://astro.uni-tuebingen.de/~TIRO ) used for this paper was constructed aspart of the activities of the German Astrophysical Virtual Observatory. This workhas made use of data from the European Space Agency (ESA) mission Gaia ( ), processed by the Gaia
Data Process-ing and Analysis Consortium (DPAC, ). Funding for the DPAC has been provided by na-tional institutions, in particular the institutions participating in the
Gaia
Mul-tilateral Agreement. The CSS survey is funded by the National Aeronautics andSpace Administration under Grant No. NNG05GF22G issued through the Sci-ence Mission Directorate Near-Earth Objects Observations Program. The CRTSsurvey is supported by the U.S. National Science Foundation under grants AST-0909182 and AST-1313422. Based on observations obtained with the SamuelOschin 48-inch Telescope at the Palomar Observatory as part of the ZwickyTransient Facility project. ZTF is supported by the National Science Founda-tion under Grant No. AST-1440341 and a collaboration including Caltech, IPAC,
Article number, page 17 of 24 & A proofs: manuscript no. UHE the Weizmann Institute for Science, the Oskar Klein Center at Stockholm Uni-versity, the University of Maryland, the University of Washington, DeutschesElektronen-Synchrotron and Humboldt University, Los Alamos National Lab-oratories, the TANGO Consortium of Taiwan, the University of Wisconsin atMilwaukee, and Lawrence Berkeley National Laboratories. Operations are con-ducted by COO, IPAC, and UW. This work includes data from the AsteroidTerrestrial-impact Last Alert System (ATLAS) project. ATLAS is primarilyfunded to search for near earth asteroids through NASA grants NN12AR55G,80NSSC18K0284, and 80NSSC18K1575; byproducts of the NEO search includeimages and catalogs from the survey area. The ATLAS science products havebeen made possible through the contributions of the University of Hawaii Insti-tute for Astronomy, the Queen’s University Belfast, the Space Telescope ScienceInstitute, and the South African Astronomical Observatory. This paper includesdata collected by the TESS mission. Funding for the TESS mission is providedby the NASA Explorer Program. This work made use of tpfplotter by J. Lillo-Box (publicly available in ), whichalso made use of the python packages astropy , lightkurve , matplotlib and numpy . IRAF is distributed by the National Optical Astronomy Observatory,which is operated by the Association of Universities for Research in Astron-omy (AURA) under a cooperative agreement with the National Science Foun-dation. Funding for the Sloan Digital Sky Survey IV has been provided by theAlfred P. Sloan Foundation, the U.S. Department of Energy O ffi ce of Science,and the Participating Institutions. SDSS-IV acknowledges support and resourcesfrom the Center for High Performance Computing at the University of Utah.The SDSS website is . SDSS-IV is managed by the Astrophys-ical Research Consortium for the Participating Institutions of the SDSS Col-laboration including the Brazilian Participation Group, the Carnegie Institutionfor Science, Carnegie Mellon University, Center for Astrophysics | Harvard &Smithsonian, the Chilean Participation Group, the French Participation Group,Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli In-stitute for the Physics and Mathematics of the Universe (IPMU) / Universityof Tokyo, the Korean Participation Group, Lawrence Berkeley National Lab-oratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institutfür Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPAGarching), Max-Planck-Institut für Extraterrestrische Physik (MPE), NationalAstronomical Observatories of China, New Mexico State University, New YorkUniversity, University of Notre Dame, Observatário Nacional / MCTI, The OhioState University, Pennsylvania State University, Shanghai Astronomical Obser-vatory, United Kingdom Participation Group, Universidad Nacional Autónomade México, University of Arizona, University of Colorado Boulder, Universityof Oxford, University of Portsmouth, University of Utah, University of Virginia,University of Washington, University of Wisconsin, Vanderbilt University, andYale University.
References
Abazajian, K. N., Adelman-McCarthy, J. K., Agüeros, M. A., et al. 2009, ApJS,182, 543Afs , ar, M. & Ibanoˇglu, C. 2008, MNRAS, 391, 802Alecian, G. & Stift, M. J. 2017, MNRAS, 468, 1023Aller, A., Lillo-Box, J., Jones, D., Miranda, L. F., & Barceló Forteza, S. 2020,A&A, 635, A128Althaus, L. G., Panei, J. A., Miller Bertolami, M. M., et al. 2009, ApJ, 704, 1605Anderson, L. S. 1989, ApJ, 339, 558Aungwerojwit, A., Gänsicke, B. T., Rodríguez-Gil, P., et al. 2007, A&A, 469,297Bainbridge, M., Barstow, M., Reindl, N., et al. 2017, Universe, 3, 32Becker, A. C., Bochanski, J. J., Hawley, S. L., et al. 2011, ApJ, 731, 17Bellm, E. C., Kulkarni, S. R., Graham, M. J., et al. 2019, PASP, 131, 018002Berengut, J. C., Flambaum, V. V., Ong, A., et al. 2013, Physical Review Letters,111, 010801Bergeron, P., Ruiz, M. T., & Leggett, S. K. 1997, ApJS, 108, 339Bo ffi n, H. M. J. & Jones, D. 2019, The Importance of Binaries in the Formationand Evolution of Planetary Nebulae (Berlin, New York, Springer-Verlag)Brinkworth, C. S., Marsh, T. R., Dhillon, V. S., & Knigge, C. 2006, MNRAS,365, 287Brown, A. J., Jones, D., Bo ffi n, H. M. J., & Van Winckel, H. 2019, MNRAS,482, 4951Burgasser, A. J., Kirkpatrick, J. D., Reid, I. N., et al. 2003, ApJ, 586, 512Chayer, P., Vennes, S., Dupuis, J., & Kruk, J. W. 2005, ApJ, 630, L169Copperwheat, C. M., Marsh, T. R., Dhillon, V. S., et al. 2010, MNRAS, 402,1824Córsico, A. H., Althaus, L. G., Miller Bertolami, M. M., & Kepler, S. O. 2019,A&A Rev., 27, 7Córsico, A. H., Uzundag, M., Kepler, S. O., et al. 2020, arXiv e-prints,arXiv:2011.03629De Marco, O., Hillwig, T. C., & Smith, A. J. 2008, AJ, 136, 323 De Marco, O., Long, J., Jacoby, G. H., et al. 2015, MNRAS, 448, 3587Drake, A. J., Djorgovski, S. G., Mahabal, A., et al. 2009, ApJ, 696, 870Drake, A. J., Graham, M. J., Djorgovski, S. G., et al. 2014, ApJS, 213, 9Dreizler, S. & Heber, U. 1998, A&A, 334, 618Dreizler, S., Heber, U., Napiwotzki, R., & Hagen, H. J. 1995, A&A, 303, L53Dreizler, S. & Werner, K. 1996, A&A, 314, 217Ferrario, L., de Martino, D., & Gänsicke, B. T. 2015, Space Sci. Rev., 191, 111Gaia Collaboration, Babusiaux, C., van Leeuwen, F., et al. 2018, A&A, 616, A10Gaia Collaboration, Prusti, T., de Bruijne, J. H. J., et al. 2016, A&A, 595, A1Gänsicke, B. T., Schreiber, M. R., Toloza, O., et al. 2019, Nature, 576, 61Geier, S. 2020, A&A, 635, A193Geier, S., Raddi, R., Gentile Fusillo, N. P., & Marsh, T. R. 2019, A&A, 621, A38Gentile Fusillo, N. P., Tremblay, P.-E., Gänsicke, B. T., et al. 2019, MNRAS,482, 4570Giammichele, N., Bergeron, P., & Dufour, P. 2012, ApJS, 199, 29Gianninas, A., Bergeron, P., & Ruiz, M. T. 2011, ApJ, 743, 138Gianninas, A., Curd, B., Thorstensen, J. R., et al. 2015, MNRAS, 449, 3966Girven, J., Gänsicke, B. T., Steeghs, D., & Koester, D. 2011, MNRAS, 417, 1210Hagen, H.-J., Groote, D., Engels, D., & Reimers, D. 1995, A&AS, 111, 195Hartman, J. D. & Bakos, G. Á. 2016, Astronomy and Computing, 17, 1Heber, U., Drechsel, H., Østensen, R., et al. 2004, A&A, 420, 251Heinze, A. N., Tonry, J. L., Denneau, L., et al. 2018, AJ, 156, 241Hermes, J. J., Gänsicke, B. T., Kawaler, S. D., et al. 2017a, ApJS, 232, 23Hermes, J. J., Kawaler, S. D., Bischo ff -Kim, A., et al. 2017b, ApJ, 835, 277Hillwig, T. C., Frew, D. J., Reindl, N., et al. 2017, AJ, 153, 24Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398Hoyer, D., Rauch, T., Werner, K., & Kruk, J. W. 2018, A&A, 612, A62Hoyer, D., Rauch, T., Werner, K., Kruk, J. W., & Quinet, P. 2017, A&A, 598,A135Hu, J., Webb, J. K., Ayres, T. R., et al. 2020, arXiv e-prints, arXiv:2007.10905Hügelmeyer, S. D., Dreizler, S., Homeier, D., et al. 2006, A&A, 454, 617Hügelmeyer, S. D., Dreizler, S., Werner, K., et al. 2005, A&A, 442, 309Isern, J., García-Berro, E., Torres, S., & Catalán, S. 2008, ApJ, 682, L109Ivezi´c, Ž., Smith, J. A., Miknaitis, G., et al. 2007, AJ, 134, 973Jenkins, J. M., Twicken, J. D., McCauli ff , S., et al. 2016, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Vol. 9913, Soft-ware and Cyberinfrastructure for Astronomy IV, ed. G. Chiozzi & J. C. Guz-man, 99133EJones, D. & Bo ffi n, H. M. J. 2017, Nature Astronomy, 1, 0117Kalirai, J. S. 2012, Nature, 486, 90Kawaler, S. D. 2004, in IAU Symposium, Vol. 215, Stellar Rotation, ed.A. Maeder & P. Eenens, 561Kawka, A. & Vennes, S. 2012, MNRAS, 425, 1394Kepler, S. O., Pelisoli, I., Jordan, S., et al. 2013, MNRAS, 429, 2934Kepler, S. O., Pelisoli, I., Koester, D., et al. 2015, MNRAS, 446, 4078Kepler, S. O., Pelisoli, I., Koester, D., et al. 2019, MNRAS, 486, 2169Kilic, M., Bergeron, P., Dame, K., et al. 2019, MNRAS, 482, 965Krtiˇcka, J., Huang, L., Jagelka, M., et al. 2018, Contributions of the AstronomicalObservatory Skalnate Pleso, 48, 170Krtiˇcka, J., Kawka, A., Mikulášek, Z., et al. 2020a, A&A, 639, A8Krtiˇcka, J. & Kubát, J. 2005, in Astronomical Society of the Pacific ConferenceSeries, Vol. 334, 14th European Workshop on White Dwarfs, ed. D. Koester& S. Moehler, 337Krtiˇcka, J., Mikulášek, Z., Prvák, M., et al. 2020b, MNRAS, 493, 2140Lallement, R., Capitanio, L., Ruiz-Dern, L., et al. 2018, A&A, 616, A132Liebert, J., Bergeron, P., & Holberg, J. B. 2003, AJ, 125, 348Lindegren, L., Bastian, U., Biermann, M., et al. 2020, arXiv e-prints,arXiv:2012.01742Löbling, L., Maney, M. A., Rauch, T., et al. 2020, MNRAS, 492, 528Luger, R., Agol, E., Kruse, E., et al. 2016, AJ, 152, 100Luger, R., Kruse, E., Foreman-Mackey, D., Agol, E., & Saunders, N. 2018, AJ,156, 99Masci, F. J., Laher, R. R., Rusholme, B., et al. 2019, PASP, 131, 018003Miller Bertolami, M. M. 2014, A&A, 562, A123Miller Bertolami, M. M., Melendez, B. E., Althaus, L. G., & Isern, J. 2014,ArXiv e-prints 1406.7712 [ arXiv:1406.7712 ]Miszalski, B., Acker, A., Mo ff at, A. F. J., Parker, Q. A., & Udalski, A. 2009,A&A, 496, 813Miszalski, B., Manick, R., Mikołajewska, J., et al. 2018a, MNRAS, 473, 2275Miszalski, B., Manick, R., Mikołajewska, J., Van Winckel, H., & Iłkiewicz, K.2018b, PASA, 35, e027Munoz, M. S., Wade, G. A., Nazé, Y., et al. 2020, MNRAS, 492, 1199Nagel, T., Schuh, S., Kusterer, D.-J., et al. 2006, A&A, 448, L25Napiwotzki, R. 1997, in The Third Conference on Faint Blue Stars, ed. A. G. D.Philip, J. Liebert, R. Sa ff er, & D. S. Hayes, 207Nebot Gómez-Morán, A., Gänsicke, B. T., Schreiber, M. R., et al. 2011, A&A,536, A43Oksala, M. E., Kochukhov, O., Krtiˇcka, J., et al. 2015, MNRAS, 451, 2015Parsons, S. G., Marsh, T. R., Copperwheat, C. M., et al. 2010, MNRAS, 402,2591 Article number, page 18 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992, Nu-merical recipes in C. The art of scientific computing (New York: CambridgeUniversity Press)Prvák, M., Krtiˇcka, J., & Korhonen, H. 2020, MNRAS, 492, 1834Prvák, M., Liška, J., Krtiˇcka, J., Mikulášek, Z., & Lüftinger, T. 2015, A&A, 584,A17Putney, A. & Jordan, S. 1995, ApJ, 449, 863Quirion, P. O., Fontaine, G., & Brassard, P. 2007, ApJS, 171, 219Rauch, T. & Deetjen, J. L. 2003, in Astronomical Society of the Pacific Confer-ence Series, Vol. 288, Stellar Atmosphere Modeling, ed. I. Hubeny, D. Miha-las, & K. Werner, 103Rauch, T., Gamrath, S., Quinet, P., et al. 2017a, A&A, 599, A142Rauch, T., Hoyer, D., Quinet, P., Gallardo, M., & Raineri, M. 2015a, A&A, 577,A88Rauch, T., Quinet, P., Hoyer, D., et al. 2016, A&A, 587, A39Rauch, T., Quinet, P., Knörzer, M., et al. 2017b, A&A, 606, A105Rauch, T., Werner, K., Biémont, É., Quinet, P., & Kruk, J. W. 2012, A&A, 546,A55Rauch, T., Werner, K., Quinet, P., & Kruk, J. W. 2014a, A&A, 564, A41Rauch, T., Werner, K., Quinet, P., & Kruk, J. W. 2014b, A&A, 566, A10Rauch, T., Werner, K., Quinet, P., & Kruk, J. W. 2015b, A&A, 577, A6Rebassa-Mansergas, A., Gänsicke, B. T., Schreiber, M. R., Koester, D., &Rodríguez-Gil, P. 2010, MNRAS, 402, 620Reif, K., Bagschik, K., de Boer, K. S., et al. 1999, in Society of Photo-Optical In-strumentation Engineers (SPIE) Conference Series, Vol. 3649, Sensors, Cam-eras, and Systems for Scientific / Industrial Applications, ed. M. M. Blouke &G. M. Williams, 109–120Reindl, N., Bainbridge, M., Przybilla, N., et al. 2019, MNRAS, 482, L93Reindl, N., Geier, S., Kupfer, T., et al. 2016, A&A, 587, A101Reindl, N., Geier, S., & Østensen, R. H. 2018, MNRAS, 480, 1211Reindl, N., Rauch, T., Werner, K., et al. 2014, A&A, 572, A117Renedo, I., Althaus, L. G., Miller Bertolami, M. M., et al. 2010, ApJ, 717, 183Scha ff enroth, V., Casewell, S. L., Schneider, D., et al. 2020, MN-RAS[ arXiv:2011.10013 ]Schlafly, E. F. & Finkbeiner, D. P. 2011, ApJ, 737, 103Schmidt, G. D., Liebert, J., Harris, H. C., Dahn, C. C., & Leggett, S. K. 1999,ApJ, 512, 916Schreiber, M. R., Gänsicke, B. T., Toloza, O., Hernandez, M.-S., & Lagos, F.2019, ApJ, 887, L4Shimansky, V., Sakhibullin, N. A., Bikmaev, I., et al. 2006, A&A, 456, 1069Shimansky, V. V., Borisov, N. V., Nurtdinova, D. N., et al. 2015, AstronomyReports, 59, 199Sion, E. M., Holberg, J. B., Oswalt, T. D., et al. 2014, AJ, 147, 129Ter Braak, C. J. F. 2006, Statistics and Computing, 16, 239Tonry, J. L., Denneau, L., Heinze, A. N., et al. 2018, PASP, 130, 064505Tremblay, P. E., Cukanovaite, E., Gentile Fusillo, N. P., Cunningham, T., & Hol-lands, M. A. 2019, MNRAS, 482, 5222Unglaub, K. & Bues, I. 2000, A&A, 359, 1042Vanderburg, A. & Johnson, J. A. 2014, PASP, 126, 948Wade, G. A. & Neiner, C. 2018, Contributions of the Astronomical ObservatorySkalnate Pleso, 48, 106Werner, K. 1996, ApJ, 457, L39Werner, K., Deetjen, J. L., Dreizler, S., et al. 2003, in Astronomical Society ofthe Pacific Conference Series, Vol. 288, Stellar Atmosphere Modeling, ed.I. Hubeny, D. Mihalas, & K. Werner, 31Werner, K., Dreizler, S., Heber, U., et al. 1995, A&A, 293, L75Werner, K., Dreizler, S., & Rauch, T. 2012, TMAP: Tübingen NLTE Model-Atmosphere Package, Astrophysics Source Code LibraryWerner, K. & Herwig, F. 2006, PASP, 118, 183Werner, K. & Rauch, T. 2015, A&A, 584, A19Werner, K., Rauch, T., & Kepler, S. O. 2014, A&A, 564, A53Werner, K., Rauch, T., & Kruk, J. W. 2018a, A&A, 609, A107Werner, K., Rauch, T., & Kruk, J. W. 2018b, A&A, 616, A73Werner, K., Rauch, T., Napiwotzki, R., et al. 2004, A&A, 424, 657Werner, K., Rauch, T., & Reindl, N. 2019, MNRAS, 483, 5291Zechmeister, M. & Kürster, M. 2009, A&A, 496, 577 Article number, page 19 of 24 & A proofs: manuscript no. UHE
Appendix A: Tables Appendix B: Figures
Article number, page 20 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
Table A.1.
Periods, mean magnitudes and amplitudes as derived from various light cures for all periodically variable UHE white dwarfs.
Name Band Datapoints Magnitude P Amplitude Comment[mag] [d] [mag]J0032 + . ± . . ± . −
182 CSS 154 15.83 2 . ± . . ± . . ± . . ± . + . ± . . ± . . ± . . ± . . ± . . ± . . ± . + . ± . . ± . . ± . . ± . . ± . + . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . + . ± . . ± . . ± . . ± . . ± . . ± . + . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . + . ± . . ± . + . ± . . ± . . ± . + . ± . . ± . . ± . + . ± . . ± . + . ± . Article number, page 21 of 24 & A proofs: manuscript no. UHE
Table A.2.
Periods, mean magnitudes and amplitudes as derived from various light cures for all periodically variable white dwarfs showing onlythe He ii line problem. Name Band Datapoints Magnitude P Amplitude Comment[mag] [d] [mag]J0821 + . ± . . ± . + . ± . . ± . . ± . + . ± . + . ± . + . ± . . ± . . ± . + . ± . . ± . Table A.3.
Periods, mean magnitudes and amplitudes as derived from ZTF DR4 light cures for all periodically variable normal hot white dwarfs.
Name Band Datapoints Magnitude P Amplitude Comment[mag] [d] [mag]KUV07523 + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + . ± . + K7VWDJ113905.98 + . ± . + . ± . + . ± . + . ± . + dM Article number, page 22 of 24icole Reindl et al.: White Dwarfs showing Ultra-High Excitation Lines - Photometric Variability
SDSSUVESTWINTWINSDSSEFOSC 1TWINTWINTWINSDSSSDSSSDSSSDSSSDSSSTISTWIN J0032+1604WD0101-182J0146+3236HS0158+2335J0254+0058HE0504-2408HS0713+3958HS0727+6003HS0742+6520J0900+2343J1059+4043J1215+1203J1257+4220J1510+6106HS2027+0651HS2115+114890 kK 7.5090 kK 7.50100 kK, 7.5070 kK 7.7580 kK 8.0085 kK 7.0065 kK 7.0090 kK 7.5080 kK 7.5060 kK 7.0090 kK 7.50100 kK 7.6055 kK 7.2595 kK 8.0080 kK 7.5080 kK 7.00 C/He = 0.03C/He = 0.003pure Hepure Hepure Hepure Hepure Hepure Hepure Hepure HC/He = 0.03C/He = 0.03pure Hpure Hepure HeHe/H = 0.004 X ( - ) V II ( - ) X I ( - ) V III ( - ) X II ( - ) I X ( - ) V ( - ) X ( - ) V I ( - ) V II ( - ) X I ( - ) V III ( - ) X II ( - ) I X ( - ) H I H I H e II H I C I V H e II C I V H e II H e II H I H e II C I V H e I H e II H I λ / A o r e l a t i v e f l u x Fig. B.1.
Spectra of all known UHE white dwarfs. The positions of photospheric lines (H i , He i , He ii and C iv ), α and β transitions betweenRydberg states ( n − n (cid:48) ) of the ionization stages v − x , and approximate line positions of the UHE features (blue) are marked. Overplotted in red areTMAP models and the e ff ective temperatures, surface gravities, and chemical compositions (in mass fractions) - as determined in pervious works(see footnote of Table 1) or here - are indicated. In gray the spectrograph used for the observation is indicated. Article number, page 23 of 24 & A proofs: manuscript no. UHE