Alkali metals in white dwarf atmospheres as tracers of ancient planetary crusts
Mark A. Hollands, Pier-Emmanuel Tremblay, Boris T. Gänsicke, Detlev Koester, Nicola P. Gentile-Fusillo
AAlkali metals in white dwarf atmospheres as tracers ofancient planetary crusts
Mark A. Hollands (cid:63) , Pier-Emmanuel Tremblay , Boris T. G¨ansicke , , Detlev Koester ,Nicola Pietro Gentile-Fusillo Department of Physics, The University of Warwick, Coventry, CV4 7AL, UK Centre for Exoplanets and Habitability, University of Warwick, Coventry, CV4 7AL, UK Institut f ¨ur Theoretische Physik und Astrophysik, University of Kiel, 24098 Kiel, Germany European Southern Observatory, Karl-Schwarzschild-Str 2, D-85748 Garching, Germany
White dwarfs that accrete the debris of tidally disrupted asteroids provide the opportunityto measure the bulk composition of the building blocks, or fragments, of exoplanets . Thistechnique has established a diversity in compositions comparable to what is observed in thesolar system , suggesting that the formation of rocky planets is a generic process . Whereasthe relative abundances of lithophile and siderophile elements within the planetary debris canbe used to investigate whether exoplanets undergo differentiation , the composition studiescarried out so far lack unambiguous tracers of planetary crusts . Here we report the detec-tion of lithium in the atmospheres of four cool ( < , K) and old (cooling ages – Gyr)metal-polluted white dwarfs, where one also displays photospheric potassium. The relativeabundances of these two elements with respect to sodium and calcium strongly suggest thatall four white dwarfs have accreted fragments of planetary crusts. We detect an infraredexcess in one of the systems, indicating that accretion from a circumstellar debris disk is on- a r X i v : . [ a s t r o - ph . E P ] F e b oing. The main-sequence progenitor mass of this star was . ± . (cid:12) , demonstrating thatrocky, differentiated planets may form around short-lived B-type stars. The accurate astrometry of the
Gaia mission enabled the identification of nearby, intrinsi-cally faint white dwarfs against much more numerous luminous background stars , and spectro-scopic observations of practically all 524 northern white dwarfs within 40 pc are now complete .We have detected absorption of the lithium 6,708 ˚A doublet in the spectra of three cool ( T eff < , K) white dwarfs (Fig. 1) within this sample (LHS 2534, WD J231726.74 + +
10, 11 , we identified a fourth system (SDSS J133001.17 + , similar to the analysis ofmeteorites to determine the composition of solar system planets . All four stars with photosphericlithium also exhibit sodium and calcium lines (Fig. 1), enabling a comparative study of the volatileand refractory content of their accreted planetesimals. The planetesimals, or fragments thereof, aremost likely scattered via gravitational interactions with more massive bodies from several au into2he tidal disruption radius of the white dwarf . An alternative way of delivering planetary materialto the white dwarf is the Kozai-Lidov mechanism in wide binaries , however, we do not detectwide companions for any of the four stars discussed here in Gaia DR2.The observational data available for these objects were analyzed using a model atmospherecode that has been specifically developed to correctly treat the complex physics in the high-densityatmospheres of white dwarfs . We fitted the effective temperature ( T eff ) and the stellar radiususing published broad-band photometry and parallax (see Methods and Extended Data Fig. 1), andsubsequently determined the photospheric abundances using spectroscopy (Extended Data Fig. 2),with the procedure repeated until convergence (Extended Data Fig. 3). The analysis of LHS 2534required additional effort as the star exhibits a magnetic field of 2.10 MG (see Methods). Wemeasured the atmospheric parameters and lithium, sodium and calcium abundances for all fourstars, and also detected magnesium, potassium, chromium and iron in LHS 2534. The effectivetemperatures, T eff = 3 , – , K, are among the lowest of any debris-accreting white dwarfs ,reflecting the selection effect imposed by the neutral lithium detection.We compare the abundance ratios of log(Li / Na) vs. log(Ca / Na) of the four white dwarfswith those of the Sun , the bulk Earth , the continental crust and CI chondrites (Fig. 2a). Allfour objects reside within a cluster, with log(Ca / Na) between − log(Li / Na) between − −
1. Because of the rapid burning of lithium in the young Sun, the solar abundance isseveral orders of magnitude below those of the four white dwarfs and solar system planetary com-positions. The composition of the planetary debris within the four systems is noticeably enhanced3n both lithium and depleted in calcium with respect to the solar system planetary benchmarks,and most closely resembles the abundances found in the continental crust. The unusually large log(Li / Na) and low log(Ca / Na) ratios can be partially explained via differential diffusion of met-als out of the convection zones since the end of the accretion episode, caused by the differentelemental sinking timescales.We computed sinking timescales for each detected element (see Methods, Extended DataFig. 4), and indicate the evolution of LHS 2534, WD J2317 + + + + ≈ Myr) or CI chondrites( ≈ . Myr). At (cid:39) Myr, log(Ca / Na) approaches the bulk Earth value, but log(Li / Na) wouldbe about an order of magnitude too low. This degeneracy is broken by the additional detectionof potassium in LHS 2534. The relative abundances of the alkali metals lithium, sodium, andpotassium are entirely incompatible with either those of bulk Earth or CI chondrites, independentof the accretion history (Fig. 2b). Instead, combined constraints from the lithium and potassiumabundances are consistent with LHS 2534 having accreted a fragment of planetary crust around2 Myr ago. Whereas the other three white dwarfs with photospheric lithium lack potassium de-tections, their close clustering near LHS 2534 in log(Li / Na) vs. log(Ca / Na) strongly suggeststhat they, too, are contaminated by fragments of planetary crust. A similar analysis is possible forWD J1824 + + log(Li / Na) vs. log(Ca / Na) as potassium is not detected. Their past trajectories point closely towards the bulk Earth, however4his origin requires many diffusion timescales to have elapsed, necessitating extremely massiveparent bodies. It is therefore much more probable that smaller parent bodies were more recentlyaccreted with compositions corresponding to particularly Li-rich crust. WD J2317 + (SDSS J0744 + + + log(Li / Na) vs. log(Ca / Na) diagram (Fig. 2a). Their log(Ca / Na) ranges from broadly re-sembling CI chondrites to a value exceeding that of bulk Earth. This corroborates our hypothesisthat the four white dwarfs with photospheric lithium are accreting planetary debris with a clearlydistinct, crust-like, composition.Crust-like debris compositions have been suggested previously
5, 19 , based on the detection oflarge calcium and aluminum abundances. However, both elements also have relatively high massfractions within the mantle of a differentiated planet, and whereas the interpretation of calcium andaluminum-rich material as signatures of differentiation is certainly plausible , it does not supporta definitive detection of crust fragments. In contrast, the mass fraction of the alkali metals lithium,potassium and sodium is one to two orders of magnitude higher in the Earth’s continental crust5han in its mantle , making them unambiguous tracers of planetary crusts.Given that the photospheric abundances reflect the composition of the entire convection zone,in which the material remains homogeneously mixed, it is possible to estimate lower limits on theaccreted planetary body masses. The properties of the outer convection zones (Extended DataFig. 4) depend sensitively on the white dwarf mass and log(H / He) ratio, and vary only mildly asfunction of T eff within the narrow range spanned by the four stars. The masses of the individualelements contained within the convection zones are reported in Extended Data Fig. 4. Scalingthe sodium mass contained within the convection zone by its mass fraction of 2.4 per cent in thecontinental crust of the Earth , we estimate the minimum masses of the crust fragments accretedinto these white dwarfs to be in the range × – × g. This compares to (cid:39) × gfor the Earth’s continental crust , hence the observed level of atmospheric contamination requiresonly relatively small splinters of the crust of an Earth-like planet.WD J2317 + + . Because accretion episodes are expected to last for – years it is therefore likely that WD J2317 + . The infrared excess is detected in the UKIRT K and WISE W and W Gaia
DR2 whitedwarf catalog and cross-matched them with WISE detections, with the further requirement of W − W uncertainties < . mag. WD J2317 + W − W (Fig. 3b). The proper motions for WD J2317 + WISE observations obtained from 2010 to 2016 agree with those determined by Gaia , corroborat-ing the association of the WISE fluxes with the white dwarf. This makes WD J2317 + . The infrared excess of the disk is L IR /L wd = 0 . .Assuming that WD J2317 + , the mass flow ratesthrough the bottom of the convection zone are identical to the accretion rates from the debrisdisk, which we compute (see Methods) to be 760 g s − , 92,000 g s − , and 37,000 g s − for lithium,sodium, and calcium. Adopting that sodium accounts for 2.4 per cent of the accreted mass (for con-tinental crust abundances ) implies a total accretion rate of (cid:39) × g s − , broadly in agreementwith the expected rate driven by the low Poynting-Robertson drag exercised by this cool whitedwarf on the dust and is consistent with the rates ( – g s − ) observed for other accretingsystems . These estimates do not account for 3D effects within convective white dwarf envelopes,and recent work suggests that these effects may result in higher accretion rates than found fromthe 1D calculations we used.There are currently few undisputed detections of planets with host star masses ≥ . (cid:12)
28, 29 . Using the empirical initial-to-final mass relation , the high mass of7D J2317 + . ± . (cid:12) ,corresponding to B-type stars, form planetary systems and that they survive to white dwarf stage.Note that despite the relatively short main sequence lifetime of the progenitor, second genera-tion planet formation can largely be ruled out, as Li-burning on the main sequence would resultin Li-poor planetesimals, unlike those observed here. WD J2317 + . ± . Gyr cooling age and . ± . Gyr total age. These mass and age measurements provide constraints for planet formationmodels that are extremely difficult to achieve from observations of planets around main-sequenceor giant stars , and the detection of a debris disk at WD J2317 + and lithium has been identified in the atmosphere of agiant exoplanet via transmission spectroscopy . The detection of lithium within white dwarf pho-tospheres originating from the accretion of planetary crust fragments represents an important linkto the overall evolution of planetary systems, providing the sensitivity to establish the compositionof the crusts of differentiated rocky planets. 8. Jura, M. A Tidally Disrupted Asteroid around the White Dwarf G29-38. Astrophys. J. Lett. , L91–L94 (2003).2. Zuckerman, B., Koester, D., Melis, C., Hansen, B. M. & Jura, M. The Chemical Compositionof an Extrasolar Minor Planet.
Astrophys. J. , 872–877 (2007).3. G¨ansicke, B. T. et al.
The chemical diversity of exo-terrestrial planetary debris around whitedwarfs.
Mon. Not. R. Astron. Soc. , 333–347 (2012).4. Doyle, A. E., Young, E. D., Klein, B., Zuckerman, B. & Schlichting, H. E. Oxygen fugacitiesof extrasolar rocks: Evidence for an Earth-like geochemistry of exoplanets.
Sci. , 356–359(2019).5. Zuckerman, B. et al.
An aluminum/calcium-rich, iron-poor, white dwarf star: Evidence for anextrasolar planetary lithosphere?
Astrophys. J. , 101– (2011).6. Bonsor, A. et al.
Are exoplanetesimals differentiated?
Mon. Not. R. Astron. Soc. , 2683–2697 (2020).7. Gaia Collaboration et al.
Gaia Data Release 2. Summary of the contents and survey properties.
Astron. Astrophys. , A1 (2018).8. Gentile Fusillo, N. P. et al.
A Gaia Data Release 2 catalogue of white dwarfs and a comparisonwith SDSS.
Mon. Not. R. Astron. Soc. , 4570–4591 (2019).9. Tremblay, P. E. et al.
Gaia white dwarfs within 40 pc - I. Spectroscopic observations of newcandidates.
Mon. Not. R. Astron. Soc. , 130–145 (2020).90. Hollands, M. A., Koester, D., Alekseev, V., Herbert, E. L. & G¨ansicke, B. T. Cool DZ whitedwarfs - I. Identification and spectral analysis.
Mon. Not. R. Astron. Soc. , 4970–5000(2017).11. Harris, H. C. et al.
An Initial Survey of White Dwarfs in the Sloan Digital Sky Survey.
Astron.J. , 1023–1040 (2003).12. Lodders, K. Solar system abundances and condensation temperatures of the elements.
Astro-phys. J. , 1220–1247 (2003).13. Debes, J. H., Walsh, K. J. & Stark, C. The link between planetary systems, dusty white dwarfs,and metal-polluted white dwarfs.
Astrophys. J. , 148 (2012).14. Petrovich, C. & Mu ˜noz, D. J. Planetary Engulfment as a Trigger for White Dwarf Pollution.
Astrophys. J. , 116 (2017).15. Koester, D. White dwarf spectra and atmosphere models .
Memorie della Societa AstronomicaItaliana, , 921–931 (2010).16. McDonough, W. The composition of the earth. In Teisseyre, R. & Majewski, E. (eds.) Earth-quake Thermodynamics and Phase Transformation in the Earth’s Interior , 5–24 (Elsevier Sci-ence Academic Press, 2000).17. Rudnick, R. L. & Gao, S. Composition of the Continental Crust.
Treatise on Geochemistry ,659 (2003). 108. Koester, D., Kepler, S. O. & Irwin, A. W. New white dwarf envelope models and diffusion.Application to DQ white dwarfs. Astron. Astrophys. , A103 (2020).19. Hollands, M. A., G¨ansicke, B. T. & Koester, D. Cool DZ white dwarfs II: compositions andevolution of old remnant planetary systems.
Mon. Not. R. Astron. Soc. , 93–111 (2018).20. Lodders, K. & Fegley, B.
Chemistry of the Solar System (RSC Publishing, Cambrige, 2011).21. Koester, D. Accretion and diffusion in white dwarfs. new diffusion timescales and applicationsto gd 362 and g 29-38.
Astron. Astrophys. , 517–525 (2009).22. Girven, J. et al.
Constraints on the lifetimes of disks resulting from tidally destroyed rockyplanetary bodies.
Astrophys. J. , 154 (2012).23. Eisenhardt, P. R. M. et al.
The CatWISE Preliminary Catalog: Motions from WISE andNEOWISE Data.
Astrophys. J. Suppl. , 69 (2020).24. Debes, J. H. et al.
A 3 Gyr White Dwarf with Warm Dust Discovered via the Backyard Worlds:Planet 9 Citizen Science Project.
Astrophys. J. Lett. , L25 (2019).25. Rafikov, R. R. Metal accretion onto white dwarfs caused by poynting-robertson drag on theirdebris disks.
Astrophys. J. Lett. , L3 (2011).26. Farihi, J. Circumstellar debris and pollution at white dwarf stars.
New Astron. Rev. , 9–34(2016). 117. Cunningham, T., Tremblay, P.-E., Freytag, B., Ludwig, H.-G. & Koester, D. Convectiveovershoot and macroscopic diffusion in pure-hydrogen-atmosphere white dwarfs. Mon. Not.R. Astron. Soc. , 2503–2522 (2019).28. Sato, B. et al.
Substellar Companions to Seven Evolved Intermediate-Mass Stars.
PASJ ,135 (2012).29. Veras, D. et al. Constraining planet formation around 6-8 M (cid:12) stars.
Mon. Not. R. Astron. Soc. , 765–775 (2020).30. Cummings, J. D., Kalirai, J. S., Tremblay, P. E., Ramirez-Ruiz, E. & Choi, J. The White DwarfInitial-Final Mass Relation for Progenitor Stars from 0.85 to 7.5 M (cid:12) . Astrophys. J. , 21(2018).31. Aguilera-G´omez, C., Chanam´e, J., Pinsonneault, M. H. & Carlberg, J. K. On Lithium-richRed Giants. I. Engulfment of Substellar Companions.
Astrophys. J. , 127 (2016).32. Chen, G. et al.
The GTC exoplanet transit spectroscopy survey. IX. Detection of haze, Na, K,and Li in the super-Neptune WASP-127b.
Astron. Astrophys. , A145 (2018).12 uthor Correspondence
All correspondence regarding this work should be directed to M. Hollands.
Acknowledgements
MAH and PET acknowledge useful discussions with Hans-G¨unter Ludwig and MatthiasSteffen regarding neutral broadening of lithium lines. We also acknowledge Jack McCleery for maintaininga database of 40 pc white dwarf spectra. MAH and DK acknowledge atomic data from Thierry Leiningerused for the Ca I Author contributions
M.A.H. performed data reduction, analysis and interpretation and wrote the ma-jority of the text. P.-E.T. and B.T.G. contributed to the data interpretation and writing of this article. D.K.developed the model atmosphere code used for the analysis. N.P.G.F. contributed to the data reduction andanalysis of photometric data. uthor Information Competing Interests
The authors declare that they have no competing interests. ,000 5,000 6,000 7,000 8,000Wavelength [Å]01234 N o r m a li s e d F LHS 2534WD J2317+1830WD J1824+1213SDSS J1330+6435(a)
Li Na K Ca
Figure 1 | Optical spectra of the four white dwarfs with photospheric lithium.
Thewavelengths of the most important transitions are indicated by the colored bars. Thespectra in the left-hand panel have been smoothed by a Gaussian with a full width halfmaximum of 3 ˚A for clarity, with the exception of SDSS J1330 + .0 0.5 0.0 0.5 1.0 1.5log(Ca/Na)54321 l o g ( L i / N a ) (a) LHS 2534WD J2317+1830WD J1824+1213SDSS J1330+6435SDSS J0744+4649SDSS J0916+2540SDSS J1535+1247 l o g ( L i / N a ) (b) Continental crustBulk EarthSolarCI Chondrite
Figure 2 | Number density abundance ratios of debris-accreting white dwarfs andSolar system benchmarks. a , The log(Li / Na) vs. log(Ca / Na) ratios of the four whitedwarfs with lithium detections (blue, orange, green and red symbols) are enhanced withrespect to the Earth’s continental crust. The hollow orange point indicates the compo- ition of the planetary body accreted by WD J2317 + + + log(Li / Na) vs. log(Ca / Na) a and log(Li / Na) vs. log(K / Na) b ratios are consistent with having accreted a fragment of planetary crust (cid:39) Myr ago. Error bars correspond to 1 σ uncertainties. .5 1.0 2.0 5.0Wavelength [ m]1920212223 A B m a g (a) G BP G RP W W (b) Figure 3 | An infrared excess at WD J2317 + , Our best fitting white dwarf model(solid curve) for WD J2317 + WISE shows a flux excess in the K , W , and W bands. An opaque opticallythick disk heated by the white dwarf with an inclination of 70 degrees, and an inner-edgetemperature of 1,500 K (dotted line), when combined with the white dwarf flux (dashedline) provides a good fit to the photometry. b , WD J2317 + n unusually red W − W color when compared to white dwarfs with similar G BP − G RP colors (gray points, from a cross-match of Gaia white dwarfs with WISE , and W − W uncertainties < . mag). Error bars correspond to 1 σ uncertainties. ethodsIdentification and observations. Three of the stars with lithium detections were found amongour observations of white dwarfs within 40 pc while the fourth one was identified from its SDSSspectrum .LHS 2534 is a nearby white dwarf located 38 pc away, and represents the first discoveredmagnetic metal-contaminated white dwarf . The Zeeman effect from the 2.1 MG magnetic field splits the photospheric lines into multiple components. For most transitions (where fine structureinteractions are much weaker than that of the magnetic field), this results in three components sep-arated by 98.0 cm − (46.686 cm − MG −
34, 35 . TheX-Shooter spectra clearly reveal the Li I π and σ components reach 0.14 and 0.10 of the continuum respectively.We observed WD J2317 + (cid:39) , as measured from the sky-spectrum. Debiasing, flat-fielding, and ex-20raction of the 1D spectra were performed using packages from the Starlink collection of software.Wavelength and flux calibration were performed using Molly (http://deneb.astro.warwick.ac.uk/phsaap/software/).As the service mode flux standards were observed with a wider slit-width (2.5 arcsec), the qualityof flux calibration and telluric removal were generally poor, though this did not affect the qualityof our subsequent fits, as the continuum is well defined. The two strongest features of the spectrumare the Na I I + × binning, resulting in an average resolu-tion of ≈ I doublet, a narrow Li 6,708 ˚A doublet,and a relatively broad Ca i 4,227 ˚A line (Fig. 1).Given the detection of lithium in three cool white dwarfs, we investigated the published spec-troscopy of metal-contaminated objects with similar temperatures and identified the Li I + . SDSS J1330 + where the lithium absorption feature is visible in one of the figures, though the authors did notcomment on the presence of photospheric lithium.The detection of photospheric lithium in the SDSS spectrum of SDSS J1330 + Gaia
DR2 whitedwarf catalog . We removed 7,396 objects that were classified by the authors as quasars on thebase of their SDSS spectroscopy.We ran an automated search on the 29,863 remaining spectra, which simply put, involvedfitting a Gaussian profile at the expected wavelength of the Li I R (cid:39) , ), the Li I σ = 5 ˚A, where the amplitudeof the Gaussian was the only free parameter. Given the width of the Gaussian, even large radialvelocity shifts of 200 km s − are contained well within the fitted profile. We visually inspected allspectra where the amplitude-parameter was measured to a significance of > σ in the direction ofabsorption, and where the reduced χ was less than 2.0.This process easily recovered SDSS J1330 + . σ and a reduced χ = 1 . . After removing multiple false positives (mostly magnetic hydrogen-atmosphere whitedwarfs with B (cid:39) MG where the σ + -component coincides with Li I Atmospheric analysis.
The spectra and available photometry were analyzed using the KoesterLTE model atmosphere code . Some improvements to the code have been implemented since its22se in previous publications, several of which are relevant to this work. Improvements to the equa-tions of state have been made to accommodate the very cool nature for these stars (WD J1824 + I .For the photometric fitting we made use of a wide range of photometry (Extended DataFig. 1). This included wherever available Pan-STARRS , SDSS , and SkyMapper in the optical.In the infrared we used 2MASS
41, 42 , UKIRT , and WISE . Note that for the latter, we havemade use of the recent catWISE catalog which provides W and W detections for all four starsdiscussed here.Prior to the photometric fit, we converted all magnitudes to the AB scale. However wechose to exclude the Gaia photometry, because when using the provided AB zero-points, we foundconsistent disagreement with other optical photometric surveys, i.e. SDSS, Pan-STARRS, andSkymapper (which were always found to be mutually in agreement). In addition to the mainparameters of T eff and radius, the parallax is included as a dummy parameter, with the Gaia valuesserving as Gaussian priors. This has the desired effect of correctly folding the parallax uncertaintyinto our radius estimates, and to some extent into the T eff estimates. The hydrogen and metalabundances were included in the models used in the photometric fits, though with their valuesfixed (to become free parameters for the spectroscopic fitting, where the T eff and radius are fixedinstead). The model fluxes, F ν ( λ ) , were scaled by the radius and parallax, and synthetic AB23agnitudes, m , were calculated from (cid:104) F ν (cid:105) = (cid:82) d λ F ν ( λ ) S ( λ ) /λ (cid:82) d λ S ( λ ) /λ , (1)and m = − . ( (cid:104) F ν (cid:105) / ,
631 Jy) , (2)where S ( λ ) is the energy-counting filter response curve. The atmospheric parameters were thenfitted via χ -minimization between the observed and synthetic magnitudes. For these nearby whitedwarfs, the effects of interstellar reddening can be considered negligible. An important caveatregards the photometric uncertainties, which for some of the deep surveys such as Pan-STARRS,can be as small as a few mmag. These data tend to dominate the fit, and result in unrealisticallysmall uncertainties ( < K on T eff ). It is therefore important to note that these photometry mayhave a relative precision at the mmag level, in particular when derived from stacked multi-epochobservations, however, the absolute fluxes have additional systematic uncertainties. To account forthis, we added a constant systematic uncertainty to all available photometry of a given object. Themagnitude of this systematic uncertainty was varied until the best-fit had a reduced χ of one. Wefound values of (cid:39) . mag were required for LHS 2534, WD J2317 + + + T eff and radius values derived from the pho-tometric fit. The surface gravity, log g , was calculated from T eff and the radius using the whitedwarf mass-radius relation . For LHS 2534 and SDSS J1330 + + + + + + T eff , and so weretypically unrealistically too small (e.g. < . dex). Therefore the spectroscopic fits were repeatedwith the best fit T eff increased by σ , with the subsequent shift in abundances added in quadratureto the statistical uncertainties.Additional details for each object are summarized in the following sub-sections, includingany departures from the general approach described above. The final results for all four whitedwarfs are compiled in Extended Data Fig. 2. The best fitting models to each of the stars areshown in Extended Data Fig. 3. Analysis of LHS 2534.
As the brightest of our four objects, LHS 2534 has a multitude of photom-etry, covering its entire spectral energy distribution (SED). However, the main challenge to fitting25his object is its 2.1 MG magnetic field. Our models are intrinsically non-magnetic, therefore toimprove the accuracy of our fits within this limitation, we triplicated the majority of spectral lines,reducing the log gf values by log (3) for each component. Exceptions are the Ca II , and Mg II resonance lines for which we used pre-computed unified line profiles.With the higher resolution spectroscopic data, we immediately determined that the Zeemantriplet located between 5,100–5,300 ˚A is in fact not from Mg I , but rather Cr I as the centralcomponent has a rest-frame (air) wavelength of 5,207 ˚A. However, we note that the σ + componentof Mg I is possibly visible at 5,155 ˚A with its other components blended with Cr I . The magnesiumabundance is further constrained from the red wing of the 2,852 ˚A Mg I resonance line. Othernotable spectral features are K I lines (discussed below), Zeeman split lines from the Na I II I lines. Wedid not detect this element for any of the other objects, however we note that for WD J1824 + + I lines. For WD J2317 + I was complicated by the fact that the interaction of the 2.1 MG magnetic fieldis comparable to the fine-structure energy separation of the K I doublet. For much smaller fields thedoublet components will be split into four and six sub-components, according to the anomalousZeeman effect. In higher fields where the spin-orbit interaction is disrupted, three components26eparated by µ B B would be observed instead. 2.10 MG falls into the intermediate regime, insteadobserving a triplet of doublets (Supplementary Fig. 1). To determine the wavelengths empirically,the energies of the upper levels can be found from the eigenvalues of E + 2 β E + β √ β
00 0 E − β √ β E − β √ β E + β
00 0 √ β E − β , (3)where E = 13 , . cm − and E = 12 , . cm − (the energies of the unperturbed P / and P / respectively), and β = 46 . cm − MG − × B . Because the lower S / level (thepotassium ground state) has no orbital angular momentum, the perturbed energies of the two sub-states are simply ± β . Valid transitions can be found according to the normal selection rules, i.e. ∆ m J = 0 , ± and ∆ m S = 0 , where m J and m S have their usual meanings. Setting B to 2.10 MG,we determined the wavelengths of the six allowed transitions finding excellent agreement with theobserved data (Supplementary Fig. 1), thus confirming the transitions belong to potassium.We started our fits by adopting earlier published parameters . Within the least squares fitto the spectrum, we found that we required a moderate hydrogen abundance, allowing for a bettermatch to the continuum slope redward of 5,000 ˚A, which was too steep for our initial hydrogenabundance of log(H / He) = − , and also a better match to the flux level blueward of 4,000 ˚A.Some of the metal lines in our the spectrum are much narrower than we were able to reproduce inour models (the cores of the Na I I lines, and the many Zeeman-split components of the Ca II log(H / He) (cid:39) − , though this came at the expense of sub-stantially reducing the fit-quality to other spectral features, in particular the Ca I T eff somewhat cooler than found in previousanalyses
10, 33, 48 . However, those studies were performed before the release of
Gaia
DR2 astrom-etry, which places an additional constraint on the radius (and therefore mass and log g ). We notethat at the higher temperature of 5,200 K found in a previous analysis , we are forced to considera log g of 8.22, whereas with our T eff of , ± K requires a more typical surface gravity of . . Furthermore, at the higher temperature we also required a hydrogen abundance closer to log(H / He) = − , in order to suppress the level of flux bluewards of , ˚A, though as notedabove, such a hydrogen abundance causes problems fitting other features of the spectrum. Becausewe computed non-magnetic models, as with all cool metal-contaminated white dwarfs, we findconvection up to the photosphere. However, it has been found that magnetic fields can inhibit con-vective processes , which is likely the case for LHS 2534 since we derive a plasma β -parametervalue of ≈ , indicating that magnetic pressure dominates over thermalpressure. However calculating our models without convection results in only minor changes to theemergent spectrum. Furthermore we emphasize that with such marginally low plasma β value,convective velocities are damped by less than one order of magnitude. These convective veloci-28ies are still large compared to microscopic diffusion velocities , suggesting that metals are stillefficiently mixed, similarly to the non-magnetic case. Analysis of WD J2317 + For this white dwarf photometry is available from SDSS, Pan-STARRS, UKIRT, and
WISE . The UKIRT J magnitude is from the UKIRT Hemisphere Survey(UHS) , with the K band from the Wide-field nearby Galaxy-cluster survey (WINGS)
43, 44 . TheSDSS u -band is poorly fitted in Extended Data Fig. 3, though the detection flags indicate that theuncertainty is underestimated in this filter . The combination of UKIRT and WISE photometryreveal collision induced absorption (CIA) is present in the atmosphere of this star.We found that it was not possible to fit all the near-infrared photometry simultaneously.Instead we used only the optical and J -band photometry to constrain the T eff and radius. Thisproduced a much more consistent fit with spectroscopy, where the width of the Na doublet and y − J color are both sensitive to the He/H ratio. Evidently from Extended Data Fig. 3 this results intoo little flux in the K and WISE bands. We noted that the W − W color is far too flat comparedto the expected Rayleigh-Jeans tail. For two photometric measurements along a Rayleigh-Jeanstail, it is expected that m − m log ( λ /λ ) (cid:39) , (4)where m , are the two AB magnitudes, and λ , , their corresponding central wavelengths. Forexample, for the W / photometry of LHS 2534, equation (4) is evaluated to be . ± . , whereasfor WD J2317 + . ± . – more than 4 σ smaller than the expected valuefor a Rayleigh-Jeans slope. We highlight this excess in Fig. 3b where we show the W − W color against the G BP − G RP color for WD J2317 + Gaia white29warf catalog and WISE photometry
51, 52 . Initially this cross-match contained 70,050 sources. Wefurther refined this be keeping only sources with white dwarf probabilities, P wd > . , reducingthe sample to 28,333. From a color-color diagram of G RP − W vs. G BP − G RP it was clear that thecross match was contaminated by a larger number of sources with very red G RP − W (i.e. flux-contamination from nearby sources, white dwarfs with main sequence companions). We thereforemade a cut of G RP − W > . . G BP − G RP ) , leaving only the main white dwarf locus,containing 4,076 objects. Finally, we removed objects with W − W uncertainties > . mag,leaving only the 116 objects shown in Fig. 3b, all of which are contained within 130 pc.We considered the possibility that the perceived flux excess of WISE photometry result fromcontamination by another object located within the large
WISE
PSF. However, the catWISE pho-tometry collected over the period 2010 to 2016 shows that the source detected by WISE has aproper motion consistent with that measured by
Gaia , strongly arguing against background con-tamination. Furthermore the excess is also seen in the UKIRT K -band, which has a much betterspatial resolution.An possible explanation that could resolve the discrepancy between the observed SED andthe model spectra would be a modification of the CIA absorption profiles, as they have been subjectto limited observational tests. While simply increasing the strength of the absorption would extendthe red-wing of the H -He opacity into the W band, this would also result in excess absorption inthe K -band. However, the H -He CIA opacity has been shown to be distorted at the high densitiesrelevant to these stars ( > . g cm − ). The opacity table used in this work has only temperaturedependence and so it is feasible that density-dependent shifts may explain our observations. Even30o, a strong argument against this, comes from the fact that we were able to fit WD J1824 + T eff .A more natural explanation is that the infrared excess arises from a circumstellar dust diskirradiated by the white dwarf. Using the simple flat disk model , we found that a reasonable fitis obtained for an inner disk-temperature of (cid:39) , K outer temperature of > K and aninclination of (cid:39) degrees (dashed curves in Fig. 3a and Extended Data Fig. 3). The fact thatWD J2317 + + log(K / He) < − . . This results in an abundance ratio upper-limit of log(K / Na) < − . . Sincethis is higher than the measurement of LHS 2534 (Fig. 2b), the true value for WD J2317 + Analysis of WD J1824 + For this object, optical photometry are available from Pan-STARRS,though because of the , mas yr − proper-motion, it appears as four separate detections, where31e list the weighted averages provided in Extended Data Fig. 1. Additionally, WD J1824 + J -band detection in the UHS . WD J1824 + T eff = 3 , ± K) with a mixed H/He atmosphere similar to WD J2317 + -He, to the extent that its effect is measurable from only thePan-STARRS z − y color, though it is further constrained by the J -band. W and W magnitudeswere also found within the catWISE data, and agree well with our best fitting model, despite thevery strong CIA. The most notable features in the spectral data are the near-saturated sodium andcalcium lines, the latter of which shows a reasonable fit with our unified profile. Analysis of SDSS J1330 + This stellar remnant has been recently modeled owing to itsextremely strong and broad sodium absorption. While the the unified sodium line profile used inthat analysis is not currently implemented in our models, we were able to obtain an adequate fit tothe data.Using the SDSS and Pan-STARRS photometry we found a T eff and log g lower than thatderived in the earlier analysis . Regardless, our model synthetic photometry is mostly in goodagreement with the data, though we note that our model slightly under-predicts the flux in the W band compared with the measurement.Two spectra available from SDSS, though the second spectrum (taken with the BOSS instru-ment) is of very poor signal-to-noise ratio. Even so, we decided to co-add these spectra to improvethe spectroscopic uncertainties. From comparison with the photometry (Extended Data Fig. 1),the flux calibration of both spectra was found to be poor, therefore re-calibration against the pho-32ometry (as described above) was required for each spectrum before they could be co-added. Wefound co-adding provided a modest S/N boost of 10 per cent in the red, and 20 per cent in the blue(relative to the better of the two spectra).The main challenge in fitting this spectrum was measuring the calcium abundance. The cal-cium resonance line is modeled here using the aforementioned unified profile and yields a reason-able fit in Extended Data Fig. 3. However, we found that the calcium and magnesium abundanceswere highly anti-correlated – because the calcium resonance line is essentially saturated even at alow abundance, a similarly good fit to both the spectrum and u -band photometry can be achievedby lowering the calcium abundance and increasing the magnesium abundance. There is insufficientinformation that could constrain the Mg/Ca ratio, and so a higher quality spectrum will be neededto measure these abundances independently. Therefore our adopted calcium abundance (ExtendedData Fig. 2) assumes for log(Mg / Ca) = 1 . dex, which is the average value found in an earlierstudy .We note that the Na and Ca abundances that we determined are significantly lower than thosein the previous analysis . This difference arises from our lower T eff measurement, resulting in achanged excitation balance. Therefore we required much lower Na and Ca abundances to producethe same strength lines. Even so, we find our Ca/Na ratio is consistent with the previous analysis( log(Ca / Na) = − . ± . vs. − . ± . in the previous work). The remaining difference inthe Ca/Na ratio (while already within 1 σ uncertainty) could be attributed to the anti-correlationbetween Ca and Mg as described above. 33iven the highly pressure broadened Na doublet, it is clear that the atmosphere of SDSS J1330 + log(H / He) = − dex, though we were still able to establish an upper-limit.We found that up to − dex, the models looked close to identical, with a small amount of CIAappearing at µ m, but otherwise continuing to agree well with all available photometry, and spec-troscopy. However at − dex we found that CIA pushed down the infrared flux compared to theoptical enough to be in disagreement with the WISE photometry. Furthermore, the Na doubletstarted to become narrower than observed in the spectrum. Therefore we adopt − dex as ourupper-limit for the hydrogen abundance. Line widths of Lithium.
In our initial attempts to derive abundances we found that the lithiumlines were systematically much narrower than predicted by our models. On its own, these narrowlines might suggest an interstellar origin , however there are multiple arguments against this.Firstly, for LHS 2534 the lithium doublet is Zeeman split by the 2.1 MG magnetic field. Secondlyall objects apart from SDSS J1330 + + ± pc away) where interstellar absorption can be considered negligible. Finally, inall four objects the observed lithium lines – while much narrower than those in the models – arestill broader than the instrumental resolution. We determined this by first measuring the spectralresolution at the location of the lithium-doublet by determining the widths of sky emission lines inthe sky spectrum. In each object, we then fitted the lithium-doublet with a Voigt profile, with theGaussian-component, σ , fixed to the spectral resolution, and with the Lorentzian-component, γ , asa free-parameter. The results are given in Supplementary Table 1, and include the radial velocities34easured from the Voigt profiles (not corrected for gravitational redshift). We thus conclude thatin all four cases the lines must be photospheric in origin.Instead we considered the possibility that the overly broad lines in our models arise frominaccurate atomic data (uncertainties can often be as large as a factor 2–3 (0.3–0.5 dex). Forlithium, we obtained atomic data from VALD
56, 57 , where the broadening constants log(Γ rad ) , log(Γ stark /n e ) , log(Γ VdW /n H ) were found to be . , − . , and − . respectively. These broad-ening constants are nominally calculated for temperatures of 10,000 K and for a single perturber,and so internal scaling is required for different temperatures, densities, and in the case of neutralbroadening, other perturbers such as He. In the cool, dense atmospheres of these four white dwarfs,the dominant line-broadening process is from perturbations by neutral particles, i.e. hydrogen, he-lium, H . Indeed we found that the lithium line widths in all objects are sensitive to adjustmentsin the neutral-broadening constant. We therefore decided to empirically determine a correction tothe neutral-broadening constant, log(Γ VdW /n H ) , from our observations.We decided to perform this measurement on a single object, comparing the other three starsfor consistency. We chose WD J1824 + γ -measurementhas the highest relative precision (Supplementary Table 1). Furthermore WD J1824 + γ/σ ratio – γ/σ is higher for SDSS J1330 + log(Γ VdW /n H ) , spanning − . to − . in steps of . dex, and log(Li / H) spanning − . to − . in 0.25 dex steps. Other atmospheric pa-35ameters ( T eff , log g , other abundances), were set to the best fitting values in Extended DataFig. 2. The optimal broadening constant was determined via a non-linear least-squares fit tothe data, interpolating the models (convolved by the 1.9 ˚A instrumental broadening) at arbitraryabundance/ log(Γ VdW /n H ) . We found the best fitting value to be log(Γ VdW /n H ) = − . ± . ,or in other words a change of − . ± . dex.The best fitting models for all four white dwarfs with the revised broadening constant aredisplayed in red in Supplementary Fig. 2. For comparison, models with the original broadeningconstant are shown in orange, although with abundances revised upwards by 0.3 dex for clarity.Naturally the improvement for WD J1824 + + + I . dyn cm − , whereas the magnetic pressure must be . dyn cm − given the 2.10 MG magnetic field. Therefore, in addition to only adjusting the lithium lines, forthis object, it was also necessary to reduce the neutral broadening constants for Cr I and K I by thesame amount, to better estimate the photospheric abundances.While we clearly find improvement with the revised broadening constant, similar issues arenot encountered in other cool stellar atmospheres with lithium lines, for instance the Solar atmo-sphere and those of giant stars. However calculations of giant star atmosphere models with thereduced neutral broadening constant show no discernible difference in the line width (M. Steffen,private communication, June 2020), indicating that other broadening processes dominate withinthose atmospheres. White dwarf masses and evolution.
For two of the stars in our sample, WD J1824 + + . ± . and . ± .
06 M (cid:12) , respec-tively). These masses are presumed to be unrealistic, as the Galaxy is too young to produce suchlow-mass white dwarfs, and are representative of the challenges common to modeling cool whitedwarfs with T eff < , K. In fact, extremely low masses are commonly derived for whitedwarfs with strong CIA absorption and imply missing opacity in the stellar models. Such diffi-culties are often understood to arise from strongly wavelength-dependent opacities such as CIA and the red wing of Lyman α .Our models include CIA opacities from H -H, H -He, H -H , H-He, and He-He-He.We also include broadening of Ly α by H . However we do not include the effects of pressure37istortion in the H -He opacity . While we do not have access to these specific data, their inclusionin our models may go some of the way to explain these low masses. The expectation is thereforethat these stars have higher true T eff than from our analysis, which would therefore allow for smallerradii, needed to remain consistent with the photometry and parallaxes, which via the mass-radiusrelation for white dwarfs, implies higher masses.In the following we assume that the derived luminosities (Extended Data Fig. 2) ofWD J1824 + + , i.e. M = 0 . ± .
122 M (cid:12) . For WD J1824 + T eff =4 , +260 − K and τ = 9 . +0 . − . Gyr for thick hydrogen layers which are appropriate for the largetotal hydrogen mass in the star. For SDSS J1330 + M = 0 . ± .
122 M (cid:12) leads to T eff = 4 , +290 − K and τ = 7 . +0 . − . Gyr for thin hydrogen layers. Clearly both whitedwarfs have long cooling times but it is not possible to estimate the main-sequence lifetime owingto the uncertainty on the mass.For WD J1824 + T eff systems), we refittedthe photometry and spectrum with the T eff fixed to 4,050 K (as described above), and with the radiusand atmospheric abundances as free parameters, to see if this may still provide an adequate solu-tion, which could be the case if our low-mass solution was simply a local minimum. While the bestmodel for this restricted fit did (by design) result in a mass close to 0.6 Msun, we found the modelfailed to accurately reproduce the shape of the SED in the both the optical and infrared, show-ing particular disagreement in the J -band of around 0.5 mag. Therefore we rule out the a second38inimum in the parameter space at higher T eff , though this does not discount the possibility thatimproved atmospheric models may shift the best solution to higher temperatures and thus towardsmore reasonable masses. Even so, the consistency in the abundance ratios of WD J1824 + + + T eff shifts the optimal abundances: log(H / He) was reducedby about . dex with all metal abundances increased by . – . dex. The similarity in metalabundance shifts implies that the location of WD J1824 + T eff .For LHS 2534 we derive a mass of . ± .
02 M (cid:12) corresponding cooling age of . ± . Gyr.We expect the magnetic field to have negligible influence on cooling age . Such a white dwarfmass implies a very long main-sequence lifetime, possibly longer than the cooling time . It ispossible that LHS 2534 is also impacted by the model systematics mentioned above, and thereforewe refrain from estimating a total age.In contrast, our fit to WD J2317 + . ± .
02 M (cid:12) and cooling ageof . ± . Gyr making it the among most massive white dwarfs detected with signatures of aplanetary system . The large mass implies a massive progenitor with a relatively small main-sequence lifetime, leading to a precise total age of . ± . Gyr using an empirical initial-to-finalmass relation and main-sequence lifetimes . 39 inematics and population membership. While we could only establish a reliable total age forone of the four analysed white dwarfs, kinematics can be useful to identify populationmembership . In Supplementary Table 2, we rely on the precise
Gaia astrometry to derivetangential velocities as well as motion in Galactic coordinates U , V and W . We had to assumezero radial velocity as this quantity is poorly constrained from our spectroscopic observations. Inearlier studies of halo white dwarf candidates , a σ halo membership required | U | > km s − or V > km s − or V < − km s − . Using the same requirements, only WD J1824 + , although all our objects have relatively largetangential velocities suggesting an old disk population , consistent with the large cooling ages.The chemical abundances in these old white dwarfs have the potential to provide constraintson planet formation around stars formed in the early history of the Galaxy, and hence possiblyunder metal-poor conditions. However, early disk membership is not necessarily linked to progen-itors of significant sub-solar metallicity
73, 74 , and further insight will require a larger sample of cooldebris-accreting white dwarfs.
Sinking times.
We used our new envelope code to determine convection zone sizes and sinkingtimescales for each element considered in our sample. With only four objects we were ableto use the best fit atmospheric models discussed in the previous sections as boundary conditionson the upper-envelope for self-consistency (as opposed to interpolating a grid of models). Theseresults are listed in Extended Data Fig. 4. Using these timescales it is possible to trace back the40tmospheric abundance histories of a metal Z (with sinking timescale τ ) using, log(Z / He)( t ) = log(Z / He)(0) + t ln(10) τ , (5)implying the relative abundances for two elements evolves as log(Z / Z )( t ) = log(Z / Z )(0) + t ln(10) (cid:2) τ − − τ − (cid:3) . (6)The convection zone masses, combined with our abundance measurements (Extended DataFig. 2) allow us to determine the mass of each element mixed within the convection zones, pro-viding lower limits on the amounts of accreted material (Extended Data Fig. 4). In the case ofWD J2317 + Astrophys. J. Lett. , L61–L63 (2001).34. Smette, A. et al.
Molecfit: A general tool for telluric absorption correction. I. Method andapplication to ESO instruments.
Astron. Astrophys. , A77 (2015).35. Kausch, W. et al.
Molecfit: A general tool for telluric absorption correction. II. Quantitativeevaluation on ESO-VLT/X-Shooterspectra.
Astron. Astrophys. , A78 (2015).36. Blouin, S. et al.
A New Generation of Cool White Dwarf Atmosphere Models. III. WDJ2356-209: Accretion of a Planetesimal with an Unusual Composition.
Astrophys. J. , 188(2019). 417. Blouin, S., Allard, N. F., Leininger, T., Gad´ea, F. X. & Dufour, P. Line Profiles of the CalciumI Resonance Line in Cool Metal-polluted White Dwarfs.
Astrophys. J. , 137 (2019).38. Chambers, K. C. et al.
The Pan-STARRS1 Surveys.
ArXiv e-prints (2016).39. Alam, S. et al.
The Eleventh and Twelfth Data Releases of the Sloan Digital Sky Survey: FinalData from SDSS-III.
Astrophys. J. Suppl. , 12 (2015).40. Wolf, C. et al.
SkyMapper Southern Survey: First Data Release (DR1).
Proc. Astron. Soc.Aust. , e010 (2018).41. Cutri, R. M. et al. VizieR Online Data Catalog: 2MASS All-Sky Catalog of Point Sources(Cutri+ 2003).
VizieR Online Data Catalog
II/246 (2003).42. Skrutskie, M. F. et al.
The Two Micron All Sky Survey (2MASS).
Astron. J. , 1163–1183(2006).43. Valentinuzzi, T. et al.
WINGS: a WIde-field nearby Galaxy-cluster survey. III. Deep near-infrared photometry of 28 nearby clusters.
Astron. Astrophys. , 851–864 (2009).44. Moretti, A. et al.
WINGS Data Release: a database of galaxies in nearby clusters.
Astron.Astrophys. , A138 (2014).45. Dye, S. et al.
The UKIRT Hemisphere Survey: definition and J-band data release.
Mon. Not.R. Astron. Soc. , 5113–5125 (2018).46. Cutri, R. M. & et al. VizieR Online Data Catalog: AllWISE Data Release (Cutri+ 2013).
VizieR Online Data Catalog
II/328 (2013). 427. Fontaine, G., Brassard, P. & Bergeron, P. The Potential of White Dwarf Cosmochronology.
Publ. Astron. Soc. Pac. , 409–435 (2001).48. Hollands, M. A., G¨ansicke, B. T. & Koester, D. The incidence of magnetic fields in cool DZwhite dwarfs.
Mon. Not. R. Astron. Soc. , 681–690 (2015).49. Gentile Fusillo, N. P. et al.
Can magnetic fields suppress convection in the atmosphere of coolwhite dwarfs? A case study on WD2105-820.
Mon. Not. R. Astron. Soc. , 3693–3699(2018).50. Tremblay, P. E. et al.
On the Evolution of Magnetic White Dwarfs.
Astron. J. , 19 (2015).51. Wright, E. L. et al.
The wide-field infrared survey explorer (wise): Mission description andinitial on-orbit performance.
Astron. J. , 1868–1881 (2010).52. Mainzer, A. et al.
Preliminary Results from NEOWISE: An Enhancement to the Wide-fieldInfrared Survey Explorer for Solar System Science.
Astrophys. J. , 53 (2011).53. Blouin, S., Kowalski, P. M. & Dufour, P. Pressure Distortion of the H -He Collision-inducedAbsorption at the Photosphere of Cool White Dwarf Stars. Astrophys. J. , 36 (2017).54. Blouin, S. Magnesium abundances in cool metal-polluted white dwarfs.
Mon. Not. R. Astron.Soc. (2020).55. Ferlet, R. & Dennefeld, M. Interstellar lithium and the 7Li/6Li ratio in diffuse clouds.
Astron.Astrophys. , 303–310 (1984). 436. Ryabchikova, T. A., Piskunov, N. E., Kupka, F. & Weiss, W. W. The vienna atomic linedatabase : Present state and future development.
Baltic Astronomy , 244–247 (1997).57. Ryabchikova, T. et al. A major upgrade of the VALD database.
Phys. Scr. , 054005 (2015).58. McCleery, J. et al. Gaia white dwarfs within 40 pc II: the volume-limited Northern hemispheresample.
Mon. Not. R. Astron. Soc. , 1890–1908 (2020).59. Kilic, M. et al.
The 100 pc White Dwarf Sample in the SDSS Footprint.
Astrophys. J. , 84(2020).60. Kowalski, P. M. & Saumon, D. Found: The Missing Blue Opacity in Atmosphere Models ofCool Hydrogen White Dwarfs.
Astrophys. J. Lett. , L137–L140 (2006).61. Karman, T. et al.
Update of the HITRAN collision-induced absorption section.
Icarus ,160–175 (2019).62. Borysow, A., Jorgensen, U. G. & Zheng, C. Model atmospheres of cool, low-metallicity stars:the importance of collision-induced absorption.
Astron. Astrophys. , 185–195 (1997).63. Borysow, A., Jorgensen, U. G. & Fu, Y. High-temperature (1000-7000 K) collision-inducedabsorption of H“2 pairs computed from the first principles, with application to cool and densestellar atmospheres.
J. Quant. Spectrosc. Radiat. Transfer , 235–255 (2001).64. Kowalski, P. M. Infrared absorption of dense helium and its importance in the atmospheres ofcool white dwarfs. Astron. Astrophys. , L8 (2014).445. Rohrmann, R. D., Althaus, L. G. & Kepler, S. O. Lyman α wing absorption in cool whitedwarf stars. Mon. Not. R. Astron. Soc. , 781–791 (2011).66. Tremblay, P.-E., Ludwig, H.-G., Steffen, M. & Freytag, B. Spectroscopic analysis of DA whitedwarfs with 3D model atmospheres.
Astron. Astrophys. , A104 (2013).67. Marigo, P. et al.
Carbon star formation as seen through the non-monotonic initial-final massrelation.
Nat. Astron. (2020).68. Hurley, J. R., Pols, O. R. & Tout, C. A. Comprehensive analytic formulae for stellar evolutionas a function of mass and metallicity.
Mon. Not. R. Astron. Soc. , 543–569 (2000).69. Oppenheimer, B. R., Hambly, N. C., Digby, A. P., Hodgkin, S. T. & Saumon, D. DirectDetection of Galactic Halo Dark Matter.
Sci. , 698–702 (2001).70. Seabroke, G. M. & Gilmore, G. Revisiting the relations: Galactic thin disc age-velocity dis-persion relation.
Mon. Not. R. Astron. Soc. , 1348–1368 (2007).71. Kilic, M. et al.
The age of the Galactic stellar halo from Gaia white dwarfs.
Mon. Not. R.Astron. Soc. , 965–979 (2019).72. Fantin, N. J. et al.
The Canada-France Imaging Survey: Reconstructing the Milky Way StarFormation History from Its White Dwarf Population.
Astrophys. J. , 148 (2019).73. Feltzing, S., Holmberg, J. & Hurley, J. R. The solar neighbourhood age-metallicity relation -Does it exist?
Astron. Astrophys. , 911–924 (2001).454. Casagrande, L. et al.
New constraints on the chemical evolution of the solar neighbourhoodand Galactic disc(s). Improved astrophysical parameters for the Geneva-Copenhagen Survey.
Astron. Astrophys. , A138 (2011). 46 ata Availability
The data that support the plots within this paper and other findings of this study areavailable from the ESO science archive facility, the GTC public archive, ING archive, and SDSS database;or from the corresponding author upon reasonable request.
Code Availability
The Koester model atmosphere and envelope codes are not publicly available, thoughdetails of their functionality can be consulted from the included references. xtended Data Figure 1 | Astrometry and photometry for the four Li-rich white dwarfs.
Pan-STARRS, SDSS and SkyMapper photometry are given in the AB-system, with the re-mainder in the Vega-system. Positions are given in the J2015.5 epoch. xtended Data Figure 2 | Atmospheric parameters for the four white dwarfs withphotospheric lithium.
The abundances are in base-10 in terms of number ratio. F [ × e r g s c m Å ] LHS 2534 171819202122 A B m a g F [ × e r g s c m Å ] WD J2317+1830 1920212223 A B m a g F [ × e r g s c m Å ] WD J1824+1213 1819202122 A B m a g F [ × e r g s c m Å ] SDSS J1330+6435 0.5 1.0 2.0 5.0Wavelength [ m]20222426 A B m a g Extended Data Figure 3 | Best fitting models compared with the spectra and pho-tometry of the four lithium-bearing sample.
In the right-panel of WD J2317 + + σ uncertainties. xtended Data Figure 4 | White dwarf envelope parameters for our sample.
The firstrow indicates the fractional convection zone mass. In subsequent rows, pairs correspondto the sinking timescale at the base of the convection zone in years, and (where abun-dances were determined) the elemental mass in the convection zone in g, i.e. ( τ Z / yr , m Z / g) .Diffusion timescales are given for all elements commonly considered in white dwarf plan-etary abundance studies. The final row, “crust”, provides estimates for the total mate-rial within the white dwarf convection zones, assuming a continental-crust composition ,scaled from the Na masses. ,000 5,000 6,000 7,000 8,000Wavelength [Å]0.00.51.01.52.02.53.03.5 N o r m a li s e d F SDSS J0744+4649SDSS J0916+2540SDSS J1535+1247(a)
Li Na K Ca
Extended Data Figure 5 | SDSS spectra of three additional cool DZs with strongmetal absorption features . Lithium lines are not detected for any of these stars. Spectrahave been smoothed by a Gaussian with a full width half maximum of 3 ˚A for clarity. ,600 7,625 7,650 7,675 7,700 7,725 7,750Vacuum Wavelength [Å]1.21.41.61.82.02.2 F l u x [ e r g s c m Å ] Supplementary Figure 1 | Zeeman splitting of K I at LHS 2534. K I is observed in theregime intermediate to the anomalous Zeeman and Paschen-Back effects. The blue dot-ted lines indicate the expected wavelengths in the field-free case, whereas the red dottedlines mark the calculated wavelengths for a 2.10 MG field. The spectrum wavelengthshave been transformed to the rest-frame. .91.0 N o r m a li s e d F l u x LHS 2534 0.900.951.001.05 WD J2317+18306,650 6,700 6,750Wavelength [Å]0.60.81.0 N o r m a li s e d F l u x WD J1824+1213 6,650 6,700 6,750Wavelength [Å]0.51.01.5 SDSS J1330+6435
Supplementary Figure 2 | Models compared with the lithium lines for each of ourstars.
Our best fitting models, with the revised neutral-broadening constant are shown inred. The models with the nominal broadening constants are shown in orange, demonstrat-ing the poor quality fits (note that abundances are increased by +0 . dex for visibility). upplementary Table 1 | Measured widths of Li I lines. The spectral resolution, σ , wasmeasured from the width of sky emission lines associated with the spectrum of eachstar. The Lorentzian component, γ , was determined from fitting a Voigt profile to eachLi-doublet (the π -component in the case of LHS 2534). Supplementary Table 2 | Tangential velocity and kinematics in the Galactic frame.
The coordinate U is radial away from the Galactic center, V is in the direction of rotation,whereas W is perpendicular to the Galactic disk. We have assumed zero radial velocity.is perpendicular to the Galactic disk. We have assumed zero radial velocity.