Variability of Cephei and SPB stars GAIA Variable Stars Working Group

C. Neiner & P. De Cat

In this manuscript, we briey characterize the 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 ’ Cep stars from a photometric point of view’ (Sterken & Jerzykiewicz 1993), ’ Cep stars from a spectroscopic point of view’ (Aerts & De Cat 2003) and ’An observational overview of pulsations in 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 Cep stars and the slowly pulsating B stars are found in the upper part of the main- sequence. Their instabilities are driven by the -mechanism acting on the Z-bump. Figure taken from Roxburgh et al. (2000). Right: The positions of the conrmed (full symbols) and candidate (open symbols) 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 ` 2, computed using the OPAL opacities for stellar models with X = 0.70 for which eects of rotation and convective overshooting were not taken into account (Pamyatnykh 1999).

1 1 Cephei stars

1.1 Introduction

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 de Cep stars are known.

Pulsation periods of 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. Scuti stars, RR Lyrae stars), the region of ionisation of HeI can not destabilise Cep stars. It was not until 1993, when new atomic data became available, that it became clear that the classical 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 ` 2 modes computed using the OPAL opacities for stellar models with X = 0.70 for which eects of rotation and convective overshooting were not taken into account (Pamyatnykh 1999).

Smith (1980) argued that the main pulsation modes of Cep stars are radial. The observed main modes are indeed usually radial, but non-radial pulsations have also been detected. Cru is a well- known Cep star for which only non-radial modes are observed (so far) (Aerts et al. 1998). A large fraction of the Cep stars is multiperiodic, which causes beating phenomena with periods of weeks to months.

Cep stars were rst thought to be restricted to slow rotators, but Shobbrock et al. (1969) discovered rapidly rotating examples. The fact that only slow rotators were rst discovered was due to selection eects. Schrijvers (1999) recently discovered a large group of rapidly rotating, candidate Cep stars.

Some Cep stars also show Balmer emission, which makes them Be stars. 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 eorts 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 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 dierent photometric passbands depend on the degree l of the pulsation mode. In general, no signicant phase lags are observed.

The full amplitude of radial velocity variations can go up to 40 km s1, and even more for Sco and BW Vul (see Fig. 3). Theoretically, the amplitude of pulsation of the 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 lters of the Geneva photometric system obtained by Aerts (2000) for observed modes of 6 Cep stars. luminosity (see Pamyatnykh 1999).

Cep stars generally show simultaneous photometric and spectroscopic variations. However, in the current photometric data-sets of Cen, no pulsation period is detected while the stars shows clear, multiperiodic line-prole variations (Ausseloos et al. 2002). This behavior is consistent with high- degree l modes.

BW Vul has the largest known amplitude of light and radial velocity variation among the 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

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-identied modes. Recently, important results from the rst 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 d1, 5.85290 c d1, and 5.50259 c d1 which are respectively identied as (`, 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 s1). Middle: the ob- served amplitude of the variations in, respectively, the radial velocity data (AV rad) and the Hipparcos 1 Hp data (AHp) as a function of v sin i. Bottom: the observed frequency obs (c d ) as a function of v sin i (km s1). The full symbols correspond to the amplitudes of the main pulsation frequencies. The SPBs and the 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 identied thanks to the seismic modelling and the photometric amplitudes as the radial fundamental, the ` = 1, p1 triplet, and two consecutive components of the ` =2, g1 quintuplet. A non-adiabatic analysis allowed to constrain the metallicity of the star to Z =0.019 0.003, the core overshooting parameter to ov = 0.10 0.05, and other global parameters of the star. Moreover, on the basis of the observation of the ` = 1, p1 triplet and part of the ` =2, g1 quintuplet, constraints on the internal rotation of this star were obtained.

The seismic analysis of Eridani based on the largest simultaneous photometric and spectroscopic multi-site campaign ever performed on a single star is still ongoing. The rst 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 × 7 9.7 Mo X=0.7 Z=0.02 1.5 10 years no overshooting

l=3 g4 g3 g2 g1 f p1

l=2 g3 g2 g1 f p1 p2

l=1 g1 p1 p2 p3

l=0 p1 p2 p3

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 Cep star 16 Lacertae with the 3 observed frequencies 5.91128 c d1, 5.85290 c d1, and 5.50259 c d1, (bottom) the SPB star HD 74195 with the 4 observed frequencies 0.35745 c d1, 0.35033 c d1, 0.34630 c d1, and 0.39864 c d1. Note that the frequency spectrum of the SPB star is much denser than the frequency spectrum of the Cep star.

2 SPB stars

2.1 Introduction

The Slowly Pulsating B stars (SPBs) were rst 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 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 de SPBs. All the bona de SPBs for which a detailed follow-up line-prole study is available, show clear line-prole

5 Figure 5: Phase diagram for [U-B], [B-V] and mV of the SPB star HD160124 during 1981 and 1983. A cosine synthetic curve is tted to the [U-B] and to the visual brightness variations. The amplitudes of the ts dier signicantly 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 classied as mid-B variables or 53 Per stars are now considered to be bona de SPBs.

The SPBs are situated in the main-sequence, just below the Cep stars in the H-R diagram (Fig. 1). Like for the Cep stars, the mechanism has to be invoked to explain the instabilities (Dziembowski et al. 1993). The light and line-prole 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 suciently long time-base.

The SPBs are considered to be slow rotators (v sin i 100 km s1), 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 lling 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 Cep stars, in general, no signicant phase lags are observed between variations in dierent photometric lters. 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 s1 (Fig. 3), because the pulsation modes are g modes.

2.3 Asteroseismology

SPBs are even more interesting objects than 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 dicult. A lot of well-identied modes are needed for this. Since mode identication is still problematic for SPBs, no in-depth asteroseismic studies for SPBs are available so far.

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