3 Stellar properties of KUPeg

Figure 2: A comparison of a spectrum of KUPeg (thick line) with a shifted and spun-up spectrum of the G9II-III standard star HD76294 (thin line). Identified are the spectral lines that are used in the Doppler-imaging analysis in Sect. 4 (a bold-face wavelength distinguishes the main mapping line from the blends included).

3.1 The rotation period

We applied the multiple period search program PERIOD98 (Sperl 1998) in single-period mode and use its Fourier option to determine the photometric period of KUPeg (Fig. 1d). The application of this program to photometry of spotted stars was recently discussed in Strassmeier et al. (1999a) and we refer the reader to this paper. The fit with the smallest $\chi ^2$ was obtained with a period of $24\hbox{$.\!\!^{\rm d}$ }6\pm0.5$ for the 1996/97 data, $25\hbox{$.\!\!^{\rm d}$ }0\pm1.1$ in 1997/98, and $23\hbox{$.\!\!^{\rm d}$ }9\pm0.8$ for the 1998/99 data (Figs. 1a-c).

By early 1997/98 the amplitude of the V-lightcurve had dropped from 0 $.\!\!^{\rm m}$07 in late 1996 to $\approx$0 $.\!\!^{\rm m}$03 in late 1997, and had risen again to 0 $.\!\!^{\rm m}$06 in 1998. The Fourier analysis of the 1997/98 V data still shows a peak near the same frequency as in 1996/97 but an alias at f=0.1 c/d appears with an even stronger amplitude than the true photometric period. Such a reduced rotational-modulation signal suggests that the active regions that were visible in 1996/97 had significantly decreased in size and/or contrast by late 1997. The lightcurves of the two seasons (Figs. 1a and b) consistently show a minimum at around phase 0.5 but the phased 1997/98-season data appear as a double-humped light curve.

The final period is obtained from the combined data set and is of higher precision due to the longer time range. We obtain $24\hbox{$.\!\!^{\rm d}$ }96\,\pm\,0.04$, which we interpret to be the stellar rotation period and use it to calculate the phases for all spectroscopic and photometric data in this paper:

$${\rm HJD} = 2\,450\,385.5 + 24.96\pm0.04 \times E .$$ (1)

The strongest peak in Fig. 1d (0.002 day^-1) is an alias resulting from the time gap between the three observing seasons. The other peak of comparable size (27.33 days) is basically due to the same reason.

3.2 Effective temperature and spectral classification

The effective temperature of KUPeg is estimated in several ways, first from a comparison of the observed $V-I_{\rm C}$ color with synthetic colors from the ATLAS-9 model atmospheres (Kurucz 1993). The bluest $(V-I)_{\rm C}$ value of $1\hbox{$.\!\!^{\rm m}$ }17\pm0\hbox{$.\!\!^{\rm m}$ }01$is observed at times of lightcurve maximum (Fig. 1) and is adopted to best represent the "unspotted'' intrinsic color of the photosphere. This value is different to the long-term average due to the color variations from spots of up 0 $.\!\!^{\rm m}$03. Comparing this V-I value with the grid of synthetic ATLAS-9 colors in the range $\log g=2.0$ to 3.0 and metal abundances of solar to 1.0 dex below solar, we find a temperature of $4700\pm150$K. This compares very well with the 4700K from the observed B-V of 1 $.\!\!^{\rm m}$13 and the calibration for a bright giant from Bell & Gustafsson (1989). Similar temperatures are obtained from the color-temperature calibration of Flower (1996) (4622K), as well as from the combined G9II, G9II-III and G9III temperatures listed in Dyck et al. (1998) ( $4686\pm192$ K), for a G9III star in van Belle et al. (1999) (4679 K), and for a K0 giant in Bell & Gustafsson (1989) (4820 K).

Another method for estimating the effective temperature is to use the temperature dependence of spectral lines. Using the calibration for giant stars from spectral line-depth ratios from Strassmeier & Schordan (2000), we calculated the V-I colors and the effective temperatures for 11 line-ratios. The resulting average effective temperature was $4835\pm62$K, in good agreement with the values derived with other methods. The average V-I-color of $1\hbox{$.\!\!^{\rm m}$ }06\,\pm\,0\hbox{$.\!\!^{\rm m}$ }05$ is 0 $.\!\!^{\rm m}$11 smaller than the observed value, which shows that the large interstellar absorption correction we apply in the next section is indeed of the right order of magnitude.

In order to compare the spectrum of KUPeg numerically with spectra of Morgan-Keenan standard stars, we make use of a computer program originally designed by Barden (1985). The standard-star spectra are Fourier transformed and subtracted from a representative KUPeg spectrum. The resulting difference spectra are iteratively minimized by changing the relative continuum intensity, the rotational broadening, and the radial velocity of the KU-Peg spectrum by means of a weighted $\chi ^2$ minimization. With this procedure, we found the best fit with a spectral type of G9 to K0III and a (preliminary) rotational velocity of $v\sin i = 28\pm2$ kms^-1. We note that both standards, $\beta$Gem (K0III) and HD76294 (G9II-III), fitted our KUPeg spectra equally well (the latter fit is shown in Fig. 2).

To obtain an independent estimate for the luminosity class of KUPeg, we use the luminosity-sensitive Sr II 4077-Å  line and compare KUPeg with $\alpha$Ari (K2III), $\beta$Gem (K0III), $\iota$Cnc (G8II), and 55Cam (G8II). Again, the program of Barden (1985) was used to minimize the residual spectra. Because the Sr II 4077 line of KUPeg is weaker than in the two available G8II spectra, but only slightly stronger than in the $\beta$Gem spectrum, we estimate KUPeg to have a luminosity class of II-III and therefore a most likely spectral classification of G9-K0 II-III.

  
3.3 Radius, luminosity, and mass

The rotational period and the projected rotational velocity determine the minimum stellar radius to be $R\sin i=13.8\pm0.5~R_\odot$. Using an inclination angle of $50\pm 10\hbox{$^\circ$ }$ - that will be derived later in Sect. 4.2 - the most likely stellar radius of KU Peg is 18 $^{+4}_{-3}~R_\odot$. This is not in agreement with the $13.9\pm0.3~R_\odot$ for an average K0III star according to van Belle et al. (1999), and just barely in agreement with the $15~R_\odot$according to the Landolt-Börnstein tables (Schmidt-Kaler 1982) but more likely indicates that the star is larger than a regular K0 giant. Using above radius and an effective temperature of $4700\pm150$K, the bolometric magnitude of KU Peg is $M_{\rm bol}=-0\hbox{$.\!\!^{\rm m}$ }74^{+0.55}_{-0.57}$.

The Hipparcos parallax of $5.33\pm0.91$ milli- $^{\prime\prime}$ (ESA 1997) puts KUPeg in a distance of 188 ⁺³⁸_-28 pc and, with the brightest V magnitude observed so far, i.e. $V=7\hbox{$.\!\!^{\rm m}$ }61$ in 1997 (see Fig. 1c), results in an absolute visual brightness of 0 $.\!\!^{\rm m}$82 ^-0.40_+0.35. An interstellar extinction correction of $A_V=0\hbox{$.\!\!^{\rm m}$ }42$ had been applied, which results from $A_V=3.2\,E(B-V)$, where E(B-V) is 0 $.\!\!^{\rm m}$13 using $B-V=1\hbox{$.\!\!^{\rm m}$ }13\pm0.02$ (Guetter 1980; Fernie 1983) and $(B-V)_0=1\hbox{$.\!\!^{\rm m}$ }0$ (Schmidt-Kaler 1982). This agrees with the $A_V=0\hbox{$.\!\!^{\rm m}$ }52$ listed in Guarinos (1992). With a bolometric correction of -0.48 (Flower 1996) the bolometric magnitude is $M_{\rm bol}=+0\hbox{$.\!\!^{\rm m}$ }34^{-0.39}_{+0.34}$, which is different by one magnitude to the above value from the combination of the minimum stellar radius, the inclination from the Doppler-imaging analysis, and the effective temperature from the spectral classification. Adopting an average bolometric magnitude and a solar value of +4 $.\!\!^{\rm m}$64, the luminosity of KUPeg is $97\pm45~L_\odot$.

A comparison of the position of KUPeg in the H-R diagram with the evolutionary tracks of Schaller et al. (1992) interpolated for 0.6 dex below solar metallicity (see Sect. 4.3), suggests a mass of $2.3\pm0.3~M_\odot$ and an age of approximately 870 Myrs.

  
3.4 Orbital period

De Medeiros et al. (1992) reported the detection of radial velocity variations with a full amplitude of 6 kms^-1 and calculated a preliminary orbit with the following elements: $P=1411\pm26$ days, $T=2\,447\,951\pm27$, $e=0.39\pm0.14$, $\gamma=-80.4\pm0.2$ kms^-1, $K_1=2.5\pm0.5$ kms^-1, and $\omega=198\pm 9\hbox{$^\circ$ }$.

The average from our radial velocity measurements from HJD 2450392-457 is -80.3 kms^-1, and agrees very well with the $\gamma$-velocity determined by De Medeiros et al. (1992). Its root mean square is 1.8 kms^-1 and the average error of our individual velocities is also 1.8 kms^-1. This values fit the published orbit when a period of 1389 days is used (which is inside the error bounds given by De Medeiros et al. 1992). The phase coverage of our spectra, however, does not allow an independent period determination but verifies the preliminary orbit.

 

 

Table 2: Stellar parameters for KUPeg.

Parameter	Value
Spectral type	G9-K0II-III
$\log g$	$2.5\pm0.5$
$T_{\rm eff}$	$4700\pm150$K
$V_{\rm max}$	7 $.\!\!^{\rm m}$61
B-V	$1\hbox{$.\!\!^{\rm m}$ }13\pm0\hbox{$.\!\!^{\rm m}$ }02$
$(V-I_{\rm C})_{\rm max}$	$1\hbox{$.\!\!^{\rm m}$ }17\pm0\hbox{$.\!\!^{\rm m}$ }01$
$v\sin i$	$28.2\pm0.7$ kms-1
Rotation period $P_{\rm phtm}$	$24.96\pm0.04$ days
Inclination i	$50\hbox{$^\circ$ }\pm$10$^\circ$
Radius R	18 $^{+4}_{-3}~R_\odot$
Equatorial velocity $v_{\rm equ}$	36.8 kms-1
Luminosity L	$97\pm45~L_\odot$
Mass M	$2.3\pm0.3~M_\odot$
Age	$\approx$870 Myrs
Microturbulence $\xi$	2.0 kms-1
Macroturbulence $\zeta_{\rm R} = \zeta_{\rm T}$	4.0 kms-1
$\log \rm [Ca]$ abundance	1.0dex below solar
$\log \rm [Fe]$ abundance	0.6dex below solar
Distance	188 +38-28 pc

  
3.5 H$\alpha$ line profiles

Figure 3: Residual H$\alpha$ profiles of KUPeg (lower panel) after subtraction of a broadened ( $v\sin i=28$ kms-1) spectrum of the inactive reference star 16Vir. The upper panel plots an unaltered H$\alpha$ spectrum of KUPeg. The two spectra labeled a and b were taken three days apart.

Our KPNO spectra from April 1998 included the wavelength region around the H$\alpha$ line, which is widely used as an activity and velocity indicator for stellar chromospheres (see e.g. Bopp et al. 1988). Our spectra show a broad and asymmetric absorption line with a weak blue-shifted emission component (Fig. 3). To extract the H$\alpha$ contribution from the active part of the chromosphere, we subtract the broadened spectrum of the inactive reference star 16Vir (K0.5III). To first order, this removes the photospheric and chromospheric flux that is unrelated to the magnetic activity. This subtraction reveals a double-peaked emission profile with unequally strong emission peaks which is typical for very active RS CVn binaries. We assume that the doubled peak results from one emission peak combined with an off-centered absorption line. Using the Gaussian deblending routine in the IRAF splot package, we find that the strong emission peak is centered at the H$\alpha$ rest wavelength, while the absorption feature appears blueshifted by $-40\pm5$ kms^-1 in spectrum a (JD 2450918) in Fig. 3 and $-30\pm5$ kms^-1 in spectrum b (JD 2450921). The full width at half maximum (FWHM) of the Gaussian for the absorption component of these fits is $1.08\pm0.05$ Å, which transforms to $v\sin i=28.6\pm1.5$ kms^-1 using the relation described in Strassmeier et al. (1990), and thus seems to originate from near the stellar surface. Although we can not draw more firm conclusions from these two H$\alpha$ spectra, we do note that the line-profile structure and its asymmetry suggest a complex flow structure in the lower chromosphere and possibly also in the outermost coronal layers, say, one stellar radius above, where hydrogen can be trapped in coronal loops.