Astron. Astrophys. 319, 535–546 (1997) ASTRONOMYAND

ASTROPHYSICS

Doppler imaging of stellar surface structure

III. The X-ray source HD 116544 = IN Virginis

K.G. Strassmeier?

Institut für Astronomie, Universität Wien, Türkenschanzstraße 17, A-1180 Wien, Austria (strassmeier@astro.ast.univie.ac.at)

Received 17 June 1996 / Accepted 30 July 1996

Abstract. We present the first Doppler image of the EXOSATX-ray source EXO 1321.8-0203, recently identified to be a chro-mospherically active star exhibiting periodic light variations andconsequently named IN Virginis. Our high-resolution spectrashow IN Virginis to be a single-lined spectroscopic binary withan orbital period of 8.2 days, very strong Ca ii emission, andan inverse P-Cygni type Hα line profile. A detailed spectrumsynthesis yields a photospheric temperature of 4600±70 K andlog g = 3.5 − 4.0 and slight overabundance of the heavy ele-ments but otherwise solar abundances. We redetermine the pho-tometric period from a new set of photometry obtained with arobotic photoelectric telescope in the years 1994 and 1995 andconclude that IN Virginis is more likely a K2-3 subgiant insteadof a K5 dwarf or K4 subgiant as previously published.

The Doppler images from March 1994 show a cool polarspot that is dominated by a large appendage reaching a latitudeof +40◦. Its average temperature difference, photosphere mi-nus polar spot, is 1000 K. Additionally, three equatorial spotsare clearly recovered but have ∆T ≈400 K. Possibly, we alsodetected a warm equatorial feature with ∆T ≈-150 K. We em-phasize that Doppler imaging of IN Virginis is very challengingbecause of both the small v sin i of the star (24.0 km s−1) and itsrelatively cool photosphere causing many weak absorption-lineblends. Still, maps from the different lines appear encouraginglysimilar.

Key words: stars: activity of – stars: imaging – stars: individual:IN Vir – stars: late-type – stars: fundamental data

1. Introduction

IN Virginis = HD 116544 (α = 13h24m24s, δ = −2◦18′48”,2000.0, V = 9.1 − 9.3 mag) is a serendipitous X-ray sourcediscovered by EXOSAT (Giommi et al. 1991) and has beenknown for a while to be a microwave emission source (Slee etal. 1987). It was previously thought to be a single, low-mass,

? Visiting Astronomer, Kitt Peak National Observatory, operated bythe Association of Universities for Research in Astronomy, Inc. undercontract with the National Science Foundation

main-sequence star of late K spectral type (Cutispoto et al. 1992,1994) although Slee et al. (1987) noted that its radius suggestsmore likely a subgiant. Tagliaferri et al. (1994) presented a studyof lithium abundances of the same stars observed by Cutispotoet al. (1992, 1994) and also obtained a (single) high-resolutionspectrum of IN Virginis. They found that its spectral appear-ance is better matched by a combination of a K4 subgiant anda G8 dwarf rather than a single K5V classification. The sec-ondary component’s spectrum, however, was not seen in the6700-Å wavelength region of their spectrum and was proposedad hoc to explain the observed colors. In this paper we showthat IN Virginis is actually a single-lined RS CVn-type binarysystem.

Cutispoto et al. (1992) discovered the light variability ofIN Virginis and found a photometric period of approximately8.15 days. They interpreted the photometric periodicity beingdue to stellar rotation and the variable light-curve amplitudebeing due to changing starspots rotating in and out of view.Therefore, we put IN Virginis on the observing program of ourlong-term Doppler-imaging project at Kitt Peak National Ob-servatory.

In this paper we present a series of moderately high-resolution optical spectra of IN Virginis obtained within lessthan two consecutive stellar rotations. New contemporaneousV (RI)C photometry was gathered throughout the entire ob-serving season in 1994. The combination of the spectroscopicand the photometric data is used to study the spatial distributionof surface activity on IN Virginis. The instrumentation and thedata reduction are described in Sect. 2. In Sect. 3 we presenta discussion of the stellar properties relevant for this study, in-cluding a first spectroscopic orbit for IN Vir, and determine allthose astrophysical parameters that are input parameters for theDoppler-imaging analysis. Hα observations and Doppler mapsfrom several spectral lines are derived and discussed in Sect. 4and Sect. 5 respectively. Sect. 6 again summarizes our conclu-sions. A description of the long-term goals of this series ofpapers was already presented in paper I on the RS CVn binaryUZ Librae (Strassmeier 1996) and in paper II on the weak-lineT Tauri star V410 Tau (Rice & Strassmeier 1996).

536 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

Table 1. Spectroscopic observations

HJD phase phase vr λ ADU(24+) (orb) (phot) (km s−1) (Å )49416.0267 0.206 0.947 +27.3 6420 200049416.9014 0.313 0.053 +59.4 6420 260049417.8993 0.435 0.174 +82.7 6420 220049418.8944 0.556 0.295 +83.5 6420 180049420.9444 0.806 0.544 +23.0 6420 250049421.8937 0.922 0.659 –5.5 6420 310049422.9574 0.052 0.789 –6.0 6420 120049426.9661 0.542 0.276 +85.9 6420 350049427.7883 0.641 0.375 +68.8 6420 300049428.9132 0.779 0.512 +33.3 6420 80049772.8983 0.782 0.299 +34.9 Hα 400049773.0239 0.798 0.314 +24.0 6420 250049773.8922 0.904 0.419 –1.8 6420 500049773.9634 0.912 0.428 +0.4 Hα 450049774.0385 0.922 0.437 . . . H&K 20049775.9650 0.157 0.671 +11.8 6420 250049776.9614 0.278 0.792 +49.7 Hα 100049778.9817 0.525 0.038 +85.3 6420 325049779.0358 0.532 0.044 +89.5 Hα 250049780.0369 0.654 0.166 +65.5 6420 300049781.0135 0.773 0.284 . . . H&K 40049781.9036 0.882 0.392 +2.2 6420 325049783.8543 0.120 0.629 +3.4 6420 70049783.9532 0.132 0.641 +5.5 6420 280049784.0252 0.141 0.650 +14.0 Hα 140050095.9444 0.229 0.541 . . . 6750 580050098.9760 0.599 0.910 . . . Ca ii irt 70050103.9608 0.208 0.515 . . . H&K 600

2. Observations

All spectroscopic observations were obtained at Kitt Peak Na-tional Observatory (KPNO) with the coudé feed telescopeduring March 1994 and again in February-March 1995. TheDoppler-imaging data in this paper are from the March 1994run while the Hα spectra are from 1995. A few more spectraat various wavelengths were taken in January 1996. The 1994and 1995 data were obtained with a 800×800 TI CCD (TI-5chip, 15µ pixels) with grating A, camera 5 and the long colli-mator giving a resolving power of 38,000 at 6420 Å. For the few1996 spectra we used the new 3000×1000 CCD (Ford F3KBchip, 15µ pixels) with an otherwise identical spectrograph setup. Table 1 is a summary of the spectroscopic observations.

All data were reduced in the same standard fashion usingIRAF and included standard bias subtraction, flat fielding andaperture extraction. Frequent wavelength comparison spectraand 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 IN Vir spectra with the IAU velocity standard16 Vir (K0.5III, vr = 35.7 km s−1) and are listed in Table 1. Thestandard error of an observation of unit weight is 1.9 km s−1.The exposure level is indicated in Table 1 in analog-to-digital

Fig. 1a–e. Representative spectra of chromospheric activity indicatorsfor IN Virginis (thick lines). The respective thin lines are shifted andbroadened spectra of the inactive star φ Ser (HR 5940), classified alsoas K2-3IV. The individual panels show: Ca iiH&K (panel a), Ca ii 8542(panel b), Ca ii 8498 (panel c), Hα (panel d), and Li i 6708 (panel e).The insert in panel e is the residual spectrum of IN Vir after subtractionof the broadened and shifted φ Ser spectrum and offset by -0.2. TheLii-6708 line is identified with a tick mark.

units (ADU) corresponding to signal-to-noise ratios between150:1 and 200:1 for the red wavelength observations and about50:1 for the Ca ii spectra. Usually twenty flat-field exposureswith a tungsten reference lamp were taken at the beginning ofthe night 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. Neither the TI CCD nor the F3KB CCDshow obvious signs of fringing near 6420 Å and no attemptswere made to correct for it other than the standard flat-field di-vision. Special care was also exercised during the continuumfitting but a very low-order polynomial was sufficient to find asatisfactory continuum solution. Several representative spectraare shown in Fig. 1.

The new photometric data were obtained with the Fair-born Observatory T7 0.75-m automatic photoelectric telescope(APT) on Mt. Hopkins, Arizona. The 151 observations weremade differentially with respect to HD 117635 as the compari-son star (V = 7.33 mag, V −RC = 0.45 mag and V −IC = 0.87mag) and HD 118330 as the check star. All photometry has beentransformed to match the Johnson-Cousins V (RI)C system.Observations started on JD 2,449,441 on the basis of severalobservations per night and cover the entire observing seasons1994 and 1995 until 2,449,870. This data and additional pho-tometry for IN Virginis, combined with data from other stars,will be presented in a forthcoming paper (Strassmeier et al.1997).

All line profiles and photometric data in this paper are con-sistently phased with our new photometric ephemeris,

HJD = 2, 449, 400.0 + 8.232± 0.003× E, (1)

K.G. Strassmeier: Doppler imaging of stellar surface structure. III 537

Fig. 2. Left: Periodogram from the 1994-1995 V -band APT data. Right: Light and color curves phased with f1 and the ephemeris in Eq.(1).The upper left panel shows the window function for the APT data with strong aliasing towards multiples of one day. The largest reduction of theresiduals is achieved with a period near the orbital period at 8.232±0.003 days (frequency f1 = 0.1215). The other indicated frequencies arejust aliases of the true f1 frequency. The right panels show the light and color curves phased with f1. Despite that these plots show all combineddata from 1994 we see a clear asymmetry in the light curve as well as in the V − IC color curve with a maximum at around phase 0.2 and aminimum at around 0.8.

where the period is the best-fit period from the combined 1994and 1995 APT photometry that we interpret to be the rotationperiod of the star, and the initial epoch is just an arbitrary pointin time. Although the orbital period is more precise than thephotometric period we use the latter to phase the data becausewe regard the orbital period still as preliminary. Whenever givenin this paper though, orbital phases were computed with the newelements in Table 2.

Fig. 2 shows the V -light curve and the V −RC and V − ICcolor curves of IN Virginis in 1994 phased with the photometricperiod as well as the periodogram from the combined 1994-1995V -band data.

3. Stellar properties of IN Virginis

Since little is known about this star I briefly rediscuss some of itsinferred properties in the light of the new data presented in thispaper. This seems important in order to evaluate the reliabilityof Doppler maps in general and because we need fundamentalstellar parameters prior to the mapping analysis, such as the rota-tion period and the rotation velocity, an estimated photospherictemperature and gravity, the abundances of chemical elementsand, last but not least, the approximate inclination of the stellarrotation axis.

3.1. The active chromosphere of IN Virginis

IN Vir has been discovered to be a coronally active star from itsdetection as a microwave emission source (Slee et al. 1987)and its moderate X-ray emission (Giommi et al. 1991). Nopublished ultraviolet spectrum seems to be available for this

star. Examples of the most prominent chromospheric-activityindicators in the optical spectrum of IN Virginis are shown inFig. 1. Most obvious are the exceptionally strong H&K emis-sion lines of Ca ii, a signature of a chromospherically veryactive star. Also in emission is the Balmer H� line redwardsof the Ca ii-H line. Our three H&K spectra show a variableemission strength with a total range of about 20% in emissionequivalent width (see Fig. 9a in Sect. 5). Following the calibra-tion procedure of Linsky et al. (1979b) we obtain absolutelycalibrated emission-line fluxes in the H and K lines and con-vert them to radiative losses by subtracting the appropriate fluxfrom a radiative equilibrium model atmosphere (i.e. withouta chromosphere). The radiative losses in the (H/K) lines are(1.56/2.07) 106 erg cm−2s−1, (1.05/1.38) 106 erg cm−2s−1, and(1.33/1.77) 106 erg cm−2s−1 for JD 2,450,103, JD 2,449,781,and JD 2,449,774, respectively.

Fig. 1 also shows the strong emission in the cores of two ofthe infrared triplet lines of singly ionized calcium (Ca ii 8542and 8498 Å). Again, the width and the strength of these emissionlines are within the range seen in other RS CVn-type binaries(e.g. Dempsey et al. 1993). Using the method described in Lin-sky et al. (1979a) we obtain an absolute emission-line flux of2.1 106 erg cm−2s−1 in a ±1 Å band around the line center ofthe 8542-Å line. These fluxes are typical for active RS CVnstars of the late spectral type of IN Virginis.

The complex profile of Hα is reminiscent of the “inverse P-Cygni”-type profile seen in other active stars with spatially inho-mogeneous chromospheres and coronae. Just recently, Hatzes(1995a,1995b) obtained simultaneous Doppler images and Hαline profiles for the RS CVn binary DM UMa and the WTT

538 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

Fig. 3. Observed and computed radial velocity curve. Dots are thevelocities from Table 1 and the line is the newly determined orbitalsolution from the elements in Table 2. Note that a zero-eccentricityorbit was adopted.

star V410 Tau. The typical DM UMa profile appeared to becomposed of two Gaussian-like emission components: a narrowand constant component and a broad and highly variable com-ponent. However, their origin is not clear and interpretationsinclude a corotating Hα emitting shell, a nonuniform and/orvariable wind, an expanding chromosphere, mass flow in a gi-gantic coronal loop, and large hydrogen flares associated withsignificant mass flow. Even more dramatic Hα changes are seenin V410 Tau where the coincidence of maximum Hα and He iD3 emission during the time when the large polar appendagetransits the disk indicates that chromospheric activity such asplages and flares cause, at least part of, the Hα emission. TheIN Vir Hα spectra will be discussed in more detail in Sect. 5.

We also plot in Fig. 1 a spectrum of the lithium-line regionat 6708Å because it is supposed to be a crude indicator of stel-lar age and thus indirectly also of chromospheric activity. Thisspectrum shows a weak but clearly observable absorption fea-ture at the lithium wavelength. The insert in Fig. 1e is the resid-ual spectrum after subtraction of a reference star of identicalM-K classification and reveals a weak Li i 6708 line consistentwith previous observations of active stars, singles and binaries(e.g., Fekel & Balachandran 1993).

3.2. The rotation period

We applied a multiple period search program (Breger 1990)to our APT photometry covering 106 nights in 1994 and 70nights in 1995. Fig. 2a shows the periodogram from the V data(lower panel) and the corresponding window function (upperpanel). The greatest reduction of the sum of the squares of theresiduals is obtained with a period of 8.232±0.003 days (f1 =0.1215 in Fig. 2a) in very good agreement with the periodsderived by Cutispoto et al. (1992, 1994, 1996). Fig. 2a alsoshows several aliases of comparable but smaller amplitude, mostnoticable at frequencies of 1− f1 and 1 + f1, but also at 2− f1a.s.o.. A frequency of f1/2 (≈ 16 days) produces only half theamplitude of less than 0.038 mag in V . The primary reason for

Fig. 4a–c. Line-depth ratio variations of IN Virginis (upper panels)and their respective calibrations from luminosity-class III and IV M-Kstandard stars against observed B − V color (lower panels). The dotsare the measured line ratios and their error bars indicate the whole rangeof values from repeated measurements with different techniques. Thedotted line in the upper panels is the scaled, simultaneous V -bandlight curve and emphasizes the relation with the line-ratio variationsdue to the common cause. Note that the line ratios are chosen withtemperature-sensitive line over temperature-insensitive line, therefore,the larger the line ratio the stronger was the temperature-sensitive line,and thus the cooler the average surface temperature. The crosses in thelower panels are the standard-star observations and the lines are the fitswith the second-order polynomials in Eq. (2).

these aliases is the one-observation-per-night windowing of theAPT observing schedule.

3.3. Orbital elements

The range of velocities in Table 1 already indicates thatIN Virginis is a single-lined spectroscopic binary. Altogether,we obtained 23 high-precision radial velocities and use them tocompute a preliminary orbit. A period search on just those 10velocities from our run in 1994 suggested a period of 8.22 days,very close to the photometric period but final orbital elements,including an improved orbital period, were derived with all 23velocities and with the differential-correction program of Barkeret al. (1967). A first run with the preliminary period convergedat an eccentricity so close to zero that a formal zero-eccentricitysolution was adopted. The standard error of an observation ofunit weight is 1.9 km s−1, but two O-C residuals were as large as5.0 km s−1 and were given half weight in the orbit computation.The elements are given in Table 2 and the computed velocitycurve is plotted in Fig. 3 along with the observations.

K.G. Strassmeier: Doppler imaging of stellar surface structure. III 539

Fig. 5. Synthetic and observed spectra for IN Virginis. The upper panel compares an unbroadened synthetic spectrum (thin line) with theobserved IN Vir spectrum (thick line). It demonstrates the amount of blending evident at the late spectral type of IN Vir. The line identificationson the top include, in addition to the element and the rest wavelength, our new value for the transition probability. The lower panel repeats theobserved spectrum (thick line) and shows the obtained fit (thin line) when appropriate rotation is included. The three strongest lines are thespectral lines used for Doppler-imaging (Ca i 6439 Å, Fe i 6430 Å and Fe i 6421 Å).

Table 2. Orbital elements for IN Virginis

Orbital element ValueP (days) 8.1895±0.0009T0 (HJD) 2,449,422.53±0.01γ (km s−1) +39.5±0.5K1 (km s−1) 48.6±0.7e 0.0 (adopted)a1 sin i (km) 5.47±0.09 × 106f (m) (M�) 0.097±0.004Standard error of an observation

of unit weight (km s−1) 1.9

3.4. Rotation velocity, spectral type, and inclination of the stel-lar rotation axis

Tagliaferri et al. (1994) obtained a high-resolution spectrumof the Li i 6708-Å wavelength region of IN Virginis and mea-sured a projected rotational velocity (v sin i) of 22 km s−1.This value is in good agreement with our own initial v sin imeasure of 23.0±1.5 km s−1 from cross-correlating a well-exposed IN Vir spectrum with 16 Vir and taking into account a

radial-tangential macroturbulence of 4 km s−1. Our final valueof 24.0±1.0 km s−1 for the v sin i was obtained from a seriesof test solutions with the Ca i-6439 profiles and the Fe i-6421profiles with fixed inclination but different equatorial velocities.

Tagliaferri et al. (1994) also conducted a spectrum-synthesisanalysis based on grids of model atmospheres mostly taken fromGustafsson et al. (1975), and determined a relatively low lithiumabundance of logn = 0.3 and a metallicity of [Fe/H] ≈ −0.2 :using a∼25-Å region around 6708 Å. Their conclusion was thatIN Vir is more likely a K4IV+G8V binary instead of a singleK5V star as proposed earlier by Cutispoto et al. (1992) frommulti-color photometry (the assumed spectral type of the unseensecondary was recently revised to G7V by Cutispoto et al. 1996).

The late-K subgiant classification is basically consistentwith our observations, just that various line ratios in the 6430-Åregion indicate a slightly earlier spectral type for the visible star.A spectrum synthesis with several reference stars in the rangeG5 to K4 and luminosity classes III, IV, and V gives the bestfit with φ Ser (=HR 5940). The spectral classification of φ Seris listed as K1IV in Gray & Nagar (1985) but Fekel (1996)assigned a K2-3IV type from high-resolution spectra and theclassification criteria of Strassmeier & Fekel (1990). We notethat its B − V color of 1.14 would be slightly too red for K1

540 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

Table 3. Stellar parameters for IN Virginis

Parameter ValueSpectral type K2-3 IVlog g 3.5-4.0Teff 4600 K(B − V )obs 1.16 magv sin i 24.0±1.0 km s−1Inclination i 60◦

Rotation period 8.232±0.003 daysMicro turbulence ξ 2.0 km s−1

Macro turbulence ζR = ζT 4.0 km s−1

log[Ca] abundance solarlog[Fe] abundance 0.05 dex above solar

anyway and fits the K2-3IV classification better. The moder-ately broad wings of strong absorption lines like Ca i 6439 Åconfirm the subgiant luminosity classification of φ Ser.

Gray & Nagar (1985) determined the projected rotationalvelocity of φ Ser to 1.1 km s−1 and its radial-tangential macro-turbulence to ≈ 4 km s−1. The line broadening in our singleφ Ser spectrum is marginally larger, on average 0.29-Å FWHM,and results in a v sin i value of 1.7±0.5 km s−1 when we takeinto account a macroturbulence of 4 km s−1.

Having the rotational velocity, the rotational period, and theluminosity class of IN Vir fixed we could, in principle, deter-mine the inclination of the stellar rotation axis from the re-lation R sin i = P (v sin i)/50.6 – if there were not the largerange of radii for an evolved star. The Landolt-Börnstein tables(Schmidt-Kaler 1982) list radii for a K IV star between 2 and10 R�. Nevertheless, the above relation still allows to computea definite minimum stellar radius from observed quantities andwe find R sin i=3.77±0.18 R� in good agreement with the M-K luminosity class IV inferred from the spectrum morphology.We note that none of our class III reference stars reproduced theIN Vir spectrum nearly as well as φ Ser and we tend to rule outa class III classification.

We can also estimate an upper limit of the inclination ofthe stellar rotation axis because we do not see eclipses in thelight curve and thus R1 + R2 must be less than a cos i. If weadopt the G7-8V estimate from Tagliaferri et al. (1994) andCutispoto et al. (1996) for the (unseen) secondary star, thusR2 = 0.85 R� from the Landolt-Börnstein tables, we obtainthe upper limit for the inclination of i ≤ 74◦. Since any hotand thus more massive secondary star of, e.g., spectral-typeF and main-sequence luminosity would be inconsistent withthe observed colors, we may also estimate a lower limit forthe inclination of the stellar rotation axis from our new massfunction of f (M ) = (M2 sin i)3(M1 + M2)−2 = 0.097 ± 0.004and the fact that no secondary lines are visible in high-resolutionred-wavelength spectra. Adopting masses between 0.79 - 0.92M� (according to G5V to K0V) for the secondary star andmasses in the range of 1.0 - 1.2 M� for the primary star, weobtain the lower limit for the inclination of i ≥ 50 ◦. Thus, ourbest estimate for the inclination of the stellar rotation axis of

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

Z Element IN Vir1 Sun2

3 Li 0.55 1.1614 Si 8.05 7.5520 Ca 6.36 6.3622 Ti 5.50 4.9923 V 4.60 4.0024 Cr 6.00 5.6725 Mn 6.35 5.3926 Fe 7.72 7.6727 Co 4.92 4.9228 Ni 6.75 6.2539 Y 2.35 2.2458 Ce 2.05 1.5563 Eu 2.00 0.511uncertainties are typically 0.07 dex except for [Fe] where it is0.02 dex and for [Ce] where we estimate 0.15 dex and [Eu] with0.3 dex.2from Grevesse & Anders (1989)

IN Virginis is ≈62±12 ◦ and we adopt 60◦ for our Doppler-imaging analysis and emphasize that the given range is not anerror estimate but that all values in the given range are equallylikely.

3.5. Average spot temperature

Compare a line-depth ratio of a particular line pair in whichone line is temperature sensitive and the other not, and monitorthis line ratio over one rotational cycle of a spotted star, thenthe changing average hemispheric temperature should modu-late mainly the temperature-sensitive line but not the other, thusmodulating the easy measurable line-depth ratio. This was pio-neered by Gray & Johanson (1991), and an improved calibrationfor several spectral-line ratios in the 6160-Å region against ef-fective temperature (actually color) was derived by Gray (1994)and recently reviewed by Gray (1996).

Unfortunately, such a calibration is not as straightforward asone might hope, because the lines are rotationally broadened,blended, perturbed by velocity fields, differentially abundant,and differently saturated if of different strength. A recent studyof the influence of macroscopic velocity fields on line-depthratios by Stift & Strassmeier (1995) also showed that only if thetwo lines in question are of comparable strength and do not differradically in their broadening parameters, will the line-depth rationot depend on stellar rotation. All of this will eventually justallow an estimate of the (average) surface temperature, but isnevertheless an additional - and independent - constraint forDoppler imaging.

Figs. 4a-d show the observed line-ratio variations for twoline pairs and their calibration withB−V color. For IN Virginiswith Teff ≈ 4600 K we chose following line pairs in the6430-Å region: the V i line at 6413.509 Å (excitation poten-tial χlow = 1.35 eV) and the close blend Ni i 6414.581 (4.15 eV)

K.G. Strassmeier: Doppler imaging of stellar surface structure. III 541

Fig. 6. Combined Doppler image of IN Virginis for the observing epochMarch 1994. This map is a combination of six maps derived from threespectral lines, Ca i 6439 Å , Fe i 6430 Å, and Fe i 6421 Å; each onewith both the V R and the V I light curves as additional constraints.All individual maps were given equal weight for the average map.

+ Si i 6414.980 (5.87 eV), and Y i 6435.004 Å (0.07 eV) +V i 6435.158 (1.94 eV) and the Fe i line at 6436.411 Å(4.19 eV). Their variations are in phase with the broad-bandlight curve (shown as a dotted line in Figs. 4a and 4c) in thesense that larger line ratios occur when the light curve shows aminimum, i.e. when a spot is in view. The observed, full ampli-tudes are 0.21±0.05 and 0.73±0.09 for the two line-pair ratios,respectively. Their uncertainties are estimated from the wholerange of repeated measurements with both a Gaussian fit to theindividual profiles using appropriate IRAF routines and by sim-ply identifying the deepest point in the absorption profile.

The lower panels in Fig. 4 present the observations of thetwo line pairs in a set of 68 Morgan-Keenan standard stars ob-tained with the same telescope and instrumental set-up as forIN Vir. A second-order polynomial fit to these data yields thefollowing calibrations,

R1 = 1.96925− 5.05606(B − V ) + 3.52709(B − V )2R2 = 3.30620− 6.81295(B − V ) + 4.23639(B − V )2, (2)

where R1 means V I(NiI+SiI) and R2 the ratio(Y I+V I)FeI . Together

with the standard (B − V )-Teff relation of Bell & Gustafsson(1989) and the respective calibrations in Eq. (2) the observedline-ratio amplitudes of 0.21±0.05 and 0.73±0.09 imply tem-perature variations between phase ≈0.3 and 0.8 of 150±20 K(4400-4550 K) and 400±30 K (4350-4750 K) from the two lineratios, respectively. Obviously, the temperatures from both lineratios at phase 0.3 agree within their formal uncertainties butthe temperatures for phase 0.8 differ by 200 K.

Errors for the absolute temperatures are larger than thosefor the variations because of errors in our calibration in Eq. (2)

as well as in the (B − V )-Teff relation of Bell & Gustafsson(1989). Furthermore, by using Eq. (2) we implicitly assumedthe same log g for all our calibration stars (and IN Virginis),although there is some evidence that the temperature differencebetween spots and photosphere depends on gravity (Saar et al.1995). Altogether, we estimate the above relative temperaturevariations to be probably no better than ±50 K.

Another possibility to estimate the surface temperature is tomodel the broad-band color curves. The V − IC-color curveof IN Vir in Fig. 2b shows an average seasonal amplitudeof 0.050±0.007 mag and a maximum value for V − IC of1.22±0.01 mag at phase ≈0.2. The corresponding V − RCvalues are 0.025±0.007 and 0.65±0.01 mag1, respectively. Al-though part of this amplitude is due to differential limb darken-ing in the V and IC bandpasses, a light and color-curve fit withwavelength-dependent limb darkening and the model of Strass-meier & Bopp (1992) with two spotted regions yields a tempera-ture difference between photosphere and spots of 1000±200 K.

3.6. Chemical surface abundances

The equivalent widths of most metal lines in the red spectrumof IN Vir are larger by approximately 10-20 % when com-pared to HD 81410 - another RS CVn binary with a qualita-tively very similar spectrum (classified as K1III by Bidelman &MacConnell 1973), almost identical v sin i and a rotation periodof around 12 days. An average difference of about 10% is stillobvious when compared to the inactive star φ Ser, which is ofidentical M-K classification as IN Vir (K2-3IV). Differences ofthe line strengths are most noticeable for the iron lines, e.g.,Fe i 6392.538, 6393.602, 6408.016 as well as our one mappingline at 6421.349 Å, but also for the Ni i-Si i blend at 6414.8 andseveral vanadium lines. We interpret this as evidence that the sur-face abundances of IN Vir deviate from solar values. Therefore,we first need to obtain specific elemental abundances beforeattempting to map the surface temperature.

The determination of chemical abundances for stars of loweffective temperature is rather prone to blending by weak linesand thus requires detailed spectrum synthesis. Because of lim-ited computing time we synthesize only a relatively small wave-length portion (6416-6442 Å) but at high wavelength resolutionthat enables to utilize lines down to a limit of 3 mÅ. The upperpanel in Fig. 5 compares a rotationally unbroadened theoreti-cal spectrum with the observed IN Vir spectrum and identifiesmost line contributions. The lower panel in Fig. 5 presents theachieved fit with the new abundances listed in Table 4. Ourtheoretical spectra use pre-computed Kurucz (1993) model at-mospheres with a microturbulence of 2.0 km s−1, pre-specifiedchemical compositions, and a modified line list including im-proved transition probabilities. The applied synthesis code hasbeen written in Ada (Stift & Könighofer 1996) and is based onthe original Fortran code of Baschek et al. (1966). The code al-lows the synthesis of blends over a large wavelength range and

1 Note that for the Ca ii flux calibration in Sect.3.1 one has to use theJohnson colors transformed with the relations, e.g., given in Bessell(1979)

542 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

Fig. 7a–c. Observed and computedline profiles for Ca i 6439.075 Å (panela), Fe i 6430.852 Å (panel b) andFe i 6421.360 Å (panel c). The plussesare the observations and the full linesare the fits. The right column showsthe maps from the individual lines in apseudo-mercator projection. Note thatthe spectral lines are arranged fromtop to bottom according to decreasingequivalent width of the main mappingline and thus approximate their depthof formation.

includes the effects of micro- and macroturbulence, rotation,and pulsation if present.

For the purposes of this paper abundances are only neededfor the blends within our mapping lines and we will only focuson these elements. Before solving for a new set of abundancesfor IN Vir we perform a check on the atomic line data by fittingthe observed solar spectrum in the same wavelength region asfor IN Vir (6390-6455 Å) but with “known” abundances fromKurucz’s (1991) solar model. Then, the only remaining uncer-tainties in the synthesis of the solar spectrum are the transitionprobabilities (log gf ) for the individual spectral lines. Similarwork was already done for the wavelength region around theDoppler-imaging line Ca i 6439 in the G5III-IV FK Comae starHD 199178 (Strassmeier et al. 1997) and around the 6240-Å re-gion in the G8III-IV RS CVn binaryλ And (Donati et al. 1995).Recently, Linnell et al. (1996) presented a spectrum synthesisof the metallic-line A3m binary EE Peg in the same wavelengthregion as in this paper.

The second step includes a fit to IN Vir with effective tem-perature as the only parameter. Only the two model atmosphereswith 4500 K and 4750 K produce reasonable good fits while, atthe same moment, log g can be varied between 3.5 and 4.0 andstill reproduce the IN Vir spectrum. The “observed” spectrumis thereby always that spectrum that is closest to the light-curvemaximum (phase 0.174) and thus represents the least spottedphase. Our fits are therefore just for an average photosphericspectrum consisting of a convolution of the normal photosphericspectrum plus a (weak) spot spectrum. The spots’ influence onthe iron line strength, however, is very small and is neglectedin our abundance study (but not in the mapping). Temperature-sensitive lines like vanadium likely have a significant spot con-tribution, but this is also neglected in our synthesis approachbecause only weak vanadium lines are present. The obtainedphotospheric temperature is then mainly constrained by the rel-ative strength of the Fe i 6430 to the Fe ii 6431 lines and yieldsan effective temperature for IN Vir of 4600±70 K.

K.G. Strassmeier: Doppler imaging of stellar surface structure. III 543

Fig. 8. Observed and computed V RI light curves. The fits are fromCa i 6439 Å (full line), Fe i 6430 Å (dotted line) and Fe i 6421 Å (dashedline). The plusses are the simultaneous and contemporaneous APTobservations included in Fig. 2b. The arrows indicate the phases of thespectroscopic observations.

The gravity determination relies mostly on the pressure sen-sitive wings of the strong Ca i-6439 line. Unfortunately, thereare several blends in the wings of this line, e.g. Eu ii and Y i,that strengths and chemical abundances are not known a priori.Consequently, our log g determination is somewhat uncertainbut must be in the 3.5-4.0 range.

The remaining final step now is to reproduce the observedspectrum by adjusting the chemical abundances. A simple trial-and-error approach is sufficiently effective and leads to the fitin the lower panel of Fig. 5 and the abundances in Table 4. Wecaution, however, that these abundances are only approximativebecause just a small portion of the optical spectrum was usedto determine them, sometimes even just from a single line (e.g.europium). Nevertheless, we note that only lines from the heav-ier elements (above Z ≈ 14 = silicon) had to be adjusted to fitthe observed spectrum.

Beside the spectrum synthesis in the 6430-Å region we alsomeasured the equivalent width of the Li i 6708-Å line fromthe residual spectrum shown in Fig. 1e to 33±3 mÅ. Usingthe curves-of-growth published by Pallavicini et al.(1987) forTeff = 4500 and log g = 3.5, we find a logarithmic lithiumabundance of logn = 0.55, somewhat larger than the 0.3 valueobtained by Tagliaferri et al. (1994).

Table 5. Detected surface features1

Feature ` b < Teff > area2

(◦) (◦) (K) (%)polarappendage 1 260 >40 3800 . . .appendage 2 120 >50 4100 . . .polar spot (total) . . . . . . 3600 9.0equatorialspot 1 26 ≈0 4250 1.4spot 2 192 ≈0 4300 1.3spot 3 333 ≈0 4250 1.41measured off the average map in Fig. 62in % of the entire stellar sphere

4. Doppler imaging

4.1. The line-profile inversion code

As for previous papers in this series, all maps were generatedwith the Doppler-imaging code of Rice et al. (1989), originallydeveloped for use with chemical abundance inhomogeneitiesof Ap stars. For temperature mapping we use a more rigoroustreatment of the local line profile than presented in Rice et al.(1989) and also solve for the relative continuum light in twophotometric bandpasses (Rice 1994, Piskunov & Rice 1993).Local line profiles are now computed with the same opacitiesas in the ATLAS-9 code (Kurucz 1993).

In this paper we chose a Maximum-Entropy regularizationalthough the program also allows a Tikhonov reconstruction.A grid of nine model atmospheres with temperatures betweenTeff = 3500 and 5500 K in steps of 250 K and log g = 3.5 weretaken from the ATLAS-9 CDs (Kurucz 1993). We found thatlog g = 4.0 fits the wings of the line profiles also very nicelybut the entire profile fits seem to be overally better when usinga log g = 3.5 atmosphere and we adopted this gravity for thefinal maps.

For each model atmosphere local line profiles were com-puted with the abundances determined in Sect. 3.6 but also in-cluded trial inversions with strictly solar abundances for all ele-ments that, however, did not result in equally good fits and wererejected. The late spectral type of IN Virginis, combined withthe limited wavelength coverage of our spectra, is such that wecan make use of only three moderately unblended lines; Ca i6439.075, Fe i 6430.852, and Fe i 6421.360 Å with log gf val-ues of +0.47,−1.85, and−2.20 and lower excitation potentialsof 2.52 eV, 2.18 eV, and 2.28 eV, respectively. The upper panelin Fig. 5 indicates the amount of blending for each of the threemapping lines and we actually synthesize a total of 9, 12, and6 blends for the 6439, 6430, and 6421-line region, respectively.We emphasize that all of these blends are included in the inver-sion simultaneously but that the three wavelength regions aretreated separately.

Other lines with comparable profile deformations were theFe i lines at 6393.602, 6400.000 and 6400.314, 6408.016 and6411.647 Å. Unfortunately, all of these lines are heavily blended

544 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

Fig. 9a and b. Line variability of chromospheric activity indicators.Panel a shows three observations of the Ca ii H-emission line taken atthe labeled times. It demonstrates that the emission strength varies onan annual timescale as well as on a timescale proportional to the rotationperiod of the star. Panel b plots our five Hα observations as a functionof rotational phase. For comparison, a broadened and shifted spectrumof the inactive (single) star φ Ser is plotted along with every IN Virspectrum. Note that this spectrum has been cut off below intensity of0.8 for better display.

with up to even 20 weak lines that, more importantly, do notshow up at solar temperature and have rather uncertain transitionprobabilities. Therefore, we chose not to use these lines formapping.

4.2. Results

The combined map from three spectral lines and three photo-metric bandpasses is shown in Fig. 6. The observed and com-puted line profiles are plotted in Fig. 7 along with the individualDoppler maps, the observed and computed light curves are com-pared in Fig. 8. We emphasize that our maps are based on ten

spectra taken on 13 consecutive nights in March 1994, i.e. withinone and a half stellar rotations (see Table 1).

The “bumps” in the absorption line profiles of IN Vir are eas-ily detectable despite the relatively small v sin i of the star. Thestrongest bump reaches an amplitude of about 5% of the contin-uum when measured in the line center and is thus comparablewith the bumps seen in other, broader-lined, active stars, e.g. inthe RS CVn system UZ Librae (Strassmeier 1996 = paper I) or inthe weak-lined T Tauri star V410 Tau (Rice & Strassmeier 1996= paper II) and others. Visual inspection of the observed lineprofiles reveal two bumps crossing the central stellar meridianat phases of around 0.25-0.30 and 0.60, respectively.

The map in Fig. 6 is dominated by a polar spot and an ap-pendage (or high-latitude spot) with a temperature differenceof 800-1000 K cooler than the photospheric temperature of4600 K and centered at a longitude of around 260◦. A sec-ond appendage of smaller contrast is present at a longitude ofaround 120◦. Furthermore, we see some detailed structure alongthe stellar equator, however, not all of it is likely real. Features atthe stellar equator can appear somewhat elongated in latitudinaldirection when only a too coarse a grid of line profiles is avail-able, and is an artifact. Our phase coverage is quite good thoughand is shown for comparison in the light curves in Fig. 8. Verysmall and/or very weak equatorial features that do not appear inthe maps from all three lines are judged to be spurious and areautomatically suppressed in the combined map although theirinclusion leads to a better fit of a particular line profile.

Despite the known elongation and resolution problem forlow-latitude features we may still identify three consistentlycool spots at longitudes of 30◦, 190◦, and 330◦ and at latitudeswithin±30◦ of the equator (Table 5). Additionally, there appearthree areas with temperatures above the photospheric temper-ature, but the only one judged significant is at a longitude of260◦ and a latitude of +15◦ with 150 K above the photospherictemperature. The line profiles at that particular phase show noevidence for systematic errors like, e.g., continuum displace-ment. This warm spot shows up with high enough contrast inall three maps and should be considered real. The other twoareas are just between 50-100 K warmer than the photosphereand are within the estimated external uncertainties of our spec-tra. In two previous images of the weak T Tauri star V410 Tau(paper II and Strassmeier et al. 1994), we have found severalhot spots with ∆T ≥500 K from the photospheric absorptionspectrum and suggested that they are caused by mass accretionfrom left-over circumstellar material. Their spectral signature,however, were much more pronounced compared to the warmareas on IN Vir.

5. Hα and Ca II line-profile variations

Fig. 9a shows three Ca ii H-line profiles of IN Virginis. Twoof them were taken in 1995 at JD 2,449,774 (φ=0.922) and2,449,781 (φ=0.773), separated by approximately one rotationperiod, and demonstrate that there can be significant variationson a short time scale. The third observation in Fig. 9a is from1996 at JD 2,450,103 (φ=0.515), separated by approximately

K.G. Strassmeier: Doppler imaging of stellar surface structure. III 545

Fig. 10. Residual Hα line profiles after subtraction of an inactive refer-ence star. The vertical, dotted line marks the Hα rest wavelength. Notethat the profile asymmetry persists throughout all rotational phases andconsequently suggests a cause that is not modulated by stellar rotation.

one year from the other two, and yet shows even stronger emis-sion than before. So we conclude that there must be also long-term variations.

Fig. 9b shows five Hα spectra as a function of rotationalphase taken in 1995, one year after our Doppler image. Obvi-ously, IN Vir exhibits a rather abnormal Hα line profile but notunexpected for a very active RS CVn binary. The profile shapeconsists of a blue-shifted emission and a narrow absorptioncomponent at the Hα rest wavelength. The absorption strengthchanges by a factor of three from phase 0.299 to phase 0.650while the emission component apparently remains more or lessconstant. We note that the precision of our rotation period allowsthe Hαphase coherence to be not better than 0.13 phases per yearbut, nevertheless, the minimum Hα emission in 1995 occuredat the same phase where we saw the light-curve maximum, i.e.the spot minimum, in 1994 (≈0.2-0.3) and the maximum Hαemission occured very near the light-curve minimum, i.e. thespot maximum. This might indicate that at least some of theprofile flux in Hα is modulated with the rotational period andcould be due to plages.

In spite of the large variations of the absorption component,no wavelength-dependent distortions or transients seem imme-diately obvious from the five profiles in Fig. 9b. To search formore subtle distortions due to discrete, chromospheric plageswe first determined residual Hα spectra by subtracting thebroadened and shifted spectrum of the K2-3IV star φ Ser. Itsspectral classification was suggested by Fekel (1996) from red-wavelength spectra and theB−V color (see Sect. 3.4). Stars ofthis M-K classification are rare and are prone to chromosphericactivity as soon as they rotate above, say, 5 km s−1. The smallv sin i of φ Ser of 1-2 km s−1, however, suggests it to be aninactive star and we therefore expect no or only insignificantchromospheric emission compared to IN Vir.

Fig. 10 shows the residual Hαprofiles of IN Vir at the five ro-tational phases. It is immediately obvious that the profile asym-metry persists throughout all five rotational phases, with an aver-age wavelength offset between line bisector and rest wavelengthof -0.2 Å (≈-10 km s−1). This suggests a cause that is not mod-ulated by stellar rotation and favors an interpretation with an(inhomogeneous) stellar wind model.

The similarity of the shape of the Hα line profile inIN Virginis to profiles seen in other active stars, e.g. inHU Virginis (Strassmeier 1994) or in HD 32918 (Vilhu et al.1991) suggest a common cause. While HD 32918 is a singleFK Comae-type star, HU Virginis (HD 106225) is a K0IV starin a single-lined spectroscopic binary with a synchronized rota-tion period of approximately 10 days, and thus in many respectsvery similar to IN Virginis. In the case of HU Vir the Hα profilelikely results from a combination of a locally enhanced velocityfield associated with two bright plage-like features 180◦ apart.Strassmeier (1994) suggested a coronal loop connecting thesetwo plages and a siphon-type mass flow within it. A similarscenario might be also the cause for the chromospheric linevariability of IN Virginis, and the observed warm spot and theadjacent polar appendage in our Doppler image could be in-terpreted as the footpoints of a magnetic loop. However, ourcurrent Hα spectra have insufficient time and phase resolutionto allow detailed phase-dependent profile modeling.

6. Summary

In this paper we presented the first Doppler images ofIN Virginis, a moderately rapid rotating K2-3 subgiant in a spec-troscopic binary system. Our main results can be summarizedas follows:

1. IN Virginis is shown to be a single-lined spectroscopic bi-nary with an orbital period of 8.1985±0.0009 days. Ournew photometric period of 8.232±0.003 days indicates asynchronized rotator with respect to the orbital motion.

2. Several observational criteria agree best with a K2-3 spectraltype and a subgiant luminosity classification.

3. The relatively small equatorial rotational velocity of 28km s−1 (v sin i=24.0 km s−1, i ≈60◦) is obviously suffi-cient for a K2-3 star to produce very strong chromosphericradiative losses.

4. From a spectrum synthesis we found an overabundance ofheavy elements compared to the Sun (e.g. 0.05 dex for iron)but roughly solar abundance for some lighter elements. Thelow-to-moderate (logarithmic) lithium abundance of 0.55 istypical for evolved RS CVn stars.

5. The overall surface temperature and their respective rota-tionally modulated variation in 1994 were determined fromthree different techniques and yielded consistent results of1000 K for the coolest, and thus dominating, features.

6. The morphology of the Doppler map of IN Vir is very sim-ilar to its “cousin” HU Virginis (K0IV,P = 10 days) andis dominated by a cool polar spot with two appendages, alarger and a smaller one. Additionally, three equatorial spotswith an average temperature difference of 400 K are seen.

546 K.G. Strassmeier: Doppler imaging of stellar surface structure. III

A warm equatorial spot with ∆T ≈-150 K has been alsorecovered from all mapping lines and is likely real.

7. From three Ca ii H&K spectra taken in 1995 and in 1996we found emission-line strengths that varied by up to 20%on time scales of approximately one rotation period and oneyear.

8. We also found a complex Hα profile consisting of a variable,narrow absorption component at the Hα rest wavelengthand a constantly blue-shifted emission component. Thesevariations are likely to be caused by a combination of rota-tionally modulated chromospheric emission due to plages orpossibly flares and a stellar wind of the order of 10 km s−1.Further studies with higher time and phase resolution areneeded, however, to uniquely determine their cause.

Acknowledgements. It is a great pleasure to thank Dr. John Rice for acritical reading of the manuscript and many fruitful discussions con-cerning Doppler imaging. KGS is very grateful to the Austrian Fondzur Förderung der wissenschaftlichen Forschung (FWF) for supportunder grant S7301-AST and S7302-AST and the Austrian Academyof Sciences for grant OWF-P40.

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