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Astron. Astrophys. 330, 1029-1040 (1998)

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3. Stellar properties of IL Hydrae

3.1. The rotation period

We first applied a multiple period search program (Breger, 1990) to the combined APT photometry to pinpoint the rotation period of IL Hydrae (Fig. 1a and b). The fit with the smallest [FORMULA] was obtained with a period of 12.730 [FORMULA] 0.004 days with an amplitude of 0.06 mag in V ([FORMULA] in Fig. 1a) in very good agreement with the periods derived earlier by Cutispoto (1995). Fig. 1a also shows several aliases of comparable but smaller amplitude, most noticable at frequencies of [FORMULA], [FORMULA] and [FORMULA] a.s.o.. A frequency of [FORMULA] ([FORMULA] 25.5 days) produces an amplitude of only 0.01 mag, and a frequency of [FORMULA] ([FORMULA] 6.3 days) an amplitude of 0.015 mag, both with more than twice the [FORMULA] of the adopted frequency [FORMULA]. The primary reason for these aliases is the one-observation-per-night windowing of the APT observations.

3.2. Spectral classification

The computer program of Barden (1985) is used to spin-up and shift 6420-Å spectra of several M-K standard stars of spectral types in the range G8 to K2 and luminosity class III to IV in order to match the spectrum of IL Hya. The standard-star spectra are Fourier transformed and subtracted from a representative IL Hya spectrum and the respective difference spectra minimized by changing the relative continuum, the rotational broadening, and the radial velocity. We found that a spectral type of K0, a giant luminosity classification, and a preliminary rotational velocity of [FORMULA] km s-1 fit best. The fit resulting in the smallest sum of the squared residuals is shown in Fig. 2. The minimum radius from the measured rotation period and the rotational broadening results, if combined with the most likely inclination as determined in Sect.  3.4, in a luminosity class somewhat fainter than III, say III-IV, in agreement with the recently published Hipparcos parallax of [FORMULA] pc and [FORMULA] mag. Standard effective temperature calibrations for K0 giants list values between 4820 K (Bell & Gustafsson, 1989) and 4650 K (Dyck et al., 1996). We finally adopted the value of 4700 K from Randich et al. (1993) derived by fitting synthetic spectra to the lithium region of IL Hydrae.

[FIGURE] Fig. 2. A comparison of a representative spectrum of IL Hydrae (thick line) with a shifted and spun-up spectrum of the K0IIIb M-K standard star [FORMULA]  Geminorum (thin line). Identified are the lines that are being used in the Doppler-imaging analysis, with a slanted-face wavelength identifying the principal mapping line and the others the included blends. Although [FORMULA]  Gem reproduces the overall spectrum of IL Hydrae best, none of our M-K standard stars would fit the shallow lines, confirming the underabundance of metals already found by Randich et al. (1993).

Note that all lines of IL Hydrae, except maybe the CaI line at 6439 Å , are weaker than in the comparison star spectrum. As we will show later this is due to a metal abundance lower than solar.

3.3. Orbital elements

Improved orbital elements were computed with the differential correction program of Barker et al. (1967) as modified and updated by Fekel (1996), using the 21 radial velocities of the primary component and the 12 radial velocities of the secondary component in Table 1 together with the 34 primary velocities taken from Balona (1987) and the two secondary velocities from Donati et al. (1997).

First, a period search from the 55 velocities of the primary component suggested an orbital period of 12.9051 days, about 1.4% longer than the photometric (rotation) period, which we used as a starting value for the differential-correction program. We then weighted the velocities with the errors of the individual observations and iteratively seeked the orbital elements of the primary component with the smallest sum of the squared residuals. The errors of our data are listed in Table 1, Balona (1987) estimates 3 km s-1 for his data, and we estimate 2 km s-1 for the data of Donati et al. (1997). Since the resulting eccentricity was smaller than the inferred error, we adopted a zero-eccentricity solution. Keeping these orbital elements fixed, we used a least-square fitting algorithm to find the secondary component's radial velocity amplitude. Final elements are given in Table 2 and the computed velocity curves are plotted in Fig. 3 along with the observations.


Table 2. Improved orbital elements for IL Hydrae

[FIGURE] Fig. 3. Observed and computed radial velocity curves. Filled circles and triangles are our velocities from Table 1, crosses are from Balona (1987) and circles are from Donati et al. (1997). The primary (solid line) and the secondary orbits (dashed line) are calculated from the elements in Table 2. Note that a zero-eccentricity orbit was adopted.

3.4. Mass, radius, and limits to the inclination of the stellar rotation axis

Knowing the rotation period, the rotation velocity, and the luminosity class of IL Hya one could, in principle, derive the inclination of the stellar rotation axis from the relation [FORMULA]. However, the large range of radii of an evolved K star makes this method fairly unreliable, e.g., the Landolt-Börnstein tables (Schmidt-Kahler, 1982) list a radius of 15 R [FORMULA], Gray (1992) gives a radius of 11 R [FORMULA], and Dyck et al. (1996) derive 16 R [FORMULA]. Nevertheless we may calculate a definite minimum stellar radius from the relation above and obtain [FORMULA].

It is still possible to estimate upper and lower limits for the inclination angle though. Since we do not see eclipses we can estimate the upper limit because [FORMULA] + [FORMULA] must be less than [FORMULA]. If we adopt the G8V estimate from Cutispoto (1995; 1997) for the secondary star and assume [FORMULA] = 0.84 R [FORMULA] from the Landolt-Börnstein tables, we obtain i [FORMULA] 62o. Using the value of [FORMULA] = 1.1 R [FORMULA] estimated by Donati et al. (1997) does not change the upper limit significantly. The lower limit is given by the measured mass function [FORMULA] and estimated values for the mass of the secondary star. Adopting 0.8-1.5 M [FORMULA] for the secondary and using our newly derived mass ratio [FORMULA] from Table 2 we get a range for the lower limit for the inclination of [FORMULA]. Note that the secondary mass has to be greater than 1 M [FORMULA] to fit the upper limit of the inclination angle as derived above. Therefore, an average of 56o [FORMULA] 6o is our preliminary estimate for the inclination of the stellar rotation axis of IL Hya. However, we emphasize that the given range is not an error but that all values within this range are equally likely.

Donati et al. (1997) recently detected the lines from the secondary star in two mean Stokes I spectra of IL Hya and, by using an estimate for the secondary's radial velocity amplitude, they derive a mass ratio of secondary to primary of 0.63 [FORMULA] 0.02 in good agreement with our orbit. By matching the radii obtained from the orbital period together with the rotational velocity, as well as from a comparison of observed colors with evolutionary models, they find an inclination of the rotational axis of IL Hya of 59 [FORMULA] 4o and obtain first estimates for the secondary's mass, radius, and temperature.

Because the [FORMULA] -factor is omnipresent in the determination of the astrophysical properties of IL Hya we will derive an independent estimate for the inclination of the stellar rotation axis in Sect.  4.2using the results from our Doppler-imaging analysis.

With the well-constrained inclination of 55 [FORMULA] 5o (see Sect.  4.2), our new mass ratio indicates a secondary mass of 1.3 [FORMULA] 0.2 M [FORMULA], somewhat higher but in agreement with the mass estimated by Donati et al. (1997); while the mass and radius of the primary star are 2.2 M [FORMULA] and 8.1 R [FORMULA], respectively. Accuracies of the masses and radii are not better than 10% but would still rather agree with a spectral type of mid to late F main sequence or [FORMULA] G0V-IV for the secondary, instead of Cutispoto's (1995), (1997) G8V estimate from multicolor photometry. Given a mass ratio of 0.59, [FORMULA] from Table 2, and [FORMULA] o , the Roche-lobe radius for IL Hya is [FORMULA] 15 R [FORMULA] and the primary is thus filling only 16% of its Roche volume.


Table 3. Stellar parameters for IL Hydrae

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© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998