Are Rotational Axes Perpendicular to Orbital Planes in Binary Systems. III. Main Sequence and Short-Period RS Cvn Stars. R

ACTA ASTRONOMICA Vol. 45 (1995) pp. 725±745

Are Rotational Axes Perpendicular to Orbital Planes in Binary Systems. III. Main Sequence and Short-Period RS CVn Stars.

by R. GøeÎbocki

Institute of Theoretical Physics and Astrophysics, University of GdaÂnsk, ul. Wita Stwosza 57, 80-952 GdaÂnsk, Poland e-mail: ®[email protected]

and A. Stawikowski N. Copernicus Astronomical Center, ul. RabiaÂnska 8, 87-100 ToruÂn, Poland e-mail: [email protected]

Received November 24, 1995

ABSTRACT

Inclinations of the rotational axes, irot , are determined for 46 main sequence binaries of F, G,

K and M spectral type and short period RS CVn systems. Seven binaries are asynchronous. The i inclinations irot are then compared with the orbital inclinations, orb , to test the alignment between

the equatorial and orbital planes. In all 39 cases of synchronous rotators irot is equal or nearly equal

to iorb . In a sample of seven asynchronous systems, at least six, and perhaps all, are non-coplanar. Key words: Stars: rotation-binaries: general-Stars: late-type

1. Introduction

Chromospherically active stars with spots present a unique possibility to de-

V i termine rotational period, Prot , and with independently measured rot sin rot to

evaluate inclination of rotational axis, irot . In late type binaries it allows for com- parison of inclination of rotational axes to the orbital plane. Our previous analyses (Stawikowski and GøeÎbocki 1994 a,b called hereinafterPaperIandPaperII)showed

that in long-period RS CVn stars an assumption of coplanarity of the equatorial ro-

= i tational and orbital planes ( irot orb ) is justi®ed for synchronous systems only. In asynchronous binaries the rotational axes are not perpendicularto the orbital plane. 726 A. A.

It contradicts generally accepted assumption and requires revision of time-scales of circularization and synchronization for non-coplanar systems. In the present study we analyze main sequence F, G, K and M binaries and short-period RS CVn stars with orbital periods smaller than about 10 days. The observational data were collected from all recently available publications, but in most cases they are based on the second edition of "A catalog of chromospherically active binary stars" Strassmeier et al. (1993), hereinafter called CABS. ThemethodoftheanalysisisthesameasinPaperIandII. Becausethe accuracy

of determination of irot is crucialfor®nalconclusions,specialattention is paid tothe determination of stellar temperatures and absolute magnitudes in¯uencing directly

error in stellar radii and in consequence error in irot . In Chapter 2 we discuss calibration and errors of our temperature and absolute magnitude scales for main sequence F, G, K and M stars.

A de®nition of synchronismin binary systems is not unique. A simple criterion

= P of Porb rot is useless because of differential rotation and "pseudo synchro-

nism" for highly eccentric orbits. Tan Huisong et al. (1993) suggest a parameter

= j(P P )P j S

S orb rot orb as a measure of synchronism, where 0 01 means

S synchronism and S 0 04 means asynchronism. The case of 0 01 0 04 means either a slight asynchronism or a highly differential rotation. We use this

parameter for discriminating asynchronous systems. It should be stressed that we

= P

assume Prot phot and we include in our analysis only stars with directly deter- V mined values of Pphot (either from periodic variations of obs or from "migration

waves" in eclipsing binaries). The values of Pphot show small seasonal variations

due to differential rotation, but the observed changes are smaller than 4%. i

In Section 3 we present the results ± our values of stellar parameters: iorb , rot

= ji i j and i orb rot . The discussion of errors is made individually for each star in Comments to Tables 2±5.

2. Observational Data

We have found 69 binary systems (short-period RS CVn or main sequenceF, G,

V i K,Mspectraltypebinaries)withknown Pphot and rot sin rot full®ling our selection

criteria. Unfortunately, only for 46 systems other stellar and orbital parameters were i known with accuracy good enough for determination of iorb and rot . They are listed in Tables 2±5. In this sample, 21 systems are eclipsing binaries providing accurate orbital inclinations, 22 non-eclipsing objects are the SB2 systems with reliable parameters for both components. For three non-eclipsing SB1 systems

(EI Eri, V833 Tau and DM UMa) evaluation of orbital inclination was possible

(m) i

because of extremely low value of the mass function, f . In such a case orb q is low and insensitive to the adopted values of mass, M , and mass ratio, (see Paper I). Vol. 45 727

When both (or at least one) components of the binary are main sequence stars,

the evaluation of iorb is made using stellar masses determined from the mass- luminosity relation. We used the relation given in Lang (1992) compendium, which is based on careful discussion of Popper (1980). Our results were always

very close to that presented in CABS. Accuracies of iorb determination in most

cases are better than 2 and not worse than 5 . Binary systems for which errors

in iorb exceed 5 were excluded from the sample. An interesting case of II Peg

for which iorb is very uncertain but spots have been observed (and modeled) by many authors is described in Section 3.

Inclinations of rotational axes were determined from the ratio of the observed

i V V projected rotational velocity, Vrot sin rot , to the rotational velocity, rot , with rot

obtained from rotational period, Prot , using the formula

= R P

Vrot 50 61 rot

R P V

where is radius in R , rot in days and rot in km/s. As in previous papers P only Prot based on direct phot measurements (or equivalent "migration wave" observations) have been used in the analysis. We are warning again that some

authors are publishing Prot based on the a priori assumption of synchronism,

especially for short-period systems. It could lead to serious errors (e.g., for VY Ari

= P = P = P = Porb 13 2 while phot 16 4 or LR Hya with orb 6 86 and phot 3 14).

There are two main sources of errors in the determination of irot : inaccuracy

i R

of Vrot sin rot measurements and evaluation of . In the estimation of error of i individual Vrot sin rot values we must rely on accuracies published in original

papers. Sometimes a few independent measurements are available. If our estimate i indicates that the error of Vrot sin rot exceeds 15% we exclude such star from the

sample. The stellar radius, R , was obtained from the estimation of the effective

T M temperature, eff , and the absolute magnitude, v . To minimize this error special attention was paid to the calibration of the temperature scale. Fortunately, most of stars in our sample are the F, G, K, M dwarfs not very distant from the Sun. For

some of them very accurate trigonometric parallaxes were available. Otherwise

M T M v v was estimated from the spectral type. The scales and errors in eff and are described in the following subsection.

2.1. Effective Temperature and Absolute Magnitude Calibration

Most accurate estimation of Teff can be obtained from a multicolor infrared

photometry. ForF,GandK typesubgiantsandgiantsformulae found by McWilliam

= f (CI ) (1990) (see his Table 6), in his extensive analysis of Teff for the BVRI

photometry, provide the most reliable values of Teff . We used these formulae for

all stars with the luminosity class IV, IV-III and III. Using Table 12 of McWilliam

= f ( ) (1990) we have constructed a relation Teff sp type . The adopted values for

Teff are the average values obtained from each color index and spectral type of a star. 728 A. A.

There are many relations of Teff versus spectral type or color index for main sequence stars, e.g.,Johnson (1966), Novotny (1973), Bohm-Vitense (1981) Gray (1992) and most frequently used Landolt-Bernstein (1982). When comparing these relations some discrepanciesand systematic shifts become evident. With increasing accuracy and number of infrared observations many independent determinations

of Teff for individual stars have been published. We used the following sources

= f ( ) T = f (CI ) for redetermination of Teff sp type and eff for late type dwarfs: Leggett et al. (1986), Blackwell et al. (1991), Buser and Kurucz (1992), Blackwell and Lynas-Gray (1994) and Taylor (1994). Additionally we included independent

Teff estimations used for the [Fe/H] determinations and published in the catalogue of Cayrel de Strobel et al. (1992). We analyzed only stars within the luminosity class V and present in the Bright Star Catalogue to avoid interstellar reddening effects. If more than one determination of temperature was available for a given star, an average value was calculated with the weight equal 2 given to Taylor's (1994) data, and the ®nal weight equal to the number of independent determinations of

Teff . Information about spectral types was obtained from SIMBAD, and the most

= f ( ) frequently cited ones were adopted. The resulting relation of Teff sp type for F, G, K and M main sequencestars is presented in columns 1 and 2 of Table 1. The catalogue of multicolor photometry of Lanz (1986) allowed to determine

relations between effective temperature and BVRI color indices in the same way.

T = f (CI ) B V V R

For BS stars with known Teff the best relations eff for , ,

I V I R and color indices were found. They are presented in columns 3, 4,

5 and 6 of Table 1. We believe that with known spectral type and infrared color

indices our calibration provides Teff with the accuracy of 50 K. Unfortunately

V for 18 analyzed binary systems only spectral type and B are known. In such

a case an accordance within 200 K is regarded as good. If the uncertainty of Teff

determination from spectral type is equal to the standard deviation of Teff foragiven

spectral type in our sample, then for F-type stars it is equal to 100 K 120 K,

for G and K-type 80 K 90 K, and for M-type stars 100 K.

Absolute magnitudes for a given spectral type (or Teff ) were determined using

catalogue of trigonometric parallaxes (Van Altena et al. 1991). For all dwarfs

T M with known eff and parallax 0. 025, v was calculated. Resulting relation

is presented in column 7 of Table 1. The width of the lower main sequence, M

i.e., v for a given spectral type, re¯ecting both errors of parallax and intrinsic

(evolutionary) changes of v , as given by standard deviation is equal to 0 45 m for F, G and early K type, and 0 40 for late K and M-type stars. Bolometric corrections shown in column 8 of Table 1 are the average values for

a given Teff after Johnson (1966), Novotny (1973) and Buser and Kurucz (1992). Temperatures and radii of the dwarf components of binary systems were determined using Table 1. The infrared color indices measured in Kron-Cousins system were converted into the Johnson's system using the relations from Bessell (1979). When both components of the binary system were visible, the difference in their Vol. 45 729

Table1

Physical parameters of main sequence stars

T B V V R R I V I M Sp. Type eff v B.C. K F0 6961 0.31 0.28 0.17 0.45 2.89 0.m00 F1 6835 0.33 0.30 0.18 0.49 3.00 -0.01 F2 6806 0.34 0.32 0.19 0.50 3.20 -0.01 F3 6653 0.37 0.33 0.20 0.54 3.35 -0.02 F4 6610 0.38 0.34 0.21 0.56 3.42 -0.03 F5 6516 0.40 0.36 0.22 0.39 3.54 -0.03 F6 6335 0.45 0.40 0.25 0.65 3.71 -0.04 F7 6239 0.48 0.42 0.26 0.68 3.92 -0.05 F8 6093 0.52 0.45 0.28 0.73 4.11 -0.05 F9 5972 0.55 0.48 0.30 0.78 4.34 -0.06 G0 5890 0.58 0.50 0.32 0.82 4.54 -0.07 G1 5825 0.60 0.52 0.33 0.84 4.66 -0.08 G2 5751 0.65 0.53 0.34 0.87 4.68 -0.08 G3 5735 0.63 0.54 0.35 0.88 4.69 -0.09 G4 5671 0.65 0.55 0.36 0.91 4.70 -0.10 G5 5616 0.67 0.56 0.37 0.93 5.06 -0.11 G6 5508 0.70 0.59 0.38 0.97 5.17 -0.13 G7 5452 0.72 0.61 0.39 1.00 5.25 -0.14 G8 5395 0.74 0.63 0.41 1.03 5.50 -0.16 G9 5341 0.76 0.64 0.42 1.06 5.71 -0.17 K0 5233 0.80 0.67 0.44 1.11 5.96 -0.20 K1 5137 0.84 0.71 0.46 1.16 6.06 -0.24 K2 5052 0.87 0.74 0.48 1.21 6.29 -0.28 K3 4841 0.96 0.81 0.53 1.35 6.64 -0.39 K4 4675 1.04 0.88 0.57 1.47 7.11 -0.47 K5 4471 1.13 0.97 0.63 1.62 7.49 -0.58 K6 4295 1.22 1.05 0.70 1.76 7.76 -0.68 K7 4133 1.29 1.12 0.76 1.90 8.19 -0.83 K8 4051 1.32 1.16 0.79 1.98 8.32 -0.91 K9 3973 1.35 1.20 0.84 2.05 8.46 -0.95 M0 3897 1.38 1.25 0.88 2.14 8.60 -1.03 M1 3749 1.42 1.33 0.98 2.30 9.27 -1.24: M2 3622 1.46 1.42 1.07 2.45 10.20 -1.61: M3 3500 1.50 1.49 1.17 2.62 10.70 -1.85: M4 3400 1.53 1.57 1.26 2.75 11.20 -2.07:

luminosities was used to separate the contributions of the hot and cool components T into Vobs and color indices. The ®nal values of eff presented in Tables 2±5 are the

average values of Teff estimated from spectral types and all color indices (using Table 1 for dwarfs and formulae of McWilliam (1990) for subgiants and giants). 730 A. A.

Table2

Physical parameters for synchronous binaries

T R

No. Name HD/BD Spectrum Mbol eff Mass

KR M 1 FF And +34 106 dM1e+dM1e 9.25 3600 0.65 0.55 2 CF Tuc 5303 K4IV+G0V 3.45 5080 2.23 1.20 3 BI Cet 8358 G5 V + G5 V 4.86 5300 1.07 0.90 4 CC Eri 16257 K7 Ve + dM6: 7.30 4000 0.61 0.53 5 LX Per 19845 K0IV+G0IV 3.00 4780 3.11 1.40 6 UX Ari 21242 K0IV+G5V 2.00 4780 5.00 1.04 7 V711 Tau 22468 K1IV+G2V 2.78 4750 3.50 1.40 8 V837 Tau 22403 G2V+K5V 4.38 5650 1.18 1.00 9 EI Eri 26337 G5 IV + ? 2.60 5400 2.93 1.60 10 V833 Tau 283750 dK5e + ? 6.90 4420 0.60 0.60 11 YY Gem 60179 dM1e + dM1e 7.80 3750 0.55 0.47 12 GK Hya +2 1993 G8IV+F8V 2.60 5000 3.41 1.45 13 RU Cnc +24 1959 K1IV+F5IV 2.00 4740 5.00 1.50 14 XY UMa 237786 G3V+K5V 4.72 5700 0.98 0.97 15 BF Lyn 80715 K2V+dK 5.92 4900 0.77 0.73 16 DM UMa +61 1211 K0-1 IV-III + ? 1.80 4750 5.50 1.60 17 RW UMa +52 1579 K1IV+F8IV 2.55 4680 4.00 1.50 18 AS Dra 107760 G4 V + G9 V 4.20 5560 1.32 0.98 19 UX Com +29 2355 K1IV+G2 2.60 4650 3.95 1.20 20 RS CVn 114519 G9IV+F4IV 2.30 5000 4.00 1.45 21 SS Boo +39 2849 K1IV+G0V 2.90 4700 3.30 1.00 22 RT CrB 139588 G2 + G5-8 IV 2.65 5400 2.86 1.40 23 TZ CrB 146361 F6V+G0V 3.68 6400 1.27 1.12 24 CM Dra CABS 134 M4 Ve + M4 Ve 10.20 3070 0.28 0.26 25 WW Dra 150708 G2IV+K0IV 2.50 4750 3.90 1.36 26 V824 Ara 155555 G5 IV + K0 V-IV 3.80 5250 1.78 1.20 27 Z Her 163930 K0 IV + F4 V-IV 3.10 5000 2.71 1.31 28 PW Her CABS 153 K0 IV + F8-G2 2.60 4750 3.80 1.56 29 V478 Lyr 178450 G8 V + dK-dM 5.20 5350 0.90 0.87 30 191262 G5 V + G5 V 5.00 5660 0.88 0.91 31 CG Cyg +34 4217 G9.5 V + K3 V 5.35 5260 0.89 0.94 32 ER Vul 200391 G0 V + G5 V 4.35 5750 1.15 1.10 33 RT Lac 209318 G9IV+K0IV 2.40 4600 4.40 0.78 34 AR Lac 210334 G2IV+K0IV 2.90 4800 3.22 1.32 35 KZ And 218738 dK2 + dK2 5.85 5000 0.77 0.74 36 RT And +52 3383 F8V+K0V 5.75 4730 0.90 0.91 37 SZ Psc 219113 K1IV+F8IV 2.00 5150 4.24 1.62 38 EZ Peg +24 4742 K0 IV + G5 V-IV 2.68 4950 3.36 1.50 39 KT Peg 222317 G5V+K6V 4.50 5600 1.13 1.02 Vol. 45 731

Table3

Orbital and rotational parameters for synchronous binaries

i P V i i i No. Name Porb orb rot rot sin rot rot days deg. days km/s deg. deg.

1 FF And 2.17 60 2.17 14 68 8 2 CF Tuc 2.80 71 2.80 35 60 11 3 BI Cet 0.52 30 0.52 60 35 5 4 CC Eri 1.56 42 1.56 15 49 7 5 LX Per 8.04 87.6 8.18 19 81 7 6 UX Ari 6.44 60 6.44 37 70 10 7 V711 Tau 2.84 33 2.84 41 44 11 8 V837 Tau 1.93 72 1.89 31 79 7 9 EI Eri 1.95 46 1.95 50 41 5 10 V833 Tau 1.79 16 1.80 6.3 22 6 11 YY Gem 0.81 86.4 0.81 40 90 4 12 GK Hya 3.59 83.7 3.59 49 90 6 13 RU Cnc 10.17 89.5 10.14 25 90 1 14 XY UMa 0.48 83.5 0.48 100 76 8 15 BF Lyn 3.80 70 3.80 10 76 6 16 DM UMa 7.49 40 7.48 27 47 7 17 RW UMa 7.33 89.5 7.33 27 79 11 18 AS Dra 5.41 72 5.41 12 76 4 19 UX Com 3.64 90 3.64 55 90 0 20 RS CVn 4.80 87 4.79 42 84 3 21 SS Boo 7.61 88.8 7.61 22 90 1 22 RT CrB 5.12 84.6 5.12 28 82 2 23 TZ CrB 1.14 28 1.17 25 27 1 24 CM Dra 1.27 89.8 1.27 13 90 0 25 WW Dra 4.63 81.4 4.63 43 84 3 26 V824 Ara 1.68 50 1.68 34 40 10 27 Z Her 3.99 83.1 3.96 34 79 4 28 PW Her 2.88 90 2.88 67 90 0 29 V478 Lyr 2.13 82.8 2.19 21 80 3 30 HD 191262 5.43 47 5.53 6 48 1 31 CG Cyg 0.63 82.4 0.63 70 79 3 32 ER Vul 0.70 67 0.69 81 74 7 33 RT Lac 5.07 89 5.07 49 90 1 34 AR Lac 1.98 87 1.98 81 82 5 35 KZ And 3.03 58 3.03 11.6 64 6 36 RT And 0.63 88.4 0.63 109 85 3 37 SZ Psc 3.97 76 3.97 54 86 10 38 EZ Peg 11.66 25 11.66 7 29 4 39 KT Peg 6.20 49 6.09 8 59 10 732 A. A.

Table4

Physical parameters for asynchronous binaries

T R

No. Name HD/BD Spectrum Mbol eff Mass

KR M

1 VY Ari 17433 K0IV+M0V 4.50 4800 1.60 1.02 2 OU Gem 45088 K3V+K5V 5.90 4950 0.76 0.73 3 TY Pyx 77137 G5 IV + G5 IV 3.75 5400 1.72 1.20 4 LR Hya 91816 K0V+K0V 5.80 5120 0.75 0.75 5 IL Com 108102 F8V+F8V 4.10 6090 1.15 1.12 6 BY Dra 234677 K4V+K7.5V 6.70 4280 0.70 0.61 7 V1285 Aql +8 142 K3.5 V +K3.5 V 9.60 3800 0.23 0.30

Table5

Orbital and rotational parameters for asynchronous binaries

i P V i i i No. Name Porb orb rot rot sin rot rot days deg. days km/s deg. deg.

1 VY Ari 13.20 57 16.42 8.6 90 33 2 OU Gem 6.99 77.5 7.36 5.6 90 12 3 TY Pyx 3.20 87.9 3.32 23 61 27 4 LR Hya 6.87 62.5 3.14 6 30 32 5 IL Com 0.96 52 0.82 35 30 22 6 BY Dra 5.98 28 3.84 8 60 32 7 V1285 Aql 10.32 32 2.90 3.6 62 30

2.2. Inclination of The Orbital Plane, iorb

For 21 eclipsing binaries iorb is close to 90 and errors are negligibly small. In i order to check the accuracy of our Mbol determinations, we recalculated orb for

these stars using orbital elements and masses from the mass-luminosity relation and

T M i our eff and v . In all cases (except CM Dra) we obtained orb very close to that

determined from the original analysis of the observed light curve (the differences

always smaller than 1 ). It con®rms a good accuracy of our determinations of v

and Teff . CM Dra is the coolest and smallest system (M4 Ve + M4 Ve) included

in our sample because other orbital and rotational parameters are well known.

Partial eclipses of this binary suggest iorb very close to 90 . Masses from our

M T i determinations of v and eff suggest orb close to 70 , evidently in error. There Vol. 45 733 are two possible sources of this error: ®rstly, for stars cooler than about 3300K

the bolometric corrections are very uncertain and sensitive to the adopted Teff ,

secondly, our determination of Teff is uncertain because very strong emission lines from both components of this binary in¯uence measured color indices. There are 23 systems in our sample without any evidence for eclipse. For these

binaries we have determined iorb using our stellar masses and compared them with

iorb originally estimated by the authors determining orbital elements from radial velocity curve. The discrepancies and errors are discussed in the comments to

individual stars. In Tables 2±5 we present the results for those systems only where

the accuracy of iorb is better than about 5 .

2.3. Inclination of the Rotational Axes, irot

V i

The procedure is the same as in Paper I and II. Prot and rot sin rot are taken

V i V

mainly from CABS, irot is calculated from the ratio rot sin rot rot . Results are

i i very sensitive to the errors in Vrot sin rot , especially for rot 75 because of the

sine function. These errors lead sometimes to values of sin irot slightly larger

= i than 1. In such a case we assumed irot 90 . The errors of rot are much larger

than those of iorb . Detailed analysis of errors is presented in Comments. In many

cases irot has been evaluated with accuracy better than 10 .

3. Results i Stellar and orbital parameters with resulting iorb and rot are presented in

Tables 2±5. The inclination of the equatorial rotational plane to the orbital plane

= ji i j i orb rot is presentedin the last columns of Tables 3 and5. It is a measured

indicator of non-coplanarity. Taking into account that the evaluation of iorb and

irot is based on many observables determined with different accuracy, we assume

that i 15 is a safe limit to con®rm non-coplanarity.

Our sample contains 39 synchronous systems with the observed difference P between Porb and rot smaller than 2.5% and 7 asynchronous systems with this difference larger than 3.8%. There are 23 main sequence binaries (17 synchronous and 6 asynchronous) and 23 short-period RS CVn binaries (22 synchronous and 1 asynchronous).

We call attention to the ambiguity in i analysis (see discussion in Paper II and

Hale 1994). Even for a rotational axis not perpendicularto the orbital plane one can i measure identical iorb and rot , if the direction of observation is perpendicular to

both vectors. The statistical analysis presented in Paper II shows that if irot is really i

at random angle to iorb then the observed average for a sample will be equal to

30 6 . The averagevalue of for 7 analyzed asynchronoussystems is equal to 27 3, while for 39 synchronoussystems it is equal to 5. 4. With 99.6% con®dence

we can claim that i is not random for synchronous binaries. This result is almost identical with that obtained in Paper I and II for long-period RS CVn binaries. 734 A. A.

As mentioned above rotational periods were taken from Pphot measurements.

Variations of Vobs are caused by stellar spots. When binary is of an SB1 type or the primary component is much brighter than the secondary one, this period is

identi®ed with Prot of visible (or much brighter) component and corresponding

i i

Vrot sin rot gives rot . When both components are identical the problem of using i

proper Vrot sin rot does not exist. There are nine such systems in our sample and i in all cases the measured values of Vrot sin rot are the same for both components. Four of these systems are rotating asynchronously, and conclusions about their

non-coplanarity are most probably valid for both components. Unfortunately, in i 15 binaries both (not identical) components are visible, two Vrot sin rot values are

known and only one Pphot is measured. The question is, which component is i spotted, and consequently which value of Vrot sin rot should be used. In most cases the level of chromospheric activity is a good indicator for presence of the spots. This question is discussed individually in Comments. On the other hand it

allows for estimation of inclinations of some secondary components. Assuming a

P = P V i

priori that phot rot sec and using rot sin rot of the secondary we can evaluate i

rot sec . The results are presented in Table 6 (see also Table 4 in Paper II). All

i values are comparable to those of the primary components. Only RW UMa i

shows large difference, but that might be caused by the error in Vrot sin rot (sec). i Increasing Vrot sin rot by 1 km/s for the secondary leads to excellent agreement

with irot of the primary. For two asynchronous systems (BY Dra and V1285 Aql) the secondaries like the primaries seem to be non-coplanar. One should bear in

mind, however, that the assumption of Pphot identical for both components is a serious oversimpli®cation.

We have excluded from our analysis II Peg. It is one of the most frequently

observed and analyzed binary system because of spectacular spot and ¯are activity.

= This SB1 main sequence (or slightly above) star with orbital period Porb 6 724 days has well established synchronousphotometric period equalto 6.718days. The best orbital parameters were determined by Vogt (1981). Recently, Byrne et al. (1995) in an extensive analysis of all previous data con®rm parameters attributed

for this star in CABS. In order to make a model of spots Byrne et al. (1995) must

= i =

assume irot 90 . Earlier photometric observations lead to rot 60 (Bopp and

Noah 1980) or between 40 60 (Poe and Eaton 1985). According to CABS

iorb 34 ; although it is rather minimum value. Bopp and Noah (1980) suggest

= i

iorb 60 coplanar with rotation. But Byrne et al. (1995) claim that rot must be

closeto 90 . Becauseoflack of any evidenceforeclipses iorb must be smaller than

i =

90 . Byrne et al. (1995) con®rm that Vrot sin rot 21 1 km/s. Trigonometric

parallax of II Peg is equal to 0 034 0 007 in very good accordance with v

from the spectral type. From the multicolor photometry and spectral type we

obtain Teff 4700 100 in very good accordance with other authors. Resulting

i i =

radius is about 1 5R . With these parameters sin rot 2. To obtain rot 90

R R i =

1 shouldbeequalto 3R and for rot 50 1 should exceed 4R , in complete Vol. 45 735

Table6

Physical parameters for the secondary components

M T R V i i i

Name Sp. type bol2 eff 2 2 Mass 2 sin rot rot 2 2

KR M km/s deg. deg.

UX Ari G5 V 4.80 5650 0.97 0.92 6 52 8 V711 Tau G2 V 4.62 5450 1.13 1.10 13 40 7 GK Hya F8 V 4.05 6090 1.18 1.25 16 74 10 RW UMa F8 IV 2.80 5950 2.30 1.60 13 69 20 AS Dra G9 V 5.20 5340 0.90 0.87 8 71 1 SS Boo G0 V 4.50 5800 1.06 1.00 8.8 90 1 RT CrB G5-8 IV 2.60 5300 3.00 1.40 31 90 5 TZ CrB G0 V 4.40 5890 1.07 1.14 26 34 6 WW Dra G2 IV 3.10 5750 2.00 1.35 22 81 0 CG Cyg K3 V 6.00 4750 0.75 0.81 58 80 2 ER Vul G5 V 4.60 5700 1.05 1.03 71 69 2 RT Lac G9 IV 2.00 5100 4.30 1.65 43 90 1 AR Lac G2 IV 3.50 5550 1.80 1.30 46 80 7 OU Gem K5 V 6.42 4470 0.74 0.65 5.6 90 12a BY Dra K7.5 V 7.60 3900 0.56 0.49 7.4 85 57a

a ± asynchronous systems disagreement with position of II Peg on HR diagram. This is very interesting case of non consistent observables. Byrne et al. (1995) assume (without mentioning) non-coplanarity for this synchronous system.

3.1. Comments on Individual Stars Listed in Tables 2 and 3 FF And = BD +34 106. SB2, both components are active, main sequence

stars of the same temperatures and masses. The error in iorb is of the order of

T M

2 . The error in eff is around 100 K, while v is uncertain by 0. 2. The

i i most uncertain is the parameter Vrot sin rot . The total error of rot is rather large,

+14 = i 68 , but the assumption of coplanarity for both components seems to be rot 17 justi®ed. CF Tuc = HD 5303. SB2, partial eclipses, active is the K type component. We

use iorb given by Kunster and Dennerl (1993) and Strassmeier (1995). Accuracy of

T iorb is equal to 4 . Ourvalueof eff is very close to that of Barrado et al. (1994).

Kunster and Schmitt (1995) suggest a slightly larger radius for K component. The

i R

error of Vrot sin rot might be as large as 2 km/s. Assuming between 2 and

V i i

2.4 R and rot sin rot between 33 and 37 km/s we obtain total error in rot equal to 10 . BI Cet = HD 8358. SB2, both components are active, main sequence stars of the same temperatures and masses. The distance to this system is well known,

736 A. A.

V i i

and therefore only the errors in Teff and rot sin rot contribute to the error in rot .

( V i (

Assuming a maximum uncertainty in Teff 150 K) and in rot sin rot 5 km/s),

the error in irot does notexceed 4 . Mostprobably both componentsare coplanar.

CC Eri = HD 16257. SB2, both components are main sequence stars. The

error in iorb is not larger than 2 . Because of high accuracy in the determination R

of Teff and for the spotted K type component, the main source of uncertainty in

V i V i i

irot is the error in rot sin rot . When changing rot sin rot by 3 km/s, rot changes from 37 to 65 .

LX Per = HD 19845. SB2, total eclipses, spotted is the cooler, K type R component. Our values of Teff , and mass are in very good agreement with those

given by Poe and Eaton (1985) and Montesinos et al. (1988). The total error in

V i = irot is less than 5 . If the CABS value of rot sin rot 9 km/s for the secondary

component is correct and coplanarity is assumed, its rotation is asynchronous with i orbital motion, while the primary is synchronous. Good determination of Vrot sin rot for G type component is desirable.

UX Ari = HD 21242. SB2, with spotted K type component. The uncertainty in

iorb does not exceed 5 . eff determined from multicolor photometry agrees with M

that given by Poe and Eaton (1985). v suggests that the luminosity class should

i =

be III±IV instead of IV given in CABS. We assume Vrot sin rot 37 km/s from i

CABS, but Strassmeier (1995) quotes 39 km/s. With this uncertainty in Vrot sin rot

the total error in irot is equal to 15 . If the secondary rotates synchronously, both components will be probably coplanar. V711 Tau = HD 22468. SB2, one of the most frequently observed RS CVn

binary, with many determinations of spots distribution (see references in Strass-

meier 1995). All authors assume iorb 33 . More active is the cool, primary R

component (Fernandez±Figueroa et al. 1994). The errors in Teff and are small.

Even if we assume error in Vrot sin rot as high as 5 km/s, the total error in

irot will remain very small, around 4 . Donati et al. (1992b) have determined

i = i = Vrot sin rot 41 km/s claiming an error of 1 km/s. Thisvalueleadsto rot 41 , still not contradicting coplanarity.

V837 Tau = HD 22403. SB2, sometimes called "early type" BY Dra system.

i T M i

orb is within 71 to 76 . Uncertainties in eff and v can lead to the error in rot

V i i

around 10 . With the uncertainty of rot sin rot ( 2 km/s) we estimate that rot

is between 65 and 90 .

(m) =

EI Eri = HD 26337. SB1 with small value of mass function, f 0 0042.

For iorb we use value 46 given in CABS and Hatzes and Vogt (1992). Our estimation suggests slightly lower value (about 40 ). With consistent set of stellar

parameters which we have accepted, the estimation of iorb leads to values higher

than 35 and lowerthan 50 . Hatzes et al. (1995) give Teff only 100 K higher than i

our estimation. Vrot sin rot is uncertain (see comments in CABS). But even using

V i i

the extreme values for R and rot sin rot , rot is always between 32 and 50 .

(m) = V833 Tau = HD 283750. SB1, f 0 00022 allows for reliable determi-

Vol. 45 737

i M i

nation of orb . Uncertainty in v leads to the error in rot equal to 5 . Earlier

determination of Vrot sin rot by Strassmeier et al. (1990) is 8 2 km/s. We usethe

more accurate value from CABS. The total error in irot does not exceed 10 . YY Gem = HD 60179= Castor C. SB2, partial eclipses, both components are

main sequencestars of the same masses, radii and temperatures. Recently, Butler et

= T al. (1995) obtained slightly smaller orbital inclination ( iorb 85 95). Values of eff

and R are known with high accuracy. For both components projected rotational

velocities are too high, leading to sin irot 1. With the new determination of

i = i

Vrot sin rot 48 km/s (Hatzes 1995b) sin rot becomes even higher. We assume

= irot 90 , but the explanation of the observed discrepancies is necessary. GK Hya = BD +2 1993. SB2, total eclipses, spotted is the primary of spectral

type G8 IV. With the best stellar parameters sin irot is close to unity. The possible

i i error in Vrot sin rot gives the lower limit of rot equal to 78 . If the secondary rotates synchronously, both components will be coplanar.

RU Cnc = BD +24 1959. SB2, total eclipses, more active is the K type

R i

component. Although the uncertainty in Teff and is rather high, rot is always

V i close to 90 . The lower limit of irot is 80 when errors in rot sin rot are included. If the secondary rotates synchronously, both components will be coplanar. XY UMa = HD 237786. SB2, partial eclipses, photometric period is related

to the brighter, G3 V type component. There is an indication of infrared excess.

V T

B leads to erroneous temperature. We estimate eff from spectral type and

multicolor photometry excluding B . The error is however large, 150 K,

V i

leading to 5% uncertainty in R . Because of the large value of rot sin rot , even an i

error of 5 km/s does not in¯uence seriously determination of rot . The total error

in irot is estimated to be equal to 13 .

BF Lyn = HD 80715. SB2, secondary is 1m weaker than the primary. Trigono-

M T metric parallax equal to 0. 034 provides accurate v . Unfortunately error in eff

+14

R i is high ( 150 K) and error in is not negligible. Our estimate of is 76 . rot 10 m m

Note the error in CABS value of M v , 5. 4 instead of 6. 4.

DM UMa = BD +61 1211. SB1. Our value of iorb agrees with that of

T M

Hatzes (1995a) and CABS. The error in eff is very small ( 70 K) while v is

V i =

uncertain by 0. 2. We use rot sin rot 27 km/s given in CABS. With Hatzes

i i

(1995a) value of 26 km/s irot becomes even closer to orb . The total error in rot

T = is about 10 . Mohin and Raveendran (1994) found eff 4700 K, and small differential rotation of the order of 0.3%.

RWUMa=BD+521579. SB2, total eclipses, spots are presenton the primary,

T M

K type component. Although accuracy of eff and v determination is not high,

our values of R are in good agreement with CABS and Montesinos et al. (1988).

i i When changing Vrot sin rot by 2 km/s, resulting rot changes from 66 to 90 . If the secondary is rotating synchronously it will be also coplanar. AS Dra = HD 107760. SB2, both components are main sequence G type stars. We assume that the photometric period is related to the brighter and hotter primary.

738 A. A.

The error in iorb is lower than 2 . Trigonometric parallax is probably in error

(see also CABS). For both main sequence components radii are determined with

i P accuracy better than 10%. The total error in rot is equal to 12 . If rot sec is

equal to the observed Pphot the secondary will be also coplanar. UX Com = BD +29 2355. SB2, total eclipses, spotted is the K type subgiant.

Secondary is most probably G type dwarf. The same Teff was obtained by Mon-

tesinos et al. (1988). Even with extreme values of v and assumption of 5 km/s

i i error in Vrot sin rot , rot is always larger than 75 .

RS CVn = HD 114519. SB2, total eclipses, spotted is the G type star. Our R

Teff and agree with that of Montesinos et al. (1988) and Randich et al. (1994).

The total error in irot does not exceed 7 . For the secondary component (F4 IV),

i = projected rotational velocity ( Vrot sin rot 11 km/s) is two times too low to agree with synchronous rotation. SS Boo = BD +39 2849. SB2, total eclipses, active is the K type subgiant. Our

stellar parameters are very similar to that in CABS and Montesinos et al. (1988).

V i

The lower limit of irot equal to 78 is obtained when the observed rot sin rot is

i i reduced by 3 km/s. For Vrot sin rot 22 km/s the value of sin rot becomes larger than unity. If the secondary rotates synchronously it will be also coplanar. RT CrB = HD 139588. SB2, partial eclipses. It is not clear which component is spotted. Mg II emissions are stronger in the cooler star (De Castro et al. 1990),

suggesting higher activity and more pronounced spots. We have estimated irot for

T R V i both components using the same Pphot . The errors in eff , and rot sin rot for

both components are the same. In Tables 2 and 3 we present results for the hotter, +

+8 0

= i =

primary component ( i 82 ). For the secondary 90 . In both cases rot 7 rot 12 rotation is coplanar with the orbital plane. TZ CrB = HD 146361. SB2, both components are main sequence stars.

Photometric period is about 2% longer than the orbital period. Slightly different

= V i

orbital elements of Duquennoy and Mayor (1991) provide iorb 30 . rot sin rot

i i

is taken from Hale (1994). When changing Vrot sin rot by 2 km/s, rot changes from 25 to 35 for both components.

CM Dra = Gl 630.1A. SB2, partial eclipses, the coolest stars in our sample i

(both of M4 Ve spectral type). All stellar parameters except Vrot sin rot are known

i = i

with very high accuracy. With Vrot sin rot 13 km/s (as given in CABS) sin rot is

i = i =

close to, but slightly larger than unity, with Vrot sin rot 12 km/s rot 90 and

i = i = with Vrot sin rot 11 km/s rot 81 . Coplanarity of the both components can not be challenged.

WW Dra = HD 150708. SB2, partial eclipses, spots are on the cooler compo- R

nent (Fernandez±Figueroa et al. 1994). Our values of Teff and are almost the i

same as those given by Montesinos et al. (1988). The error in Vrot sin rot equal to

T R i 2 km/s plus errors in eff and lead to the total error of rot equal to 9 . V824Ara=HD155555. SB2, active is the primary hottercomponent,regarded by many authors as pre-main-sequence star (see e.g.,Mathieu 1994). Accuracy of

Vol. 45 739

V i

the determination of iorb is better than 4 . We use the value of rot sin rot from

i T

Donati et al. (1992a). The errors in Vrot sin rot and eff ( 180 K) are the main

contributors to the error in irot , which is rather high, equal to about 15 . We still regard this system as coplanar.

Z Her = HD 163930. SB2, partial eclipses, spotted is the primary K type R component. Ourvaluesof Teff and agreeverywellwiththatgivenbyMontesinos

et al. (1988) and Barrado et al. (1994). Slightly different data given by Randich et

= al. (1994) lead to irot 73 . Using both sets of data and adding errors we evaluate

+11 = the most probable value of i 79 , con®rming coplanarity.

rot 9 0

h m

= =

PW Her RA 18 10 , 33 24 . SB2, total eclipses, active is the cool,

V i

K type component. Main source of error of irot is uncertainty of rot sin rot .

i i

Changing Vrot sin rot from 67 km/s to 64 km/s leads to rot equal to 80 . With

i i

Vrot sin rot higher than 67 km/s sin rot becomes larger than unity. If the cited in

i = CABS value of Vrot sin rot 15 km/s for the secondary component is correct and

coplanarity is assumed, its rotation will be asynchronouswith orbital motion, while i the primary is synchronous. Good determination of Vrot sin rot for the secondary is desirable.

V478Lyr=HD178450. SB1, partialeclipses, spotted is G8 Vtype component.

V i According to Hall et al. (1990) error of iorb is equal to 0 5. rot sin rot from Fekel et al. (1986) and Tan Hui-song and Liu Xue-fu (1986) are the same, but

the error is unknown. Remaining parameters are known with very high accuracy.

i i Reducing Vrot sin rot by 2 km/s reduces rot to 70 . We can assume that real value

+10 = of i 80 . Differential rotation ranging from 0.4% faster than synchronous rot 10 to 0.5% slower than synchronous is quoted in CABS. HD 191262 = BD +15 4057. SB2, both components are identical G5 V type

stars. Detailed analysis made by Popper (1994) allows to estimate the error of iorb

T R

to be equal to 2 . Our determinations of eff and agree very well with that i

of Popper (1994). Value of Vrot sin rot as measured by Strassmeier et al. (1990) is

i equal to 6 km/s, but error of 1 km/s leads to the error in rot equal to 12 .

CG Cyg = BD +34 4217. SB2, partial eclipses, both components are active. R

The orbital inclination is taken from Zeilik et al. (1994). Our Teff and values i agree with that given by Montesinos et al. (1988). For Vrot sin rot we assume an

+11

i = T R error 2 km/s. The resulting error of 79 . Values of and derived by

rot 9 eff

= Zeilik et al. (1994) lead to irot 90 . For the secondary component (assuming the

+10

P V i = i =

same , and the measured sin 58 km/s) 80 . Therefore, phot rot rot rot sec 10 probably both components are coplanar. ER Vul = HD 200391. SB2, partial eclipses, spotted is the hotter, primary

component. Analyses made by Olah and Budding (1993) and Olah et al. (1994)

prove that iorb is between 65 and 72 . Our values of are very close to that i

obtained by Grif®n (1982) and Olah et al. (1994). Taking Vrot sin rot from Olah et

i R i al. (1994) and including the errors in Vrot sin rot and , we obtain for rot value 74+12 . Montesinos et al. (1988) obtained slightly larger radius leading to lower 12

740 A. A.

= i value of irot 68 , almost exactly equal to orb . RT Lac = HD 209318. SB2, total eclipses, both components are active, but according to Fernandez±Figueroa et al. (1994) the cooler component is responsible for the emissions. Uncertainty of parameters is described in details in Notes in

CABS. Varying the stellar parameters within their limits of error, for the primary as

wellasforthesecondary,wehavealwaysobtained irot 80 . Forbothcomponents irot is therefore, very close to 90 . AR Lac = HD 210334. SB2, total eclipses. According to Walter et al. (1983) spotted is the hotter component, but new analysis of Hatzes et al. (1995) and Lanza

et al. (1995) show that spotted is the cooler, K type component. Our values of Teff

and R for both components, agree very well with those presented in these analyses i as well as with those given by Ottman and Schmitt (1994). We use Vrot sin rot

values from Hatzes et al. (1995) with assumed error 2 km/s. Applying the same

+8 = photometric period for both components we obtain for K type star i 82 rot 7

+9 = and for G type star i 80 . We conclude that either the spotted star or both rot 8 components are coplanar. KZ And = HD 218738. SB2, both components are identical main sequence K

type stars. According to Randich et al. (1994) and Montes et al. (1995) both are

T active. The error of iorb might be as large as 5 . Small errors of eff ( 50 K),

M V i i

v ( 0. 2) and rot sin rot ( 1 km/s) give the total error of rot equal to 8 .

RT And = BD +52 3383. SB2, total eclipses, active is the cooler K type component. Lower limit for iorb is equalto 81 as shown by Wang Xiumei and Lu

Wenxian (1993). Recently Arevalo et al. (1995) derived the same values of Teff , M

R and for both components as those given in Table 2. Because of the large

i value of Vrot sin rot , even the error of 5 km/s does not in¯uence seriously the

+5 i evaluation of i . Resulting is equal to 85 . rot rot 10

SZ Psc = HD 219113. SB2, partial eclipses, spotted is the cooler, K type

V i component. The error of iorb is of the order of 1 . rot sin rot is taken from

Randich et al. (1994). All parameters are known with reasonable accuracy ( Teff , M R and agree with determinations of Randich et al. (1994) and Kalimeris et al.

(1995) and the resulting i is equal to 86 . rot 11

EZ Peg = BD +24 4742. SB2, active is the cooler, K type component. iorb

uncertain up to 5 . Trigonometric parallax gives v of the K type component

typicalfor main sequencestar. All spectroscopicdata indicatethatthis isa subgiant.

T M V i

Small error in eff ( 50 K) together with uncertainty of v and errorof rot sin rot

i (estimated to be about 2 km/s), give the total error of rot equal to 10 .

KT Peg = HD 222317. SB2, active is the hotter, primary component. Both

T M

components are main sequence stars. eff , v and M can be determined with high

V i accuracy. The error of iorb is less than 2 . Accuracyof rot sin rot determination

+13

i = i = is notwellestablished. Assuming V sin 8 1 km/s we obtain 59 . rot rot rot 12 Vol. 45 741

3.2. Comments on Individual Stars Listed in Tables 4 and 5

VYAri=HD17433. SB1, the primary is of K0 IV±V spectral typeand the secondary is main sequence M type star. Pronounced asynchronism, with rotational

M =

period 32% longer than the orbital period. v 4. 95 is determined from the

= ) trigonometric parallax ( 0. 050 . The location of the primary above the main

sequence agrees very well with the spectroscopic characteristics. Multicolor photometry allows for accurate determination of Teff ( 60 K). The mass of the primary

is close to 1 M . With similar parameters Duquennoy and Mayor (1988a) esti-

i = mated i equal to 60 with the upper limit equal to 62 . We obtain 57 .

orb orb 4 i The value of Vrot sin rot is not well known. In CABS 6 km/s, as estimated by Saar

and Linsky (1986), is quoted. Duquennoy and Mayor (1988a) publish a value of

95 1 km/s obtained with CORAVEL. We assume 8 2 km/s. Discussion of photometric period is presented in Notes in CABS and in the paper of Duquennoy and Mayor (1988a). Several photometric periods are observed, but there is no

doubt that the rotational period is between 16 and 17.5 days. All combinations of

i P i

Vrot sin rot and rot in the range given above lead to sin rot slightly larger than

unity. We conclude that irot is equal or very close to 90 . Non-coplanarity of i rotation seems to be certain, but accurate measurements of Vrot sin rot are needed. OU Gem = HD 45088. SB2, both main sequence K type components are

active. A slight asynchronism, the rotational period is only 5% longer than the

d = M

orbital period. This is a nearby binary system ( 14 9 pc) and v is very accurate. The brightness difference between the components is known, and a separation of measured total color indices between both stars is possible. From the BVRI photometry and spectral types, the temperature of both components was

established with the accuracy of 50 K. Our radius determination for the brighter

R =

component ( 0 76R ) is in very good accordance with Hale (1994), who

R = i V i obtained 0 8R . He also estimates rot as close to 90 . Values of rot sin rot

given in CABS are taken from Saar and Linsky (1986), where the accuracy is claimed to be 0 5 km/s. Using the above data (with allowance for errors) we

obtain sin irot between 0.98 and 1.08. We support the conclusion by Hale (1994)

= that irot 90 , with the lower limit equal to 79 . Well known position of the components on HR diagram allows the determination of masses of both main

sequence stars with reliable accuracy. In consequence we can put the lower limit

for iorb to 75 and the upper limit to 80 . Because no trace of eclipses have been found in many photometric observations iorb must be less than 85 . No

de®nite conclusion about coplanarity for this system can be drawn. New, accurate i measurements of Vrot sin rot are desirable. TY Pyx = HD 77137. SB2, partial eclipses, both active subgiants are of the

same spectral type. Slight asynchronism, the rotational period is 4% longerthanthe M

orbital period. Although v is not known with high accuracy, our determinations R

of Teff and are in good agreement with that of Barrado et al. (1994) and Randich

V i et al. (1994). The main source of error in irot is the uncertainty of rot sin rot . We

742 A. A. i are using the updated values of Vrot sin rot given in CABS, and with the assumed

i = i error of 2 km/s we obtain 61 . Because is well de®ned from partial rot 8 orb

eclipses, we regard this system as non-coplanar. A de®nite answer will be possible i after accurate measurements of Vrot sin rot . LR Hya = HD 91816. SB2, both components are main sequence stars with the identical parameters. Photometric period is 54% shorter than the orbital period.

Well known trigonometric parallax and temperature (error 80 K) minimize errors

V i

in R . The error of rot sin rot is not known. Fekel et al. (1986) obtained 6 km/s

= V i

for both components, leading to irot 30 . Error of rot sin rot , aslarge as2km/s,

can change irot value up to 41 . We estimate error of rot to be equal to 11 .

Fekel et al. (1988) obtained for iorb value 61 . Our parameters give value 64 . +

= i We assume i 62 5 . In order to achieve coplanarity ( close to 60 )

orb 3 rot i

Vrot sin rot should be increased to 11 km/s, value almost two times larger than the i measured one. Although new determination of Vrot sin rot would be very useful, non-coplanarity of the rotation in this binary seems to be certain. IL Com = HD 108102. SB2, both active components are main sequence F8 type stars with identical parameters. The photometric period is shorterby 15% than

the orbital period. Among asynchronous late type binaries this is a system with the

shortest orbital period. We estimate the error in masses to be equal to 0 2M .

T M

The error of eff is equal to 80 K, and v is known with the accuracy of m

0. 2. The resulting values of orbital and rotational inclinations are the following: +

+7 5

= i =

i 52 and 29 5 . Becausethe componentsof the binary are identical, orb 4 rot 4 non-coplanarity is likely for both of them. BY Dra = HD 234677. SB2, prototype of BY Dra systems. Both components are K type main sequence stars. Both are active. The primary is more than

m P 1 brighter than the secondary. We assume that Pphot is related to the primary. rot

(Mavridis et al. 1995) is shorter than Porb by 56%. Orbital inclination has been

discussedby many authors. We assume iorb 28 given in CABS. Our parameters

= i

give iorb 29 . Analysis of errors proves that orb is known with accuracy not

T worse than 3 . Multicolor photometry allows the determination of eff with

M V i accuracy 70 K.Theerrorin v is not larger than 0. 2. The error of rot sin rot determination in unknown. We use value 3.6 km/s given in CABS, assuming that the error might be as large as 20%. When all errors are taken into account, we

+11

= P obtain i 60 . If the secondary is responsible for the observed , its rot 9 phot

i =

85 , also indicating non-coplanarity. rot sec 15 V1285 Aql = BD +8 142. SB2, both components are main sequence stars with

the identical parameters. Pphot is much shorter (2.9 days) than the orbital period

(10.3 days). Orbital inclination can be determined with accuracy better than 2 .

d = M

This nearby binary ( 11 pc) allows for very precise evaluation of v . Unfor-

V T

tunately, only B index is known. The error in eff is large (about 200 K). i

Vrot sin rot is taken from Duquennoy and Mayor (1988b). Because of very low

i i value of Vrot sin rot , its error is crucial for the accuracy of rot determination. Our

Vol. 45 743

= T V i i

value of irot 62 is not certain. Errors in eff and rot sin rot can change rot

2 = from 55 up to 90 . With i 32 the system is most probably non-coplanar.

orb 2

i T Good measurements of Vrot sin rot and eff are necessary for de®nite conclusion.

4. Conclusions =

Presented analysis of 46 binary system broadens our investigation of i

ji i j orb rot to main sequence and short-period RS CVn stars. Together with

Paper I and II it gives 78 late type binary systems with known i . Results shown in Tables 2 and 3 con®rm previous ®nding that synchronous binaries rotate with equatorial plane parallel to the orbital plane, while in general asynchronoussystems are non-coplanar. This is probably true for both components. Among 46 F, G, K, M spectral type binaries with periods less thanabout10days, we found 7 asynchronous and non-coplanar. It proves that any a priori assumption about synchronism or coplanarity even for binaries with short periods is dangerous. If we add data from Paper I and II a general conclusion can be made: in late type binary systems independently of the period (up to about 100 days), position on HR diagram, mass ratio and eccentricity synchronous systems rotate coplanarily,

while in asynchronous ones, inclination of the rotational axis to the orbital plane is in general random. Extension of the analysis to Porb 100 days is recommended. An interesting case of II Peg requires further observations and analysis either to

correct fundamental parameters (especially iorb ) or to show that it is an exception from the above rule. It also shows how hazardous are some generalizations.

Acknowledgements. ThispaperwassupportedbyKBNgrantNo.2P30402007.

REFERENCES

Arevalo M.J., Lazaro, C., and Claret, A. 1995, 9th Cambridge Workshop: Cool Stars, Stellar Systems and the Sun, in press. Barrado, D., Fernandez±Figueroa M.J., Montesinos, B. and De Castro, E. 1994, Astron. Astrophys., 290, 137. Bessell, M.S. 1979, P.A.S.P., 91, 589. Blackwell, D.E., and Lynas-Gray, A.E. 1994, Astron. Astrophys., 282, 899. Blackwell, D.E., Lynas-Gray, A.E., and Petford, A.D. 1991, Astron. Astrophys., 245, 567. Bopp, B.W., and Noah, P.V. 1980, P.A.S.P., 92, 717. Bohm-Vitense, E. 1982, Ann. Rev. Astr. Astrophys., 19, 295. Buser, R., and Kurucz, R.L. 1992, Astron. Astrophys., 264, 557. Butler, C.J., Budding, E., and Doyle, J.G. 1995, 9th Cambridge Workshop: Cool Stars, Stellar Systems and the Sun, in press. Byrne, B.P., Panagi, P.M., Lanzafame, A.C., Avgoloupis, S., Huenemoerder, D.P., Kilkenny, D., Marang, F., Panov, K.P., Roberts, G., Seiradakis, J.H., and van Wyk, F. 1995, Astron. Astrophys., 299, 115. Cayrel de Strobel, G., Hauck, B., Francois, P., Thevenin, F., Friel, E., Mermilliod, M., and Borde, S. 1992, Astron. Astrophys. Suppl. Ser., 95, 273. 744 A. A.

De Castro, E., Fernandez±Figueroa, M.J., Cornide, M., and Reglero, V. 1990, Astrophys. Sp. Sci, 170, 99. Donati, J.-F., Semel, M., and Rees, D. 1992a, Astron. Astrophys., 265, 669. Donati, J.-F., Brown, S.F., Semel, M., Rees, D.E., Dempsey, R.C., Mathews, J.M., Henry, G.W., and Hall, D.S. 1992b, Astron. Astrophys., 265, 682. Duquennoy, A., and Mayor, M. 1988a, Astron. Astrophys., 195, 129. Duquennoy, A., and Mayor, M. 1988b, Astron. Astrophys., 200, 135. Duquennoy, A., and Mayor, M. 1991, Astron. Astrophys., 248, 485. Fekel, F.C., Moffett, T.J., and Henry, G.H. 1986, Astrophys. J. Suppl. Ser., 60, 551. Fekel, F.C., Gillies, K., Africano, J., and Quigley, R. 1988, Astron. J., 96, 1426. Fernandez±Figueroa, M.J., Montes, D., De Castro, E., and Cornide, M. 1994, Astrophys. J. Suppl. Ser., 90, 433. Gray, D.F. 1992, The Observation and Analysis of Stellar Photospheres, Cambridge Univ. Press, p.431. Grif®n, R.F. 1982, MNRAS, 201, 487. Hale, A. 1994, Astron. J., 107, 306. Hall, D.S., Henry, G.W., and Sowell, J.R. 1990, Astron. J., 99, 396. Hatzes, A.P. 1995a, Astron. J., 109, 350. Hatzes, A.P. 1995b, Poster Proceedings: IAU Symp. 176, ed. K.G. Strassmeier, Univ. Vienna, p. 90. Hatzes, A.P., Vogt, S.S., Ramseyer, T.F., and Misch, A. 1995, Poster Proceedings: IAU Symp. 176, ed. K.G.Strassmeier, Univ. Vienna, p. 9. Johnson, H.L. 1966, Ann. Rev. Astr. Astrophys., 4, 193. Kalimeris, A., Mitron, C.K., Doyle, J.G., Antonopoulou, E., and Rovithis-Livaniou, H. 1995, Astron. Astrophys., 293, 371. Kunster, M., and Schmitt, J.H.M.M. 1995, Poster Proceedings: IAU Symp. 176, ed. K.G.Strassmeier, Univ. Vienna, p. 200. Landolt-Bornstein 1982, Numerical Data and Fundamental Relationships in Science and Technology, Vol. 2b. Springer-Verlag, p. 453. Lang, K.R. 1992, Astrophysical Data: Planets and Stars, Springer-Verlag, New York, p. 116. Lanz, T. 1986, Astron. Astrophys. Suppl. Ser., 65, 195. Lanza, A.F., Pagano, I., Rodono, M., and Catalano, S. 1995, Poster Proceedings: IAU Symp. 176, ed. K.G.Strassmeier, Univ. Vienna, p. 75. Legget, S.K., Montain, C.H., Selby, M.J., Blackwell, D.E., Booth, A.J., Haddock, D.J., and Petford, A.D. 1986, Astron. Astrophys., 159, 217. Mathieu, R.D. 1994, Ann. Rev. Astr. Astrophys., 32, 465. Mavridis, L.N., Avgoloupis, S.J., Seiradakis, J.H., and Varvoglis, P.P. 1995, Astron. Astrophys., 296, 705. McWilliam, A. 1990, Astrophys. J. Suppl. Ser., 74, 1075. Mohin, S., and Raveendran, A.V. 1994, Astron. Astrophys., 286, 824. Montes, D., Fernandez±Figueroa, M.J., De Castro, E., and Cornide, M. 1995, Poster Proceedings: IAU Symp. 176, ed. K.G. Strassmeier, Univ. Vienna, p. 167. Montesinos, B., Gimenez, A., and Fernandez±Figueroa, M.J. 1988, MNRAS, 232, 361. Novotny, E. 1973, Introduction to Stellar Atmospheres and Interiors, New York Univ. Press, p. 10. Olah, K., and Budding, E. 1993, ASP Conference Series, 38, 385. Olah, K., Budding, E., Kim H.-I., and Etzel, P.B. 1994, Astron. Astrophys., 291, 110. Ottmann, R., and Schmitt, J.H.M.M. 1994, Astron. Astrophys., 283, 871. Poe, C.H., and Eaton, J.A. 1985, Astrophys. J., 289, 644. Popper, D.M. 1980, Ann. Rev. Astr. Astrophys., 18, 115. Popper, D.M. 1990, Astron. J., 100, 247. Popper, D.M. 1994, Astron. J., 108, 1092. Randich, S., Giampapa, M.S., and Pallavicini, R. 1994, Astron. Astrophys., 283, 893. Saar, S.H., and Linsky, J.L. 1986, Cool Stars, Stellar Systems, and the Sun, ed. M.Zeilik and Vol. 45 745

D.M.Gibson, p. 278. Soderblom, D.R. 1982, Astrophys. J., 263, 239. Stawikowski, A., and GøeÎbocki, R. 1994, Acta Astron., 44, 33 (Paper I). Stawikowski, A., and GøeÎbocki, R. 1994, Acta Astron., 44, 393 (Paper II). Strassmeier, K.G. 1995, Stellar Surface Structure, IAU Symp. 176, in press. Strassmeier, K.G., Fekel, F.C., Bopp, B.W.,Demsay, R.C., and Henry, G.W. 1990, Astrophys. J. Suppl. Ser., 72, 191. Strassmeier, K.G., Hall, D.S., Fekel, F.C., and Scheck, M. 1993, Astron. Astrophys. Suppl. Ser., 100, 173. Tan, Hui-Song, and Liu, Xue-Fu 1986, Acta Astr. Sinica, 27, 130. Tan, Hui-Song, Wang, Xun-Hao, and Pan, Kaike 1993, ASP Conference Series, 38, 374. Van Altena, W.F., Truen-Liang Lee, J., and Hof¯eit, D. 1991, The General Catalogue of Trigonometric Parallaxes, Yale University Observatory, New Heaven. Vogt, S.S. 1981, Astrophys. J., 247, 975. Walter, F.M., Gibson, D.M., and Basri, G.S. 1983, Astrophys. J., 267, 665. Walter, F.M., Neff, J.E., Gibson, D.M., Linsky, J.L., Rodono, M., Gary, D.E., and Butler, C.J. 1987, Astron. Astrophys., 186, 241. Wang, Xiumei, and Lu, Wenxian 1993, ASP Conference Series, 38, 280. Zeilik, M., Gordon, S., Jaderlund, E., Ledlow, M., Summers, D.L., Heckert, P.A., Budding, E., and Banks, T.S. 1994, Astrophys. J., 421, 303.