ASTRONOMY AND ASTROPHYSICS. Doppler imaging of stellar surface structure

Transcription

1 Astron. Astrophys. 336, (1998) Doppler imaging of stellar surface structure VIII. The effectively single and rapidly-rotating G8-giant HD = CM Camelopardalis ASTRONOMY AND ASTROPHYSICS K.G. Strassmeier 1, J. Bartus 2, Zs. Kővári 2, M. Weber 1, and A. Washüttl 1 1 Institut für Astronomie, Universität Wien, Türkenschanzstrasse 17, A-1180 Wien, Austria (strassmeier@astro.univie.ac.at; weber@astro.univie.ac.at; wasi@venus.astro.univie.ac.at) 2 Konkoly Observatory, Hungarian Academy of Sciences, H-1525 Budapest, Hungary (bartus@buda.konkoly.hu; kovari@buda.konkoly.hu) Received 30 March 1998 / Accepted 14 May 1998 Abstract. We present first Doppler images of HD from observations in 1994, 1995, 1996 and 1997, and find evidence for a vanishing polar spot in accordance with the system s longterm brightness increase. Several small spots with T 500 K appear also at low latitudes. Our cross-correlation maps indicate a latitude-dependent phase-shift pattern between annual maps. New and continuous BVRI photometry from 1996 to 1998 is presented and suggest a photometric period of ±0.004 days, that we interpret to be the stellar rotation period. Additional optical spectroscopy and the Hipparcos data are used to obtain absolute stellar parameters for HD A comparison with evolutionary tracks and the assumption of angularmomentum and magnetic-flux conservation suggest that the main-sequence progenitor was a very rapidly-rotating Bp star with a several kilogauß magnetic field. We also examine the Hα line profiles in this star and find some evidence that its equivalent width is modulated with the stellar rotation period in phase with the photospheric starspots. Our radial velocities indicate that HD is likely a long-period ( 10 yrs) spectroscopic binary and a preliminary orbit is presented. We emphasize that HD is an interesting target for studies of evolutionary angular-momentum loss because it is effectively single, significantly evolved but still rapidly rotating. Key words: stars: activity stars: imaging stars: individual: HD stars: late-type starspots 1. Introduction HD (V=7 ṃ 0, G8III-II, P =16 days, α =07 h 04 m 15 ṣ 3, δ= , ) is one of the few examples of an effectively single star that somehow has maintained its angular momentum through its evolution off the main sequence. It was previously thought to be a single main-sequence star of spectral type K2 (Fleming et al. 1989) but that was revised to K0III by Visiting Astronomer, Kitt Peak National Observatory, operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation Fekel & Balachandran (1994) from high-resolution red wavelength spectra. Bidelman (1994) found it with strong Ca ii H&K emission lines on the Michigan objective-prism survey plates at Kitt Peak which were confirmed by Strassmeier (1994) from high-resolution spectra with the Coudé feed telescope at Kitt Peak. The star also shows strong x-ray emission (Fleming et al. 1989, Stocke et al. 1991) and too large a lithium abundance for a normal late-type giant (Fekel & Balachandran 1994). Its brightness is modulated with a period of approximately 16 days (Henry et al. 1995b) and it has a projected rotational velocity of v sin i 46 km s 1 (Fekel 1997). It has recently received the variable star designation CM Cam (Kazarovets & Samus 1997). Besides being magnetically active and thus an interesting star, its single status raises the question how an evolved star that is not a member in a close binary system, can preserve its angular momentum throughout the expansion phase due to the termination of hydrogen core burning. There seem to be two roads to an answers. Either the star is not single or the proposed dynamo saturation, thought to account for the high number of ultra-rapidly rotating stars in young open clusters (e.g. Barnes & Sofia 1996), does also apply for post main-sequence stars. The first who concluded that HD is (apparently) single was Fleming et al. (1989) from optical observations following the Einstein medium sensitivity survey, and was later confirmed by Fekel & Balachandran (1994) and Henry et al. (1995b) from eight radial-velocity observations between 1991 November and 1993 April. Recently, in his list of rotational velocities of late-type stars, Fekel (1997) lists it to be a suspected SB1 on the grounds of annually inconsistent radial velocities. On the second possible avenue, Solanki et al. (1997) have shown that a decreased angular momentum loss induced by a stellar wind along predominantly polar magnetic field lines of a pre-main-sequence star would have the equivalent effect on the stellar rotation than a field saturation by the dynamo itself and could thus also maintain the star s rapid rotation until the ZAMS is reached. However, it is not clear whether this picture would also apply to post-main-sequence evolution since HD is at least a class III giant but, if possible and of correct magni-

2 588 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII tude, this mechanism would predict long-lived polar spots on evolved and rapidly rotating giants. Fortunately, the phenomena of dynamo saturation and fields concentrated in polar spots can not act at the same time and, more or less, exclude each other. It is one of the goals in the present series of papers to find observational evidence for or against polar starspots by means of Doppler imaging. Our observations are described in Sect. 2, Sect. 3 summarizes our results from seven years of photometric monitoring, Sect. 4 presents 66 radial velocities that show the star to be a long-period spectroscopic binary and then, in Sect. 5, we derive Doppler images from five different spectral-line regions and for four consecutive years along with a determination of the fundamental stellar parameters of the HD system. Sect. 6 compares chromospheric Hα line profiles from 1996 and 1997 with the photospheric activity in these years and, finally, Sect. 7 summarizes our conclusions. 2. Observations 2.1. Spectroscopy All spectroscopic observations in this paper were obtained with the Coudé feed telescope at Kitt Peak National Observatory (KPNO) during five runs in March 1994, February March 1995, January 1996, April 1997, and January The 1994, 1995 and 1998 data were obtained with a TI CCD (TI-5 chip, 15µ pixels) with grating A, camera 5, and the long collimator resulting in a resolving power of 38,000 at 6420 Å. For the 1996 and 1997 spectra we employed the larger CCD (Ford F3KB chip, 15µ pixels) with an otherwise identical spectrograph set-up but centered at 6500 Å. The latter chip allows for a full 300-Å wavelength field but at the somewhat lower instrumental resolution of 32,000. Table 1 is a summary of the spectroscopic observations. Plots of representative spectra are shown later in Fig. 5. All data were reduced with IRAF and consisted of bias subtraction, flat fielding and optimized aperture extraction. Frequent wavelength comparison spectra and spectra of bright radial-velocity standards were obtained at least once during each night to ensure an accurate wavelength calibration. Radial velocities of HD were then derived from nightly cross correlations with the IAU velocity standards 16 Vir (K0.5III, v r = km s 1 ), β Gem (K0III, v r = 3.23 km s 1 )or α Tau (K5III, v r =54.10 km s 1 ) and IRAF s fxcor routine. The results are listed in Table 1 along with the errors from a Gaussian fit to the cross correlation peak (σ vr ). The analog-to-digital units in the continuum at 6500 Å correspond to signal-to-noise ratios of 200:1. Integration time was either 3000 or 3600 sec depending upon seeing conditions. Twenty flat-field exposures with a tungsten reference lamp were taken at the beginning of the night and again at the end of the night. These fourty flat fields were co-added and used to remove the pixel-to-pixel variations in the stellar spectra. Neither the TI CCD nor the F3KB CCD show obvious signs of fringing near Å and no attempts were made to correct for it other than the standard flat-field division. Continuum fitting with a Table 1. Radial velocities and observing log HJD Phase v r σ vr λ c (244+/24+) (Eq. 1) (km s 1 ) (km s 1 ) (Å) 1994: : : : :

3 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 589 Fig. 1. Long-term V-band observations of HD from 1992 through Note the increase of the average brightness since the discovery of the light variability and the flattening of this trend in around The individual observing seasons referred to in Table 2 are indicated by the letter S and a number. Also shown are the times of our Doppler-imaging observations (bars) at Kitt Peak National Observatory in the years 1994, 1995, 1996, and 1997 (marked KPNO plus the year). very low-order polynomial was sufficient to find a satisfactory continuum solution Photometry Throughout the years 1996 to 1998, continuous V(RI) c photometry has been obtained with Wolfgang-Amadeus, the 0.75m Vienna Observatory Twin Automatic Photoelectric Telescope at Fairborn Observatory in southern Arizona (WA-APT, Strassmeier et al. 1997b). BV data for the season 1995/96 were kindly made available by G. Henry at Tennessee State University prior to publication (Henry 1997). Altogether, 597 new VI measures for 1997/98, 118 VRI points for 1996/97, and 20 VRI and 92 BV measures for 1995/96 were obtained, each the mean of three readings of the variable and four readings of the comparison star. Johnson BV photometry prior to 1995 was taken from Henry et al. (1995b), whose data were gathered with the 0.4m Vanderbilt/TSU robotic telescope also at Fairborn Observatory. All V- band data are plotted in Fig. 1. Note that the WA-APT data were transformed to the Johnson-Cousins V(RI) c system and used HD (V=7 ṃ 51, B-V=1 ṃ 03, V-I=0 ṃ 98; ESA 1997) and HD as the comparison and check star, respectively while the Vanderbilt/TSU APT data were transformed to the Johnson UBV system with the same comparison star but HD as the check star. The standard error of a nightly mean from the overall seasonal mean was for both telescopes 0 ṃ 004 in B and V(0 ṃ 0025 for the WA-APT since Oct. 1997) and 0 ṃ 006 in R c and I c. Fig. 2. Periodogram (upper panel) from the combined and prewhitened V-band data of HD The lower panel shows the window function. A period of days fits the data best and is consistent with the measured v sin i and the giant luminosity classification. 3. Results from photometric monitoring 3.1. The long-term light-curve variability Fig. 1 shows all differential V-band photometry of HD since the discovery of its light variability in 1992 by Henry et al. (1995b). The average light level increased by 0 ṃ 08 until 1996 and the rotational-modulation amplitude reached a maximum of 0 ṃ 05 when the system appeared brightest around 1996/97. The latest data from 1997/98 show now a stagnation of the long-term brightness increase and possibly even indicate a decrease. Not plotted in Fig. 1 are the check minus comparison star magnitudes but visual inspection showed them to be of constant value to within the expected external errors. Thus, the long-term brightness variation is real and most likely the sign of a starspot cycle probably similar to the Sun s 11-year cycle. Previous longterm photometry of spotted and evolved stars (e.g. Strassmeier et al. 1997a, Olàh et al. 1997, Cutispoto 1995, Rodonó etal. 1995, Henry et al. 1995a) indicate either more or less erratic variations or (pseudo)periodicities 1 of the order of years. However, the interpretation of such variations is severely hampered because most of the targets are components of relatively close RS CVn binaries while HD is an effectively single star. In case the long-term brightness variation in Fig. 1 turns out to be periodic and the data in season 1992 (S1) represent the overall minimum then we may expect a long-term period near 11 years The rotational period Since HD is effectively a single star we have no reference clock like the orbital period in close binaries and thus rely on the photometric variations to determine the rotational period. Our first attempt was to find the best seasonal periods by using 1 Because usually only one cycle or less has been covered.

4 590 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Table 2. Seasonal photometric periods Set Year Average V Max. V Period brightness amplitude (mag) (mag) (days) S S ±0.04 S3a (14.8±0.7) S3b ±0.08 S : 0.025:... S ±0.05 S ±0.2 S ±0.042 All ±0.005 the seasonal periods. To take into account the long-term trend seen in Fig. 1 we first prewhitened the data with two frequencies near ( 2800 days) but different amplitudes in order to eliminate the long-term trend in the data and then searched for the best-fitting period and found ±0.004 days (Fig. 2). All spectroscopic and photometric data in this paper were then phased with the ephemeris 2, 448, ± E (1) where the zero point is just an arbitrary point in time The short-term light and color variations Fig. 3. a The V observations during the observing season 1997/98. b The combined V and V-I magnitudes folded on the photometric period. The full V and V-I amplitudes were 0 ṃ 030 and 0 ṃ 010, respectively. The line is a fit with a two-spot model to obtain an estimate of the spotted area and average surface temperature. a Fortran program that performs a multiple frequency search through minimization of the residuals with a Fourier option (Kollath 1990). Quoted errors are estimated from the width of the frequency peak at χ 2 min + χ2 min /(n m) where n is the number of data points and m =4the number of free parameters. Table 2 lists the best results for the data sets as indicated in Fig. 1. Note that season S3 was split into two parts due to a rapid increase of the light curve amplitude within approximately 20 days; one prior to 2,449,280 (S3a) and one therafter (S3b). The cause of this amplitude increase from 0 ṃ 02 to 0 ṃ 053 in V is likely caused by a redistribution of starspots but the phenomenon has not repeated in our data. Since we did not have sufficient photometry to compute a period for the 1995 observing season a season with spectroscopic data for Doppler imaging we decided not to use the seasonal periods for phasing but rather use the period from the combined photometry from Such a period likely represents an average rotation period and is probably even better suited for intercomparison of annual Doppler images than are The Wolfgang-Amadeus APT photometry from 1997 October through 1998 January (Fig. 3a) is used to search for shortterm variations of the light-curve shape due to intrinsic variations of the spot distribution. The folded seasonal V magnitudes and V-I colors (Fig. 3b) show a peak-to-peak amplitude of 0 ṃ 029±0 ṃ 002 and 0 ṃ 008±0 ṃ 002, respectively and both curves have their minima at around phase 0. p 35 and maxima at around phase 0. p 95. The high quality of the data allows the application of a geometric starspot model to infer starspot positions and temperatures and we adopt the maximum V and I magnitudes observed so far, i.e. V=6 ṃ 935 and V-I=0 ṃ 95 during 1996/97, as the unspotted magnitudes. Only the spot positions and sizes are treated as free parameters of the Levenberg- Marquardt method used here to minimize the χ 2 for a given bandpass (see, e.g. Kővári & Bartus 1997). The spot temperature is then obtained by simultaneously fitting the V-I color curve. As can be seen in the lower panel in Fig. 3 the observed light and color curves of HD deviate significantly from a sinusoid and our spot-modelling code finds the best fit with two, cool, circular spots with T = 500 K, at longitudes of 121 and 271, latitudes of +65 and +56, and radii of 15.3 and 6.0, respectively. The combined spotted area amounts to 2.0 % of the total sphere. Errors in longitude and area are within 1 2%, while errors in latitude are certainly model dependent and can amount to 10% or even more. The error of the relative temperature, 500±300 K, is also comparably large, mostly due to the small V-I amplitude of just 0 ṃ 008 and the, therefore, barely discernable modulation due to wavelength dependent limb darking.

5 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 591 Table 4. Astrophysical data for HD Fig. 4. Radial velocities of HD obtained with the KPNO Coudé feed telescope in the years The plusses are from this paper and the crosses from Fekel (1998). The line is the preliminary orbit from Table 3 and T 0 indicates the time of periastron passage. Table 3. Preliminary orbital elements for HD Orbital element Value P (days) (adopted) T 0 (HJD) 2,449,572.0 γ (km s 1 ) 18.7±0.3 K 1 (km s 1 ) 7.0±0.3 e 0.60±0.07 ω 272 ±10 a 1 sin i (km) 290± f (m) (M ) 0.069±0.021 Standard error of an observation of unit weight (km s 1 ) 1.7 The rms residual of the fit is below ±5 mmag while the rms of a single data point is on average 2.5 mmag. Although formally larger than the observational error, considering that we combined observations from 90 continuous nights, i.e. more than five stellar rotations, it indicates a relatively stable light curve in 1997/ Radial velocities and a preliminary orbit Fig. 4 plots all available radial velocity data for HD and reveals long-term variations consistent with a wide but rather eccentric spectroscopic binary. Included in the figure are the data from Table 1 and additional 15 velocities from Fekel (1998), partly already mentioned in Henry et al. (1995b), that were also taken with the KPNO Coudé feed telescope plus the TI CCD. The probable errors are between km s 1 for the TI CCD data and km s 1 for the F3KB-CCD data (Table 1). The cause for the different uncertainties is the three times larger wavelength range of the F3KB CCD and the resulting narrower cross-correlation function. Note that significantly better radial velocities are hard to achieve because of the relatively large line broadening and the variable line profiles due to spots. Altogether, 66 radial velocities are used to compute a preliminary orbit with the help of a modified version of the differentialcorrection program of Barker et al. (1967). The orbital period is estimated by eye to be 10 yrs based on a systemic velocity of around 19 km s 1 (the dotted line in Fig. 4) and a time of pe- Parameter Value Classification G8±0.5IIIa-IIb Distance (Hipparcos) 275±45 pc Luminosity L log g 2.5±0.2 T eff 4950±50 K (B-V) Hipparcos 0 ṃ 943±0 ṃ 007 (V-I) Hipparcos 0 ṃ 93±0 ṃ 01 v sin i 47.0±1.0 km s 1 Inclination i 60 ±10 Rotation period ±0.005 days Minimum radius R min 14.9±0.4 R Most probable radius R R Micro turbulence ξ 1.0 km s 1 Macro turbulence ζ R = ζ T 3.0 km s 1 Chemical abundances solar riastron passage in late 1994, and remains fixed throughout the iterative solution for the orbital elements. The formally best solution gives a standard error of an observation of unit weight of 1.7 km s 1, thus comparable to our observational uncertainties, but the O-C residuals for the eight velocities from are systematically too high (by km s 1 ). Thus, we emphasize that our orbit is just preliminary and based on a rough estimate of the period. The elements are given in Table 3 and the computed velocity curve is plotted in Fig. 4 along with the observations. 5. Doppler imaging of HD The line-profile inversion code TempMap Our Doppler-imaging code is based on the Ap-star code by Rice et al. (1989) and Rice (1991). Its late-type star variant has been described and tested in previous papers of this series (e.g. Rice & Strassmeier 1998, Strassmeier & Rice 1998) and we refer the reader to these papers. Briefly, our approach includes a full spectrum synthesis via a solution of the equation of transfer through a set of Kurucz (1993) model atmospheres with 72 depth points and for effective temperatures between 5750 and 3500 K in each of the observed wavelength regions at all limb angles. Simultaneous inversion of up to twenty lines as well as two photometric bandpasses using either a maximum-entropy or a Tikhonov regularisation is possible. For this paper we chose maximum entropy. All computations for HD were either performed on a DEC Alpha 500 workstation in Vienna or on a Sun Ultra-2 at Konkoly Observatory and required on average CPU-minutes for one run with 9 blends and 15 iterations Astrophysical parameters for the HD system The parallax measured by Hipparcos (ESA 1997) results in a distance of 275±45 pc and, with a maximum V magnitude of 6 ṃ 935±0 ṃ 005 in 1996/97, in an absolute magnitude of M V = 0 ṃ 26±0 ṃ 34 (interstellar extinction is assumed to be negligible

6 592 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Fig. 5a d. Representative spectra of HD for several wavelengths of interest (thick lines). a the singly ionized calcium H and K lines, b Balmer Hα, c the Li i 6708-Å line region and, d the 6420-Å region with the photospheric lines selected for Doppler imaging. The thin lines are spectra of MK-standard stars; o Vir (G8IIIa) in panel b and d, and 16 Vir (K0.5III) in c. at δ = +75 ). This clearly confirms the giant luminosity classification already suggested from the H&K emission-line reversals (Strassmeier 1994, see also Fig. 5a) and from the combination of rotation period and line broadening (Fekel & Balachandran 1994). The relevant astrophysical data of HD are summarized in Table 4. Our Doppler-imaging procedure allows to redetermine the equatorial rotational velocity with better accuracy than with any other method because one takes into account all line blends within the broadened stellar line profile during the disk integration as well as the line deformations due to spots and a misfit from a wrong v eq shows up as an excessively dark or bright band at the corotating latitude. Zeeman broadening, however, is neglected. Our best value for HD is v sin i =47.0±1.0 km s 1 in very good agreement with the recent measurement of 46.5±2 3 km s 1 by Fekel (1997). Together with the photometric period this results in a minimum stellar radius of 14.9±0.4 R. With v sin i being fixed we solve for the best inclination by recomputing a series of maps with inclinations between 20 and 90. A plot of the sum of the squares of the residuals from all profiles and the photometry versus inclination, along with a consistency check of the computed maps, then yielded the most probable inclination of i =60 ±10 and thus the most probable radius of R. Note that the ±- values are in this case not error bars but merely give the range within each value is equally likely. The Hipparcos B-V color of 0 ṃ 943±0 ṃ 007 would be consistent with a G7.5III giant with T eff of 4970 K, M V =+0 ṃ 7, and R 9 10 R or 12.5 R according to the tables of Gray (1992) or Schmidt-Kaler (1982), respectively. The effective temperature from the bolometric brightness radius relation log T eff = 1 2 (log R/R +0.2M bol 8.47) (2) is K (adopting B.C.= 0.33 from Flower (1996), M V = 0 ṃ 26 from the parallax, and the most probable radius from above). The maximum temperature from Eq. (2) is then 5080 K in case the minimum radius is inserted, while Flower (1996) lists a formal value of 4955 K for B-V=0 ṃ 943. A comparison of all these values strongly indicate that HD is, first, intrinsically brighter than a G7.5III star by almost a magnitude and has a luminosity of L (on the M bol, =4 ṃ 64 scale; Schmidt-Kaler 1982), second, has a 20 50% larger minimum radius than a G7.5 giant and, third, is slightly cooler. We suggest that a G8IIIa-IIb classification (following the notations of Keenan & McNeil 1989) is more appropriate and also agrees with the fact that log g=2.5 atmospheres produce a significantly better fit to the photospheric absorption line profiles than log g=3.0 atmospheres. The latter gravity would also require an overabundance for Fe and Ca of 0.2 dex to match the observed line strength. Furthermore, a single blue high-resolution spectrum shows a strong Sr ii 4077-Å line typically indicative of a bright giant spectrum (Gray & Garrison 1989). A straight-

7 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 593 forward comparison of the position of HD in the H-R diagram with the evolutionary tracks of Schaller et al. (1992) for solar metallicity suggests a mass within 3.1±0.1 M. With the primary s mass fixed, we may use the preliminary orbital elements from Table 3 to estimate fundamental stellar parameters for the secondary star. If we furthermore assume that the rotational axis of the primary is perpendicular to the orbital plane, we may also adopt the inclination angle of 60 that is obtained from the Doppler imaging as the orbital inclination. The mass function then implies a secondary mass of 1.3 M and M sec /M pri 0.4. This mass is consistent with either a F7V, F2III, or F9III star according to the tables of Gray (1992). Since the primary is G8III-II and relatively young (see next paragraph) it is likely that the secondary had not enough time yet to significantly leave the main sequence and we adopt F7V for its spectral classification but emphasize again that the secondary s parameters are based on a preliminary orbit. The mass ratio and the approximate a 1 sin i from Table 3 combine then to a = a 1 + a km (i.e. 7.7 AU or 100 R pri ). From a distance of 275 pc this would be at most in the tangential plane and hardly detectable. However, a spectrum at ultraviolet wavelengths might show the secondary s continuum. With the new parallax and proper motions from Hipparcos and our revised average radial velocity, we determine the (U,V,W) space-motion components of HD relative to the Sun in a right-handed coordinate system to be (+4.2±2.5, 15.1±0.9, 15.6±1.5) km s 1. The error in U is mostly due to the uncertainty of the systemic radial velocity given in Table 3. According to the (U,V)-plane classifications of Eggen (1989) these space motions are consistent with the young disk population. Note, however, that HD appears 125±20 pc above the galactic plane. The relatively young age is also consistent with the existence of a moderately strong Li i 6707 Å line as shown in Fig. 5c. After subtraction of a velocity shifted and broadened spectrum of the inactive K0.5III star 16 Vir we measure an equivalent width for Li i of 120±10 må, compared to 230±10 må for the nearby Ca i 6717-Å line. The appropriate non-lte curve of growth from Pavlenko & Magazzú (1996) converts this to an abundance of log n(li)=2.0 (on the usual log n(h)=12.00 scale) while their LTE version results in a slightly larger abundance. Our full spectrum synthesis of the Å region with solar log gf values gives the best fit with a Li abundance of log n(li)=2.0 with an estimated error of ±0.1, in excellent agreement with the curves-of-growth method but only in fair agreement with the value of 1.5 obtained by Fekel & Balachandran (1994) who adopted T eff =4800 K and log g=3.0. Finally, we also need to know the values for micro- (ξ) and macroturbulence (ζ) but, since HD is a rapidly rotating star, their effects will be of minor nature. We simply adopt the typical values for a late G giant as given in Gray (1992), i.e. ξ=1.0 km s 1 and ζ=3.0 km s 1. Several test inversions with microturbulences between 0.5 and 2.2 km s 1 indicated lowest χ 2 and the most consistent maps when using above values. Within the known shortcomings of our LTE treatment, the assumption of solar abundances as given by Grevesse & Anders (1991), and the assumption of equal radial and tangential components for ζ, a value for ξ as large as 2.0 km s 1 must be nevertheless excluded. From the test inversions we estimate the internal error in ξ to be ±0.2 km s Atomic parameters The basic atomic parameters for our mapping lines were taken from the Kurucz-(1993) linelist but were adjusted by fitting synthetic profiles to a spectrum of the Sun. Several log gf values as well as wavelengths had to be changed to obtain a good fit. For the actual numbers we refer to previous papers in this series (e.g. Strassmeier & Rice 1998 and Strassmeier et al. 1997c) and also to Johns-Krull & Hatzes (1997) for the 6400-Å line. The latter authors noted that they had trouble fitting the Fe i 6411-Å line due to unknown blends and omitted this line from their analysis of the T Tauri star Sz 68. For the present paper we re-examined this wavelength region and obtained a reasonable good fit to the solar line when using altogether 7 blends including two Ti i lines and one V i line. A plot of this wavelength region for the solar Fe i 6411 Å line has already been shown in Strassmeier (1996). Fig. 5d shows a representative spectrum of the entire Å region of HD with the five main Doppler-imaging lines marked: Ca i Å(W λ =290 må, n=8), Fe i Å (W λ =280 må, n=7), Fe i Å (W λ =220 må, n=8), Fe i Å (W λ =205 må, n=8), and Fe i Å (combined W λ =335 må, n=6), where W λ is the measured equivalent width for the main mapping line and n the total number of blends included in the local-line profile computation. An overplot with the G8IIIa M-K standard star o Vir (v sin i 2 km s 1 ) visualizes the expected amount of blending. Note that the 6400-Å line is actually a very close blend of two, almost equally strong Fe lines but of quite different excitation potential. We emphasize that all of the blends are included in the inversion simultaneously, but that the five wavelength regions are treated separately Images for dataset April 1997 For this season 12 spectra and 20 VRI light-curve points were available. The spectroscopy was obtained within 14 consecutive nights while the photometry was combined from altogether 32 nights centered around the spectroscopy. Fig. 6a-e show the Doppler images from all five lines plus the observations and respective fits. The figure allows a visual comparison of the line-to-line consistency of the reconstructed surface temperature along with the unavoidable differences from real spectra of limited S/N and basically unknown external errors. HD had several significant spots in 1997 with T 500 K and centered at longitudes of 10, 180, 240, and possibly also near 330. The latter spot covers 50 in longitude and its contrast is not reconstructed equally from the individual lines and, consequently, the formal average temperature is not as well constrained as for the other main features. We thus regard this feature as uncertain. In one image (Fe i 6400 Å) the data

8 594 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Fig. 6a e. Doppler images of HD from April Each panel presents the results from one spectral region and shows a pseudo-mercator projection of the reconstructed surface temperature (top), the observed line profiles and their fits (middle), and the light curve in two bandpasses and their respective fits (bottom). The σ of the line-profile fit is given below each map. Rotational phase is indicated to the left of each line profile and also marked with arrows. The main spectral lines are identified at the top of each map and are arranged in order of decreasing equivalent width from panel (a) through (e). require a bright feature at 180 which obviously stems from the very distorted profile at phase 0. p 597 but disappears if this line profile is given zero weight in the inversion. Despite that this profile s distortion is qualitatively the same as in the other lines, it appears significantly exaggerated in Fe i 6400 Å and does not repeat properly in the subsequent phase. We have nevertheless chosen to keep this profile for the inversion since there is nothing obviously wrong with this exposure and the Doppler-imaging code is very good in differentiating between phase-dependent and purely time-dependent distortions. There is no dominant cap-like polar spot in 1997 as seen on many evolved RS CVn binaries. The one image (Fe i 6430 Å) that possibly does show a weak polar feature with T 250 K is reconstructed from a blend with the strong Fe ii Å line that is not only located 1.8 Å to the red of the main mapping line and thus prone to produce high-latitude artefacts (see, e.g.,

9 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 595 Fig. 7a e. Individual Doppler images for January Otherwise as in Fig. 6a e. Note the splitted feature near a longitude of 180 (e.g. in panel e) and how it is recovered from the individual lines. Compared to the 1997 maps in the previous figure (e.g., again with panel e) suggests its persistent existence for over 28 stellar rotations. Unruh & Collier Cameron 1995) but also singly ionized and thus sensitive to electron pressure and some caution is advised. We thus conclude that there is no polar cap-like spot on HD in 1997 but a single high-latitude ( ) spot at longitude 240. The remaining features group along an average latitude of Images for data set January 1996 In spectra and 24 BV light-curve points were available. The photometry was combined from a 48-day interval centered around the mid time of the spectroscopic observations while the spectroscopy was obtained within 14 consecutive nights. Fig. 7a e visualizes the data and the mapping results. As in 1997, no dominating polar cap-like spot is seen. A single, high-latitude feature at l=15 with T 400 Kis recovered from the three strong lines but is not so obvious from the two weaker lines (Fe i 6411 and 6400 Å) where its contrast is

10 596 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Fig. 8a e. Individual Doppler images from February March No photometric input was used for this season but is nevertheless plotted in the respective light-curve panels. The straight line is the adopted average magnitude for this season. See text. Note that the radial structures in the maps are due to the sparse phase coverage. Otherwise as in Fig. 6a e. only about K below the nominal photospheric value of 4950 K. Several but slightly cooler spots ( T K) are seen at latitudes between 0 and +30 and at longitudes of l=30,90, 140, 180 and around 300. Note that the two spots, termed splitted spot in the figure caption, that were dominating the 1997 Fe i 6400-Å map (compare with Fig. 6e) are strikingly similar to the feature in this year s map, even in shape. The whole group appears to be shifted by 40 toward smaller longitudes compared to 1997 though. In Sect. 5.8, we try to quantify the likelihood of similarities between the annual images by means of cross correlation Images for data set February March 1995 For 1995 just 6 spectra and no simultaneous light-curve points were available. The photometry closest in time was 70 days (more than four stellar rotations) prior to the spectroscopic observations and could not be used for the imagery. While the spectroscopic observations are fairly well distributed in phase

11 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 597 Fig. 9a e. Individual Doppler images from March Otherwise as in Fig. 6a e. and taken within a single stellar rotation we must regard the 1995 map as less reliable than the others. To estimate such (external) uncertainties we inverted all spectral-line regions in 1995 also with photometric input but gave lower weight to the photometry of 0.10 relative to the line profiles. As expected there were no obvious differences in the reconstructed surface features, indicating that the photometric variations must have been relatively constant, but the maximum temperatures were on average 100 K cooler than without photometric input. Fig. 8a e shows the data and the mapping results without photometric input. However, since our Doppler-imaging code works on absolute rather than relative photometry we still need to supply a phase averaged B-V color. Its value is indicated in the light-curve panels in Fig. 8a e as a straight line and was adopted from the BV photometry of Henry et al. (1995b) in December Again, our maps show a high-latitude feature at +60 and at longitude of l 70. Two of the lines (Ca i 6439 and Fe i 6430 Å) require a small polar cap-like spot of significant temperature difference with the high-latitude feature at +60 and another region near l = 240 as its appendages. The large number of low-latitude features of lesser contrast ( T K) suggest that even smaller features, say with projected area 1%, can be also very persistent. We note that the time scale for the

12 598 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Fig. 10a d. The evolution of surface features on HD Shown are the average temperature maps for the years 1994 through Each map is the non-weighted average from the five maps already shown individually in Figs. 6a e 9a e. The bar below each map plots the standard deviations in Kelvin along binned longitudes. Their grey scale is also indicated. Note the weak polar spot in 1994 and possibly in 1995, the single high-latitude spot at l 10 in 1996, and the absence of the polar spot in stability of any spot pattern is an uncertainty that cannot be resolved on the basis of even annual Doppler maps but there is abundant evidence that polar spots are long lived and equatorial spots short lived (e.g. Vogt & Hatzes 1996). Multicolor photometric monitoring of HD throughout 1997/98 (see Sect. 3) showed the star with a relatively constant light curve shape (Fig. 3a) but sudden amplitude variations did occur, e.g. in early Images for data set March 1994 In 1994 altogether 16 spectra and 15 BV light-curve points were available. The photometry was combined from a 29-day interval centered around the mid time of the spectroscopic observations which was obtained within 14 consecutive nights. Fig. 9a e shows again the data and the results. Contrary to the years , all line regions in 1994 recovered a moderately size cap-like polar spot with T 800 K, i.e. at least 200 K cooler than the coolest feature seen in the other data sets. This is an interesting result because, first, a polar spot never has been seen to develop or vanish and, second, it explains the long-term brightness changes in Fig. 1. Of course, one is also tempted to propose the same cause for the many spotted stars having large long-term brightness variations (periodic or not) and we suspect that polar spots are a common feature on active stars. Besides the polar feature we see again several low-latitude spots of moderate temperature difference ( T K). Two elongated features at l = 170 and 240 even reach the polar spot. The respective profiles at phases around 0. p 5 and 0. p 65 reveal two bumps in the line core, which give rise to the two latitudinally elongated features Average maps and image correlations In Fig. 10 we compare the average maps from the four years. The averaging has the advantage of suppressing spurious features from the individual lines but emphasizing features that were reconstructed consistently. The only shortcoming when interpreting an average map is that it is not directly constrained from observations. We find cool spots with an average temperature difference with respect to the unspotted photosphere

13 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 599 Table 5. Coefficients for the cross-correlation fits Years a sin 2 φ + b a b χ a sin 4 φ + b sin 2 φ + c a b c χ Fig. 11a c. Surface cross-correlation functions. The annual variations for each latitude bin are cross-correlated against each other. a from 1994 to 1995, b from 1995 to 1996 and, c: from 1996 to Pixel size is 5 in longitude and a grey scale is plotted at the given values of the linear correlation coefficient (the higher the correlation coefficient the darker the grey scale). of 500 K, the strongest feature being the polar spot in 1994 with T 800 K. The smaller structures are mostly located to within a latitude of 0 and +30. However, this region is near the sub-solar line at +30 which is most sensitive to line-profile variations and, if a particular phase region is undersampled, the code tends to put spots preferably along this latitude. We can not rule out that the many small, low-latitude features are actually arranged symmetrically along the stellar equator. By cross correlating strips from different maps at sucessive latitudes, we may derive the amount and the sign of an eventual phase lag in time, which could then be interpreted as differential surface rotation (Donati & Collier Cameron 1997, Weber & Strassmeier 1998). And, when comparing different latitudinal strips, we may additionally obtain information on the appearance and subsequent latitudinal movement of particular features, e.g. a poleward drift as in the Doppler images of HR 1099 (Vogt & Hatzes 1996). Our maps are made up by pixels of size five-by-five degrees, starting from the southern limb of the stellar disk at a latitude of i up to the visible pole. The annual cross-correlation maps in Fig. 11 were derived by sucessively cross correlating two maps consecutive in time and at constant latitudes. They already indicate the tendency of a curved latitude-dependent correlation function. The pixelshift then indicates the shift in phase (or longitude) that was required to find the optimum correlation, the latter expressed with a standard linear correlation coefficient (0 means no correlation, 1 is perfect correlation). All cross correlations were computed with the IRAF fxcor routine (see IRAF V2.11 manual, From the annual maps in Fig. 10, we can already see numerous surface features up to a latitude of +70 and the crosscorrelation functions mostly reveal more than one significant peak per latitude bin. The portion of the stellar surface below 30 is especially prone to artifacts and its cross correlation is thus less reliable than on other parts of the surface. To obtain a single estimate on the phase lag per latitude slice, we fit a Gaussian to the most significant peak of the cross-correlation function whenever well defined and plot the results in Fig. 12a c. The error bars on these lags are typically only a few pixels and were adopted to be proportional to the FWHM of the cross-correlation peak and estimated from repeated measurements with different fitting routines within the IRAF package. The full lines in Fig. 12a c are then least-squares sin 2 φ and sin 4 φ fits to these phase lags versus stellar latitude φ, and may represent several variants of surface differential rotation (Table 5). As already pointed out by Donati & Collier Cameron (1997) and by Unruh et al. (1995) for the rapidly-rotating K-dwarf

14 600 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII Fig. 12a c. The distribution of the cross-correlation peaks versus phase and their fits with sin 2 φ (full lines) and sin 4 φ (dotted lines) terms. φ is the stellar latitude. The points are from a Gaussian fit to the most significant cross-correlation peak shown in Fig. 11. The individual panels are again for the annual cross correlations between , , and AB Dor (P =0.5 days), we caution that it is entirely possible that the spot distribution has completely re-arranged within our annual maps, and that the interpretation of the phase shifts with differential rotation could therefore be spurious. However, the long rotational period of 16 days together with a low-gravity atmosphere, and the relative constancy of the seasonal light curves from 1997/98 in Fig. 3 argue against a complete re-arrangement of spots. Also, our maps from 1996 show at least one feature dubbed the splitted spot in Fig. 7a e that is also seen in Note though that there were 22, 20, and 28 stellar rotations between the , , and maps, respectively. We conclude that there is good evidence for latitude dependent phase shifts on the surface of HD but whether these are due to differential rotation remains to be seen once higher time-resolution maps are available. 6. Hα line variations in 1996 and 1997 The Hα line profiles of HD are relatively stable from year to year as demonstrated in Fig. 13 though small variations occured on a time scale comparable to our data taking rate of one spectrum per night. The Hα profile always appears as an absorption line with a filled-in line core and very narrow wings quite typical for late-g/k giants (see also Fig. 5b). Due to the existence of significant chromospheric Ca ii H&K emission we interpret the Hα core filling also to be due to chromospheric emission. We have subtracted velocity-shifted and broadened standard star spectra, that were obtained with the same instrumental configuration as HD 51066, in order to remove the non-magnetic part of the spectrum. The resulting difference spectra are furtheron called residual spectra. The best match to the photospheric lines was found when using β Gem (K0IIIb). A fit with o Vir (G8IIIa) results in (photospheric) line cores consistently too shallow by 10% with respect to HD 51066, while 37 Com (G9IIICH-2) has lines consistently deeper by 10%, as does 16 Vir (K0.5III). We had no M-K class III-II reference spectrum to compare with. In Fig. 13 are plotted the residuals after the β Gem subtraction for 1996 January (top) and 1997 April (bottom). In general, all residual spectra show, also if using other standard stars, a blue-shifted emission superimposed on a residual absorption feature. The latter originates most likely from systematic mismatches in the Hα line wings above a normalized intensity of 0.9 of the continuum, i.e. the upper 1/3 of the absorption profile shown in Fig. 5b. We suspect that this is an artifact due to the difference in luminosity class between our standard(s) and HD The residual core emission, however, is real and appears blueshifted by 20±7 kms 1 with respect to the line center. Its presence implies that at least this part is formed in active surface regions with a net outflow velocity of approximately 20 km s 1. Single Gaussian fits to the emission profiles reveal a variable and possibly phase-dependent Hα-core equivalent width whose minima and maxima are likely anti-correlated with the visual light curve (Fig. 14). The average equivalent width of the residual emission is 270 må compared to Å of the non-residual profile. While the residual profiles in Fig. 13 appear relatively stable, the one spectrum at JD 2,450, (ϕ=0. p 846) is particularly deviant. It shows a broad absorption wing on the blue side but not on the red side. Since this is only seen in one out of 23 spectra further analysis is impossible but we note that a timedependent phenomenon like an erupting coronal prominence could produce the observed absorption at velocities larger than the projected rotational velocity ±v sin i. Examples of similar

15 K.G. Strassmeier et al.: Doppler imaging of stellar surface structure. VIII 601 Fig. 14. a Hα-core equivalent width versus rotational phase for 1997 April. Note that the internal error of a single measure is of the order of the symbol size. b The combined V-band light curve from three consecutive rotation cycles in 1997 March April. Fig. 13. Time series of residual Hα profiles in 1996 and 1997 (the 1996 data has been offset by for better visibility). The thick line in the 1997 graph is part of a non-residual spectrum. Note that in 1997 the one spectrum at HJD 2,450, (ϕ=0. p 846) significantly deviates from the rest. Sharp features marked with are residual water lines. Hα profiles for, e.g., the active K-dwarf AB Dor were reviewed by Collier Cameron (1996). 7. Discussion and conclusions We have presented annual Doppler images of the effectivelysingle giant HD = CM Cam from four consecutive years. The 1994 image reveals a weak but significant cool polar-cap like spot, which became even weaker in 1995 and was absent in 1996 and The simultaneously observed brightening since the discovery of the light variability in 1992 suggests a common cause, namely, the slow decay of the polar spot. The overall spot temperature is only 500 K cooler than the nominal photospheric value of 4950 K, in excellent agreement with independent spot modelling of high-precision V and V-I light curves from 1997/98. Our annual cross-correlation maps contain some evidence for latitude-dependent phase shifts from consecutive (annual) maps but we can not unambiguously interpret them to be due to differential rotation because there is mostly more than one correlation peak per latitude slice. However, the polar feature and the persistent existence of low-latitude inhomogeneity possibly suggests that spot activity on HD takes place in two belts, a nearly uniformly spotted equatorial belt and at high-latitudes with either one (in 1997 and 1996) or at most two (in 1995 and 1994) isolated features. Since the high-latitude features are generally recovered with cooler temperature than the equatorial features we may suspect them to be areas of higher magnetic flux density. This leads us to speculate that these regions could form bi-polar groups with the numerous spots of lesser field density in the equatorial belt. Such a closed field geometry, or better the absence of an open field geometry, could also explain the anomalously high rotation of HD by a lack of magnetic braking. However, it would imply that a similarly organized field structure must have already existed during the pre main-sequence stage, otherwise the star would have already considerably slowed down once it had spent a significant part of its lifetime on the main sequence. Today s field strength can be estimated indirectly by assuming that the surface-averaged value is close to, but less than what is required to be in equilibrium with the gas pressure. This would be consistent with the fact that many main-sequence stars show a saturation of activity with rotation (e.g. Vilhu 1984) and that direct field measurements of active dwarf stars indicate B /B eq 1 for rapid rotators (Saar 1996), where B eq =(8πp gas ) 1/2. With the approximate scaling law p gas, /p gas, g /g, and log g of 2.5 we get B 160 G for HD when we adopt B eq, =1500 G. However, HD was not a solar-type star when on the main sequence. With the absolute magnitude from Hipparcos and the stellar parameters determined in this paper we can evolve HD backwards to the main sequence if we assume conservation of mass, angular momentum, and magnetic flux. The values in Table 4 convert then to a spectral type of B7 8, an effective temperature of 12 13,000 K, a radius of 2.2 R (Gray 1992) and nearly the same luminosity as today. Following the analysis of Stȩpień (1993) for the single, but slowly rotating, active G8 subgiant HR 1362 we may also estimate the rotational and magnetic main-sequence parameters.