We announce the discovery of the most massive pulsating hydrogen-atmosphere (DA) white dwarf (WD) ever discovered, GD 518. Model atmosphere fits to the optical spectrum of this star show it is a 12,030 +/- 210 K WD with a log(g) = 9.08 +/- 0.06, which corresponds to a mass of 1.20 +/- 0.03 Msun. Stellar evolution models indicate that the progenitor of such a high-mass WD endured a stable carbon-burning phase, producing an oxygen-neon-core WD. The discovery of pulsations in GD 518 thus offers the first opportunity to probe the interior of a WD with a possible oxygen-neon core. Such a massive WD should also be significantly crystallized at this temperature. The star exhibits multi-periodic luminosity variations at timescales ranging from roughly 425-595 s and amplitudes up to 0.7%, consistent in period and amplitude with the observed variability of typical ZZ Ceti stars, which exhibit non-radial g-mode pulsations driven by a hydrogen partial ionization zone. Successfully unraveling both the total mass and core composition of GD 518 provides a unique opportunity to investigate intermediate-mass stellar evolution, and can possibly place an upper limit to the mass of a carbon-oxygen-core WD, which in turn constrains SNe Ia progenitor systems.
We searched through the entire Gaia EDR3 candidate white dwarf catalogue for stars with proper motions and positions that are consistent with the stars having escaped from the Alpha Persei cluster within the past 81~Myr, the age of the cluster. In this search we found five candidate white dwarf escapees from Alpha Persei and obtained spectra for all five. We confirm that three are massive white dwarfs sufficiently young to have originated in the cluster. All three are more massive than any white dwarf previously associated with a cluster using Gaia astrometry, and possess some of the most mass…
We report the discovery of four massive ($M > 0.8\,M_\odot$) ZZ Ceti white dwarfs, including an ultramassive $1.16\,M_\odot$ star. We obtained ground based, time-series photometry for thirteen white dwarfs from the Sloan Digital Sky Survey Data Release 7 and Data Release 10 whose atmospheric parameters place them within the ZZ Ceti instability strip. We detect mono-periodic pulsations in three of our targets (J1053, J1554, and J2038) and identify three periods of pulsation in J0840 (173, 327, and 797 s). Fourier analysis of the remaining nine objects do not indicate variability above the $4\la…
With the Keck I Low-Resolution Imaging Spectrometer we have observed nine white dwarf candidates in the very rich open cluster NGC 2099 (M37). The spectroscopy shows seven to be DA white dwarfs, one to be a DB white dwarf, and one to be a DZ white dwarf. Three of these DA white dwarfs are consistent with singly evolved cluster membership: an ultramassive (1.28$^{+0.05}_{-0.08}$ M$_\odot$) and two intermediate-mass (0.70 and 0.75 M$_\odot$) white dwarfs. Analysis of their cooling ages allows us to calculate their progenitor masses and establish new constraints on the initial-final mass relation…
We use Gaia DR2 kinematic data and white dwarf evolutionary models to determine that the young and ultramassive white dwarf GD 50 is a likely member of the AB Doradus moving group. Comparison with the Montréal white dwarf evolutionary models and the MIST main-sequence lifetimes imply a total age of 117 $\pm$ 26 ($\pm$ 13 statistic, $\pm$ 22 systematic) Myr, accounting for all possible C/O/Ne core compositions and using the Pleiad white dwarf LB 1497 as a comparison benchmark. This is the first white dwarf cosmochronology age for a nearby young moving group, and allows us to refine the age of t…
We search for merger products among the 25 most massive white dwarfs in the Montreal White Dwarf Database 100 pc sample through follow-up spectroscopy and high-cadence photometry. We find an unusually high fraction, 40%, of magnetic white dwarfs among this population. In addition, we identify four outliers in transverse velocity and detect rapid rotation in five objects. Our results show that $56^{+9}_{-10}$\% of the $M\approx1.3~M_{\odot}$ ultramassive white dwarfs form through mergers. This fraction is significantly higher than expected from the default binary population synthesis calculatio…
The precise astrometric measurements of the Gaia Data Release 2 have opened the door to detailed tests of the predictions of white dwarf cooling models. Significant discrepancies between theory and observations have been identified, the most striking affecting ultramassive white dwarfs. Cheng et al. (2019) found that a small fraction of white dwarfs on the so-called Q branch must experience an extra cooling delay of $\sim 8\,$Gyr not predicted by current models. $^{22}$Ne phase separation in a crystallizing C/O white dwarf can lead to a distillation process that efficiently transports $^{22}$N…
The internal structures of pulsating white dwarfs can be explored only with asteroseismology. Time series photometric observations were made for the pulsating DA white dwarf (ZZ Ceti star) WD~0246+326 during 9 nights in 2014 with a bi-site observation campaign. Eleven frequencies were detected including 1 triplet, 2 doublets, and 4 single modes, which are identified as either $l=1$ or $l=2$ modes with the complementarity of frequencies present in the literature. From the multiplets, the rotation period of \astrobj{WD~0246+326} is derived as $3.78\pm 0.11$ days. The average period spacing of th…
White dwarf stars are the most common end point of stellar evolution. Of special interest are the ultramassive white dwarfs, as they are related to type Ia Supernovae explosions, merger events, and Fast Radio Bursts. Ultramassive white dwarfs are expected to harbour oxygen-neon (ONe) cores as a result of single standard stellar evolution. However, a fraction of them could have carbon-oxygen (CO) cores. Recent studies, based on the new observations provided by the {\it Gaia} space mission, indicate that a small fraction of the ultramassive white dwarfs experience a strong delay in their cooling…
Ultramassive white dwarfs are extreme endpoints of stellar evolution. Recent findings, such as a missing multi-Gyr cooling delay for a number of ultramassive white dwarfs and a white dwarf with a quasi-Chandrasekhar mass, motivate a better understanding of their evolution. A key process still subject to important uncertainties is the crystallization of their dense cores, which are generally assumed to be constituted of $^{16}$O, $^{20}$Ne, and a mixture of several trace elements (most notably $^{23}$Na and $^{24}$Mg). In this work, we use our recently developed Clapeyron integration technique …
The distribution of white dwarf rotation periods provides a means for constraining angular momentum evolution during the late stages of stellar evolution, as well as insight into the physics and remnants of double degenerate mergers. Although the rotational distribution of low mass white dwarfs is relatively well constrained via asteroseismology, that of high mass white dwarfs, which can arise from either intermediate mass stellar evolution or white dwarf mergers, is not. Photometric variability in white dwarfs due to rotation of a spotted star is rapidly increasing the sample size of high mas…
We report the discovery of a nearby massive white dwarf with He-H atmosphere. The white dwarf is located at a distance of $74.5\pm0.9$ pc. Its radius, mass, effective temperature, H/He ratio and age are $R=2500\pm100$ km, $M=1.33\pm0.01$ $\rm M_{\odot}$, $T_{\mathrm{eff}}=31200\pm 1200$ K, ${\mathrm{H/He}}\sim0.1$ and $330\pm40$ Myr, respectively. The observed spectrum is redshifted by $V_{\mathrm{r}}=+240\pm15$ km s$^{-1},$ which is mostly attributed to the gravitational redshift. The white dwarf shows a regular stable photometric variability with amplitude $Δg\approx0.06^{\mathrm{m}}$ and pe…
Following the discovery of the T8 subdwarf WISEJ200520.38+542433.9 (Wolf 1130C), with common proper motion to a binary (Wolf 1130AB) consisting of an M subdwarf and a white dwarf, we set out to learn more about the old binary in the system. We find that the A and B components of Wolf 1130 are tidally locked, which is revealed by the coherence of more than a year of V band photometry phase folded to the derived orbital period of 0.4967 days. Forty new high-resolution, near-infrared spectra obtained with the Immersion Grating Infrared Spectrometer (IGRINS) provide radial velocities and a project…
We present a set of ultramassive white dwarf models, focused on masses above $1.3\,M_\odot$. Given the uncertainties about the formation and compositions of such objects, we construct parameterized model sequences, guided by evolutionary calculations including both single star and double white dwarf merger formation channels. We demonstrate that the cooling of objects with central densities in excess of $10^9\,\rm g\,cm^{-3}$ is dominated by neutrino cooling via the Urca process in the first $\approx 100$ Myr after formation. Our models indicate that the recently discovered ultramassive white …
We report the most rapid rate of period change measured to date for a pulsating DA (hydrogen atmosphere) white dwarf (WD), observed in the 292.9 s mode of WD 0111+0018. The observed period change, faster than 10^{-12} s/s, exceeds by more than two orders of magnitude the expected rate from cooling alone for this class of slow and simply evolving pulsating WDs. This result indicates the presence of an additional timescale for period evolution in these pulsating objects. We also measure the rates of period change of nonlinear combination frequencies and show that they share the evolutionary char…
We report the discovery of the first pulsating extremely low mass (ELM) white dwarf (WD), SDSS J184037.78+642312.3 (hereafter J1840). This DA (hydrogen-atmosphere) WD is by far the coolest and the lowest-mass pulsating WD, with Teff = 9100 \pm 170 K and log g = 6.22 \pm 0.06, which corresponds to a mass ~ 0.17 Msun. This low-mass pulsating WD greatly extends the DAV (or ZZ Ceti) instability strip, effectively bridging the log g gap between WDs and main sequence stars. We detect high-amplitude variability in J1840 on timescales exceeding 4000 s, with a non-sinusoidal pulse shape. Our observatio…
The Sloan Digital Sky Survey has allowed us to increase the number of known white dwarfs by a factor of five and consequently the number of known pulsating white dwarfs also by a factor of five. It has also led to the discovery of new types of variable white dwarfs, as the variable hot DQs, and the pulsating Extremely Low Mass white dwarfs. With the Kepler Mission, it has been possible to discover new phenomena, the outbursts present in a few pulsating white dwarfs.
We present an analysis of the most massive white dwarf candidates in the Montreal White Dwarf Database 100 pc sample. We identify 25 objects that would be more massive than $1.3~M_{\odot}$ if they had pure H atmospheres and CO cores, including two outliers with unusually high photometric mass estimates near the Chandrasekhar limit. We provide follow-up spectroscopy of these two white dwarfs and show that they are indeed significantly below this limit. We expand our model calculations for CO core white dwarfs up to $M=1.334\ M_\odot$, which corresponds to the high-density limit of our equation-…
We report the discovery of two new pulsating extremely low-mass (ELM) white dwarfs (WDs), SDSS J161431.28+191219.4 (hereafter J1614) and SDSS J222859.93+362359.6 (hereafter J2228). Both WDs have masses <0.25 Msun and thus likely harbor helium cores. Spectral fits indicate these are the two coolest pulsating WDs ever found. J1614 has Teff = 8880 +/- 170 K and log g = 6.66 +/- 0.14, which corresponds to a roughly 0.19 Msun WD. J2228 is considerably cooler, with a Teff = 7870 +/- 120 K and log g = 6.03 +/- 0.08, which corresponds to a roughly 0.16 Msun WD, making it the coolest and lowest-mass pu…
Time-resolved low resolution Hubble Space Telescope ultraviolet spectra together with ground-based optical photometry and spectra are used to constrain the temperatures and pulsation properties of six cataclysmic variables containing pulsating white dwarfs. Combining our temperature determinations for the five pulsating white dwarfs that are several years past outburst with past results on six other systems shows that the instability strip for accreting pulsating white dwarfs ranges from 10,500-15,000K, a wider range than evident for ZZ Ceti pulsators. Analysis of the UV/optical pulsation prop…
The unprecedented extent of coverage provided by Kepler observations recently revealed outbursts in two hydrogen-atmosphere pulsating white dwarfs (DAVs) that cause hours-long increases in the overall mean flux of up to 14%. We have identified two new outbursting pulsating white dwarfs in K2, bringing the total number of known outbursting white dwarfs to four. EPIC 211629697, with T_eff = 10,780 +/- 140 K and log(g) = 7.94 +/- 0.08, shows outbursts recurring on average every 5.0 d, increasing the overall flux by up to 15%. EPIC 229227292, with T_eff = 11,190 +/- 170 K and log(g) = 8.02 +/- 0.0…
We present observations of a new phenomenon in pulsating white dwarf stars: large-amplitude outbursts at timescales much longer than the pulsation periods. The cool (Teff = 11,010 K), hydrogen-atmosphere pulsating white dwarf PG 1149+057 was observed nearly continuously for more than 78.8 d by the extended Kepler mission in K2 Campaign 1. The target showed 10 outburst events, recurring roughly every 8 d and lasting roughly 15 hr, with maximum flux excursions up to 45% in the Kepler bandpass. We demonstrate that the outbursts affect the pulsations and therefore must come from the white dwarf. A…
We report the discovery of the first millisecond pulsar with a pulsating white dwarf companion. Following the recent discoveries of pulsations in extremely low-mass (ELM, <0.3 Msol) white dwarfs (WDs), we targeted ELM WD companions to two millisecond pulsars with high-speed Gemini photometry. We find significant optical variability in PSR J1738+0333 with periods between roughly 1790-3060 s, consistent in timescale with theoretical and empirical observations of pulsations in 0.17 Msol He-core ELM WDs. We additionally put stringent limits on a lack of variability in PSR J1909-3744, showing this …
The Kepler spacecraft provides new opportunities to search for long term frequency and amplitude modulations of oscillation modes in pulsating stars. We ana- lyzed nearly two years of uninterrupted data obtained with this instrument on the DBV star KIC 08626021 and found clear signatures of nonlinear resonant mode coupling af- fecting several triplets. The behavior and timescales of these amplitude and frequency modulations show strong similarities with theoretical expectations. This may pave the way to new asteroseismic diagnostics, providing in particular ways to measure for the first time l…
At present, a large number of pulsating white dwarf (WD) stars is being discovered either from Earth-based surveys such as the Sloan Digital Sky Survey, or through observations from space (e.g., the Kepler mission). The asteroseismological techniques allow us to infer details of internal chemical stratification, the total mass, and even the stellar rotation profile. In this paper, we first describe the basic properties of WD stars and their pulsations, as well as the different sub-types of these variables known so far. Subsequently, we describe some recent findings about pulsating low-mass WDs…
White dwarfs are the burnt out cores of Sun-like stars and are the final fate of 97% of all stars in our Galaxy. The internal structure and composition of white dwarfs are hidden by their high gravities, which causes all elements, apart from the lightest ones, to settle out of their atmospheres. The most direct method to probe the inner structure of stars and white dwarfs in detail is via asteroseismology. Here we present the first known pulsating white dwarf in an eclipsing binary system, enabling us to place extremely precise constraints on the mass and radius of the white dwarf from the lig…
Two low-mass pre-white dwarfs, which could be precursors of ELM white dwarfs, have been observed to show multiperiodic photometric variations. They could constitute a new class of pulsating low-mass pre-white dwarf stars. We present a detailed nonadiabatic pulsation study of such stars, employing full evolutionary sequences of low-mass He-core pre-white dwarf models. We have considered models in which element diffusion is accounted for and also models in which it is neglected. We confirm and explore in detail a new instability strip in the domain of low gravities and low effective temperatures…
We present analysis of a new pulsating helium-atmosphere (DB) white dwarf, EPIC~228782059, discovered from 55.1~days of {\em K2} photometry. The long duration, high quality light curves reveal 11 independent dipole and quadruple modes, from which we derive a rotational period of $34.1 \pm 0.4$~hr for the star. An optimal model is obtained from a series of grids constructed using the White Dwarf Evolution Code, which returns $M_{*} = 0.685 \pm 0.003 M_{\odot}$, $T_{\rm{eff}}= 21{,}910 \pm 23$\,K and $\log g = 8.14 \pm0.01$\,dex. These values are comparable to those derived from spectroscopy by …
We present a preliminary analysis of the cool pulsating white dwarf GD 1212, enabled by more than 11.5 days of space-based photometry obtained during an engineering test of the two-reaction-wheel-controlled Kepler spacecraft. We detect at least 19 independent pulsation modes, ranging from 828.2-1220.8 s, and at least 17 nonlinear combination frequencies of those independent pulsations. Our longest uninterrupted light curve, 9.0 days in length, evidences coherent difference frequencies at periods inaccessible from the ground, up to 14.5 hr, the longest-period signals ever detected in a pulsatin…
Many extremely low-mass (ELM) white-dwarf (WD) stars are currently being found in the field of the Milky Way. Some of these stars exhibit long-period nonradial $g$-mode pulsations, and constitute the class of ELMV pulsating WDs. In addition, several low-mass pre-WDs, which could be precursors of ELM WDs, have been observed to show short-period photometric variations likely due to nonradial $p$ modes and radial modes. They could constitute a new class of pulsating low-mass pre-WD stars, the pre-ELMV stars. Here, we present the recent results of a thorough theoretical study of the nonadiabatic p…
White dwarfs correspond to the final stages of stellar evolution of solar-type stars. In these objects, production of energy by nuclear burning has ended which means that a white dwarf simply cools down over the course of the next billion years. It is now known that white dwarfs spend some of their cooling history in an instability strip. The pulsating white dwarfs with an hydrogen atmosphere (called DAV or ZZ Ceti stars) show non-radial oscillation modes with periods in the range 100 - 1200s. In this work we try to illustrate how the oscillation p-mode frequencies of idealized white dwarf mod…
Pulsating low-mass white dwarf stars are white dwarfs with stellar masses between 0.30~M$_{\odot}$ and 0.45~M$_{\odot}$ that show photometric variability due to gravity-mode pulsations. Within this mass range, they can harbour both a helium- and hybrid-core, depending if the progenitor experienced helium-core burning during the pre-white dwarf evolution. SDSS J115219.99$+$024814.4 is an eclipsing binary system where both components are low-mass white dwarfs, with stellar masses of 0.362$\pm$0.014~M$_{\odot}$ and 0.325$\pm$0.013~M$_{\odot}$. In particular, the less massive component is a pulsat…
We present a dedicated search for new pulsating helium-atmosphere (DBV) white dwarfs from the Sloan Digital Sky Survey using the McDonald 2.1m Otto Struve Telescope. In total we observed 55 DB and DBA white dwarfs with spectroscopic temperatures between 19,000 and 35,000K. We find 19 new DBVs and place upper limits on variability for the remaining 36 objects. In combination with previously known DBVs, we use these objects to provide an update to the empirical extent of the DB instability strip. With our sample of new DBVs, the red edge is better constrained, as we nearly double the number of D…
Recent years have witnessed the discovery of many low-mass ($\lesssim 0.45 M_{\odot}$) white dwarf (WD) stars --- expected to harbor He cores--- in the field of the Milky Way and in several galactic globular and open clusters. Recently, three pulsating objects of this kind have been discovered: SDSS J1840+6423, SDSS J1112+1117, and SDSS J1518+0658. Motivated by these very exciting findings, and in view of the valuable asteroseismological potential of these objects, we present here the main outcomes of a detailed theoretical study on the seismic properties of low-mass He-core WDs based on fully…
We present an analysis of the ultraviolet light curves of five Hot DQ white dwarfs recently observed with the Cosmic Origins Spectrograph (COS) on board the Hubble Space Telescope (HST). These light curves were constructed by extracting the time-tag information from the FUV and NUV spectroscopic data. Single-color light curves were thus produced in 60 s time bins. The Fourier analysis of these data successfully recovers the main pulsation modes of the three stars previously known to be variable from ground-based observations. We also report the discovery of pulsations in another object, SDSS J…
The pulsating hydrogen atmosphere white dwarf star G 117-B15A has been observed since 1974. Its main pulsation period at 215.19738823(63) s, observed in optical light curves, varies by only (5.12+/-0.82)x10^{-15} s/s and shows no glitches, as pulsars do. The observed rate of period change corresponds to a change of the pulsation period by 1 s in 6.2 million years. We demonstrate that this exceptional optical clock can continue to put stringent limits on fundamental physics, such as constraints on interaction from hypothetical dark matter particles, as well as to search for the presence of exte…
We propose a novel and feasible method to detect dark matter (DM) electron interaction via pulsating white dwarfs (WDs) in the central region of globular clusters. Annihilation of the DM particles captured by those WDs can provide additional energy source along the natural cooling evolution of WDs and the cooling print can be well offered by precise asteroseismology. The measurement of the long time scale physical quantity -- the rates of period variation of pulsation modes -- could be used to constrain the cross section between DM particles and electrons ($σ_{e}$), when DM particle mass $m_χ …
Convective driving, the mechanism originally proposed by Brickhill (1991, 1983) for pulsating white dwarf stars, has gained general acceptance as the generic linear instability mechanism in DAV and DBV white dwarfs. This physical mechanism naturally leads to a nonlinear formulation, reproducing the observed light curves of many pulsating white dwarfs. This numerical model can also provide information on the average depth of a star's convection zone and the inclination angle of its pulsation axis. In this paper, we give two sets of results of nonlinear light curve fits to data on the DBV GD 358…
We employ a state-of-the-art asteroseismological model of G117-B15A, the archetype of the H-rich atmosphere (DA) white dwarf pulsators (also known as DAV or ZZ Ceti variables), and use the most recently measured value of the rate of period change for the dominant mode of this pulsating star to derive a new constraint on the mass of axion, the still conjectural non-barionic particle considered as candidate for dark matter of the Universe. Assuming that G117-B15A is truly represented by our asteroseismological model, and in particular, that the period of the dominant mode is associated to a puls…
We present two new GW Vir-type pulsating white dwarf stars, TIC\,0403800675 (WD\,J115727.68-280349.64) and TIC\,1989122424 (WD J211738.38-552801.18) discovered in the Transiting Exoplanet Survey Satellite (TESS) photometric data. For both stars, the TESS light curves reveal the presence of oscillations with periods in a narrow range between 400 and 410\,s, which are associated with typical gravity ($g$)-modes. Follow-up ground-based spectroscopy shows that both stars have similar effective temperature ($T_\mathrm{eff} = 110,000 \pm 10,000$\,K) and surface gravity ($\log g = 7.5 \pm 0.5$), but …
We present a follow-up analysis of the unique magnetic luminosity-variable carbon-atmosphere white dwarf SDSS J142625.71+575218.3. This includes the results of some 106.4 h of integrated light photometry which have revealed, among other things, the presence of a new periodicity at 319.720 s which is not harmonically related to the dominant oscillation (417.707 s) previously known in that star. Using our photometry and available spectroscopy, we consider the suggestion made by Montgomery et al. (2008) that the luminosity variations in SDSS J142625.71+575218.3 may not be caused by pulsational in…
Many pulsating low-mass white-dwarf stars have been detected in the last years in the field of our Galaxy. Given that some of them exhibit multiperiodic variation of brightness, it is possible to probe their interiors through asteroseismology. We present a detailed asteroseismological study of all the known low-mass variable white dwarf stars based on a complete set of fully evolutionary models representative of low-mass He-core white dwarf stars. We employed adiabatic radial and nonradial pulsation periods for low-mass white dwarf models with stellar masses ranging from $0.1554$ to $0.4352\ M…
We present a theoretical assessment of the expected temporal rates of change of periods ($\dotΠ$) for low-mass ($M_{\star}/M_{\sun} \lesssim 0.45$) and extremely low-mass (ELM, $M_{\star}/M_{\sun} \lesssim 0.18-0.20$) white-dwarf stars, based on fully evolutionary low-mass He-core white dwarf and pre-white dwarf models. Our analysis is based on a large set of adiabatic periods of radial and nonradial pulsation modes computed on a suite of low-mass He-core white dwarf and pre-white dwarf models with masses ranging from $0.1554$ to $0.4352 M_{\sun}$. We compute the secular rates of period change…
A secular variation of the gravitational constant modifies the structure and evolutionary time scales of white dwarfs. Using an state-of-the-art stellar evolutionary code and an up-to-date pulsational code we compute the effects of a secularly varying $G$ on the pulsational properties of variable white dwarfs. Comparing the the theoretical results obtained taking into account the effects of a running $G$ with the observed periods and measured rates of change of the periods of two well studied pulsating white dwarfs, G117--B15A and R548, we place constraints on the rate of variation of Newton's…
We present the results of the asteroseismological analysis of two rich DAVs, G38-29 and R808, recent targets of the Whole Earth Telescope. 20 periods between 413 s and 1089 s were found in G38-29's pulsation spectrum, while R808 is an even richer pulsator, with 24 periods between 404 s and 1144 s. Traditionally, DAVs that have been analyzed asteroseismologically have had fewer than half a dozen modes. Such a large number of modes presents a special challenge to white dwarf asteroseismology, but at the same time has the potential to yield a detailed picture of the interior chemical make-up of D…
SDSS J111215.82+111745.0 is the second pulsating extremely low-mass white dwarf discovered. Two short-period pulsations, 107.56 and 134.275 s, were detected on this star, which would be the first observed pressure mode ($p$-mode) pulsations observed on a white dwarf. While the two potential $p$-modes have yet to be confirmed, they make SDSS J111215.82+111745.0 an interesting object. In this work, we analyzed the whole set of seven periods observed on SDSS J111215.82+111745.0. We adopt three independent period-spacing tests to reveal a roughly 93.4 s mean period spacing of $\ell=1$ $g$-modes, w…
