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Astron. Astrophys. 336, 637-647 (1998)

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6. The red giant

6.1. Effective temperature

We compared our BX Mon low resolution near IR spectrum spectrum with spectral standards. This leads to a spectral type M[FORMULA] with no definite luminosity classification. Iijima (1985) determined the spectral type to be M5 - M6. Viotti et al. (1986) classified it as M6[FORMULA] III with some uncertainty in the luminosity class. Schulte-Ladbeck (1988) finds a spectral type M4 with no luminosity classification. For the rest of this paper, we adopt a spectral type of M[FORMULA]. The effective temperature scale for late giants from Dyck et al. (1996) yields an effective temperature [FORMULA].

6.2. Radius and luminosity

We determine the radius of the M-star in BX Mon with the K magnitude, the [FORMULA]-colour and the distance. J and K magnitudes are given in Whitelock & Catchpole (1983), Viotti et al. (1986) and Munari et al. (1992). They vary only very slightly with a [FORMULA]-scatter of 0.1 mag and are consistent with no light variations of the red giant. We use the average [FORMULA] and [FORMULA] or de-reddened [FORMULA] and [FORMULA]. Taking the surface brightness relation [FORMULA] for M-giants given in Schild et al. (1998), we find a M-star radius:


where d is the distance in kpc. According to Dumm & Schild (1998) this radius is typical for a star with this spectral type and mass. Together with the effective temperature, this leads to a luminosity [FORMULA].

With our luminosity [FORMULA] and effective temperature [FORMULA] we estimate a red giant mass from evolutionary tracks. RGB and AGB evolutionary tracks for stars of more than [FORMULA] coincide. Taking the [FORMULA] versus [FORMULA] diagram of RGB and AGB models by Bessell et al. (1989) leads to [FORMULA]. This is consistent with the value derived from the radial velocity curves.

6.3. Stellar rotation

Single M giant stars are expected to have negligible rotation velocities, due to their large moment of inertia. In Fig. 7 the spectrum of a M5 III star, shows considerably narrower absorption lines than BX Mon. The additional line broadening is understood in terms of a rotating M-star in BX Mon, expected as a consequence of binary tidal forces. Stellar rotation analysis methods can be split into those based on stellar disk integration methods and those using convolution techniques. The convolution method is identical to the disk integration method if line-broadening is constant over the whole stellar surface. For late type stars, Marcy & Chen (1992) have compared calculated line profiles using convolution techniques with those calculated by disk integration. They find that for M stars with projected rotational velocities as small as [FORMULA], the two methods lead to the same line profiles with a precision of 5 percent, therefore we make use of the simpler convolution methods.

[FIGURE] Fig. 7. High resolution spectrum of BX Mon (solid), a standard M5 III spectrum (dotted) and the M5 III spectrum convolved with the rotational broadening function corresponding to [FORMULA] (dashed).

We derive the rotational velocity of the M star by comparing its absorption lines with those of spectral standards which are believed to be single stars. We assume that the line broadening is only a function of spectral subtype. We can then use the non-rotating spectral standards as a template. We find, that the line widths in our M4 III and M5 III spectral standards are identical with a precision of [FORMULA].

As pressure broadening is much smaller than micro-turbulence, and macro-turbulence broadening in M-giants, we do not expect to introduce significant errors by employing non-rotating reference stars of different masses. The uncertainty in the spectral type of BX Mon is expected to introduce an error [FORMULA]. The line-broadening in BX Mon can then be written as:


where R stands for the rotational broadening function which depends only on [FORMULA] and limb-darkening which is approximated by a linear darkening, with limb darkening coefficient 0.6, Gray (1992). [FORMULA] stands for the line profile of the non-rotating M5 III-spectral standard and [FORMULA] for the measured line profile in BX Mon. After Fourier transformation this equation can be written as :


or, when solved for [FORMULA],


We determine the rotation velocity in two ways. First we convolve the non-rotating star with the rotational broadening function belonging to various [FORMULA]. According to Tsuji et al. (1994), measurable saturation effects are expected for absorption lines stronger than 0.80 relative to a continuum normalized to 1. We have therefore chosen an interval containing weak lines, which are expected to show little or no saturation effects. The rotation velocity, that leads to the best fit is [FORMULA] (see Fig. 7).

The second method, which is described in detail in Marcy & Chen (1992) and Gray (1992), fits the Fourier transform of the rotational broadening function to the ratio of the Fourier transforms of the spectra of BX Mon and the spectral standard. The spectrum employed for this procedure covers the range 7425-7475 Å. By choosing a large spectral interval, we reduce the effect of the imperfect normalization on the Fourier transform. The result of this procedure is shown in Fig. 8. At frequencies above [FORMULA] cycles/Å , the power spectrum of BX Mon is dominated by noise. We find [FORMULA]. This agrees well with the value found by the direct fitting of weak absorption lines and we retain [FORMULA].

[FIGURE] Fig. 8. Ratio of Fourier transform of BX Mon and of the M5 III spectral standard. Overlayed are Fourier transforms of the rotational broadening function belonging to the values [FORMULA].

With the photospheric radius [FORMULA] of the red star, inclination [FORMULA] and equatorial rotation velocity v, we calculate the rotation period of the M-star as


with the equatorial rotation velocity


In BX Mon we are facing a system that has an eccentric orbit, co-rotation is therefore not possible. Torques from tidal forces depend strongly on the binary separation (Zahn 1977). Thus in an eccentric orbit the torque will be strongest at periastron passage leading to a rotation period shorter than the orbital period P. This is in agreement with our values.

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© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998