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Astron. Astrophys. 347, 932-936 (1999)

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4. Stellar parameters

4.1. Teff, log g , and metallicity

For determining atmospheric parameters of the primary, the 53 SOFIN spectra were averaged, and the resulting spectrum with S/N[FORMULA]1000 covering almost all the region from 5500 Å to 8500 Å was used in the analysis. The spot contribution to the averaged spectrum was found to be insignificant. The effective temperature [FORMULA], surface gravity log g , metallicity [M/H], and microturbulence [FORMULA] are determined as a self-consistent set of parameters using the synthetic spectra calculations.

A list of atomic line parameters for a given wavelength region was obtained from VALD (Piskunov et al. 1995). It was checked by comparison of the calculated spectrum with the observed one of a slow rotating normal giant [FORMULA] Gem (K0 IIIb), as was done in our recent analysis of the other active star II Peg (Berdyugina et al. 1998). A great number of molecular lines have been added to the list, since their presence in spectra of cool giants is quite noticeable. Stellar model atmospheres used are from Kurucz (1993). A code used for the synthetic spectrum calculations is described in detail by Berdyugina (1991).

Estimates of the projected rotational velocity obtained by different authors are somewhat scattered: 24 km s-1 (Ottmann et al. 1998), 25[FORMULA]1 km s-1 (Donati et al. 1997), 25.6[FORMULA]1 km s-1 (De Medeiros & Mayor 1995), 28.2[FORMULA]1 km s-1 (Fekel 1997). Possessing the excellent quality observed spectrum, we have obtained our own estimates of the rotational velocity, v sini , and macroturbulence, [FORMULA]. A number of strong and well isolated lines were studied with the Fourier transform. The following values were determined: v sini =26.5[FORMULA]0.5 km s-1 and [FORMULA]=4.0[FORMULA]0.5 km s-1.

To determine the atmospheric parameters, a total of about 20 lines of Fe I , Fe II , Si I , Si II , and Ca I were chosen. Assuming first an appropriate pair of [FORMULA] and log g , we produced a set of curves (loci of the best fitted lines) on a diagram of metal abundance, [M/H], as a function of microturbulence [FORMULA] (Fig. 2). The curves intersected in a narrow region which provided an initial estimate for a pair of [M/H] and [FORMULA]. With these values, a set of loci on a diagram of [FORMULA] versus log g was calculated. Their intersection gave an initial estimate of a pair of [FORMULA] and log g values. After a few iterations a self-consistent set of the parameters was found. These are presented in Table 3.

[FIGURE] Fig. 2. Diagrams for the self-consistent determination of the atmospheric parameters of the primary of IM Peg: metallicity [M/H], microturbulence [FORMULA] (upper panel ) and effective temperature [FORMULA], surface gravity log g (low panel ). Curves present loci of the best fitted spectral lines with the synthetic spectrum: Fe I , Si I and Ca I (solid curves) and Fe II and Si II (dashed curves). The curves intersect in narrow regions which provide estimates of the parameters. These are presented in Table 3.


Table 3. Atmospheric parameters of the primary of IM Peg

With the atmospheric parameters obtained, the primary of IM Peg is classified as K2 III, in reasonable agreement with the previous classification. It has solar metallicity with an uncertainty of [FORMULA]0.1 (assuming for the Sun Fe/H=7.55, Si/H=7.50, Ca/H=6.32). The spectrum of the star was recently analysed by Ottmann et al. (1998). As a temperature indicator they used the H[FORMULA] line which is significantly disturbed by the variable emission, as seen in our spectra. This resulted in remarkable overestimation of the effective temperature and, as a consequence, the surface gravity.

4.2. The CNO abundances

The abundances of the CNO-elements are good indicators of the stellar evolution. In the spectrum of IM Peg many appropriate features can be found for determining the carbon and nitrogen abundances: rotational transitions in vibrational bands of the CN ([FORMULA]) red system and C2 ([FORMULA]) Swan system. For the oxygen abundance, no good features can be found: high-excitation lines of O I are obviously disturbed by the active chromosphere, and the line of [O I ] at 6363 Å is blended too much. Therefore, it is reasonable to assume that the oxygen abundance in IM Peg is of the solar value (O/H=8.92, Lambert 1978) and we can then determine the abundances of C and N.

For the synthetic spectra calculations we used the line lists provided by Davis & Phillips (1963) and Phillips & Davis (1968). The band oscillator strengths and molecular constants were obtained from the RADEN database (Kuznetsova et al. 1993). Lower level excitation energies and rotational intensity factors were calculated with formulae from the book by Kovacs (1969). The number densities of CN and C2 were calculated under the assumption of their dissociative equilibrium with a great number of atoms and molecules. The procedure used for determining the CNO abundances is similar to that described by Berdyugina (1993).

The carbon abundance, [C/H]=-0.32, was determined from the head of the C2 (0,1) band at 5633 Å. The feature is blended partly by atomic lines, but the accuracy of about 0.1 for the abundance can be easily achieved. The nitrogen abundance, [N/H]=0.30, was determined from the heads of the CN (2,0) and (3,1) bands and numerous features from those bands in the regions 7895-7900 Å and 8039-8065 Å. The internal accuracy of the nitrogen abundance is about 0.05. The resulting C/N ratio of 1.15 corresponds well to an evolved giant which has undergone the first convective mixing in its atmosphere on the Red Giant Branch.

4.3. Fundamental parameters of the components

The value of the unspotted V magnitude of the star is important for estimating the fundamental parameters of the binary components. It can be determined from the variability of the TiO bands. The effective temperature of the primary is too high to show evidence of the TiO bands in the spectrum from the unspotted photosphere. Nevertheless, a noticeable depression due to TiO lines is seen at [FORMULA]7054 Å, at the head of the strong band [FORMULA](0,0)R3, that is typical for spotted G-K stars. The depth of the band correlates well with the V magnitude, in other words, with the spot visibility (Fig. 3). The quasi-simultaneous photometric observations used will be presented in our forthcoming paper. We suggest that the zero value of the central depth corresponds to the unspotted magnitude of the star, V0. Then, from the linear regression fitted to the data we estimate V0=5[FORMULA]55[FORMULA]0[FORMULA]05. It is close to the brightest maximum of V=5[FORMULA]6 ever observed (Strassmeier et al. 1997). The value of V0 should be corrected for the interstellar extinction, but the latter is expected to be of the same order as the uncertainty of V0. Thus, with the parallax value of 0[FORMULA]01033 from the Hipparcos Catalogue, an absolute magnitude [FORMULA]=0[FORMULA]62 can be found. It is very close to the statistical value of 0[FORMULA]5 for K2 III stars (Lang 1992). This is in good agreement with the newly determined atmospheric parameters of the primary.

[FIGURE] Fig. 3. The variation of the central depth of the TiO [FORMULA](0,0)R3 band at 7054 Å with the V magnitude (dots with error bars). The line represents a linear regression fitted to the data and indicates the unspotted V magnitude of IM Peg when the depth of the TiO band is equal to zero.

The projected rotational velocity of 26.5 km s-1 and the photometric period of the star of 24[FORMULA]39 (Strassmeier et al. 1993) result in the relation [FORMULA]. This corresponds to the radius of a giant with a spectral class of K0-K2 III. From the mass function [FORMULA](m) a mass-mass diagram for various combinations of masses and orbital inclination can be calculated (Fig. 4). Under the assumption that the stellar rotational axis is perpendicular to the orbital plane, one can estimate the masses of the binary components, the primary's radius and the inclination. Such an assumption is justified for synchronously rotating RS CVn binaries (Glebocki & Stawikowski 1995). The low limit of R1 and the value of log g =2.4[FORMULA]0.1 determine the probable range for the masses of the binary components. This range can be restricted from above by the upper limit of the secondary's mass. Since with present observing techniques the secondary is invisible at all wavelengths, its luminosity should be at least 100 times less than that of the primary, i.e. [FORMULA] [FORMULA] [FORMULA]. This corresponds to a G8 main sequence star with a mass of 0.9 [FORMULA] (Lang 1992). Then, in the mass-mass diagram the probable range for all parameters is significantly reduced. With log g =2.4[FORMULA]0.1 one can find the following values: [FORMULA]=1.5[FORMULA]0.2, [FORMULA]=13.3[FORMULA]0.6, 65o[FORMULA]80o, [FORMULA]=0.8[FORMULA]0.1. Note that the secondary's mass cannot be less than 0.7 [FORMULA] because of the low limit of log g . Therefore, it could be e.g. a K0 dwarf.

[FIGURE] Fig. 4. The mass-mass diagram for IM Peg (in solar units). The thin solid curves are calculated for the fixed values of the radius of the primary and the inclination (numbers in the left). The dashed lines are loci of the primary with a fixed value of log g (numbers at the bottom). The probable parameters of the binary components are in the area restricted by the heavy solid lines with R1 [FORMULA] 12.7 [FORMULA] and [FORMULA] and next to log g =2.4

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Online publication: June 6, 1999