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Astron. Astrophys. 347, 225-234 (1999)

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3. Astrophysical parameters of HD 12545

All previous investigations of this star were hampered by the fact that no trigonometric parallax was available. Distance estimates had therefore an unacceptable large range of 77-340 pc, depending on the adopted spectral classification (see the discussion in Bopp et al. 1993). Here, we use the new Hipparcos parallax to redetermine the fundamental astrophysical parameters of HD 12545.

3.1. Distance, effective temperature, luminosity, gravity, and mass

The Hipparcos satellite (ESA 1997) measured a parallax of 5.08[FORMULA]1.1 milli-arcsec and finally fixed the distance of HD 12545 to 197[FORMULA] pc. With the brightest, i.e. presumably unspotted, V magnitude of 7:m 875 observed in early 1998 (Fig. 1a), the absolute visual magnitude of HD 12545 is [FORMULA]. However, as we will show later in Sect. 4.4, the brightest magnitude is affected by a large warm spot and is probably too bright for the true unspotted magnitude. The estimated difference is approximately 0:m 1 and, if taken into account, would change the absolute brightness only by 1/4-[FORMULA] because its error bars are dominated by the uncertainty of the parallax. In any case, the absolute brightness of about +1:m 2 confirms the class III giant luminosity classification from the optical spectrum (Strassmeier & Oláh 1992, Bopp et al. 1993). Interstellar absorption was taken into account with 0:m 1 per 100 pc. Such a value is in agreement with the observed B-V color from Hipparcos and that of a K0III star from the tables of, e.g. Gray (1992), which would suggest E(B-V)[FORMULA]0:m 09[FORMULA]0.03, or [FORMULA]0:m 3[FORMULA]0.1, in accordance with our adopted value of 0:m 2. We note that a B-V excess of 0:m 11 from our new BV photometry and the K0III classification would result in a slightly higher value of [FORMULA]0:m 35 instead of 0:m 2. However, even the bluest B-V color ever observed is likely affected by the heavy spottedness of HD 12545 and is not recommended to be used for spectral classification.

[FIGURE] Fig. 1. Photometry of HD 12545. a  The long-term V light curve from 1985 through 1999. Data prior to 1996.5 were taken from Strassmeier et al. (1997a) and literature cited therein, data after 1996.5 are from the present paper. Notice that the star was at its brightest level ever in January 1998 (JD 2,450,820). The x-axis is given as JD minus 2,400,000 days. Years minus 1900 are indicated as well. b  Seasonal 1997/98 V data (the lower panel shows the differential check minus comparison magnitudes). The time of our Doppler-imaging observations at KPNO is marked and coincided with the time of the star's highest brightness. c  The same data as in panel b but phased with our ephemeris in Eq. (1). Notice that the scatter in the light and color curves is mostly due to intrinsic changes from one rotation to the next and not due to instrumental scatter (however, U-B has about 10 times higher scatter than V). All color variations are in phase with the V-light curve, suggesting a common cause.

Our gravity estimate relies on the spectrum synthesis of the pressure sensitive wings of the strong Ca I 6439-Å line. There are several blends in the wings of this line, e.g. Eu II and Y I , whose strengths and chemical abundances are not known. Consequently, our [FORMULA] determination is uncertain but must be in the 2.5-3.0 range, in agreement with the canonical values for a K0 giant (e.g. Gray 1992).

The dereddened B-V color of 1:m 04 indicates [FORMULA] of 4750 K according to the tables of Gray (1992) and Flower (1996). With a bolometric correction of -0.437 (Flower 1996), the bolometric magnitude of HD 12545 is +0:m 765 and, with an absolute magnitude for the Sun of [FORMULA] (Schmidt-Kaler 1982), the luminosity must be approximately 35[FORMULA] [FORMULA]. The position of HD 12545 relative to the evolutionary tracks of Schaller et al. (1992) for solar metallicity suggests then a mass of 1.8[FORMULA] [FORMULA] (Fig. 2). The fact that a strong lithium line was detected in the spectrum of HD 12545 ([FORMULA](Li)[FORMULA]1.7; Strassmeier & Oláh 1992, Bopp et al. 1993) favors the picture that the star is on the red-giant branch and not yet in the helium-core burning phase.

[FIGURE] Fig. 2. The observed position of HD 12545 (dot) in the H-R diagram. Shown are post-main-sequence tracks for 2.0, 1.7, and 1.5 solar masses from Schaller et al. (1992) that suggest a mass for HD 12545 of around 1.8 [FORMULA].

3.2. Rotational velocity and stellar radius

Doppler imaging allows a more accurate determination of the projected rotational velocity, [FORMULA], than any other technique. This is because the line asymmetries due to the spots are explicitely modeled. A wrong [FORMULA] would produce a pronounced, artificial band encircling the star being either bright or dark depending whether the adopted [FORMULA] was too large or too small, respectively (see, e.g., Vogt et al. 1987). Avoiding such a feature yields our value for the projected rotational velocity of 20.8[FORMULA]0.5 km s-1. Together with the rotation period of 24.0 days it results in a minimum radius of [FORMULA] [FORMULA]. If [FORMULA]60[FORMULA]10o is the correct inclination, as indicated later in Fig. 4, the stellar radius is [FORMULA]11.4[FORMULA] [FORMULA]. The unprojected equatorial rotational velocity, [FORMULA], would then be 24.0 km s-1.

3.3. Radial velocities, orbital period, and space kinematics

Bopp et al. (1993) presented a first zero-eccentricity SB1 orbit and found a period of 23.9729[FORMULA]0.0022 days from 44 radial velocities taken between 1985 and 1992. We add our 14 velocities from Table 1 to refine the orbital elements. The adopted velocities for our cross-correlation stars were 3.2 km s-1 for [FORMULA] Gem (K0III), -14.5 km s-1 for [FORMULA] Ari (K2III), and +54.3 km s-1 for HR 8551 (K0III-IV) (Scarfe et al. 1990). No systematic velocity differences were evident, but two of the velocities from Bopp et al. (1993) were given zero weight. The radial velocity curve is plotted in Fig. 3 and the revised elements are: [FORMULA] days, [FORMULA] km s-1, [FORMULA] (adopted), [FORMULA] km s-1, [FORMULA] km, and [FORMULA]. The standard error of an observation of unit weight was 1.23 km s-1, slightly higher than the average internal error of a single observation (Column [FORMULA] in Table 1). We attribute this to the fact that the spots cause systematic line asymmetries and thus asymmetric cross-correlation functions. The radial velocities along with the observed minus computed velocities, O-C, are listed in Table 1.

[FIGURE] Fig. 3. Radial velocity curve and orbit. The open circles are from Bopp et al. (1993) and the full circles are from the present paper. Zero weight was given to the two deviant points at phase 0.40 and 0.15.

[FIGURE] Fig. 4. The dependence of the normalized goodness of fit ([FORMULA]) on the adopted stellar inclination angle as discussed in Sect. 4.3. The different line styles are for the different spectral regions.


Table 1. Spectroscopic observing log and radial velocities

Throughout this paper phase is always computed from a time of maximum positive radial velocity with the revised orbital period,


Together with the distance and proper motions from Hipparcos, the revised space velocities of HD 12545 relative to the Sun in a right-handed coordinate system are (U,V,W)=(+55[FORMULA], +9[FORMULA], [FORMULA]) km s-1. The space velocity vector, [FORMULA], is then 58 km s-1, typical for old disk and halo stars according to the criteria of Eggen (1969). The nominal age from the tracks of Schaller et al. (1992) is 1.8[FORMULA] yr.

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999