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Astron. Astrophys. 334, 606-608 (1998)

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4. Discussion

We have demonstrated the presence of rapid photometric oscillations in the A (p EuSrCr) star HD 213637. These oscillations can be described by the superposition of two signals with frequency [FORMULA] =1452 µHz and [FORMULA] =1411 µHz. Owing to the sparse sampling in our data, both of these frequency identifications are subject to 1 cycle d-1 alias ambiguities.

Notwithstanding the uncertainties in our frequency identifications, the oscillations in HD 213637 are indisputably modulated in amplitude, as is evident in Fig. 2. This modulation may arise due to a number of causes, possibly acting in combination. These causes are rotation, the presence of multiple pulsation modes, and intrinsic growth or decay of pulsation modes. The presence of each of these factors yields further information about the star.

Rotational modulation arises in roAp stars because the pulsation axis is locked to the magnetic axis, which is generally inclined to the rotation axis. This causes non-radial modes to be viewed from variable aspect as the star rotates. The modulation clearly occurs with exactly the rotation frequency of the star, [FORMULA]. The Fourier manifestation of this phenomenon is that each frequency [FORMULA] is split into a multiplet of [FORMULA] frequencies with equal spacing [FORMULA]. The components of these multiplets are usually asymmetric in amplitude as a consequence of the strong magnetic fields in Ap stars. The phenomenological model describing these rotationally induced modulations is called the oblique pulsator (Kurtz 1990). If such rotational splitting is observed in HD 213637, it could yield information on the rotation frequency of the star, its inclination, the degree [FORMULA] of the pulsation mode, and an integrated measure of the internal magnetic field.

The possible presence of multiple pulsation modes offers the prospect of applying the techniques of p -mode asteroseismology to this star. The asymptotic theory of low-degree, high-overtone ([FORMULA]) p modes (Tassoul 1990) predicts an eigenspectrum consisting of a comb of equally spaced frequencies [FORMULA] given by

[EQUATION]

to first order, where [FORMULA] is the degree of the mode, n is the overtone, and [FORMULA] is a constant which depends on the equilibrium structure of the star. The quantity [FORMULA] is the spacing of consecutive overtones ([FORMULA]) for a given [FORMULA]. The overtone spacing may be expressed in terms of structural parameters as

[EQUATION]

Using the mass-luminosity relation one may show that loci of constant [FORMULA] are essentially lines of constant R in a theoretical H-R diagram (e.g. Shibahashi & Saio 1985). Thus, the detection of multiple modes in HD 213637 would allow the evolutionary stage of this star to be established.

The final cause for rapid amplitude modulation, intrinsic mode growth/decay, is more difficult to establish conclusively. The main difficulty here lies in disentangling the real modes from spurious frequencies introduced by the growth/decay of the modes, and also the aliases. Continuous multi-site data is required for this. Demonstrating intrinsic mode growth/decay in roAp stars is useful because it would constrain the mode selection and excitation mechanisms in these stars.

Future work on this star should concentrate on eliminating the alias ambiguities of the two identified frequencies. A definitive measurement of [FORMULA], combined with H [FORMULA] photometry will allow a determination of the asteroseismological luminosity of this star. A more intensive study should reveal the rotational sidelobes of the pulsation frequencies if they are being modulated with rotation. A noise level lower than the 0.2-mmag level of the present study could result in the detection of additional frequency components. In order to meet these goals an intensive study spanning several weeks is required. This study should be conducted on 1-m class telescopes to improve photon statistics for this V =9.6 star and to minimize the scintillation noise.

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© European Southern Observatory (ESO) 1998

Online publication: May 15, 1998

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