Variability of β Cephei and SPB stars

Variability of β Cephei and SPB stars GAIA Variable Stars Working Group C. Neiner & P. De Cat In this manuscript, we briefly characterize the β Cephei and SPB stars, two classes of hot pulsating stars found in the upper part of the main-sequence (Fig. 1, left panel). They are also described in the book Light curves of variable stars: a pictorial atlas written by Sterken & Jaschek (1996). For the most recent overview articles, we refer to β Cep stars from a photometric point of view (Sterken & Jerzykiewicz 1993), β Cep stars from a spectroscopic point of view (Aerts & De Cat 2003) and An observational overview of pulsations in β Cep stars and slowly pulsating B stars (De Cat 2002). Figure 1: Left: Location of the main classes of variable stars in a theoretical Hertzsprung-Russell diagram. The β Cep stars and the slowly pulsating B stars are found in the upper part of the mainsequence. Their instabilities are driven by the κ-mechanism acting on the Z-bump. Figure taken from Roxburgh et al. (2000). Right: The positions of the confirmed (full symbols) and candidate (open symbols) β Cep stars (circles) and Slowly Pulsating B stars (squares) in the main-sequence. We also show the ZAMS (lower dotted line), the TAMS (upper dotted line) and the theoretical instability strips (full lines) for Z = 0.020 for modes with pulsation degree l 2, computed using the OPAL opacities for stellar models with X = 0.70 for which effects of rotation and convective overshooting were not taken into account (Pamyatnykh 1999). 1

1 β Cephei stars 1.1 Introduction β Cep variables, known since 1902, are early-b stars (spectral types B0.5 to B2, luminosity class II-III to V) that exhibit coherent short-period light and radial velocity variations. They are main-sequence or slightly evolved stars in the core hydrogen burning stage. Today, about 100 bona fide β Cep stars are known. Pulsation periods of β Cep variables range from about 3 to 8 hours and are associated with low-order p and/or g modes. Their driving mechanism was not understood for a long time. In contrast to several other variable classes of stars (e.g. δ Scuti stars, RR Lyrae stars), the region of ionisation of HeI can not destabilise β Cep stars. It was not until 1993, when new atomic data became available, that it became clear that the classical κ mechanism acting on iron-peak elements deep in the envelope of the star causes the pulsations in these stars (Dziembowski & Pamyatnykh 1993; Gautschy & Saio 1993). In the right panel of Fig. 1, we show the theoretical instability strip for l 2 modes computed using the OPAL opacities for stellar models with X = 0.70 for which effects of rotation and convective overshooting were not taken into account (Pamyatnykh 1999). Smith (1980) argued that the main pulsation modes of β Cep stars are radial. The observed main modes are indeed usually radial, but non-radial pulsations have also been detected. β Cru is a wellknown β Cep star for which only non-radial modes are observed (so far) (Aerts et al. 1998). A large fraction of the β Cep stars is multiperiodic, which causes beating phenomena with periods of weeks to months. β Cep stars were first thought to be restricted to slow rotators, but Shobbrock et al. (1969) discovered rapidly rotating examples. The fact that only slow rotators were first discovered was due to selection effects. Schrijvers (1999) recently discovered a large group of rapidly rotating, candidate β Cep stars. Some β Cep stars also show Balmer emission, which makes them Be stars. β Cep itself, the prototype of this class, is a Be star, but a slowly rotating one. This latter point is relevant, since most of the theoretical efforts to explain Be stars have been concentrated on rapid rotation. 1.2 Variability Although the amplitude of light variation is rather small (i.e. less than 0.1 magnitude, except for BW Vul), most of the β Cep stars are discovered photometrically. As the main mode is usually radial and the amplitude of the other modes is much smaller, the light curves often look quasi-sinusoidal. In the Geneva photometric system, the amplitude of the variations generally decreases from the U band towards the G band (Fig. 2). The relative amplitudes of the variations in different photometric passbands depend on the degree l of the pulsation mode. In general, no significant phase lags are observed. The full amplitude of radial velocity variations can go up to 40 km s 1, and even more for σ Sco and BW Vul (see Fig. 3). Theoretically, the amplitude of pulsation of the β Cep stars has its peak at the center of the instability strip, next to the main sequence, and decreases towards both directions of 2

Figure 2: The amplitudes in the 7 filters of the Geneva photometric system obtained by Aerts (2000) for observed modes of 6 β Cep stars. luminosity (see Pamyatnykh 1999). β Cep stars generally show simultaneous photometric and spectroscopic variations. However, in the current photometric data-sets of β Cen, no pulsation period is detected while the stars shows clear, multiperiodic line-profile variations (Ausseloos et al. 2002). This behavior is consistent with highdegree l modes. BW Vul has the largest known amplitude of light and radial velocity variation among the β Cep stars. It shows strong non-linear behavior. The light curve is marked by a stillstand phase, whose beginning precedes time of maximum by about 0.05 day. The duration of the stillstand phase is close to 0.3 day. The peak-to-peak amplitude of the light variation is 0.2 magnitude in the visual domain and increases to 1.2 magnitude at ultraviolet wavelengths. The period of variation is approximately 5 hours and is secularly increasing at a rate of about 2 seconds per century (Sterken et al. 1993). 1.3 Asteroseismology β Cep stars as supernova progenitors are very interesting objects from an asteroseismic point of view. Since their frequency spectrum is not too dense (see top panel of Fig. 4), asteroseismic modelling becomes possible even with only a few well-identified modes. Recently, important results from the first in-depth seismic modelling studies were obtained. Thoul et al. (2003) performed an asteroseismic modelling of 16 (EN) Lacertae based on three modes with frequencies 5.91128 c d 1, 5.85290 c d 1, and 5.50259 c d 1 which are respectively identified as (l, m) = (0,0), (2,0) and (1/2,0) by Aerts et al. (2003). Under the assumption that convective overshooting does not occur, they found a mass M = 9.62 ± 0.11 M and an age of 15.7 million years. For HD 129929, a timeseries of 1493 high-quality multicolour Geneva photometric data with a time 3

Figure 3: Top: the distribution of the projected rotational velocity v sin i (km s 1 ). Middle: the observed amplitude of the variations in, respectively, the radial velocity data (A V rad ) and the Hipparcos H p data (A Hp ) as a function of v sin i. Bottom: the observed frequency ν obs (c d 1 ) as a function of v sin i (km s 1 ). The full symbols correspond to the amplitudes of the main pulsation frequencies. The SPBs and the β Cep stars are given in the left and right panels respectively. Figure taken from De Cat (2002). base of 21.2 years was analysed by Aerts et al. (2004b) and Dupret et al. (2004). Evidence for the presence of at least six frequencies is found, which are respectively identified thanks to the seismic modelling and the photometric amplitudes as the radial fundamental, the l = 1, p 1 triplet, and two consecutive components of the l =2, g 1 quintuplet. A non-adiabatic analysis allowed to constrain the metallicity of the star to Z =0.019 ± 0.003, the core overshooting parameter to α ov = 0.10 ± 0.05, and other global parameters of the star. Moreover, on the basis of the observation of the l = 1, p 1 triplet and part of the l =2, g 1 quintuplet, constraints on the internal rotation of this star were obtained. The seismic analysis of ν Eridani based on the largest simultaneous photometric and spectroscopic multi-site campaign ever performed on a single star is still ongoing. The first results are given by Handler et al. (2004) and Aerts et al. (2004a). Some 20 sinusoidal components are found, of which 8 correspond to independent pulsation frequencies. 4

9.7 M o X=0.7 Z=0.02 1.5 10 7 years no overshooting l=3 g 4 g 3 g 2 g 1 f p 1 l=2 g 3 g 2 g 1 f p 1 p 2 l=1 g 1 p 1 p 2 p 3 l=0 p 1 p 2 p 3 0.50 0.60 0.70 0.80 0.90 1.00 log f (c/d) Figure 4: The frequency spectrum obtained with a theoretical model, together with the observed frequencies (dashed lines), for: (top) the β Cep star 16 Lacertae with the 3 observed frequencies 5.91128 c d 1, 5.85290 c d 1, and 5.50259 c d 1, (bottom) the SPB star HD 74195 with the 4 observed frequencies 0.35745 c d 1, 0.35033 c d 1, 0.34630 c d 1, and 0.39864 c d 1. Note that the frequency spectrum of the SPB star is much denser than the frequency spectrum of the β Cep star. 2 SPB stars 2.1 Introduction The Slowly Pulsating B stars (SPBs) were first introduced by Waelkens (1991) as a distinct group of variables B2 to B9 stars, with masses ranging from 3 to 7 M showing multiperiodic light variations. Typical periods are 0.5 to 3 days, thus too long and too unstable to be associated with β Cep variability. The Hipparcos mission greatly increased the number of known SPB stars: only 12 SPBs were known before Hipparcos while 72 new SPB candidates were discovered with this satellite (Waelkens et al. 1998). This is not surprising, since oscillation periods of the order of 1 day are hard to detect from the ground. Currently, about 40 stars are considered as bona fide SPBs. All the bona fide SPBs for which a detailed follow-up line-profile study is available, show clear line-profile 5

Figure 5: Phase diagram for [U-B], [B-V] and m V of the SPB star HD160124 during 1981 and 1983. A cosine synthetic curve is fitted to the [U-B] and to the visual brightness variations. The amplitudes of the fits differ significantly from one to another. Most of the residual scatter is intrinsic. Figure taken from Waelkens & Rufener (1985). variations. Note that the majority of the stars previously classified as mid-b variables or 53 Per stars are now considered to be bona fide SPBs. The SPBs are situated in the main-sequence, just below the β Cep stars in the H-R diagram (Fig. 1). Like for the β Cep stars, the κ mechanism has to be invoked to explain the instabilities (Dziembowski et al. 1993). The light and line-profile variations are interpreted in terms of non-radial pulsations of high-order g modes (Dziembowski & Pamiatnykh 1993). Most of the SPBs are multi-periodic, which causes beating phenomena with periods of months to years. A detailed study of SPBs therefore needs observations with a sufficiently long time-base. The SPBs are considered to be slow rotators (v sin i 100 km s 1 ), but the extensive list of candidate SPBs contains rapidly rotating stars. A spectroscopic follow-up campaign is needed to exclude binarity and/or rotational modulation as causes of the observed variations. Moreover, the recent observation of a rapid filling of the equivalent width of H and He I lines in the B2.5 IV star 53 Psc (Le Contel et al. 2001) seems to indicate that some of the SPB stars also show the Be phenomenon. 6

2.2 Variability SPB stars have an amplitude of light variations of less than 0.1 magnitude, which decreases with increasing wavelengths. Like for β Cep stars, in general, no significant phase lags are observed between variations in different photometric filters. The colour variations are in phase with the light variations and the colour-to-light ratio remains constant (Fig. 5). The observed variability in amplitude on a cycle-to-cycle and even a year-to-year base is caused by multi-periodicity. Radial velocity variations are also detected in SPB stars, but their full amplitude rarely exceeds 15 km s 1 (Fig. 3), because the pulsation modes are g modes. 2.3 Asteroseismology SPBs are even more interesting objects than β Cep stars from an asteroseismic point of view. Indeed, since they are pulsating in g modes, the deep interior of these stars can be probed. Unfortunately, their frequency spectrum is very dense (see bottom panel of Fig. 4), which makes asteroseismic modelling very difficult. A lot of well-identified modes are needed for this. Since mode identification is still problematic for SPBs, no in-depth asteroseismic studies for SPBs are available so far. References Aerts, C. 2000, A&A, 361, 245 Aerts, C. & De Cat, P. 2003, Space Science Reviews, 105, 453 Aerts, C., De Cat, P., Cuypers, J., et al. 1998, A&A, 329, 137 Aerts, C., De Cat, P., Handler, G., et al. 2004a, MNRAS, 347, 463 Aerts, C., Lehmann, H., Briquet, M., et al. 2003, A&A, 399, 639 Aerts, C., Waelkens, C., Daszyńska-Daszkiewicz, J., et al. 2004b, A&A, 415, 241 Ausseloos, M., Aerts, C., Uytterhoeven, K., et al. 2002, A&A, 384, 209 De Cat, P. 2002, in ASP Conf. Ser. 259: IAU Colloq. 185: Radial and Nonradial Pulsations as Probes of Stellar Physics, 196 Dupret, M.-A., Thoul, A., Scuflaire, R., et al. 2004, A&A, 415, 251 Dziembowski, W. A., Moskalik, P., & Pamyatnykh, A. A. 1993, MNRAS, 265, 588 Dziembowski, W. A. & Pamiatnykh, A. A. 1993, MNRAS, 262, 204 Dziembowski, W. A. & Pamyatnykh, A. A. 1993, MNRAS, 262, 204 Gautschy, A. & Saio, H. 1993, MNRAS, 262, 213 Handler, G., Shobbrook, R. R., Jerzykiewicz, M., et al. 2004, MNRAS, 347, 454 7

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