The EC stars VII. PG , a star with many pulsation modes

Transcription

1 Mon. Not. R. Astron. Soc. 296, (998) The EC 426 stars VII. PG , a star with many pulsation modes C. Koen, D. O'Donoghue, 2 D. Kilkenny, A. E. Lynas-Gray, 3 F. Marangl and F. van Wyk South African Astronomical Observatory, PO Box 9, Observatory 7935, South Africa 2Department of Astronomy, University of Cape Town, Rondebosch 77, South Africa 'Department of Physics, University of Oxford, Keble Road, Oxford OX 3RH Accepted 997 December 8. Received 997 December 8; in original form 997 September 3 ABSTRACT We report the discovery of large-amplitude (.25 mag) pulsations in the bright (V= 2.8) sdb star, PG The dominant period is 48 s, but more than 2 periods were present on at least three separate occasions. Frequency analysis of the complete data set yields more than 3 periods. A few of these are harmonics or linear combinations of the strongest modes. Excluding the latter, the periods span a range of almost 4 s, which contrasts with the typical range < 2 s for most other EC 426 stars. Analysis of multicolour photometry limited any cool companion to being a mainsequence star of type MO or later. Balmer line profile fitting yielded an effective temperature of 32 + K and a log g of , significantly smaller than in the other stars of the EC 426 class, and possibly indicative of a more evolved state. The lower gravity is probably responsible for the fact that the pulsation periods and amplitudes are respectively much longer and larger than in other stars of the class. This star is an obvious target for asteroseismological investigation using a multilongitude photometric campaign. Key words: stars: individual: PG stars: oscillations stars: variables: other. INTRODUCTION The recent discovery of short-period pulsations in the EC 426 stars (Kilkenny et al. 997a, hereafter Paper I; Koen et al. 997a; hereafter Paper II; Stobie et al. 997, hereafter Paper III; O'Donoghue et al. 997, hereafter Paper IV) has prompted us to conduct a survey for pulsations in sdb stars. In this paper we show that PG (Green, Schmidt & Liebert 986) is also an EC 426 star, but with pulsation properties and atmospheric parameters distinctly different from the stars already published (Papers I IV; O'Donoghue et al. 998, hereafter Paper VI). The interested reader can find two recent reviews of the properties of the EC 426 stars in Koen et al. (997b,c); only a brief summary of the class attributes is presented here. The EC 426 stars are named for the first pulsating subdwarf B star to be discovered (Paper I). The pulsations are rapid periods typically lie in the range -2 s and the amplitudes low, more often than not less than. mag. All the EC 426 stars are multiperiodic; usually two or three periods are seen, in a very narrow interval (e.g.,, 2, 2 s for EC , EC , EC respectively). The derived gravities (log g 5.9) and temperatures (T e 35 K) of the stars are all very similar. The four EC 426 stars described in Papers I IV are all binaries, although this may reflect no more than the very high incidence of binarity amongst sdb stars generally (e.g. Kilkenny et al. 997b). Beyond its appearance in the Palomar Green catalogue, the Simbad data base contains only two references to PG : it is listed in the subdwarf catalogue compiled by Kilkenny, Heber & Drilling (988), and measurement of the star in the StrOmgren photometric system is reported by Wesemael et al. (992). 998 RAS on 2 February 28

2 38 C. Koen et al. 2 FREQUENCY ANALYSIS OF THE OBSERVATIONS The observations logged in Table were obtained in 7 high-speed photoelectric photometric runs with time resolution of s, obtained sporadically over an interval of 38 d. The total run time is 5 h. All observations were made using the Modular Photometer attached to the.5-m telescope at the Sutherland site of the South African Astronomical Observatory (SAAO). With a telescope of this size, a star with V- 2.8, and bearing in mind the low amplitudes of some of the pulsation modes, the preferred mode of operation would have been to maximize the photon detection rate by using no filter in the light beam. However, as discussed in Paper II, the GaAs photomultiplier tube in the Modular Photometer has red sensitivity, whereas photometers in use on the other SAAO telescopes are sensitive only to shorter wavelength radiation. This has the effect that unfiltered observations obtained on different telescopes are in different effective passbands, and that the amplitudes of variation are therefore not necessarily directly comparable. As we had planned to combine observations from different telescopes, a wide-band CuSO 4 filter was placed in the lightbeam of the red-sensitive photomultiplier tube; its passband then resembles that of the blue-sensitive photomultiplier tubes used on other SAAO telescopes. A typical light curve is shown in Fig.. Oscillations with a maximum peak-to-peak amplitude of.25 mag, and a dominant period of about 8 min, are obvious. The variable amplitude of the oscillations, due to interference between different modes, is also clearly visible. An amplitude spectrum of one of the longest runs (5.6 h) is plotted in Fig. 2 (top panel). The richness of the pulsation spectrum becomes clearer if the data are pre-whitened by sinusoids with frequencies corresponding to the largest peaks in the amplitude spectrum. The middle and bottom panels show the result of pre-whitening by respectively the most prominent, and two most prominent, frequencies in the top panel. Judging by the information in the diagram, PG may have 5 or more pulsation frequencies. Note, though, that the lowest frequency features (e.g., the double-peaked structure near.2 mhz) should be ignored; experience of high-speed photometry of constant stars shows that these features are due to slow changes in the atmospheric extinction, and cannot be corrected for in observations with our one-channel photometer. It is for this reason that all the material presented below is based on spectra calculated for frequencies larger than mhz (i.e., periods shorter than about 7 min). Frequency components from the five longest runs were extracted by successive pre-whitening. In all five cases, the 22 frequencies corresponding to the largest ordinates in the amplitude spectrum were identified. 26 frequencies which were common to at least two runs are listed in Table 2; of these, 2 were found in three or more of the runs. These runs were 5-6 h long, and the frequencies are determined to typically. mhz. The frequency resolution may be improved by combining all the data, at the expense of introducing aliasing into the amplitude spectrum. The window function of all the data is plotted in Fig. 3, which clearly shows the one cycle per day alias pattern. The amplitude spectrum of all the data is plotted in the top panel of Fig. 4; the next four panels show the spectra of the residuals after pre-whitening by, 2, 3 and 37 frequencies respectively. It is clear that there is still an excess of power above the general noise level at several frequencies even after removing 37 sinusoids. However, at Table. Log of the 49.8 h of 'white light' high-speed photometric observations of PG All data were obtained using the Modular Photometer attached to the SAAO.5-m telescope at Sutherland, South Africa. Starting Time Run Length JD245+ (Hours) -..,, IN, JS, IN i *%. / %-, e. _ l'*".. :' E\,.r.. y P"'vip. Nu..; Ps% ; iien, No/ 'tor - \v/e %id t,,,,,e," " \of.n... if N'ate \Me % v. P `-. Pe. =4\ _ \, i,. TIME (minutes) A A A %ṡ. Figure. A 4.5-h section of the light curve of PG , obtained during the run on HJD Each panel has a vertical extent of.36 mag. Low-frequency drifts in the data have been corrected by subtraction of a straight line fitted to the full observation run. on 2 February 28

3 The EC 426 stars - VII. PG Table 2. Frequencies (in mhz) found by fitting sinusoids to the five longest individual runs. The runs are labelled with the Julian Days on which the data were acquired P ji t42&&2, FREQUENCY (mhz) Figure 2. Top panel: the amplitude spectrum of the run on HJD Middle panel: the spectrum after pre-whitening by the 2.7-mHz frequency corresponding to the largest peak in the top panel. Bottom panel: the spectrum after pre-whitening by the 2.7- and 2.27-mHz frequencies corresponding to the two largest peaks in the top panel. The vertical scales of the three panels, which are in mag, are different the low-frequency end of the plotted spectra some of the excess power may be due to slow variations in atmospheric transparency. Furthermore, even for frequencies which are due to the star, choosing the correct alias becomes progressively more difficult as the amplitude decreases, due to the confounding influences of both noise and other modes. The frequency extraction process was therefore terminated at an amplitude of 2 mmag. The frequencies and amplitudes of 35 components were extracted using a simultaneous non-linear least-squares fit to the data and are listed in Table 3. We hesitate to ascribe errors to the quantities in Table 3: the frequencies were derived from successive amplitude spectra using a 'mechanistic' approach to pre-whitening the data. As already mentioned, it is possible that, in view of the poor duty cycle (5 h in 38 d), some of the frequencies listed suffer from aliasing and interference from nearby frequencies. Furthermore, the phases are more vulnerable to such distortions, are therefore not realistically determined, and so are not listed. We caution that the frequencies listed in Table 3 should not be used in any model fitting. A data set suitable for such a procedure has been obtained and will be described by Kilkenny et al. (in preparation). Given the superior frequency resolution possible with the full data set, it is not surprising that Table 3 has more entries FREQUENCY (,uhz) Figure 3. The window function of the complete set of observations. The frequency spacing of the seven conspicuous peaks is.57 phz; these represent the true frequency and its one, two and three cycle per day aliases. than Table 2. There are none the less frequencies in Table 2 which do not appear in Table 3; of these, the frequencies in the ranges.4-.8 and mhz are in parts of the spectrum which show a great many very low-amplitude features (cf. the bottom panel of Fig. 4). These components on 2 February 28

4 32 C. Koen et al. Table 3. Frequencies and amplitudes of sinusoids fitted to all the observations by a non-linear least-squares method. Frequency (mhz) Period (sec) Amplitude (mmag) Frequency (mhz) Period (sec) Amplitude (mmag) I FREQUENCY (mhz) Figure 4. Amplitude spectrum calculated from all the observations (top panel). The next four panels show the spectra of the residuals after pre-whitening by, 2, 3 and 35 frequencies respectively. Isolated low-amplitude peaks which were subjected to further scrutiny are indicated by arrows. The vertical scale is in mag. may therefore be present but not conspicuous. This leaves the frequencies near 3.36 and 3.97 mhz. Two arrows in the bottom panel of Fig. 4 point to relatively strong spectral features close to these positions. The top panel of Fig. 5 shows the amplitude spectrum near 3.36 mhz, and the bottom panel shows the spectrum of the residuals after pre-whitening by the frequency corresponding to the largest peak in the top panel (f = mhz). It is evident that most of the excess power in this part of the spectrum is due to this single frequency. Similar remarks apply to the frequency mhz, where the reduction in power on pre-whitening is even more dramatic (Fig. 6). Given the extraordinary number of frequencies which appear in the spectra in Fig. 4, the reader will be excused for suspecting that many of these may be due to artefacts of one sort or another (e.g., substantial time gaps between observational runs). It is hoped that Figs 5 and 6 go some way towards allaying these fears; these diagrams illustrate the point that there are indeed many spurious peaks in the spectra, but that the frequency identification procedure will not identify all of these as 'significant'. Put differently, it is reassuring that not all the peaks in the spectra correspond to 'significant' frequencies: that would indeed have signalled severe data inadequacies. It is possible to interpret some of the frequencies found above as being due to non-linear effects. Thus /2 = mhz, which may be compared to the frequency mhz of the largest amplitude periodicity in the data. The correspondence between the observed frequency mhz and the sum of and on 2 February FREQUENCY (mhz) Figure 5. Top panel: the amplitude spectrum over the range 3.32 to 3.44 mhz. Bottom panel: the amplitude spectrum after prewhitening by a sinusoid with frequency mhz (corresponding to the largest peak in the top panel). 998 RAS, MNRAS 296,

5 The EC 426 stars - VII. PG on Table 4. Frequencies and amplitudes of additional sinusoids corresponding to isolated amplitude spectrum peaks. The values in the table were obtained by linear least-squares fitting at the frequencies of spectral maxima. Frequency Period Amplitude (mhz) (sec) (mmag) FREQUENCY (mhz) Figure 6. Top panel: the amplitude spectrum over the range 3.9 to 4. mhz. Bottom panel: the amplitude spectrum after pre-whitening by a sinusoid with frequency mhz (corresponding to the largest peak in the top panel). 4. Table 5. Log of the photometric observations of PG obtained through filters. The U- and V-band observations were made using the University of Cape Town Photometer attached to the SAAO.75-m telescope, the J-band observations were made through the SAAO MkIII infrared photometer attached to the SAAO.9-m telescope, and all other observations were made using the St Andrews Photometer on the SAAO.-m telescope. Starting (namely ) is similarly impressive. Time It is Filter Run Length also possible to find various combinations of the frequencies JD245+ (Hours) in the range mhz which agree reasonably well (typically to better than one tillz) with the three frequencies identified in the range mhz (e.g., Johnson U Johnson V = ; 2 x = ), J but the correspondences are not as compelling as for the StrOmgren b StrOmgren u.7 first two cases quoted above. An examination of the spectrum near the expected position at 3 x = mhz of the second har StrOmgren y Cousins I 2.8 monic of the mean peak showed a maximum at mhz, which is evidently a one cycle per day alias of the expected frequency. On pre-whitening, it is found that the 3 FURTHER HIGH-SPEED PHOTOMETRY maximum in the spectrum of the residuals occurs at mhz, which appears to be a one cycle per day alias In principle, the comparison of the light curves in different of mhz, the second harmonic of f= wavebands can provide information useful in mode identification (e.g. Cugier, Dziembowski & Pamyatnykh 994; mhz. Similarly, a plot of the spectrum over the range mhz shows a maximum at mhz, which Heynderickx, Waelkens & Smeyers 994). In the case of is a one cycle per day alias of the first harmonic at PG , the nature of the pulsation spectrum (a mhz of the variation with f = mhz. great many frequencies, some of which are very closely Spurred on by the apparent success of identifying the first spaced) will probably necessitate many hours of photometry and second harmonics of the largest amplitude variation, it through filters, spread over an extended timebase, for this to was decided to scrutinize the spectrum also at the putative be feasible. In ignorance, before realizing just how many positions of higher harmonics. The spectrum in the vicinity modes we were dealing with, we obtained a few short, highspeed runs using various filters - see the log in Table 5. of the position of the third harmonic has its highest peak in the range mhz at the frequency mhz, All of these observations were made at least partially which is quite close to 4 x = mhz. The contemporaneously with runs reported in Table. The largest amplitude in the pre-whitened spectrum (over this amplitude spectra of the observations for the two longest range) is at mhz, which corresponds reasonably runs in Table 5 are compared with the overlapping white well with 4 x = mhz. No sign of even light observations in Figs 7 and 8. It is interesting that the higher harmonics could be found in the spectrum. Table 4 two main amplitudes seen through the b filter are slightly summarizes the properties of the frequencies extracted in smaller than the corresponding amplitudes in 'white light' addition to those listed in Table 3. (i.e., through the CuSO4 filter), despite the fact that the on 2 February 28

6 322 C. Koen et al amplitudes in I and white light, although the primary variation is substantially larger in white light. Careful examination of all the observations through different filters did not allow any unassailable general conclusions to be drawn, and we stress that the remarks in the preceding paragraph may apply only to the particular time at which the observations were made. It does none the less seem likely that colour changes during the pulsations are seen, and that valuable information may be contained in multifilter observations. Finally, an attempt to detect the oscillations in the J band was made (Table 5). No periodic signal was detected with an upper limit on the semi-amplitude of.2 mag in the frequency range - mhz. This is not a particularly stringent limit by comparison with the amplitude of the optical oscillations. FREQUENCY (mhz) 4 6 Figure 7. Amplitude spectra of contemporaneous StrOmgren b (top panel) and white light (bottom panel) observations. The vertical scale is in mag FREQUENCY (mhz) Figure 8. Amplitude spectra of contemporaneous Cousins I (top panel) and white light (bottom panel) observations. The vertical scale is in mag. oscillations originate in the very hot subdwarf star (Paper II). By contrast, both the first harmonic of the most prominent frequency, the non-linear interaction mode (near 5 mhz) have larger amplitudes in b than in white light. The non-linear interaction mode is also more prominent in the I- band observations than in white light. It is also remarkable that the secondary frequency in Fig. 8 has very similar 4 THE PHYSICAL PARAMETERS OF THE STAR The pulsations of PG described above are of longer period and larger amplitude than in any EC 426 star so far discovered. This strongly suggests that the structure of this star is somewhat different from the previously known stars. In order to investigate this possibility, we attempted to determine the effective temperature and gravity of the star using a number of different techniques which will now be discussed. The large-amplitude variability, which may (at least in part) be due to effective temperature changes, should be remembered in considering the results. 4. Optical spectroscopy Low- ( 3.5 A) and medium- ( -.2 A) resolution spectra of PG were acquired in 996 May using the SAAO.9-m telescope equipped with an intensified Reticon spectrograph. The data acquisition and reduction are as described in Paper IV. Briefly, the low-resolution data were obtained with Grating 6, and cover the range A with a total exposure time of 38 s and a signal-to-noise ratio of. The medium-resolution data were acquired with Grating 9, covering the wavelength range A with a signal-to-noise ratio of 5. Individual exposures were obtained with a 96-s exposure time in an attempt to average over any phase-dependent line profile variations or shifts caused by the dominant 48-s pulsation period. The spectra are illustrated in Fig. 9. The Grating 9 (higher resolution) data are displaced upward by 4. x ' erg s - cm -2 A.- with respect to the Grating 6 (low-resolution) data for clarity. Broad, strong Balmer lines can be seen, superimposed on a blue continuum. The Balmer series is visible to H2. He 2426 A is marginally visible in the Grating 9 data; He 2447 A is marginally visible in the Grating 6 data. The Ca II K line is very narrow and most probably arises from interstellar absorption. The features in the Grating 6 spectrogram near 4287 A and in the Grating 9 spectrogram near 455 A are likely to be spurious, because they are not seen in the other spectrogram. These features probably arise in on 2 February 28

7 The EC 426 stars VII. PG rr). O r--i. 8 X ri Wavelength Figure 9. Spectrograms of PG during 996 May. The top curve is the Grating 9 spectrogram, and the lower curve is the Grating 6 spectrogram (see text and Paper IV for details). The smooth curve superimposed on the Grating 9 data is the line profile fit discussed in the text, the abscissa is in A, and the ordinate is in erg s - cm -2 A -. The Grating 9 spectrum (and line profile fit) have been shifted up by 4 x -4 erg s - cm -2 A- for clarity. the flat-field calibration spectrum. Overall, Fig. 9 is typical of the spectrum of an sdb star (Saffer et al. 994). 4.. Spectroscopic limit on the presence of a cool companion to the sdb star The sdb features in the spectrum and the presence of rapid, multiperiodic oscillations strongly suggest that PG is an EC 426 star. In contrast to the first four EC 426 stars (Papers I IV), however, there is no spectroscopic evidence in Fig. 9 for a cooler companion to the sdb star: neither photospheric Ca II K lines, nor the G band, nor any other features attributable to a cooler companion can be seen. The same conclusion was reached in Paper VI for the EC 426 star PG : any companion would have to be a main-sequence star of spectral type KO or later to be undetectable in the wavelength range and with signal-to-noise similar to that in Fig The effective temperature and gravity of the sdb star from line profile fitting As the Balmer lines in PG are free from the contribution of a cool companion, they can be fitted with a grid of model profiles using the Levenberg Marquardt algorithm (Saffer et al. 994; Paper IV). The models used have been fully described (Paper IV, section 3.2). We chose the grid with zero He abundance. The models with N(He)/ N(H) =. would produce He i lines far stronger than the marginal detections in Fig. 9. The five Balmer lines Hy to H9 were used in the fitting procedure. The results are T eff= K, log g = for the Grating 6 spectrum, and Teff = K, log g= for the Grating 9 spectrum. The best fit to the Grating 9 data is shown by the smooth solid line superimposed on the observed Grating 9 spectrum in Fig. 9. The errors given are the formal errors of the fitting procedure and almost certainly underestimate the true error. It is clear that the effective temperature derived for PG depends on the grating used, being 23 K higher for the Grating 6 data than for the Grating 9 data. Exactly the same effect was seen in the analysis of PG (Paper VI). The origin of this discrepancy can be seen in Fig. 9, which shows that the Balmer lines in the Grating 6 spectrum are a few per cent shallower than in the Grating 9 spectrum (remember that the Grating 9 spectrum has been shifted with respect to the Grating 6 spectrum but is otherwise on the same vertical scale). It was on 2 February 28

8 324 C. Koen et al. found in Paper VI that the different instrumental resolution of the two gratings was not responsible for this difference. This discrepancy must be investigated in the future. A number of sdb stars were observed in common with a list provided by Rex Saffer (private communication); see Paper VI for our results. One of the stars, PG , was found to have Tell = K, log g = from its Grating 9 spectrum. These values are very similar to those obtained by Saffer (private communication): Teff = K, log g = As our Grating 9 results for PG are similar to the Grating 9 values for PG , we believe that the estimates of Tell and log g from the Grating 9 spectrum are more reliable than the Grating 6 results. We therefore adopt T,=32 + K, log g = for PG The errors on these quantities are, of course, systematic in nature, but are believed to be realistic. 4.2 Optical and infrared photometry Johnson UBV(RI) c, StrOmgren uby and infrared JHK photometry of PG can be used to check the effective temperature determined above, and to search for the presence of a companion. Repeated UBV and Cousins RI measurements of PG over - 35 min were obtained on two nights. The overall mean results are V= 2.84 (.5), B-V= -.23 (.3), U-B=-.2 (.3), V-R= -. (.4) and V- I = -.7 (.), the values in brackets being the standard deviations of the 69 individual measurements. These results agree reasonably with those in the Palomar-Green catalogue (Green et al. 986): V= 2.78, B -V= -.23, U - B = -.7. StrOmgren photometry has been published by Wesemael et al. (992): y = 2.92 (.7), b -y = -.2 (.2), u -b = -.7 (.3) and m i =.9 (.2). We derive y = 2.93, b -y = -.7, u - b = -.6 from the high-speed photometry listed in Table 5 (with zero-points determined from observations of a few standard stars). Attempts were made to monitor PG in the infrared on 996 July 8 using the SAAO.9-m telescope and Mk III Infrared Photometer, using an Insb detector (Glass 973). Reduction to the Johnson photometric system was based on Carter's (99) list of SAAO infrared standards. No attempt was made to observe at K, and the sensitivity at J and H was insufficient to show obvious variability using -s integrations; means were therefore taken, giving J= (45 integrations) and H= (2 integrations), the quoted uncertainties being standard deviations in the mean. All these data were converted to fluxes using the calibration of Bessell (979) for UBVRI, Fabregat & Reig (996) for uby, and Wilson et al. (972) for JHK. The resulting fluxes are shown in Fig. and are labelled by the corresponding filter names. Note that there are differences of several per cent amongst the different measurements of the optical photometry and between the y and V fluxes. This is most likely due to the large-amplitude variability (and any associated colour changes) in the star which went unrecognized in the earlier photometry and were not perfectly averaged out in the data reported in this paper; this is also the on 2 February 28 cause of the high standard deviations in the magnitudes and colours listed above An infrared search for a cool companion to the sdb star The main panel of Fig. shows a fit to the fluxes using models consisting of two components: one component is a Teff = 32 K, logg = 5. energy distribution from Kurucz (992). The radius of this component was taken to be.26 Ro, appropriate for an sdb star with M=.5 Mo and log g = 5.3 (Saffer et al. 994). The other component is also an energy distribution from Kurucz (992) with log g = 4., and an effective temperature of either 35 or 375 K. The radius of this component was taken to be that of a mainsequence star of the corresponding effective temperature as given in Lang (992). The sdb component was scaled to fit the by and BV fluxes (on the basis that any cooler companion would have negligible contribution at these wavelengths). The U and u fluxes were omitted from the model scaling because, as will be discussed below, they do not fit the 32 -K model. The contribution of the cooler component was then fixed by the relative temperatures and radii. Three models were constructed: the sdb component alone, the sum of the sdb component and the 35-K component, and the sum of the sdb component and the 375-K component. A comparison of the observed fluxes with these three models shows the following. () The BVR and by fluxes are well fitted by the sdb component alone. (2) The I flux might suggest the presence of a companion substantially hotter than 35 K. However, this possibility is ruled out by the J and H fluxes which are far too low to be consistent with the I flux. The time-series observations through the I filter have a strong trend of unknown cause (which, incidentally, is responsible for the large standard deviation in V- / listed above). We believe that the apparent excess flux at I should therefore be treated with caution. (3) On the basis of the by and BVRJH fluxes, the energy distribution of PG is consistent with a single component. Adopting a conservative approach, if a companion is present, it must be less luminous than a mainsequence star of 375 K, corresponding to a spectral type of MO or later (Lang 992). (See Paper VI for a similar limit for PG and a fuller discussion.) Photometric estimates of the effective temperature of the sdb star The inset in Fig. shows the fluxes in the blue region. Three (different) models are also shown. Each model consists of a single component with R =.26 Ro, logg = 5. and effective temperature of 28, or 3 or 32 K from Kurucz (992). The models were normalized so as to agree with the H flux. Both the UBV and uby fluxes suggest a temperature of 28 K, distinctly lower than the spectroscopic determination (32 + K). The result depends critically on the U and u fluxes, as the other fluxes cannot distinguish between the three models due to the significant error in their values.

9 The EC 426 stars VII. PG m cv Models : T = 32 K R =.26 Ro T2 =, 35, 375 K ci) Cu CD Models : T.26 Ro y 32 K 3 K 28 K I Log A (A) 375 K 35 K Figure. UBVRI, uby and JHK photometry of PG converted to fluxes (in units of erg s - cm _ 2 Hz - ). All fluxes are labelled by the corresponding photometric symbol. UBVRIJH fluxes are plotted with filled circles, and uby fluxes are plotted with filled triangles. The continuous lines correspond to three models, each of which contains a 32 -K, log g = 5. Kurucz (992) energy distribution. Two of the models have, in addition, contributions from log g = 4., 35- and 375-K Kurucz energy distributions respectively. See text for more details. Inset: UBV and uby fluxes (plotted on linear scales) with 28 -, 3 - anjd 32 -K Kurucz energy distributions. The models have been scaled to the H flux. The same discrepancy in temperature determination from spectroscopy and StrOmgren photometry was found for PG in Paper VI, where it was suggested that the cause was in the absolute calibration of the u flux (Fabregat & Reig 996). In the case of PG , however, care was taken to obtain spectra averaged over the dominant 48-s pulsation cycle; it is possible that they will yield a more reliable mean Teff (and log g) than the photometry which, as pointed out above, has significant internal scatter. Another way of determining the temperature is to use the calibration of the reddening-free index Q' = (u b).56(b y) againt Teff in Wesemael et al. (992). For PG , Q' =.5 for the uby values reported in this paper, and Q' =.7 for the Wesemael et al. (992) results. These values give effective temperatures of 3 K (uby from this paper) and 32 5 K (uby from Wesemael et al. 992) for the Olson (974) calibration. Other calibrations shown in fig. of Wesemael et al. (992) are from Schulz (978) and Lester, Gray & Kurucz (986), and they indicate Teff = 28 K (uby from this paper) and 3 K (uby from Wesemael et al. 992). Similar discrepancies for PG are discussed in Paper VI. 4.3 IUE spectrophotometry PG was observed with the IUE satellite on 986 May 2 by Dr F. Wesemael. Spectra (SWP 2835 and LWP 8244) covering both wavelength regions were retrieved from the Final Archive, both images having been reduced following Nichols & Linsky (996). Exposure times of 9 and 63 s were used for LWP 8244 and SWP 2835 respectively; these are not a multiple of the 48-s dominant pulsation period, and are not therefore averaged over the same phase interval. The results, dereddened assuming E(B V) =.3 (see below), are shown as filled symbols in Fig. (top). The vertical scale is in units of the underreddened V flux, 2.6 x -4 erg s' cm -2 A". As expected, the spectrum shows a continuum rising steeply to short wavelengths. Some pixels near 3 A were saturated, which limits the number of identifiable ultraviolet features. Lyman a absorption is visible as well as C iv A55 A AND C III /75 A. While there appeared to be an absorption feature near 393 A, there was no evidence for a corresponding feature near 43 A; photospheric Si iv could not therefore be identified. These data are a useful diagnostic of the effective tem- on 2 February 28

10 326 C. Koen et al. Solid lines: log g = 5., 28 K & 32 K models Points: PG65+72 SWP+LWP spectra Dereddened by E(B-V)= Wavelength H Solid lines: log g = 5., 28 K & 32 K models Points: PG65+72 SWP+LWP spectra Dereddened by E(B-V)= ' 28 3 Wavelength Figure. Top panel: IUE spectrophotometry of PG plotted as filled symbols. The observed fluxes have been dereddened assuming E(B V) =.3 mag. The ordinate is F2, normalized by the underreddened observed Vflux, 2.6 x -4 erg s - cm -2 A-. The two solid curves plotted as histograms are Kurucz models with log g = 5. and Teff = 28 and 32 K. Bottom panel: as for the top panel, except that the observed fluxes have been dereddened by E(B V) =.7 mag. perature of the sdb star. In order to exploit them for this purpose, the Grating 6 spectrum (Fig. 9) was carefully fluxcalibrated so that it reproduced the StrOmgren u and b fluxes, and joined smoothly on to the StrOmgren y flux. In addition, the VRI data were used to define the long-wavelength flux range. The flux distribution of PG was thus specified over the wavelength range 5-79 A. The method of Remie & Lamers (982, section 3) was then used to determine the effective temperature. This requires an estimate of the unobserved part of the spectrum containing essentially all the remaining flux (essentially at wavelengths shortward of 5 A). The log g = 5. models of Kurucz (992) were used for this purpose. The results are quite sensitive to reddening: for E(B V) =., Teff = 26 3 K; for E(B V) =.3, Teff = 28 2 K; for E(B V) =.5, Teff = 3 2 K; and for E(B V) =.7, Teff = 32 5 K. Two of these solutions are illustrated in Fig. : the solid lines (plotted as histograms) in the top panel are Kurucz (992) log g = 5. models with Teff 28 and 32 K. The lower panel shows the observed data, dereddened assuming E(B V) =.7, and the same two models. It is clear that the data dereddened assuming E(B V) =.3 (top panel) fit the 28 -K model best, while the data dereddened assuming E(B V) =.7 are best explained by the 32 -K model. Unfortunately, there is little direct information about the reddening: it is certainly not zero, as a narrow Ca K line is present in the Grating 9 spectrum (Fig. 9). However, as demonstrated by Hobbs (974), the strength of Ca H and K cannot be used to give a reliable estimate of the interstellar absorption. As the distance to PG is at least a few hundred parsec, and it is at moderately high, galactic latitude, it is well beyond the region of most Galactic absorption. The Burstein & Heiles (982) reddening maps can thus be used to estimate the reddening: the map appropriate for the galactic longitude and latitude of 998 RAS, MNRAS 296, on 2 February 28

11 The EC 426 stars VII. PG PG (/ = 9?, b = 39? 3) suggests E(B V) between.3 and.6. In spite of intense scrutiny, we could not be confident of the presence of the 22-A interstellar absorption feature in the LWP spectrum. We shall adopt E(B -- V) =.5, giving Teff = 3 2 K. E(B V) =.7 is required to give an effective temperature consistent with the line profile fitting determination. As the IUE spectra are not averaged over the dominant 48-s pulsation cycle, as is the case for optical spectra, they cannot be expected to yield the same effective temperature. Moreover, the SWP and LWP spectra cover different phase intervals, and so combining them in a determination of effective temperature is likely to produce a result not directly comparable with that obtained from the line profile analysis of the optical spectra. 4.4 Comparison with PG We conclude this section of the paper by comparing the atmospheric parameters of PG with those of PG The reason for this is that, as discussed above, the different methods of estimating the effective temperature of PG produce slightly inconsistent results. The same was found to be true (Paper VI) for PG As will now be shown, however, the relative values of the effective temperature and gravity of the two stars is much more securely determined: PG is hotter by 3 K. Three pieces of evidence show that this difference is real. First, the slope of the IUE spectrum of PG is steeper than that of PG (although a large, but unlikely, difference in reddening could be responsible for this). Second, the U B and u b colours of PG are significantly bluer than those of PG , indicating a higher temperature. Third, inspection of fig. 2 of Saffer et al. (994) shows that the H8 Balmer line is relatively insensitive to gravity but strongly dependent on temeprature. The high-order Balmer lines (including H8) of PG are significantly shallower than in PG (both stars were observed on the same nights with the same instrumental configurations), again suggesting a higher temperature. The value of log g for PG is.5 dex larger than for PG This result is supported by a comparison of the ratio of the spectra of the two stars with the ratio of pairs of model spectra. In models of the same log g but with different temperature, the ratio of the model spectra (in the sense hotter model/cooler model) has absorption features of constant width at the positions of the Balmer lines. For models with different temperature and different gravity, the ratio of the spectra has features with widths which vary along the Balmer series. The latter is clearly seen in the ratio of the observed spectra, showing that there are differences in both effective temperature and gravity between the two stars. 5 CONCLUSIONS The wealth of frequencies seen in the amplitude spectra is of considerable interest, and makes PG the most promising candidate for asteroseismology amongst the known EC 426 stars. The very large number of frequencies extracted above is remarkable. It is commonly encoun- tered, however, amongst large-amplitude pulsating white dwarfs that modes wax and wane in strength on a relatively short time-scale. Thus some of the frequencies may not be normal modes of pulsation (Cox 98), but present in the amplitude spectrum to account for intrinsic changes in the strength of other frequency components. The pulsation periods seen in PG are considerably longer than those seen in the other EC 426 stars: up to 54 s in PG , as compared to typically 5 s for the other class members. Given the close similarity of the other EC 426 stars, it may be tempting to assume that different pulsation modes are being observed. However, the atmospheric parameters of PG place the star in a region of the Teff log g plane different to that of the other EC 426 stars. Assuming the same mass, the radius of the star is significantly larger than in the other stars..the period versus root mean density relation for pulsating stars implies that a difference in period of a factor of 2 is expected for a difference in log g of.4 in a star that is otherwise the same. In PG , log g is approximately.5 dex smaller than in other EC 426 stars, and its periods are a factor longer. Bearing in mind the crudity of these estimates, we may infer that the pulsation modes of PG are most likely low-order, lowdegree p-modes as found for the other EC 426 stars (Papers I IV and VI) (as opposed, for example, to g- modes). It is also conceivable that the large amplitude of the principal pulsation in PG (.2 mag peak-topeak) about a factor of larger than typically seen in these stars may be due to its lower gravity. The fact that this star is the only class member known to show mode interaction may again be a consequence of the large pulsation amplitudes. We note in passing that the small value of log g suggests that the evolutionary state of the star is further advanced than the exhaustion of He in the core (fig. 8 of Paper IV). Finally, along with PG , but in contrast to the first four stars to be announced (Papers I IV), PG is not an obvious binary. Any companion would have to be later than an early M main-sequence star. ACKNOWLEDGMENTS We are grateful to Patricia Whitelock (SAAO) for obtaining an infrared measurement of PG , and also to Rex Saffer for permission to quote his results on PG in advance of publication. This research has made use of the Simbad data base, operated at CDS, Strasbourg, France. REFERENCES Bessell M. S., 979, PASP, 9, 589 Burstein D., Heiles C., 982, AJ, 87, 65 Carter B. S., 99, MNRAS, 242, Cox J. P., 98, Theory of Stellar Pulsation. Princeton Univ. Press, Princeton Cugier H., Dziembowski W. A., Pamyatnykh A. A., 994, A&A, 29, 43 Fabregat J., Reig P., 996, PASP, 8, 9 on 2 February 28

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