Two New White Dwarfs With Variable Magnetic Balmer Emission Lines

We report the discovery of two apparently isolated stellar remnants that exhibit rotationally modulated magnetic Balmer emission, adding to the emerging DAHe class of white dwarf stars. While the previously discovered members of this class show Zeeman-split triplet emission features corresponding to single magnetic field strengths, these two new objects exhibit significant fluctuations in their apparent magnetic field strengths with variability phase. The Zeeman-split hydrogen emission lines in LP $705{-}64$ broaden from $9.4$ MG to $22.2$ MG over an apparent spin period of $72.629$ minutes. Similarly, WD J$143019.29{-}562358.33$ varies from $5.8$ MG to $8.9$ MG over its apparent $86.394$-minute rotation period. This brings the DAHe class of white dwarfs to at least five objects, all with effective temperatures within $500$ K of $8000$ K and masses ranging from $0.65{-}0.83\,M_{\odot}$.


INTRODUCTION
White dwarf stars are typically photometrically stable objects; 97% of those observed by the late Kepler Space Telescope between its original mission and K2 Campaign 8 are apparently non-variable to within 1% in the Kepler filter bandpass (Howell et al. 2014;Hermes et al. 2017b). The remaining 3% host a wide variety of variability mechanisms including pulsations (Warner & Robinson 1972;Winget et al. 1981), magnetic spots (Maoz et al. 2015), and interactions with binary companions, planets, and planetary debris (Vanderburg et al. 2015;Hallakoun et al. 2018;Vanderbosch et al. 2020). This variable sample provides a means to understand stellar activity and evolution, both intrinsic (e.g. internal structure and dynamics) and extrinsic (e.g. planetary system evolution and interactions with host stars).
Some particularly enigmatic variable white dwarfs stand out from this sample as evading explanation. Among these are the growing class of DAHe white dwarfs: apparently isolated stars whose spectra are characterized by magnetically split (DH) hydrogen Balmer (DA) emission (De), which also exhibit both photometric variability and corresponding time-dependent variations in their Balmer features. The first object discovered in this class was GD 356, and it remained the only member for 35 years (Greenstein & McCarthy 1985). Across these three-and-a-half decades, astronomers studied GD 356 and speculated as to the source of the emission despite there being no apparent companion to feed it.
The prevailing model for most of this time involved a conducting planet orbiting through the stellar magnetosphere, inducing an electromotive force which excites the stellar atmosphere into emission, in a unipolar inductor configuration akin to that which is active in the Jupiter-Io system (Li et al. 1998;Goldreich & Lynden-Bell 1969). It was further proposed that this planet could have formed from material cast off in a double white dwarf merger, similar to how planets ★ E-mail: jsreding@unc.edu are hypothesized to form around millisecond pulsars (Wickramasinghe et al. 2010;Podsiadlowski et al. 1991). However, GD 356 is only a low-amplitude variable ( rot ≈ 115 min) due to its rotation axis orientation never moving its emission region fully out of our line-of-sight, so behavior exhibited elsewhere on the stellar surface cannot be observed to provide additional information (Brinkworth et al. 2004;Walters et al. 2021).
A second discovery finally established the DAHe class with the identification of SDSS J1252−0234 (Reding et al. 2020), which presents significant (∼5%) photometric variability in SDSS-g on a dominant period of 5.3 minutes. The Balmer features in SDSS J1252−0234 (particularly H ) also transition on this photometric period from moderately broadened absorption at photometric maximum to Zeeman-split triplet emission at photometric minimum, which confirms that the emission region is localized on the stellar surface to magnetic spots. The rapid rotation is anomalous compared to typical white dwarf rotation periods of 0.5−2.2 days (Hermes et al. 2017a), which might indicate that the object formed from a previous stellar merger (Ferrario et al. 1997;Tout et al. 2008;Nordhaus et al. 2011). Gänsicke et al. (2020) then discovered a third object, SDSS J1219+4715, which bears more of a resemblance to GD 356 with its Balmer emission never fully disappearing, but rotates on a slower timescale ( ≈ 15.3 hr).
In addition to their mysterious behavior, the DAHe white dwarfs also exhibit a remarkable uniformity in their physical characteristics. All three have masses near the white dwarf population average (0.62 ; Genest-Beaulieu & Bergeron 2019), effective temperatures 7500 K < eff < 8500 K, and mega-gauss magnetic fields ( GD356 = 11 MG, Greenstein & McCarthy 1985; J1252 = 5 MG, Reding et al. 2020; J1219 = 18 MG, Gänsicke et al. 2020). This homogeneity, and the non-detection of a planetary companion to GD 356 with targeted study, suggest that the emission behavior may in fact be intrinsic to white dwarfs at this evolutionary phase (Walters et al. 2021). The recent discovery of a similar apparently isolated white dwarf with variable emission, but yet undetectable Here we announce the discovery of two new DAHe white dwarfs, LP 705−64 (Gaia = 16.9 mag) and WD J143019.29−562358.33 ( = 17.4 mag; henceforth J1430), which each present a unique twist on the established Zeeman-split triplet emission seen in the previous three DAHe. LP 705−64 shows two different emission poles in its spectral variability, with one prominently featuring the classical Zeeman triplet emission at H and H like in GD 356, before transitioning to reveal significantly broader Zeeman emission measurable only at H . J1430 shows a pole of Zeeman-split triplet absorption in H , which is filled asymmetrically by broader triplet emission half a rotation cycle later, while H simultaneously reveals fainter triplet emission across the same transition. Both maintain the other established similarities to the known members of the DAHe class, including in temperature, mass, magnetic field strength, and location in observational Hertzsprung-Russell diagrams.
We describe our survey strategy which uncovered these objects and the corresponding observations in Section 2, and follow with a description of our analysis in Section 3. We then discuss the context and broader implications of these objects, and summarize our conclusions in Section 4.

VARINDEX Survey and Gaia Archival Data
We discovered the unusual activity in LP 705−64 (Gaia DR3 2375576682347401216) and J1430 (Gaia DR3 5892465542676716544) using a survey strategy specifically formulated to identify likely DAHe candidates from the broader white dwarf population. We used the Gaia DR2 VARINDEX metric, whose calculation is described in Guidry et al. (2021), to identify the most likely variable objects from over 260,000 high-probability white dwarf candidates in Gaia DR2 (Gentile Fusillo et al. 2019). Given the physical similarity of the DAHe objects discovered so far, with masses 0.65−0.75 and effective temperatures ∼7700 K (Gänsicke et al. 2020), we then limited the selection to the region of the Gaia DR2 Hertzsprung-Russell diagram where DAHe white dwarfs are most likely to reside (12 < < 14, 0.2 < BP − RP < 0.5; Figure 1). We then collected identification spectra of the highest VARINDEX objects, and, if there were suggestions of DAHe activity, determined a variability period from archival sources or follow-up photometry, and ultimately collected time-series spectroscopy folded on the variability period to produce a complete chronology of the spectral activity. Details of these observations for LP 705−64 and J1430 are described in the subsections below. Among our first ∼100 survey candidates, LP 705−64 and J1430 are the first two confirmed DAHe; observations of the remaining objects will be detailed in a future manuscript.
LP 705−64 and J1430 have Gaia DR2 VARINDEX values of 0.0063 and 0.0131, respectively; this places LP 705−64 near and J1430 well within the top 1% of variable white dwarfs (VARINDEX DR2 > 0.0074; Guidry et al. 2021). The parallaxes for these objects are precise enough and suggest a small enough distance ( < 0.1 kpc) such that using = 1/ should provide a sufficiently accurate estimate of the true distance (Luri et al. 2018). Using this distance value and the updated Gaia DR3 proper motions and , we calculate tangential velocity for each object, and find that LP 705−64 has a particularly large tan that is consistent with <30% of low-mass (0.5−0.75 ) and a vanishingly small fraction of intermediate-mass (0.75−0.95 ) white dwarfs (Wegg & Phinney 2012). We discuss the implications of this further in Section 4. These two objects lack sufficient archival survey photometry in the optical and ultraviolet to perform consistent spectral energy distribution fits for eff and log /mass, so we adopt the atmospheric parameters calculated by Gentile Fusillo et al. (2021) using Gaia photometry and hydrogen-atmosphere white dwarf models with thick ( H / WD = 10 −4 ) hydrogen layers (Kowalski & Saumon 2006;Tremblay et al. 2011). This collected information is listed in Table 1. We note that the use of non-magnetic model atmospheres may make photometrically derived effective temperatures and masses artificially low, as magnetism is known to suppress flux particularly in the Gaia BP band, but systematic study suggests this effect is insignificant for stars in the DAHe parameter space (Gentile

SOAR/Goodman HTS Identification Spectra
Upon sorting our DAHe candidates by VARINDEX, we began collecting identification spectra to detect evidence of spectral activity using the Southern Astrophysical Research (SOAR) 4.1-m telescope and Goodman High-Throughput Spectrograph (HTS) at Cerro Pachón, Chile (Clemens et al. 2004). We acquired three 300-second spectra of J1430 on 7 April 2021 using a 400 line mm −1 grating and 3.2 slit, corresponding to a slit width of 21 Å. Our spectral resolution was therefore limited by the wind-impacted observing conditions at a FWHM of 17 Å (2.5 ). We bias-subtracted the data and trimmed the overscan regions, then completed reduction using a custom Python routine (Kaiser et al. 2021). We flux-calibrated the spectra using standard star EG 274, wavelength-calibrated using HgAr and Ne lamps, and applied a zero-point wavelength correction using sky lines from each exposure. These spectra, when averaged, showed jagged Balmer features suggestive of activity, and we marked J1430 for time-series follow-up.
Similarly, we collected five 180-second spectra of LP 705−64 on 6 August 2021 using the same grating but with a 1 (7 Å) slit. Zeemansplit triplet emission features at H and H were clearly visible in these single spectra, thereby confirming LP 705−64 as a DAHe.

TESS Photometry
The Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) observed LP 705−64 (TIC 136884288) in Sector 30 with 120-second exposures, collected from 23 September through 19 October 2020, and J1430 (TIC 1039012860) in Sector 38 with 120-second exposures, collected from 29 April through 26 May 2021. We extracted these light curves for periodogram analysis using the LIGHTKURVE Python package (Lightkurve Collaboration et al. 2018). The periodograms each show one significant peak, whose corresponding periods ( LP705-64 = 36.315 min, J1430 = 86.394 min; Figure 2) we adopted for planning our time-series spectroscopy. Later analysis revealed nuance in this variability, which we discuss further in Section 3.1.

SOAR/Goodman HTS Time-Series Spectroscopy
Following our detection of DAHe activity and discernment of photometric variability periods for LP 705−64 and J1430, we returned to SOAR and the Goodman HTS to investigate spectral feature variations corresponding to the photometric variability using time-series spectroscopy. On 13 July 2021, we collected 5.4 hours (approximately four presumed variability cycles) of time-series spectra for J1430 in 10-minute exposures using the same 400 line mm −1 grating and 3.2 slit as the identification spectra. The spectra were seeinglimited at 1.5 , and the average overhead for each acquisition was 5.45 seconds. We performed the same reductions as were used in the SOAR/Goodman HTS identification spectra (Section 2.2).
We targeted LP 705−64 in a similar fashion on 30 August 2021 using 539-second exposures to reflect equal divisions of the apparent TESS variability period, accounting for the overhead time between subsequent exposures. We collected 24 exposures in this set across 3.6 hours, corresponding to six presumed variability cycles. We discuss folding and combining spectra in these data sets on divisions of the objects' respective variability periods in Section 3.1.

Variability and Time-Series Spectroscopy
We performed least squares fits of a sinusoidal signal sin[2 ( / + )] to the LP 705−64 and J1430 TESS light curves using the software P 04 (Lenz & Breger 2014), where is the amplitude, is the variability period, is the phase shift, and is the observation epoch. Our best-fit value for the period of LP 705−64 is 36.315 ± 0.002 minutes ( = 39.653±0.002 day −1 ), with an amplitude of 1.6±0.2%, and the best-fit period for J1430 is 86.394 ± 0.008 minutes ( = 16.668 ± 0.002 day −1 ), with an amplitude of 9.8 ± 0.8%.
Emulating our process of creating binned spectra for SDSS J1252−0234 in Reding et al. (2020), we folded our individual spectra of LP 705−64 and J1430 into eight equally spaced phase bins, each covering one-eighth of the respective variability periods. We then averaged the exposures within each bin into composite spectra. Our selected exposure time for the LP 705−64 set provided perfect temporal alignment of spectra within each bin, allowing for simple averaging, while for J1430 we accounted for blending across phase bins by weighting spectra during rebinning according to the fraction of the acquisition time spanning each bin.
The brightnesses of our objects and relatively long exposure times made the Zeeman-split Balmer features visible even in single spectra. For LP 705−64, the folded time-series spectroscopy revealed two distinct emission phases presenting different magnetic field strengths, but which were unexpectedly separated by four ∼9-minute acquisitions; i.e., one TESS period separated the two emission phases, rather than reflecting a full variability cycle. This suggests that a halfrotation, rather than a full rotation, is occurring on this timescale. The true rotation period of LP 705−64 must therefore be twice that of the TESS signal at LP705-64 = 72.629±0.004 minutes; we have adopted this convention throughout. Our other target, J1430, returned to its original orientation on the same period as the TESS signal, so we infer its rotation period to be LP705-64 = 86.394 ± 0.008 minutes.
Past DAHe discoveries all present maximal emission at photometric minimum, and LP 705−64 and J1430 appear to follow this same trend by visual inspection of the slopes of spectral continuathe emission phases are present when the continua have the flattest slopes. However, for both of our objects, these slopes eventually become unreliable due to encroaching clouds in the final few exposures. Consequently, we do not attempt to convolve our binned spectra of LP 705−64 and J1430 with theoretical filter profiles to obtain rough "light curves" of our acquisitions, as we did for SDSS J1252−0234 in Reding et al. (2020). We also did not select acquisition times based on anticipated photometric variability phases projected from TESS ephemerides, as our time-series spectroscopy was too far separated in time from the TESS photometry to predict times of maxima or minima with sufficient accuracy. Instead, our division of the variability periods into eight bins provides enough temporal resolution to select spectral phases close to expected photometric maxima and minima.
For LP 705−64, the maximum magnetic field strength visible in the top panels of Figure 3 occurs at a phase within 5% of the photometric minimum of the TESS observations. The maximum field strength (emission phase) for J1430 also occurs significantly closer to the TESS photometric minimum than the weaker magnetic absorption phase. However, extrapolating the ephemeris uncertainties forward to our spectral acquisition times produces error bars on these associations that span nearly a full variability cycle. We therefore invite additional photometric observations that can better reveal the light curve morphology and confidently associate the notable spectral phases with maxima and minima.

Magnetic Field Strengths
To determine magnetic field strengths, we performed least squares fits of the H and H profiles at maximum emission and absorption phases using the Python package LMFIT (Newville et al. 2014). We used a Lorentzian profile for wide absorption features, where applicable, and Gaussian profiles for individual Zeeman components. After finding centroid locations of the feature components, we converted these into magnetic field strength estimates using the magnetic transitions catalogued in Schimeczek & Wunner (2014). Unlike previously analyzed DAHe, both LP 705−64 and J1430 host magnetic fields that evolve significantly across their rotational periods (Figure 3).
For LP 705−64, H and H manifest as Zeeman-split emission with no underlying absorption in both notable spectral phases. In the narrower triplet emission phase, both features are consistent with a field strength of = 9.4 ± 0.6 MG, before they disappear into the continuum and reappear as significantly wider Zeeman emission corresponding to a field strength of = 22.2 ± 0.9 MG. These values represent the weighted averages of the individual field strength estimates from each Zeeman component, with weights determined by respective uncertainties. The overall uncertainty on the weighted average is the standard deviation of the maximally dispersed component estimates.
J1430 mimics SDSS J1252−0234 in exhibiting H absorption at apparent photometric maximum, and emission at photometric minimum. However, unlike its predecessor, in J1430 this absorption is Zeeman-split with a magnetic field strength of = 5.8 ± 0.3 MG, which becomes partially and asymmetrically filled by emission from a stronger magnetic field of = 8.9±1.4 MG at the opposite phase. H more prominently displays this emission as a fully resolved triplet, allowing for easy calculation of this field strength. Reding et al. (2020) found that SDSS J1252−0234 transitions across its variability period from presenting slightly broadened, but not Zeeman-split, Balmer absorption features at photometric maximum, to revealing its significant H Zeeman triplet emission at photometric minimum. This indicates that the magnetic spot, above which the emission manifests and displays the strongest concentration of magnetic field lines, is oriented along our line of sight at photometric minimum. This orientation consequently provides the best measure of the polar magnetic field, while the absorption center in the opposite phase returns closer to the rest-frame wavelength of H . This evolution of the apparent magnetic influence on Balmer features with stellar rotation illustrates that we observe different hemisphereaveraged magnetic fields across the variability phases.

Magnetic Field Geometries
J1430 behaves similarly in transitioning from absorption to emission with an apparent growing magnetic field strength, but differs in its strongly Zeeman-split absorption phase. Furthermore, the J1430 emission phase does not seem to show a clean single-field feature as was seen in SDSS J1252−0234; rather, the previous Zeeman absorption seems to still be present and asymetrically filled, possibly indicating a superposition of two apparent magnetic field signatures. H , conversely, does not show as complicated a transition, with its emission phase presenting an easily measurable feature corresponding to a single field.
LP 705−64 adds further complexity in magnetic field presentation by never showing absorption, but instead exhibiting two emission phases corresponding to drastically different magnetic field strengths at its photometric minima. These two new discoveries therefore break the previous DAHe mold by presenting multiple distinct magnetic field signatures, while the previous three members only displayed Zeeman splitting corresponding to single field strengths. However, as with other known magnetic white dwarfs (e.g., Martin & Wickramasinghe 1984), it is often difficult to distinguish offset dipole emission from higher-order field geometries.

Companion Limits
Owing to their small sizes, the only potential binary systems that can fit within non-overluminous apparently isolated white dwarf spectral Table 2. LP 705−64 and J1430 magnetic field strengths as measured from H and H at notable spectral phases (Figure 3). Field strength estimates are derived from least squares Gaussian profile component fits and magnetic transitions calculated in Schimeczek & Wunner (2014 Table 2. The absorption feature at ∼6900 Å in the H spectra of LP 705−64 (b) is telluric, which partially obscures the + Zeeman component in the wide emission phase. Given the uncertainty in projecting the TESS ephemerides forward to our spectral acquisition times, we instead present the midpoints of the binned spectra in BMJD TDB as markers for future analysis. The data behind this figure are available in the article's online supplementary material. energy distributions are double degenerate systems containing at least one white dwarf of very high mass, or substellar companions which emit most strongly in infrared wavebands. The former case invokes a super-Chandrasekhar-mass binary system, which has never been observed even in targeted searches for the most extreme supernova Ia progenitors (Rebassa-Mansergas et al. 2019). We disregard this for LP 705−64 and J1430 given the lack of substantial radial velocity variability, and only assess potential substellar companions.
The Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) collected infrared photometry of both LP 705−64 (WISE J003513.00−122510.8) and J1430 (WISE J143019.77−562357.5) in 2015, which was reported in the CatWISE2020 catalog (Marocco et al. 2021). We use these measurements and the averaged WISE photometry for late-spectral-type objects from the Database of Ultracool Parallaxes (Dupuy & Liu 2012) to place limits on potential substellar companions to each white dwarf. Because the peak wavelengths of these substellar objects fall in the far-infrared, their fluxes typically rise when moving from the 1 to 2 bands, which runs opposite to the declining trend seen in white dwarfs whose peak wavelengths push into the ultraviolet. The 2 band therefore places the strongest constraints on companion spectral type. We find that 2 photometry of spectral type T4 exceeds the corresponding point for LP 705−64 by over 3-, while spectral type T2 similarly exceeds the 2 photometry of J1430. We therefore rule out a stellar or substellar companion earlier than spectral type T.
Using time-series spectroscopy from the 4.1-m SOAR Telescope, we captured signatures of evolving magnetic fields in each star with rotational phase, setting them apart from the previously discovered members of this class which only presented Zeeman splitting corresponding to single magnetic field strengths. LP 705−64 appears to rotate at 72.629 minutes and displays Zeeman-split Balmer emission at two separate emission phases, corresponding to magnetic field strengths of = 9.4 ± 0.6 MG and = 22.2 ± 0.9 MG. At its weakest, J1430 presents Zeeman-split Balmer absorption corresponding to a magnetic field strength of = 5.8 ± 0.3 MG. Half an 86.394minute rotation cycle later, the absorption appears superimposed with Balmer emission corresponding to a stronger magnetic field strength of = 8.9 ± 1.4 MG. As with the previously known DAHe, the maximum magnetic field strength appears coincident with the photometric minimum from the TESS observations, although phasing over a many-months baseline carries uncertainty. In the case of LP 705−64 we have shown that DAHe white dwarfs can show two magnetic poles.
With five members now known, the DAHe class remains relatively homogenous in its physical characteristics, with all members having mega-gauss magnetic fields, effective temperatures 7500−8500 K, and masses slightly higher than but near the white dwarf population average of 0.62 (Genest-Beaulieu & Bergeron 2019). The nature of the mechanism driving their emission remains elusive, however, 1 After receipt of this paper's referee report, a preprint was posted announcing spectroscopic identification of 21 northern-hemisphere DAHe white dwarfs from the Dark Energy Spectroscopic Instrument (DESI) survey (Manser et al. 2023). as all are apparently isolated with no detectable stellar companion. As pointed out by Walters et al. (2021), the physical similarities of known DAHe strongly suggest the variability mechanism is not extrinsic, and likely represents a phase of evolution for at least some white dwarf stars.
Thus, the origin of DAHe white dwarfs remains a mystery. In addition to strong magnetism, most of the known DAHe rotate significantly faster than a typical white dwarf. One way to generate strong magnetism and rapid rotation in white dwarfs is via a past stellar merger, especially of two white dwarfs (Ferrario et al. 1997;Tout et al. 2008;Nordhaus et al. 2011). Double-degenerate mergers may produce more massive white dwarfs, but the merger of two lowmass white dwarfs ( 0.4 ) can produce a single remnant with a mass near the white dwarf average (Dan et al. 2014). It has also been speculated that planetary engulfment may spin up white dwarfs enough to generate magnetic dynamo activity (Kawka et al. 2019;Schreiber et al. 2021).
Another indicator of a merger origin is a mismatch between expected cooling age and apparent age as inferred from kinematics. This reasoning was used to classify hot carbon-atmosphere (DQ) white dwarfs as likely merger products (Dunlap & Clemens 2015). If descended from single stars without external interactions, initialfinal mass relations and cooling models suggest that the DAHe white dwarfs should have ∼3 progenitors and roughly 2-Gyr total ages Bédard et al. 2020). Kinematic outliers could help reveal if any DAHe are merger byproducts, though this is best performed on a population rather than a single object (Cheng et al. 2020). In this context, the relatively fast kinematics of LP 705−64 ( tan = 52.89 km s −1 ) are interesting, although are not necessarily direct evidence of a past interaction. The other known DAHe have relatively slow kinematics, with tan ≈ 5−35 km s −1 . Discovery and analysis of a larger sample of DAHe will better inform the kinematic ages of this sample.
ing for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.