Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.sao.ru/Doc-en/Science/Public/Conf/magstars-2010/p342.pdf Äàòà èçìåíåíèÿ: Mon Aug 15 11:43:47 2011 Äàòà èíäåêñèðîâàíèÿ: Mon Feb 4 15:59:54 2013 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: guide 8.0

Magnetic Stars, 2011, pp. 342 ­ 354

Study of Pulsations in the Atmosphere of the roAp star HD 137949
Sachkov M.1 , Hareter M.2 , Ryab chikova T.
1 2 3 4

1,2

, Wade G.3 , Ko chukhov O.4 , Weiss W. W.2

Institute of Astronomy, Russian Academy of Sciences, Moscow, Russia Institut fur Astronomie, Universit¨ Wien, Wien, Austria ¨ at Department of Physics, Royal Military College of Canada, Kingston, Ontario, Canada Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden

Abstract. The roAp star HD 137949 (33 Lib) shows the most complex pulsational behaviour among all roAp stars. Mkrtichian et al. (2003) found nearly anti­phase pulsations of Nd II and Nd III lines, which they attribute to the presence of a pulsation node high in the atmosphere of HD 137949. This was confirmed by Kurtz at al. (2005), who also find that in some REE lines the main frequency, corresponding to 8.27 min, and its harmonic have almost equal RV amplitudes. Based on high accuracy observations Ryabchikova et al. (2007a) studied pulsational characteristics of the HD 137949 atmosphere in detail. In general, spectroscopy provides 3D resolution of modes and allows to search for the photometrically undetectable frequencies. The high­accuracy space photometry provides very high­precision measurements of detected pulsation frequencies and enables an accurate phasing of multi­site spectroscopic data. A combination of simultaneous spectroscopy and photometry represents the most sophisticated asteroseismic dataset for any roAp star. In 2009 the star HD 137949 became a target of an intense observing campaign that combined ground­based spectroscopy with space photometry, obtained with the MOST satellite. We collected 780 spectra using the ESPaDOnS spectrograph mounted on the 3.6­m CFHT telescope; 374 spectra were obtained with the FIES spectrograph mounted on the 2.56­m NOT to perform the time­resolved spectroscopy of HD 137949. In addition, we used 111 UVES spectra (2004) from the ESO archive to check the mode stability. The frequency analysis of the new radial velocity (RV) measurements confirmed the previously reported frequency pattern (two frequencies and the first harmonic of the main frequency), and revealed an additional frequency at 1.991 mHz. The new frequency solution fits perfectly the RV variations from the 2004 and 2009 observational sets providing a strong support for the p­mode stability in the roAp star HD 137949 for at least 5 years. Key words: stars: atmospheres ­ stars: chemically peculiar ­ stars: magnetic fields ­ stars: oscillations ­ stars: individual: HD 137949

Based on observations collected at the European Southern Observatory, Paranal, Chile (program 077.D­0491 and a program 077.D­0150, retrieved through the ESO archive) and at the Nordic Optical Telescope (NOT).


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1

Intro duction

The rapidly oscillating peculiar A­type (roAp) stars are the key ob jects for asteroseismology, which presently is the most powerful tool for testing the theories of stellar structure. Deep within the 3D envelope of a pulsating star, acoustic waves are excited and propagate through regions of varying temperature, density and composition, which influence the wave speed, frequency and direction. Conventional asteroseismology has focused on the interpretation of the light and radial velocity variations produced by these waves as they arrive at the stellar surface. This is a tremendous limitation because the complex 3D details of the acoustic wave pattern (e.g. relative phase of waves, radial evolution of wave amplitude, running vs. standing waves, etc.) are nearly impossible to unravel from such simple 2D surface observations. However, peculiar atmospheres of magnetic roAp stars provide a unique possibility of extending observational asteroseismology to the radial dimension, and to thereby build a complete 3D model of a pulsating stellar atmosphere. This capability is a consequence of element stratification in Ap atmospheres (Wade et al., 2001; Ryabchikova et al., 2002, 2003) where spectral lines of different elements are formed at different heights. According to the elemental diffusion theory (Michaud, 1970) the iron­peak elements in atmospheres of cool Ap stars tend to concentrate near the photospheric layers, while the heavier elements, like rare earths are pushed out by the radiative force and may produce overabundant "clouds" in the upper atmosphere. This property extends the optical depth range, accessible for determining the pulsation velocity by orders of magnitude. This capability has been demonstrated for the roAp stars Equ (Ryabchikova et al., 2002), HD 24712 (Ryabchikova et al., 2007a,b) and 10 Aql (Sachkov et al., 2008a). The basic idea for vertically resolving the stellar atmosphere and determining the depth dependence of the pulsation velocity field is to measure the pulsation amplitude and phase of the amplitude maximum in the spectral lines as a function of optical depth. As we all know, the absorption line wings are formed statistically deeper in the atmosphere than the line cores (since the opacity in the core is larger, escaping photons must originate, on the average, at a smaller continuum optical depth). A corollary of this is that the cores of weak lines are formed deeper in the atmosphere than the cores of strong lines. Using these properties, observers are able to use the absorption lines formed in the spectrum of any star to coarsely trace the atmospheric properties (including, say, the pulsation velocity field) as a function of atmospheric depth. This ability is fundamentally limited by the fact that the lines are usually formed over a broad range of depths within the atmosphere, and consequently our vertical "vision" is blurry. In the case of roAp stars, the presence of REE clouds dramatically enhances this capability to vertically resolve the atmosphere (e. g., Ryabchikova et al., 2007a). Because the spectral lines of REEs are formed almost entirely within the relatively dense clouds, the line formation depths are extremely well­defined. As the pulsational distortions of a line must correspond to the acoustic wave properties at the characteristic (and well­defined) height of formation of the line, we are able to vertically resolve the waves with a relatively high precision. One of the reasons why oscillations of roAp stars are so important lies in the fact that many oscillation frequencies are excited simultaneously giving a great potential for asteroseismic studies. Usually the researchers try to find a regular "large spacing" and a "small spacing". The regular frequency spacing in the oscillation spectra of solar­type and roAp stars is a signature of the excitation of consecutive overtones of high overtone p­modes. The "large frequency spacing" is the spacing between the consecutive overtones of modes of the same degree: = f (n, l) - f (n - 1, l), where n is radial order and l the degree of the mode. The "small spacing" is the frequency difference of modes of the same parity = f (n, l) - f (n - 1, l + 2). In the roAp stars the magnetic field of a few kG can change the pulsation frequency by 10 ­ 30 µHz, depending on the latitudinal degree l. The frequencies of l = 0 and l = 3 modes tend to be affected more strongly (Saio, 2005). Thus the resulting frequency spacings can be quite different from those expected without a magnetic field. All but one papers on roAp modeling dealt with the detailed comparison between the observed


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and nonadiabatic theoretical frequencies for the best fitting models: Cir (Bruntt et al., 2009), 10 Aql (Huber et al., 2008), Equ (Gruberbauer et al., 2008), HD 101065 (Mkrtichian et al., 2008). These models vary in stellar masses, chemical compositions (X , Z ) (where X and Z are the mass fractions of hydrogen and heavy elements), T ­ relation above the photosphere as well as the l value and magnetic field strength. In the paper by Saio et al. (2010) for the roAp star HD 24712 for the first time the distributions of the phase and amplitude of RV variations as a function of atmospheric height were modelled and compared with the observed distributions. The gradual outward increase of the phase lag in the outermost layers is well reproduced by the theoretical results obtained with a running­wave outer­ boundary condition. Although the described models agree with most of the observed properties of the oscillations in the atmosphere of HD 24712, no excited oscillation modes with frequencies appropriate for this star were found, e. g. all the modes examined are damped. The ­mechanism does not seem to be strong enough to excite the supercritical high­order p­modes in HD 24712. Based on realistic models of wave propagation in magnetised stellar atmospheres, the pulsation theory in the presence of the magnetic field (see, e. g. Sousa & Cunha, 2008) argues that in the magnetically­dominated regions of the stellar envelope waves are decoupled into the orthogonal standing magnetic and running acoustic components. These oscillations are oriented perpendicular and along the magnetic field lines, respectively. The total pro jected pulsation velocity, produced by a superposition of these two components, can have a widely different apparent vertical profile, depending on the magnetic field strength, inclination and aspect angle. For certain magnetic field parameters and viewing geometries the two components cancel out, creating a node­like structure, or imitate an inwardly running wave. Using a method based on these concepts, phase jumps in the radial velocity curves, indicating a nodal surface, were discovered in the roAp star HD 137949 by Mkrtichian et al. (2003), and in 10 Aql by Sachkov et al. (2008a). Kurtz et al. (2006) subsequently obtained a time series of 2 hours (111 VLT/UVES spectra) of HD 137949 indicating the frequencies undetectable by the ground­ based photometry for which a highly controversial interpretation could be the stochastic variations of pulsation amplitudes in the magnetoacoustic boundary layer. A reanalysis of the UVES spectra (Ryabchikova et al., 2007a) confirmed a phase jump, they also found spectral lines formed close to the position of the nodal zone showing variations at half (!) of the pulsation period (a resonant excitation of the harmonic oscillation?). HD 137949 with its nodal zone seems to allow for testing the pulsation theory. Thus, this star represents a unique laboratory for guiding the theoreticians towards a physically consistent model of dynamic roAp star atmospheres. At the same time, the current observational data are clearly unable to provide an unambiguous picture and confrontation with the theory. Therefore, we suggest to obtain a much longer spectroscopic time series of HD 137949 and a simultaneous MOST photometry. This combination of the spectroscopy (which provides a 3D resolution of waves as well as sensitivity to the frequencies undetectable photometrically) with the photometry (which provides a very high precision diagnosis of detected pulsation frequencies, allowing for accurate phasing of the spectroscopic data) will represent the most sophisticated asteroseismic dataset for any roAp star.

2

Observations and Data Reduction

Spectroscopic monitoring of 33 Lib was performed using the ESPaDOnS spectrograph mounted on the 3.6­m CFHT during 3 nights: May 02, 05, and 11 2009 and with Fibre­fed Echelle Spectrograph (FIES) mounted on the 2.56­m Nordic Optical Telescope (NOT) during 5 nights: April 29, May 05, 12, 17, and 21 2009. 780 high­quality spectra were obtained with the ESPaDOnS and 374 spectra were obtained with the FIES. These spectra were acquired simultaneously with allocated ultra-


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Table 1: Journal of observations of 33 Lib Start HJD (245 0000+) 53071.76313 54951.52764 54953.89440 54957.55330 54957.87190 54962.84950 54964.54251 54969.51152 54973.50093 End HJD (245 0000+) 53071.84598 54951.64601 54954.07997 54957.67169 54958.05284 54963.08189 54964.66090 54969.62990 54973.61941 Spectral range, ° A 4960 ­ 6990 4766 ­ 7364 4950 ­ 7200 4766 ­ 7364 4950 ­ 7200 4950 ­ 7200 4766 ­ 7364 4766 ­ 7364 4766 ­ 7364 No. of exposures 111 74 240 75 240 300 75 75 75 time resolution, s 69 140 67 140 67 67 140 140 140 Typical S/N 100 80 90 80 90 65 80 80 80 Instr. UVES FIES ESPaDOnS FIES ESPaDOnS ESPaDOnS FIES FIES FIES

precise broadband photometry by the MOST minisatellite between April 23 and May 22. In addition we used 111 UVES spectra extracted from the ESO archive to check the mode stability. A journal of observations is presented in Table 1, where the Julian Date of the beginning and the end of each time series, the spectral range, the number of exposures and S/N ratio are given.

2.1

Time­Series ESPaDOnS Sp ectra

To adequately time­resolve the dominant 8­minute pulsation period of HD 137949, individual exposure times are limited to a maximum duration (including readout) of about 60 seconds. Using a fast readout mode (readout time = 25 s) and R = 80000 spectroscopic mode, this will provide a peak S/N per spectrum of 150:1 (according to the ESPaDOnS ETC), sufficient to achieve a spectral quality suitable for analysis of the line profile variations in the spectral orders 25 ­ 50.

2.2

Time­Series FIES Sp ectra

We have used the Fibre­fed Echelle Spectrograph (FIES) at the 2.56­m Nordic Optical Telescope (NOT) to perform the time­resolved spectroscopy of 33 Lib. The observations were obtained during 5 nights (April 29, May 05, 12, 17, 21) about 3 h each night. We collected 374 stellar spectra using an exposure time of 90 s. With the overhead of 48 s this gave us a sampling rate of approximately one spectrum every 138 s, sufficient to achieve a spectral quality suitable for the analysis of the line profile variations with a dominant 8 min pulsation period of this star. The FIES instrument was configured to use the medium-resolution mode, which provides a wavelength coverage of the 4765 ­ 7360 ° region at the resolving power of R = 47000. We used the A reduce package (Piskunov & Valenti, 2002) to perform the standard steps of the echelle spectra reduction (construction of the master flat field and bias frames, order location, flat­fielding and wavelength calibration), followed by the optimal extraction of the stellar spectra. The typical signal­ to­noise ratio of the individual observations is 80 around 5000 ° A.

3

Mo del Atmosphere, Line Identification and Radial Velo city Measurements

A self­consistent model atmosphere of HD 137949 was calculated iteratively with the ll models code using the abundances and stratification of Si, Ca, Cr and Fe derived at each iteration. Ex-


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Table 2: Summary of the RV pulsational analysis in 33 Lib Ion HI Eu II Y II Dy II Dy III Tb III Th III La II Frequencies detected f1 f3 f1 f1 f2 f1 f1 f1 f2 f1 f1 Amplitudes, m/s 302 53 210 85 30 90 40 100 56 190 100 Central wavelength of lines used, ° A Hcore 6562 6438, 6645 5546, 5663, 5728 5164, 5169 5730 5847, 6092, 6323, 6687 5375, 6599 5805, 5808, 6100, 6262, 6320, 6399, 6642 6707 5292, 5681, 6165 5300, 6160, 6866, 7030

Li I Pr II Pr III

Nd II

Nd III

Fe I Fe II

f1 f1 f2 f1 f2 f3 f4 f1 f2 f3 f4 f1 f2 f3 f4 f1 f1

110 130 40 94 39 34 42 114 53 25 20 78 28 23 26 25 30

5132, 5311, 5534, 6650 5051, 5803, 6145,

5182, 5277, 5320, 5486, 5804, 6638, 5152, 5677, 5845, 5851, 6327

5415, 5424, 5676 5414, 5425, 6247

tended tables of observed and predicted lines of the rare­earth elements were used for line opacity calculations. For the final model we adopted Teff = 7500 ± 100 K and log g = 4.0 ± 0.1. With the Hipparcos parallax we estimated the radius of HD 137949 as R = 2.05 R To perform a careful line identification and choose lines suitable for the pulsation analysis, we have synthesized the observed spectral region for the star with these parameters. Atomic data were extracted from the Vienna Atomic Line Database (VALD, Kupka et al., 1999) and the synthetic spectrum calculations were carried out with the synthmag code (Kochukhov 2007). The radial velocities were measured with a centre­of­gravity technique. We used spectral lines that were selected in our previous study (Ryabchikova et al., 2007a). Taking into account the observed pulsation amplitudes and accuracy of RV measurements, we have selected about 100 lines for the frequency analysis and the study of the pulsational wave propagation through the stellar atmosphere.


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Table 3: Frequencies for the RV data Label H core f1 f3 Eu II f1 Nd II f1 f2 f3 f4 Nd III f1 f2 f4 f3 Pr III f1 f4 f2 f3 Frequency, d-1 174.075204 170.978821 174.070340 174.074649 348.147294 171.554097 155.482824 174.071151 348.140230 155.727163 170.973465 174.073599 155.738266 348.146463 170.971336 Significance Amplitude, m/s 301 53 211 114 53 25 20 78 28 26 23 94 42 39 34 Phase [- , ] -2.895628 -1.726288 0.907241 -1.625773 2.638426 -2.937492 -0.936600 0.133982 1.458686 2.509509 -2.983738 -2. -1. -0. -3. 905973 850699 631134 010928

117.9 6.8 61.7 104.3 39.2 9.8 6.5 81.6 14.9 13.8 11.3 39.2 9.4 8.0 6.7

Aiming to improve the signal­to­noise ratio of the RV data, we averaged measurements of different lines of the same ions with close pulsational phases and amplitudes. In Table 2 we report the lines for which the RV measurements were averaged.

4

Frequency Analysis

HD 137949 is a unique case where different lines reveal a different set of frequencies. The most demonstrative examples are the H and Pr III lines. The H core pulsates with the highest dominant amplitude about 0.3 km/s, but we are able to see only two frequencies. At the same time, the Pr III lines having a 3 times less dominant amplitude (0.1 km/s) pulsates with at least 4 periods. We carried out the frequency analysis by applying the standard combination of the discrete Fourier transform (DFT) and the least­squares fitting. First we applied the DFT to the RV data. The period corresponding to the highest pulsation amplitude value was then improved by the sine­ wave least square fitting of the RV data with pulsation period, amplitude, and phase treated as free parameters. This fit was removed from the data and then the Fourier analysis was applied to the residuals. This procedure was repeated for all the frequencies with the significance above 5. The frequency analysis was performed on the RV data of the H core and the averaged RV data of Eu II, Nd II, Nd IIIand Pr III lines using the SigSpec (Reegen, 2007) and Period04 (Lenz & Breger, 2005) codes. Due to the problems with aliasing, the data of the ESPaDOnS and FIES were merged and analysed as one data set. Nine nights spanning over 22 days are available. The frequencies detected are given in Table 3. In the Nd III data, f3 has a value of 170.97 while in the Nd II data the value is different by +0.58, however, the phases are equal ( -2.9 in both cases). The


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1

0.8

Amplitude

0.6

0.4

0.2

0 -6 -5 -4 -3 -2 -1 0 1 Frequency [c/d] 2 3 4 5 6

Figure 1: Spectral window of the combined FIES and ESPaDOnS data. spectral window shows strong aliasing with 0.22, 0.78 and 1.0 d-1 . The Nd III data have a better point­to­point scatter than the Nd II data, hence it is more probable that the value of 170.97 d-1 is correct, compared to 171.55 d-1 . For Nd II and Nd III a phase lag of is expected. To check for phase­dependent aliasing we subtracted 170.97 d-1 from the Nd II residuals after pre-whitening with the dominant frequency and its harmonic. Then we added again 170.97 d-1 but with different phases and checked the Fourier transforms. At phases close to 0.1 (i. e. -3+ ) a peak at 171.55 d-1 shows the highest amplitude. This is a strong evidence that 171.55 d-1 is an alias, even though the spectral window (see Fig. 1) does not show a pronounced aliasing peak at 0.58. Figure 2 illustrates this circumstance. Figure 3 shows the Fourier transform of the original data and Fig. 4 shows the Fourier transforms after pre-whitening with the dominant frequency and its harmonic. For the Nd II data (the middle panel), the peak at 171.55 d-1 is the highest, while in the Nd III data (the upper panel), the highest peak in the corresponding range is found at 170.97 d-1 . Pre-whitening with f4 does not change the picture significantly. For the sake of completeness, the same is demonstrated for the Pr III data.

5

Phase Relations Between Photometry and Sp ectroscopy

Spectroscopic and photometric techniques provide information on the boundary zone, relevant for any pulsation model and giving access to different modes and hence atmospheric layers. An observed phase lag between luminosity and RV variations is an important parameter for a first step towards modeling the stellar structure. To determine this phase lag, one needs simultaneous photometric and spectroscopic observations. Until now this was done only for two roAp stars: HD 24712 (Ryabchikova et al., 2007b) and 10 Aql (Sachkov et al., 2008a). For HD 137949 our spectroscopic


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0.03 0.025 0.02 0.015 0.01 0.005

0.03 0.025 0.02 0.015 0.01 0.005 0 0.03 0.025 0.02 0.015 0.01 0.005 0

Amplitude [km/s]

0 0.03 0.025 0.02 0.015 0.01 0.005 0

165

170

175

165

170

175

165

170

175

165

170

175

Frequency [c/d]
Figure 2: Phase­dependent aliasing. The input frequency is indicated by the arrow. Upper left: DFT of the residuals adding f3 from Nd III without the phase lag. Lower left: the same but with the phase lag of +1. Upper right: the same but with the phase lag of +2. Lower right: phase lag 3.1.

time­series were carried out simultaneously with the MOST photometry. The high S/N and spectral resolution of present observations of HD 137949 allow us to derive phase lags for individual ions, sampling different atmospheric layers. In order to minimize the influence of the higher (with respect to the spectroscopic observations) point­to­point scatter of the photometric observations, we have constructed an artificial light curve based on the frequencies, amplitudes and phases of two frequencies (f1 and f2 ), as derived by a multi­sine fit to the MOST data. In the next step the artificial time­series were cross­correlated with the RV observations. The time interval for the cross­correlation was chosen from plus to minus 8.27 minutes (the period of the main frequency, f1 ), with an increment of 1 second. The results of the cross­correlation analysis for the Hcore and for the averaged Eu II, Nd II, and Nd III lines are given in Table 4, where we define the phase lag as the difference between the RV maximum and the photometric maximum, expressed in seconds, or as a fraction of the main period P = 8.27 min. The error of the phase lag determination was estimated as follows. We added a normally distributed random signal to both the spectroscopic and photometric data, assuming that the noise amplitude corresponds to the observational error. For spectroscopy the error was derived from the RV determinations, and for photometry the MOST team recommended to use 2% of the signal. A phase lag was derived from these noisy data and repeated 200 times. The resulting standard deviation was adopted as an error of the phase lag determination.


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0.08 0.04 0 100 Amplitude [km/s] 0.08

NdIII

150

200

250

300

350

400

NdII 0.04 0 100 0.08 0.04 0 100

150

200

250

300 PrIII

350

400

150

200

250 Frequency [c/d]

300

350

400

Figure 3: Fourier Transforms for the three RV data sets. Table 4: Phase lags (seconds and fractions of the main period P = 8.27 min) between the maxima of luminosity and RV variations of different chemical species in the atmosphere of HD 137949 Ion HI Eu II Nd II Nd III Phase lag Seconds Period fraction -20 ± 5 -0.24 ± 0.01 -64 ± 8 -0.32 ± 0.01 319 ± 9 0.43 ± 0.02 74 ± 8 -0.05 ± 0.02

6

Mo de Stability

Pulsation amplitude modulation for roAp stars were discussed in the literature as a consequence of a limited mode life time or beating frequencies. Studying Equ, the second brightest roAp star, Kurtz (1983) has detected a pulsation frequency of 1.339 µHz with an amplitude varying between 0.32 and 1.43 mmag. Beating with a closely spaced frequency has been proposed as the cause of amplitude modulation of this very slow rotating star (rotation period 77 years). Based on a cross­correlation radial velocity (RV) study, Libbrecht (1988) has discovered three frequencies at 1.365 µHz, 1.369 µHz and 1.427 µHz. He suggested that the amplitude modulation observed in the spectra of roAp stars may not be due to closely spaced frequencies, but rather caused by short ( 1 day) mode lifetimes. Martinez et al. (1996) analysed a multi­site 1992 campaign data, 26 nights in


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0.03 0.02 0.01 0 140 0.03 Amplitude [km/s] 0.02 0.01 0 140 0.05 0.04 0.03 0.02 0.01 0 140 145 150 155 160 165 Frequency [c/d] 170 175 180 NdIII

145

150

155

160

165

170

175

180

NdII

145

150

155

160

165

170

175 PrIII

180

Figure 4: Fourier Transforms for the three RV data sets after pre-whitening with f1 and f2 .

total. They also suggested short life times of pulsation modes because different frequencies appeared in their analysis of individual nights. Based on the continuous 19 day data, obtained by the Canadian mini­satellite MOST (Gruberbauer et al., 2008) 7 frequencies were identified including a new one, f2 = 1.365411 µHz, which is very close to the known frequency f1 = 1.364594 µHz. This discovery explained the puzzling amplitude modulation in Equ as a beating of two closely spaced frequencies. Analysing these MOST photometric data and the spectroscopic data, obtained a year before with the NES spectrometer at the SAO RAS 6­m BTA telescope, Sachkov et al. (2008b) concluded that in Equ the excited frequencies are stable on the time scale of several years because the common photometric/RV solution reproduces the amplitude modulation seen in the light and RV curves. As it was first noted by Kochukhov & Ryabchikova (2001) for Cir, the time­resolved spectroscopic observations of roAp stars seemed to indicate that the pulsation amplitudes of REE lines can be modulated on a time­scale of a few hours. This was later observed by Kurtz et al. (2006) for a few other roAp stars. Since in many cases this modulation cannot be linked to the known photometric pulsation frequencies, Kurtz et al. (2006) suggested that such an amplitude modulation in spectroscopy means the discovery of a new type of a pulsational behaviour in the upper atmospheres of roAp stars. They proposed three possible explanations for the newly discovered frequencies: (1) there exist modes with nodes near the level, where the photometry samples that can be easily detected at the higher level of the Pr III lines formation; or (2) there are higher­degree, l, non­radial oblique pulsation modes that are detectable in the spectroscopy because the Pr III is concentrated towards the magnetic poles, where such modes have their highest amplitudes, but averaged out over the visible hemisphere in the photometry which samples the star's surface more uniformly; or (3) there is a significant growth and decay of the principal mode amplitudes on a


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Figure 5: RV curves for the Nd III lines for the UVES (top) and ESPaDOnS data sets. time­scale of just a few pulsation cycles at the high level of formation of the Pr III lines and the core of the H line. Sachkov et al. (2008a) concluded that short observational data sets (typically 2­h long) do not allow to resolve the frequency spectrum of multiperiodic roAp stars. In HD 137949, the frequency solution based on our extensive 2009 data perfectly fits the UVES data obtained five years earlier (see Fig. 5). This fact allows us to conclude that the modes in the star HD 137949 are stable over the time scale of at least 5 years. At the same time, the complex pulsational behaviour of the roAp star HD 137949, where different lines show a different set of frequencies, probing different layers of the stratified stellar atmosphere can be explained using the ideas by Kurtz et al. (2006).

7

Pulsations Across the 33 Lib Atmosphere

We performed a pulsation analysis of HD 137949 using the phase­amplitude diagrams (Fig. 6). Pulsation properties of this star are of considerable interest because together with 10 Aql these are the only roAp stars with clear signatures of a radial node in the upper atmosphere.

8

Discussions

As in many other recent studies of RV variations in roAp stars, one can interpret the measurements of RV amplitude and phase in terms of the outward propagation of pulsation waves in a chemically­ stratified stellar atmosphere. The time­resolved spectroscopic observations acquired during several


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600
H core Nd II Nd III Pr II Pr III Dy II Dy III Tb III La II Eu II Y II Th III

500

RV amplitude, m/s

400

300

200

100

0 -0.2

0

0.2

0.4

0.6

0.8

1

Pulsation phase
Figure 6: Amplitude­phase diagram for HD 137949. The phases are given as fractional pulsation period. nights with a continuous photometric monitoring by the MOST at the same time allow us to directly derive the phase lag between the photometric and spectroscopic pulsational variations, which provide useful constraints for the subsequent modelling of oscillations. A comparison of the pulsation properties of HD 137949 and 10 Aql is of considerable interest because these are the only roAp stars with clear signatures of a radial node in the upper atmosphere that may be interpreted as a superposition of standing and running pulsation waves, mimicking an inwardly propagating wave, as discussed by Sousa & Cunha (2008). A detailed study of the chemical stratification and atmospheric structure of both stars is required for a secure interpretation of pulsation results and the subsequent theoretical modelling. A strong sensitivity of the RV pulsation amplitude with atmospheric height is typical for roAp stars. As it was mentioned above, the roAp star HD 137949 shows a unique pulsation behaviour when different sets of frequencies are derived from the lines of different ions. Understanding that different lines probe different layers of the chemically stratified roAp atmosphere, and suggesting that a different mode can arise at (or can rich) a different height in such an atmosphere, one can explain the fact that different ion lines yield different pulsation frequencies. This is an analogue of explanation of the frequency analysis differences of the spectroscopic and photometric observations by Kurtz et al. (2006). The original motivation of the simultaneous MOST and spectroscopic observations was to take an advantage of the accurate photometric frequency information in the analysis of spectroscopic data. Note that the high amplitudes of RV variations potentially allow to obtain mode frequencies even for rather short spectroscopic data strings, but with the penalty of an aliasing problem for such data sets with a poor duty cycle. A a high duty cycle, on the other hand, there is the strength of the continuous MOST data, but which, on the other hand, suffer of very small photometric amplitudes for more complex modes. A new frequency 170.9788 d-1 was detected in our spectroscopic data for HD 137949. Additional spectroscopic frequencies could offer a new view on the large frequency


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separation , a crucial factor for asteroseismology, which is directly connected to the mean density in the star and describes the separation of consecutive radial overtones for the high­order acoustic pulsation. The fact that the frequency solution, derived from our extensive 2009 spectroscopic data perfectly fits the UVES data, obtained in 2004 allows us to use the more precise UVES data together with the (non simultaneous) MOST photometric data for modelling. We also conclude that the modes in the star HD 137949 are stable on the time scale of at least a few years.
Acknowledgements. This work was partially supported by the Presidium RAS program.

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