Precise Spectropolarimetric Measurements of Magnetic Fields on

THE ASTROPHYSICAL JOURNAL, 514 : 402È410, 1999 March 20 ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A.

PRECISE SPECTROPOLARIMETRIC MEASUREMENTS OF MAGNETIC FIELDS ON SOME SOLAR-LIKE STARS S. I. PLACHINDA Crimean Astrophysical Observatory and Isaac Newton Institute of Chile, Crimean Branch

AND T. N. TARASOVA Crimean Astrophysical Observatory, Crimea, Ukraine Received 1998 February 10 ; accepted 1998 October 23

ABSTRACT Results of precision measurements of the net longitudinal component of magnetic Ðeld strength (B ) e performed for Procyon (a CMi, F5 IVÈV) and three solar-type starsÈb Com (G0 V), f Her (F9 IV), b Aql (G8 IV)Èare reported. All stars observed are weak solarlike activity analogs. We outline an improved observational technique (Stokesmeter plus CCD detector) and data reduction process that permits determination of the mean longitudinal Ðeld strength, B , with an accuracy within the range 1È5 G. The average value of B \ [1.34 ^ 1.0 G was estimated fore Procyon using 10 spectral lines in the e region 6285È6350 AŽ . A substantial magnetic Ðeld value was detected on only one occasion for f Her : B \ [10.1 ^ 3.1 G. e Subject headings : stars : individual (a Canis Minoris) È stars : individual (b Aquilae) È stars : individual (b Comae) È stars : individual (f Herculis) È stars : late-type È stars : magnetic Ðelds 1.

INTRODUCTION

known about the global conÐguration of other types of stars with weak magnetic Ðelds (Landstreet 1982). The absence of such information is connected with the difficulties of carrying out spectropolarimetric magnetic Ðeld measurements with an accuracy of 1È10 G (Landstreet 1992). Direct spectropolarimetric observations of several RS CVn stars reveal the presence of circular polarization at speciÐc locations within magnetically sensitive spectral lines (Donati, Semel, & Rees 1992b). The authors suggest that the polarization is due to the magnetic Ðelds of spots on these stars. They have calculated strengths of the general conÐgurations of the required magnetic Ðelds and Ðnd them to be equal to hundreds of Gauss within the errors of observations. From Zeeman-Doppler imaging of the circularly polarized spectra of the bright component of the RS CVn system HR 1099 (K1 IV ] G5 V) it was established (Donati et al. 1992a) that the magnetic Ðeld is concentrated in two main regions where it is toroidally directed. A ring of negative polarity Ðeld (D[300 G) surrounds the cool polar spot, while a region of positive polarity Ðeld (D700 G) is detected above the equatorial cool spot. The magnetic Ðeld is presumably in spots (covering up to half of the visible hemisphere of the star) on the surface of the RS CVn star j And was spectroscopically detected previously by Giampapa, Golub, & Worden (1983). They measured a magnetic Ðeld strength equal to 1290 ^ 320 G. Borra et al. (1984) have executed an extensive search for organized magnetic Ðelds on late-type stars with the use of a multislit magnetometer (the mask was made on the basis of the a Boo spectrum). Observations were made for more than 40 stars of luminosity classes IIIÈV. Global magnetic Ðelds were detected for a Aur (G8 III ; RS CVn) : in three separate epochs the measured Ðeld was 9.2 ^ 2.6 G, 11.2 ^ 3.7 G, and [5.0 ^ 1.7 G. They also detected signiÐcant values of magnetic Ðeld strengths on a Boo (K2 III, 3.3 ^ 0.5 G), k Gem (M3 III, 9.1 ^ 2.0 G), and m Boo A (G8 Ve, 25.0 ^ 6.4 G). In the study by Hubrig et al. (1994), a search for global

All luminosity class IIIÈV stars of spectral types F-G-K2 demonstrate the presence of coronae (Haisch, Schmitt, & Rosso 1991). In some stars the presence of a chromosphere and a wind is revealed (Cram & Kuhi 1989). Some dwarfs show strong cyclic activity similar to the solar one, with periods from several years up to tens of years (Baliunas et al. 1995). Owing to investigations of the solar activity it is known that the magnetic Ðeld is a keystone in the physics of this phenomenon. A dynamo process is believed to be the generator of magnetic Ðelds in these stars. There exists on the solar surface not only local magnetic conÐgurations (spots, etc.) with strengths up to 4 kG, but also a global (general) magnetic Ðeld conÐguration on the Sun as a star with strength of D1 G. The global conÐguration is formed by thin structures (the network of quiet magnetic regions), consisting of small elements with dimensions up to several tenths of an arcsecond and with strengths from units up to several tens of Gauss having di†erent signs (positive or negative magnetic Ðeld). Variations of the characteristics of both local and global magnetic Ðelds reveal the 22 yr activity cycle of the Sun. During maximum solar activity there is the largest amount of active phenomena on the solar surface. The strength of the general magnetic Ðeld of the Sun is also increased at the stage of its maximum activity (Kotov et al. 1998). To increase our understanding of the physics related to these phenomena, knowledge concerning local and global magnetic Ðelds on solarlike stars is very important. Currently, we have a wealth of spectroscopic information on magnetic Ðeld strengths on the surfaces of main- and preÈmain-sequence stars of F-G-K-M spectral classes (being of 0.5È5.0 kG ; see, for example, Marcy 1984 ; Saar 1988 ; Cram & Kuhi 1989 ; Landstreet 1992 ; Johns-Krull & Valenti 1996 ; Valenti et al. 1996 ; Rueedi et al. 1997). Unfortunately, there is practically no information about the global conÐgurations of magnetic Ðeld on these stars (Borra, Edwards, & Mayor 1984). Additionally, little is 402

MEASUREMENTS OF MAGNETIC FIELDS magnetic Ðelds of 12 late-type giants using the Stokesmeter and advanced analysis technique (discussed in this paper) was reported. SigniÐcant magnetic Ðeld strengths in the range of some tens of Gauss were found on four giants : c Tau, v Tau, v Leo, and m Her ; the maximum value was equal to 49.2 ^ 6.1 G for v Leo. Hubrig et al. (1994) also obtained magnetic Ðeld observations of the main-sequence star m Boo A (G8 Ve) on 10 nights with signiÐcant detections on two occasions : 46.5 ^ 13.7 G and 55.0 ^ 14.9 G. Because of the lack of direct observations of global magnetic Ðelds in late-type stars, further observations are needed to make meaningful comparisons with theoretical predictions. A key problem in such studies is the difficulty in obtaining accurate measurements of magnetic Ðeld strengths ; therefore, in this paper we pay particular attention to the observational technique and data processing and their connection to the reliability of the information obtained. 2.

OBSERVATIONS AND DATA REDUCTION

The observations have been carried out at the coude focus of the 2.6 m Shajn telescope of the Crimean Astrophysical Observatory. The polarization analyzer (Stokesmeter) was mounted in front of the entrance slit of the spectrograph. The device consists of an entranceretarding achromatic quarter-wave plate (the working region is 4000È6800 AŽ ), a plate of Iceland spar, and an exit achromatic quarter-wave plate for converting the resulting linearly polarized light after the Iceland spar plate into circularly polarized light. This last step is needed to balance di†erences in the reÑectivity of the two light beams from the di†raction grating. The plate of Iceland spar separates the fast and the slow linearly polarized beams by D5A. As a rule, the entrance slit dimension on the sky was 0A. 8. An analogous device is described by Donati & Semel (1990). After passing through the exit quarter-wave plate and entrance slit of the spectrograph, these two beams are projected on the plane of the CCD EEV15-11 (1024 ] 256 pixels) as two spectra with di†erent circular polarization. This device allows the recording of all four Stokes parameters on four exposures if instrumental polarization is low. However, the optical layout of the coude focus includes one inclined Ñat mirror for spectropolarimetric observations, which results in signiÐcant instrumental linear polarization. Therefore, we measure only circular polarization in spectral lines. In this case instrumental e†ects are signiÐcantly less and they are well understood (Severny, Kuvshinov, & Nikulin 1974). Since only circular polarization is recorded, we are sensitive only to a net longitudinal component of magnetic Ðeld, averaged over the visible disk of a star. This is the so-called e†ective magnetic Ðeld, or mean longitudinal magnetic Ðeld, designated as B or B . More correctly, B is e z Ñux density weighted e some average value of the magnetic by the physical inhomogeneities on the surface of the star combined with the limb-darkening proÐle of the stellar disk. This treatment is amply discussed in the literature (for instance, see Mathys 1989 or Landstreet 1992). Finally, subsequent on-source exposures are carried out with the entrance quarter-wave plate rotated by ^90¡. As a result of this procedure, spectra with di†erent circular polarizations obtained in two consecutive exposures are projected on the same section on the CCD. With this observational technique there are two methods for calculating the measured component of the mean longi-

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tudinal magnetic Ðeld strength (B ) : using two spectra e obtained in one exposure (classical technique) or using four spectra obtained in two exposures. In the Ðrst case, the accuracy of B is limited by the following : e 1. The signal level accumulated on the CCD ; 2. The accuracy of the Ñat-Ðelding procedure, which corrects the pixel-to-pixel sensitivity of the detector ; 3. The accuracy in determining the inclination of the CCD plane in the focal plane of the spectrograph ; 4. The accuracy of guiding the star on the slit of the spectrograph ; 5. The accuracy in wavelength calibration of the two spectra. For instance, wavelength calibration using a Th-Ar lamp typically produces an error in the wavelength determination equal to 0.002 AŽ ; for a line at j6000 and Lande factor z \ 1 this results in an error in magnetic Ðeld calculation *B \ 60 G, or *V \ 100 m s~1 in velocity units. To obtain the required accuracy in magnetic Ðeld measurements *B \ 10 G for a given spectral line with j6000 and Lande factor z \ 1, it is necessary to detect a shift between the Zeeman p components of the spectral line equal to 2*j \ 0.00034 AŽ , B or *V \ 17 m s~1. It is clear that the measurement of accurate (*B \ 10 G) magnetic Ðelds is a very difficult task. Therefore, we developed a data reduction procedure using four spectra obtained in two exposures with a turn of the quarter-wave plate by 90¡ ; we labeled this procedure ““ Flip-Flop Zeeman Measurement ÏÏ (FFZM). A very similar method has been developed by Semel, Donati, & Rees (1993). As was mentioned above, stellar spectra with right circular polarization obtained in the Ðrst exposure and left circular polarization in the second exposure are projected in turn on the same section of the CCD detector using this technique. Thus, errors in the Ñat-Ðelding procedure for two spectra with opposite circular polarization will be practically the same and will not a†ect the calculation of B in the case of weak e magnetic Ðelds. Additionally, this observational technique automatically allows us to rule out shifts of spectral lines caused by inaccurate adjustment of the CCD plane to the focal plane of the spectrograph and instrumental drift of contours of spectral lines during the second exposure relative to the Ðrst one. 2.1. ““ Flip-Flop ÏÏ Zeeman Measurement T echnique Let the entrance quarter-wave plate be o†set by 90¡ during the second exposure relative to its position during the Ðrst exposure. Then the displacement caused by the splitting of atomic energy levels in the magnetic Ðeld of a star produces a wavelength shift *j equal to B *j \ (e/4nm c2)zj2B \ 4.67 ] 10~13zj2B , (1) B e e e where e is the electronic charge, m is its mass, c is the e velocity of light, z is the e†ective Lande factor, j is the wavelength in AŽ , and B is in Gauss. Denote a center of egravity of a line with right circular polarization obtained during the Ðrst exposure by j , and with left circular polarization by j . The same1rcp designations for the second exposure are 1lcp j and j . Then, 2rcpmagnetic2lcp using equation (1) the mean longitudinal Ðeld is B@ \ k(j [ j )/2 \ k(^2*j ^ *j)/2 (2) e 1rcp 2lcp B for the Ðrst pair of lines, where *j is resulting displacement

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PLACHINDA & TARASOVA

of a line due to the above-mentioned instrumental e†ects, k \ 1/(4.67 ] 10~13zj2) and B@@ \ k(j [ j )/2 \ k(