## 3. Stellar properties of IL Hydrae## 3.1. The rotation periodWe 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
was obtained with a period of 12.730
0.004 days with an amplitude of 0.06 mag in
## 3.2. Spectral classificationThe 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
km s
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 elementsImproved 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
## 3.4. Mass, radius, and limits to the inclination of the stellar rotation axisKnowing 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 . 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 , Gray (1992) gives a radius of 11 R , and Dyck et al. (1996) derive 16 R . Nevertheless we may calculate a definite minimum stellar radius from the relation above and obtain . 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 +
must be less than . If we
adopt the G8V estimate from Cutispoto (1995; 1997) for the secondary
star and assume = 0.84 R
from the Landolt-Börnstein tables, we obtain Donati et al. (1997) recently detected the lines from the
secondary star in two mean Stokes Because the -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
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© European Southern Observatory (ESO) 1998 Online publication: January 27, 1998 |