doppler imaging of stellar surface structureaa.springer.de/papers/8330003/2301029.pdf1030 m. weber &...

Astron. Astrophys. 330, 1029–1040 (1998) ASTRONOMYAND

ASTROPHYSICS

Doppler imaging of stellar surface structure

V. The long-period RS CVn binary HD 81410 = IL Hydrae

M. Weber and K.G. Strassmeier?

Institut für Astronomie, Universität Wien, Türkenschanzstraße 17, A-1180 Wien, Austria([email protected], [email protected])

Received 26 August 1997 / Accepted 16 October 1997

Abstract. Multiwavelength Doppler images of the long-periodRS CVn binary IL Hydrae from March 1994 and Feb.-March1995 reveal a cool polar spot and several features at low lat-itudes. Their average temperature is approximately 500 K be-low the photospheric temperature of 4700 K. Due to the rela-tively small rotational velocity of 26.5±1 km s−1 and the rel-atively cool, low-gravity atmosphere with many weak absorp-tion blends, Doppler imaging of IL Hydrae is challenging butresulted in encouragingly similar maps from altogether sevenspectral regions near 6400 Å.

Latitude-dependent differential rotation is detected from ourDoppler maps and indicate faster rotation at the stellar equatoras compared to the polar regions.

Lines from the secondary component are sometimes seenin our red-wavelength spectra and a double-lined spectroscopicorbit is presented. We also give a more precise rotational periodfrom three consecutive years of V -band photometry. A spectralclassification of K0III-IV and a mass of 2.2±0.2 M� for theprimary, and mid to late F main sequence or maybe ≈G0V-IVand a mass of 1.3±0.2 M� for the secondary, are suggested.

Hα equivalent widths measured over a single rotation cy-cle exhibit a sinusoidal variation in phase with the photosphericV -band light curve. The maximum of the residual Hα emissioncoincides with the lightcurve minimum and is thus likely linkedto the starspot-covered stellar surface. A steady, redshifted ab-sorption component possibly indicates an isotropic inward flowat the Hα line-forming region at approximately 60 km s−1.

Key words: stars: activity of – stars: imaging – stars: individual:IL Hya – stars: late-type – binaries: spectroscopic

Send offprint requests to: K.G. Strassmeier? Visiting Astronomer, Kitt Peak National Observatory, operated bythe Association of Universities for Research in Astronomy, Inc. undercontract with the National Science Foundation

1. Introduction

IL Hydrae = HD 81410 (α = 9h24m49s, δ = −23◦49′33”,2000.0, V = 7.25-7.9 mag) is an evolved double-lined spectro-scopic binary with very strong Caii H & K emission. This andthe fact that the photometric period is very close to the orbitalperiod of 12.9 days (Raveendran et al. 1982) makes IL Hydraea typical RS CVn star (Fekel et al. 1986). It was also found to bea radio source (Slee et al. 1984; Mutel & Lestrade 1985), a X-ray source (Dempsey et al. 1993) and an emitter of microwaveradiation (Mitrou et al. 1996). Randich et al. (1993) performeda spectrum synthesis in the 6700-Å region and found an ironabundance of 0.5 dex below solar and a moderate Lithium abun-dance of logn(Li) = 1.35. The secondary star can not be seenin near-ultraviolet spectra (La Dous & Giménez 1994) but fromthe difference of the measured UBV (RI)C colors of IL Hya tostandard values Cutispoto (1995) estimated the secondary to bea G8V star. Just recently, the secondary component was detectedby Donati et al. (1997) in two spectra at optical wavelengths.

The large amplitude of the light and color curves ofIL Hydrae – discovered by Eggen (1973) – already suggestedthat a large fraction of the stellar photosphere must be coveredwith spots. Simply looking at the observed line profiles onecan already identify the changing profile asymmetries due topseudo-emission “bumps” from cool spots. Even though the ro-tational velocity and thus the rotational broadening of the lineprofiles is small, the strength of these bumps is comparable tothose observed in more rapidly rotating RS CVn stars.

In this paper we present a series of twelve moderately high-resolution spectra in the 6420-Å region taken in 1994 and ninein the Hα region taken in 1995. Each data set was obtainedwithin a single stellar rotation. V (RI)C photometry was gath-ered from fall 1992 until spring 1995. The combination of thesespectroscopic and photometric data is used to study the spa-tial distribution of the photospheric activity on IL Hydrae in1994 and 1995. The instrumentation and the data reductionsare described in Sect. 2, the stellar properties relevant for theDoppler-imaging analysis are determined in Sect. 3. Doppler

1030 M. Weber & K.G. Strassmeier: Doppler imaging of stellar surface structure. V

Fig. 1a–c. Left: Periodogram from the entire 1992–1995 V -band APT data (panel a) and the window function showing strong aliasing towardsmultiples of one day (panel b). The largest reduction of the residuals is achieved with a period near the orbital period at 12.730±0.004 days(frequency f1 = 0.0785). The other indicated frequencies are just aliases of the true f1 frequency. Right: Light and color curves for the threeseasons from 1992 to 1995 phased with the elements in Table 2 (panel c). Notice that most of the scatter in the data is due to intrinsic variationsof the starspot distribution and not observational scatter.

maps from several spectral regions are derived in Sect. 4, andthe Hα spectra collected in 1995 are presented in Sect. 5. Adescription of the long-term goals of our Doppler-imaging pro-gram has already been presented in the previous papers of thisseries, i.e. paper I on the RS CVn binary UZ Librae (Strassmeier1996), paper II on the weak-lined T Tauri star V410 Tau (Rice& Strassmeier 1996), paper III on the RS CVn binary IN Vir(Strassmeier 1997) and paper IV on the rapidly-rotating G5III-IV star IN Comae (Strassmeier et al. 1997c).

2. Observations

All spectroscopic observations were obtained at Kitt Peak Na-tional Observatory (KPNO) with the coudé feed telescope dur-ing March 1994 and February–March 1995. The 6420-Å datain this paper are from March 1994 while the Hα spectra arefrom February–March 1995. Both data sets were obtained witha 800×800 TI CCD (TI-5 chip, 15µ pixels) with grating A,camera 5, and the long collimator enabling a resolving powerof 38,000 and a useful wavelength range of 80 Å. Table 1 is asummary of the spectroscopic observations.

All data were reduced in the same standard fashion usingIRAF and included bias subtraction, flat fielding, cosmic-ray re-moval and optimal aperture extraction. Th-Ar comparison spec-tra and spectra of bright radial-velocity standards were obtainedseveral times throughout the night to ensure an accurate wave-length calibration. Radial velocities were derived from crosscorrelating the IL Hya spectra with spectra of the IAU veloc-ity standards 16 Vir (K0.5III, vr = 35.7 km s−1) and HR 3145(K2III, vr = 70.9 km s−1) and are listed in Table 1 along withthe corresponding standard errors. The exposure level for bothwavelength regions corresponds to a signal-to-noise ratio of ap-

Table 1. Spectroscopic log and radial velocity data (vr). ”P” and ”S”indicate the primary and secondary component, respectively.

HJD phase phase vPr σPobs v

Sr σ

Sobs λ

(244+) (orb) (phot) (km s−1) (km s−1) (Å )9415.725 0.946 0.496 31.1 1.6 -75 12 64209416.702 0.022 0.573 34.7 1.8 -79 7 64209417.700 0.099 0.651 25.9 1.5 -62 14 64209418.695 0.176 0.730 9.2 0.9 -41 11 64209420.829 0.342 0.897 -33.0 0.7 29 12 64209421.719 0.411 0.967 -45.4 1.0 51 13 64209422.717 0.488 0.045 -51.5 0.7 . . . . . . 64209423.757 0.569 0.127 -47.8 0.6 . . . . . . 64209424.720 0.643 0.203 -35.0 0.9 35 16 64209425.741 0.722 0.283 -15.0 0.8 . . . . . . 64209426.785 0.803 0.365 4.7 0.9 . . . . . . 64209427.680 0.873 0.435 20.5 1.1 -57 13 64209770.827 0.463 0.391 -45.7 4.1 58 11 Hα9772.835 0.618 0.548 -34.8 4.2 . . . . . . Hα9773.753 0.689 0.620 -19.8 4.1 . . . . . . Hα9775.769 0.846 0.779 17.9 3.4 . . . . . . Hα9776.790 0.925 0.858 29.2 3.6 -70 13 Hα9778.801 0.081 0.017 29.8 3.0 -69 17 Hα9779.817 0.159 0.097 17.0 2.6 . . . . . . Hα9781.748 0.309 0.248 -19.1 3.5 . . . . . . Hα9783.747 0.464 0.405 -46.6 3.4 60 12 Hα

proximately 200:1. Usually twenty flat-field exposures with aTungsten reference lamp were taken at the beginning of thenight and again at the end of the night. These fourty flat fieldswere co-added and used to remove the pixel-to-pixel variationsin the stellar spectra. The TI CCD does not show obvious signs

M. Weber & K.G. Strassmeier: Doppler imaging of stellar surface structure. V 1031

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 starβ Geminorum (thin line). Identified are the lines that are being used in the Doppler-imaging analysis, with a slanted-face wavelength identifyingthe principal mapping line and the others the included blends. Although β Gem reproduces the overall spectrum of IL Hydrae best, none of ourM–K standard stars would fit the shallow lines, confirming the underabundance of metals already found by Randich et al. (1993).

of fringing near 6420 Å or Hα and no attempts were made tocorrect for it other than the standard flat-field division.

The new photometric data were obtained with the Fair-born Observatory T7 0.75-m automatic photoelectric telescope(APT), then still on Mt. Hopkins, Arizona and now part of theUniversity of Vienna twin APTs at the new Fairborn Obser-vatory at Washington Camp in Southern Arizona (Strassmeieret al. 1997b). The 211 observations were made differentiallywith respect to HD 81904 as the comparison star (V = 8.02mag, V −RC = 0.51 mag, V − IC = 0.98 mag) and HD 80991as the check star. All photometry has been transformed to matchthe Johnson-Cousins V (RI)C system. Observations started onJD 2,449,022 on the basis of one observation per night and cover51 nights in 1992/93, 101 nights in 1993/94 and 59 nights in1994/95. This data and additional photometry for IL Hydrae,plus data for other stars, was presented in Strassmeier et al.(1997a).

Fig. 1 shows the V -light curve and the V −RC and V − ICcolor curves of IL Hydrae in 1992/93, 1993/94 and 1994/95 aswell as the periodogram from the combined 1992–1995 V -banddata.

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 periodof IL Hydrae (Fig. 1a and b). The fit with the smallest χ2 wasobtained with a period of 12.730±0.004 days with an ampli-tude of 0.06 mag in V (f1 = 0.0785 in Fig. 1a) in very good

agreement with the periods derived earlier by Cutispoto (1995).Fig. 1a also shows several aliases of comparable but smalleramplitude, most noticable at frequencies of 1 − f1, 1 + f1 and2 − f1 a.s.o.. A frequency of f1/2 (≈ 25.5 days) produces anamplitude of only 0.01 mag, and a frequency of 2 × f1 (≈ 6.3days) an amplitude of 0.015 mag, both with more than twice theχ2 of the adopted frequency f1. The primary reason for thesealiases is the one-observation-per-night windowing of the APTobservations.

3.2. Spectral classification

The computer program of Barden (1985) is used to spin-up andshift 6420-Å spectra of several M–K standard stars of spec-tral types in the range G8 to K2 and luminosity class III to IVin order to match the spectrum of IL Hya. The standard-starspectra are Fourier transformed and subtracted from a repre-sentative IL Hya spectrum and the respective difference spectraminimized by changing the relative continuum, the rotationalbroadening, and the radial velocity. We found that a spectraltype of K0, a giant luminosity classification, and a preliminaryrotational velocity of v sin i = 26 ± 2 km s−1 fit best. The fitresulting in the smallest sum of the squared residuals is shownin Fig. 2. The minimum radius from the measured rotation pe-riod and the rotational broadening results, if combined with themost likely inclination as determined in Sect. 3.4, in a luminos-ity class somewhat fainter than III, say III-IV, in agreement withthe recently published Hipparcos parallax of d = 120 pc andMV = 1.95 mag. Standard effective temperature calibrationsfor K0 giants list values between 4820 K (Bell & Gustafsson1989) and 4650 K (Dyck et al. 1996). We finally adopted the


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

value of 4700 K from Randich et al. (1993) derived by fittingsynthetic spectra to the lithium region of IL Hydrae.

Note that all lines of IL Hydrae, except maybe the Cai lineat 6439 Å, are weaker than in the comparison star spectrum. Aswe will show later this is due to a metal abundance lower thansolar.

3.3. Orbital elements

Improved orbital elements were computed with the differen-tial correction program of Barker et al. (1967) as modified andupdated by Fekel (1996), using the 21 radial velocities of theprimary component and the 12 radial velocities of the secondarycomponent in Table 1 together with the 34 primary velocitiestaken from Balona (1987) and the two secondary velocities fromDonati et al. (1997).

First, a period search from the 55 velocities of the primarycomponent suggested an orbital period of 12.9051 days, about1.4% longer than the photometric (rotation) period, which weused as a starting value for the differential-correction program.We then weighted the velocities with the errors of the individualobservations and iteratively seeked the orbital elements of theprimary component with the smallest sum of the squared resid-uals. 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 thedata of Donati et al. (1997). Since the resulting eccentricity wassmaller than the inferred error, we adopted a zero-eccentricitysolution. Keeping these orbital elements fixed, we used a least-square fitting algorithm to find the secondary component’s radialvelocity amplitude. Final elements are given in Table 2 and the

Table 2. Improved orbital elements for IL Hydrae

Orbital element ValueP (days) 12.90513±0.00009T0 (HJD)a 2,449,403.49±0.023γ (km s−1) -8.0±0.3K1 (km s−1) 41.9±0.4K2 (km s−1) 71.0±2.2e 0.0 (adopted)a1 sin i (km) 7.443±0.075 × 106a2 sin i (km) 12.60±0.39 × 106f (M ) (M�) 0.098±0.003M1 sin3 i (M�) 1.21±0.09M2 sin3 i (M�) 0.72±0.03M2/M1 0.590±0.025Primary componentAvg. error of 6420-Å data (km s−1) 1.05Avg. error of Hα data (km s−1) 3.85

Secondary componentAvg. error (km s−1) 12.5aTime of the primary’s maximum positive radial velocity

computed velocity curves are plotted in Fig. 3 along with theobservations.

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

Knowing the rotation period, the rotation velocity, and the lu-minosity class of IL Hya one could, in principle, derive the in-clination of the stellar rotation axis from the relation R sin i =P (v sin i)/50.6. However, the large range of radii of an evolvedK star makes this method fairly unreliable, e.g., the Landolt-Börnstein tables (Schmidt-Kahler 1982) list a radius of 15R�, Gray (1992) gives a radius of 11 R�, and Dyck et al.(1996) derive 16 R�. Nevertheless we may calculate a defi-nite minimum stellar radius from the relation above and obtainR sin i = 6.66± 0.26 R�.

It is still possible to estimate upper and lower limits for theinclination angle though. Since we do not see eclipses we can es-timate the upper limit becauseR1 +R2 must be less than a cos i.If we adopt the G8V estimate from Cutispoto (1995; 1997) forthe secondary star and assume R2 = 0.84 R� from the Landolt-Börnstein tables, we obtain i≤ 62◦. Using the value ofR2 = 1.1R� estimated by Donati et al. (1997) does not change the upperlimit significantly. The lower limit is given by the measured massfunction f (M ) = (M2 sin i)3(M1 +M2)−2 = 0.098±0.003 andestimated values for the mass of the secondary star. Adopting0.8–1.5 M� for the secondary and using our newly derived massratioM2/M1 from Table 2 we get a range for the lower limit forthe inclination of i ≥ 73− 50◦. Note that the secondary masshas to be greater than 1 M� to fit the upper limit of the incli-nation angle as derived above. Therefore, an average of 56◦±6◦ is our preliminary estimate for the inclination of the stellarrotation axis of IL Hya. However, we emphasize that the given


Table 3. Stellar parameters for IL Hydrae

Parameter ValueSpectral type K0 III-IVlog g 2.5 ± 0.5Teff 4700 ± 250 K(B − V )obs 1.02 magv sin i 26.5 ± 1.0 km s−1Inclination i 55◦± 5◦Mass M 2.20+0.29−0.20 M�Radius R 8.1+0.9−0.7 R�Rotation period Pphtm 12.730 ± 0.004 daysEquatorial velocity vequ 32.3 ± 3.5 km s−1Microturbulence ξ 2.0 km s−1

Macroturbulence ζR = ζT 4.0 km s−1

log[Ca] abundance 0.9 dex below solarlog[Fe] abundance 0.9 dex below solar

range is not an error but that all values within this range areequally likely.

Donati et al. (1997) recently detected the lines from thesecondary star in two mean Stokes I spectra of IL Hya and, byusing an estimate for the secondary’s radial velocity amplitude,they derive a mass ratio of secondary to primary of 0.63±0.02 ingood agreement with our orbit. By matching the radii obtainedfrom the orbital period together with the rotational velocity, aswell as from a comparison of observed colors with evolutionarymodels, they find an inclination of the rotational axis of IL Hyaof 59±4◦ and obtain first estimates for the secondary’s mass,radius, and temperature.

Because the sin i-factor is omnipresent in the determinationof the astrophysical properties of IL Hya we will derive an inde-pendent estimate for the inclination of the stellar rotation axis inSect. 4.2 using the results from our Doppler-imaging analysis.

With the well-constrained inclination of 55±5◦ (seeSect. 4.2), our new mass ratio indicates a secondary mass of1.3±0.2 M�, somewhat higher but in agreement with the massestimated by Donati et al. (1997); while the mass and radius ofthe primary star are 2.2 M� and 8.1 R�, respectively. Accura-cies of the masses and radii are not better than 10% but wouldstill rather agree with a spectral type of mid to late F main se-quence or ≈G0V-IV for the secondary, instead of Cutispoto’s(1995,1997) G8V estimate from multicolor photometry. Givena mass ratio of 0.59, a = a1 + a2 from Table 2, and i = 55◦,the Roche-lobe radius for IL Hya is≈15 R� and the primary isthus filling only 16% of its Roche volume.

4. Doppler imaging

4.1. The line-profile inversion code

As for the previous papers in this series, all maps were gen-erated with the Doppler-imaging code TempMap (Rice et al.1989), originally developed for use with chemical abundanceinhomogeneities of Ap stars. For temperature mapping we usea more rigorous treatment of the local line profile than origi-

Table 4. Logarithmic elemental abundances relative to hydrogen(logN (H) = 12.00)

Z Element IL Hya1 Sun2

20 Ca 5.42 6.3622 Ti 4.9 4.9923 V 3.5 4.0026 Fe 6.73 7.6727 Co 4.4 4.9228 Ni 6.2 6.2563 Eu −0.2 0.511uncertainties are typically 0.1 dex for Ca and Fe; 0.3 dex otherwise.2from Grevesse & Anders (1989)

Table 5. Atomic parameters of the mapping lines

Line log gf Excitation Number ofpotential blends

Fei 6393.60 −1.62 2.430 6Fei 6400.00 −0.52 3.603 10Fei 6400.31 −4.05 0.915 . . .Fei 6411.65 −0.42 3.654 7Fei 6419.94 +0.23 4.733 12Fei 6421.35 −2.25 2.279 . . .Fei 6430.84 −2.00 2.176 8Cai 6439.08 +0.47 2.526 8Fei 6546.24 −1.90 2.759 3

nally discussed in Rice et al. (1989) and also simultaneouslysolve for the relative continuum light in two photometric band-passes (Rice 1995; Piskunov & Rice 1993). Local line profilesare computed for a series of limb angles from a solution of theequation of transfer through precomputed model atmospheresincluding updated opacities as implemented in the latest versionof ATLAS-9 (Kurucz 1993).

A grid of nine model atmospheres with log g = 2.5 andtemperatures from Teff = 3500 K to 5500 K in steps of 250 Kwas taken from the ATLAS-9 CDs (Kurucz 1993). Using a log gof 3.0 leads to similar line-profile fits, but the resulting metalabundances were even more deviant from the solar values inTable 4 than for log g = 2.5 and we therefore adopted the lattervalue for the final maps. Solutions with log g = 3.5 and 2.0 didnot result in satisfactory fits.

Due to the late spectral type combined with the wavelengthcoverage of our spectra, seven moderately blended lines couldbe used: Fei 6393, Fei 6400 (actually a close blend of twoiron lines at 6400.000 and 6400.314 Å), Fei 6411, Fei 6419.94and 6421.35 (refered to as Fei 6420), Fei 6430, Cai 6439, andFei 6546 Å with log gf values between −3.9 and +0.47 andlower excitation potentials between 0.915 and 4.733 eV. Sinceall seven lines are blended to a certain degree, the number oflines which had to be synthesized was 6, 10, 7, 12, 8, 8, and 3 forthe 6393, 6400, 6411, 6420, 6430, 6439, and 6546-line regions,respectively (Table 5). All these blends were included in the in-version and treated simultaneously with the primary mapping


Fig. 4a–d. The variation of χ2 as a function of the inclination of thestellar rotation axis (panel a), the projected equatorial rotational veloc-ity (panel b), the iron abundance (panel c), and the calcium abundance(panel d). The adopted values are marked.

lines but only one spectral region can be handled per solution.In this paper we used a Maximum-Entropy regularization but inpractice the program also allows a Tikhonov regularising func-tional (see, e.g., Piskunov & Rice 1993).

4.2. Redetermination of the rotational velocity and the inclina-tion of the stellar rotation axis

Since the Doppler-imaging analysis is rather sensitive to therotational velocity and to the inclination of the stellar rotationaxis, it can be used to refine these two parameters with higheraccuracy than with the methods described in Sect. 3 (see also,e.g., Unruh 1996). Changing these two parameters one at a time,while all others are held constant, yields a certain variation of theχ2 from the resulting line-profile fits. The value of the parametercorresponding to the smallest χ2 is the one we think is closestto the true value. The variation of χ2 with the rotational velocityv sin i and the inclination of the stellar rotation axis i are plottedin Fig. 4a and b, respectively. A minimum is seen in both cases:for the inclination around 50–60◦ and for the rotational velocitybetween 26 and 27 km s−1 , except for the Cai 6439 line where itis near 28 km s−1. Since the latter velocity leads to a small brightband at the sub-observers latitude – usually the sign for too higha rotational velocity – the true rotational velocity may be closerto 26 than 28 km s−1. The adopted final values correspond tothe grand minimum χ2 and are v sin i = 26.5 ± 1 km s−1 andi = 55± 5◦.

Table 6. Detected surface features

` b ∆T2 area3 Notes(◦) (◦) (K) (%)

19941

P . . . 90 800 8.0 polar spotA 40 30 600 1.2 at higher b in 6400B 75 30 600 1.9C 155 15 350 0.7 merged with D in 6400D 200 50 500 1.4 low contrast in 6420?E 270 40 500 1.3F 330 30 600 1.6 at higher b in 64001995P . . . 90 700 6.5 polar spotA 300 40 700 2.1B 345 5 400 1.0C 70 35 300 1.5D . . . . . . . . . . . . not seen in 1995E 150 35 600 1.7F 240 30 600 1.51measured off the average map2Tphot − Tspot3in % of the entire stellar sphere

4.3. Finetuning the abundances

To determine more accurate elemental abundances we evaluatethe run of the χ2 of the line profile fits from a series of solutionsstarting with abundances of 0.5 dex below solar abundance andincreasing that in steps of 0.05 dex. The transition probabili-ties, damping constants and laboratory wavelengths were keptconstant. We then adopted the abundances that resulted in theminimum χ2, i.e. logn(Fe) = 6.73 and logn(Ca) = 5.52 accord-ing to Fig. 4c and 4d. The same steps were then performed todetermine the abundances of the line elements that are blended,leading to the values listed in Table 4. Although a consistent setof parameters, the abundances are mathematically not uniquebecause test runs with different sets of fixed parameters (i.e.different log g and ξ) resulted in similar Doppler maps but withindividual abundances different by up to 0.2 dex.

4.4. Running TEMPMAP

Now that we have determined all necessary astrophysical in-put parameters we can generate the final Doppler images. Onespectral region and two photometric bandpasses per run, alter-nately with V I and then with V R, are used to produce twomaps for each spectral region. All computations are performedon a DEC-AXP 250/266 workstation and require between 25 to60 min CPU time depending on the number of blends and thenumber of input model atmospheres. The resulting V I mapsalong with the observed and computed line profiles for 1994and 1995 are plotted in Fig. 5 and in Fig. 6, respectively, whilethe observed and computed lightcurves for 1994 are shown inFig. 7.


Fig. 5a–c. Observed and computed line profiles for Fei 6393.602 Å (row a) with an average equivalent width of 270 mÅ, Fei 6400 Å with acombined equivalent width of 368 mÅ or ≈184 mÅ each (row c), and Fei 6411.647 Å with 186 mÅ (row c). The plusses are the observationsand the full lines are the fits. The right column shows the maps from the individual lines in pseudo-mercator projection. Note that the spectrallines are arranged from top to bottom according to increasing wavelength.

4.5. Doppler maps for 1994 and 1995

The average map from all but the Fei 6420 spectral region isshown in Fig. 8. For the averaging the individual maps weregiven equal weight and the lower panel in Fig. 8 shows the dis-tribution of the standard deviations from the mean. The averagestandard deviation is only around ±20 K per pixel while thepeak deviations reach ±40 K. Thus, the individual maps areencouragingly similar, not only in morphology but also in ab-

solute temperature. The only discordant map is the map fromFei 6420 Å being on average 200 K warmer than the othersbut still showing the same features than from the other lines.We note that the 6420-Å map was recovered from a larger thanusual wavelength region containing not only two main mappinglines instead of one but also several temperature-sensitive vana-dium blends with poorly determined atomic parameters. If notproperly taken into account, these vanadium blends cause either


Fig. 5d–f. As previously but for Fei 6419.639+6421.349 Å (row d) with 168 and 194 mÅ, respectively, Fei 6430.852 Å with 223 mÅ (row e)and Cai 6439.075 Å with 272 mÅ (row f).

additional or missing equivalent width that is then accounted forwith a generally increased surface temperature.

The average map from 1994 clearly reveals a cool polarspot (dubbed P in Fig. 8), three large and also cool spots closeto the equator and at longitudes of ` = 40◦, 75◦, and 330◦ that wenamed A, B, and F, respectively, two further, also relatively coolfeatures at longitudes of 200◦ and 270◦ (D and E) and one sig-nificantly warmer spot at ` ≈ 155◦ (C). Spots A, B, and F havetemperatures of about 600 K below the effective photospherictemperature while spots D and E are recovered at ∆T ≈500 Kand spot C with 300–400 K. The latitudinal elongation of some

spots might not be real because features at low latitudes migratethrough the line profile very quickly and thus their latitudinalextension is less well determined. Typical errors for the cen-tral latitudes of the spots are likely to be ±10◦ despite that thestandard deviations for the consistent features from the averagemap are just “a few degrees”. The major uncertainty for an er-ror quotation of the latitude (and the longitude) of a particularspot arises simply from the imperfect definition of its centroidlocation. The values in Table 6 were measured off the combinedmap by trailing the temperature along latitudinal strips.


Fig. 6. Fei -6546 map from February-March 1995 and the corresponding line profile fits. The arrows indicate the times of observation.

Fig. 7. Observed and computed V RI light curves for March 1994.The fits are from Fei 6393 Å, Fei 6400 Å, Fei 6411 Å, Fei 6420Å, Fei 6430 Å and Cai 6439 Å. The plusses are the contemporane-ous APT observations from Fig. 1c. The arrows indicate the phases ofthe spectroscopic observations. Note that the individual fits are almostidentical.

There is also some detail in the individual maps in Fig. 5which is not equally well seen in the combined map, despite thatthe spot morphology in the individual maps and in the combinedmap is basically identical. Five out of six spots in the averagemap always have a counterpart in the individual maps. Partic-ularly unreliable is the latitude of feature D, which appears asan appendage of the polar spot in the Fei 6393, 6400, and 6411maps and possibly with weaker contrast also in the 6420 mapbut as an isolated, high-latitude spot in the 6430 and Cai 6439maps. This discrepancy can not be explained with the differ-ent line-formation depths because the lines in question are notsimply either the weak or the strong ones but have mixed equiv-alent widths. Possibly, the inconsistent recovery of feature D isan artifact due to the external uncertainities of our spectra.

It is also interesting to compare the 1994 maps with thesingle-line map obtained from the Fei 6546-Å line one year laterin 1995 (Fig. 6). The V RI light curves in Fig. 1 had alreadyindicated a shift of about 0.p3 to smaller phases or 110◦ on thestellar surface. This can also be seen from the Doppler images

and it is thus likely that the light-curve minimum in 1995 wascaused by the same spot or groups of spots than in 1994. A crosscorrelation of the entire 1995 map with the average 1994 mapleads to four maxima at ` =−110◦,−50◦, +25◦, and +90◦. Themaximum at ` = −110◦ is the strongest and also correspondsbest with the shift in the light curve and we use it to reidentifythe individual spots in the 1995 map.

Spots A and F dominate the 1995 map and appear now at` = 300◦ and 240◦ , respectively. They stretch from their orig-inal latitudinal position between 10–50◦ up to the polar spotabove 60◦ in 1995. Spot B is only half the size than in the 1994map and of significantly weaker contrast (Tspot B (1994)=600 andTspot B (1995)=400 K) while spot C remained at approximatelythe same latitude and with similar contrast. Instead of the spotpair D and E in 1994, one single spot (marked E) appeared inthe 1995 map accompanied by two smaller, adjacent spots oflower contrast and about 30◦ closer to the equator than spot Ein 1994.

The reasonable consistently recovered latitude (and shape)of the individual spots – and the more or less stable overall spotmorphology during the time span of the two maps (one year orapproximately 27 stellar rotations) – may indicate that the life-time of the individual spots is usually longer than the typicallyencountered variability time scale of spotted stars from contin-uous photometry (≈ 1 month). We take this as evidence thatstarspots can indeed be used as tracers for differential surfacerotation despite that they are possibly made up of many littlespots with individual lifetimes shorter than that of the entirespot region. The intrinsic scatter of our seasonal light curves inFig. 1 could be attributed to such a scenario.

4.6. Differential surface rotation

In spite of the fact that our 1995 map is derived from a singlespectral region that has not been available for the 1994 map, thetwo maps have nevertheless a surprisingly similar appearance.By cross correlating longitudinal strips from the two maps atsucessive latitudes we may derive the amount and the sign ofthe differential rotation on IL Hydrae if we assume that the indi-


Fig. 8. A comparison of the average Doppler map from 1994 (top)with the surface distribution of its standard deviations (bottom). Theaverage map is a combination of altogether 10 maps derived from fiveof the spectral regions shown in Fig. 5 (except Fei 6420), each onewith both the V R and the V I light curves as additional constraint.Individual surface features are identified as described in the text. Thearrows below each panel indicate the phases of the observations and thegrey-scale bar plots the standard deviations along binned longitudes.

vidual surface features in 1995 are indeed the same as in 1994.As can be seen from the maps in Fig. 6 and Fig. 8 (top panel),isolated structures are identified up to a latitude of ≈50–60◦and the cross-correlation function reveals a significant peak butdoes indeed flatten out above 50◦ so that no single, strong peakis evident anymore. We then fitted a Gaussian to the peak of thecross-correlation function whenever well defined and plot itsphase lag versus latitude in Fig. 9. The error bars on these lagswere adopted to be proportional to the FWHM of the cross-correlation peak and were estimated from repeated measure-ments with different fitting routines within the IRAF package.The full line in Fig. 9 is a least-squares sin2 b fit to the phase lagsversus stellar latitude b and leads to the following differentialrotation law for IL Hya

Ω(b) = Ω0 − Ω1 sin2 b == 28.149− 0.103 sin2 b in ◦/days, (1)

Fig. 9. The differential rotation profile on IL Hya. The points arethe phase shifts between each constant-latitude strip of the mapsfrom 1994 and 1995 as derived from least-square Gaussian fits to thecross-correlation function. Above a latitude of approximately 50◦ thecross-correlation peak becomes too weak due to the extent of the polarspot.

where Ω0 = 360◦/Pequator is the equatorial rotation rate and Ω1is defined via the differential rotation coefficient α = (Ω0 −Ωpole)/Ω0. The negative sign for the second term in Eq. (1)indicates that the equatorial regions of IL Hya rotate faster thanthe polar regions and that α is thus positive and of order +0.004,i.e. 1/∆Ω ≈ 3500 days, smaller by a factor of 30 than thesolar value. However, we caution that this differential rotationlaw is not only just based on two maps one year apart, i.e. 27stellar rotations, but also suffers from the inevitable north-southmirroring effect in Doppler imaging, which affects mostly the“southern” latitudes below, say, −20◦ in case of i = 55◦.

Time-series Doppler images have now been obtained forfour other RS CVn binaries (HR 1099, EI Eri, UX Ari, andHU Vir) and differential rotation was likely detected in all ofthem. The fastest rotator within the four, EI Eridani (P = 1.95days), only showed a marginal amount of differential rotationand, if correct at all, then in the sense that the equatorial re-gions rotate faster than the polar regions (Hatzes & Vogt 1992),in accordance with the solar picture. However, this result maybe questioned because in a recent time-series Doppler-imagingstudy by Washüttl et al. (1997) with much higher time resolu-tion than in Hatzes & Vogt (1992) the equatorial features on EIEridani exhibited lifetimes of as short as 3 weeks. Another, prob-ably similar, case is HR 1099, where Vogt & Hatzes (1996) hadfound very weak differential rotation but in the opposite sensethan on the Sun, the poles rotating faster than the equator. Theother two stars are slower rotators than EI Eri and HR 1099, i.e.P = 6.4 days for UX Ari (Vogt & Hatzes 1991) and P = 10.5days for HU Vir (Strassmeier 1994, Hatzes 1997). For them thededuced differential-rotation rates are approximately a factorof 10 stronger than the two shorter-period stars (but still a fac-


Fig. 10. Variation of the Hα equivalent width as a function of orbitalphase for Feb.-March 1995 (filled circles) and a sinusoidal fit of the1994/95 V -lightcurve (dashed line). Note that minimum absorption,i.e. maximum residual emission, coincides with a time of lightcurveminimum, i.e. when the most spotted hemisphere is viewed. This sug-gests a spatial relation between spots and plages on IL Hya.

tor of 10 weaker than on the Sun), but both in the sense that thepoles rotate faster than the equator. IL Hydrae on the other hand,with its 12.7 day rotation period, shows only weak differentialrotation with the poles rotating slower than the equator, thus be-ing an exception compared to the other (long-period) RS CVnsystems mentioned above.

5. Hα line-profile variations

All spectra from February-March 1995 show Hα as a relativelynormal absorption line with an average equivalent width of0.9 Å, but plotting its equivalent width against orbital or ro-tational phase reveals a nearly sinusoidal variation very simi-lar in shape and phase to the contemporaneous V -light curve(Fig. 10). Relative to a pseudo continuum the full amplitude ofthe variation reaches 600±50 mÅ or approximately 100%. Wetake this as evidence that at least part of the Hα flux must belinked to the fraction of the star’s surface that is covered withcool spots and therefore the plages are presumably on top ofthese spots in agreement with solar analogy.

To examine the Hα flux of the active part of the chromo-sphere we subtract a broadened and shifted spectrum of theinactive K0.5III star 16 Vir from each IL Hya spectrum. Thisreference spectrum is assumed to represent the non-magneticpart of the chromosphere of IL Hya but, of course, can not ac-count for eventual differences in the atmospheric structure of thetwo stars. Fig. 11 shows the resulting nine residual Hα profilesrevealing a strong and variable residual emission componentcentered at the rest wavelength of Hα and a small, redshiftedabsorption feature. The latter feature’s redshift, obtained fromtwo-Gaussian fits to the residual profiles, remains constant at ap-proximately 1.24±0.12 Å or 57±5 km s−1 (rms) throughout arotational cycle and thus can not be explained with a plage-likefeature on the stellar surface. Using β Gem (K1IIIb) instead of

Fig. 11. Residual Hα line profiles of IL Hya (lower panel) after thesubtraction of a spectrum of the inactive reference star 16 Vir (dashedline). The number adjacent to each profile is the orbital phase. Notethe permanently redshifted absorption by 1.24 Å ≈ 57±5 km s−1 asobtained from a two-Gauss fit. The upper panel shows a representativespectrum of IL Hya (thick line) and the unbroadened spectrum of 16 Viras well as the difference spectrum of 16 Vir to yet another referencestar (β Gem, K1III, shifted by +0.2 for better visibility).

16 Vir gives practically the same result with marginally differ-ent emission strengths but identical wavelength shifts as demon-strated in the upper panel of Fig. 11.

Similar Hα-line profiles were already seen in other activestars, most notably in IN Vir with a redshifted absorption of≈60km s−1 (Paper III) and HU Vir where a red feature appearedshifted by even 100 km s−1 (Strassmeier 1994, Hatzes 1997),but also in HD 17433 (Bopp et al. 1989), HD 12545 (Bopp etal. 1993) and the single star HD 9746 (Fekel et al. 1986). Thesingle giant HD 32918 = YY Men shows qualitatively a sim-ilar profile, but with blue-shifted emission (by approximately−80 km s−1) and an absorption feature at the Hα rest wave-length (Vilhu et al. 1991). Furthermore, some of the most ac-tive stars exhibit very strong, broad and structured emissionprofiles, e.g. FK Comae with an emission width at the contin-uum level of 1000 km s−1 (Oliveira et al. 1997), or the Pleiadesstar HII 1883 with 700 km s−1 (Marcy et al. 1985), or IN Co-mae with 800 km s−1 (Paper IV) while others, most notably ABDoradus and V471 Tauri, show a periodically variable absorp-tion profile due to prominence activity (e.g. Collier Cameron &Robinson 1989). To confuse the phenomenology even further,Hatzes (1995) found that the Hα spectrum of the single-linedRS CVn binary DM UMa (K0III, P = 7.5 days) consists of anarrow emission component and a broad absorption component,both unshifted with respect to the rest wavelength, but only thebroad component also showed phase-dependent variations.


Due to such a large variety of the observed phenomenologyit is likely that several processes, and most likely a combina-tion of them, are the cause for the Hα profiles of active stars:stellar plages in direct analogy to solar plages (see, e.g., Neff1996); fluctuations of both the column density and tempera-ture gradient within the chromosphere as suggested earlier bySmith & Dupree (1988) to explain the Hα profiles of metal-deficient red giants; local velocity fields and mass motions dueto magnetic field inhomogeneities possibly coupled with a loop-like geometry as believed to have been detected on HU Virginisfrom pseudo 3D Doppler maps (Strassmeier 1994); and, nat-urally, classical stellar winds and even antiwinds as indicatedfrom redshifted UV-emission lines of e.g. Capella (Linsky et al.1995). The approach of phase-resolved Hα spectra is certainlypromising and allows to separate rotational modulation fromother time-dependent processes, but more observations of moretargets with higher time resolution are clearly necessary to es-tablish a firm explanation of the Hα profiles of active stars.

Acknowledgements. Thanks go to John Rice for his continuous discus-sions and inspirations concerning TempMap and to Frank Fekel for acopy of Barker’s SB2 orbit program. Since money makes the world goaround we are, as usual, especially indepted to the Austrian Fond zurFörderung der wissenschaftlichen Forschung (FWF) for support undergrants S7301-AST and S7302-AST.

References

Balona, L.: 1987, SAAO Circ. 11, 1Barden, S. C.: 1985, ApJ 295, 162Barker, E. S., Evans, D. S., Laing, J. D.: 1967, R. Obs. Bull. 130Bell, R. A., Gustafsson, B.: 1989, MNRAS 236, 653Bopp, B. W., Fekel, F. C., Aufdenberg, J. P., Dempsey, R., Dadonas,

V.: 1993, AJ 106, 2502Bopp, B. W., Saar, S. H., Ambruster, C. et al., 1989, ApJ 339, 1059Breger, M.: 1990, Comm. in Astroseismology 20Collier Cameron, A., Robinson, R. D.: 1989, MNRAS 236, 57Cutispoto, G.: 1995, A&AS 111, 507Cutispoto, G.: 1997, A&AS, in pressDempsey, R. C., Linsky, J. L., Fleming, T. A., Schmitt, J. H. M. M.:

1993, ApJS 86, 599Donati, J. F., Semel, M., Carter, B. D., Rees, D. E., Collier Cameron,

A.: 1997, MNRAS, in pressDyck, H. M., Benson, J. A., Van Belle, G. T., Ridgway, S. T.: 1996,

AJ 111, 1705Eggen, O. J.: 1973, PASP 85, 42Fekel, F. C.: 1996, private communicationFekel, F. C., Moffett, T. J., Henry, G. W.: 1986, ApJS 60, 551Gray, D. F.: 1992, The observation and analysis of stellar photo-

spheres, Cambridge University Press, 2nd editionGrevesse, N., Anders, E.: 1989, in C. Waddington (ed.), Cosmic abun-

dances of matter, IAP Minneapolis, p. 1Hatzes, A. P.: 1995, AJ 109, 350Hatzes, A. P.: 1997, A&A, in pressHatzes, A. P., Vogt, S. S.: 1992, MNRAS 258, 387Kurucz, R. L.: 1993, ATLAS–9 CDLa Dous, C., Giménez, A.: 1994, International Ultraviolet Explorer -

Uniform low dispersion archive. Chromospherically active binarystars, ESA SP-1181

Linsky, J. L., Wood, B. E., Judge, P., Brown, A., Andrulis, C., Ayres,T. R.: 1995, ApJ 442, 381

Marcy, G. W., Duncan, D. K., Cohen, R. D.: 1985, ApJ 288, 259Mitrou, C. K., Doyle, J. G., Mathioudakis, K., Antonopoulou, E.:

1996, A&AS 115, 61Mutel, R., Lestrade, J.: 1985, AJ 90, 493Neff, J. E.: 1996, in K. G. Strassmeier & J. L. Linsky (eds.), Stellar

Surface Structure, IAU Symp. 176, Kluwer Academic PublishersDordrecht, p. 113

Oliveira, J., Foing, B. H., Beaufort, T., et al.: 1997, in R. A. Donahue &J. A. Bookbinder (eds.), Tenth Cambridge Workshop, Cool Stars,Stellar Systems and the Sun, PASPC, in press

Piskunov, N. E., Rice, J. B.: 1993, PASP 105, 1415Randich, S., Gratton, R., Pallavicini, R.: 1993, A&A 273, 194Raveendran, A. V., Mekkaden, M. V., Mohin, S.: 1982, MNRAS 199,

707Rice, J. B.: 1995, private communicationRice, J. B., Strassmeier, K. G.: 1996, A&A 316, 164, (Paper II)Rice, J. B., Wehlau, W. H., Khokhlova, V. L.: 1989, A&A 208, 179Schmidt-Kahler, T.: 1982, in K. Schaifers & H. H. Voigt (eds.),

Landolt-Börnstein, Vol. 2b, Springer Verlag Berlin HeidelbergNew York

Slee, O. B., Haynes, R. F., Wright, A. E.: 1984, MNRAS 208, 865Smith, G. H., Dupree, A. K.: 1988, AJ 95, 1547Strassmeier, K. G.: 1994, A&A 281, 395Strassmeier, K. G.: 1996, A&A 314, 558, (Paper I)Strassmeier, K. G.: 1997, A&A 319, 535, (Paper III)Strassmeier, K. G., Bartus, J., Cutispoto, G., Rodonò, M.: 1997a,

A&AS 125, 11Strassmeier, K. G., Boyd, L. J., Epand, D. H., Granzer, T.: 1997b,

PASP 109, 697Strassmeier, K. G., Hubl, B., Rice, J. B.: 1997c, A&A 322, 511,

(Paper IV)Unruh, Y. C.: 1996, in K. G. Strassmeier & J. L. Linsky (eds.), Stellar

Surface Structure, IAU Symp. 176, Kluwer Academic PublishersDordrecht, p. 35

Vilhu, O., Gustafsson, B., Walter, F. M.: 1991, A&A 241, 167Vogt, S. S., Hatzes, A. P.: 1991, in I. Tuominen, D. Moss & G. Rüdiger

(eds.), The sun and cool Stars: activity, magnetism, dynamos, IAUColloquium No.130, Springer-Verlag Berlin Heidelberg New York,p. 297

Vogt, S. S., Hatzes, A. P.: 1996, in K. G. Strassmeier & J. L. Linsky(eds.), Stellar Surface Structure, IAU Symp. 176, Kluwer Aca-demic Publishers Dordrecht, p. 245

Washüttl, A., Strassmeier, K. G., Collier Cameron, A.: 1997, in R. A.Donahue & J. A. Bookbinder (eds.), Tenth Cambridge Workshop,Cool Stars, Stellar Systems and the Sun, PASPC, in press

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