The Missing Link? Discovery of Pulsations in the Nitrogen-rich PG 1159 Star PG 1144+005

White dwarf stars are the most common end point of stellar evolution with up to 98% of all single stars eventually reaching this phase. Despite their importance, detailed knowledge of the interior structure of only a limited number of white dwarfs is available. White dwarf stars pulsate in certain zones of instability along their cooling curves that define the three classical types of white dwarf pulsators (e.g., Winget & Kepler 2008) within the growing family of (pre–)white dwarf pulsators (Córsico et al. 2019). The first pulsational instability strip entered by a post–asymptotic giant branch (AGB) star is that of the GW Vir stars, followed by the domains of the DB and DA white dwarf pulsators. White dwarfs residing in the GW Vir domain span a large range of effective temperatures (≈75–250 kK) and surface gravities (log g ≈ 5.5–8). Some stars show photometrically detectable pulsations with periods as short as a few minutes due to nonradial gravity modes driven by the κ mechanism associated with the partial ionization of the K-shell electrons of carbon and/or oxygen in the envelope (Starrfield et al. 1983, 1984).

GW Vir pulsators are distinguished by their spectra: most are of the PG 1159–type but there are also [WC]-types, central stars of planetary nebulae with Wolf-Rayet spectra of the carbon sequence (Crowther et al. 1998). Such stars are thought to be formed as a result of a "born-again" episode (a very late thermal pulse (VLTP) experienced by a hot white dwarf during its early cooling phase) or a late thermal pulse that occurs during the post-AGB evolution when H burning is still active (e.g., Iben et al. 2003; Blöcker 2001; Miller Bertolami & Althaus 2006). They are supposed to be the main progenitors of H-deficient white dwarfs, which makes them important to study in the context of stellar evolution. PG 1159 stars exhibit He-, C- and O-rich surface abundances, but strong variations of the He/C/O ratio were found from star to star (Dreizler & Heber 1998; Werner 2001), as were traces of other, heavier elements. The presence of H (such stars are classified as "hybrid PG 1159") together with a N dichotomy (N rich, about 1% in mass and N poor, below about 0.01% in mass, stars) are tracers of the evolutionary history, i.e., when the progenitor experienced the final thermal pulse (Herwig 2001; Werner et al. 2008). The variety of surface abundance patterns observed in PG 1159 stars indeed poses a challenge to the theory of stellar evolution, but its understanding may be key in revealing their evolutionary history.

The instability strips of the pulsating DA and DB white dwarfs are believed to be pure, i.e., all stars within their respective borders do pulsate. Consequently, the pulsators are otherwise normal white dwarfs and their interiors—which can be studied using the technique of asteroseismology—represent the interiors of all white dwarfs. This is not the case for the PG 1159 stars, as the GW Vir instability strip is not pure; according to the literature (e.g., Quirion et al. 2004) only about 50% of them pulsate. This raises the questions of what separates the pulsators from the nonpulsators and whether there are fundamental differences in their interior structures and thus evolutionary histories.

The observed nitrogen dichotomy, i.e., N-rich stars are pulsators, whereas N-poor stars are all nonpulsators (Dreizler & Heber 1998), suggests that N may play a role in driving pulsation, despite its rather small abundance even in N-rich stars. Quirion et al. (2007) refuted this idea finding that a high O abundance is predominantly responsible for driving pulsation. The whole picture, however, is more complicated, involving the physical parameters and chemical compositions of PG 1159 stars, including metallicity and the role of helium "poisoning" the driving of pulsations. The part played by nitrogen as a tracer of the previous evolutionary history of GW Vir stars is therefore interesting in this context. Is a VLTP a necessity for achieving the chemical mixture required to destabilize a star to develop pulsations? This would allow the important conclusion that the GW Vir stars have a fundamentally different evolutionary history than the nonpulsators. In this regard, one final culprit however still remained: PG 1144+005. Ever since the detection of strong N V emission lines in its spectrum (Werner & Heber 1991) and the realization that all pulsating PG 1159 stars are N rich (Dreizler & Heber 1998) it was the only known N-rich PG 1159 star that was never discovered to pulsate.

PG 1144+005 (T_eff = 150,000 ± 15,000 K, $\mathrm{log}g=6.5\pm 0.5$, Werner & Heber 1991) is a G = 15.1734 mag star (Gaia Collaboration 2018) found in the Palomar-Green (PG) Survey by the UV excess (Green et al. 1986). A number of authors observed PG 1144+005 since then, over the last 30 yr. In the pioneering search for extremely hot pulsating stars, Grauer et al. (1987a, 1987b) did not find any variability consistent with pulsations among the program stars, including PG 1144+005, regrettably not providing the detection limit. Over a decade later, Schuh et al. (2000) observed it twice, with a null result. Unfortunately, again, these authors did not note the detection limit of these observations. Finally, Steininger et al. (2003) revisited the object and observed it for four nights on the 1 m telescope at Piszkestetö. Data collected over 5.6 hr showed a light curve with no visible variability and a semiamplitude of about 0.02 mag. The lack of variability was then reflected in the Fourier amplitude spectrum over the range from about 50 day⁻¹ to about 700 day⁻¹, where no peak exceeded an amplitude of 4 mmag. No further time-series observations of the star have been reported since.

We included PG 1144+005 in a sample of PG 1159 stars selected for a survey for variability (P. Sowicka et al. 2021, in preparation). The observations were carried out on 2018 January 17 with the 10 m Gran Telescopio Canarias (GTC) equipped with OSIRIS in one observing block as a filler target. OSIRIS consists of a mosaic of two CCDs of 2048 × 4096 pixels each and has an unvignetted field of view (FOV) of 78 × 78. We used a Sloan r' filter with an exposure time of 6 s and standard readout time, resulting in a duty cycle of about 29 s, over the 1.1 hr length of observations. The data were reduced using standard Astropy (Astropy Collaboration et al. 2013, 2018) ccdproc (Craig et al. 2017) routines consisting of bias subtraction, flat-field and gain correction.

PG 1144+005 is a challenging object for differential photometry. Because of the lack of suitable nearby comparison stars in the typical small FOV of relatively large telescopes, we used a "master" comparison star created as a sum of flux from three stars after making sure they are photometrically constant: MGC 24209, MGC 24219, and MGC 24226, to improve the signal-to-noise ratio (S/N) in the light curve as all those stars are at least 1 mag fainter than the target in r'.

We performed aperture photometry using our own procedures utilizing scaled adaptive aperture sizes to the seeing conditions, as described in Sowicka et al. (2018), in this case characterized by a scaling factor of 1.5 × FWHM for each frame. The differential light curve was then corrected for differential color extinction. Figure 1 shows the final light curve with clear variability, and its Fourier amplitude spectrum up to the Nyquist frequency of 1439 day⁻¹, calculated using Period04 (Lenz & Breger 2005).

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The semiamplitude is about 5 mmag in the light curve, while the median noise level of the Fourier amplitude spectrum is 0.36 mmag (calculated in the range 400–1439 day⁻¹). We identified two peaks, f₁ = 81.60 ± 0.82 day⁻¹ with amplitude A₁ = 5.37 ± 0.37 mmag (S/N of 14.92) and f₂ = 124.036 ± 1.70 day⁻¹ with A₂ = 2.60 ± 0.37 mmag (S/N of 7.22).

This is good evidence that the only remaining N-rich PG 1159 star, PG 1144+005, is a pulsating star and therefore belongs to the GW Vir family. However, the short light curve and the relatively long variability periods called for confirmation.

Follow-up observations were carried out on five nights in 2021 May 6, 8, 9, 10, 11. We observed PG 1144+005 using the 1 m Lesedi telescope located at the South African Astronomical Observatory (SAAO), equipped with the Sutherland High Speed Optical Camera (SHOC; Coppejans et al. 2013) instrument SHA. Thanks to Lesedi's 57 × 57 FOV, the G = 12.8 mag star MGC 24274 (saturated in GTC observations) could be used as the primary comparison star. PG 1144+005 was visible for about 5 hr in the first half of each night and we collected 24.06 hr of data. We varied the exposure time during the nights to adjust to the changing atmospheric conditions and airmass, to avoid saturation of the comparison star, and to mitigate possible Nyquist frequency ambiguities. Table 1 shows the detailed log of observations.

We performed data reduction (including bias, flat-field, and gain correction) and differential aperture photometry using TEA-Phot (Bowman & Holdsworth 2019). TEA-Phot is a data reduction and photometry package designed especially to work with data cubes from the SHOC instruments. It uses adaptive elliptical apertures to extract photometry, where the optimum major and minor axes of the apertures are calculated for each frame from an initial guess from the user based on examination of the displayed curve of growth for the target and comparison star separately. We then corrected each combined nightly light curve for differential color extinction and removed outlying points (3.5σ clipping) and bad-quality parts of data (observations through thick clouds). Figure 2 shows the final light curves from each night, and binned in 40 s overplotted to show the variability more clearly.

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The best quality data (in terms of observing conditions) come from the end of the run. The time base of the whole run is ΔT = 5.1554 days. The frequency resolution needed to resolve the modes and determine the amplitudes and phases correctly is calculated as Δf = 1.5/ΔT (Loumos & Deeming 1978) and equals Δf = 0.29096 day⁻¹. We first calculated Fourier amplitude spectra of each nightly light curve separately. Then we combined the data and calculated the amplitude spectrum of the whole run, together with the spectral window (a single sine wave of arbitrary, constant amplitude—in our case 1—sampled at the times of our time-series data, which shows the aliasing pattern around each frequency in the data). The nightly light curves, amplitude spectra, and the spectral window are shown in Figure 2. Frequencies, amplitudes, and phases were determined by simultaneously fitting a nonlinear least-squares solution to the data using Period04 (Lenz & Breger 2005) and the formal solution is presented in Table 2, where we omitted frequencies below 10 day⁻¹ that we judged to have originated in the Earth's atmosphere.

In the new data we detect the presence of peaks at the same frequency ranges as in our exploratory GTC run, with the main pulsation modes grouped around 40, 55, 97, and 112 day⁻¹. With the caveat that the two higher-frequency groups may be combination frequencies of the two lower-frequency ones, the detected frequencies are consistent with g-mode pulsations excited by the κ-mechanism due to partial ionization of carbon and/or oxygen in the envelopes of PG 1159 stars. The frequencies correspond to periods of about 700–3000 s, in agreement with the period ranges of other known variable PG 1159 stars (e.g., Figure 7 in Córsico et al. 2006). We also find that the amplitude spectrum of PG 1144+005 is variable, with amplitudes of the modes changing between consecutive nights, but the frequencies remaining the same within the temporal resolution. It can be most clearly seen in the case of the region around 55 day⁻¹ in the insets in Figure 2, where the amplitudes change between less than 4 mmag to over 6 mmag. This kind of temporal variability has been shown for other GW Vir stars, either as highly variable amplitudes and/or frequencies, or even as a complete disappearance of the pulsations for a period of time. A more conservative interpretation is the beating of closely spaced pulsation frequencies.

Also, according to Córsico et al. (2009), PG 1144+005 lies in the overlapping region in the H-R diagram where both the κ- and -mechanism can operate. We therefore inspected our nightly amplitude spectra for the presence of high-frequency, -driven modes. We did not find any peaks above the detection threshold of 1 mmag for frequencies above 150 day⁻¹.

Even though we do not attempt to create an asteroseismic model for PG 1144+005, our most important result is the confirmation of the variability preliminarily detected in our GTC run.

We obtained new observations of the N-rich PG 1159 star PG 1144+005 allowing for the discovery of long sought-after pulsations in this star. The first, short, run from the GTC allowed us to estimate the expected frequencies and amplitudes (80–130 day⁻¹ and 3–6 mmag). Follow-up observations over 5 nights at SAAO clearly showed low-amplitude multiperiodic pulsations of PG 1144+005. The pulsations mainly appeared in four regions: 40, 55, 97, and 112 day⁻¹, while the amplitudes were variable over the course of observations. The detected variability is consistent with g-mode pulsations excited in PG 1159 stars.

The g-mode pulsations of PG 1159 stars are low amplitude and high frequency in nature. Most PG 1159 stars are faint, making required high-speed and high-quality follow-up observations challenging. To resolve individual modes and rotational splittings, the time base of a few days is needed (depending on the rotation period). The application of multisite campaigns for the study of these stars, as well as other pulsating white dwarfs and subdwarfs, has already been successfully shown, although only for a handful of the brightest targets. Usually many large telescopes are needed, and the observing time is hard to get. Are the future space telescopes for faint blue stars the only way to study the faintest ones (especially the PG 1159 stars discovered in the Sloan Digital Sky Survey)?

Our discovery of the pulsations in PG 1144+005 provides the last missing piece for the current picture of the excitation mechanism and abundance patterns in PG 1159 stars. Is the N problem thus solved, and the whole picture complete? Or will we find more N-rich nonpulsators or N-poor pulsators if we push the detection limit down?

Out of 55 known PG 1159 stars only 14 objects have their nitrogen abundance, or its upper limit, assessed. These are: the N-rich stars PG 1144+005, PG 1159-035, PG 2131+066, PG 1707+427, PG 0122+200, and A43, and N-poor stars PG 1520+525, PG 1424+535, HS 1517+7403, MCT 0130-1937, HS 0704+6153, H 1504+65, RXJ 0439.8-6809, and NGC 7094. Prerequisites for this type of analysis were spectroscopic observations in (far-)ultraviolet and model atmospheres for such high effective temperatures. Therefore the stars with their nitrogen abundance assessed are those having good-quality Hubble Space Telescope spectra available, with nitrogen lines ideally not blended with strong interstellar absorption. In only a few cases could additional optical N lines have been used. Even though the evolutionary link to the nitrogen abundance appears to hold, this is still statistically a small number considering the total number of known PG 1159 stars. A detailed assessment of elemental abundances for a larger sample of stars is needed.

For the time being, however, there is a clear separation: PG 1159 stars with significant amounts of nitrogen in the atmosphere pulsate, the others do not. This is evidence that pulsating and nonpulsating PG 1159 stars have different evolutionary histories. It seems necessary that a star has to undergo a VLTP to become a pulsator, and that nitrogen is a tracer of this history.

We thank Bruno Steininger for discussions and for supplying his observational data. P.S. and G.H. acknowledge financial support by the Polish NCN grant 2015/18/A/ST9/00578. D.J. acknowledges support from the Erasmus+ program of the European Union under grant No. 2020-1-CZ01-KA203-078200. This paper uses observations made at the South African Astronomical Observatory (SAAO). Based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, in the island of La Palma.

Facilities: GTC (OSIRIS) - , SAAO: Lesedi (SHOC). -

Software:Astropy (Astropy Collaboration et al. 2013, 2018), ccdproc (Craig et al. 2017), Matplotlib (Hunter 2007), Period04 (Lenz & Breger 2005), TEA-Phot (Bowman & Holdsworth 2019).