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Mon. Not. R. Astron. Soc. 000, 000--000 (0000) Printed 11 November 1997 (MN L a T E X style file v1.4)
On the rotation­activity correlation for active binary stars
A. G. Gunn 1;2? , C. K. Mitrou 2;3 and J. G. Doyle 2
1 University of Manchester, Nuffield Radio Astronomy Laboratories, Jodrell Bank, Macclesfield, Cheshire, SK11 9DG, UK
2 Armagh Observatory, College Hill, Armagh, BT61 9DG, N. Ireland
3 Section of Astrophysics, Astronomy and Mechanics, Dept. of Physics, University of Athens, Athens 15783, Greece
Accepted 1997 Received 1997 in original form June 1997
ABSTRACT
We present an investigation of rotation­activity correlations using IUE SWP mea­
surements of the Civ emission line at 1550 š Afor 72 active binary systems. We use a
standard stellar evolution code to derive non­empirical Rossby numbers, R o , for each
star in our sample and compare the resulting Civ rotation­activity correlation to that
found for empirically derived values of Rossby number and that based on rotation
alone. For dwarf stars our values of R o do not differ greatly from empirical ones and
we find a corresponding lack of improvement in correlation. Only a marginal improve­
ment in correlation is found for evolved components in our sample. We discuss possible
additional factors, other than rotation or convection, that may influence the activity
levels in active binaries. Our observational data implies, in contrast to the theoreti­
cal predictions of convective motions, that activity is only weakly related to mass in
evolved stars. We conclude that current dynamo theory is limited in its application
to the study of active stars because of the uncertainty in the angular velocity­depth
profile in stellar interiors and the unknown effects of binarity and surface gravity.
Key words: stars: activity ­ stars: late type ­ stars: binaries: close ­ stars: flare ­
stars: variables
1 INTRODUCTION
The work of Wilson (1963), Kraft (1967) and Skumanich
(1972) led to the hypothesis that rotation plays a crucial role
in the generation of stellar magnetic activity. This is evident
in strong correlations of magnetic activity indicators with ro­
tational velocities, rotational periods, or, in the case of syn­
chronously rotating members of close binary systems, orbital
periods. For single stars relations have been reported be­
tween rotation and coronal emission (Pallavicini et al. 1981;
Walter 1981; Schrijver, Mewe & Walter 1984; Jordan & Mon­
tesinos 1991; Montesinos & Jordan 1993; Hempelmann et
al. 1995), chromospheric emission (Middelkoop 1981; Hart­
mann et al. 1984) and transition region line fluxes (Vilhu
1984). For RS CVn systems, generally containing at least
one evolved component, similar rotation­activity correla­
tions have been found in UV line fluxes (Oranje, Zwaan
& Middelkoop 1982; Vilhu & Rucinski 1983; Basri, Laurent
& Walter 1985), Hff and Caii emissions (Strassmeier et al.
1989), X­rays (Walter & Bowyer 1981) and in the radio re­
gion (Drake, Simon & Linsky 1989; Gunn 1996).
The observance of chromospheric activity in main­
sequence stars with (B--V) – 0.4 suggests that it coincides
? email: agg@jb.man.ac.uk (AGG), kam@rigel.da.uoa.gr (CKM),
jgd@star.arm.ac.uk (JGD)
with the onset of a convective envelope and is therefore a re­
sult of a dynamo mechanism (Parker 1970, 1977). Using this
assumption Durney & Latour (1978) showed that the level
of activity should be a function of rotational period, Prot , di­
vided by an appropriate convective turnover time­scale, Üc ,
in the outer convection zone. This dependence on Rossby
number (Ro=Prot=Üc) was confirmed by Noyes (1983) who
found that Caii emission levels could be approximated by
the product of angular rotation rate and a function of spec­
tral type similar to Üc for main­sequence stars. Ro is an
important indicator in hydro­magnetic dynamo theory and
measures the extent to which rotation can induce both he­
licity and differential rotation required for dynamo activity.
The variation of Üc along the lower main­sequence has
been studied using stellar evolution and structure codes
(Gilman 1980; Gilliland 1985; Kim & Demarque 1996). Al­
though there are inherent differences in the formulation of
the mixing length theory used to describe convective motion
these studies all generally agree on the form of the (B--V)­Üc
relationship for main­sequence stars. For (B--V) – 0.8 the
variation of Üc is small so magnetic activity is more heavily
dependent on rotation. The overall chromospheric activity
is found to be well parametrised by an empirical Rossby
number (Noyes et al. 1984; St¸epie'n 1994) whose functional
dependence on (B--V) is obtained from the observational
data themselves. For example, Noyes et al. (1984) derived
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2 A. G. Gunn et al.
a (B--V)­Üc dependence by minimising the scatter for an
empirical fit to the models of Gilman (1980). This semi­
empirical relationship is therefore inappropriate for a study
of rotation­activity correlations in anything other than the
original sample of main­sequence stars.
The main drawback of the Noyes et al. (1984) relation­
ship is that it does not apply to the evolved components of
active binaries. The evolved state of these stars (see Barrado
et al. 1994) places them in a region of the HR diagram where
the internal structure is significantly altered from main­
sequence stars. Consequently activity levels may undergo
quite rapid variations over a narrow range of temperature.
However, studies to date consistently indicate the dynamo
generation of activity from the lower chromosphere through
the corona, although the dependence on luminosity class,
spectral type and binarity is far from clear. Given the ad hoc
nature of empirical (B--V)­Üc relationships and the complex­
ity of convection zone dynamical evolution the only method
of studying the dependence of activity on Rossby number is
to use theoretical (non­empirical) values. Although the vari­
ability of convective parameters during post­main­sequence
evolution is found to be quite complex (Gilliland 1985) mod­
els are sufficiently refined to be of use.
This paper reports our attempts to study the rotation­
activity correlation for a sample of 72 active binaries using
the Civ emission line detected by the IUE (International
Ultraviolet Explorer) and non­empirical values of Rossby
number. This is a viable test of the applicability of current
dynamo theory to stellar activity, since, for evolved stars,
with the large departure of Üc from the values correspond­
ing to main­sequence stars of the same (B--V), a significant
increase in correlation should be found using non­empirical
Ro as opposed to empirical Ro or Prot . In Section 2 we de­
scribe the observations of our sample, in Section 3 we intro­
duce our assumptions and describe the sample, in Section
4 we discuss the stellar evolution code used to model the
stellar interiors and in Section 5 we discuss the results of
our analysis.
2 OBSERVATIONS
As activity indicator in this rotation­activity study we used
the flux radiated in the Civ emission lines at 1548 š A and
1551 š A. This doublet originates in the transition region and
features as the strongest line (showing as a single line at ¸
1550 š A) in the low­resolution SWP IUE spectra. The line
flux is representative of the total radiative losses due to
mechanical heating. This conclusion is based on work by
Doyle (1996a) who showed that a relationship (originally
derived from solar data by Bruner & McWhirter 1988) ex­
ists between the Civ 1550 š A line flux and the total radiative
losses as derived by an emission measure technique for active
dwarfs and sub­giants. There is however some evidence that
this may under­estimate the radiative losses for the faster
rotators (Houdebine et al. 1996; Doyle 1996b) although this
is still questionable. We note that Civ –1550 measurements
have previously been used in rotation­activity correlation
studies for single and binary stars by Vilhu & Rucinski
(1983), Basri, Laurent & Walter (1985), Basri (1987), Rut­
ten & Schrijver (1987) and Simon & Fekel (1987). Basri,
Laurent & Walter (1987) rejected the use of luminosities
Figure 1. Relationship between (B--V) colour index and effective
temperature for dwarf stars (triangles) and giant stars (squares)
taken from Gray (1992). A single polynomial fit (solid line) is suf­
ficient for both dwarfs and giants between spectral types F0 and
M2 but with a shift in spectral type­temperature correspondence
(shown on diagram).
in their study of F to K dwarfs whilst Rutten & Schrijver
(1987) found empirically that the flux density F , not lumi­
nosity L, was the appropriate unit for studies of magnetically
controlled radiative emission. Some authors have chosen to
adopt a normalised flux R = F/oeT 4
eff which may or may
not improve correlations. In our study we have adopted the
standard practice of analysing correlations with surface flux
FCIV which necessarily draws errors in radii and distances
into the results.
Our sample of stars consists of 72 active binary systems
listed by Strassmeier et al. (1993) that have been observed
with the SWP camera on the IUE. We excluded any sys­
tems with unknown distances and/or radii, those which con­
tain white dwarf components and stars with masses 0.4M fi
? M ? 2.2M fi since our convective models are unreliable for
masses outside this range (see Section 4). We conducted a
full search of the IUE archives and collected for each system
those data that were available by June 1996. To analyse the
IUE images we used the STARLINK packages IUEDR (Gid­
dings et al. 1996) and DIPSO (Howarth, Murray & Berry
1996). For the determination of the Civ flux, we used the av­
erage of several (quiescent) spectra whenever possible. The
emission line fluxes in Table 2 were derived by averaging the
value from a least squares gaussian fit to the line and the
value of a trapezoidal integration. The two averaged values
usually differed by less than 10%. We attributed the total
of the observed flux to the active component (as defined
in Strassmeier et al. 1993), unless both components were
characterised as Caii emitters, in which case we divided the
observed flux equally between them. A zero value in the last
column of Table 2 indicates that the flux originates from the
hot component, a 1 that the cool component is the active
one and 0.5 that both stars contribute equally. Some of the
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On the rotation­activity correlation for active binary stars 3
Table 1. The individual parameters for the stars in the sample (see text for description). Notes: (1) Inferred from (B--V) or from the
spectral type using the results of Gray (1992), (2) Basri, Laurent & Walter (1985), (3) Simon & Fekel (1987), (4) Dempsey et al. (1993),
(5) Cayrel de Strobel et al. (1994), (6) Donati, Henry & Hall (1994), (7) Drake, Simon & Linsky (1989), (8) Slee et al. (1987), (9) Singh,
Drake & White (1996), (10) mass estimated from the star's position in our HR diagram. The luminosity class of the secondary component
of AR Psc is taken from Fekel, Mofett & Henry (1986).
Hot Component Cool Component
Index Name Class R? Note M? Note T eff Class R? Note M? Note T eff Temperature
(R fi ) (M? ) (K) (R fi ) (M? ) (K) Code
1 AP Psc III 41.0 1.90 10 4106 b
2 13 Cet V 1.25 1 1.26 1 6214 V 1.3 4 1.00 1 5708 c
3 CF Tuc IV 1.67 1.06 5948 IV 3.32 1.21 4452 c
4 BI Cet V 0.90 0.96 1 5570 V 0.90 0.96 1 5570 a
5 AR Psc V IV 1.52 9 1.18 5162 a
6 UX For V 1.00 1 0.94 1 5516 V 1.00 1 0.94 1 5516 c
7 LX Per IV 1.64 1.24 6004 IV 3.05 1.32 4998 a
8 UX Ari V 0.83 0.93 5678 IV 5.43 1.09 5048 c
9 V711 Tau IV 1.30 1.10 5385 IV 3.90 1.40 4912 c
10 V837 Tau V 1.05 1.00 5819 V 0.74 0.67 4557 c
11 AG Dor V 0.85 1 0.79 1 4976 b
12 V818 Tau V 0.93 1 0.95 1 5626 V 0.67 1 0.64 1 4408 c
13 27691 V 1.14 1 1.12 1 6004 b
14 V833 Tau V 0.68 1 0.70 1 4680 b
15 3 Cam III 12.00 7 1.90 10 4712 b
16 12 Cam III 16.00 2 2.00 10 4608 b
17 TW Lep IV III 10.5 4 1.20 10 4540 b
18 V1149 Ori III 15.0 3 1.80 10 4568 b
19 SZ Pic V 0.92 1 0.85 1 5310 b
20 TY Pic V III 7.00 8 1.50 10 4820 c
21 OU Gem V 0.75 1 0.74 1 4925 V 0.63 1 0.68 1 4557 c
22 TZ Pic III 12.0 7 1.40 10 4546 c
23 SV Cam V 1.11 0.93 5793 V 0.74 0.67 4791 c
24 oe Gem III 14.00 4 1.80 10 4608 b
25 54 Cam IV 3.14 1.64 5964 IV 2.64 1.61 5385 c
26 VX Pyx III 10.0 8 1.20 10 4976 b
27 TY Pyx IV 1.59 1.22 5546 IV 1.68 1.20 5436 a
28 IL Hya III 12.00 2.20 10 4820 b
29 IN Vel III 20.0 8 2.10 10 4506 b
30 DH Leo V 0.97 0.83 5273 V 0.67 0.58 4258 c
31 DM UMa III 5.90 1.10 10 4722 b
32 ¸ UMa(B) V 0.86 5 0.85 5 5912 a
33 EE UMa III 16.0 7 1.00 4312 b
34 HU Vir IV 6.30 1.40 10 4820 b
35 DK Dra III 14.30 1.92 4611 III 14.30 1.92 4611 a
36 AS Dra V 0.97 1 1.00 1 5723 V 0.84 1 0.85 1 5386 c
37 IL Com V 1.10 0.85 6138 V 1.10 0.82 6138 a
38 RS CVn IV 1.99 1.44 6478 IV 4.00 1.44 5068 a
39 114630 V 1.05 1 1.11 1 5880 V 1.05 1 1.11 1 5880 a
40 BL CVn IV III 14.80 1.33 4568 b
41 BM CVn III 16.00 3 1.70 10 4526 b
42 BH CVn IV 3.10 1.50 6727 IV 2.85 0.80 4794 c
43 V851 Cen IV 3.50 0.80 10 4718 b
44 UV CrB III 16.1 4 1.06 4368 b
45 GX Lib V III 8.25 1.70 10 4820 b
46 LS TrA IV 2.83 8 0.80 10 4778 IV 2.83 8 0.90 10 4778 a
47 TZ CrB V 1.22 1.12 6332 V 1.21 1.14 5948 c
48 WW Dra IV 2.12 1.36 5880 IV 3.90 1.34 4650 a
49 V792 Her IV 2.58 1.41 6370 III 12.3 1.47 4714 a
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Table 1. continued.
Hot Component Cool Component
Index Name Class R? Note M? Note T eff Class R? Note M? Note T eff Temperature
(R fi ) (M? ) (K) (R fi ) (M? ) (K) Code
50 V824 Ara IV 1.61 1.11 5385 IV 1.25 1.03 5048 c
51 Z Her IV 1.85 1.61 6540 IV 2.73 1.31 5048 c
52 V772 Her V 1.00 1.04 5914 b
53 V815 Her V 0.97 0.99 5542 b
54 o Dra III 14.30 1.40 10 4466 b
55 V775 Her V 0.85 0.82 1 5273 c
56 V478 Lyr V 0.94 0.89 1 5490 b
57 V1762 Cyg III 9.20 1.40 10 4670 b
58 V4139 Sgr III 20.0 8 1.70 10 4406 b
59 V1764 Cyg III 24.9 1.50 4350 b
60 ER Vul V 1.07 1.10 5948 V 1.07 1.10 5678 c
61 AS Cap III 14.0 7 2.00 10 4668 b
62 42 Cap IV 3.00 2 1.50 10 5738 b
63 RT Lac IV 3.40 1.66 5140 IV 4.20 0.78 4886 c
64 HK Lac V III 15.00 2 2.20 10 4692 b
65 AR Lac IV 1.52 1.23 5616 IV 2.72 1.27 5048 c
66 V350 Lac III 12.70 1.10 4506 0.90 b
67 IM Peg III 7.00 1.00 10 4608 b
68 TZ PsA V 0.95 1 0.90 1 5570 b
69 RT And V 1.17 1.50 6115 V 0.84 0.99 5273 c
70 SZ Psc IV 1.50 1.28 6406 IV 5.10 1.62 4864 a
71 – And III 7.00 6 1.30 10 4842 b
72 II Peg IV 2.20 0.90 10 4842 b
systems have not been extensively observed by the IUE so
that fluxes are sometimes based on a single measurement.
Such values may well be susceptible to general variability,
flare activity or orbital phase dependence. We have followed
the usual practice of arbitrarily ascribing half of the emission
to each component, for systems where both stars are known
to be active, this, in addition to the empirical flux uncer­
tainty, places some question on the accuracy of the fluxes.
A flux error estimate is also difficult to provide since it de­
pends on the S/N of individual spectra and the subjective
position of the continuum. Based on a comparison of our
two methods of deriving f we estimate that the errors are
¸10% (comparable to those given by Simon & Fekel 1987)
but may be much higher for systems with two active compo­
nents. We emphasise, however, that this sample is the most
accurate and up­to­date compilation of Civ –1550 fluxes for
active binary stars. For several stars in our list Civ fluxes
are given for the first time.
3 STELLAR PARAMETERS
The parameters of the sample stars are shown in Table
1 where we list an arbitrary index number in increasing
RA, the stars' more usual name or HD number, luminos­
ity classes, radii, masses, and effective temperatures for hot
and cool components and a code for our temperature assign­
ment (see below). In Table 2 we list for each star the distance
in parsecs, the rotation period Prot , the Civ –1550 emission
line flux observed at Earth, fCIV , in units of 10 \Gamma13 erg cm \Gamma2
s \Gamma1 , the convective turnover time­scales (in days) resulting
from our modelling (see Section 4) and those derived using
the semi­empirical (B--V)­log Üc relationship of Noyes et al.
(1984), and a code indicating to which star the flux is at­
tributed (see Section 2). Unless explicitly stated otherwise
we used values for periods, distances, spectral types, lumi­
nosity classes, colours, radii and masses given by Strassmeier
et al. (1993). In this study we assume all stars in our sample
display orbital­rotational synchronicity. Classically the pe­
riod limit for synchronicity is ¸ 20 days (Linsky 1983) for
dwarfs and subgiants but is possibly much higher for giants.
In our sample 27% of stars have Porb – 20 days but only
17% are listed as showing evidence of asynchronism in the
study by Tan, Wang & Pan (1991).
Gray (1992) lists (separately for dwarfs and giants) the
correspondence between (B--V) colour and temperature for a
wide range of spectral types. Fitting these data with a third
order polynomial, we derived the relation between (B--V)
and log Teff which is shown in Figure 1. Note that a single
polynomial suffices to fit the data for both dwarfs and giants
of spectral types between F0 and M2. We therefore derived
temperatures for each component using the above (B--V))­
log Teff correspondence according to the criteria described
below and indicated in the last column of Table 1. These
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On the rotation­activity correlation for active binary stars 5
Table 2. Additional parameters and results for the sample (see text for details). Notes: (1) Drake, Simon & Linsky (1989), (2) Slee et
al. (1987).
System Parameters Hot Component Cool Component
Index Name Distance Note log Prot f CIV log Üc (E) log Üc (NE) log Üc(E) log Üc(NE) Activity
(pc) (days) (10 \Gamma13 erg (days) (days) (days) (days)
cm \Gamma2 s \Gamma1 )
1 AP Psc 140 1.984 4.1 1.415 1.076 1
2 13 Cet 21 0.318 2.8 1.099 1.182 1
3 CF Tuc 54 0.447 4.2 1.390 1.481 1
4 BI Cet 60 ­0.288 1.4 1.186 1.237 1.186 1.237 0.5
5 AR Psc 17 1.155 6.4 1.329 1.743 1
6 UX For 35 ­0.020 3.2 1.214 1.256 1.214 1.256 0.5
7 LX Per 130 0.905 1.0 1.351 1.940 1
8 UX Ari 71 0.809 15.5 1.346 1.750 1
9 V711 Tau 36 0.453 38.1 1.359 1.967 1
10 V837 Tau 55 0.286 6.5 1.034 1.123 0
11 AG Dor 32 0.409 3.7 1.353 1.390 0
12 V818 Tau 45 0.750 0.2 1.394 1.510 1
13 27691 45 0.602 0.4 0.840 0.977 0
14 V833 Tau 17 0.252 3.4 1.375 1.452 0
15 3 Cam 85 2.083 2.0 1.372 1.913 0
16 12 Cam 134 1.908 2.9 1.379 1.845 0
17 TW Lep 220 1.452 1.6 1.384 1.587 1
18 V1149 Ori 164 1.729 2.4 1.382 1.751 0
19 SZ Pic 30 0.695 1.5 1.295 1.312 0
20 TY Pic 110 2.028 1.1 1.365 1.898 1
21 OU Gem 12 0.845 1.8 1.357 1.403 1.383 1.477 0.5
22 TZ Pic 160 1 1.135 1.1 1.383 1.642 0
23 SV Cam 74 ­0.227 0.7 1.366 1.432 1
24 oe Gem 59 1.292 35.2 1.379 1.800 0
25 54 Cam 38 1.044 2.6 0.872 0.660 1.270 1.642 0.5
26 VX Pyx 135 1.654 1.6 1.353 1.918 0
27 TY Pyx 55 0.505 4.5 1.201 1.448 1.250 1.540 0.5
28 IL Hya 138 1.111 4.0 1.365 2.033 0
29 IN Vel 590 2 1.718 0.3 1.386 1.733 0
30 DH Leo 32 0.030 2.8 1.405 1.544 1
31 DM UMa 130 0.875 1.0 1.372 1.776 0
32 ¸ UMa(B) 7.9 0.600 8.3 0.931 1.062 0
33 EE UMa 195 1 1.874 0.3 1.400 1.317 0
34 HU Vir 220 1.017 5.0 1.365 1.900 0
35 DK Dra 130 1.809 4.6 1.379 1.825 1.379 1.825 0.5
36 AS Dra 29 0.733 1.5 1.099 1.176 1.270 1.294 0.5
37 IL Com 86 ­0.017 2.1 0.699 0.822 0.699 0.822 0.5
38 RS CVn 180 0.681 5.0 1.343 1.911 1
39 114630 25 0.627 2.2 0.960 1.084 0.969 1.084 0.5
40 BL CVn 300 1.272 1.9 1.382 1.643 1
41 BM CVn 250 1.314 5.5 1.384 1.680 0
42 BH CVn 53 0.417 17.2 1.368 1.815 1
43 V851 Cen 80 1.079 4.0 1.372 1.795 0
44 UV CrB 230 1.271 2.4 1.396 1.357 0
45 GX Lib 219 1.047 1.7 1.365 1.945 1
46 LS TrA 96 2 1.694 2.9 1.368 1.836 1.368 1.836 0.5
47 TZ CrB 21 0.057 18.1 0.441 0.499 0.902 1.030 0.5
48 WW Dra 180 0.666 0.9 1.376 1.737 1
49 V792 Her 310 1.440 1.0 1.372 1.822 1
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6 A. G. Gunn et al.
Table 2. continued.
System Parameters Hot Component Cool Component
Index Name Distance Note log Prot f CIV log Üc (E) log Üc (NE) log Üc (E) log Üc (NE) Activity
(pc) (days) (10 \Gamma13 erg (days) (days) (days) (days)
cm \Gamma2 s \Gamma1 )
50 V824 Ara 39 0.226 7.1 1.270 1.553 1.346 1.750 0.5
51 Z Her 100 0.601 1.8 1.346 1.883 1
52 V772 Her 42 ­0.056 3.2 0.931 1.060 0
53 V815 Her 31 0.258 4.5 1.201 1.246 0
54 o Dra 138 2.141 2.9 1.389 1.531 0
55 V775 Her 24 0.459 2.6 1.302 1.323 0
56 V478 Lyr 26 0.328 2.7 1.227 1.265 0
57 V1762 Cyg 90 1.456 6.3 1.375 1.778 0
58 V4139 Sgr 480 2 1.655 0.5 1.393 1.475 0
59 V1764 Cyg 390 1.604 1.0 1.397 1.346 1
60 ER Vul 46 ­0.156 4.0 0.902 1.030 1.119 1.197 0.5
61 AS Cap 360 1 1.691 0.9 1.375 1.899 0
62 42 Cap 34 1.120 4.3 1.079 1.210 0
63 RT Lac 205 0.705 1.1 1.333 1.907 1.360 1.742 0.5
64 HK Lac 150 1.388 2.8 1.373 1.957 1
65 AR Lac 47 0.297 13.9 1.154 1.387 1.346 1.883 0.5
66 V350 Lac 69 1.249 2.9 1.386 1.536 0
67 IM Peg 50 1.392 11.7 1.379 1.641 0
68 TZ PsA 46 0.216 2.3 1.186 1.237 0
69 RT And 95 ­0.201 0.4 1.302 1.323 1
70 SZ Psc 100 0.598 5.1 1.362 1.956 1
71 – And 24 1.312 30.2 1.363 1.898 0
72 II Peg 29 0.828 9.1 1.363 1.870 0
criteria, based on data availability, are: (a) if individual (B--
V) are quoted for the components, then a straightforward
application of the above relation was used, (b) if the spec­
tral type (usually of class III) of only one component along
with a single value for (B--V) is given, then the observed
(B--V) is assumed to correspond to this star, and (c) if two
individual components are mentioned by spectral type, but
only one value for (B--V) is available, we accept the spec­
tral type classification as accurate, and adopt as each star's
(B--V) and temperature the values given by Gray (1992)
for that particular spectral type and luminosity class. In
the absence of a reliable set of temperatures for subgiant
stars we assume the temperature of luminosity class IV to
be the mean between the temperatures of a dwarf and a
giant star of the same spectral type. In the absence of reli­
able bolometric measurements for this sample we calculated
bolometric luminosities (L bol ) from effective temperatures
and radii and normalised these to the solar value. We chose
the temperature scale of Gray (1992) because it is based on
several studies, is therefore general, and is more appropriate
for cooler stars than the Johnson scale. We do note, however,
that recent work (Amado & Byrne 1996, 1997) implies that
late­type stars may show a (B--V) dependence on activity
itself. Any errors in Teff in our sample will not effect our
results significantly because most stars lie in a region where
convective turnover time­scale varies slowly with Teff (al­
though differences between main­sequence and evolved stars
are significant). Besides, whatever temperature scale is used,
its consistent use still implies that correlation changes would
be noticeable. Uncertainties in d and R yield errors in the
observed surface fluxes and luminosity which would effect
the correlation study. For dwarf stars and subgiant compo­
nents (most of which are eclipsing) the radii should be fairly
accurate. Hence we rely, as we must, on published values of
d and R.
For several systems, and in particular for binaries
comprised of non--eclipsing evolved components, individual
masses are not given in Strassmeier et al. (1993). For those
systems (noted in Table 1) we inferred the mass from the
stars' positions in our HR diagram (see below). In order to
test the accuracy of this method for mass determination, we
compared the masses so­obtained for the whole sample to
those given by Strassmeier et al. (1993) and found them to
be in very good agreement (better than 0.2 M fi ). Errors in
M will also effect the results but where most of the stars
lie on the HR diagram there is little difference in convective
turnover time­scale for stars with mass differences of up to
0.5M fi . We have taken every precaution with the accuracy
of the stellar parameters for this study and believe the er­
rors are not sufficient to mask any significant changes in the
correlation results.
Using our values for Teff and L=L fi we have plotted
in Figure 2 the position of each star in the HR diagram for
this sample of active binaries. Numerical codes on this di­
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On the rotation­activity correlation for active binary stars 7
Figure 2. Hertsprung­Russell diagram showing the positions of stars in the sample (numerical codes correspond to index numbers in
Tables 1 and 2; not all stars are identified). Symbols denote dwarfs (triangles), subgiants (squares) and giants (circles). Also shown are
the results of the stellar models, including the ZAMS track, evolutionary tracks for stellar masses 0.4­2.2M fi at steps of 0.2M fi and
isochrones for some higher masses (dashed lines).
agram correspond to the index numbers in Tables 1 and 2
and symbols are triangles for dwarf (MS) stars, squares for
subgiants and circles for giants (to avoid confusion not all
stars are identified). The available parameters allow us to
place 103 individual stars on the HR diagram, 31 systems
with both components represented, 8 systems with only hot
components and 33 systems with only cool components. In
Figure 2 we also show the zero­age main­sequence (ZAMS)
track as well as evolutionary models for stellar masses 0.4­
2.2M fi (at steps of 0.2M fi ) calculated using our evolution
code (see Section 4 for details). Our HR diagram compares
well with the limited study to date in this area. Popper &
Ulrich (1977) plotted a small sample of active binaries in
the mass­colour, mass­radius and colour­luminosity planes
and concluded that they evolve from non­emission binaries
as they enter the Hertzsprung gap. This is strongly sugges­
tive that active binaries are active due to their evolutionary
state. Montesinos, Gim'enez & Fern'andez­Figueroa (1988)
found by comparing a sample of 22 active binaries to evo­
lutionary models that the majority had metallicities equal
to or greater than the solar value in agreement with their
post­MS status. More recently Barrado et al. (1994) used a
sample of 50 active binaries and found very good agreement
between the ages of system components even when the lumi­
nosity classes differed. They also interpret the activity of RS
CVn binaries as due to the evolution of internal structure.
Our HR diagram again confirms the preponderance of ac­
tive binaries in the post­MS state. As mentioned above the
position of stars in the HR diagram is in general consistent
with their masses and we find little evidence of incorrectly
assigned temperatures or radii. The scarcity of objects in the
Hertzsprung gap also gives us confidence in the parameters
of this sample.
We find that the systems Z Her, RT Lac and SZ Psc
show evidence, when plotted in the luminosity­temperature
plane, of anisochronism. Barrado et al. (1994) also found
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8 A. G. Gunn et al.
Figure 3. The behaviour of the convective turnover time­scale
log Üc with log T eff for main sequence stars and for stars with
masses 0.8, 1.0, 1.2, 1.6 and 2.2M fi . Changes in Üc for stars evolv­
ing to lower temperatures are very significant. Solid lines indicate
tracks calculated in the present study. For comparison the semi­
empirical relationships derived by Noyes et al. (1984), Rucinski &
Vandenberg (1986), St¸epie'n (1989) and Gilliland (1985) are also
shown.
evidence of unequal ages in Z Her and RT Lac whilst Mon­
tesinos, Gim'enez & Fern'andez­Figueroa (1988) suggested
that the components of RT Lac and SZ Psc have not evolved
as individual stars. Observational evidence for mass­transfer
in the RT Lac system has been given by Huenemoerder
(1985) and Huenemoerder & Barden (1986) whilst Hff pro­
files observed for the SZ Psc system by Huenemoerder &
Ramsey (1984) have suggested transient periods of mass­
exchange in this system. More recently Kalimeris et al.
(1995) noted that the SZ Psc system is undergoing period
variations of a large magnitude which may indicate the ex­
istence of an enhanced stellar wind giving rise to mass loss
and/or mass transfer in this system. This may account for
its anisochronic behaviour in the HR diagram. We also note
the possibility of anisochronism in the 54 Cam and BH CVn
systems. This again raises the question of the possibility of
Algol­type evolution in some active binary systems.
4 THE STELLAR EVOLUTION CODE
For the computation of stellar structure we used the evolu­
tion code described by Eggleton (1971, 1972, 1973) and Han,
Podsiadlowski & Eggleton (1994). This code solves simulta­
neously for structure and composition in a single implicit
Newton­Raphson iterative step, includes semi­convective
mixing and is appropriate for evolutionary studies up to the
end of central C burning or to the He flash for high and
low mass stars respectively. The code is similar to that used
to study the convective zone evolution in pre­main­sequence
and evolved stars by Gilliland (1985, 1986). Some signifi­
cant differences between these programs are the inclusion
Figure 4. A detailed comparison of the behaviour of the convec­
tive turnover time­scale log Üc with log T eff during evolution for
stars of mass 1.0M fi and 1.6M fi . The solid lines are tracks from
the present study while dotted lines show the results of Rucinski
& Vandenberg (1986). The ZAMS track from the present study is
also shown. The results of the present study are in broad agree­
ment with previous results.
of a better convective zone resolution in the self­adapting
numerical grid of the models, the use of updated nuclear re­
action rates, neutrino losses and opacities (those of Rogers &
Iglesias (1992) and the low temperature molecular opacities
of Weiss, Keady & Magee (1990)), an interpolative method
of computing convective zone properties and the use of the
refined equation of state described by Pols et al. (1995). In
this code mixing length theory is treated as a diffusion pro­
cess and we have set the ratio of the mixing length to the
local pressure scale height, ff, to 2. We refrain here from
a full discussion of the methods and results of our calcu­
lations which will be described in detail in a subsequent
paper (Gunn 1997). However, we stress the importance of
these new calculations for the convective effects on activity
in cool main­sequence and evolved stars. We also remark
that the basic properties of the Sun (L, T and age) are well
matched with a reasonable helium abundance of 0.28 for z
= 0.0128 and ff = 2 using this code (Pols et al. 1995). In our
models we have used the solar metallicity since this quan­
tity is poorly known for the stars in our sample and this
seems to be a reasonable assumption for most active binary
systems (Montesinos, Gim'enez & Fern'andez­Figueroa 1988).
Since temperature at the base of the giant branch depends
rather strongly on metallicity this may not be wholly appli­
cable to many of the more evolved systems. However, the
results of our analysis are much more dependent on the ac­
curacy of the stellar parameters. We have also assumed that
the evolution of the binary components can be conveniently
isolated, since, for most active binary stars in our sample,
both components normally lie within their Roche surfaces
(see Section 3).
In our calculations we have considered the variation
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On the rotation­activity correlation for active binary stars 9
of the convective turnover time­scale Üc along the main­
sequence and along evolutionary tracks for stellar masses
from 0.4M fi to 2.2M fi at intervals of 0.1M fi . This mass res­
olution matches the likely errors in the stellar masses. The
purpose of these calculations was to provide for each of the
stars in the sample a theoretical value for Üc and hence a non­
empirical Rossby number Ro . Using the position of stars in
the HR diagram (see description in Section 3) we were able
to infer Üc from T , M and L. Figure 3 shows examples for
certain stellar masses of the change in Üc with temperature as
stars evolve off the main­sequence. The main sequence Üc --T
relationship is also shown in this diagram and is somewhat
different to the semi­empirical relationship of Noyes et al.
(1984). For comparison the semi­empirical ZAMS relation­
ship provided by St¸epie'n (1989) and the theoretical ZAMS
relationships given by Rucinski & Vandenberg (1986) and
Gilliland (1985) are also shown in Figure 3. We have con­
verted all these relationships from (B--V) to one in Üc and
T by use of the polynomial relationship between (B--V) and
T for dwarf stars described in Section 3. The difference be­
tween the semi­empirical and non­empirical relationships is
not surprising considering their origins. Our ZAMS model
is similar to that of Gilliland (1985) for log T ! 3.82 and is
best matched by that of St¸epie'n (1989) for log T ? 3.82. A
more detailed comparison between the evolutionary tracks
from the present study and those of Rucinski & Vandenberg
(1986) is shown in Figure 4. A broad agreement is found
between the tracks although the present results show con­
sistently higher values of Üc .
In Figure 3 and 4 the changes in log Üc available
for evolving stars, particularly during H­core collapse in
stars with M – 1.25M fi and for stars evolving across the
Hertzsprung gap and towards the AGB, are quite signifi­
cant. It is evident that the peak in Üc occurs at the base of
the giant branch for all stellar masses. In highly evolved stars
Üc declines with temperature with little difference between
masses and forms a congruence at log Teff ¸ 3.62. We refer
the reader to Gunn (1997) for a full discussion of the im­
plications of these effects and the differences between these
and previous results. In this paper we are concerned only
with a discussion of whether the Civ rotation­activity cor­
relation improves if these evolutionary effects on convective
efficiency are taken into account. Using our stellar models
we ascribed to each star with the necessary parameters the
non­empirical values of Üc(NE) shown in Table 2. For com­
parison the empirical Üc(E) values derived using the Noyes
et al. (1984) relationship are also given in Table 2. We used
convective turnover times Üc and rotational (in fact orbital)
periods Prot to compute empirical and non­empirical Rossby
numbers. The available parameters allowed us to derive Üc
for 87 individual stars, 15 systems with both components
represented, 34 systems with only hot components and 23
with only cool components. This sample then comprises of
32 dwarf stars, 26 subgiants and 29 giants.
5 RESULTS
In Figure 5 we plot the logarithm of the Civ surface flux,
log FCIV against log Prot for our sample of active binaries.
There is a strong correlation of activity level as measured
by Civ flux with rotation period. We also show linear fits to
Figure 5. Civ flux, log FCIV , against period, log Prot , for the
sample of active binaries in this study. The plot shows linear
fits to subsets of the sample. Symbols are for dwarfs (triangles),
subgiants (squares) and giants (circles).
Figure 6. Values of log Üc (E)/Üc(NE) against log T eff for the
sample of active binaries in this study. This plot emphasises
the differences between empirical and non­empirical convective
turnover timescales for each luminosity class. Symbols as in Fig­
ure 5.
the data separately for dwarfs, subgiants and giants, evolved
components only and the entire data set. The scatter in
the diagram is such that it is not possible to attach any
significance to the different slopes of the fits for each lu­
minosity class. All classes do, however, appear to show a
good degree of correlation. A summary of the linear fits
and correlation coefficients for each luminosity group for
log P , log Ro(E) (empirical) and log Ro(NE) (non­empirical)
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10 A. G. Gunn et al.
Figure 7. Civ flux, log FCIV , against Rossby number, log Ro ,
derived from our evolutionary models of Üc , for the sample of
active binaries in this study. Linear fits are shown for subsets of
the sample. Symbols as in Figure 5.
is shown in Table 3. Simon & Fekel (1987) have provided
a detailed investigation of rotation­activity correlations us­
ing several UV emission lines, including Civ, for both single
and binary stars of different luminosity classes. They found
log FCIV = 5:91 \Gamma 1:34 log Prot for single dwarf stars with
Prot – 2 days, log FCIV = 5:69 \Gamma 0:44 log Prot for giants in
binary systems and log FCIV = 6:05 \Gamma 0:64 log Prot for all lu­
minosity classes in binary systems. The stronger dependence
on log Prot for single stars is suggestive of additional factors
on activity for evolved binary stars. We note that our re­
sults for all binary systems (log FCIV = 5:902 \Gamma 0:69 log Prot)
is very similar to these previous results but, surprisingly,
with a sample size almost 2.5 times bigger, we find a de­
crease in correlation from ­0.860 to ­0.806. Our results for
giant stars show a greater dependence on log Prot than pre­
vious results and a slightly improved correlation coefficient
(­0.510 to ­0.589). Montesinos & Jordan (1988) also exam­
ined the FCIV --Prot correlation and found for dwarfs that
log FCIV / \Gamma1:22 log Prot which is closer to our value than
that of Simon & Fekel (1987). However, both the Simon &
Fekel (1987) and Montesinos & Jordan (1988) samples are
dominated by single dwarf stars as opposed to binary dwarfs.
Figure 6 shows log Üc(E)/Üc(NE) against log Teff for
the stars in our sample. For dwarf stars the differences in Üc
are small along most of the main sequence, never exceeding
about 0.3 dex. For giants and subgiants the differences are
much more significant, reaching about 1.6 dex at the base
of the AGB. The small difference for dwarf stars results in
little change in correlation for this subsample.
In Figure 7 we show the Civ surface flux, log FCIV
against non­empirical values of the Rossby number log Ro .
The data again show a high degree of correlation as ex­
pected but the linear fits (see Table 3) do not differ sig­
nificantly between the luminosity classes. We note that the
lowest degree of correlation is found for subgiant compo­
Figure 8. The normalised activity parameter log S (see text)
for each star in our sample plotted against log T eff . Symbols as
in Figure 5, their size proportional to mass. Also shown is the
(arbitrary) position of the ZAMS track and evolutionary models
of Üc for masses of 0.8M fi and 2.2M fi (see text).
nents. Although the empirical Rossby numbers should be
meaningless for evolved components we do note an increase
in correlation when using non­empirical values. A similar de­
crease in correlation is, however, seen in dwarf components
so the improvement for evolved stars cannot be claimed to
be significant. This is opposite to the results of Simon &
Fekel (1987) who found no correlation between UV emission
and Rossby numbers for active giants. However, their Rossby
numbers were predicted qualitatively from the limited mod­
elling of Gilliland (1985). In our results there are some indi­
cations that the use of Rossby number is preferable to rota­
tion period and that non­empirical values are preferable to
the empirical values of Noyes et al. (1984). These results are
surprising considering the differences between empirical and
non­empirical Rossby numbers for the evolved components.
We note that systems in our sample showing comparatively
high Civ flux values are UX Ari, V711 Tau, oe Gem, BH
CVn, TZ CrB, AR Lac, IM Peg and – And. Many of these
are already known to be highly active binary systems.
We have attempted to interpret these results by assign­
ing to each star in the sample a normalised activity param­
eter S such that
S =
F\Omega o
Fo\Omega /
Üc
Üco ; (1)
where\Omega is rotation rate, F is the Civ flux and the `o' sub­
script refers to the values for some arbitrary star in the sam­
ple. Thus S will have the same functional form as log Üc . We
have used the highly active star HR 1099 as our reference
and show in Figure 8 the normalised activity parameter log S
plotted against log Teff for all stars in our sample. As usual
symbols denote luminosity class and the symbol sizes repre­
sent the stellar mass of the component. In order to compare
with the expected trend we assume that the log S ­ log Üc
relation is indeed linear and scale our main­sequence log Üc
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On the rotation­activity correlation for active binary stars 11
Table 3. Results of linear fits between Civ –1550 surface flux, log FCIV , and log Prot , log Ro(E) and log Ro(NE) for luminosity subsets
of the sample. For each fit we show the number of points in the sample n, the gradient a, constant b and correlation coefficient r.
log P log Ro(E) log Ro(NE)
Group n a b r a b r a b r
dwarfs 32 ­0.950 5.866 ­0.696 ­0.717 5.003 ­0.631 ­0.757 4.910 ­0.607
subgiants 26 ­0.400 5.886 ­0.546 ­0.490 5.315 ­0.533 ­0.516 5.097 ­0.570
giants 29 ­0.750 5.928 ­0.589 ­0.742 4.892 ­0.596 ­0.650 4.666 ­0.663
evolved 55 ­0.817 6.111 ­0.775 ­0.860 5.007 ­0.796 ­0.775 4.744 ­0.831
all 87 ­0.690 5.902 ­0.806 ­0.775 4.997 ­0.808 ­0.816 4.770 ­0.791
­ log Teff relationship by fitting the linear part of the curve
(in the range 3.64 Ÿ log Teff Ÿ 3.74) to the main­sequence
points in the log S ­ log Teff plane. We similarly show in Fig­
ure 8 scaled curves for stellar masses of 2.2M fi and 0.8M fi .
Although these scalings do not represent an exact corre­
spondence between log S and log Üc this diagram reveals an
interesting feature of the observational data; the normalised
activity parameter is not linearly commensurate with stellar
mass as we would expect from the stellar models. We expect
to see a clear distinction of masses for evolved stars in the
log S ­ log Teff plane. Thus, in contrast to the theoretical
predictions of convective zone evolution for stars of different
masses, activity as measured by Civ surface flux appears to
be only weakly related to mass. Although the position of
the peak log S for evolved stars does appear to be broadly
consistent with the models, Figure 8 implies the existence of
either errors in our assumptions and/or system parameters
or an additional factor other than rotation and convective
motion influencing the levels of activity in evolved active
stars.
We also considered whether the subtraction of a `basal'
Civ flux from our sample affected the degree of correlation.
We estimated Civ basal flux for each star using (B--V) colour
and data provided by Rutten et al. (1991) but found them
to be 2­3 orders of magnitude less than the observed val­
ues and hence insignificant in the correlation analysis. We
note that Schrijver (1987) does not find evidence for the
existence of a basal flux level in the Civ line in late­type
stars. We further investigated the possibility of a gravity
dependence in the correlation. For each star we calculated
surface gravity (normalised to solar) and derived correlation
coefficients for functions of the form log F = a0 + a1 log P
+ a2 log g. We find that for the entire sample there is no
significant change in correlation although a noticeable in­
crease for the non­empirical Rossby number is found. For
the sample of evolved stars there is no significant change in
correlation. Interestingly we find a 5­10% increase in corre­
lation for dwarf stars. Although in some instances there is
some evidence of improved correlation using an additional
gravity term the dispersion in the results renders them in­
conclusive. The gravity dependence results are interesting in
that they show a fairly consistent increase in correlation for
P to Ro(E) to Ro(NE) which is not shown in the simpler re­
lationship. We note that the proposed g dependence of the
rotation­activity correlation seen in the Civ line by Mon­
tesinos & Jordan (1988) for evolved stars is not apparent in
our data. As discussed by Jordan & Montesinos (1991) the
difference between dwarf and evolved stars is probably not
simply due to surface gravity.
We have discussed the observational errors and the er­
rors in the stellar parameters elsewhere in this paper. We
conclude that these are small so that the lack of improve­
ment in correlations which we present are evidence for addi­
tional factors in the connection between rotation, convection
and activity. Below we discuss some possibilities for these
additional factors.
6 DISCUSSION
The above results cause us to speculate on the possibility of
effects on activity which have not previously been considered
in detail. The application of dynamo theory in cool stars is
sufficiently uncertain that the Rossby number may not be
the best single parameter to describe the dynamo action. If
dynamo theory were essentially correct the magnetic field
generation and hence the release of magnetic energy in the
form of chromospheric heating etc. should depend only on
atmospheric structure (or spectral/luminosity class) and ro­
tation rate. In mean­field dynamo theories a minimum con­
straint for the amplification of magnetic fields is given by
the dynamo number Nd (Parker 1979),
Nd =
ff\Omega 0 d 4
j 2
(2)
where ff is the product of mean convective helicity and the
convective turnover
time,\Omega 0 is the radial gradient of angu­
lar velocity across the convection zone, d is the characteris­
tic length scale of convection and j is a turbulent magnetic
diffusivity. Durney, Mihalas & Robinson (1981), Durney &
Robinson (1982) and Robinson & Durney (1982) provide
convincing arguments that Nd is the relevant parameter de­
scribing dynamo efficiency. Making some assumptions about
the form of ff
and\Omega 0 , Hartmann & Noyes (1987) point out
that,
Nd ¸ R \Gamma2
o (3)
where Ro is the classical Rossby number (Prot/Üc ). How­
ever, this characterisation of the dynamo effect suffers from
several fundamental assumptions.
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12 A. G. Gunn et al.
Firstly, calculations of Üc are performed one pressure
scale height above the base of the convection zone. This is
chosen because in higher regions buoyancy mechanisms act
too quickly to allow significant field amplification and in the
stable region just below the convective boundary fields are
maintained for time­scales inconsistent with observed cycle
periods. However, the actual zone across which the dynamo
is operating is not known and, since Üc is strongly depth
dependent, this could significantly alter these simple models.
The possibility that the dynamo is rooted in quite different
parts of the convection zone for stars of different mass and
age has not yet been investigated.
Secondly, in the usual formulation of mixing length the­
ory used to describe the stellar interior convection, the ratio
of mixing length to pressure scale height, l/H, also often
called ff, is essentially a free parameter. Calibration of ff
is possible only with helioseismological studies of the Sun
which directly measure the depth of the convection zone
(Gough 1986). Rucinski & Vandenberg (1986) used a value
of ff = 1.6 in computing stellar convective envelopes because
derived isochrones based on this value best reproduce the
observed colour­magnitude diagrams for globular clusters
with wide­ranging age and composition (Vandenberg 1983,
1984). Using a standard mass­colour relationship Noyes et
al. (1984) used an iterative fitting procedure to the models
of Gilman (1980) and found that observational data were
best described by ff = 1.9. Gilliland (1985) showed that
different colour­temperature relations require quite different
values of ff necessary to reproduce the Noyes et al. (1984)
relationship. Although various studies to date place ff in the
range 1.5--2.0 we have used ff = 2.0 since small changes in
this parameter do not cause significant departures from the
log Üc­log Teff evolution shown in Figure 3. Nevertheless, the
uncertainty in the formulation of mixing length theory, and
in particular the value of ff, may affect our ability to derive
adequate rotation­activity relations for evolved stars.
Thirdly, the classical Rossby number involves the use
of surface rotation rate (or in fact orbital period in the case
of close binaries) and therefore does not take account of the
radial differential rotation required to produce the dynamo.
This arises because of the assumption
that\Omega 0 is propor­
tional to \Omega\Gamma d for which there is no firm theoretical basis.
The fact remains that we do not know the form of the angu­
lar velocity­depth profile for any star and certainly cannot
predict its evolution. Based on data obtained by Duval et
al. (1984), Durney (1985) found that in the Sun the shear
in angular velocity is proportional to the surface angular
velocity. In contrast, some of the solar results of Brown et
al. (1989) imply that the angular velocity­depth profile in
stars may be dependent on spectral type but have little or
no dependence on surface rotation. Obviously the use of Ro
is extremely questionable if we cannot be sure of the shear
dependence on Prot or otherwise. We suggest that one factor
which may be important, particularly for the evolving sys­
tems, is the dredging of angular momentum from the core
to the envelope which may alter the angular velocity­depth
profile (Pinsonneault et al. 1989; Simon & Drake 1989). The
non­linear dependence of S on mass may be implying that
evolved stars can have very different angular velocity­depth
profiles. The very rapid variation in internal structure also
poses the question of whether an efficient dynamo can oper­
ate, be maintained and be simply parametrised.
This point also leads us to a discussion of the effects of
binarity on stellar activity, since our sample of evolved stars
are all members of close binary systems. Young & Koniges
(1977) noted that giants in binary systems with circular or­
bits appear to show enhanced chromospheric emission in
the Caii lines. Strassmeier et al. (1989) also noted a simi­
lar effect; Hff and Caii emissions from giant stars in binary
systems display higher activity levels than dwarf stars of
the same rotation rate. Active close binaries also appear
to be more active than single stars (with similar proper­
ties) in the radio (Gibson 1980) and X­ray regimes (Rutten
1987). Based on a study of synchronised binaries Basri, Lau­
rent & Walter (1985) concluded that enhanced activity in
these stars may be caused by either their evolutionary state
or tidal effects. Basri (1987), Strassmeier et al. (1990) and
Dempsey et al. (1993) have all concluded that binarity itself
is not a strong factor in determining activity levels but is im­
portant in its ability to induce and maintain high rotation
rates. However, more recently, de Medeiros & Mayor (1995)
found, from studying X­ray fluxes, that orbital circularisa­
tion was necessary for enhanced emission. In close binaries
the effects of mass transfer could also have an effect on activ­
ity; Young & Koniges (1977) suggest that another relevant
parameter for activity studies in binaries is the ratio of the
stellar to the Roche radius. We conclude that the binarity
of the stars in our sample may affect activity levels, either
by mass transfer effects or, more likely, tidal effects on the
normal operation of the stellar dynamo; perhaps by altering
the angular velocity­depth profile. In order to address this
problem a study of single evolved active stars is required.
We should also address the possibility of a different
manifestation of magnetic activity in evolved stars even if
the dynamo description is essentially correct. Jordan & Mon­
tesinos (1991) studied the dependence of coronal tempera­
tures and emission measures on Rossby numbers and found
that the dynamo number, Nd = (Rc=Hp) 0:5 R \Gamma1
o , where Rc is
the radius and Hp the pressure scale­height at the base of the
convection zone, produced a better agreement between cor­
relations for dwarfs and subgiants. In addition they found
that the correlations involved a small gravity dependence.
Montesinos & Jordan (1993) also investigated this gravity
dependence. However, on the basis that (Rc=Hp) \Gamma0:5 ¸ 1
for evolved stars they point out that Ro provides as good a
correlation as Nd for active binary systems, but that Nd
seems to give better agreement when considering a mix­
ture of dwarfs and evolved stars. Nevertheless, much of the
work in this area presupposes a unique dependence of pho­
tospheric fields Bs on Ro or that Bsfs , where fs is the filling
factor, depends on Ro . If we assume conservation of mag­
netic flux as a flux tube is transported to the stellar surface
then we can write the photospheric field as
Bs = Bcz
`
L
2Rph
' 2
(4)
where Bcz is the field strength at the base of the convec­
tion zone, Rph is the radius of the magnetic flux tube at
the photosphere and L is the pressure scale height. But
if we further assume equipartition the pressure outside the
flux tube, the photospheric pressure Pg , constrains Bs such
that Bs ¸
p
8úPg . Even in this simplified view it is clear
that stellar luminosity or evolutionary state can determine
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On the rotation­activity correlation for active binary stars 13
to some extent the B--Ro dependence and hence rotation­
activity correlations for many active stars. As discussed we
have found no conclusive evidence for gravity dependence in
our data.
We also draw attention to the fact that the activity
indicator units could mask correlations with rotation. Sur­
face fluxes may well indicate the effects of individual flux
tubes and eliminate the stellar radius dependence while to­
tal luminosity may refer to the total number of such flux
tubes. Hence the choice of units relies on our belief that lo­
cal structures in stars of different surface gravities are sim­
ilar. Schrijver, Mewe & Walter (1984) suggest an inherent
difference in the coronal temperatures and loop structures
between dwarfs and giants while Gunn, Doyle & Houdebine
(1997) suggest dwarfs and giants show different manifesta­
tions of activity in the form of plage­like and prominence­like
features respectively. Basri (1987), however, found that ac­
tivity structures are similar on all stars. In this study we
therefore chose to use surface flux. Although this topic has
received a lot of attention in the literature we refrain from
a full discussion here.
This work would benefit from further development. A
full deduction of any additional factors involved in the con­
nection between rotation, convection and activity in late­
type stars requires analyses of samples of single evolved stars
and unevolved close binaries in an attempt to disentangle the
effects of evolution and binarity. All such studies require bet­
ter sets of stellar parameters, particularly distances which
may be available from the forthcoming Hipparchos results.
Although already complex, there is scope for improvement
of stellar convection models using mixing­length theory, the
details of dynamo generation of magnetic fields and the man­
ifestation of those fields in stars of different spectral type and
gravity. Further investigation of the applicability of Ro , or
alternatively Nd , in such studies is also required. We believe
an area requiring immediate attention is the question of the
form of the angular velocity­depth profile and its effects on
dynamo activity in late­type stars.
7 CONCLUSIONS
We have investigated the rotation­activity correlations us­
ing IUE SWP measurements of the Civ emission line at
1550 š A for a sample of 72 active binary systems. We char­
acterise the stellar dynamo efficiency with a non­empirical
Rossby number derived from stellar evolution models. For all
luminosity classes a distinct correlation exists but no signif­
icant improvement of the correlations was found when using
non­empirical as opposed to empirical Rossby numbers for
main­sequence stars. We have further found that activity
in evolved stars does not appear to be linearly commen­
surate with mass as expected from the stellar models and
shows no significant dependence on surface gravity. With­
out knowledge of the radial differential velocity gradients in
active stars the study of rotation­activity correlations using
the classical Rossby number is perhaps unwarranted. We be­
lieve this, in addition to the unknown effects of binarity and
surface gravity, and errors in the stellar parameters, are re­
sponsible for the lack of improvement in correlation. This
study therefore highlights the limitation of current dynamo
models when applied to evolved active stars.
ACKNOWLEDGEMENTS
Research at Armagh Observatory is grant aided by the Dept.
of Education for N. Ireland. We also acknowledge the com­
puter support by the STARLINK project funded by the UK
PPARC. This research has, in part, made use of the Sim­
bad database operated at CDS, Strasbourg, France. CKM
acknowledges support by a joint UK/Greek research pro­
gram in astronomical science (ATH/882/2/ASTRO) and by
the Greek Ministry of Industry, Research and Technology
PENED Program (70/3/2811). AGG would like to thank
Armagh Observatory for a research scholarship and several
travel grants during the period of this work. AGG is in­
debted to P. P. Eggleton for his invaluable assistance and
hospitality during the modification of the stellar evolution
code for this research.
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