Pulsations in Subdwarf B stars C. Simon Jeffery 1

J. Astrophys. Astr. (0000) 00, 000 000 Pulsations in Subdwarf B stars C. Simon Jeffery 1 1 Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland 2005 May 6 Abstract. Subdwarf B stars play a significant role in close binary evolution and in the hot star content of old stellar populations, in particular in giant elliptical galaxies. While the question of their origin poses several problems for stellar evolution theory, one of their most fascinating properties is the presence of multi-periodic 2 3 minute oscillations. Interpreting these oscillations optimally requires the correct identification of the modes. Partial identifications can be obtained using high-speed observations of radial velocity and colour variations. We review some of the several attempts to make such observations, most recently with the Multi-Site Spectroscopic Telescope campaign and with ULTRACAM. Key words: stars: oscillations stars: variables: other (EC14026/sdBV) stars: individual: KPD2109+4401, PB8783, PG1605+072, HS0039 +4302, PG0014+067. 1. Introduction An examination of a false-colour ultraviolet photograph of the globular cluster NGC2808 reveals a number of blue stars too bright to be white dwarfs, and too faint to be upper main-sequence stars (Brown et al. 2001). Similarly, the ultraviolet spectra of giant elliptical galaxies, although devoid of massive hot stars, reveal a flux excess that cannot be explained by the visible cool-star population (Brown et al. 2000). It is clear that old stellar systems are dominated by a population of subluminous hot stars. The subluminous B (or sdb) stars were first identified as an important spectral class by Greenstein & Sargent (1974). In their survey of faint blue stars in the Galactic halo, they demonstrated that, on the Hertzsprung-Russell diagram, the sdb stars lie between the upper main sequence and the white dwarf sequence, possibly on a blue extension of the horizontal branch similar to that observed in globular clusters. This was confirmed by subsequent fine analyses of sdb stars in the field and extremely blue horizontal-branch stars in globular clusters (Heber et al. 1984, Heber 1986, Heber et al. 1986). These studies established that sdb stars are corehelium burning stars of 0.5 M with a very thin surface layer of hydrogen. With 1

2 C. S. Jeffery effective temperatures 25 000 T eff /K < 35 000, the atmospheres of these stars are entirely radiative. Combined with high surface gravities (5 < log g < 6), the radiative atmospheres provide ideal conditions for the competition between radiative levitation and gravitational settling to act differentially on different atoms. While levitation is governed by the radiative cross-section of the dominant ion of a given atomic species, the atomic mass governs the gravitational force. The resulting diffusion affects the chemical stratification in the atmosphere. In sdb stars, the diffusion timescale ( 10 5 y) is short compared with evolution timescales, thus leading many sdb stars to appear depleted in helium (Michaud et al. 1989) and to demonstrate other unusual abundance characteristics (O Toole 2004). The sdb stars represent the quintessential horizontal branch star problem: How can a star lose virtually all of its hydrogen-rich outer layers before it ignites helium reactions in its core? Originally thought to be mainly single stars, an increasingly large fraction of sdbs are now known to be binaries. The companions are either cool main-sequence stars (e.g. Allard et al. 1994, Aznar Cuadrado & Jeffery 2001) or white dwarfs (Maxted, Marsh & North 2000). This provides mass transfer by Roche lobe overflow near to the tip of the first giant branch, i.e. just before core-helium ignition, as a natural mechanism for removing the outer hydrogen. It remains important to verify this hypothesis by measuring their core and envelope masses directly, to explain in detail the general properties of the sdb stars and to account for exceptional cases. Indeed, there is evidence that up to a third of sdbs may be single. It has been suggested that these were formed as the result of a merger of two helium white dwarfs (Iben & Tutukov 1985, 1986; Iben 1990; Saio & Jeffery 2000). 2. Discovery of sdb pulsations The discovery of pulsations in sdb stars was almost fortuitous. Kilkenny et al. (1997) had been searching for variability in a number of white dwarf candidates including one EC 14026 2647. Finding short-period low-amplitude variability they investigated further and discovered that the star was an sdb star with an F-type companion. Extended photometric monitoring demonstrated a light curve with at least two independent frequencies which could only be attributed to a non-radial oscillation in one or other but most likely the sdb star. Subsequently, photometric monitoring of a much larger sample of sdb stars led to the discovery of several more EC14026 2647 or sdb variables (sdbvs), although the non-variables far outnumbered the variables. The second to be analysed was PB 8783 (Koen et al. 1997). Following the discovery paper, an extended multi-site photometric campaign was able to resolve a spectrum of closely-spaced frequencies between 7 and 10 mhz (O Donoghue et al. 1998), indicating that several non-radial oscillations were being excited at the same time. Meanwhile, and independently of the SAAO group, Charpinet et al. (1996,1997) had been making theoretical calculations which predicted that some sdb stars should

Pulsations in Subdwarf B stars 3 pulsate. They had been searching for sdb pulsators with little success until they observed PG1047+003 (Billères et al. 1997) and KPD 2109+4401 (Billères et al. 1998). Meanwhile the latter star had formed part of the SAAO survey; Koen et al. (1998) published its power spectrum in the same year. Both groups obtained nearly identical light curves, with a clutch of frequencies between 5 and 6 mhz. Many sdbvs were discovered from photometry covering only one or two hours. This is an effective way of establishing whether oscillations with periods of 100 to 500 seconds (2 10 mhz) are present, but selects against longer period oscillations. More careful observations covering many hours have recently established the presence of a second-group of pulsating sdb stars with periods of 1800 s and upwards (< 0.5 mhz; Green et al. 2003). These long-period sdbvs are almost universally cooler than the short-period sdbvs. The increasing number of sdbvs now known, their frequency spectra and their general properties are reviewed elsewhere (O Donoghue 1999, Charpinet, Fontaine & Brassard 2001, Kilkenny 2002). 3. Excitation mechanism Stellar pulsations are found in stars distributed widely across the Hertzsprung- Russell diagram (Gautschy & Saio 1995, 1996). Radial pulsations are driven by instabilities related to opacity arising from the ionization of different ions. Thus δ Cepheid and RR Lyrae pulsations, inter alia, are driven by He II ionization, whilst β Cepheid pulsations are associated with ionization of iron-group elements (Febump opacities). Even hotter stars GW Vir variables are associated with highly ionized species of carbon and oxygen (CO-bump) (Saio 1996). Each of these driving zones gives rise to an instability strip. Still other mechanisms produce pulsating variables elsewhere in the HR digram. Examples include roap, δ Scuti, γ Doradus, 53 Persei and Luminous Blue variables. Most of these stars pulsate in non-radial modes of low radial order (k) and low spherical degree (l). The sdbvs represent one of these groups. They may lie roughly on the low-luminosity extension of the Fe-bump instability strip. Febump excitation, possibly in a region just beneath the stellar atmosphere enriched in metals as a consequence of chemical diffusion, is the most promising interpretation for their origin (Charpinet et al. 1997). However, since both non-radially oscillating and non-variable sdb stars occur with very similar overall dimensions ( T eff, log g), the extent and mechanism by which the atmosphere becomes stratified needs to be understood more clearly. The importance of studying non-radial oscillations lies in their ability to provide information about the stellar interior this is the science of asteroseismology. For example, oscillations in hot white dwarfs can be used to study the stellar mass (period spacing), the depth and composition of the outer layers (mode trapping), luminosity (both of the above), rotation speed and magnetic field (mode frequency splitting), and evolution time scales (period changes) (Vauclair 1996). To make

4 C. S. Jeffery Figure 1. Template spectra of sdbvs KPD 2109+4401 and PB 8783 formed by coadding several hundred short-exposure spectra (Jeffery & Pollacco 2000). Note the broad Balmer lines due to the sdb star in both cases, and the sharp metallic line spectrum of the companion F star in PB 8783. the most of the observations, it is helpful to be able to identify the mode of each oscillation. These modes are generally spherical harmonics denoted by three integers, k radial order, l spherical degree and m azimuthal wavenumber. Due to cancellation, it is usually only possible to observe low-degree modes (l, m < 4) in stars other than the Sun, and it is normally difficult to disentangle these from the light curve alone. Mode identification generally requires information from other sources, e.g., colours, velocities and line profiles. This has motivated the work described in subsequent sections. 4. Radial velocity observations Immediately after the discovery of sdbv pulsations, we recognized the potential for spectroscopy to contribute to the subject. Mode identification from single-band photometry alone is challenging, and could be assisted by the identification of lineprofile variations, whilst the comparison of radial and light amplitudes could be used to determine stellar radii directly. Spectroscopy might also demonstrate the presence of higher-order modes not detected photometrically. The limitations are that the periods are short (100-500s) compared with conventional CCD readout times, the stars are faint (> 11 th mag.), and the photometric amplitudes are typically only a few tenths of one per cent. High-resolution high-s/n multi-line studies such as those obtained for non-radial oscillations in rapidly rotating bright O and B stars (e.g. Reid et al. 1993, Telting, Aerts & Mathias 1997) would not appear to be feasible. However, the development of new techniques offered the possibility to acquire high-speed spectroscopy of sdbvs.

Pulsations in Subdwarf B stars 5 Figure 2. Amplitude spectra from WHT radial velocity observations and schematic representations of the photometry amplitude spectra (inset) for sdbvs KPD2109+4401 and PB8783 (from Jeffery & Pollacco 2000). 4.1 1998: PB8783 and KPD2109+4401 Observations of two bright sdbvs PB8783 and KPD2109+4401 were obtained in 1998 October with the 4.2m William Herschel Telescope using the blue arm of the intermediate dispersion spectrograph ISIS. The R1200B grating and the TEK1 CCD with 1124 2 24µm pixels yielded an instrumental resolution (2 pixel) R = 5 000 in the wavelength interval 4020 4420 Å. This wavelength region was chosen because it contains two strong Balmer lines and, potentially, a number of neutral helium and minor species lines that are normally observed in early-b stars. It also maximises the photon collection rate. The CCD was read out in low-smear drift mode (Rutten et al. 1997), in which only a small number j of CCD rows (parallel to the dispersion direction) are read out at one time. A dekker is used to limit the slit-length, thus only a fraction of the CCD window, j rows, is exposed at one time. After exposing for a short interval, typically 10s, the CCD contents are stepped down by j rows. Each set of j rows is accumulated into a data cube containing n individual 2D spectra, stacked adjacent to one another. More complete details of the instrumental setup and data reduction have been given by Jeffery & Pollacco (2000). The significance of these data was that they provided high

6 C. S. Jeffery Figure 3. Amplitude spectra from WHT and AAT radial velocity observations (dotted line, labelled right) and schematic representation of the photometry amplitude spectra (solid line, labelled left) for sdbv PG1605+072 (from Woolf, Jeffery & Pollacco 2002). time resolution and good wavelength stability with reasonable photon statistics. Conventional methods would have, at that time, resulted in unacceptable dead time due to the read-out time for the CCD. The final data product is a set of files each containing n 1-dimensional wavelength-calibrated flux-normalized spectra. Each spectrum is time-tagged. A template spectrum was constructed by coadding all of the data in a time series (Fig. 1). Individual velocities v(t) were measured by cross-correlation with the template. The functions v(t) were then investigated for periodic content by means of their amplitude spectrum (or discrete Fourier transform) F. The amplitude spectra F are shown in Fig. 2, together with a representation of the principal frequencies and amplitudes 1 discovered photometrically P (O Donoghue et al. 1998, Koen 1998). In this particular experiment, the information required from the amplitude spectrum is not the significance of the peaks but rather the amplitude associated with expected frequencies. Over the entire range 0.1 2/Σnδt < ν/mhz < 1/δt 90, F shows many peaks of comparable amplitude which on their own have little statistical significance. However the coincidence in Fig. 2 of the highest peaks in F with the highest peaks in P is more remarkable. 1 The term amplitude applied here to periodic signals refers to the semi-amplitude a of the sine function a sin(2πνt + φ).

Pulsations in Subdwarf B stars 7 The resolution 2/nδt 0.1mHz in F is insufficient to resolve the fine structure observed in much longer photometric time series. On closer inspection we found that the cross-correlation function for PB 8783 consisted of a broad and a narrow component. The narrow component, corresponding to the metal lines arising in the cool companion, had a mean velocity trend (b(t)) opposite to that of the broad component, corresponding to the Balmer lines in the sdb star. There were no high frequency components in the cool star ccf. While the low-frequency drifts b(t) could be due to mutual acceleration in the binary system, with a period of roughly 0.5 3 days, the oscillations are clearly seen to arise in the sdb star and not in the F star. 4.2 2000: PG1605+072 O Toole et al. (2000) had announced preliminary results of independent radial velocity observations of the brightest sdbv PG1605+072. This star has both the largest number of observed frequencies (> 50, Kilkenny et al. 1999) and the largest amplitudes (> 0.025mag), making it an ideal target for asteroseismological study. O Toole et al. found a 14 km s 1 amplitude periodic variation at the principal frequency of 2.10 mhz from a low-dispersion campaign carried out over 14 nights at a 2m telescope with a duty cycle for individual observations of 60 75s. Therefore during 2000 we observed PG1605+072 in the same way as before using the WHT and the Anglo-Australian Telescope (Stathakis & Johnston 1997) in an effort to obtain near continuous spectroscopy with a duty cycle of 13 22s. Regrettably, the original plan to observe this target for nearly 72 hours was reduced to something like 16 hours. Datasets from both telescopes were combined and analysed as before (Woolf, Jeffery & Pollacco 2002). A section of the power spectrum is shown in Fig. 3, with a schematic representation of the photometric power spectrum superimposed (Kilkenny et al. 1999). While amplitudes of weaker modes could now be measured, the frequency resolution of the dataset was limited. 4.3 2002: PG1605+072: MSST Following these campaigns it was clear that progress in understanding the radial velocity amplitudes of the principal modes in sdbvs would only be obtained by substantially longer observing runs. Thus, in May 2002, a large consortium set out to obtain 4m high-speed spectroscopy of PG1605+072 with 24h coverage over several nights. This campaign was strongly supported by spectroscopy from 2m telescopes, and by photometry from a large network of smaller telescopes, including the Whole Earth Telescope. Both of the latter were extremely successful; preliminary results have been reported by Heber et al. (2003) and O Toole et al. (2004). Regrettably, the 4m campaign was again severely limited by weather and telescope allocations and instrumental problems. Formal reports will be published shortly.

8 C. S. Jeffery Figure 4. Partial ULTRACAM light curves in u, g and r for sdbvs KPD 2109+4401 and HS 0039+3202 (adapted from Jeffery et al. 2004). Gaps are due to cloud. Figure 5. Amplitude ratios a x /a u are shown for both KPD 2109+4401 and HS 0039+4302. The frequencies for each mode (mhz) are shown on the right. Modes in which a u < 1.4 mmag are shown as dashed lines. Error bars for each value are shown with small horizontal offsets for clarity. Earlier photometry of KPD 2109+4401 (a X /a U ; Koen 1998) is shown for comparison. The lower right panel shows theoretical colour amplitude ratios for a model with M = 0.5M, T eff = 32 000 K, log g = 5.8, f = 5.4 mhz and for l = 0,..., 4 from Ramachandran, Jeffery & Townsend (2004). Figure from Jeffery et al. (2004).

5. Multicolour high-speed photometry Pulsations in Subdwarf B stars 9 An alternative and much more powerful approach to the partial identification of non-radial modes is the amplitude ratio method (Heynderickx, Waelkens & Smeyers 1994). This makes use of the fact that the ratio of the photometric amplitude at one wavelength to the amplitude at another wavelength (a λ /a λ0 ) is a function of the spherical degree l of the oscillation and is independent of the inclination of the pulsation axis i and the azimuthal wavenumber m. The method is simplified for use in broadband multicolour photometry by using the ratio of the amplitudes in different wavebands (e.g. a r /a u if using Sloan Digital Sky Survey filters). Koen (1998) had already made an attempt to identify modes in KPD2109+4401. While indicative, his results showed room for improvement in terms of time-resolution and photometric precision. ULTRACAM is a high-speed 3-channel CCD camera. Dichroics split the light up into ultraviolet, visual and red wavelengths which are simultaneously imaged with frame transfer CCDs (1024 by 1024 imaging area). These CCDs use a masked area to shunt exposures rapidly from the imaging area, which can then be read out while the next exposure is running. Mounted on the 4.2m William Herschel Telescope, the combination of high throughput and high time resolution provides an outstanding new tool with which to explore pulsating sdb stars. 5.1 2002: KPD2109+4401 and HS0039+4302 First observations were obtained in 2002 September for the targets KPD2109 +4401 and HS0039+4302. A portion of the light curves for each of these targets is shown in Fig. 4. From amplitude spectra obtained with these light curves, the amplitudes of several modes were measured in each of the three ULTRACAM channels, being u, g and r of the SDSS system. The ratios a g /a u and a r /a u were computed and are shown in Fig. 5. Meanwhile, theoretical models of the colour amplitude ratios expected for non-radial oscillations of different spherical degree in sdbvs were computed by Ramachandran, Jeffery & Townsend (2004). From Fig. 5 it was clear that at least one oscillation in each target had to be a relatively high-degree (l = 4) mode. Predicted ratios for low-degree modes (l = 0, 1, 2) lie close together, so it is not possible to identify the degree of the observed modes so easily. Assuming the observed frequencies belong to modes with unique k, l values (i.e. there is no rotational splitting), an additional constraint can be used. For a given degree l, modes of successive radial order k must be well-spaced in frequency, so modes of similar frequency cannot have the same l. By imposing such a constraint and by comparing the colour-amplitude ratios, it is possible to assign k and l values with some confidence. It is then possible to compare the observed frequency spectrum with theoretical models for non-radial oscillations in extended horizontal branch stars (cf. Charpinet et al. 2002), and hence to select which models best represent the star observed in terms of total mass, envelope mass, age, and other character-

10 C. S. Jeffery Figure 6. Two sections of the white light curve of PG 0014+067 together with the 19- frequency solution. Time (t) is JD-2453230. The change of amplitude of the dominant mode on a timescale of days is clearly visible. This is probably a consequence of rotational splitting of the dominant mode. This figure is reproduced from Jeffery et al. 2005. istics. A full description of the observations and the identification of the modes in these two stars is given by Jeffery et al. (2004). 5.2 2004: PG0014+067 A second ULTRACAM run to observe pulsating sdbvs was executed in 2004, September. The target was the magnitude 16.5 star PG0014+067, previously the subject of a successful asteroseismological study by Brassard et al. (2001). This star shows 20 independent frequencies in its light curve with frequencies between 5.7 and 12.9 mhz. Our aim was to check mode identifications deduced from the theoretical model that best fitted the frequency spectrum, and also to support a subsequent Whole Earth Telescope campaign to improve the overall frequency resolution. Although a much more challenging target than the 2002 targets, it was possible to observe this object with the WHT for 6 hours on each of 6 successive nights. The results were less conclusive than before, but it was possible to show that the two dominant modes must be l = 0, 1 or 2, and to find evidence that the rotational period should be nearer to 4d than to the 1.35d reported previously (Fig. 6). Most major frequencies identified previously were confirmed, although cycle d 1 aliases still contribute some uncertainties. Full details will be published by Jeffery et al. (2005). 6. Conclusions We have shown how asteroseismology offers excellent prospects for exploring the internal structure and evolutionary status of subdwarf B stars. With ULTRACAM, we can obtain outstanding 3-channel light curves for pulsating sdbs down to 16 th mag. These amplitudes are measurable to precisions < 0.5 millimags. and have enabled us to detect new frequencies. We have been able to identify l-values for modes with l up to 4 by ranking colour amplitude ratios and we have been able to assign the radial order n by demanding a realistic cadence from nodes of the

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