A new class of rapidly pulsating star - III. Oscillations in EC and pulsation analysis

Transcription

1 997MNRAS S Mon. Not. R. Astron. Soc. 85, (997) A new class of rapidly pulsating star -. Oscillations in EC 8-95 and pulsation analysis R. s. Stobie/ s. D. Kawaler, D. Kilkenny/ D. O'Donoghue 3 and c. Koen South African Astronomical Observatory, PO Box 9, Observatory 7935, Cape, South Africa Department of Physics and Astronomy, owa State University, Ames, A 5, USA 3Department of Astronomy, University of Cape Town, Rondebosch 77, South Africa Accepted 996 October 5. Received 996 October 8; in original form 996 May 9 ABSTRACT EC 8-95 is the third pulsating sdb + star to be announced. High-speed photometry reveals three periods present in the range P = 39-5 s with semiamplitudes of less than mmag. All periods show evidence of variable amplitude. Pulsation models have been calculated for sdb stars with logg'" 6. and Teff '" 35 K. These all have radial and non-radial modes with periods in the observed range. No unique mode identification is possible at present, but it is clear that at least some of the modes are non-radial. No stars have been predicted to pulsate in this region of the Hertzsprung-Russell (HR) diagram and the cause of the pulsation is not yet understood. Key words: surveys - binaries: general - stars: individual: EC stars: oscillations - sub dwarfs - stars: variables: other. NTRODUCTON The discovery of rapid oscillations in a class of sdb + stars has been announced by Kilkenny et al. (997a). The sdb + stars are spectroscopically composite consisting of an sdb star and a cooler companion, whose presence is indicated from the Ca K line and sometimes the G band as well. n all stars observed so far the oscillations have been found to be multiperiodic with periods in the narrow range p= -6 s, and to be of extremely low amplitude. Study of the oscillation amplitude as a function of wavelength has shown that it is the sdb star that is the source of the pulsations and not the cooler star (Koen et al. 997). n a spectroscopic investigation of the brighter members, the sdb stars appear to have logg~6., Teff~35 K (O'Donoghue et al. 996). Comparison with the atmospheric properties of field sdb stars (Saffer et al. 994) shows that these parameters are consistent with the extreme hot end of the extended horizontal branch where stars contain so little envelope hydrogen that they are almost on the helium main sequence. This paper presents the results of high-speed photometry of the sdb + star EC8-95, the second star discovered to be a member of the EC46 class. Pulsation analysis of sdb models in the appropriate logg-teff range is carried out and comparison made with the observed frequencies. HGH-SPEED PHOTOMETRY EC 8-95 was discovered to be a blue stellar object in the Edinburgh-Cape (EC) Blue Object Survey (Stobie et al. 997). t has 95. coordinates (X=hm48~ and b = '5" accurate to ~ arcsec. ts magnitude and colours are V = 5.88, B - V =. and U - B = -.98, with uncertainties of ~. mag (Kilkenny et al. 997b). These colours place it close to the blackbody line. A A mm- spectrogram obtained with the.9-m telescope at Sutherland shows it to be a composite sdb + F / G-type star. The presence of the F / G star is revealed by the Ca K line and the G band, which would not be expected to be visible in a sdb spectrum. EC 8-95 has spectroscopic properties similar to those of the prototype EC , and for this reason high-speed photometric data were obtained (Table ). n total 33 h of data on nights were secured. All observations were obtained in white light with lo-s time resolution using the South African Astronomical Observatory (SAAO).-m telescope with two photometer systems. Photoelectric photometry with a blue-sensitive photomultiplier tube on the St Andrews Photometer was obtained on five nights. With offset guiding capability it was only necessary to interrupt the measurements to obtain sky readings about every -3 min. These sky readings were interpolated with a cubic spline to subtract from the star readings 997 RAS Downloaded from on February 8

2 997MNRAS S 65 R. S. Stobie et al. and the sky-subtracted data were corrected for mean extinction using coefficients appropriate to the Sutherland site. High-speed CCD photometry was obtained with the University of Cape Town (UCT) CCD camera developed by one of us (DO'D). This uses a Wright nstruments bluesensitive CCD chip in frame-transfer mode, so that there is no dead time. The chip size in frame transfer mode is 89 x 43 pixel, and with each pixel covering.8 arcsec on the.-m telescope, the field of view is.3 x. arcmin With this size of field it is normally possible to obtain a comparison star at least as bright as the programme star within the same field and which can be used as an extinction monitor. The CCD chip can be read out in pre-binning mode which can be chosen to optimize the signal-to-noise ratio of the profile-fitted magnitudes, depending upon the quality of the seeing. Twilight sky frames were used to determine the flat-field response. Batch mode DOPHOT routines were used for the reductions to give aperture magnitudes and profile-fitted magnitudes of the stars on the frame. The profile-fitted magnitudes gave higher precision photometry by deriving Table. Observing log of EC Runid Date JD.tart Length Pe or eed 44+ (hr) a6 3/3/ ccd /3/ pe /3/ pe /3/ pe dmk 8/4/ ccd dmk4 9/4/ ccd ck6 7// pe ck64 9// pe rss3 4// ccd rss5 5// ccd rss6 6// ccd differential magnitudes of the programme star relative to the comparison stars. n practice, for EC 8-95 only one comparison star was sufficiently bright to be usable. A portion of the light curve of the differential CCD magnitudes for the longest run on JD 9 is shown in Fig.. The oscillations that are present in these data are not easily visible because of their low amplitude. The periodogram of this night of data (Fig. ) shows three peaks well above the noise at P= 39.8, 47.5 and 5.3 s, all with amplitudes of less than. mag. Periodograms were calculated for all the runs in Table using the techniques of Balona (983) and Deeming (975) modified by Kurtz (985). Each technique gave the same results. The frequency range from to 5 mhz was searched for periodic signals. As no power was found in the frequency range -5 mhz above an amplitude of.6 mmag, we concentrate on the - mhz region. Periodograms for a number of nights are shown in Fig. 3. The data of each night have been de-trended by a parabola to remove the residual long-term extinction variations. The power at frequencies < mhz is primarily caused by extinction variations not matching the extinction correction, and is not intrinsic to the star. Table lists the significant frequencies identified on each night together with their semiamplitude in mmag (except for runs S5836 and S584, for which the data were too noisy to extract any significant frequencies). Of the three frequencies identified on JD 9 only f =7.54 mhz is clearly present on every night on which data were collected. Both of the other two frequencies, f = mhz and f3 = 6.78 mhz, are present on more than one night, but on some nights were not measurable above the noise level. t is apparent from Fig. that the two lowest frequencies have variable amplitude relative to the principal frequency fl' The best night (JD 9) shows no evidence for any other frequencies in the range -5 mhz (the Nyquist frequency) above a level of.6mmag. As the main frequency f was present on every night we attempted to refine this frequency by combining nights. By combining the last three nights (JD 458-3) this fre-. &. -.& (S)." : :...: :.:...:: :":::""..:- :..:' "'"...: :: &..:. :.. +:... :. '.,.... ~:.:' ~ eo '...:....., &. & '.. ':':"'..:.':.:.,..:...:._ :...:.. '" :. ":." :"... '.:.,. : "... ' :.....':':-.:. :'....'.' : :. ::. _.:...:..... '.:.' ::... : _ _.. o. ' '" : " ~...- ::...' ' - -..' '.':... ' ":.: :.,...,.. &.. 8. Figure. A portion of the white light CCD observations of EC 8-95 with lo-s time resolution obtained on JD The time axis of each panel spans 3 min (running left to right, from top to bottom) and the height of each panel corresponds to. mag. 997 RAS, MNRAS 85, Downloaded from on February 8

3 997MNRAS S PEROD (5) A new class of rapidly pulsating star ,---L----L--~----~--~----~--~_r.8 AMPLTUDE 4.4. ~--~~~~~~~~~~~~~----~o.ooo o FREQUENCY (MHz) Figure. Periodogram from - mhz of all the data obtained on JD PEROD (S) 49' '3 6 '3. o... o.. o. ~~~~~~~~~~~~~~~~~~~~O.OO o FREQUENCY (MHz) Figure 3. Periodograms from - mhz of the high-speed photometry of EC 8-95 in order from top to bottom for JD 978,9836, 9837, 9 and 3. The ordinate scale of each panel is mmag in amplitude. quency was refined to =7.536 ±. mhz with no ambiguity in cycle count. As analysis of the main frequency in EC 7-44 has revealed evidence for a variable frequency (O'Donoghue et al. 997), possibly caused by the light-time effect of the sdb star in the binary, we searched for similar evidence in EC Searching in the vicinity of the =7.536 peak, other groups of nights gave =7.55 ±.3 mhz (JD ), =7.54 ±. mhz (JD ) and = ±.5 mhz (JD 45 -). All frequencies from groups of nights are the same within the errors. Thus there is no evidence for any light-time effect with these data. t was not possible to refine the frequency further because the gaps between the groups of nights were too large for a unique cycle count. 3 MODEL PULSATON RESULTS Given their high surface gravities, these stars are obviously highly evolved. They populate a region of the Hertzsprung Russell (HR) diagram corresponding to the bluest extent of the horizontal branch of globular clusters. Therefore, to model their interiors the starting point is naturally a model 997 RAS, MNRAS 85, Downloaded from on February 8

4 997MNRAS S 654 R. S. Stobie et al. Table. Frequencies and amplitudes present in Ee 8-95t. Runid / P al h P aa fa P3 a3 (mhz) (8) (mmag) (mhz) (8) (mmag) (mhz) (8) (mmag) a S dmk dmk ck ck rssl rssl rs8l tthe error associated with each value appears on second line. that has lost significant mass following the helium core flash. We constructed such 'standard' zero-age horizontal branch (ZAHB) models to compare their pulsation periods to those seen in these stars. n this very preliminary calculation, we assumed a metallicity of Z =., and an initial helium mass fraction of.4. The helium core mass was taken as.485 Mo' which is representative of stars of this metallicity (see, for example, Dorman, Rood & Connell 993), and the assumed C enrichment at the flash was 3 per cent. Above the helium core was a thin transition region to the primordial mixture of X =.759, Y=.4, Z =., with a composition profile from Sweigert & Gross (976) but with a thickness of. Mo. The model integration proceeded from the centre outwards and the surface inwards to a common fitting point; Toff, LLo' the central pressure and the central temperature were then adjusted until convergence was reached. n the model-building code, we used the OPAL opacities; other input physics is described in Dehner & Kawaler (995) and Kawaler & Bradley (994). The models produced with this technique are very similar to those of other investigators such as Dorman et al. (993), and Lee & Demarque (99). They are representative of standard ZAHB models. We computed the radial and nonradial adiabatic pulsation periods of these models, along with the growth rates for the radial and non-radial modes, using the pulsation codes described in Kawaler (993) and Kawaler & Bradley (994). Results of the calculations are summarized in Table 3 below. With a core mass of.485 Mo' a hydrogen layer thickness of only. 5 Mo was required to bring the temperatures of the models to within the range spanned by these stars; we note that the thickness of this region is usually about 3 times thicker in standard horizontal branch models. Note that the model with a mass of.485 Mo represents an extreme horizontal branch (EHB) star that has lost mass down into the former hydrogen-burning shell; the surface mass fractions of hydrogen and helium are equal for this model. The final line in the table shows the periods for a model in which the entire hydrogen envelope has been removed. We note that to produce models with Toff in excess of 35 K the surface HelH must be larger than primordial. We recognize that the metallicity of these stars is probably higher than Z =., given the fact that their mainsequence companions are most likely more massive than the Sun. With higher metallicity, however, the effective temperatures of the models are in general significantly lower than the estimates for these stars. For a core mass consistent with solar metallicity, for example, of.47 Mo the maximum effective temperature (on the He main sequence) is 344 K. A model with the same metallicity and core mass, but with a surface YX of, has an effective temperature of about 3 K. The last two models in Table 4 show the periods for these higher Z models; the periods themselves are sufficiently similar to those for the lower Z models that our conclusions based on the lower Z models are not affected. We note that in these ZAHB models, the radial (t=o) fundamental (n = ) mode period is approximately 5 s, 997 RAS, MNRAS 85, Downloaded from on February 8

5 997MNRAS S Table 3. Model parameters for ZAHB models. M Teff log 9 M , , , Y/X= , HeMS.47 3, Y/X=.47 34, HeMS n l A new class of rapidly pulsating star P l P l P (s) (8) (8) Table 4. Periods observed in EC46 starst. Star P P P3 (s) (s) (s) EC EC EC PB8783* tthe error associated with each period is listed on second line. *PB 8783 has two other lower amplitude periods at.6 and 7. s. Also, the power at P =.67 s turns out to be the two closely spaced periods barely resolved at P =.68 and.65 s. and is very insensitive to the precise envelope mass (and composition). Similarly, the t = fundamental period is fixed at about 63 s. The t = fundamental mode does not exist in these stars. Of the higher overtones, the n = modes also show nearly unchanged periods from model to model, although these periods were shorter than any observed in the EC 46 stars. Other modes, such as the odd n modes and all of the t = modes, do show a significant dependence on mass and surface composition. t is clear that the observed periods are all in the range of the low-overtone radial and non-radial modes in these stars. The periods seen are frequently too close together to be attributable to a single t; to obtain period differences of a few seconds, as seen in each of the stars, we require that at least some modes are non-radial modes in these stars (see below). t is perplexing to note that none of these preliminary models are pulsationally unstable. t is possible that they are driven by the heavy-metal opacity bump identified such as in the f3 Cephei and slowly-pulsating B-type (SPB) stars (see Moskalik 995 and Dziembowski & Pamyatnykh 993). While the heavy-metal opacity bump does provide some driving in the models with Z =., this driving is overcome by radiative damping interior to the driving zone. We are currently in the process of making a more thorough exploration of evolutionary models in this part of the HR diagram in order to explore the question of what drives the observed pulsations. 4 COMPARSON BETWEEN MODELS AND EC 46 STARS The periods discovered in the four EC 46 stars analysed are listed in Table 4. All stars are multiperiodic with periods in the range P= to 6 s. The character of the PB 8783 oscillations is somewhat different from that of the other three pulsators in the sense that many more close frequencies have been found, and even the main period, at P =.67 s, appears to consist of two closely spaced frequencies at P =.68 and.65 s (Koen et al. 997). t is worth noting that the close frequency-splitting found in PB 8783 may also be present in the other EC 46 pulsators. The reason that this has not been discovered yet is that the distribution of observations in the other stars was not suitable for the resolution of close frequencies. n Fig. 4 comparison is made between the periods of the observed pulsators and the periods of the radial modes of the model pulsators. Assuming that the log g and Teff values are close to the range of the model values considered it is clear that of the radial modes only the fundamental and first overtone have periods in the observed range, as second and higher overtones all have periods P < s. Furthermore, it is also clear from the stars with three observed periods that not all modes can be radial and at least one non-radial mode must be involved. n the case of PB 8783 one must invoke many non-radial modes. The results of Section 3 show that both radial and non-radial modes can have periods in the observed range. With the limited number of observed stars no obvious pattern emerges in Fig. 4 that aids in the mode 997 RAS, MNRAS 85, Downloaded from on February 8

6 997MNRAS S 656 R. S. Stobie et al. 8 EC EC7-44 EC8-95 PB8783 Models - (a) (b),'. (c) radial modes. P(s} 4 6 Figure 4. Comparison of periods identified in the four EC 46 stars that have been analysed with the periods of radial modes of oscillation in the model subdwarfs. The height of each panel corresponds to an amplitude of mmag. The amplitude of the model radial modes is arbitrary. Models (a), (b) and (c) correspond to the first three models in Table 3. identification. Nevertheless, it is remarkable that the four observed pulsators all have periods in such a narrow range. This indicates a narrow range of properties amongst the observed stars. The fact that the model periods for the stars of logg ~ 6. and Teff ~ 35 K are in the right range is further evidence that what we are witnessing is pulsation in the hot subdwarf. From spectroscopic data we know that the pulsating sdb stars have properties of logg ~ 6. and Teff ~ 35 K ZAHB stars can only occur in this Teff region if the H layer mass on top of the helium core is no thicker than - 4 Mo - otherwise, the models will be too cool. Models with these logg, Teff values are found to have pulsation periods that are in the observed narrow range of periods only for low n and low t. n classical pulsation theory these are the modes one expects to be excited and, furthermore, the low-t modes are most likely to be visible observationally. This presents a remarkably consistent picture from independent spectroscopic and photometric observational data and model pulsation results. Assignment of unique mode identifications for the observed periods is not yet possible with this preliminary grid of models. These stars are most likely to be at least somewhat evolved beyond the ZAHB; the periods of the models change significantly with evolution. n the (logg, Teff) plane, the evolution off the horizontal branch first decreases in logg, then increases in logg and moves to higher temperature. Therefore, it is possible that the effective temperatures of these stars can be matched with evolved EHB stars. We are in the process of computing a more extensive grid of evolutionary models in order to explore the evolutionary status of these stars. t is clear, however, that non-radial pulsation plays a role. We therefore expect that the observed pulsations will soon provide useful probes of the interiors of these stars, their evolutionary status, and their rate of evolution. ACKNOWLEDGMENTS We gratefully acknowledge observations obtained by Brian Warner and Margaret Harrop-Allin, and the usefulness of the software developed by Luis Balona for batch mode CCD reductions and period analysis. REFERENCES Balona L. A, 983, SAAO Circ., 7, Deeming T. J., 975, Ap&SS, 36, 37 Dehner B. T., Kawaler S. D., 995, ApJ, 445, L4 Dorman B., Rood R. T., O'Connell R. W., 993, ApJ, 49, 596 Dziembowski W., Pamyatnykh A, 993, MNRAS, 6, 4 Kawaler S. D., 993, ApJ, 44, 94 Kawaler S. D., Bradley P. A, 994, ApJ, 47, 45 Kilkenny D., Koen C., O'Donoghue D., Stobie R. S., 997a, MNRAS, 85, 64 (Paper, this issue) Kilkenny D., O'Donoghue D., Koen c., Stobie R. So, Chen A, 997b,~RAS,subntitted Koen c., Kilkenny D., O'Donoghue D., van Wyk F., Stobie R. S., 997, MNRAS, 85, 645 (Paper, this issue) Kurtz D. W., 985, ~RAS, 3, 773 Lee Y. W., Demarque P., 99, ApJS, 73, 79 Moskalik P., 995, in Stobie, R. S., Whitelock P. A, eds, ASP Com. Ser. 83, Astrophysical Applications of Stellar Pulsation. Astron. Soc. Pac., San Francisco, p. 44 O'Donoghue D., Lynas-Gray A E., Kilkenny D., Stobie R. S., Koen C., 997, MNRAS, 85, 657 (Paper V, this issue) Saffer R. A, Bergeron J., Koester D., Liebert J., 994, ApJ, 43, 35 Stobie R. S. et al., 997, ~RAS, submitted Sweigert A, Gross P., 976, ApJS, 3, RAS, MNRAS 85, Downloaded from on February 8