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An Asteroseismic Study of the Β Cephei Star Β Canis Majoris

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An Asteroseismic Study of the Β Cephei Star Β Canis Majoris A&A 459, 589–596 (2006) Astronomy DOI: 10.1051/0004-6361:20064980 & c ESO 2006 Astrophysics An asteroseismic study of the β Cephei star β Canis Majoris A. Mazumdar1,2, M. Briquet1,, M. Desmet1, and C. Aerts1,3 1 Instituut voor Sterrenkunde, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium e-mail: [email protected] 2 Astronomy Department, Yale University, PO Box 208101, New Haven, CT 06520-8101, USA 3 Department of Astrophysics, University of Nijmegen, PO Box 9010, 6500 GL Nijmegen, The Netherlands Received 7 February 2006 / Accepted 11 July 2006 ABSTRACT Aims. We present the results of a detailed analysis of 452 ground-based, high-resolution high S/N spectroscopic measurements spread over 4.5 years for β Canis Majoris with the aim of determining the pulsational characteristics of this star, and then using them to derive seismic constraints on the stellar parameters. Methods. We determined pulsation frequencies in the Si III 4553 Å line with Fourier methods. We identified the m-value of the modes by taking the photometric identifications of the degrees into account. To this end we used the moment method together with the amplitude and phase variations across the line profile. The frequencies of the identified modes were used for a seismic interpretation of the structure of the star. Results. We confirm the presence of the three pulsation frequencies already detected in previous photometric datasets: f1 = −1 −1 −1 3.9793 c d (46.057 µHz), f2 = 3.9995 c d (46.291 µHz), and f3 = 4.1832 c d (48.417 µHz). For the two modes with the highest amplitudes, we unambiguously identify (1, m1) = (2, 2) and (2, m2) = (0, 0). We cannot conclude anything for the third mode −1 identification, except that m3 > 0. We also deduce an equatorial rotational velocity of 31 ± 5kms for the star. We show that the mode f1 must be close to an avoided crossing. Constraints on the mass (13.5 ± 0.5 M), age (12.4 ± 0.7 Myr), and core overshoot (0.20 ± 0.05 HP)ofβ CMa are obtained from seismic modelling using f1 and f2. Key words. stars: early-type – stars: individual: β Canis Majoris – techniques: spectroscopic – stars: oscillations 1. Introduction photometric measurements of a multisite campaign dedicated to the star. Many breakthroughs have recently been achieved in the field of Aerts et al. (1994) collected spectroscopic data in order to asteroseismology of β Cephei stars. Observing a few pulsating identify the modes of the known frequencies of β CMa. In this modes led to constraints not only on global stellar parameters paper, we present a similar analysis but base it on a much larger but also on the core overshoot parameter and on the non-rigid number of spectra and use the version of the moment method rotation of several β Cephei stars. In particular, modelling has improved by Briquet & Aerts (2003). We then construct stel- been performed for HD 129929 (Aerts et al. 2003a; Dupret et al. lar models that show oscillations in accordance with our unique 2004) and ν Eri (Pamyatnykh et al. 2004; Ausseloos et al. 2004). identification of the modes of β Canis Majoris. β Our aim is to add other Cephei stars to the sample of those The paper is organised as follows. Section 2 describes the with asteroseismic constraints. results from our spectroscopic observations, including data re- β β The B 1 II-III bright Cephei star Canis Majoris duction, frequency analysis and mode identification. In Sect. 3 V = . (HD 44743, HR 2294, mag 1 97) is particularly interesting we present our seismic interpretation of β CMa. We end the pa- to study. Indeed, earlier photometric and spectroscopic data re- per with a discussion of our results in Sect. 4. veal that this object exhibits multiperiodicity with rather low fre- quencies in comparison with the frequencies of other β Cephei stars, which would indicate that β CMa is either a reasonably 2. Spectroscopic results evolved star or that it oscillates in modes that are different from the fundamental. 2.1. Observations and data reduction The variability of β CMa has been known for one century Our spectroscopic data were obtained with the CORALIE during which the star has been extensively studied. We refer to échelle spectrograph attached to the 1.2 m Leonard Euler tele- Albrecht (1908), Henroteau (1918), Meyer (1934), and Struve scope in La Silla (Chile). Since the beat period between the two (1950) for the first spectroscopic measurements of β CMa. Later known dominant frequencies is about 50 days, we collected data Shobbrook (1973) found three pulsation frequencies from exten- over a long time span. Observations were collected during sev- sive photometric time series. The same three frequencies were eral runs spread over 4.5 years. The number of observations and recently confirmed by Shobbrook et al. (2006) who analysed the ranges of their Julian Dates are given in Table 1. In total, we Based on spectroscopic data collected with the CORALIE échelle gathered 452 spectra during 1692 days. spectrograph attached to the 1.2 m Swiss Euler telescope at La Silla, An online reduction of the CORALIE spectra, using the Chile. INTER-TACOS software package, is available. For a descrip- Postdoctoral Fellow of the Fund for Scientific Research, Flanders. tion of this reduction process we refer to Baranne et al. (1996). Article published by EDP Sciences and available at http://www.aanda.org or http://dx.doi.org/10.1051/0004-6361:20064980 590 A. Mazumdar et al.: Asteroseismology of β Canis Majoris Table 1. Observing logbook of our spectroscopic observations 6 of β CMa. 4 Number of JD + ) 2 observations 2 450 000 -1 Start End 22 1591 1598 0 > (km s 26 1654 1660 1 70 1882 1894 <v -2 62 1940 1953 60 2227 2239 -4 27 2569 2582 2 2624 2624 -6 91 2983 2994 0 0.2 0.4 0.6 0.8 1 54 3072 3085 Phase (f = 3.9793 c d-1) 38 3271 3283 6 4 We did a more precise correction for the pixel-to-pixel sensi- ) 2 tivity variations by using all available flatfields obtained during -1 the night instead of using only one flatfield, as is done by the 0 online reduction procedure. Finally, all spectra were normalised > (km s 1 to the continuum by a cubic spline function, and the heliocen- <v -2 tric corrections were computed. For our study of the line-profile variability, we used the Si III triplet around 4567 Å. This triplet -4 is very suitable for studying β Cephei stars since the lines are strong, dominated by temperature broadening, and not too af- -6 fected by blending (see Aerts & De Cat 2003). 0 0.2 0.4 0.6 0.8 1 Phase (f = 3.9995 c d-1) 6 2.2. Frequency analysis We performed a frequency analysis on the first three velocity 4 moments v1, v2 and v3 (see Aerts et al. 1992, for a definition ) 2 of the moments of a line profile) of the Si III 4553 Å line by -1 means of the program Period04 (Lenz & Breger 2005). For some β Cephei stars (see Schrijvers et al. 2004; Telting et al. 1997; 0 > (km s 1 Briquet et al. 2005) a two-dimensional frequency analysis on <v -2 the spectral lines led to additional frequencies compared to the one-dimensional frequency search in integrated quantities such -4 as moments. Consequently we also tried to find other frequencies for β CMa by means of this latter method. -6 Despite the strong aliasing of our dataset, our frequency 0 0.2 0.4 0.6 0.8 1 analysis reaffirmed the presence of the already known three Phase (f = 4.1832 c d-1) = −1 = pulsating frequencies of β CMa: f1 3.9793 c d , f2 1 = −1 −1 −1 Fig. 1. From top to bottom: phase diagram of v for f1 3.9793 c d , 3.9995 c d ,and f3 = 4.1832 c d (Shobbrook 1973; −1 for f2 = 3.9995 c d after prewhitening with f1 and for f3 = Shobbrook et al. 2006). Unfortunately, no other frequencies −1 4.1832 c d after prewhitening with f1 and f2. could be discovered in our new spectroscopic data. Phase dia- v1 f f f grams of for 1, 2,and 3 are shown in Fig. 1. The frequen- mode identification for the β Cephei star θ Ophiuchi. We refer to v1 cies and amplitudes that yielded the best fit of are listed in that paper for a detailed explanation of our chosen process. Table 2. These three frequencies reduce the standard deviation of the first moment by 72%. Figure 2 shows the variations across the Si III 4553 Å line for f1, f2,and f3 (see Telting & Schrijvers 2.3.1. Adopted -identifications 1997; Schrijvers et al. 1997, for a definition). We make use of spectroscopy to identify the values of the az- We also performed a frequency analysis on the equivalent imuthal number, m, which are not accessible from photometry. width (EW) but we could not find any significant frequency. In order to limit the number of parameters in our spectroscopic This is not uncommon since significant EW variations have been mode identification, we adopt the degree, , as obtained from found in only a few β Cephei stars with photometric variations photometric mode identification. Recently, Shobbrook et al. up to now (De Ridder et al. 2002). (2006) found 1 = 2 for the first mode, f1,and2 = 0forthe second mode, f2. However, the degree of the third mode could 2.3.
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