CA II H AND K EMISSION FROM LATE-TYPE STARS
PROEFSCHRIFT
TER VERKRIJGING VAN DE GRAAS VAN DOCTOR IN DE WISKUNDE EN NATUURWETENSCHAPPEN AAN DE RIJKSUNIVERSITEIT TE UTRECHT, OP GEZAG VAN DE RECTOR MAGNIFICUS PROF. DR. M.A. SOUMAN, VOLGENS BESLUIT VAN HET COLLEGE VAN DECANEN IN HET OPENBAAR TE VE^EDIGBN OP MAANDAG 5 JULI 1982 DES NAMIDDAGS TE 4.IS UUR
DOOR
FRANS MIDDELKOOP
GEBOREN OP 30 JANUARI 1953 TE ROTTERDAM •\
PROMOTOR: PROF.DR.C.ZWAAN opgedragen aan:
Ans de Jong (mijn vrouw), Adrianus Middelkoop {mijn vader), Alie Twigt (mijn moeder). De hemelen vertellen Gods eer en het uitspansel verkondigt het werk zijner handen Psalm V9:2 Dankbetuiging Graag wil Ik alle personen en Instellingen die bijgedragen hebben tot de totstandkoming van dit proefschrift van harte bedanken. In de eerste plaats dank Ik mijn promotor, Prof.Dr. Kees Zwaan. Zijn steun en begeleiding zijn, vooral in het eerste jaar van dit onderzoek, van groot belang geweest. Zijn enthousiasme en toewijding hebben mij altijd zeer gestimuleerd. Ook ben ik veel dank verschuldigd aan mijn vriend en collega Barto Oranje. De vele gesprekken die ik met hem heb gevoerd hebben duidelijk invloed op dit proefschrift gehad. Dr. Rene' van Helden heeft mij, op bijzonder prettige en leerzame wijze, de eerste beginselen van de sterrekunde bijgebracht en mij in contact gebracht met mijn promotor. Dr. Tony Hearn stond altijd voor mij klaar als de Interne referee van mijn publikaties.
I am also indebted to Dr. Arthur Vaughan who has instructed me on how to use his excellent Ca II H and K photometer. Be and his wife Ann never failed to make me feel at home in California. Among the many pleasant people I met in the U.S.A. I mention as well James Frazer, who often helped me as night assistent. I will always remember the many hours we did our job singing loudly (and probably out of tune). De adviezen en programma's van Ed van der Zalm hebben mij veel tijd bespaard. Ik dank hem voor de prettige wijze waarop hij mij altijd heeft bijgestaan. Ook gaat mijn dank uit naar Jan Odljk die al mijn typewerk heeft verricht, Evert Landre' dia alle figuren heeft verzorgd en de heer Repelaer van Driel die veel ponswerk voor mij heeft gedaan. Een groot deel van dit onderzoek is gesteund door de Stichting Astronomisch Onderzoek in Nederland (ASTRON) met financiële steun van de Nederlandse Organisatie voor Zuiver-Wetenschappelijk Onderzoek. Ik ben dankbaar voor de soepele wijze waarop deze steun is verleend. I am also grateful for the hospitality of Mt.Wilson Observatory; the measurements with the Ca II H and K photometer at the 60 inch telescope axe essential for this thesis. Tenslotte dank ik mijn vrouw Ans voor alles wat zij voor de totstandkoming van dit proefschrift heeft overgehad. CONTENTS
page
CHAPTER SURVEY 9
CHAPTER II ROTATION MODULATION
11.1 Indications for Rotation Modulation and Short- 19 Term Variations in the Ca II H and K Emission from Cool Main-Sequence Stars
11.2 Stellar Rotation in Lower Main-Sequence Stars 27 Measured from Time Variations in H and K Emission-Line Fluxes I: Initial Results
CHAPTER III MAIN-SEQUENCE STARS
111.1 Magnetic Structure in Cool Stars III: Ca II H and K Emission and Rotation of Main-Sequence Stars
111.2 Magnetic Structure in Cool Stars 49 IV : Rotation and Ca II H and K Emission of Main-Sequence Stars
CHAPTER IV EVOLVED STARS
IV.1 Magnetic Structure in Cool Stars 59 I : The Ca II H and K Emission from Giants
IV.2 Magnetic Structure in Cool Stars 73 VI: C.a II H and K Fluxes from Evolved Stars
SAMENVATTING 87
I CHAPTER I: SURVEY
1. INTRODUCTION The Ca II H and K resonance lines at 3934 A and 3968 & are an important diagnostic for the study of stellar chromospheres. In a number of main-sequence stars of spectral type later than 9a F5, and in nearly all giants of spectral type later than GO, emission features are visible in the cores of both of these lines (Fig. 1 and 2). This thesis is based on a study of these emission features. The Sun is among the late-type stars showing Ca II H and K emission. A picture of the Sun in one of the Ca II H and K line-cores clearly shows (Fig. 3) that the emission originates predominantly in discrete regions. These regions are cospatial to within 1" with discrete magnetic features (see Zwaan 1978) (Fig. 4). Hence we assume that the stellar Ca II H and K flux increases with the magnetic flux passing through the stellar surface. Except for the Sun, magnetic fields on stars can only be measured directly for bright and magnetically active stars (see Sect. 2). Hence,indirect methods to measure magnetic fields on stars have to be used to study a large sample of stars with a strongly differing magnetic activity. The measurement of the Ca II H and K emission of stars is one way to do just that. In this investigation the Sun is used as an example and guide for the study of stellar Ca II H and R emission. The amount of information contained in the Ca II H and K emission cores is enormous. It ranges in time from information about flare-like behavior on time-scales of minutes through information about stellar rotation periods on time-scales of days (weeks, months) and stellar activity cycles on time-scales of years to information about stellar evolution on time-scales of 1010 years. The width of the emission cores is a measure of the absolute magnitude of the star (Wilson and Bappu, 1957, Wilson 1976) while the intensity.in combination with the width contains information about the mass of stars (Sect. 3). Although this. Investigation is based on a tiny fraction of the electromagnetic spectrum it addresses fundamental characteristics of stars such as: mass, rotation period as a function of age, evolutionary phase and last but not least magnetic activity as a function of age.
2. DIRECT MEASUREMENTS OF MAGNETIC FIELDS On the Sun magnetic fields can be measured through the polarization effect in the magnetic Zeeman splitting of absorption lines. However, this method does not apply to cool stars, probably because opposite polarities produce opposite polarization effects, Like on the Sun, magnetic fields of cool stars are expected to appear 1B bipolar regions occupying a fraction of the stellar disk. The net polarization effect of the visible part of the star's surface will therefore be very small and undetectable for most stars (for example: the average magnetic field measured for the sun in this way would be f>a-\ Gauss (Scherrer et al. 1977). A method of measuring magnetic fields of late-type stars and the fractional area they cover has been applied by Robinson et al. (1980). It relies on the fact that magnetic Zeeman splitting (for a simple Zeeman triplet) produces two a components separated from the unshifted n component by an amount depending only on field strength (Unno (1956)). The method results in the average absolute value of the 10
It
Fig. 2: Ca II H and K emission cores in speetva (Wilson and Bappu (195?)}
CalK line core index CaUK emission index
(indices defined relative to some continuum 1iux)
Fig.2: Ca II H and K emission aores; definitions
\ 11
Fig.3: Filtergram of the Sun in the core of the Ca II K line (courtesy B.J. Oranje)
Fig.4: A mature active region: a) Filtergram in the core of the Ca II K Vine: b) magnetogram; the comparison between (a) and (b) demonstrates the dose spatial correspondence between faculae (as observed in Ca II K emission) and magnetic flux outside sunspots (Big Bear Solar Observatory, courtesy H. Zirin)
L 12
magnetic field strength present and the area covered by magnetic fields. It requires a high spectral resolution and a large signal-to-noise ratio. For a signal-to-noise ratio of 100:1, field strengths of 1000 Gauss or more can be measured if they cover at least 3-4X of the stellar surface. Hence this method is limited to bright and magnetically active stars. Promising results on two stars have been published (Robinson et al. 1980) and the technique has been applied to a number of stars by Marcy (1981) who reports magnetic fields in at least 50% of the observed stars. In most cases the fraction of the surface covered by magnetic fields is small. This and the direct observation of magnetic fields in stars supports the idea of the presence of magnetic field in discrete magnetic structures on late-type stars and it adds to our confidence in using the Sun as an example and guide for the observation of magnetic activity In other late-type stars.
3. THE CA II H AND K PHOTOMETER AT MT. WILSON All the observations presented in this thesis were obtained wltf the Ca II H and K photometer at the 60 Inch telescope of Ht. Wilson. A short description of this instrument is given here; for a more detailed description I refer to Vaughan et al. (1978). The Ca II H and K photometer (Fig. 5) is a'four-channel photon-counting spectrophotometer consisting of an off-piane flat—field Ebert spectrometer equipped with a multi-exit slit and a chopper for measuring the fluxes in four spectral passbands sequentially at a chopping frequency of about 30 Hz, with a single detector. The spectrum can be shifted parallel to the dispersion to compensate for Doppler shifts. A data system displays and records the results. The four channels measured are the Ca II H and K line-cores with the instrumental profile shown in Fig. 6 and two reference windows on either side of the H and K lines as shown in Fig. 7. The Ca II H and K line-core index S is then defined as:
where %, %, Ny and NR refer to the number of counts corrected for background in the different channels. The factor a is deduced from the observations of standard stars to compensate for instrumental effects. Some advantages of this instrument are that: (1) owing to the effectively simultaneous measurement, changes in atmospheric transmission are the same in all four channels. Hence observations may continue as long as a sufficient signal-to-noise ratio is received which, in practice, means that bright stars can even be measured through a relatively thick haze. (2) Because all four channels are effectively simultaneously measured with the same detector the reduction is straightforward and easy. A disadvantage of the reduction procedure is that the division of the number of counts in the H and K channels by the number of counts in the V and R channels introduces a spectral-type dependence, since Ny and NR decrease with decreasing effective temperature. Chapter III presents a method to reduce the Ca II H and K line-core index to the total flux in the H and K bands per unit area at the stellar surface.
I 13
1 1 I I 1 i i i
y—K-bond 1 \ \ 2 0.5 - A W- FWHP-1.O9A. H-bond^ï \ S ' i 0.0 1 1 «"\ 1 1\. 1 - I -3 -2 -I 0 I Z 3 4 Slit Offset in Units of fOO microns
Fig.5: Ca II H and K photometer Fig.6: Instrumental profile for Ca II H (Vaughan et al. 1978) and K photometer (Vaughan et at. 1978)
Fig.7: The four ohannels measured by the Ca II B and K photometer .-<•.
4. CLASSICAL PROPERTIES OF THE CA II H AND K EMISSION
a) Ca II H and K emission of stars with similar effective temperature Te££ and surface gravity g may be very different (Fig. 1). This cannot be explained with the classical theory of stellar atmospheres. It Indicates that, besides T' xc and g, at least a third parameter is needed to describe a stellar atmosphere. b) It has been known for a long time (see Hiltner 1947, Gratton 1950) that short-period (P < 10 d) spectroscopie binaries exhibit particularly strong Ca II H and K emission. c) The Ca II H and K emission decreases with age. This anticorrelation with age has been demonstrated by comparing the amounts of Ca II H and K emission for various open clusters (Wilson, 1963}, for different values of the C] color excess in Strömgren's photometric system (Wilson and Skumanich (1964) and for different values of parameters characterizing the galactic orbits of the stars (Wilson and Woolley 1970, Vaughan and Preston 1980). d) Kraft (1967) showed that the average rotational velocity is higher among stars with Ca II H and K emission visible in 10 A/mm spectra than among those without. e) Wilson (1978) observed the Ca II H and K emission of 91 main-sequence stars, ranging from spectral type F5 to M2, for 9-11 years. About a dozen stars show variations resembling the solar activity cycle, with periods ranging from 6 to 10 years while another dozen may turn out to show cyclic behavior if the observations are continued over a longer period. f) O.C. Wilson, the pioneer in this field of research found that the width V. (Fig. 2) of the emission profile is proportional to the absolute magnitude of the star (Wilson and Bappu 1957).
5. A HYPOTHESIS FOR STELLAR MAGNETIC ACTIVITY
The solar example, together with some of the properties of Ca II H and K emission discussed in Sect. 4 suggested to Zwaan (1977, 1981) the hypothesis that guided this investigation. It consists of four components: a) In stars with convective envelopes the magnetic field has been concentrated in discrete elements to large field strengths, with very low field strengths in between. This is based on the Sun where the magnetic field has been concentrated in discrete elements which form a sequence from the large dark sunspots down to the bright small elements in the magnetic network (Zwaan 1980). These discrete elements may be modelled as magnetostatic flux tubes. b) The emission in the cores cf the Ca II H and K resonance lines originate predominantly from the magnetic elements. This part of the hypothesis is again based on the Sun where the Ca II H and K emission originates in chromospherlc patches that are cospatial to within 1" with discrete magnetic elements.
Although the dynamo theory for solar magnetism is still rather sketchy, it seems plausible that similar dynamos operate in other stars with convective envelopes. The number density of magnetic flux tubes in the stellar atmosphere depends on the efficiency of this dynamo. Since the dynamo is thought to depend on differential rotation brought about by convection and rotation it seems plausible that the measure of differential rotation depends on the mean rotation rate. c) The efficiency of the dynamo decreases with decreasing rotation rate. This idea has been explored already by Skumanich (1972) who derivated 15
quantitative relations between rotational velocity and age and between Ca II H and K emission and age* d) Stellar rotation is efficiently braked by a stellar wind streaming out along the coronal and circumstellar magnetic fields (Schatzman 1959, 1962, 1965). The loss of angular momentum per unit mass in the stellar wind is quite large since the outflowing matter is forced to corotate with the star to a large distance because of the magnetic field.
Note that this hypothesis quantitatively explains most of the known properties of the Ca II H and K emission. The difference in Ca II H and K emission among stars of similar effective temperature and surface gravity is explained by a different rotational velocity. Since the rotation rate decreases with time due to the magnetic braking, the Ca II H and K emission decreases with age. Activity cycles can be detected through the observation of Ca II H and K emission because this emission predominantly originates in discrete magnetic structures while the number of magnetic structures depends on the phase of the activity cycle. Until recently the relatively high Ca II H and K emission of short-period binaries had been explained as the results of tidal interaction affecting the chromospheric heating in some unspecified way (Young and Koniges 1977, Glebocki and Stawlkowski 1977). Our hypothesis explains the high Ca II H and K emission as the result of the rapid rotation enforced upon these stars by tidal friction. This investigation presents evidence that supports this idea.
6. TOPICS OF THIS INVESTIGATION
A) Rotational modulation Presumably the Ca II H and K emission depends on the number and size of active regions. The solar active regions are not uniformly distributed. Therefore rotational modulation is expected in the Ca II H and K signal for the Sun and solar-type stars. An indication for the non-uniform distribution of active areas on stars are the very active M-type dwarfs called BY Draconis stars (Bopp et al. 1981), and the very active RS CVn stars (short-period binaries of which one component usually is an evolved star, Popper and Ulrich 1977). These stars show small periodic changes in visual light which are explained as the result of large dark starspots so that the amount of visual light radiated by the star is smaller when the spot is on the visible part of the stellar surface than when it is on the invisible part. O.C. Wilson (1978) concluded, from his activity cycle observations, that all stars show scatter in the seasonal groups of observations, indicating variations on time scales from 1 day to several months. rotational modulation is one of the possible explanations for these seasonal variations. Two of the prime goals of this investigation were (i)to investigate whether rotation periods can be determined from time series of Ca II H and K fluxes and (ii)if so,to find rotation periods for a sample of G- and K-type main-sequence stars. Such a program requires a large amount of observing time. I was fortunate enough to participate in observing programs at Mt. Wilson Observatory using the Ca II H and K photometer. In Chapter II it is shown that indeed rotation periods can be determined from a modulation in the Ca II H and K signal for many stars in a broad range of spectral types. 16
Even relatively large rotation periods can be determined by this method: the maximum period derived up to the present is 54 days. Clearly the' maximum detectable rotation period is limited by the lifetime of complexes of magnetic structure. Note that this method measures the rotation period of the star independent of the inclination axis i.
B) The relation between Ca II H and K emission and rotation Since the Ca II H and K emission originates in magnetic elements, the number density of these elements depends on the dynamo efficiency, and the dynamo efficiency is expected to decrease with decreasing rotational velocity, the Ca II H and K emission is expected to decrease with rotational velocity. Kraft (1967) has already shown that for stars with Ca II H and K emission visible in 10 A/mm spectra the average rotational velocity is higher than for stars without visible emission. However, the quantitative relation between Ca II H and K emission and rotational velocity had not yet been established. Two of the main goals of this investigation were (i) to search for a rotation-emission relation among main-sequence stars as well as evolved stars and (ii) to establish quantitatively the relation for main-sequence stars. Chapters III and IV demonstrate that for main-sequence stars as well as for giants the relatively rapid rotators s'.jv a relatively high Ca II H and K emission. The main problem in establishing the quatitative relation between Ca II H and K emission and rotational velocity is the determination of the rotational velocity for late-type stars because of the high detection limit ( «^ 10 km/s in conventional spectroscopy). Recently two new techniques, viz. the rotation modulation in the Ca II H and K signal (discussed in Sect. 6A) and the Fourier analysis of line profiles (Smith and Gray 1976, Soderblom 1980) lowered the detection limit considerably. Results of these new techniques are used in Chapter III to show that at least for active main-sequence stars a clear correlation exists between Ca II H and K emission and rotational velocity. There is an indication for a (probably color-dependent) critical velocity at which the Ca II H and K emission suddenly drops. Rotational velocities have been measured for a rather small number of late-type stars. Therefore the quantitative relation between Ca II H and K emission and rotational velocity presented here is preliminary. To check this relation more rotational velocities should be measured, preferably by the rotation-modulation technique yielding the rotation period of the star independent of its inclination angle.
C. Ca II H and K emission, rotational velocity and the evolution of stars Chapter III.2 gives an evolutionary scenario for main-sequence stars, using the rotational velocity as a basic parameter. Chapter IV discusses the dependence of Ca II H and K emission (and thus magnetic activity) on the rotation rate for evolved stars. One of the conclusions is that the Ca II H and K emission is probably a clue to the evolutionary phase of giants. Detailed observations of stars in open clusters are suggested for investigating this intriguing possibility. Unfortunately such a study is beyond the scope of this thesis but may serve as a key topic for a later investigation. This thesis consists of three Chapters. Chapter II discusses the rotational modulation in the Ca II H and K signal. Chapter III discusses main-sequence stars and Chapter IV evolved stars. 17
REFERENCES Bopp, B.W., Noah, P.V., Klimke, A., and Africano, J.: 1981, Astrophys. J. 249, 210 Glebocki, R., and Stawikowski, A.: 1977, Acta Astron. 27, 225 Gratton, L.: 1950, Astrophys. J. Ill,, 31 Hiltner, W.A.: 1947, Astrophys. J. 106, 481 Kraft, R.P.: 1967, Astrophys. J. 150, 551 Marcy, G.: 1981, in abstracts of the second UCL Astronomy Colloquium Popper, D.M., and Ulrich, R.K.: 1977, Astrophys. J. 212, L 131 Robinson, R.D., Worden, S.P., and Harvey, J.W.: 1980, Astrophys. J 236, L 155 Schatzman, E.: 1959, in J.L. Greenstein (ed.): I.A.U. Symp No. 10, p. 129 Schatzman, E.: 1962, Ann. Astrophys. 25, 18 Schatzman, E.: 1965, in R. Lust (ed.): Stellar and Solar Magnetic Fields, I.A.U. Symp. No. 22, p. 153 Scherrer, P.H., Wilcox, J.H., Kotov, V., Severny, A.B. and Howard, R.: 1977 Solar Phys. 52, 3 Skumanich, A.: 1972, Astrophys. J. 171, 565 Smith, M.A., and Gray, D.F.: 1976, Publ. Astron. Soc. Pacific 88, 809 Soderblom, D.: 1980, Dissertation, University of California at Santa Cruz Unno, W.: 1956, Publ. Astron. Soc. Japan 8, 108 Vaughan, A.E., and Preston, G.W.: 1980, Publ. Astron. Soc. Pacific 92, 385 Vaughan, A.H., Preston, G.W., and Wilson, O.C.: 1978, Publ. Astron. Soc. Pacific 90, 267 Wilson, O.C.: 1963, Astrophys. J. 138, 832 Wilson, O.C.: 1976, Astrophys. J. 205, 823 Wilson, O.C.: 1978, Astrophys. J. 226, 379 Wilson, O.C., and Bappu, M.K.: 1957, Astrophys. J. 125, 661 Wilson, O.C., and Skumanich, A.: 1964, Astrophys. J. 140, 1401 Wilson, O.C., and Woolley, R.: 1970, Mon. Not. R. Astron. Soc. 148, 463 Young, A., and Koniges, A.: 1977 Astrophys. J. 211, 836 Zwaan, C.: 1977, in B. Caccin and M. Rigutti (eds.): "The Sun, a Tool for Stellar Physics", Hem. Soc. Astron. Italiana 48, 525 Zwaan, C: 1978, Solar Phys. 60, 213 Zwaan, C: 1980, in S.D. Jordan (ed.):"The Sun as a Star", NASA-CNRS Publication Zwaan, C: 1981, in R.M. Bonnet and A.K. Dupree (eds.): "Solar Phenomena in Cool Stars and Stellar Systems", (D. Reidel, Dordrecht, Holland) 19
CHAPTER II: ROTATION MODULATION
II.1: Indications for Rotation Modulation and Short-Term Variations in the Ca II H and K Emission from Cool Main-Sequence Stars
F Middelkoop, (*) A.H. Vaughan and G.H. Preston(**)
published in Astronomy and Astrophysics, 96, 401
SUMMARY Ca II H and K emission fluxes from 14 F-, G- and K-type main-sequence stars have been monitored over a span of 10 successive nights. The results suggest that rotation periods may be inferred for some of the stars from a corresponding modulation in the Ca II H and K signal. Most stars also show variations that are much shorter in duration than the expected rotation periods.
Key words: Stellar chromospheres - stellar rotation - late type main-sequence stars
1. INTRODUCTION Emission in the cores of the Ca II H and K resonance lines has been observed in stars with outer convection zones (Wilson 1966a, 1968, 1976). Since this emission is thought to arise from active regions (Wilson 1976, 1978, Zwaan 1977, 1980) temporal changes in the Ca II emission strength may be expected at several time scales because of rotation, changes associated with the growth and decay of active regions and activity cycles analogous to the solar cycle. The activity cycle of stars has been investigated by O.C. Wilson (1978). For about a dozen of stars in a sample of 91 main-sequence stars, he found periods ranging from 6 to 10 years (which is the total length of the records). Wilson (1978) also noted scatter within the seasonal groups of observations indicating changes on time scales ranging from 1 day to several months. This scatter is present in varying degree in all stars of his sample.
(*) The Astronomical Institute, Zonnenburg 2, 3512 NL Utrecht, The Netherlands (**) Mt. Wilson Observatory, 313 Santa Barbara Street, Pasadena, California 91101, U.S.A. 20
Rotational effects in the Ca II emission of the Sun have been demonstrated in studies of the time variations of the H and K emission from the integrated disk and detailed Ca II spectroheliograms of the disk (Jebsen and Mitchell 1978, Oranje 1982). An extensive program to investigate the feasibility of determining rotation periods of stars from the expected rotation modulation is planned during 1980. It consists of about 90 nights of observation time on the 60 inch telescope of Mt. Wilson, using the Ca II H and K photometer (Vaughan et al., 1978). The work will be carried out by observers of Mt. Wilson Observatory, the Center for Astrophysics (Cambridge, Massachusetts), Sacramento Peak Observatory and Utrecht Observatory. During November 1979 we dedicated part of our observation time on the 60 inch telescope of Mt. Wilson as a pilot test for the 1980 campaign. To this end the Ca II emission index of 14 main-sequence stars was measured at least once a night, weather permitting. Seven of these stars are observable during the 1980 summer campaign.
2. SELECTION OF STARS The program stars are listed in Table 1. Except for HD 52711 they wer-j selected from O.C. Wilson's cycle program (Wilson 1978) according to two criteria, viz.: (i) The Ca II emission index is large for the spectral type. This criterium has been used since a dependence between the Ca II emission and the rotational velocity of late type stars is suggested by O.C. Wilson (1966a,b) and Kraft (1967) for main-sequence stars and by Middelkoop and Zwaan (1981) for giants. Since the observation run extended over 10 days only, stars with periods probably shorter than 10 days had to be selected.
Table 1: Program stars Column 4 and 6 give the average Ca II emission index and the standard deviation (expressed as percent of the average) respectively* as given by Wilson (1978).
H.D. Sp. (B-V) Ave S.D. Flux 1835 G2 V 0.66 0.349 0.402 6.4 16673 F6 V 0.52 0.212 . 0.364 5.9 17925 K0 V 0.87 0.629 0.524 6.1 20630 G5 V 0.68 0.339 0.612 4.8 22049 K2 V 0.88 0.472 0.442 3.7 25998 F7 V 0.54 0.257 0.381 5.5 26913 G3 V 0.70 0.365 0.412 7.2 26923 GO V 0.59 0.270 0.414 6.5 30495 Gl V 0.64 0.281 0.503 5.5 33608 F5 V 0.46 0.210 0.421 5.9 35296 F8 V 0.53 0.288 0.383 5.0 39587 GO V 0.59 0.289 0.387 4.4 52711 G4 V 0.58 - - 5.0 75332 F7 V 0.49 0.264 0.310 6.1 21
.06 9562 G2 .OS 13421 F8 can Index . * ' * *
.05
4 6 10 -04. TIME (days)
-;5 G3 45067 Ffl
.06
5 2 4 6 8 10 ° 0 2 4 6 8 10
0?r 76572 F3
06
0 2 4 6 8 10
Fig.l: Ca II H and K index versus time: standard stars
It has been shown that the Ca II emission index of main-sequence stars declines with age (Wilson 1963, 1966b, Wilson and Skumanich 1964, Wilson and Woolley 1970, Skumanich 1972, Vaughan and Preston 1980, Vaughan 1980). Therefore this criterium leads to the selection of relatively young stars. The program for the 1980 summer campaign will also contain "old" stars, (ii) The star shows a large seasonal spread in Wilson's (1978) measurements. This criterion attempts to avoid stars that are observed "pole on".
3. OBSERVATIONS AND REDUCTIONS The observations were obtained by means of the Ca II H and K photometer (Vaughan et al«, 1978). We recall that the fluxes measured in the H and K line cores are normalized with the fluxes measured in two reference windows seperated by 100 A on either side of the H and K cores. The Ca II 22
,15r 1835 G2 •10r 16673 F6 Can index
•091- • • t
—I I ' ' • ' • .06 O 4 6 8 10 O 2 4 6 8 10 TIME Bays)
.17 26913 G3
20630 G5, .18
* *
10
.13 30495 G1 .09 33603 F5
10
Fig. 2: Ca II H and K index versus time: program stars
emission index is defined as: (Ng + Ng )/(% + NR ), where Ng , NR , Ny and NR refer to the number of counts, corrected for background, in the H and K bands and in the reference bands on the violet and red side of the E and K region, respectively. In addition to the program stars, we observed five standard stars every night (except for the first night when the observing conditions were very bad) as a check on instrumental variations. These stars are also used as standards in the continuation of Wilson's cycle program by two of the authors (A.B.V. and G.W.P.). The results for the standard stars are plotted in Fig. 1. Because we did not expect to detect measurable intrinsic variations in standard stars in a period of 10 days, the times of observations were not 23
recorded for these stars. Hence the data are plotted at nominal Intervals of one day. Our observations usually consisted of 6000 counts per star in the K-band (in the case of the bright stars HD 20630, HD 22049, HD 39587 and HD 52711 10 000 counts per star). This results in a formal accuracy 0«l/(N + u )£) of 0.9% (resp. 0.7%). H K The mean standard deviation for a single observation, derived from repeated observations of standard stars on a timescale of several minutes, is 1.0%. On a timescale of 10 days the standard stars show variations up to 6% (Fig. 1). However, the variations found among standard stars on the same night are not correlated over this 10-day period. Assuming that there are no major instrumental variations during one night, we therefore conclude that the standard stars show intrinsic variations and that any instrumental variations during this 10-day period were too small to be detected by this standard measurement procedure. The assumption that there are no major instrumental variations during one night must, however, be verified by an improved standard measurement procedure. Probably the best procedure in the future is to use a standard lamp. Alternatively one might observe the standard stars at a.wavelength well outside the line core where intrinsic variations are no longer expected, or observe stars without Ca II emission, for example 0, B, A-type stars. Our conclusion that the standard stars show intrinsic variations is in accord with the conclusion drawn by Wilson (1978) from the fact that the standard deviations (for a single observation, calculated from large numbers
.22 22049 K2 can index
.20
17925 KO .19 CaJI index
.26
.25 .17-
4 6 4 6 TIME (days) TIMECdays)
Fig. 3: Ca II H and K index versus time: program steers L
24
of observations) differ considerably among these stars» In order to ensure fair time coverage, we occasionally observed during poor conditions» Moreover, stars measured more than once a night were observed at different zenith distances. From these observations we could find no significant dependence of the Ca II emission index upon extinction or zenith distance. For the program stars we recorded the actual times of observation. The results appear in Figs. 2, 3 and 4.
4. DISCUSSION AND CONCLUSIONS The primary goal of this pilot project was, first, to test the technical feasibility of studying short-term H and K flux variations in main-sequence stars, and second, to provide a first detailed look at the scale and
.12 2599B F7 26923 GO H Can • **
.11 -
1 1 1 1 1 t If) •'0. A 6 10 TIMECdays)
35296 F8 .13 39587 GO
.12
.nj- 1 i ' 1 O 2 4 6 8 10 2 4 6 8 10
52711 G4 75332 F7
osi—"- 10 •10
Fig. 4: Ca II H and K index versus time: program stars 25
character of the variations encountered, as an aid in planning the strategy of future efforts. The technical feasibility of such observations appears well established by our results. Indeed, all program and "standard" stars show variations in excess of the accuracy (1%) for a single observation. Moreover, a considerable variety of time-dependent behavior is exhibited by these stars even in a 10-day interval (on timescales ranging from days to our arbitrary time-resoluticn limit of a few hours). On the basis of the results shown in Figs. 1-4 we conclude that in most cases one observation per night would suffice to reveal, in the course of time, the essential character of the variation, although in quite active stars two or more observations per night may be necessary to resjlve the fluctuations. This means that a major program could effectively ui Jertake to follow a large number ( The present run of ten days is, of course, too short to support conclusive astrophyslcal interpretations of the results, for which a much longer time-base will be necessary. It is useful, however, to attempt a preliminary characterization of the observed variations. In particular, it is worthwhile to search for possible effects of stellar rotation in such measurements. Many of the variations present in Figs. 1-4 may be interpreted in terms of chromospheric activity which is similar to solar activity. For instance, the total Ca II emission Increases or decreases when a large active region is coming around the stellar limb, or passing around the opposite limb, respectively. The rapid growth of an active region produces a sharp increase in the Ca II index. Flare-like brightenings appear as sharp upward spikes. However, it should be pointed out that we cannot yet offer an explanation for the sharp minima, as shown by HD 26913 (Fig. 2) and HD 22049 (Fig. 3) during the sixth day. Clearly, the short-term variations interfere with the rotation modulation. Yet the Ca II indices of the stars plotted in Fig. 2 exhibit a wave-like variation which we tentatively identify with rotational modulation. The rotation period of these stars may be shorter than 10 days. The stars shown in Figs. 3 and 4 do not show wave-like variations that could be attributed to rotational modulation. The two stars in Fig. 3 are the only K-type stars in our sample, with very large Ca II indices as compared to other stars of the same spectral type. (note that the Ca II emission index tends to exaggerate activity in progressively cooler stars because the H and K flux is compared with a decreasing continuum flux). Possibly there are many active regions on these stars, with frequent transient processes. Note the interesting case of HD 22049, with its rapidly varying signal during the first six days, and a rather constant signal during the last part of the observing period. The stars shown in Fig. 4 display an intrinsic scatter about a constant (mean) Ca II index. Possible reasons for the constancy are: (i) the active regions were uniformly distributed about the rotational axis, (ii) the star is observed pole-on, and (ill) the rotation period is much longer than the program duration of 10 days. Rotation modulation may be detectable in some of the stars plotted in Figs. 3 and 4. This requires a careful analysis of series of measurements covering several rotation periods, with some tens of measurements per rotation period. Such an analysis may also reveal other timescales of interest, such as typical lifetimes of active regions. Clearly, the planning of efficient measurement series becomes easier with increasing insight in L 26 r the Ca II H and K variability. Finally we conclude that a systematic investigation of the short-term variations (on time scales between one hour and one month) in the Ca II index of cool main-sequence stars would be very rewarding. ACKNOWLEDGEMENTS We wish to thank J. Frazer for assistance in making the observations. One of the authors (F.M.) was supported by a travel grant from the Netherlands Organization for the Advancement of Pure Research (Z.tf.O.). We are also indebted to Dr. C. Zwaan for his interest and for critically reading the manuscript and profited from constructive criticism by the referee. Mrs. J.G. Odijk prepared the typescript, and or. E. Landre the figures. REFERENCES Jebsen, D.E. and Mitchell, W.E. Jr.: 1978, Solar Phys. 57, 309 Kraft, R.P.: 1967, Astrophys. J. 150, 551 Middelkoop, F. and Zwaan, C: 1981, Astron. Astrophys. 101, 26 Oranje, B.J.: 1982, in preparation Skumanich, A.: 1972, Astrophys. J. 171, 565 Vaughan, A.H.: 1980, Publ. Astron. Soc.Pacific 92, 392 Vaughan, A.H. and Preston, G.W.: 1980, Publ. Astron. Soc.Pacific, 92, 385 Vaughan, A.H., Preston, G.W. and Wilson, O.C.: 1978, Publ. Astron. Soc.Pacific 90, 267 Wilson, O.C.: 1963 Astrophys. J. 138, 832 Wilson, O.C.: 1966a, Science 151, 1487 Wilson, O.C.: 1966b, Astrophys. J. 144, 695 Wilson. O.C.: 1968, Astrophys. J. 153, 221 Wilson, O.C.: 1976, in V. Bumba and J. Kleczek (eds.): Basic Mechanisms of Solar Activity, p. 447 Wilson, O.C.: 1978, Astrophys. J. 226, 379 Wilson, O.C. and Skumanich, A.: 1964, Astrophys. J. 140, 1401 Wilson, O.C. and Woolley, R.: 1970, Mon. Not. R. Astron. Soc. 148, 463 Zwaan, C: 1977, Mem. Soc. Astron. Italians 48, 525 Zwaan, C: 1980, in R. Bonnet and A.K. Dupree (eds.): Proceedings of the NATO Advanced Course on "Solar Phenomena in Stars and Stellar Systems", (Reidel, Dordrecht, The Netherlands). 27 CHAPTER II: ROTATION MODULATION II.2: Stellar Rotation in Lower Main-Sequence Stars Measured from Time Variations In H and K Emission-Line Fluxes I. Initial Results Arthur H. Vaughan (1), Sallie L. Baliunas, (2), Frans Middelkoop, (3), Lee W. Hartmann, (2), Oimitri Mihalas, (4), Robert W. Noyes, (2) and George W. Preston,(!)(*) published in Astrophysical Journal, 250, 276 SUMMARY Fluxes at 1 A bands at the centers of the H and X lines in 46 lower main sequence field stars and in eight selected subgiants and giant stars, have been measured at nightly intervals in the course of a nearly continuous 14-week observing run. In 19 stars we have found clear evidence of rotational modulation, from which values of the rotational periods can be assigned by inspection. In nine others, periods have been found by an auto- correlation analysis of the flux records. The periods obtained imply rotation velocities that are in good accord with spectroscopically determined values of vsinl in the literature for 13 of the stars we have observed. Much of the short term scatter in H and K flux observed by Wilson appears to be caused by rotational modulation, although variations on other time scales are also present. As many as 80% of the chromospherically active (i.e., young) stars display prominent rotational modulation and in some cases the phase of the modulation remained unchanged for the entire observing period, suggesting that markedly asymmetric and long-lived distributions of active regions are common in such stars. At a given (B-V) < 1.0, the strength of H and K emission is shown to vary as a function of rate of rotation, suggesting that rotation, rather than initial conditions or age per se, is the chief parameter influencing chromospheric output. (*) (1) Mount Wilson and Las Campanas Observatories, Carnegie Institution of Washington, 813 Santa Barbara St., Pasadena, CA 91101 (2) Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 (3) Sonnenborgh Observatory, University of Utrecht, Zonnenburg 2, Utrecht, The Netherlands (4) Sacramento Peak Observatory, operated by Associated Universities for Research in Astronomy under contract AST 78-17292 with the National Science Foundation, Sacramento Peak Observatory, Sunspot, NM 88349 28 From data on stellar activity cycles available at present, it is suggested that periodic cycles resembling the Sun's are almost exclusively found in stars with rotation periods in excess of about 20 days; and, except for this threshold effect, the cycle periods are uncorrelated with rotation rate. Key Words: Ca II emission - stars: chromospheres - stars: late-type - stars: rotation I. INTRODUCTION In his study of chromospheric variations in main sequence stars, Wilson (1978) called attention to the fact that in the observed chromospheric H and K flux variations a periodic component might be present as the result of rotational modulation, if active regions giving rise to the emission are nonuniformly distributed in longitude, as is often the case in the Sun. Re suggested that frequent observations over several weeks might yield rotational periods for such stars. Knowledge of rotational periods found in this way would allow many questions to be explored anew concerning the evolution of stellar angular momentum and the connection between chromospheric activity and rotation. We were thus motivated to look for rotational modulation in the H and K fluxes of 46 late-type main-sequence stars and eight subgiants and giants, in an observing run that extended almost continuously from 1980 July 1 through October 15, on the 1.5m telescope of the Mount Wilson Observatory. The present article is a brief account of the initial results of our survey and of the most evident conclusions that we believe can be drawn from it. A more detailed analysis of the data is in preparation. II. OBSERVATIONS AND ANALYSIS Our observations were obtained with the four-channel chopping spectrometer (HKF2) at the Mount Wilson 1.5m telescope. The instrument and its operation have been described by Vaughan, Preston and Wilson (1978). An LSI-11/2 computer-controlled flexible disk datalogging system and a television slit viewer were implemented for this project. Each integration with the HKP2 yields the value of a flux index, S (defined in Vaughan et al., 1978), proportional to the total equivalent width of the Ca II H and K emission reversals and residual photospheric light in 1 A bands centered at H and K. Doppler wavelength shifts corresponding to each star's geocentric velocity were computed for each night and compensating offsets were introduced manually with a nominal precision of about 1 km/s (i.e., 0.01 A). Temperature drifts in the calibration of the zero-point wavelength degraded the final precision to only 3-5 km/s. Such drifts were unimportant on some nights when the temperature changed little: on other nights, as necessary, the drift was compensated by frequent recalibration. In our standard procedure three integrations were made for each star, each to a preset count of 2000 in the K-channel, so that the formal statistical accuracy of the derived mean flux index was near IX. The count was increased for the brightest stars to ensure integrating times in excess of 30s in order to hold chopper noise below 1Z. The count was sometimes decreased for the faintest stars, or when extinction by clouds required, to keep net 29 integrating times below an upper limit of about 600s. The instrumental and sky background was measured between every few stars or with each star as conditions required; the flux indices presented here have been corrected accordingly. Five of the stars routinely followed in our program were "standard stars" found by Wilson (1978) to exhibit low and nearly constant values of H and K flux. As an additional check on the stability of the equipment, we made daily measurements of an artificial continuum light source mounted so as to simulate the f/16 beam of the telescope. These measurements of artificial and standard star sources should ultimately permit any systematic instrumental effects to be estimated and corrected in the data. Such corrections have not been applied to the data we present here; instead, a constant scale factor derived from the mean measures of standard stars ha6 been applied, merely to bring the flux index scale into registration with previously published work (cf. Vaughan and Preston 1980). Our inspection of the data indicates that any systematic instrumental effects were actually quite small, probably not exceeding the 1 or 2% level. Table 1 lists in order of color index the identifications and spectral types of the stars selected for observation (cols.(l) and (2), the (B-V) color index (col.(3)), the span of time, AT, over which our observations extended for each star (col.(4)), the mean value Table 1 Stars observed for Rotational Modulation in Ca II H and K Emission (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) Star Sp B-V At 207978 + F0 0.42 95 0.150 8 < 6 K67 2454 F2 .43 86 .160 7 - - 8 K67 3229 F2 .44 86 .216 6 - - <10 W66 182101 F6 .45 95 .210 8 - - ~13 K67 187013 4- F5 .46 95 .148 6 - - 9 K67 194012 F5 .51 95 .194 7 _ 6 K67 16673 44- F6 .52 91 .210 10 ( 6.2) 10 < 6 K67 212754 4- F5 .52 85 .139 7 (13 ) 5 ~ 7 K67 25998 44- F7 .54 72 .282 9 2.5 23 22 K67 13421 4- F8 .56 95 • 125 5 - - ao K66 187691 4- F8 .56 95 .146 6 (15 ) 4 < 6 K67 26923 44- GO .57 72 .281 9 - < 6 K67 154417 F8 .57 95 .259 9 7.6 7 < 6 K67 206860 GO .58 95 .319 9 4.7 11 11 K67 6920 F8 .60 86 .199 7 (13 ) 4 - - 30495 Gl .61 36 .290 8 _ _ _ .. 190406 Gl .61 86 .190 13 14.0 4 3-5 Kt7 12235 Gl .62 86 .160 7 - - <10 H66 161239 G6 .65 86 .134 8 - - <10 W66 1835 44- G2 .66 95 .336 11 7.9 6 ~ 7.0+0.7 S081 224930 G2 .66 86 .175 7 _ _ < 6 K67 217014 G5 .68 85 .148 6 - - 1.740.8 S081 20630 4-f G5 .68 92 .348 12 8.5 6 <15 HS55 26913 4+ G3 .70 71 .380 11 7.2 7 < 6 K67 10700 G8 .72 95 .168 4 - - 2.44O.7 S081 152391 G8 .76 95 .412 17 11.0 4 _ _ 219834A G8 .79 86 .155 9 - - <15 HS55 149661 KO .81 53 .331 21 21.0 2 ~ - - 26965 Kl .82 27 .191 5 - - - - 10476 Kl .84 95 .172 8 — — <20 HS55 3651 KO .85 86 .171 8 _ _ _ 155885 Kl .86 95 .399 13 23 1.8 - - 155886 Kl .86 95 .337 11 21 2.0 - - 17925 44- KO .87 88 .606 8 6.9 6 - - 166620 K2 .87 95 .210 8 (43 ) 1 - - 31 Table 1 (continued) (1) (2) (3) (5) (6) (7) (8) (9) (10) Star Sp B-V P* V Vsini Reference (days) Percent (days) (Ws) 22049 -I K2 0.88 71 .533 10 11.8 4 HS55 4628 K4 .89 86 .194 8 (20 ) 2 219634B K2 .91 85 .201 29 160346 K3 .96 95 .314 13 34 1 16160 K4 0.97 85 .231 6 (45 ) 0.8 32147 K5 1.07 36 .302 9 190007 K4 1.12 95 .767 25 29 1.3 156026 K5 1.16 95 .893 22 17 2.2 201091 K5 1.18 95 0.694 16 37 1.0 2 (4) VF79(SM79) 201092 K7 1.38 95 1.088 18 48 0.7 <25 SL63 GL-685 MO 1.45 90 2.213 40 ( 9 ) 3.5 - 6903 F5III 0.69 95 0.294 18 100 FD70 2186S8 G2III .76 95 .220 19 HS55 27022 G5III .81 49 .181 6 <20 HS55 148387 G8III .91 95 .110 6 HS55 23249 KOIV .92 70 .133 3 2.2+0.9 SD79 24555 G8III 0.94 58 .166 19 HS55 29317 KOIII 1.07 29 .218 18 HS55 222107 G8IV-III 1.07 91 0.931 28 54 <20 HS55 Wilson Standard Also observed in november 1979 test run (Middelkoop et al., 1981) Likely periods deduced from autocorrelation analysis alone are given in parenthesis References to spectroscopie determinations of vsini: FD70 Faber and Danziger (1970) 13.6 A/mm SD79 Smith and Dominy (1979) HS55 Herbig and Spalding (1955) 11.0 l/mm S081 Soderblom (1981) K67 Kraft (1967) 5.0, 4.5 and 2.4 X/mm VF79 Vogt and Fekel (1979) SL63 Slettebak (1963) 28 A/mm «66 Wilson (1966) SM79 Smith (1979) 32 5 90 .'• ?••.. ?' V? ' V 1966 1970 1974 H't 20 30 «0 50 £0 70 80 90 100 tiO 120 130 VEM TIME (DAYS) Fig.l: Mean H and K fluxes vs. time for seleated main-sequence stars (right) as observed at daily intervals in present study; values along horizontal axis are JD-2,444,400 (left) previous long-term flux variations, from Wilson (1978) and subsequent unpublished measurents by Preston and Vaughan. Bars indicate the range of variation observed in 1980. significant level in the data, but do not show significant periodicity, (b) the amplitude of stellar fluctuations, whether produced by rotation or not, is undetectably small compared to the fluctuation level of the data (as evidenced by variations among the normally three observations during each night), or (c) detectable fluctuations exist, but the total length of the observing program for the star in question (col.(4) of Table 1) is too short to allow unambiguous determination of rotational periods. For many of these stars rotational periods may be derived in the future from analysis of the present data or from further data currently being acquired. If the periodicities in the observed records are caused by rotation, there should be agreement between the period P and the spectroscopically determined projected velocity of rotation, vsini, in the sense that for a star with radius R and inclination i of its rotation axis, 2TTR/P j> vsini. Nominal values of 2-dK/V » V, estimated from an adopted mass-radius relation (Harris, Strand and Worley 1963) are given in column (8) of Table 1, 33 00 «00 TOOO OOO 1000 2000 3000 «000 90D0 HOO TOOO O00 VOO 2000 3000 «000 3003 «ODO TOOO 1 000 K>00 2000 WOO 4000 1000 «000 TOOO OOO «00 2000 3OO0 «000 MOO aöooïöoöTÏTOL Fig.2: Fractional autocorrelation functions of H and K flux variations in selected main-sequence stars observed at daily intervals. along with values or upper limits of vsini in column (9), found In the literature for 34 of the observed stars. In 13 of these we have determined rotation periods and for these stars, as may be judged from the data in Table 1, agreement with the observed vsini appears to be virtually universal. In HD 201091 (61 Cyg A) our determination of the period of rotation does not agree with the line broadening reported by Vogt and Fekel (1979), although both methods indicate slow rotation. The equatorial velocity of this star according to our result (1.0 ka/s) would lie below the expected spectroscopie detection limit (Smith 1978) of about 2 km/s. In an independent autocorrelation analysis, Stimets and Giles (1980) reported rotational modulations for 10 stars, based on Wilson's (1978) much more sparsely spaced data. Of the three stars overlapping our program stars, there is excellent agreement for two (HD 206860 and HD 201091; see Table 1). For the third, HD 155886, Stimets's period is a factor of 3 smaller than ours. Because HD 155886 is one of the stars whose rotational modulation is visible by inspection, as well as through study of its autocorrelation, we believe that our quoted period is in fact the correct one and that Stimets and Giles's analysis may have suffered from aliasing, produced by an undersampling of the period. 34 III. DISCUSSION AND CONCLUSIONS a) The Incidence of Rotational Modulation The observations reported here demonstrate that, as foreseen by Wilson (1978), rotational modulation occurs in stars at a discernible level. This modulation provides a powerful new way to measure stellar rotation even when the rate of rotation is far too small to be detected by classical spectroscopie means. Periods determined from rotational modulation do not depend upon the (usually unknown) orientation of the rotation axis. Thus, by amassing sufficient data, it should be possible to investigate directly the distribution function of angular momentum among chromospherically active stars. Our observations show that the "short-term" fluctuations in H and K flux observed by Wilson (1978) are produced largely by rotation (see Fig. 1b). Variations on other time scales are also present, however. Virtuallly all stars display measurable night—to-night fluctuations at levels well above the limits of observational error. In some stars, fluctuations are measurable in time scales of a few minutes (Baliunas et al., 1981). In some instances, we have also observed the rotational modulation to wax and wane, or to drift in phase, as would be expected (and is observed in the Sun) when individual active regions grow and decay. Among 25 stars in our survey that could be classified according to H and K fluxes as "young" (cf. Vaughan 1980), clearly defined rotational modulation was easily seen in about 20 of them. This suggests that such stars spend a large fraction (perhaps 80%) of their time with markedly asymmetric distributions of active regions on their surfaces. In several cases the modulation shows remarkable persistance in amplitude and phase. The modulation has been observed through as many as a dozen or more rotations in the case of rapidly rotating stars such as HD 25998 and HD 206860. Recent observations by J. Frazer at Mount Wilson (private communication) show that the rotational modulation we found in HD 20630, HD 190007 and HD 201092 has persisted essentially unchanged in phase over a duration of almost S months. By analogy with the Sun, the active regions responsible for the observed modulation are likely to be associated with, and dominated by, strong photospheric magnetic fields. Evidence of a similar, although perhaps less pronounced, long persistance of activity complexes in the Sun has been reported (Bumba and Howard 1965; Wilcox et al., 1970) and has also been noted by LaBonte (1980, private communication). Wilson (1978) showed that among stars of all spectral types the short-term fluctuation (expressed as a percentage of the mean H and K flux) varies more or less in proportion to the mean flux. Our observations are in accord with this result. Thus in "old" stars, rotational modulation is relatively hard to detect; we have detected it in only 6 out of 20 such chromospherically less active stars in our survey. Evidently the area occupied by active regions, their surface brightness relative to "quiet" regions, or both, decrease as the stars age. Among the six stars of luminosity class III in our survey, we found the amplitude of scatter (i.e., signal contrast, in col.(6) of Table 1) to be small - about 6% - in two of them (HD 27022, G5 III and HD 148387, G8 III) and significantly larger - 15-20% - in the other three (HD 6903, F5 III; HD 218658, G2 III and HD 24555, G8 III). In a conservative assessment of our measurements we do not find clear evidence of periodic modulation in these giants, although more detailed analysis may reveal significant periodicities. 35 HYADE5 logS.(B-V) f RELATION OBSERVATIONAL R LIMIT Fig.3: (Log S, (B-V)) -diagram for main-sequence stars listed in Table 1. Filled airales represent stars whose period (printed beside each point, in days) was determined in the present work. Open oiroles are stars for which periods oould not be ascertained in the data. Vertical bar represents the Sun's H and K flux and its variation, after Wilson (1978). Dashed lines indi- cate upper and lower boundaries of the distribution o f H and Kf luxes observed among main-sequence field stars by Vaughan and Preston (1980). Shaded area depicts (log S, (B-V)) -relation observed by Wilson (1973) for Hyades cluster. Solid lines tentatively represent transformed Loci of vertical cuts in Fig. 4, in which log S is plotted against period of rotation. In HD 222107 (X And, G8 III-IV) the scatter is large - 25% - and in this one case a component of variation is clearly present with P~54d. This period matches the period found in broad-band measurements in the continuum (LandIs et al., 1978); furthermore, the maximum of H and K emission in our data for this star occurs at the time of minimum photometric brightness, as would be expected if the "dark spots" postulated by Landis et al., are associated with enhanced chromospheric activity (Baliunas and Dupree 1980). In the dwarfs and subgiants that showed a large amplitude of scatter in S, significant variations occurred on a shorter time scale than we could resolve with only one observation per night. For some of these, a more frequent sampling schedule was followed during a few nights by one of us (S.L.B.); the results will be published separately. b) The Dependence of H-K Emission upon Rotation Fig. 3 is the (log S,{B-V))-diagram from the data listed in Table 1 for stars whose periods of rotation have been determined in the present work. 36 1 1 1 1 1 1 • 1 ' 1 -0.1 - -0.2 -0.3 - •s. -0.4 - \ o XN 05 " * \ \ s -06 0.T o\ \ \ tO 4628 ^\ \ 0.8 \ \ na 1 1 1 1 1 1 i 1 1 to 20 30 40 Prot, doyi Fig.4: Log S vs. period of rotation for stars in selected narrow intervals of (B-V). For a given color, the points appear to lie along well-defined sequences, which have been arbitrary fitted heve by straight lines in the diagram. Such trends indicate that chromospheria activity is driven by rotation. The number printed beside each point is the rotational period in days. The diagram indicates the observed upper and lower limits ot H and K flux among main — sequence stars and the region occupied by the Hyades lower main sequence, from Fig. 1 of Vaughan and Preston (1980). Inspection of Fig- 3 reveals that at a given (B-V), the strength of H and K emission increases with increasing stellar rotation rate. This result dramatically confirms the proposals of Wilson (1963), Wilson and Skumanich (1972) and Xraft (1967) that H and K emission and rotation in main sequence stars both decline with advancing stellar age. In addition, periods of rotation can be seen to increase toward the right in Fig. 3. This result confirms and extends to later types the well known trend of decreasing vsini with advancing spectral type (see Slettebak 1970). Among stars of a given (young) age, namely those lying along the band defined by the (log S,(B-V))-relation for the Hyades cluster (see Fig. 3), it appears that periods of rotation are essentially independent of spectral type for stars later than F8. The dispersion in the rotation periods of these youngest stars (P = 7.3W..8 s.d. days) is remarkably small in comparison with the overall range of the periods we have observed among stars of all ages. These periods are essentially in agreement with observed values of vsini in the same spectral type range among Hyades cluster members (Kraft 1965). Indications as to the possible form of a relationship connecting H and K emission, spectral type and rotation can be extracted from the results now in hand, although much more data will be required for a definitive treatment. L 37 As a tentative suggestion of the form such a relationship might take, we have plotted, in Fig.4, the observed mean values of log S against F (from Table 1) for selected stars whose colors are confined to a few narrow intervals. For stars in the range 0.86 £ (B-V) < 0.89, it is particularly apparent that a linear relation between log S and P represents the observations fairly well; thus, for these stars S «? 0.78e~p/30, provided S is large enough that a correction for the photospherlc component of emission is unimportant. At other colors (and hence masses) the slope of the relation between log S and P appears to be different, being somewhat steeper for earlier types and less steep for later types. The exponential relation suggested here seems to fit the observations about as well as the linear relation S a P"1 implied in Skumanich's (1972) discussion of the age-dependance of H and K flux and rotation. Our presentation In terms of an exponential relation does not mean that we believe such a law Is necessarily correct. If the linear relations noted in Fig. 4 are taken at face value and a smooth interpolation Is made, a grid of lines of constant P can be constructed. These lines, drawn in Fif>. 3, are tentative and are intended only to be suggestive of the form of the actual relationship that may be revealed by sufficient additional data. In particular, we note that stars redder than (B-V) - 1.0 do not fit a straight line extrapolation of the grid from earlier types. Also, in the case of HD 4628, at (B-V) » 0.89, the rotation period we find (20d) is about half that required to be consistent with its position in the (log S, (B-V))-diagram according to our supposed relations among these parameters. Although a 20d periodicity is seen clearly in the flux record of this star, it is possible that this period is a harmonic of the true period of rotation, caused by multiple active regions on the stellar surface. Despite such uncertainties, the trends seen in Figs. 3 and 4 are clear enough to suggest that conditions prior to a star's arrival on the zero-age main sequence are either universal or, more likely, are completely arased at an early stage and play little or no role in controlling the excitation of stellar chromospheres. The mechanisms that give rise to the chromospheric activity seem to depend primarily or solely upon the rate of stellar rotation, which in turn (in view of independent evidence of the age dependence of chromospherlc activity) declines continuously with advancing age. This observational Inference supports the validity of notions previously advanced implicitly or. explicitly by others (cf. Kraft 1967; Skumanlch 1972; Zwaan 1977, 1981 and 1979, private communication; see also Skumanich 1981). c) Rotation and the Incidence of Activity Cycles Wilson (1978) concluded that about a dozen of the stars in his survey had essentially completed a cycle of H and K flux variation in the interval 1966-1977. In an as yet unpublished continuation of his survey since 1977 by Vaughan and Preston, another four or five have completed an apparent cycle. For six of these cyclic stars the rotation periods are now also known. Of these, HD 4628, HD 16160, HD 16620 and probably HD 201092 have cycles lasting 10-12 years and rotation periods ranging from 20 to over 40 days. Among these the cycle duration shows no relation to either spectral type or rotation, except insofar as these stars, like the Sun, are slow rotators. In HD 160346 and HD 201091 these cycles clearly have durations of only about 7 years; these are also very slowly rotating stars. In the case of HD 155885/6, both of which rotate in about 20 days, it is difficult to assign L 38 cycle periods, although variations on a 5-10 year time scale are present. HD 17925 has declined In activity since 1970 or earlier, with a possible recovery beginning in 1980 and thus a possible cycle in excess of 10-12 years; the rotation period we find for this star (6.9 days) is the shortest of any star showing a cycle, in this case not a particularly clear one. If any generalization can be made from the meager data avail .ble at this point, it is that obvious, 10-12 year activity cycles are found almost exclusively among stars with rotation periods longer than about 20 days and the periods of these cycles are uncorrelated with the rotational velocities. This dichotomy, if supported by further observations, may imply that at least two modes of magnetic-field generation occur in late-type stars; globally organized cyclic activity in slow rotators (P > 20d) and incoherent (i.e., non-cyclic) eruptions in faster rotators (P < 20d). Such behavior may be related to the existence of the gap in the (S,(B-V))-diagram (see Vaughan and Preston 1980; Vaughan 1980) and, further, may place important constraints on theories of stellar magnetic field generation and dynamos. ACKNOWLEDGEMENTS This work was supported in part by a grant (AST-7921070) from the National Science Foundation to the Carnegie Institution of Washington. The participation of Middelkoop was made possible by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). One of us (S.L.B.) wishes to acknowledge support from the Langley-Abbott Program. We are indebted to Ken Clardy for assistance in data system software development and to Jonathan Selinger for assistance in data processing» We acknowledge with special thanks the collaboration of James Frazer as our principal night assistant for this project. We have benefitted from the ideas and material assistance of our colleagues Drs. Olin C. Wilson, C. Zwaan, Jack Zirker, Ed. Spiegel, A. Skuraanich and undoubtedly many others. REFERENCES Baliunas, S.L. and Dupree, A.K.: 1980, SAO Special Report 389, p. 101 Baliunas, S.L., Hartmann, K., Vaughan, A.H., Liller, W., and Dupree, A.K.: 1981, Astrophys. J. 246, 473 Bumba, V. and Howard, R.F.: 1965, Astrophys. J. 141, 1502 Faber, S.M. and Danziger, I.J.: 1970, Kitt Peak Contribution No. 491 Harris, D.L., Strand, K.A. and Worley, C.W.: 1963, in Stars and Stellar Systems, Vol. 3. ed. G.P. Kuiper (Chicago: university of Chicago Press), pp. 273-292 Herbig, G.H. and Spalding, J.F.: 1955, Astrophys. J. 121, 118 Kraft, R.P.: 1965, Astrophys. J. 142, 681 Kraft, R.P.: 1967, Astrophys. J. 150, 551 Landis, H.J., Lovell, L.P., Hall, D.S., Henry, G.W. and Renner, T.R.: 1978, Astron. J. 83, 176 Middelkoop, F., Vaughan, A.H. and Preston, G.W.: 1981, Astron. Astrophys. 96, 401 Skumanich, A.: 1972, Astrophys. J. 171, 565 Skumanich, A.: 1981, in Solar Phenomena in Cool Stars, ed. R.M. Bonnet and A.K. Dupree (Dordrecht: Reidel) Slettebak, A.: 1963, Astrophys. J. 138, 118 Slettebak, A.: 1970, IAU Colloquium on Stellar Rotation, ed. A. Slettebak (Dordrecht: Reidel), p. 3 I L 39 Smith, M.: 1978, Astrophys. J. 224, 584 Smith, M.: 1979, Publ. Astron. Soc. Pacific 91, 737 Smith, M. and Dominy, J.: 1979, Astrophys. J. 231, 477 Soderblom, D.: 1981, Astrophys. J., in press Stimets, R.H. and Giles, R.: 1980, Astrophys. J. (Letters), 242, 1 37 Vaughan, A.H.: 1980, Publ. Astron. Soc. Pacific 92, 392 Vaughan, A.H. and Preston, G.W.: 1980, Publ. Astron. Soc. Pacific 92, 235 Vaughan, A.H., Preston, G.W. and Wilson, O.C.: 1978, Publ. Astron. Soc. Pacific 90, 267 Vogt, S.S. and Fekel, F., Jr.: 1979, Astrophys. J. 234, 958 Wilcox, J.M., Schatten, K.H., Tannenbaum, A.S. and Howard, R.F.: 1970, Solar Phys. 14, 255 Wilson, O.C.: 1963, Astrophys. J. 138, 832 Wilson, O.C.: 1966, Astrophys. J. 144, 695 Wilson, O.C.: 1978, Astrophys. J. 226, 379 Wilson, O.C. and Skumanich, A.: 1964, Astrophys. J. 140, 1401 Zwaan, C.: 1977, Mem. Soc. Astron. Italiana, 48, 525). Zwaan, C: 1981, in Solar Phenomena in Cool Stars, ed. R.M. Bonnet and A.K. Dupree (Dordrecht: Reidel). CHAPTER III: MAIN-SEQUENCE STARS III<1: Magnetic Structure in Cool Stars III: Ca II H and K Emission and Rotation of Main-Sequence Stars published in Astronomy and Astrophysics, 101, 295 SUMMARY Ca II H and K fluxes were measured in 31 rapidly rotating main-sequence stars of spectral type F and in 7 single-line main-sequence spectroscopie binaries with periods less than 10 days. Most of the rapidly rotating stars observed appear to have relatively high fluxes compared to the slowly rotating stars of the same spectral type. Calculations show that the effect of rotational broadening is negligible and that the fluxes greater than normal measured in these stars must be a result of an increased Ca II H and K emission. All main-sequence binaries with periods less than 9 days show eccentricities smaller than 0.1, which indicates that in these systems the rotational and orbital motions are probably synchronized. The five binaries observed with periods of less than 7 days show a Ca II H and K flux greater than normal whereas the two binaries with periods larger than 7 days show a relatively normal Ca II H and K flux compared with single stars of the same spectral type. The observations of both the single stars and the binaries are consistent with the hypothesis that Ca II H and K emission decreases with decreasing rotation rate. Key words: stellar chromospheres - stellar rotation - late-type main-sequence stars - spectroscopie binaries 1. INTRODUCTION It Is well known that late-type main-sequence stars of similar effective temperature and surface gravity may show very different Ca II H and K emis- sion (Wilson, 1966a, 1968). This indicates that the two parameters generally used to describe a stellar atmosphere, viz. the effective temperature and the gravitational acceleration, are insufficient to represent the observations. Investigations by Wilson, (1963, 1966b, 1970), Wilson and Skumanich (1964), and Wilson and Woolley (1970) show that the Ca II H and K emission of main-sequence stars declines with age. But it is difficult to accept the age by Itself as an extra parameter determining the structure of the chromosphere. The stellar rotation rate is a more attractive candidate for an extra parameter. There are a number of reasons for this suggestion: 1. Kraft (1967) showed that the average rotational velocity of stars which show Ca II emission on 10 A/mm plates is higher than for those which do not. 42 2. Differences in Ca II H and K emission among giants may be explained by differences in rotation rate (see Middelkoop and Zwaan, 1981). 3. In the Sun the Ca II H and K emission predominantly originates in discrete magnetic elements. Probably the magnetic flux on the Sun is the result of convection and (differential) rotation in some dynamo mechanism, which suggest that the stellar rotation rate may be a plausible third param- eter (see Zwaan, 1977, 1980). 4. Kraft (1967) showed that the rotational velocity of main-sequence stars declines with age. The decline of Ca II emission with age is then readily explained by the decline of rotational velocity with age. 2. RAPIDLY ROTATING F-TYPE STARS O.C. Wilson, (1968) published flux measurements of the Ca II emission of 139 main-sequence stars with 0.24 < b-y < 0.44. A striking increase in the spread of the Ca II fluxes of stars was found for b-y > 0.29, which Wilson, termed the "chromospheric bulge". This value of b-y is almost identical with the value of b-y of 0.285 at which a sharp decline in the average rotational velocity of main-sequence stars is found (Wilson, 1966b). Are these facts related? Wilson, (1968) selected only stars with vsini less than 15 km/s, to avoid significant widening of the Ca II H and K emission features due to ro- tational line broadening. This constraint does not bias the sample of stars with b-y > 0.31 since hardly any stars with vsini > 15 km/s can be found in this range (cf. Wilson, 1966b). However, a substantial fraction of stars with b-y < 0.31 do show vslnl larger than 15 km/s. If the Ca II emission does decline with decreasing rotation rate, then the sample of stars observed by Wilson, (1968) is biased, favoring stars of relatively low Ca II emission. In order to investigate the effect of rotation, 31 stars with vsini > 10 km/s were selected from Wilson, (1966b). During November 1979 we measured the Ca II emission fluxes of these stars only once, using the Ca II H and K photometer (see Vaughan et al., 1978) at the 60 inch telescope of Ht. Wilson. The results of these measurements were converted to Wilson's (1968) scale of fluxes using the procedure given by Vaughan et al., (1978). The results are listed in Table 1 and plotted in Fig. 1, along with the data published by Wilson, (1968). The upper dashed line represents the upper boundary found by Wilson, (1968) showing the chromospheric bulge. The majority of stars with vsini > 25 km/s show Ca II fluxes close to or above this upper boundary. 3. THE INFLUENCE OF ROTATIONAL LINE BROADENING The lower boundary in Fig. 1 rises on the left starting at b-y «s 0.35. This is due to the weakening of the H and K lines with increasing temperature so that more and more of the inner wings are included in the 1 k band. Rota- tional broadening will then fill in the line core and enhance the measured flux. To investigate this effect we scanned the core and inner wings of the Ca II H and K lines of a star with vsini < 10 km/s and a relatively low Ca II flux (viz. HD 82328, b-y - 0.314, F - 0.142) by changing the observed wavelength in steps of 0.13 A (Vaughan et al., 1978). The result of this scanning procedure is given in Fig. 2. The ordinate in Fig. 2 is N +N H +N proportional to H KV V R where NH ,NJJ , Ny and NR refer to the number of counts, corrected for background, in the H and K bands (bandwidth 1 A) and in the continuum reference bands (bandwidth 20 X) on the 43 Fig.l: Ca II H and K fluxes are plotted against oolor for the F- and G-type stars as observed by Wilson (1968) and the author. The upper and lower dashed tines represent the upper and lower boundary, defined by Wilson, (1968). violet and red side of the H and K region, respectively (see Vaughan et al., 1978). Since the bandwidth of the reference bands is about 20 A, NV + NR ls assumed to be constant during the scan. Therefore the profile plotted in Fig. 2 is regarded as the sum of the H and K profiles convoluted with the instrumental profile of the Ca II H and K photometer. The influence of rotation is investigated by convoluting the H and K profiles with a rota- tional broadening profile. Since a convolution is a commutative operation the rotational broadening profile may be applied directly to tts measured profile plotted in Fig. 2. The resulting profile then represents the profile that would be measured with the Ca II H and K photometer for a star with the same Ca II emission index as HD 82328 but with a different but larger vsini value. The rotational broadening profiles used were calculated from the formula given by Gray (1976) using a limb darkening coefficient E « 0.6 (The results are not very sensitive to this coefficient). The resulting broadened profiles are also plotted in Fig. 2. We conclude that for stars with vsini <50 fcm/s and b-y ^ 0.31 rotational broadening enhances the measured flux by less than 0.011. Similar calculations on H and K profiles of HD 110379 (b-y - 0.245) and HD 110380 (b-y - 0.245) (given by linsky and Worden, (1979)) indicate that the flux enhancement due to rotational line 44 Table 1: Single stars Column 2: Color b-y fvcm Strömgren and Perry, (1965) Column 3: Measured Ca II H and K fluxes, reduced on the scale of Wilson, (1968) Column 4: Rotation group from Wilson, (1966a) \ Rot. group 0+ 1 2 3 4 5 vsini (in km/s) 10-15 15-25 25-35 35-45 45-55 55- H.D. b-y F Rot.Group 1671 .288 .215 3 6210 .356 .211 2 6301 .294 .184 0+ 8799 .288 .228 4 11151 .264 .190 3 13871 .288 .167 0+ 15524 .273 .231 4 16176 .320 .187 1 16327 .306 .227 3 16399 .281 .239 0+ 16647 .268 .212 1 18256 .308 .167 0+ 18404 .277 .198 1 28271 .346 .256 3 30652 .299 .205 0+ 35984 .308 .219 3 40832 .290 .166 0+ 48737 .288 .217 4 67483 .313 .228 3 74243 .299 .191 1 89449 .297 .175 0+ 111456 .319 .282 3 217926 .276 .224 4 218804 .302 .213 1 219291 .309 .258 5 219487 .276 .201 1 220117 .296 .170 0+ 222451 .272 .190 2 223346 .308 .188 0+ 223421 .277 .235 5 223552 .258 .268 5 broadening for stars with vsini <50 km/s and b-y = 0.24 cannot be more than 0.02. The difference between the upper and lower boundary in Pig. 1 is much larger (up to 0.12 for b-y = 0.29) than can be accounted for by rotational line broadening. Therefore it is concluded that the greater than normal fluxes measured in rapidly rotating stars cannot be explained by rotational line broadening but must be mainly due to a greater than normal H and K emis- sion in these stars. This is in agreement with the hypothesis that the Ca II H and K emission decreases with decreasing rotation rate. i | I l i i i i i 3000 i i NH*NK i a- i IV Nv i 2750 / 2500 2250 1, -v sin i •'/ ' 2000 1 1 i 1750 \\\ ilLv sin i =50 1500 J km vsini=0-10 vsini=25 /Sec i i i l iii) 2 1.5 1 0.5 O 0.5 1 1.5 2 Fig. 2: The influence of rotational broadening on the Ca II U and K flux. The rotationally broadened profiles are explained in the text. Crosses represent the measured Ca II fluxes for BD 82328. 4. SINGLE-LINE SPECTROSCOPIC BINARIES Since the rotational velocities of main-sequence stars with b-y > 0.33 cannot (yet) be measured spectroscopically, the assumed relationship between Ca II emission and rotational velocity is not known. This lack of fast rotators indicates that these stars lose most of their angular momentum before or shortly after they have reached the zero-age main-sequence (Kraft, 1967). However, if the star belongs to a synchronized short-period binary, then the loss of angular momentum is partially replenished by the large amount of angular momentum present in the double star system, which results in a relatively rapid rotation compared with single stars (This idea has been explored for giants by Middelkoop and Zwaan, 1981). 46 The theory of tidal friction predicts that, apart from synchronization between the rotation of the star and the orbital motion of the system, the orbits will also become circular (Zahn, 1977). This occurs in such a way that synchronization is always achieved before the orbit is circular. In Fig. 3 the eccentricity is plotted against period for all main-sequence binary systems with spectral types FO - G9 and orbital periods smaller than 50 days present in the catalogue of Batten et al., (1978). All binary systems with periods smaller tban 9 days have eccentricities smaller than about 0.1. Therefore we conclude that binary systems with periods smaller than 9 days are probably synchronized. Seven main-sequence single-line spectroscopie binaries were observed during November 1979. The results are listed in Table 2 and plotted in Fig. 1, where the numbers represent the orbital period of the system. The dashed bars indicate the maximum possible effect of the secondary component on the measured Ca II flux. This has been estimated by assuming that the secondary is a main-sequence star being at least one visual magnitude fainter than the primary. (This seems a reasonable assumption because all observed binaries are single-lined). For the Ca II flux of the secondary we assume the largest flux value found by Vaughan and Preston (1980) for the spectral type corresponding to the assumed spectral type of tbe secondary star. The reason is that the secondary component will also be synchronized and therefore a relatively large Ca II flux is to be expected. It appears that the binaries with periods less than about 7 days which have been observed show a relatively large Ca II flux. CONCLUSION The results of the observations of rapidly rotating, single stars and synchronized short-period binaries are in agreement with the hypothesis that Ca II emission decreases with decreasing rotation rate. Although many of the stars with vsini > 15 km/s show Ca II fluxes above the upper boundary found by Wilson, it seems that the shape of this boundary does not change. Therefore we conclude that from b-y = 0.29 onwards the dependence of the Ca II emission with rotational velocity increases sharply with decreasing effective temperature. This conclusion seems to be supported by the observations of synchronized binaries. Although the binary systems with periods of 7.8 and 9.1 days (HD 7345 and HD 92168) are presumably also synchronized they show a relatively low Ca II flux. Since the estimated equatorial velocities of 7.1 km/s and 6.3 km/s are well below 10 km/s this may indicate that their rotation periods are close to the rotation periods of old, single stars of the same spectral type. All other observed binaries show an enhanced Ca II emission indicating that their rotation periods are relatively short compared to stars of the same spectral type. However, it remains to be demonstrated that a synchro- nized binary produces the same Ca II H and K flux as a single star of the same rotation rate, surface gravity and effective temperature. The only indication that supports this idea so far, is the similarity between the calculated equatorial rotational velocity of the binary component HD 203454 (v - 17.2 km/s) and the vsini value of the single star HD 35296 (vsini - 15 km/s, Kraft, (1967), F - 0.285, b-y = 0.348). Both stars show about the same effective temperature and Ca II flux. The fact that this Ca II flux is larger than the flux measured for HD 28271, HD 6210, HD 111199 and HD 66011, which are stars of about the same spectral type and comparable or even larger vsini values (indicated by the letters a, b, c and d, Table 2 : Single-line binary stars Column 3 : b-y values given in parenthesis were derived from speotral type otherwise from StrSmgren and Perry (196S) Column 4,5 : Orbital periods and eaoentrioities from Batten et al., (1978) Column 6 : Measured Ca II B and K fluxes* reduced on the scale of Wilson, (1968) Column 7 : Equatorial velocity of the primary component assuming that the rotation period is equal to the orbital period. Stellar radii were derived from spectral type using kllsn (1976). Spectral Period H.D. type b-y (in days) 7345 F7 V (0.32 ) 9.1 0.03 .154 6.3 27130 G8 V (0.48 ) 5.6 0.04 .482 7.8 44982 GO V (0.38 ) 0.6 0.0 .447 87.5 92168 F8 V (0.35 ) 7.8 0.02 .132 7.1 98230 GO V (0.38 ) 4.0 0.0 .408 13.1 203454 F8 V 0.349 3.2 0.02 .278 17.2 222317 G5 V (0.44 ) 6.2 0.02 .335 7.5 0.5 0.4 0.3 0.2 0.1 -0.8 -O.4 0 0.4 0.8 1.2 1.6 2.O log P(days) Fig.3: Eccentricity is plotted against period for main-sequenae spectroscopie binaries of spectral typeFO - G9. Some systems with zero eccentricity have been plotted below zero. 48 respectively, in Fig. 1), may be explained by the relatively large Strömgren cj index of the latter stars which indicates that they are evolved stars (see also Wilson, 1968). Therefore the Ca II flux of these stars may not be directly comparable with the Ca II flux of normal main-sequence stars with an identical rotation rate. ACKNOWLEDGEMENTS This investigation was made possible by the hospitality of Mt. Wilson Observatory and by the kind help of A.H. Vaughan and G.W. Preston. I would like to thank J. Frazer and H. Lanning for assistance in making the observa- tions. This work was supported by a travel grant from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). I am also indebted to C. Zwaan and B.J. Oranje for several valuable discussions and to C. Zwaan and A.G. Hearn for critically reading the manuscript. Mrs. J.G. Odijk prepared the typescript and mr. E. Landre the figures. REFERENCES Allen, C.W.: 1976, Astrophyslcal Quantities (3rd ed; : London Athlone Press) Batten, A.H., Fletcher, J.M., and Mann, P.I: 1978, Publ. Dominion Astrophys. Obs. 15, 5 Gray, D.F.: 1976, The Observation and Analysis of Stellar Photospheres (New York: Wiley-Interscience), Ch. 17 Kraft, R.P.: 1967, Astrophys. J. 150,551 Linsky, J.L., and Worden, S.P.: 1979, Astrophys. J. Suppl. 41, 47 Middelkoop, F., and Zwaan, C: 1981, (Paper I) Astron. Astrophys. 101, 26 Strömgren, B., and Perry, C: 1965, Photoelectric uvby Photometry for 1217 Stars Brighter than 6.5 mostly of spectral classes A, F and G (2nd ed.; Princeton, New Jersey: Institute of Advanced Study) Vaughan, A.H. and Preston, G.W.: 1980, Publ. Astron. Soc. Pacific 92, 385 Vaughan, A.H., Preston, G.W., and Wilson, O.C.: 1978, Publ. Astron. Soc. Pacific 90,267 Wilson, O.C.: 1963, Astrophys. J. 138,832 Wilson, O.C.: 1966a, Science 151, 1487 Wilson, O.C.: 1966b, Astrophys. J. 144, 695 Wilson, O.C.: 1968, Astrophys. J. 153, 221 Wilson, O.C.: 1970, Astrophys. J. 160, 225 Wilson, O.C., and Skumanich, A.: 1964, Astrophys. J. 140, 1401 Wilson, O.C., and Woolley, R..: 1970, Mon. Not. R. Astron. Soc. 148, 463 Zahn, J.-P.: 1977, Astron. Astrophys. 57, 383 Zwaan, C.: 1977, in B. Caccin and M. Rigutti (eds.): The Sun, a Tool for Stellar Physics, Mem. Soc. Astron. Italiana, 48, 525 Zwaan, C: 1980, in R. Bonnet and A.K. Dupree (eds.): Proceedings of the NATO Advanced Course on "Solar Phenomena in Stars and Stellar Systems", (Reidel, Dordrecht, Holland) 49 CHAPTER III: MAIN-SEQUENCE STARS III.2: Magnetic Structure In Cool Stars IV: Rotation and Ca II H and K Emission of Main-Sequence Stars published In Astronomy and Astrophysics, 107, 31 SUMMARY The measured Ca II H and K emission indices of stars are converted to surface fluxes + FK ). This conversion largely eliminates the dependence on spectral type in the relation between the uncorrected Ca II R and K emission which has been found by Vaughan et. al. This relation holds for single main-sequence stars as well as for short-period binaries indicating that the enhanced emission in short-period binaries is a result of rapid rotation enforced by tidal coupling. A plot of surface fluxes against vsini values suggests a color-dependent discontinuity in the relation. This discontinuity may explain the two branches in (Ig + FK ) for (B-V) < 1.00 among main-sequence stars. From the relation between (Fg + % ) and rotational velocity it is deduced that the average rotational velocity of late-type main-sequence Hyades decreases with decreasing effective tempera- ture. Key words: stellar chromospheres - stellar rotation - late-type main-sequence stars - spectroscopie binaries INTRODUCTION It is well known that the Ca II H and K emission of late-type main-sequence stars declines with age (Wilson, 1963, 1966, 1970; Wilson and Skumanich, 1964; Wilson and Woolley, 1970) and also that the rotational velocity declines with age (Kraft, 1967; Skumanich, 1972; Smith, 1979; Soderblom, 1980). Several investigators therefore anticipated that Ca II H and K emission declines with decreasing rotational velocity (Kraft, 1967; Zwaan, 1977; Middelkoop, 1981). However, the relation between Ca II H and K flux and rotation rate has not yet been quantitatively established. The main problem in establishing the relation between Ca II H and K emission and rotational velocity is the determination of the rotational velocities of late-type main-sequence stars which are typically below 10 km/s. Considerable progress has been made recently in measuring rotational velocities by means of Fourier-analysis techniques (Smith, 1979; Soderblom, 1980) which lower the detection limit to about 2 km/s. Another powerful method of determining rotation periods of late-type stars is the detection of rotational modulation in the Ca II H and K emission itself. One of the advantages of this method is that the inclination i of the rotational axis does not enter into the results. Applying this method Vaughan et. al. (1981) were able to measure rotation periods of late—type stars with periods ranging from 2.5 to 54 days. From the results they found that for stars of a given 50 spectral type a strong correlation between the measured Ca XI H and K emission and the rotation period of a star exists, but that the form of this correlation strongly depends on spectral type. The Ca II H and K flux was measured relative to a nearby continuum flux. This index exaggerates Ca II H and K flux for progressively cooler stars. Section 1. presents a method of converting the measurements to relative surface fluxes in 1 A wide bands centered on the H and K line in arbitrary units. We will apply the conversion to main-sequence stars and discuss the results. Section 2. discusses the relation between Ca IT H and K line-core flux and rotation while Section 3. discusses the Ca II H and K line-core flux of stars in the solar neighborhood and Hyades. 1. CA II H AND K LINE ANALYSIS Ca II H and K fluxes of many main-sequence stars have been measured by Wilson (1968, 1978) using the Coude' scanner of the 100-inch telescope at Mt. Wilson and by Vaughan and Preston (1980) using the Ca II H and K photometer (Vaughan et al., 1978) at the 60-inch telescope of Mt. Wilson. Vaughan et al. (1978) give the relation between the measurements with these instruments. In this section we discuss the measurements as obtained by the Ca II H and K photometer. The procedure is that the Ca II H and K line-core fluxes are normalized with the fluxes measured in two reference windows separated by 100 X on either side of the Ca II H and K line cores. The Ca II H and K line-core index is defined as rt ~ a(NH Nr (1) where o is a normalizing factor derived for each observing night from the observations of standard stars to remove instrumental effects; ct will be treated as a constant in this paper. Ng , Ng , Ny- and NR refer to the number of counts, corrected for background, in the H and K bands and in the reference bands on the violet and red side of the H and K region, respectively. Since the continuum flux decreases the index S tends to increase through the spectral sequence. This hampers the comparison of the Ca II H and K measurements for stars of different spectral type. This paper adopts the total flux in the H and K bands (FWHP = 1.09 A) per unit area at the stellar surfaceSry +3*K as a parameter to describe the amount of chromospheric emission in the H and K lines. If we neglect wavelength dependent factors in the conversion from number of counts to fluxes (like photon energy and extinction coefficient) we can write (2) where V (3) where f3 is constant and f, . and FjjOj are the apparent and absolute bolometric flux of the star. They can be written as: BC) fbol (4) and 51 F (5) boi eff where y and O are constants, mv is the apparent visual magnitude, BC is the boloraetric correction and Teff is the effective temperature of the star. In this paper BC and Tef£were derived from color using Johnson (1966). If we write (6) then combining (2) through (6) results in: where 10 Jl* is arbitrarily chosen to provide nice numbers. I i i i i * 0 iogccf \ •V -0.5 - \ • -1.0 V Q4 0.6 0.8 1.2 1.4 1.6 B-V Pig.l: The logarithm of the conversion factor Cof against color f or selected stars in the solar neighborhood. The data points were fitted by least squares to a third order polynominal represented by the curve. 52 The relation between Ccf and color is found using the Ca II H and K observa- tions by Vaughan and Preston (1980) of stars in the solar neighborhood. The number of counts in the different channels depends on the (unknown) seeing and extinction coefficients at the time of observation and the way In which the star was guided during the observation. Note that the Ca II H and K photometer was not designed to measure absolute fluxes (Cf. Vaughan et al., 1978) and that no special precautions were taken to measure the stars in comparable conditions. The effect of differential extinction was minimized by selecting obser- vations at airmass x < 1.15. The measurement errors were limited by selecting stars which had been observed three times or more. The selected stars are plotted in Fig. 1. Although the observations are not corrected for differences in guiding and observing conditions the spread in Fig. 1 is relatively small. The curve is a cubic polynomial which has been fitted to the points by a least square method: 3 2 Log Cc£=l.l3(B-V) -3.91(B-V) +2.84(B-V)-0.47 (8) 0.45 <_ (B-V) _< 1.50 Relation (8) used in Eq. (7) makes it possible to calculate (Fjj + FR ), the Ca II H and K surface flux for individual main-sequence stars in arbitrary units. Fig.2: Surface fluxes (7(BX) +7(Kl))^ published by Linsky et al. (1979) •plotted against (Fg + F%) presented in this paper. Vertical bars connect different observations of the same star. Spectral types are indicated. 53 Linsky et al. (1979) published 120 ml resolution photographic spectrograms of the cores and wings of the Ca II H and K lines. These spectrograms were calibrated using Wilstrop's (1964) narrow band photometry and the Barnes and Evans (1976) relations for stellar angular diameters. Linsky et al. estimate an uncertainty of + 15% in their resulting flux scales. From the spectrograms they deduced surface fluxes SF(H]) and 3F (Kj), defined as the total flux in the Ca II H and K line profiles between the Hj minima and Kt minima, respectively. Although the passbands thus defined differ from the instrumental profile of the Ca II H and K photometer (Vaughan et al., 1978) we found that 7 (Hj) and JF(Kj) differ by less than 10% from the fluxes determined by applying the instrumental profile to the spectra published by Linsky et al. Fig. 2 shows the correlation between (SXHj) +Jr(Ki)) and (FH + FR )• The large spread may partly be caused by temporal variations in the Ca II H and K emission of stars (see Wilson 1978) and partly by the uncertainty of + 15% in the flux scales of Linsky et al. A weak spectral type dependence, in the sense that G-type stars are located systematically below the drawn line while K-type stars are located above it, may also be visible in Fig. 2. According to Fig. 2 our arbitrary unit of (FH + Fjj ) corresponds to 7.6xl0s ergs cm^s"1. This paper is restricted to main-sequence stars. However, plotting the results of Wilstrop's (1964) absolute photometry In the 3975 - 4025 X bandpass against (B-V) for dwarfs, giants and supergiants shows that the stellar flux in this bandpass is independent of luminosity class for stars with 0.4 _< (B-V) _< 1.8. A similar conclusion was drawn by Linsky et al. (1979) for the 3925 - 3975 & bandpass. This suggests that the reference windows of the Ca II H and K photometer are similarly independent of luminosity class so that the same correction factor can be applied for supergiants, giants and main-sequence stars. Note however that in the case of giants and supergiants the effective temperature of a main-sequence star of comparable color should be used in Eq. (7). 2. CA II H AND K EMISSION AND ROTATION Equations 7 and 8 were used to calculate surface fluxes (Fg + Fg) for the main-sequence stars for which rotation periods are given by Vaughan et al. (1981). The results are plotted in Fig. 3. Also plotted are the Sun and short-period single-line spectroscopie binaries (Middelkoop, I981) assuming that the rotation period of the star is equal to the orbital period of the system. Although there is a spread in Fig. 3, it reveals a clear correlation between Ca II H and K flux and rotational velocity. Apparently the conversion of observed values to specific surface fluxes largely eliminates the strong dependence on spectral type found by Vaughan et al. (1981) in their plot of S versus rotation period. A plot of (FH + FK ) against log P reveals an almost equally good correlation as found in Fig. 3. From the present data we cannot decide whether the rotation period or the rotational velocity is the best parameter to describe the Ca II H and K line-core flux. The full line in Fig. 3 is a linear fit calculated by assigning double weight to stars for which the rotation periods seem well established. This linear fit can be written as: FH+ FK=3 '65 loSv + °-55 (9) r -0.2 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Fig. 3: Surface fluxes (Fn and F%), in arbitrary units, plotted against equatorial rotational velocities. m Well established rotation period (Vaughan et al. (198D). . Probable rotation periods (Vaughan et al. (198D). + Single-line short-period spectroscopie binaries assuming that the rotation period of the primary is equal to the orbital period of the system. The numbers next to the symbols represent (B-V) values. The full line represents a linear fit. The dashed line connects stars with (B-V) w 0.87. Although the spread in Fig. 3 is larger for double stars than for single stars the double stars do not deviate systematically from the single stars. This indicates that the relatively high Ca II H and K flux found in short-period binaries is the result of rapid rotation enforced by tidal coupling (Middelkoop and Zwaan, 1981; Middelkoop, 1981) and not of tidal interaction affecting the chromospheric heating as suggested by Young and Koniges (1977) and Glebocki and Stawikowsky (1977). It would not be justified to conclude from Fig. 3 that the relation between (FJJ + FJJ ) and rotational velocity is strictly independent of spectral type. All stars plotted in Fig. 3 with (Fg + FK ) < 2 have (B-V) > 0.80. Moreover the line connecting the six stars with (B-V)«w 0.87 (the dashed line in Fig. 3) shows a somewhat different slope from the linear fit. 55 0.2 0.4 0.6 0.8 1.0 1.2 log(v sin i) Fig.4: (Fu + F%) against vsini values observed by Soderblom and Kraft (encircled points) A Stars with 0.45 £ (B-V) g 0.52 • Stars with 0.52 ,r (B-V) « 0.63 x Stars with 0.63 < {B-V) ^0.73 The full line represents the linear fit found from Fig. 3 (eq.9) plotted under the assumption that sin i= 1. In order to further investigate the relation between (Fg + FR ) and rotational velocity we turn to the large sample of vsinl measurements for solar-type stars (0.45 < (B-V) < 0.73) published by Soderblom (1980). Stars for which the Ca II H and K emission was known to us are plotted In Fig. 4 together with eight stars for which vsini is given by Kraft (1967). Generally the data are in accord with the relation calculated from Fig. 3 but the spread is remarkably large. The (F„ + F„ ) values of stars with (B-V) £ 0.52 and log (vsini) > 0.8 are systematically too low compared with the linear fit of Fig. 3. This is compatible with the conclusion that for (B-V) • 0.52 the dependence of Ca II emission on rotational velocity suddenly changes (Middelkoop, 1981). Note also that Soderblom's vsini values of stars with (B-V) > 0.52 and log (vsini) ^0.7 are systematically lower than expected from Eq. (9). What is surprising in Fig- 4 is the sharp change in the Ca II H and K emission near log(vsini) » 0.65 for stars with 0.52 < (B-V) _< 0.63. A similar drop may occur for stars with 0.63 < (B-V) £ 0.73 near log(vsini) « 0.45. 56 8 1 8 " - •I. • * • t .•!».;/'•.«.•.;«.:: ..\:,v i I i • • * • . ' •s.'jï»"!--:.! 0.4 0.6 0.8 1.0 1.2 1.4 B-V Fig. 5: (F„ + F^) against (B-V) for stars in the solar neigborhood (.) and Hyades (x). The full line is a second order polynomial fitted to the Hyades data. (Fg + FK ) and rotational velocity seem to be uncorrelated for rotational velocities smaller than this critical velocity. But this conclusion depends heavily on the accuracy of the vsini measurements. Although Soderblom lists rotational velocities down to 0.8 _+ 0.8 km/s, Smith (1979) regards 2.0 to 2.5 km/s as the ultimate limit for the method of Fourier profile analysis. 3. CA II H AND K EMISSION IN MAIN-SEQUENCE STARS Fig. 5 shows stars in the solar neighborhood observed by Vaughan and Preston (198*0) and Hyades stars observed by Wilson (1979, private communication). The full line in Fig. 5 is a second order polynomial fitted to the Hyades data: FH + FR - -4.9(B-V)* + 0.6(B-V) + 5.6 (10) Using Eq. (9) and (10) we conclude that the average rotational velocity in the Hyades, which consists of stars of the same age, decreases with increasing color (B-V) from v 13.5 for (B-V) •• 0.50 to v « 2.8 for (B-V) • 0.90. 57 What is striking in Fig. 5 are the two branches in (Fg + % ) for (B-V) < 1.00 with a gap in between, found first by Vaughan and Preston (1980). It is unlikely that this is due to a selection effect in the sample which contains all late-type stars within 25 parsecs of the Sun and north of the equator. The gap in Fig. 5 and the discontinuity in the relation between (FH + FK ) and rotational velocity suggested by Fig. 4 nay be related. We suggest the following evolutionary scenario for late-type main-sequence stars with (B-V) < 1.00. A star arrives on the zero-age main-sequence with a relatively large rotational velocity. Due to magnetic braking (Schatzman, 1962, 1955) the star loses angular momentum and the flux ( Fg + Fg ) decreases with decreasing rotational velocity according to Eq. (9), until a critical velocity is reached. Then (FJJ + Fg ) drops rapidly with time which explains both the discontinuity in Fig. 4 and the gap in Fig. 5. After this drop the rotational velocity still decreases with time (although the deceleration rate may have changed). The rotational velocities available at present for old, slowly rotating stars are not accurate enough to determine whether there is some relation between the flux (FJJ + FR ) anc* tne rotational velocity after the rotation has dropped below the critical value. The discontinuity in Fig. 4 and the gap in Fig. 5 support the idea of two distinct dynamo modes (Zwaan, 1981). ACKNOWLEDGEMENTS I would like to thank A.H. Vaughan and O.C. Wilson for sending me the data of the solar neighborhood survey and the Hyades. This work was supported by the Netherlands Foundation for Astronomical Research (ASTRON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). I am also indebted to C. Zwaan and B.J. Oranje for several valuable discussions and to C. Zwaan and A.G. Hearn for critically reading the manuscript. I profited from constructive criticism by the referee. Mrs. J.G. Odijk prepared the typescript and mr. E. Landre the figures. REFERENCES Barnes, T.G., and Evans, D.S. 1976, Mon. Not. R. Astron. Soc. 174, 489 Glebocki, R., and Stawikowski, A.:1977, Acta Astron. 27, 225 Johnson, H.L.:1966, Ann. Rev. Astron. Astrophys. 4, 193 Kraft, R.P.:1967, Astrophys. J. 150,551 Linsky, J.L., Worden, S.P., McClintock, W., and Robertsen, R.M.:1979, Astrophys. J. Suppl. 41, 47 Middelkoop, F.:1981, Astron. Astrophys., 101, 295 Middelkoop, F., and Zwaan, C:1981, Astron. Astrophys., 101, 26 Roman, N.C.:1949, Astrophys. J. 110, 205 Schatzman, E.:1962, Ann. Astrophys. 25, 18 Schatzman, E.:1965, in R. LÜst (ed.): Stellar and Solar Magnetic Fields, Ï.A.U. Symp. No. 22, p. 153 Skumanich, A.:1972, Astrophys. J. 171, 565 Smith, M.A.:1979, Publ. Astron. Soc. Pacific 91, 737 Soderblom, D.:1980, Dissertation, University of California at Santa Cruz Vaughan, A.H., and Preston, G.W.:1980, Publ. Astron. Soc. Pacific 92, 385 58 Vaughan, A.H., Baliunas, S.L., Middelkoop, F., Hartmann, L.W., Mlhalas, D., Noyes, R.W., and Preston, G.W.:1981, Astrophys. J. 250, 276 Vaughan, A.H., Preston, G.W.,» and Wilson, O.C.:1978, Publ. Astron. Soc. Pacific 90, 267 Wilson, O.C.:1963, Astrophys. J. 138, 832 Wilson, O.C.:1966, Astrophys. J. 144, 695 Wilson, O.C.:1968, Astrophys. J. 153, 221 Wilson, O.C.:1970, Astrophys. J. 160, 225 Wilson, O.C.:1978, Astrophys. J. 226, 379 Wilson, O.C*, and Skumanich, A.:1964, Astrophys. J. 140, 1401 Wilson, O.C., and Woolley, R.:1970, Mon. Not. R. Astron. Soc. 148, 463 Wilstrop, R.V.:1964, Mem. Roy. Astron. Soc. 69, 83 Young, A., and Koniges, A.:1977, Astrophys. J. 211, 836 Zwaan, C.:1977, in B. Caccin and M. Rigutti (eds.): The Sun, a Tool for Stellar Physics, Mem. Soc. Astron. Italiana, 48, 525 Zwaan, C.:1981, in R.M. Bonnet and A.K. Dupree (eds.): "Solar Phenomena in Cool Stars and Stellar Systems", (D. Reidel, Dordrecht, Holland) 59 CHAPTER IV: EVOLVED STARS IV.1: MAGNETIC STRUCTURE IN COOL STARS I: The Ca II H ard K Emission from Giants F.Middelkoop and C. Zwaan(*) published in Astronomy and Astrophysics, 101, 26 SUMMARY Wilson's (1976) eye estimates of the Ca II H and K emission from evolved cool stars are reanalysed. G-type giants show a large spread in H and K emission; giants with broadened spectral lines tend to produce enhanced emission. The H and K emission from stars of metalliclties deviating from the solar metallic!ty is relatively small. For spectroscopie binaries we find a critical period (between 120 and 200 days) below which the orbits tend to be circular, indicating that rotation and orbital motion are probably synchronized. For periods less than the critical period the emission strength is enhanced; the emission is stronger according as the orbital period is shorter. The data are consistent with the hypothesis that Ca II H and K emission depends on the dynamo action in the convective envelope, the dynamo efficiency decreasing with decreasing rotation rate. The H and K emission decreases with time because of the magnetic braking of rotation. G-type giants with enhanced emission are interpreted as rapidly rotating stars which have just developed convective envelopes and dynamos. In synchronized binaries the phase of enhanced emission lasts much longer because of the large reservoir of angular momentum in binary systems. Key words: stellar chromospheres - stellar rotation- stellar dynamos - cool giants — spectroscopie binaries. 1. INTRODUCTION Emission features in the cores of the Ca II H and K lines are observed in spectra of many main-sequence stars later than about F5 (Wilson 1966) and of nearly all giants later than GO (Wilson 1976). Stars of the same spectral type and luminosity class may display very different amounts of H and K (*) The Astronomical Institute, Zonnenburg 2, 3512 NL Utrecht, The Netherlands 60 emission (Wilson 1968, 1970, 1976). The properties of the Ca II H and K emission from main-sequence stars have been investigated In quite some detail. The H and K emission decreases rapidly with age (Wilson 1963, 1966; Wilson and Skumanlch 1964; Wilson and Woolley 1970). Probably this dependence on age is due to the rotation rate decreasing with age (Kraft 1967; Skumanich 1972; Klppenhahn 1973). Indications for a direct relation between H and K emission and rotation for F-type stars have been found by Middelkoop (1981). The interpretation of the Ca II H and K line-core fluxes requires an extra parameter, viz. the rotation rate, in addition to the effective temperature and surface gravity. This rules out a global, non-magnetic acoustic heating as the main mechanism for hot chromospheres of cool stars (Zwaan 1977). A more attractive hypothesis (see Zwaan 1981) is that the H and K emission originates predominantly from discrete magnetic elements, like in the Sun. The suggested similarity between the Sun and other stars showing Ca II H and K emission is based on the convective envelope that is common to all these stars. The convective envelope is the seat of the dynamo mechanism and the cause for the discreteness of the magnetic field. The H and K emission flux, proportional to the number density of magnetic elements, depends on the efficiency of the dynamo, which is assumed to decrease with decreasing rotation rate (Skumanich 1972). The decrease of the stellar rotation rate with time is attributed to the efficient braking resulting from the stellar wind streaming out along the coronal magnetic field (Schatzman 1962, 1965). This paper reanalysis Wilson's (1976) eye estimates of the Ca II H and K emission intensities for some 500 subgiants, giants and supergiants. We investigate whether the hypothesis outlined above holds for evolved stars as well. 2. WILSON'S INTENSITY CLASSES FOR GIANTS Wilson (1976) estimated the brightness of the H and K emission features in the Ca II H and K line cores relative to the neighboring "continuum" background in six intensity classes I, ranging from I - 0 (no emission cores visible) to I - 5 (brightness of emission peaks equal to or larger than the continuum background (Wilson and Bappu 1957)). The intensity classes were estimated from 10 I/mm spectrograms which are sufficiently exposed to show the intensity profiles in the Ca II H and K line cores. Wilson's (1976) data form a rather homogeneous sample of bright evolved stars, down to about tnv = 6.0. However, Wilson omitted double-line spectroscopie binaries and stars showing large rotational line broadening. He added some fainter stars with metallic!ties differing from the Sun. At our request Wilson kindly furnished some intensity class estimates not Table 1: Additional data by Wilson (19?73 private communication) HD I rotational broadening 58972 3 moderate 59148 1 considerable 62044 5 (very strong) considerable 111812 some (we put: 1) large (plate overexposed) 61 entered in his table, because the emission is exceptionally strong or the line broadening is too large to estimate the Wilson-Bappu width Wo . These data are given in Table 1. In Fig. 1 (*) the intensity classes are plotted against color (B-V) for the stars in Wilson's (1976) sample which satisfy +3.5 > M > -3.0. We excluded a dozen faint stars (mv > 6.2) which Wilson included because of abundances differing from the solar abundances. Fig. 1 shows the following features: The vast majority of the K- and M-type giants and many lace 6-type giants and subgiants constitute a band of intensity class I increasing with (B-V). We refer to this band as the main I(B-V) trend. Wilson (1976) has pointed out that this trend may be due to the- reference continuum decreasing with increasing (B-V). i i i 1 1 1 1 1 1 i i i 1 20 5 - «15 2O»ao t 18 oOo • • — s • 4 - • • o* • O • oOC^DOo - X «120 3 - O •• a» O «120 oooo gJQOoo. - 39 9 - OOO • 50 - 2 •13.2 °o o ooC£0Oo o o 73 ^ o 20 1 O O O( )Oo o 10 XXX X ^XK XXX 5 o 2 0 1 n • • € 1 1 1 1 1 1 i 1 1 1 1 0.6 0.8 1.0 12 1.4 1.6 1.8 2.0 B-V Fig.2: Intensity alass I versus (B-V) for zhe stars in Wilson's (1976; sample with +3.5 > M > -3.0. Circular synibols indicate giants of luminosity classes II, II-III and III-IV; subgiants (LC IV) are plotted individually by crosses (x). Binaries with periods P < 120 days -xre represented by asterisks (*)3 with periods in days. The heavy line marks the main I(B-V) trend. (The arrow points at SD 817993 which is discussed in the Appendix). (*) This presentation has been prepared in collaboration with B.J. Oranje I 62 The G-type giants show a large spread in the H and K intensity class (1 <_ I £ 4); the corresponding area in Fig. 1 seems to be bounded on the red side near (B-V) = 0.95. For the majority of subgiants the spread in intensity class is small: I = 0 or I = 1. The main I(B-V) trend among the M- and K-type giants seems to continue as the lower envelope for the G-type giants and subgiants. It is well known that spectroscopie binaries of short orbital period exhibit strong Ca II H and K emission (see Hiltner 1947; Gratton 1950). From Fig. 1 it appears that binaries with periods up to at least 100 days show enhanced H and K emission. 3. THE MEASURE A/a FOR THE CA II H AND K EMISSION For a further analysis of Wilson's data the Ca II H and K emissions of stars of different spectral type and intensity class have to be compared. To overcome this problem we introduce an approximate measure for the departure of the Ca II H and K emission from the main I(B-V) trend. As the first step we plotted for each of Wilson's intensity classes histograms against (B-V), selecting giants and subgiants by setting lower limits to ttv : M > -1 if (B-V) <_ 1.20, My > -2 if 1.20 < (B-V) < 1.50, and My > -3 if (B-V) 2 1.50. For M^ we adopted the absolute visual magnitude M (K) that Wilson (1976) derived from the Wilson-Bappu relation; in cases where My (K) is lacking (for instance, for I » 0) we used the luminosity class as the selection criterion. The histogram for I « 3 is shown in Fig. 2. The histograms for 1=1, 2, 3 and 4 are similar: the majority of the stars in each class I are contained within a narrow range of (B-V), while some stars have a much smaller (B-V). The histogram for I » 5 (see Fig. 1) is less regular: the number of stars with I « 5 is rather small, and the definition for I « 5 sets only a lower limit to the emission. The shape of the histogram for I «• 0 is irregular: the number of stars is small, the selection criterion is only an upper limit to the emission, and on the blue side the histogram is bounded by the stars of the lowest (B-V) values in Wilson's sample ((B-V) t» 0.60). For each of the classes we determined the median Table 2: Medians 0 (0.73) (0.12) 11 1 1.00 0.08 263 2 1.19 0.13 131 3 1.42 0.12 119 4 1.57 0.08 99 5 (1.67) (0.11) 33 63 A measure A /a for the strength of a star's Ca II H and K emission is defined by means of the main I(B-V) trend as follows (see Fig. 2): Fig.2: Histogram N(B-V) for steers of intensity elass I = 3. The determination of the relative strength A/a is explained for 57 Gem (HD 57?2?, G8 III, (B-V) =0.89). 64 70 - N 60 - 50 • Fig.3a: Histogram N(h/a) for all stars in Wilson's (1976) sample witli M > -3.0. Binaries with periods P > 120 days are indicated in black. Fig. Sb: Histograms N(b/a) for stars showing spectral-line broadening. Binaries are indicated in black for P<120 days and hatched for P> 120 days. in case of quantitative measurements of the H and K index the vertical departure from the lower envelope were the obvious measure of the relative H and K emission strength. However, for analysis of Wilson's I classes this does not seem the best procedure, because the trend is not well defined in the range of the G stars. 4. CA II H AND K EMISSION FROM SINGLE STARS From plots of the intensity classes I versus (B-V) and from the analysis of {y/a histograms it appears that stars of luminosity classes II, II-III and III-IV show the same behavior as the giants of the luminosity class III. Therefore we treat these luminosity classes as one group in this paper. From Fig. 1 we have concluded in Sect. 2, that the I(B-V) behavior of the subgiants (luminosity class IV) overlaps and complements the I(B-V) behavior of the giants; we treat the subgiants as a separate group. 65 HD Sp B-V V I MV(K) P <2 remarks (days) 3421 G5 III 0.90 5.5 3 4.3 -3.6 _ 4502 KI II 1.12 4.1 5 5.1 - 17.8 0.00 large rot. broadening 10072 G8 III 0.89 5.0 4 8.2 1.0 - 13480 G5 III 0.78 4.9 5 8.3 -2.1 14.7 0.04 - 24555 G6 III 0.68 4.5 3 6.1 0.5 - 26659 G8 III 0.87 5.5 3 4.5 1.4 32008 dG4 0.80 5.4 4 9.3 2.4 - 32357 K0 III - 6.2 5 6.0 -1.5 80..1 0..35 data Abt et al., (1969) 57727 G8 III 0.89 5.0 3 4.3 1.8 - 62044 KI III 1.12 4.3 5 5.1 - 19..6 0..0 rot. broadening 74485 G5 III 0.93 6.1 3 4.0 0.1 — 81799 SK:! 1.14 4.7 4 5.2 0.4 - 82210 G4 III-IV 0.77 4.5 4 9.7 2.3 • 82635 G8 III 0.92 4.5 4 7.8 1.4 - 126868 G2 III 0.70 4.8 3 5.9 2.0 slight rot. broadening 141714 G8 III-IV 0.80 4.6 3 5.1 2.0 — 153751 G5 III 0.90 4.2 3 4.3 - 39.,5 0.. 04 rot. broadening 181391 G8 III-IV 0.92 5.0 3 4.1 1.5 266.,5 0.83 - 191026 KO IV 0.86 5.4 4 8.6 3.1 - 203387 G8 III 0.90 4.3 4 8.1 0.4 - 206301 G2 IV 0.65 5.2 2 4.3 2.1 13.2 0.16 - 210460 GO 0.70 6.2 3 5.9 2.5 - 216380 G8 III-IV 0.78 5.6 3 5.2 2.4 • 222107 G8 III-IV 1.02 3.9 5 6.1 - 20.5 0.04 - Table 3: Giants and subgiants with strongly enhanced CallH and Remission (A/a > +4.0). The spectral type, luminosity alass, color (B-V), visual magnitude V, intensity class J, and the absolute visual magnitude M (K) derived from the Wilson-Bappu width are from Wilson (1976); the periods P and eccentricities for spectroscopie binaries are from Batten et al. (1978). Under remarks Wilson's comments on rotational line broadening are copied. Wilson's (1976) sample includes several G-type stars classified as luminosity class V; the intensity classes range from I - 0 to I - 5. These stars are not included in this analysis. The behavior of the Ca II H and K emission from superglants, luminosity class I, differs from Fig. 1: the intensity classes plotted against (B-V) form a broad strip, rising from I(H+K) na 2 near (B-V) - 0.80 to I(H+K) f» 4 near (B-V) - 1.70; for (B-V) > 1.80 the intensity class I(B+K) tends to decrease. We exclude the supergiants from further analysis. The large spread in the Ca II H and K emission from G-type giants raises the question whether the emission depends on the stellar rotation rate, as is the case for main—sequence stars, (see Sect. 1.). Wilson (1976) has commented on the stars showing abnormal broadening of spectral lines; Fig. 3b presents the histogram of the strengths A/cr for these stars. This category includes 66 spectroscopie binaries and several single G-type giants. Indeed there is an excess of H and K emission strength A/a > +2.0. However, there are still some stars with line broadening that have A/a < +1.0. We see two possible explanations: (i) the rotation broadening is so large that the emission features are so much broadened that the peaks are reduced and hence I is underestimated; (ii) the spectrum has been contaminated by light from a star of earlier spectral type, which would make the spectral lines more shallow. The latter explanation fits the large fraction of spectroscopie binaries with periods longer than 120 days among stars with A/a < +1.0 in Fig. 3b. He conclude that relatively rapidly rotating G-type giants tend to show enhanced Ca II H and K emission. This suggests that among subgiants and giants the Ca II H and K emission may depend on the rotation rate, as is the case for main-sequence stars (see Sect. 1.). Wilson (1976) added to the sample fainter stars of metallicities deviating from the solar metalliclty. They contribute to the negative wing in the N(A/a) distribution, their mean value of A/a is -2.1 + 1.7 (s.d.). These nine faint stars contain two hydrogen-deficient stars, viz. HD 137613 and HD 182040, with A/a = -4.1 and -3.5, respectively. This dependence on chemical composition is a reminder that the quantitative interpretation of the Ca II H and K emission flux should include the effects of departures from the solar composition. Linsky and Haisch (1979) classify the 1UE short-wavelength spectra of cool stars in two groups: "solar-type" stars showing all the chroraospheric and transition-region emission lines, and "non-solar-type" stars showing no transition-region lines, only chromospheric lines indicating temperatures up to 20 000 K. It is of interest to note that the domain of solar-type stars coincides approximately with the region of the G-type giants, whereas the non-solar type stars concur with the K- and M-type giants in the main I(B-V) trend. 5. SPECTROSCOPIC BINARIES: SYNCHRONIZATION AND CA II H AND K EMISSION Two recent papers discuss the Ca II H and K emission from spectroscopie binaries. Glebocki and Stawikowski (1977) plotted the intensity class I against the orbital period for binaries among G- and early K-type giants. They conclude that the H and K emission decreases monotonically with the period. Young and Koniges (1977), discussing main-sequence stars and giants, found that many - but not all - binaries with periods less than 100 days show enhanced H and K emission. They noticed a tendency towards circular orbits among binaries with enhanced emission. Both papers attempt to interpret the enhanced Ca II H and K emission as a direct result of tidal interaction affecting the chromospheric heating. We investigated some properties of the spectroscopie binaries among the giants in the samples of Wilson (1976) and Glebocki and Stawikowski (1977), using the relative strength A/a defined in Sect. 3. Fig. 4 shows that the H and K emission is enhanced for periods shorter than about 120 days; for P > 200 days the emission is normal for the spectral type. Among the binaries with periods longer than 200 days only the G-type binaries may show enhanced Ca II H and K emission (Fig. 4), but in that respect they do not differ from single G-type giants (Fig. I). 67 logPtiays) Fig.4: H and K emission strength h/a versus period Pfor spectroscopie binaries with +3.5 > Mv > -3.0. Circles: from Wilson (1976); triangles: from Glebocki and Stawikowski (1977). G-type giants ((B-V) < 0.95) are indicated by filled symbols. Virtually circular orbits (e <0.05)are marked by circles around the sybols. (Stars whose symbols are indicated by numbers are discussed in the Appendix). to 3.5 Fig.5: Eccentricity e versus period P for binaries in the samples of Wilson (1976, circles) and Gleboaki and Stawikowski (197?3 triangles). 68 Short-period binaries with enhanced H and K emission are also found for (B-V) > 0.95, outside the region where single G-type giants with enhanced H and K emission are found. The absence of binaries with periods F < 120 days for (B-V) > 1.20 is due to the scarcity of such binaries among the red giants; there Is none in Wilson's (1976) sample. Recent measurements by one of us (F.M.) confirm that K-type giants with (B-V) > 1.20 and periods smaller than about ISO days exhibit enhanced Ca II H and K emission (Oranje et al. 1982). It is striking that the majority of the binaries with enhanced emission have virtually circular orbits (e < 0.05). Fig. 5 shows a transition from nearly circular orbits to random eccentricities for a period somewhere between 120 and 200 days. This critical period is about equal to the period separating giants with enhanced H and K emission from giants with normal emission. We suggest that the G- and K-type binaries with periods less than about 120 days are in revolution-rotation synchronization, which makes the primaries rotate faster than the typical single giants of the same color. The H and K strength ^/cr decreasing with increasing period is consistent with the hypothesis that the dynamo efficiency decreases with decreasing rotation rate (see Sect. 1.). The circularity of the orbits supports the idea of synchronization: the theory of tidal friction in components with convective envelopes predicts that the synchronization of rotation and orbital motion is completed before the orbits become circular (Zahn 1977). Some particular stars are indicated by numbers in Figs. 4 and 5, and briefly discussed in the Appendix. 6. CONCLUSIONS AND DISCUSSION For the vast majority of the late G-, the K- and M-type giants the Ca II H and K emission, estimated relative to the neighboring continuum, increases with increasing (B-V); the spread about this trend is quite small (a Of0.10 In the direction of (B-V)). Supergiants do not share this behavior. The subgiants overlap the giants near the lower limit in the I versus (B-V) diagram. There are two groups of evolved stars with enhanced H and K emission: (i) The G-type giants show a large spread in the Ca II H and K emission; many G-type giants exhibit a much larger emission than the subgiants; (11) Short-period binaries among giants and subgiants show an enhanced H and K emission which is stronger according as the orbital period is shorter. We find a critical period between 120 and 200 days below which the Ca II H and K emission Is enhanced and the orbits are cirular for the majority of the systems. We suggest that in both cases enhanced emission is due to a relatively large stellar rotation rate, and in Sectó. 4 and 5 we discussed some indications supporting this idea. This explanation concurs with similar findings for main-sequence stars, referred to in Sect. 1. Two important problems remain to be settled: (i) the quantitative dependence of the absolute Ca II H and K flux on rotation rate, effective temperature and surface gravity; and (ii) the question whether a synchronized binary produces the same H and K emission flux as a single star of the same rotation rate, surface gravity and effective temperature. 69 -3.0 -2.0 -1.0 o 1.0 2.0 3.0 4.0 5.0 6.0 7.0 .30 .40 .50 .60 .70 .80 .90 1.00 1.50 B-V Fig.6: Evolutionary tracks in the Hertzsprung-Russell diagram. The vegion of G-type giants of different levels of activity is indicated by a horizontal hatching; the regions of the hot and cool aomponents of RS CVn binaries with periods P < 10 days by cross hatchings (data from Topper and Ulrich (1977). The evolutionary tracks were kindly supplied by Th.J. van der Linden, Amsterdam. We incorporate the role of the rotation rate and ideas about stellar dynamos and braking of stellar rotation (see Sect. 1.) in an evolutionary scenario which attempts to explain the variation of the Ca II H and K emission across the Hertzsprung-Russell diagram (Fig. 6). (i) Single Stars Stars with masses smaller than 1.5 solar masses have thick convective envelopes throughout their evolution from main-sequence star to subgiant. Because of the steady loss of angular momentum during the main-sequence phase the dynamo efficiency drops and so does the Ca II H and K emission. These stars evolve further as slowly rotating G to K subgiants, showing little Ca II H and K emission; they follow the main I(B-V) trend (Fig. 1). Most of the stars with masses between 1.5 and 4 solar masses are rapidly rotating during the main-sequence phase. Because such a star has no significant convective envelope there is no magnetic activity. We suggest 70 that the star evolves without appreciable loss of angular momentum until it enters the giant branch where a convective envelope develops. Then the dynamo is turned on; because of the still rapid rotation the level of activity is very high. However, at the same time the star starts losing angular momentum and hence the Ca II H and K emission drops. Eventually the rotation rate has dropped to such a low value that the dynamo efficciency is small. From there on, the K > M-giant follows the main I(B-V) trend (see Fig. 1). The observational data indicate that the active phase of rapid rotation lasts for i:he short period of evolution through spectral type C; if this picture is correct then the loss of angular momentum shoud be very efficiënt. The spread in the Ca II H and K index for G-type giants is attributed to a spread in rotation rate; to some extent the rotation rate depends on the stellar mass. The scenario suggests that slowly rotating magnetic Ap stars evolve into G-type giants that are not very active (although transient active phenomena may happen when the onset of convection destroys the original dipole-like magnetic structure). (ii) Short-period Binaries If the orbital period is below some critical period, then the orbital motion and the rotation of a component will synchronize some time after that component has developed a convective envelope. After synchronization the component rotates rapidly, consequently the level of activity is high. For the loss of angular momentum the star can draw from the total angular momentum in the binary system, which is orders of magnitude larger than the rotational momentum in the single star. One important consequence is that for a primary in a synchronized binary the active phase of the stellar evolution lasts much longer than for a single star of the same mass. This is consistent with the data discussed in Sect. 4 and 5: whereas for single giants the enhanced activity lasts only through spectral type G ((B-V) < 0.95), primaries of binaries with periods less than about 100 days show enhanced activity, even for (B-V) > 1.00. The scenario predicts that all single subgiants show little activity. However, subgiants in synchronized binaries are expected to be very active, as is the case. The so-called RS CVn variables, the very active binaries of very short period, fit the scenario as extreme case». The positions of the components of short-period RS CVn variables are indicated in Fig. 6. One of us (F.M.) is surveying the giants using the Mt.Wilson H and K photometer (Vaughan et al., 1978). The quantitative results obtained so far support and specify the conclusions in this paper and they are in agreement with the above scenario. Some preliminary results will be published in a forthcoming paper by Oranje et al. (1982). ACKNOWLEDGEMENTS We wish to thank O.C. Wilson for advice and for additional data. B.J. Oranje contributed to the presentation of the results by stimulating discussions and practical suggestions. He and A.6. Beam critically read the manuscript. E.J.B. van der Zalm has been helpful in handling the data, E. Landre has drawn the figures and Mrs. J.G. Odijk prepared the typescript. 71 APPENDIX Five stars stand out by a behavior that seems to deviate from the properties discussed In Sects. 4 and S. Four binaries are indicated by numbers in Figs. 4 and 5, and briefly commented upon below. No.l: HD 206301, G2 IV, P » 13.2 days, e - 0.16: for main-sequence stars the critical period separating active binaries with a strong tendency for circular orbits from the other binaries is about 9 days (Middelkoop, 1981), which is much smaller than the critical period of about 120 days for giants. This suggests that the critical period depends strongly on the luminosity class, so the orbit of this subgiant may not yet be circular because the period is close to the critical period. No. 2: HD 32357 (12 Cam), K0 III; P - 80.2 days, e - 0.35 (Abt et al., 1969). This remarkably active binary is synchronized (Hall 1980); but the orbit is not yet circular. No. 3: HD 28 Kl III; P * 72.9 days, e - 0.27. In comparison with 12 Cam this star presents the problem why these seemingly similar binaries differ so strongly in the Ca II H and K emission. Perhaps Wilson's estimates of the luminosities offer the clue: whereas 12 Can is a bright giant (MV(K) « -1.5), HD 28 is a rather faint giant: M^K) - +2.4 corresponds better to a subgiant. He suggest that HD 28 may not yet be synchronized. No. 4: HD 222107 ( X And), G8 III-IV, P - 20.5 days, e - 0.04: the photometric variation indicates a period of 54 days (Landis et al., 1978), hence it appears that this binary is not synchronized. The metallicity of X And is smaller than the solar metallicity (Heifer and Wallerstein 1968; Campbell 1978) which suggests that it is an old system. This system raises an interesting question: may a binary, after rotation and orbital motions had become synchronized, and the orbits circular, slip out of synchronization, for instance because the time scale for loss of angular momentum is smaller than the time scale for synchronization? The arrow in Fig. 1 indicates HD 81799, gK3, (B-V) « 1.14. This star, showing a strong Ca II H and K flux ( A/a - 5.2), is situated between the main I(B-V) trend and the domain of C-type giants. It may be a yet undiscovered binary, with a period between 20 and 100 days. REFERENCES Abt, H.A., Dukes, R.J. and Weaver, W.B.: 1969, Astrophys. J. 157, 717 Batten, A.H., Fletcher, J.M. and Mann, P.J.: 1978, Publ. Dominion Astrophys. Obs. 15, 5 Campbell, B.: 1978, Astron. J. 83, 1430 Glebocki, R. and Stawikowski, A.: 1977, Acta Astron. 27, 225 Gratton, L.: 1950, Astrophys. J. Ill, 31 Hall, D.S.: 1980, private communication Heifer, H.L. and Wallerstein, G.: 1968, Astrophys. J. Suppl. 16, 1 Hiltner, W.A.: 1947, Astrophys. J. 106, 481 Kippenhahn, R.: 1973, in S.D. Jordan and E.H. Avrett (eds.): Stellar Chromospheres, NASA Sp. 137, p. 265 Kraft, R.P.: 1967, Astrophys. J. 150, 551 Landis, H.J., I.ovell, L.P., Hall, D.S., Henry, G.W. and Renner, T.R.: 197S, Astron. J. 83, 176 LInsky, J.L. and Haisch, B.M.: 1979, Astrophys. J. 229, L 27 Middelkoop, F.: 1981, Astron. Astrophys. 101, 295 (Paper III) 72 Oranje, B.J., Zwaan, C. and Middelkoop, F.:1982, accepted by Astron. Astrophys. Popper, D.M. and Ulrich, R.K.: 1977, Astrophys. J. 212, L 131 Schatzman, E.: 1962, Astron. Astrophys. 25, 18 Schatzman, E.: 1965, in R. Lust (ed.): Stellar and Solar Magnetic Fields, I.A.U. Symp. No. 22, p. 153 Skumanlch, A.: 1972, Astrophys. J. 171, 565 Vaughan, A.H., Preston, G.W. and Wilson, O.C.: 1978, Publ. Astron. Soc. Pacific 90, 267 Wilson, O.C.: 1963, Astrophys. J. 138, 832 Wilson, O.C.: 1966, Science 151, 1487 Wilson, O.C.: 1968, Astrophys. J. 153, 221 Wilson, O.C.: 1970, Astrophys. J. 160, 225 Wilson, O.C.: 1976, Astrophys. J. 205, 823 Wilson, O.C.: 1977, private communication Wilson, O.C.: 1978, Astrophys. J. 226, 379 Wilson, O.C. and Bappu, M.K.: 1957, Astrophys. J. 125, 661 Wilson, O.C. and Skumanich, A.: 1964, Astrophys. J. 140, 1401 Wilson, O.C. and Woolley, R.: 1970, Mon. Not. R. Astron. Soc. 148, 463 Young, A. and Koniges, A.: 1977, Astrophys. J. 211, 836 Zahn, J.-P.: 1977, Astron. Astrophys. 57, 383 Zwaan, C.: 1977, Mem. Soc. Astron. Italians 48, 525 Zwaan, C.: 1981, in R.M. Bonnet and A.K. Dupree (eds.): "Solar Phenomena in Cool Stars and Stellar Systems", (D. Reidel, Dordrecht, Holland) 73 CHAPTER IV: EVOLVED STARS IV.2: Magnetic Structure in Cool Stars VI: Ca II H and K fluxes from Evolved Stars accepted by Astronomy and Astrophysics, March 1982 SUMMARY Ca II H and K line-core fluxes were measured for 335 evolved stars. The results confirm the conclusions drawn by Middelkoop and Zwaan from Wilson's eye estimates of the Ca II H and K emission features: there Is a large spread in the fluxes from stars with (B-V) < 0.95 while the Ca II H and K flux of single stars with (B-V) > 0.95 correlates with color with little spread, except for some intrinsically bright stars. Short-period binaries show a relatively high Ca II H and K flux indicating that high Ca II H and K fluxes result from rapid rotation, independent of spectral type. The data are consistent with the hypothesis that Ca II H and K emission depends on dynamo action in the convective envelope, the dynamo efficiency decreasing with decreasing rotation rate. The evolution of Ca II H and K emission is discussed as a function of stellar mass. It is shown that stars which leave the main - sequence with relatively low (high) rotational velocities show a relatively low (high) Ca II K and K flux. The high Ca II H and K flux lasts up to higher (6-V) values for progressively higher masses. For giants with Mv< 42 and 0.84 < (B-V) < 0.95 the plot of Ca II H and K index against (B-V) shows two branches, with a gap in between. Three possible explanations are given: the gap may be due to (1) a sharp transition in the relation between Ca II H and K emission and rotational velocity, (2) the presence of giants of different mass, or (3) the occurrence of two different evolutionary phases in the same domain of the color-absolute magnitude diagram. Key words: stellar chromospheres - stellar rotation — stellar dynamos - cool stars - spectroscopie binaries 1. INTRODUCTION Wilson (1976) estimated the brightness of the Ca II H and K emission features of /v500 giants relative to the neighboring continuum background. In nearly all giants with spectral type later than GO these emission features are visible. However, G-type giants display very different amounts of Ca II H and K emission. Reanalysing Wilson's data, Middelkoop and Zwaan (1981, hereafter referred to as Paper I) found that the data is consistent with the hypothesis that Ca II H and K emission depends on dynamo action in the convective envelope, the dynamo efficiency decreasing with decreasing rotation rate. The Ca II K and K emission decreases with time because of magnetic braking of 74 rotation (see Schatzman 1962, 1965). In synchronized short-period binaries the phase of enhanced emission lasts much longer because of the large reservoir of angular momentum present in binary systems. This paper presents and discusses quantitative measurements of the Ca II H and K flux of 335 evolved stars. The measurements were obtained with the Ca II H and K photometer (Vaughan et al., 1978) at the 60 inch telescope of Mt. Wilson. 2. SELECTED STARS AND OBSERVATIONS The majority of observed stars has been selected from Wilson's (1976) sample. In Paper I it was found that the Ca II H and K emission of single K-type giants shows little spread whereas G-type giants show a large spread in Ca II H and K emission. Therefore preference was given to G-type giants from Wilson's sample. One of the goals of this investigation is to find out how the Ca II H and K emission develops along evolutionary tracks. To this end we added stars with (B-V) _< 0.80 to Wilson's sample. They were selected from the Strömgren-Perry (1965) catalogue, using the c. index to determine the absolute magnitude of the star (Strömgren 1963). Fig. 1: Absolute magnitude against (B-V). a-jsses (+) indicate short-period binaries^ with periods given in days. Stars with relatively high Ca II H and K fluxes (see Seat. 4) and (B-V) > 0.60 are enciraled. Evolutionary traeks of 1, 2, 3 and 4 M^ore represented by full lines. The stars were divided into four mass groups (A, B3 C and D) separated by the dashed lines. The HD number is given for some of the stars discussed in the text. 75 Short-period binaries (P 4 110 days) show an enhanced Ca II H and K emission even if (B-V) > 0.95. In Paper I it was found that the Ca II H and K emission of these binaries increases with decreasing orbital period. We selected all short-period spectroscopie binaries from Wilson's sample. Since all of these short-period binaries have (B-V) < 1.15 we added two spectroscopie binaries, viz. HD 352, (B-V) - 1.38, P - 96 days and HD 184398, (B-V) = 1.16, P - 108 days (Batten et al., 1978). The selected stars for which both absolute magnitude 1^ and color (B-V) are known to us are plotted in Fig. 1. The evolutionary tracks drawn in Fig. 1 were kindly furnished by Van der Linden (1982). The observations were obtained during November 1979 and June 1980 with the Ca II H and K photometer (Vaughan et al., 1978) at the 60 inch telescope of Mt. Wilson. The measurements yield the value of the line-core flux index S - ot(NH+ NK)/(NV + NR (1) where Ng , NJJ , Ny and NR refer to the number of counts, corrected for background, in the H and K bands (bandwidth 1 £) and in the reference bands on the violet and red side of the H and K region, respectively. The factor a is deduced from observations of standard stars as described by Vaughan et al. (1978). The observations usually consisted of 5000 counts per star in the K-band, resulting in a formal accuracy ( 96 (NH + NK )~i ) of 1%. For the very red giants ((B-V) > 1.5) the formal accuracy may be slightly worse (2 - 3%). The results of spectroscopie binaries should be used with care. First, we did not correct the average radial velocity of these stars for orbital variations; the uncertainty in S introduced is estimated to be lower than 15%. Second, although only single-line spectroscopie binaries were selected, we cannot exclude a significant contribution to S from the secondary. The results of our measurements are plotted in Fig. 2 and listed in Table 1. Fig. 2 largely confirms the results of Paper I: for (B-V) < 0.95 there is a large spread in the S—indices. For the majority of single stars with (B-V) > 0.95 the S-lndices are confined to a narrow band, except for some intrinsically bright giants. All short-period (P 4- HO days) spectroscopie binaries, that are presumably synchronized (see Paper I), show a relatively high S-index. This is especially clear for binaries with (B-V) > 0.95. Even the reddest binary from our sample (viz. HO 352, (B-V) - 1.38, P - 96 days) shows a strongly enhanced flux indicating that at least up to (B-V) » 1.38 relatively rapid rotation results in relatively high Ca II H and K emission. Four stars show a remarkably low S-index. One of these (HD 182040) is known to be a hydrogen deficient star (Warner 1967). The other three (viz. HD 23230, HD 159026 and HD 210459) are among the intrinsicallly brightest (Mv < +0.5) F-type stars in the sample. The S-lndex exaggerates magnetic activity in progressively cooler stars because the H and K flux is compared with a decreasing continuum flux. This effect hampers the comparison of stars of different spectral type. Middelkoop (1982) presents a method of converting the measured S-index of main-sequence stars to the total flux (FJJ + Fg ) in 1 X bandpasses per unit area at the stellar surface. He suggests that the same method can be applied for evolved stars. Applying this method we constructed Fig. 3. Note that the decline in(FH + FK) for (B-V) > 0.60 is steeper than the decline of the bolometric surface flux. Since this method of converting S-indices to surface fluxes is only practical for 0.45 _< (B-V) £ 1.50, and since there is 76 1 1 I l l i 1 ogS 20^25 0 - 96 V5 • • • » o. • -0.5 r „•.».• • • " * • • * ' . +ft? - '. • . •• ••: . . -»Ï • • « • ••• • • • • • • • • •• -1.0 " 210ÜJ5S. .159026 1 -23230 | 182040 t i 0.4 0.6 08 1.0 1.2 1.4 1.6 te B-V Fig. 2: Logarithm of the Ca II H and K index S against (B-V). Crosses (+) indicate short-period binaries, with periods in days. The data points surrounded by full lines all represent intrinsically bright stars. only indirect evidence for the validity of this method for giants, we will use the S-index instead of (F» + ÏW ) throughout the following sections. Note that the width of the Ca II H and K emission features depends on the absolute magnitude of a star (Wilson and 5appu (1957), Wilson (1976)). The FWHP of 1 A of the Ca II H and K passbands used in the measurements is smaller than the Wilson-Bappu width of the Ca II H and K features of the intrinsically brighter stars in our sample, (e.g. the Wilson-Bappu width of a star with absolute magnitude My - +1.2 is 1 X). Therefore the S-index may only be used for a quantitative comparison of the Ca II H and K emission for stars which have a similar absolute magnitude. 3. EVOLUTIONARY SCENARIO One of the main objectives of this investigation is to determine how the Ca II H and K emission develops along evolutionary tracks. Middelkoop and Zwaan (Paper I) found that the subgiants show a relatively low Ca II H and K emission as compared to normal giants. Their explanation is that the subgiants have had convection zones on the main sequence and lost most of their initial angular momentum due to magnetic braking, whereas the normal giants do not lose (much) angular momentum during their main-sequence phase, resulting in a relatively high Ca II H and K emission in their G-type giant phase (with the exception of the evolved versions of slowly rotating magnetic Ap stars). To investigate further the evolution of Ca II H and K emission for 77 0.4 0.6 Fig. 3: Logarithm of the surfaae flux (Fjj + F%) (per unit area at the stellar surfaae) against (B-V). Symbols ave the same as in Fig. 2. The dashed line represents the logarithm of the bolometria surface flux of giants as given by Flower (19??). different stellar masses the single stars were divided into four mass groups (A, B, C and D) separated by the dashed lines in Fig. 1. Group A: Presumably these stars with H«l H, have had a convection zone on the main sequence and therefore they are expected to be slow rotators with low Ca II H and K emission. Fig. 4a shows that indeed only upper boundaries are found for the rotational velocities and nearly all of these stars show relatively low S-indtces. There are two stars in Fig. 4a with a relatively high S-index. One of these (HD 160269) is still very close to the main sequence and may not yet be evolved. The other one (HD 82885) Is the only remarkable exception in Fig. 4a. Three possible explanations for the high S-index are: HD 82885 Group B: These stars with M s*l,5 Mj, probably have A- to FS-type progenitors on the main-sequence. Schatzman (1959, 1962) has pointed out that the transition between main-sequence stars with envelopes in radiative equilibrium and those with well developed convection zones occurs among the early F-types. A sharp decline in rotational velocities of main-sequence stars occurs near spectral type F5 (Wilson 1966, Kraft 1967). Therefore 78 group B is an Intermediate group containing stars that lost angular momentum during the main-sequence phase like the stars of group A and stars that did not lose angular momentum during the main-sequence phase like the stars of groups C and D. Indeed two groups may be distinguished in Fig. 4b for 0.45 £ (B-V) £ 0.70: (1) Stars with high vsini values (up to 100 km/sec) which tend to have relatively high Ca 11 H and K emission and (2) Stars with low vsini values and relatively low Ca II H and K emission. It is not possible to distinguish these two groups in Fig. 1, probably because of the limited accuracy of the absolute-magnitude determinations. Group C: According to the evolutionary tracks most stars of this group with (B-V) < 0.80 have masses of & 2 M© (see Fig. 1) while the majority of stars with (B-V) _> 0.80 have masses larger than 2 MQ . Since we do not expect a major difference in chromospheric evolution for stars in this mass range they are plotted together in Fig. 4c. Probably the stars of group C lose little - if any - angular momentum throughout the main-sequence and subsequent phase until they develop a convective envelope. Indeed all stars with (B-V) < 0.70 for which the rotational broadening has been measured show relatively high vsini values. (Fig. 4c may be simplified by elimination of HD 210459, HD 82543 and HD 196755. The latter two are both classified as subgiants and therefore probably belong in group B or even A instead of C.) Two branches are visible in Fig. 4c. In one of these the S-index rises with (B-V) for 0.50 < (B-V) ^ 0.77 and declines for 0.77 < (B-V) _< 0.95, while for the other branch, starting at (B-V) a* 0.85, the stars are confined to a narrow band of low S-indices (referred to as the main trend in Paper I). For 0.84 j< (B-V) Group D: Like the stars of group C these stars leave the main sequence with large rotational velocities. They are plotted in Fig. 4d. In contrast to Fig. 4c, Fig. 4d shows a large fraction of stars with (B-V) > 1.00 showing enhanced Ca II H and K emission which we explain again by relatively rapid rotation. This indicates that the loss of angular momentum due to magnetic braking is not large enough to slow down all of these rapidly evolving stars before (B-V) - 0.95. Inspection of Fig. 2 shows that none of the observed single stars with (B-V) > 1.30 shows a relatively high S-index with respect to the stars representing the main trend. 4. DISCUSSION Stars with (B-V) > 0.60 showing a relatively high Ca II H and K emission (S > 0.175 for stars plotted in Fig. 4a-b and S > 0.15 for stars plotted in Fig. 4c-d) were encircled in Fig. 1. Again we see the absence (except for HD 160269 and HD 82885) of high emission stars along the 1 Me track. We 79 also see the boundary at (B-V) a/ 0.95 beyond which there are no high-emission stars among stars with 2 MQ <_ M <_ 3MO , in contrast with stars with M > 3 MQ among which high emission stars are present up to (B-V) = 1.30. All these features can be explained by the loss of angular momentum in different evolutionary phases. Stars belonging to group A (and part of group B) have lost most of their angular momentum before leaving the main sequence. The more massive stars (part of group B, group C and group D) start to lose significant angular momentum after they have developed a convective envelope in the giant stage. Whereas stars of groups B and C show relatively small S-indices for (B-V) > 0.95, there is a substantial fraction of stars of group D showing relatively large S-indices up to (B-V) = 1.30. This may be explained by the rapid evolution of stars of group D. Moreover the average rotational velocity during the main-sequence phase is higher than the average rotational velocity of the stars of group C so that they can maintain a relatively high rotational velocity up to higher (B-V) values. This explanation assumes (1) that the loss of angular momentum does not decrease with mass and (2) that the loss of angular momentum is primarily due to magnetic braking. This assumption is supported by Fig. 4c where vsini values up to 100 km/sec are found up to (B-V) as 0.70 while for (B-V) > 0.70 only upper boundaries are measured. This indicates that the drop of rotational velocity occurs over a very small (B-V) interval and therefore cannot be explained by the change in radius of the star. + v sin f unknown 10 GROUP A GROUP C .40 o .30 I3BB5 .20 82543 196755 .10 210459 =H 1- H— .40 GROUP B GROUP D .30 •• •• .20 .10 159026 • T . f* .° dj .40 .50 .60 .70 .80 .90 100 .40 .50 .60 .70 .80 .90 100 1.10 1.20 B-V B-V Fig. 4a-d: The Ca II H and K index S against (B-V) for the four different mass groups defined by the dashed lines in Fig. 1. Vsini values are from the CSI catalogue (Oehseribein, 1981). 80 Table 1: Observed stars (B-V) HD M V HD (B-V) 28 1.04 2.4 .115 13174 .33 ( LD .191 352 1.38 .767 13421 .56 ( 2.9) .133 1522 1.22 .2 .119 13480 .78 -2.1 .459 3546 .87 1.5 .112 13520 1.48 .3 .221 3627 1.28 .5 .123 13530 .93 2.4 .118 3712 1.17 -0.8 .121 13974 .61 3.7 .232 3795 .70 ( 4.3) .156 14129 .96 1.3 .104 3817 .89 .9 .113 14489 .37 ( •2) .407 4502 1.12 ( 1-6)) .641 14872 1.53 .1 .217 4757 .37 1.9 .205 15596 .90 ( 2.7) .121 5234 1.21 .8 .129 16141 .66 ( 4.2) .145 5395 .96 1.3 .112 16161 .87 (( 1-0)) .111 5516 .94 .8 .216 16327 .47 ( 2.7) .236 6186 .96 1.4 .111 17361 1.11 1.2 .109 6210 .54 ( 2.8) .218 17484 .43 ( 1-8) .175 6497 1,.18 1.7 .129 17878 .74 ((- -7)) .317 6734 .85 3.7 .131 18322 .11 1.2 .118 6860 1,.58 -0.8 .319 18884 .64 -1.6 .331 6903 r.69 ( 1-8) .288 18970 .02 1.4 .104 6920 .60 ( 3.5) .190 19058 1.65 - .8 .289 7106 1,,09 .8 .104 19476 .98 1.7 .110 7318 1.,04 .5 .117 19656 1.11 .9 .111 8491 1.,05 1.6 .106 19787 1.03 1.0 .110 8512 1.,06 .9 .105 20084 .92 1.5 .126 8949 1.,12 1.2 .104 20644 1.55 -1.0 .215 9408 1.,00 1.5 .103 20894 .88 .3 .109 9562 64 { 3.8) .146 21120 .89 .6 .114 9927 1.28 .4 .117 21552 1.35 .4 .158 10072 89 1.0 .199 21754 1.12 .4 .104 10348 1.01 0.0 .109 22211 .63 ( 2.6) .272 10380 1.36 .1 .159 23183 1.01 1.1 .109 10761 .96 .4 .104 23230 .42 (-1.0) .079 11353 1.14 .6 .111 23249 .92 4.6 .135 11559 94 1.7 .153 24555 .68 .5 .178 11749 1.06 .9 .109 25025 1.59 - .6 .284 11909 92 .126 25604 1.07 .106 12235 m62 3.5) .163 25975 .95 3.7 .128 12533 1.20 -1.6 .184 26546 1.08 .8 .109 12929 1.15 1.1 .118 26659 .87 1.4 .191 12953 61 .373 26722 .80 « 1-5)) .215 81 Table 1: oonHnued HD (B-V) (B-V) 26846 1.17 1.0 .125 59148 1.11 (( i.o)) .123 27022 .81 1.1 .179 60522 1.54 - .5 .241 27348 .94 1.7 .200 61935 1.02 1.1 .105 27382 1.15 1.3 .128 62044 1.12 (( •«)) 1.050 28100 .98 .3 .126 62345 .93 1.0 .123 28271 .52 ( 2.7) .267 62509 1.00 1.6 .127 62721 1.45 .1 .201 29317 1.07 .2 .245 65345 .92 1.6 .112 29859 .54 ( 3.4) .128 65695 1.21 1.0 .126 32008 .80 2.4 .307 66011 .57 ( 2.8) .157 32357 1.12 -1.5 1.134 66216 1.12 (( 1-3)) .115 34559 .93 .4 .128 67228 .63 ( 3-5) .138 35369 .96 1.0 .116 67328 ( -65) 3.5 .146 35984 .45 ( 2.7) .226 67767 .81 2.8 .174 36079 .82 - .2 .124 67827 .59 3.8 .129 37160 .95 2.5 .121 68290 .95 2.0 .211 38751 1.01 .7 .168 69976 .97 1.3 .117 40035 1.00 1.2 .109 70523 1.05 1.6 .109 40801 .97 2.7 .119 71369 .84 0.0 .120 43023 .94 1.3 .112 72324 1.02 .7 .114 43039 1.02 1.3 .108 72779 .68 ( 2.0) .283 45410 .94 3.0 .127 73108 1.17 .9 o 124 45416 1.18 -1.3 .127 73593 .99 1.9 .117 47442 1.15 - .2 .166 74442 1.08 1.4 .106 47914 1.48 - .1 .185 74485 .94 .1 .191 48432 .96 1.6 .120 75528 .64 ( 3.7) .149 48433 1.16 .6 .122 75958 .86 1.1 .121 49161 1.40 - .9 .198 79452 .86 1.1 .111 49293 1.11 .4 • 111 80499 .93 .5 .121 50384 .94 1.4 .162 80586 .93 1.1 .148 50551 1.49 - .1 .198 8180f) .64 ( 4.1) .162 50778 1.43 .3 .183 82210 .77 2.3 .398 54716 1.45 .1 .165 8234J .62 ( .8) .146 54810 1.03 2.2 .117 82635 .92 1.4 .308 55280 1.07 1.2 .118 82741 .99 1.7 .111 57264 1.08 1.7 .117 82885 .77 4.1 .291 57423 1.52 - .2 .223 85444 .92 1.1 .223 57727 .90 1.8 .222 86728 .66 ( 3.7) .155 58207 1.03 1.2 .109 88737 .56 ( 3.3) .246 58367 1.01 " -1.9 .168 89010 .67 ( 3.9) .146 82 r Table 1: aontinued HD (B-V) HD (B-V) 89744 .54 ( 3.3) .140 148786 .92 .7 .104 91190 .96 1.3 .115 148856 .94 .3 .113 111199 .55 ( 2.6) .180 150680 .65 ( 3.4) .146 111812 .67 ( 3.2) .377 150997 .92 1.3 .193 117176 .71 3.2 .145 152863 .92 2.1 .112 120066 .63 ( 3-6) .134 153751 .89 .333 121370 .58 ( 2.6) .145 154619 .87 1.9 .182 122563 .90 .2 .107 155646 .50 ( 3.1) .141 124294 1.33 .7 .154 156014 1.44 -1.9 .211 124570 .54 ( 3.4) .137 156283 1.44 -1.1 .172 125560 1.23 .7 .105 156697 .39 ( .2) .190 126868 .70 2.0 .336 157482 .68 ( 2.1) .358 127334 ( -70) ( 3.8) .173 157527 .93 .6 .247 127665 1.30 - .1 .136 159026 .49 (- .3) .094 129336 .94 1.3 .105 159870 .59 (-2.1) .138 129972 .98 1.0 .108 160269 .61 3.8 .267 129989 .97 - .6 .338 160365 .56 ( LD .246 130952 .98 1.3 .132 161149 .42 ( .6) .164 131873 1.47 .1 .198 161230 ( .67) ( 2.6) .138 133208 .97 - .4 .111 161239 .65 ( 2.6) .139 133216 1.70 - .2 .295 161797 .75 ( 4.0) .142 133582 1.24 .7 .124 162076 .94 1.7 .232 135722 .95 1.5 .112 163917 .99 .9 .103 136726 1.37 a .152 163993 .94 1.3 .196 137510 .60 ( 2.9) .165 164058 1.52 - .6 .228 138716 1.01 2.9 .118 164136 .39 ( 0.0) .157 139195 .95 1.6 .112 165438 .96 3.4 .124 139446 .86 1.0 .113 165760 .96 1.4 .106 140027 .90 2.5 .113 166208 .91 .5 .200 141477 1.62 - .3 .288 167042 .94 3.6 .128 141714 .80 2.0 .299 167768 .89 1.0 .116 142357 ( -43) ( 1.9) .226 168322 .99 1.5 .105 143107 1.23 .3 .134 168532 1.53 .185 144608 .84 .4 .113 168656 .91 1.6 .119 145001 .95 .6 .230 168723 .94 2.2 .133 145328 1.01 2.9 .118 169156 .95 1.6 .116 146051 1.58 - .4 .251 171443 1.33 .3 .138 146791 .96 1.6 .111 172424 .96 1.0 .114 147677 .97 1.5 .107 173399 .90 2.4 .176 148387 .91 2.0 .115 173949 .96 1.6 .115 83 Table 1: aontinued V 175225 .84 2.9 .195 197752 1.18 .8 .105 175306 1.19 .1 .230 197912 1.05 .6 .154 175535 .90 .6 .175 197989 1. '3 1.1 .104 175679 .97 1.9 .162 198084 .54 3.4) .147 176303 .53 ( 3.2) .193 196149 .92 2.8 .127 178449 .34 ( 1.8) .263 198809 .83 1.3 .198 181276 .96 1.3 .109 199870 .97 1.0 .124 181391 .92 1.5 .218 199960 .63 3.6) .150 181984 1.25 .7 .109 200723 < -38) 1.4) .189 182040 1.07 .071 201381 .94 1.2 .113 182572 .77 3.6 .141 201507 .37 2.1) .233 182694 .92 1.4 .158 203387 .90 .4 .294 182762 .98 1,.9 .110 203784 ( -52) 1.7) .261 182900 .47 ( 2•7) .182 203842 .47 1.8) .219 184398 1.16 .829 204381 .91 1.1 .112 185351 .93 2,.4 .205 205435 .89 1.5 .173 185734 .97 ((-1,.1)) .128 206301 .65 2.1 .245 185758 .78 -1..9 .196 206453 .88 1.4 .111 186155 .40 ( 1.•5) .180 209166 .34 1.8) .169 186408 .64 ( 3.•9) .151 210434 .98 1.5 .190 186675 i.95 «,7 .107 210459 .46 • 2) .094 186760 .56 ( 3-3) .134 210460 .69 2.5 .254 186791 1..52 -1.9 .267 210702 .95 3.3 .118 188119 i.89 1.2 .113 210807 .92 .7 .179 188512 i.86 4.0 .133 210855 .51 2.9) .167 189005 •,90 4 .110 211073 1.39 • .5 .185 190360 •,73 4.0 .148 211391 .98 1.3 .109 190940 1.32 1 .140 212943 1.05 2.4 .113 191026 a85 3.1 .330 214850 .72 3.3 .157 192806 l.26 •1 .163 215182 .86 • .4 .248 192836 1.04 1.9 .104 215549 .92 3.7 .117 192947 94 1.5 .187 216131 .93 1.0 .114 194069 l.07 .207 216380 .78 2.4 .27'4 194317 l.33 .4 .148 216489 1.12 1.050 195506 1.13 1.0 .115 216953 .94 1.4 .106 195564 69 4.4 .130 217014 .67 4.1) .153 196574 95 ^ •3 .115 217926 .39 2.2) .232 196755 *71 2.2 .144 218658 .80 1.0 .238 196925 *92 2.9 .123 218935 .94 2.6 .120 197101 34) ( 1.4) .198 219291 .45 2.5) .270 84 Table 1: continued HD (B-V) 219615 .92 1.6 .110 219834 .79 (( 2.8)) .160 219916 .84 1.6 .122 220657 .61 ( 2.7) .269 220954 1.07 1.3 .108 221115 .94 1.1 .147 221148 1.09 3.1 .120 222107 1.01 2.0 1.281 222399 .35 ( 1.9) .201 222404 1.03 2.8 .124 222493 1.00 .9 .124 222842 .95 1.7 .116 223165 1.11 .5 .101 223252 .94 1.3 .112 224533 .93 1.8 .119 224784 1.01 1.0 .109 Table 1: Observed stars. Column 2: Color (B-V) as given by the CSI catalogue (Ochsenbeinetal., 1981), (B-V) when given in paranthesis is derived from (b-y); Column 3: the abso- lute magnitude Mv as given by Wilson (1976). Mv given in paranthesis is cal- culated from the Strömgren c-± index (sing'ie parenthesis) or from paratlax (double parenthesis). A remarkable feature in Fig. 4c is the existence of two branches with a gap in between for 0.84 _< (B-V) Second, the evolutionary tracks may be such that the two branches are formed by stars of different mass (see also Ayres et al., 1980). In that case the upper branch contains rapidly rotating stars with M > 1.5 Mo while the lower branch contains slowly rotating stars of M < 1.5 Mo . Note that this explanation is not in accord with the theoretical tracks as given by Van der Linden (see Fig. 1) and Iben (1967). According to these tracks stars with M < 1.5 Mg in the hydrogen-shell burning phase will never be part of group C. However, cluster diagrams of old open clusters, like M67 (Racine 1971) and NGC 188 (McClure and Twarog 1977) Beem to indicate that stars with M < 1.5 Mo do enter the group C domain in the hydrogen-shell burning phase. At present it cannot be decided which of the three explanations appplies to the patterns in Fig. 3c; more than one mechanism may be responsible. This problem may be investigated by the study of Ca II H and K indices of giants belonging to open clusters of different ages. The study of the Ca II H and K line-core fluxes in cluster stars will yield basic information, not only concerning magnetic activity in evolved stars, but also on stellar evolution in general. Eventually a criterion may be discovered to distinguish stars of different mass, or of different evolutionary phase, among stars of similar color and absolute magnitude. ACKNOWLEDGMENTS This work was supported by the Netherlands Foundation for Astronomical Research (ASTRON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.). I am indebted to C. Zwaan for several valuable discussions and to C. Zwaan and A.G. Hearn for critically reading the manuscript. Mrs. J.G. OiZijk prepared the typescript and mr. E. Landre the figures. REFERENCES Ayres, T.R., Marstad, N.C. and Linsky, S.L.: 1980, Astrophys. J. 247, 547 Batten, A.H., Fletcher, J.M. and Mann, P.J.: 1978, Fubl. Dominion Astrophys. Obs. 15, 5 Cannon, R.D.: 1970, Hon. Not. R. Astr. Soc. 150,111 Faulkner, D.J. and Cannon, R.D.: 1973, Astrophys. J. 180, 435 Flower, P.J.: 1977, Astron. Astrophys. 54, 31 Iben, I.J.: 1967, Ann. Rev. Astron. Astrophys. 5, 571 Kraft, R.P.: 1967, Astrophys. J. 150, 551 McClure, R.D. and Twarog B.A.: 1977, Astrophys. J. 214, 111 Mermilliod, J.-C: 1981, Astron. Astrophys. 97, 235 Middelkoop, F.: 1981, Astron. Astrophys. 101, 295 Middelkoop, F.: 1982, Astron. Astrophys. 107, 31 Middelkoop, F. and Zwaan, C: 1981, Astron. Astrophys. 101, 26 Ochsenbein, F., Bischoff, M. and Egret, D.: 1981, Astron. Astrophys., Suppl. Ser. 43, 259 Racine, R.: 1971, Astrophys. J., 168, 393 Schatzman, E.: 1959, in J.L. Greenstein (ed.): I.A.Ü. Symposium No. 10, p. 129 Schatzman, E.: 1962, Ann. Astrophys. 25, 18 Schatzman, E.: 1965, in R. Lust (ed.): Stellar and Solar Magnetic Fields, I.A.U. Symp. No. 22, p. 153 Strömgren, B.: 1963, Q.J.R. Astron. Soc. 4, 8 86 Strb'mgren, B. and Perry, C: 1965, Photoelectric uvby Photometry for 1217 Stars Brighter than V - 6.5 mostly of spectral classes A, F and G (2nd ed.; Princeton, New Jersey: Institute of Advanced Study) Van der Linden, Th.J.: 1982, Dissertation, University of Amsterdam Vaughan, A.H. and Preston, G.W.: 1980, Publ. Astron. Soc. Pacific, 92, 385 Vaughan, A.H., Preston, G.W. and Wilson, O.C. 1978, Publ. Astron. Soc. Pacific 90, 267 Warner, 6.: 1967, Mon. Not. R Astron. Soc. 150,111 Wilson, O.C.: 1966, Astrophy6 J. 14, 695 Wilson, O.C 1968, Astrophys J. 153, 221 Wilson, O.C 1976, Astrophys. J. 205, 823 Wilson, O.C. and Bappu, M.K.V. 1957. Astrophys. J. 125, 661 I 87 SAMENVATTING In dit proefschrift wordt de Zon, de enige ster die voldoende dicht bij staat om structuur op het oppervlak te kunnen onderscheiden, gebruikt als leidraad voor het bestuderen van de magnetische activiteit van andere min of meer soortgelijke sterren. Onder min of meer soortgelijke sterren verstaan we hier sterren met een convectieve mantel (*) , die magnetische activiteit kunnen vertonen. Het magneetveld op de Zon is geconcentreerd in discrete elementen. De eigenschappen van deze elementen hangen af van de totale magnetische flux in zo'n element. Grote magnetische elementen treden op als donkere zonnevlekken met een levensduur van dagen, weken en soms zelfs maanden. Kleine elementen zijn zichtbaar als heldere fakkels en netwerkelementen. De netwerkelementen, geconcentreerd in zogenaamde netwerkvlokken zijn zichtbaar in Fig. 3 van Hoofdstuk I als heldere punten die over de hele schijf te zien zijn. De fakkels, gegroepeerd in fakkelvelden, en de zonnevlekken treden voornamelijk op in zogenaamde actieve gebieden (de grote heldere gebieden in Fig. 3 van Hoofdstuk I waarin de zonnevlekken zichtbaar zijn als zwarte "pitten"). Deze actieve gebieden komen voor in een band evenwijdig aan de zonsequator. Alhoewel de precieze vorn en samenstelling van zo'n gebied op korte tijdschaal kan veranderen, hebben grotere actieve gebieden een levensduur van enkele maanden. Op de Zon is het magneetveld direkt meetbaar met behulp van het polarisatie-effect bij magnetische Zeemansplitsing (zie Fig. 3b van Hoofdstuk I, zwarte en witte gebieden geven magneetvelden van tegengestelde polariteit aan) . Tegengestelde polariteiten geven tegengestelde polarisatie-effecten die elkaar opheffen als we integreren over een bipolair actief gebied. Aangezien de gemeten Ca II H en K emissie van sterren afkomstig is van het gehele zichtbare halfrond is het netto resultaat. zeer klein, en in de meeste gevallen onmeetbaar. Er moeten dus indirecte methoden gebrulkit worden om de magnetische activiteit van sterren te meten. Een methode is het waarnemen van de emissiepieken in de kernen van de Ca II H en K resonantielijnen (zie Fig. I van Hoofdstuk I). Het blijkt namelijk dat de plaatsen op de Zon waar de Ca II H en K emissie wordt waargenomen, binnen een boogseconde (de nauwkeurigheid van de waarnemingen) overeenkomen met de plaatsen waar zich magneetveld bevindt (Fig. 4 van Hoofdstuk I). We nemen in dit proefschrift dan ook aan dat de intensiteit van de Ca II H en K emissie toeneemt met de totale magnetische flux die in de steratmosfeer aanwezig is. Een groot deel van de magnetische flux is op de Zon geconcentreerd in de actieve gebieden (zie Fig. 3 van Hoofdstuk I), die niet uniform zijn verdeeld over het oppervlak. Dit betekent dat de totale intensiteit van de Ca II H en K emissie, afkomstig van het zichtbare halfrond van de Zon, gemoduleerd is met de rotatieperiode van de Zon. Als dat ook voor andere steren geldt moet het mogelijk zijn om uit tijdreeksen van Ca II H en K emissie metingen rotatieperioden van sterren te bepalen. Aangezien een dergelijk programma een grote hoeveelheid waarneemtijd vraagt is samenwerking gezocht en gevonden met andere instituten. In Hoofdstuk II worden de resultaten gepresenteerd (zie o.a. Fig. 1, Hoofdstuk II.2). Inderdaad blijkt het mogelijk rotatie- (*) Sterren hebben een convectieve mantel, waarin het energietransport voornamelijk plaats vindt door bewegingen van het gas, indien de temperatuur zo laag is dat waterstof en helium niet volledig geïoniseerd zijn. CalH en K Emissie ft Aktieve Gebieden ft Ca II H en K emissie neemt toe Dynamo .ft met toenemende rotatieheid Differentiële Rotatie ft Rotatie Convectie Fig.l perioden van sterren met een convectieve mantel te meten uit de variatie in het Ca II H en K signaal. Twee grote voordelen van deze methode zijn dat: a) ook de relatief lange rotatieperioden, die veel voorkomen onder dit type sterren, meetbaar zijn, en: b) de periode gevonden wordt onafhankelijk van de hoek 1 tussen de gezichtslijn en de rotatie-as van de ster. Dit is niet het geval bij de bepaling van de rotatiesnelheid v van de ster uit de dopplerverbreding van de in de atmosfeer gevormde lijnen, waaruit altijd vsini afgeleid wordt. Het derde hoofdstuk behandelt het verband tussen de Ca II H en K emissie en de rotatiesnelheid van een hoofdreeksster (*) . Naar analogie van de Zon verwachten we dat de discrete magnetische veldstructuren het gevolg zijn van een dynamowerking in de ster. Deze dynamo ontstaat uit een samenspel tussen de convectie en de rotatie (zie schema Fig. 1). Het ligt dan ook voor de hand te verwachten dat de magnetische activiteit (en dus ook de Ca II H en K emissie) toeneemt met toenemende rotatiesnelheid van een ster. (*) Nadat een ster is ontstaan door samentrekking van een gaswolk,treedt in het centrum kernfusie op waarbij waterstof wordt omgezet in helium; in de dan volgende langdurende evolutiefase verandert er nauwelijks iets aan de totale hoeveelheid licht die de ster per seconde uitzendt, noch aan de temperatuur van zijn atmosfeer. Zowel deze temperatuur als de totale lichtkracht hangen af van de totale massa van de ster en wel zo dat, naarmate de massa groter is, zowel de temperatuur als de lichtkracht hoger zijn. In het diagram waarin de totale lichtkracht uitstaat tegen de temperatuur, vormen deze sterren dan ook een nauwe band: de hoofdreeks genaamd. Van alle hoofdreeks— sterren met een massa kleiner dan ongeveer 1.5 zonsmassa is de oppervlakte temperatuur zo laag dat zij een convectieve mantel bezitten. 89 Tot nu toe was het niet mogelijk de relatie tussen Ca II H en K emissie en rotatiesnelheid quantltatief vast te stellen, omdat de rotatiesnelheid van dit type sterren meestal ver onder de 10 km/s ligt hetgeen tot voor enkele jaren de grens was voor het meten van rotatieverbreding van spectrale lijnen. De laatste paar jaar zijn echter twee nieuwe methoden ontwikkeld waarmee wel lage rotatiesnelheden gemeten kunnen worden; namelijk de rotatiemodulatie in het Ca II H en K signaal (HII) en een nieuwe methode voor het vinden van de dopplerverbreding in lijnprofielen (HUI). Beide methoden worden in Hoofdstuk III gebruikt voor het bepalen van het quantitatleve verband tussen Ca II H en K emissie en rotatiesnelheid. Interessant is dat de relatie een sprong lijkt te vertonen: sterren met een rotatiesnelheid groter dan een zekere kritische waarde geven een aanzienlijke Ca II H en K emissie die afneemt met afnemende rotatiesnelheid. Sterren met een rotatiesnelheid kleiner dan de kritische snelheid vertonen een veel lagere Ca II H en K emissie. Het is nog onduidelijk of ook voor deze sterren de Ca II H en K emissie afneemt met afnemende rotatiesnelheid. Het is bekend dat hoofdreekssterren, voor wat betreft hun Ca II H en K emissie, onderverdeeld kunnen worden in twee, duidelijk gescheiden groepen: jonge, actieve sterren met dus een hoge Ca II H en K emssie en oudere, minder actieve sterren (waaronder de Zon) met een lage Ca II H en K emissie. Ook is bekend dat de rotatiesnelheid van een ster afneemt met de leeftijd. Dit wordt verklaard als gevolg van een relatief klein massaverlies dat door het uitwaaierende magneetveld tot grote afstand met de ster verbonden blijft waardoor een relatief grote hoeveelheid impulsmoment verloren wordt; dit effekt wordt magnetische remming genoemd. Samen met de gevonden relatie tussen Ca II H en IC emissie en de rotatie- snelheid leiden deze gegevens tot het volgende evolutieschema voor hoofdreeks s terren: in het begin van zijn bestaan zal een hoofdreeksster een hoge rotatiesnelheid (dus hoge Ca II H en K emissie) hebben. Door magnetische remming zullen de rotatiesnelheid en de Ca II H en K emissie geleidelijk afnemen totdat de kritische rotatiesnelheid wordt bereikt. Op dat moment valt de Ca II H en K emissie in korte tijd drastisch af. Daardoor ontstaan de twee groepen sterren: een groep met jonge, actieve sterren en een groep met oudere, minder actieve sterren. In Hoofdstuk IV wordt de Ca II H en K emissie van geëvolueerde sterren (*) besproken. Ook voor deze sterren verwachten we een verband tussen de Ca II H en K emissie en de rotatiesnelheid. Aangetoond wordt dat alle geëvolueerde sterren die op de hoofdreeks een convectieve mantel en dus magnetische activiteit hebben gehad (massa kleiner dan 1.5 zonsmassa), een relatief lage rotatiesnelheid en dus ook een lage Ca II H en K emissie vertonen. Dit wordt verklaard uit het feit dat deze sterren op de hoofdreeks veel impulsmoment hebben verloren door magnetische remming. Dit is niet het geval voor sterren die op de hoofdreeks geen convectieve mantel hebben gehad (*) Wanneer in een hoofdreeksster de waterstof in het centrale deel van de ster is "opgebrand" treedt kernfusie op in een schil om de kern. Hierdoor zetten de buitenste lagen van de ster uit, met als gevolg een lagere temperatuur aan de oppervlakte. Sterren die op 90 (massa groter dan 1.5 zonsmassa). Deze sterren zullen dus, als zij in de reuzenfase een convectieve mantel ontwikkelen, snel roteren, met als gevolg een hoge Ca II H en K emissie. Tegelijkertijd evenwel zet de magnetische remming in, waardoor de rotatiesnelheid en de Ca II H en K emissie afnemsn totdat alle sterren nagenoeg dezelfde Ca II H en K flux vertonen. Het is interessant dat ook de geëvolueerde sterren, net als de hoofdreekssterren, te verdelen zijn in twee, duidelijk gescheiden groepen: namelijk sterren met een aanzienlijke Ca II H en K emissie die van ster tot ster sterk kan verschillen, en sterren met een lage Ca II H en K emissie met weinig spreiding. Het ligt voor de hand ook deze twee groepen te verklaren als het gevolg van een kritische rotatiesnelheid waarbij de Ca II H en K emissie drastisch afvalt. In dit geval zijn echter ook nog andere verklaringen mogelijk. Gesuggereerd wordt dat door het waarnemen van de Ca II H en K emissie van geëvolueerde sterren in open sterhopen (*) een of meer van de mogelijke verklaringen kan worden uitgesloten. Het is al lang bekend dat kort-periodieke dubbelsterren een verhoogde Ca II H en K emissie vertonen. Dit is in het verleden altijd verklaard als het gevolg van de getijdenwerking die, op een verder ongespecificeerde wijze, de atmosferische verhitting beïnvloedt. In Hoofdstuk III en IV wordt aannemelijk gemaakt dat de verhoogde Ca II H en K emissie het gevolg is van de hoge rotatiesnelheid van deze sterren. De snelle rotatie wordt veroorzaakt door de getijdenwerking, waardoor de rotatieperiode van de ster gelijk wordt aan de baanperiode van het systeem. Aangezien de baanperiode kort is zal de rotatiesnelheid van de ster dus hoog zijn. (*) Groep sterren die gezamelijk zijn ontstaan en dus dezelfde leeftijd hebben. I CURRICULUM VITAE Frans Middelkoop werd geboren op 30 januari 1953 in Rotterdam. In 1972 behaalde hij het diploma Atheneum B aan de Scholen- gemeenschap Comenius te Capelle aan den IJssel. In datzelfde jaar begon hij met de lerarenopleiding in de vakken Wis- en Natuurkunde aan de S.O.L. te Utrecht waar hij in 1977 de akte van bekwaamheid van de tweede graad verwierf. De studie werd vervolgd met de opleiding M.O. I Natuurkunde aan de Rijks- universiteit te Utrecht. Het benodigde onderzoek werd gedaan bij de vakgroep Sterrekunde waar hem gevraagd werd een promotieonderzoek te doen. Het hiervoor benodigde doktoraal examen legde hij in 1979 af met hoofdvak algemene sterrekunde en met het predikaat " met genoegen ". Sinds 10 oktober 1979 is hij verkzaam als wetenschappelijk assistent van het Sterrekundig Instituut te Utrecht. Hij is getrouwd met Ans de Jong, zij hebben twee kinderen. I Stellingen behorende bij het proefschrift: Ca II H and K emission from late-type stars 1. Voor actieve hoofdreekssterren van laat spectraal type bestaat een wel- bepaald verband tussen de gemiddelde Ca II H en K flux en de rotatie- snelheid van de ster. Dit proefschrift, hoofdstuk II.2 and III 2. Geëvolueerde sterren die een convectiezone hebben gehad op de hoofdreeks roteren langzaam en vertonen een lage Ca II H en K flux. Daarentegen kunnen geëvolueerde sterren, die geen convectiezone hebben gehad op de hoofdreeks, gedurende enige tijd in het reuzenstadium snel roteren én een hoge Ca II H en K flux vertonen. Dit proefschrift, hoofdstuk IV 3. De rotatieperiode van een actieve hoofdreeksster van laat spectraal type kan gevonden worden uit de rotatiemodulatie in de Ca II H en K flux, tenzij de ster op de pool wordt gezien. Dit proefschrift, hoofdstuk II 4. Hoofdreekssterren van laat spectraal type kunnen onderverdeeld worden in twee duidelijk gescheiden groepen, namelijk: jonge actieve sterren, en oude, minder actieve sterren. Deze scheiding kan verklaard worden door een drastische afval in magnetische activiteit zodra de rotatiesnelheid van een ster is afgenomen tot een kritische rotatiesnelheid. Dit proefschrift, hoofdstuk III.2 5. De drie door Smith gebruikte argumenten om aan te tonen dat de Zon een abnormaal langzaam roterende ster is, zijn alle onjuist. M.A. Smith, Publ. Astron. Soc. Pacific 91, 737, 1979 6. Nagenoeg alle reuzen in open sterhopen jonger dan de Hyaden en een fractie van de reuzen in open sterhopen ouder dan de Hyaden fuseren helium in de kern. Hiermee moet rekening worden gehouden bij het vergelijken van deze open sterhopen met theoretisch berekende isochronen. 7. Door voor de sterhoop NGC 7789 dezelfde massaverdeling aan te nemen als Cannon maar gebruik te maken van numeriek berekende stermodellen, inplaats van homologe stexmodellen, kan worden aangetoond dat de massa- spreiding in de geëvolueerde sterren van NGC 7789 ongeveer 1 zonsmassa is (inplaats van 0.16 zonsmassa volgens Cannon), terwijl de massa van de zwaarste ster in de sterhoop 3 zonsmassa is (inplaats van 1.7 zonsmassa volgens Cannon). R.D. Cannon, Mon, Not. Royal Astr. Soc. 150, 111, 1970 8. De belasting van het schijvengeheugen voor "permanent files" zou belangrijk verminderen indien de gebruiker massageheugen ("tape units, floppy-disc drives", etc.) in eigen beheer heeft dat direkt verbonden is met de centrale computer. 9. De massaverhouding q tussen de componenten van een dubbelstersysteem waarvan de helderste component een geëvolueerde ster is, kan voor 0.9 <, q <, 0.4 geschat worden uit de afwijking van het systeem van de relatie tussen (B-V) en (R-I) voor enkelvoudige sterren. 10. Een belangrijke .".aak van een wetenschappelijk onderzoeker is het overdragen van door hem verworven inzichten. Een op dit doel gerichte didaktische instir.tie dient dan ook onderdeel van zijn opleiding te zijn. 11. In het algemeen neemt het salaris toe met de leeftijd van een werknemer, hetgeen in de meeste gevallen niet in overeenstemming is met het verloop van zijn prestatieniveau. Een ander nadeel is dat een discontinuiteit optreedt in het besteedbaar inkomen bij het bereiken van de pensioen- gerechtigde leeftijd. 12. De hoge jeugdwerkloosheid wordt veroorzaakt door een complex van onderling samenhangende factoren: de relatief hoge leerplichtige leef- tijd, de relatief hoge minimum jeugdlonen, en een schoolsysteem dat te weinig op de praktijk gericht is. 13. De populariteit van het trimmen in onze westerse maatschappij is wel- licht een gevolg van het besef dat men sterke benen nodig heeft om de weelde te kunnen dragen. of the H and K flux during this time and the observed range, AS, relative to , expressed as percentage (cols. (5) and (6)). Where rotation periods could be deduced from the observations, these are listed and compared with published vsini values (cols.(7) - (9)), as discussed below. The first 46 entries in Table 1 are main-sequence stars, comprising nearly all of Wilson's (1978) list within the right ascension limits set by the observing season. An active Ml dwarf (Gliese 685) from the survey by Vaughan and Preston (1980) was included although the long-term behavior of chromospheric activity is unknown for this star. The final eight entries in Table 1 are of luminosity classes III and IV; a more extensive discussion of these than can be given here is in preparation. In most cases each star was observed once per night. This frequency of observation was deemed sufficient on the basis of earlier studies, Including a preliminary two-week test run at Mount Wilson in 1979 november by Middelkoop, Vaughan and Preston (1981). The frequency of observation allowed periods of only a few days to be determined, while the overall length of the program made possible detection of periods as long as SO days. These choices also provided sufficient sampling to distinguish "random" chromospheric fluctuations from periodic rotational modulation for a large fraction of the stars. Examination of the records of the H and K fluxes of the observed main-sequence stars reveals that about 40% show clear periodic variations; these are sufficiently unambiguous that approximate periods can be determined simply by inspection of the data. Examples of several such records are illustrated in Fig. 1. An additional 20% of the stars show fluctuations suggestive of periodic behavior, but insufficiently clear to allow a period to be assigned with confidence by Inspection. We have computed autocorrelation functions for the 54 stars in our survey (see Fig. 2). Of these, 28 show clear evidence of periodic variations through their autocorrelation functions, including those already mentioned whose periods are directly measurable. The rotation periods for these 28 stars, measured from autocorrelation functions, are listed in column (7) of Table 1. For the remaining 26 stars, rotational periods have not been determined, for one or more of the following reasons: (a) fluctuations are present at a 30 dS/ P* V Vsini Reference (days) Percent (days) (km/s)