An Isolated White Dwarf with 317 s Rotation and Magnetic Emission

The Kepler K2 mission observed J1252 with long-cadence (29.4 minutes) exposures during Campaign 10, which ran from 2016 July 6 through September 20. Vanderburg & Johnson (2014) processed this light curve using their K2SFF task.

J1252 unfortunately fell on CCD Module 4, which failed just over 7 days into Campaign 10. Despite this, the data collected were still sufficient to suggest variability with a semiamplitude of at least 0.24%. However, we were not confident that we could identify the correct Nyquist alias from this periodogram alone (Figure 1). We therefore marked J1252 as a candidate for ground-based follow-up.

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The discovery of J1252's rapid variability resulted from three independent, yet serendipitous, hardware failures: the failure of the Kepler reaction wheels, launching the K2 mission; the failure of CCD Module 4 during K2 Campaign 10, necessitating J1252's inclusion in our ground-based photometry plan; and the temporary failure of the Goodman High-Throughput Spectrograph’s (HTS; Clemens et al. 2004) slit-mask motor on our observing night. We observed J1252 on the 4.1 m Southern Astrophysical Research (SOAR) Telescope on 2018 April 24 as part of a backup photometry plan, after this final failure left us unable to collect spectroscopy using Goodman. We collected a total of 2.9 hr of integration time with 20 s exposures using an S8612 broad-bandpass red-cutoff filter, with an overhead time between subsequent images of approximately 2.7 s.

We bias- and flat-field-corrected the data using median-combined master calibration images. We then used the Python package photutils (Bradley et al. 2019) to centroid and fit a two-dimensional Gaussian profile to sources to determine a theoretically optimal circular aperture (r_ap ∼ 1.6σ; Mighell 1999). These apertures were typically 4–5 pixels in radius, and were surrounded by a background annulus starting 5 pixels from the terminus of the aperture and extending radially a further 10 pixels. Using these parameters we performed photometry, detrending for long-term effects using a quadratic polynomial and clipping the resultant light curve by 3σ. We also applied a barycentric correction to the GPS-synced exposure midpoint timestamps using the Python package astropy (Astropy Collaboration et al. 2013, 2018). We isolated our analysis to the final ∼30 minutes of this observation set, which were marginally less occulted with clouds.

Owing to the poor quality of the SOAR data, we collected additional photometric measurements of J1252 using the Otto Struve 2.1 m Telescope at McDonald Observatory, Fort Davis, TX, on 2018 May 18–19 and on 2019 March 7. We used the ProEM 1024B frame-transfer CCD for data acquisition, which has been adapted to execute and repeat a user-defined sequence of filter changes. This enables collection of nearly simultaneous multiband photometry by alternating the filters, making this system useful for exploring color-dependent behavior in variable objects.

On 2018 May 18, we observed J1252 for 1.43 hr at a 10 s cadence using a BG40 filter, which has a similar transmission profile to the S8612 filter used in our SOAR data. On May 19, we swapped between SDSS-g and -i filters in consecutive frames. This executed for 2.38 hr at a 10 s cadence, with a 3 s blank frame between each exposure to allow the filter wheel to rotate. We then collected a final set with these same observation parameters on 2019 March 7 for 2.56 hr.

We bias-, dark-, and flat-field-corrected the McDonald data using standard calibration frames taken before each night of observations. Then, we performed circular aperture photometry to generate light curves using the Image Reduction and Analysis Facility (IRAF; Tody 1986) routine CCD_HSP (Kanaan et al. 2002). Treating each night and filter’s light curve individually, we divided the light curves by the weighted mean of the comparison stars and normalized them by the average object flux. We clipped out any extreme outliers and detrended the light curves with quadratic polynomials to remove long-term trends. We tested a range of aperture sizes and defined the optimal aperture based on the light curve with the minimum average point-to-point scatter. Lastly, we used the WQED software suite (Thompson & Mullally 2013) to apply a barycentric correction to the midexposure timestamps of each image.

We collected 2 hr of time-series spectroscopy of J1252 in 2 minute exposures with SOAR and the Goodman HTS on 2019 June 1 using a 400 line mm⁻¹ grating and 3.2″ slit, corresponding to a slit width of 21 Å. Our spectral resolution was therefore seeing-limited by the sky conditions at an FWHM of 7 Å (1″). The average overhead for each acquisition was 5.45 s. We bias-subtracted the data and trimmed the overscan regions, then completed reduction using a custom Python routine. We flux-calibrated the spectra using standard star EG 274, wavelength-calibrated using HgAr lamps, and applied a zero-point wavelength correction using sky lines from each exposure.

We computed a Lomb–Scargle periodogram from the K2 light curve using the astropy.stats Python package. In our periodogram, we ignore the first few integer harmonics of 47.2 μHz, as these result from the K2 drift correction thruster firing every 5.9 hr (Howell et al. 2014). We used the same tools to produce periodograms for our SOAR and McDonald data, whose rapid acquisition cadence allowed us to identify the correct K2 periodogram alias (Figure 1).

After identifying the true alias, we performed a least squares fit of a sinusoid to the K2 light curve data with the software Period04 (Lenz & Breger 2014), using the peak frequency of 3152 μHz as an initial guess. Our best-fit value for the period of J1252 from K2 is 317.278 ± 0.013 s (3151.807 ± 0.013 μHz). When fitting to the ground-based data, we used this period as an initial guess, and performed nonlinear least squares fits to determine if the period was consistent for all data sets (Table 2).

Because white dwarf rotation rates are typically on the order of hours to days (Berger et al. 2005; Hermes et al. 2017b), we were surprised to find that the period of this object was far shorter, falling at over 11 times the Kepler long-cadence Nyquist frequency (283.5 μHz). Murphy (2014) presents the function by which periodogram amplitude diminishes with super-Nyquist signals as , where t_exp is the instrument sampling rate, and P is the object period. For J1252, the measured amplitude from the Kepler long-cadence sampling rate is diminished by a factor of 17.79 compared to the intrinsic. The inferred intrinsic amplitude from this is 4.20%, which is comparable to the 4.56% amplitude from the McDonald BG40 data (Figure 1). The remaining difference is attributable to the respective Kepler and BG40 filter bandpass shapes and wavelength ranges.

We detected a significant difference in color amplitude, with ratio g/i = 2.26 ± 0.22 in our multicolor light curves, but did not detect a significant phase shift between the two colors (Figure 2). The individual fits also show evidence of period and phase modulations. The 2018 McDonald BG40 and SDSS filter sets were separated in acquisition by one day, but show a 2–3σ difference in the object period. In addition, there is significant power asymmetry in the lobes of the primary feature of the Fourier transform for the observational data, indicative of phase modulation. More data are needed to explore these phenomena further.

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We present the phase-binned 400 l mm⁻¹ SOAR spectra of J1252 in Figure 3. To produce these, we folded our individual spectra into five equally spaced phase bins, each covering one-fifth of the K2 variability period (63.46 s; 12 spectra per bin). We then averaged the spectra within each bin, using only those whose acquisition completely covered the phase window. We note that our acquisition times are larger than the phase windows, and so the resultant smearing between binned spectra complicates phase analysis. Also, given the apparent modulation in phase, we were unable to extrapolate phase associations for these window centers from previous data. Instead, we determined approximate phase values by convolving the binned spectra with the SDSS-g filter transmission profile (Doi et al. 2010) and integrating to produce “flux” measurements, and fitting a sinusoid to these with period fixed to the K2 value. We defined the photometric maximum from this process as phase ϕ = 0°.

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The time-resolved 400 l mm⁻¹ data revealed Balmer absorption features that deepen and diminish with variability phase, where the diminishment corresponds with the appearance of Zeeman-split emission. Variability and Zeeman-split Balmer emission has been seen before in GD 356 (Greenstein & McCarthy 1985), which was classified by Wesemael et al. (1993) as a DAEH (hydrogen-dominated with magnetic emission) white dwarf. J1252 is thus the second star to bear this classification. To determine the magnetic field strength, we performed a least squares fit of the Hβ profile at both absorption and emission maximum with the Python package lmfit (Newville et al. 2014), using a Lorentzian profile for the wide absorption feature and Gaussian profiles for the emission peaks. The Zeeman emission is consistent with a surface-averaged magnetic field for J1252 of 5.0 ± 0.1 MG (Table 3 and Figure 4), as calculated using the Hβ magnetic transitions cataloged in Schimeczek & Wunner (2014). This single value is a weighted average of the individual magnetic fields associated with each line shift, with weights determined by respective uncertainties. The spectral variability indicates that the magnetic spot is oriented along our line of sight at photometric minimum, which is the site of the strongest concentration of magnetic field lines. Therefore, this orientation provides the best measure of the polar magnetic field. Consequently, the absorption center in the phase of maximum absorption does not align with the central emission peak in the phase of maximum emission. This can be an effect of different hemisphere-averaged magnetic fields in the two phases.

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Table 3.  Line Locations and Associated Magnetic Field Strengths for Hβ Profile Fit at Emission Minimum and Maximum (Figure 4)

Line	Wavelength (Å)	B (MG)
Absorption	4860.3 ± 2.3	⋯
Em. π	4855.3 ± 0.8	5.2 ± 0.3
Em.	4797.0 ± 0.8	5.2 ± 0.2
Em.	4906.2 ± 1.0	4.7 ± 0.2

Note. Field strength estimates are derived from Schimeczek & Wunner (2014).

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Unfortunately, the effect of magnetism makes spectroscopic fitting of Balmer features to determine temperature and gravity for J1252 unreliable. We confirmed this by comparing our binned spectrum at the deepest absorption phase to model spectra from Koester (2010; convolved with the night’s seeing at 7 Å), and found that even Balmer features corresponding with were narrower than those we observed in J1252. Likewise, the expected equatorial rotation velocity of J1252 at ∼ () would introduce Doppler broadening (Δλ/λ = v/c) on the order of 2.5 Å at Hβ, a negligible effect compared to our observed feature widths.

Continuum fitting offers an alternative method to measure these parameters. Gentile Fusillo et al. (2019) produced estimates for and T_eff for over ∼260,000 white dwarfs, including J1252, by fitting Gaia reddening-corrected absolute photometry to both hydrogen- and helium-model atmospheres (Holberg & Bergeron 2006; Kowalski & Saumon 2006; Bergeron et al. 2011; Tremblay et al. 2011). Using hydrogen, the authors calculate best values for J1252 of T_eff = 7642 ± 99 K and , which corresponds to a mass of 0.56 ± 0.03M_⊙.

To improve on the Gentile Fusillo et al. (2019) results, we used the narrower-band SDSS survey photometry to produce more comprehensive photometric estimates of and T_eff for J1252. Because our time-series spectroscopy revealed Balmer absorption, we performed fitting of hydrogen-model atmospheres to the recalibrated SDSS catalog PSF magnitudes (Holberg & Bergeron 2006). We interpolated the Bergeron DA models bicubically, and generated model photometry at each point for a grid of values spanning 7.50–8.50 at a resolution of 0.01, and T_eff spanning 7000–9000 K every 1 K. At each point in this grid, we evaluated the reduced χ² of the observed photometry as fit to the generated model, and selected the T_eff and combination, which produced a closest to 1. We noted that there is a large mismatch between the observed and predicted photometry for the near-UV range of ∼2000–3000 Å, so we only perform fits using the SDSS-griz points. We speculate on the origin of this deficit in Section 4.2.

The uncertainties in and T_eff include the photometric variability of the source, whose variability phase was unknown at the time of the SDSS acquisition. In order to account for this, we performed a Monte Carlo simulation. We perturbed each of the SDSS points 1000 times according to a probability distribution function produced by convolving a Gaussian noise profile, generated from the mean errors on the SDSS PSF magnitudes, with an arcsine probability distribution expected from the assumed sinusoidal variability signal in each filter band, and performed model fitting with these new points. We did not correct the photometry for reddening, as J1252 is less than 100 pc from Earth, where reddening effects should be negligible (Genest-Beaulieu & Bergeron 2014).

Our best estimates for J1252 are T_eff = 8237 ± 206 K and (Figure 5), suggesting a mass of 0.65 ± 0.03M_⊙, which is higher than the Gentile Fusillo et al. (2019) result and slightly above the average for white dwarfs (0.62M_⊙; Genest-Beaulieu & Bergeron 2019).

Our observations of periodic Zeeman-split Balmer emission confirm that J1252's photometric variations are consistent with a magnetic surface spot rotating in and out of view, with the photometric period corresponding to the star’s rotation. The appearance and disappearance of the emission with rotation phase suggests that the excitation region is localized on the stellar surface.

J1252 is also apparently isolated, with no detectable mass transfer from a stellar companion that might enhance its rotation rate and variability (Figure 6). To place limits on the possibility of a stellar companion, we used the Database of Ultracool Parallaxes (Dupuy & Liu 2012; Dupuy & Kraus 2013; Liu et al. 2016) to produce spectral energy distributions (SEDs) for late-type stellar objects that had both WISE photometry and known parallaxes. We then compared these SEDs to that of J1252 to determine the earliest companion spectral type, which could be consistent with J1252's AllWISE photometry. While there was significant variation in W1 and W2 magnitudes for the brown dwarf regime, the WISE photometry of the latest L-dwarfs (∼L9) consistently exceeded that of J1252 by approximately 3σ or more. We therefore may rule out a stellar or substellar companion earlier than spectral type T.

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We also considered the possibility of an unseen white dwarf companion by fitting composite white dwarf models to the measured SED. These exercises show that we cannot formally rule out a very cool, very high-mass (≲5000 K, ≳1.2M_⊙) white dwarf companion, or a binary of two white dwarfs with roughly equal temperatures to J1252 whose combined mass is significantly super-Chandrasekhar (≳1.9M_⊙). While these contrived systems are consistent with our SED, we do not think them likely and they do not provide explanatory power for the observed magnetic emission. Absent any compelling evidence for binarity, we adopt the simplest fit to the SED of an apparently isolated white dwarf.

The only other isolated white dwarf observed to exhibit Zeeman-split hydrogen emission is GD 356 (T_eff = 7510 K, ), which has a 13 MG polar magnetic field (Greenstein & McCarthy 1985; Bergeron et al. 2001; Wickramasinghe et al. 2010). It also shows low-amplitude (∼0.2%) variability on a 115 minute timescale, suggesting a surface spot that is never fully out of view due to the star’s rotation axis orientation (Brinkworth et al. 2004). Balmer emission is the only recognizable feature in GD 356's spectrum, though its SED fitting suggests a helium-dominated atmosphere (Bergeron et al. 2001).

Li et al. (1998) first suggested what has become the predominant model by which GD 356 exhibits emission. This model consists of a white dwarf with a dipole magnetic field that is orbited by a conducting body, such as a rocky planet. The orbit of this conducting body through the star’s magnetosphere induces an electromotive force (and therefore a current) that is oriented along the magnetic field lines connecting the star and the companion. This type of system represents an example of a unipolar inductor. The closing of this “circuit” at either end heats both the orbiting object and the upper atmosphere of the star at its magnetic poles. If the companion is more conductive than the white dwarf (e.g., a rocky planet with no atmosphere, or a hotter white dwarf; Li et al. 1998), ohmic dissipation of the energy from the system will occur preferentially in the primary white dwarf atmosphere, producing temperatures capable of exciting chromospheric gas into emission (Wickramasinghe et al. 2010). This mechanism is known to be active in the Jupiter-Io system, where Io’s orbit through Jupiter’s magnetic field induces emission in both the radio and UV (Goldreich & Lynden-Bell 1969; Connerney et al. 1993; Clarke et al. 2002).

Wickramasinghe et al. (2010) suggest that a rocky planet driving the unipolar inductor in GD 356 potentially formed as the result of a double white dwarf merger, because it is unlikely that a rocky planet would survive the later stages of single-star evolution. The authors hypothesize that during a merger, one star may fully tidally disrupt and form a disk around the more massive companion. The disk may then cool from the exterior and begin to form dust and rocky material, and eventually planetary objects. This model has also been hypothesized for the origin of planets around millisecond pulsars (Podsiadlowski et al. 1991).

A binary merger can produce a remnant with anomalously high-mass, which neither GD 356 nor J1252 appear to possess. However, Dan et al. (2014) suggest that the merger of two low-mass white dwarfs (≲0.4M_⊙) can produce a single remnant with a mass near the white dwarf average. Furthermore, invoking a merger scenario potentially explains the appearance of high magnetic fields in GD 356 and J1252, which may be generated exclusively through mergers (Tout et al. 2008; Nordhaus et al. 2011). If the unipolar inductor model is also applicable to J1252, these two objects may represent a new class of white dwarf merger remnants—magnetic emission line systems driven by a planetary dynamo mechanism.

During our SED fitting process to determine estimates of J1252's atmospheric parameters, we noted that the near-UV filter fluxes (GALEX NUV and SDSS-u) fell well under the DA model atmosphere predictions. Gentile Fusillo et al. (2018) identify a source for this discrepancy by using the weakly magnetic WD2105-820 to show that white dwarf magnetism suppresses convection to the extent that radiative stellar models fit more accurately to observed spectra, even in temperature regimes where atmospheres should be convective (T_eff < 12,000 K; Tremblay et al. 2011). This effect is particularly pronounced in the near-UV, where flux can be diminished on the order of 20%. Because J1252 is within this convective temperature regime and is strongly magnetic, the inclusion of convective mixing in the Bergeron models makes them a poor calibrator for J1252's near-UV flux.

We note as well that our SDSS-g/i amplitude ratio outscales more strongly magnetic white dwarfs with similar multicolor photometry (Scholz et al. 2018). A potential explanation for both this and the UV deficit is the blanketing of flux in the near-UV due to metal pollution, which is then reemitted in the optical. This “fluorescence” process (Maoz et al. 2015) is not an outlandish consequence of a system with potential rocky planetary debris; an estimated 30%–50% of white dwarfs experience metal pollution (Koester et al. 2014). Furthermore, the amplitude of this variability may be accentuated by the channeling of material onto localized areas of the stellar surface, which results from magnetic activity. We speculate as well that the presence of strong emission at Hβ also contributes to our large amplitude discrepancy.

In order to explore remaining questions on the presence of an unseen companion or near-UV activity, we encourage infrared and ultraviolet observations be taken for J1252. Furthermore, the unipolar inductor process may induce magnetic braking on the rotation of J1252, which would gradually slow the stellar rotation rate. Therefore, we also encourage ongoing monitoring of the variability period for J1252 in order to constrain this possibility, and to investigate the apparent phase modulation.