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A&A manuscript no.
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Your thesaurus codes are:
02.12.1; 02.12.2; 08.01.2; 08.03.3; 08.12.1
ASTRONOMY
AND
ASTROPHYSICS
August 23, 1999
The Wilson­Bappu Relation for RS CVn Stars
F.F. ¨
Ozeren 1;2 , J.G. Doyle 1 and D. Jevremovic 1;3
1 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
emails: jgd@star.arm.ac.uk
2 Dept. of Astronomy, Science Faculty of Ankara University, 06100 Tando~gan­Ankara/Turkey
email: ferhat@astro1.science.ankara.edu.tr
3 Belgrade Observatory, Volgina 7, 11000 Belgrade, Yugoslavia
email: darko@aob.aob.bg.ac.yu
the date of receipt and acceptance should be inserted later
Abstract. We investigate the extent to which the
Wilson­Bappu relationship holds for chromospherically
active binaries using the Mg ii h&k lines of 41 RS CVn
stars observed with IUE. The resulting fits are different
from the relationships obtained for single, less active stars.
The parallax used were those from the hipparcos cata­
logue, these give a much better correlation than the mag­
nitudes taken from CABS. Within a particular luminosity
class the relationship is good, however it tends to break
down when we incorporate objects ranging in luminosity
from class i to v. From model calculations there is very lit­
tle dependence of the Mg ii line width on effective temper­
ature. The line width does however depend on the column
mass at the transition region boundary showing increased
line width at lower column mass. There is also a depen­
dence on the column mass adopted for the temperature
minimum, however, the major and dominant parameter is
the surface gravity scaling as g \Gamma1=4 . Within a luminosity
class more active objects will show larger lines widths re­
flecting a higher column mass deeper in the atmosphere,
e.g. at the temperature minimum level.
Key words: Wilson­Bappu effect --- Mg ii h&k lines ---
stellar chromospheres --- column mass
1. Introduction
The Wilson­Bappu relationship (hereafter the WB rela­
tionship) was first established as a relation between the
absolute visual magnitude (M v ) and the line width of
Ca ii H&K emission lines for late type stars by Wilson &
Bappu (1957). Subsequent work, based on COPERNICUS
data for a very limited sample of K giants (McClintock et
al. 1975) extended it to other lines, notably Mg ii h&k
and Ly ff. Many other authors, (e.g. Kondo et al. 1976;
Stencel 1977; Weiler & Oegerle, 1979; Vladilo et al., 1987,
Send offprint requests to: Ferhat Fikri ¨
OZEREN
Montes et al. 1994) have looked at the WB relationship
attempting to explain the under­laying physics.
There are two plausible basic theories to explain the
WB relationship i) Doppler broadening with stellar ab­
solute magnitude ii) column density above the tempera­
ture minimum. These were discussed in papers by Engvold
& Rygh (1978), Ayres (1979), Linsky (1980) and Lutz &
Pagel (1982). The dominant parameter seems to be the
chromospheric mass column density.
To extend and test the WB relationship for low lumi­
nosity objects, the red dwarf stars AU Mic, AT Mic and
AD Leo were used (ElgarÜy, 1988, Ambruster et al., 1989).
These new data points fitted well with the result of Vladilo
et al. (1987). Going to the more active stars, Gurzadyan
(1991) used 10 RS CVn­type objects. He concluded that
the observed magnesium emission was generated by ion­
ized gas in the space between the components of the bi­
nary systems. Montes et al. (1994) used Ca ii H&K for
28 chromospherically active binary systems and 18 single
active stars. They noted that there is a systematic differ­
ence among the behaviour of stars belonging to different
groups. ElgarÜy et al. (1997), working with Mg ii h&k data
for 78 single stars observed with IUE noted that the active
stars show a somewhat larger spread in line widths than
the `quieter' objects, thus showing a different WB rela­
tion. Recently, a re­calibration of the WD relationship has
been done for 94 stars with absolute magnitudes derived
from the parallax's reported from hipparcos (Scoville &
Mena­Werth, 1998)
Due to the prolific output from IUE during it's 19 years
of operation, an excellent dataset of Mg ii h&k line pro­
files has been obtained for a large selection of RS CVn
binaries. With the exception of the latter few references,
most of the developed WB relationships have excluded RS
CVn's, due to their intense chromospherically activity and
binary nature. Here, we look again at the WB relationship,
confining ourselves only to the RS CVn's using the abso­
lute magnitudes based on the new hipparcos parallax's.
The parallax parameter along gives substantially different

2 F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's
Table 1. The individual parameters for the stars in the sample.
NO CABS HIP Star Name HD Sp Porb(day) P rot (day) Log g Teff
1 3 664 AP Psc 352 ¸ F/K1III 96.439 ­/2.78 4106 2
2 5 2762 13 Cet 3196 F7/G4 2.082 ­/4.46 5708 2
3 7 3693 i And 4502 /K1III 17.7692 ­/2.78 4481 1
4 8 4157 CF Tuc 5303 G0V/K4IV 2.79786 2.798 4.39/3.37 4452 2
5 9 5007 6286 G2V 91.9 4.40
6 10 5951 AY Cet 7672 WD/G5III 56.824 77.22 ­/3.07 ­/4930 1
7 16 9630 12545 K0III 23.9824 24.3 2.89
8 22 13118 VY Ari 17433 K3­4 V­IV 13.198 16.42 4.50
9 29 16846 V711 Tau 22468 G5IV/K1IV 2.83774 2.841 3.71/3.55 4912 2
10 48 23743 BM Cam 32357 K0III 80.895 85 2.89 4510 1
11 71 YY Gem dM1e/dM1e 0.8142822 0.8143 4.67/4.67
12 81 44134 TY Pyx 77137 G5IV/G5IV 3.198584 3.32 3.71/3.71 5436 2
13 85 46159 IL Hya 81410 K1III 12.908 12.89 2.78 4650 2
14 96 56862 GT Mus 101379 A0/K2­4III 61.36 56.03 ­/2.36 9520/4808 1
15 112 65187 BM CVn 116204 K1III 20.625 20.6 2.78 4424 1
16 116 67013 V851 Cen 119285 K2IV­III 11.989 12.05 2.63 4311 1
17 118 V841 Cen 127535 K1IV 5.998 5.929 3.55 4389 1
18 120 72848 131511 K2V 125.369 4.55
19 125 UZ Lib ¸ A8/K0III 4.767885 4.7357 ­/2.89
20 132 79607 TZ CrB 146361 F6V/G0V 1.139791 1.1687 4.30/4.39 6352/5948 2
21 136 81519 WW Dra 150708 G2IV/K0IV 4.629617 4.62961 3.77/3.57 4650 2
22 137 82080 ffl UMi 153751 A8­F0V/G5III 39.4809 4.28/3.07 7370/5011 1
23 141 84586 V824 Ara 155555 G5IV/K0V­IV 1.681652 1.682 3.71/3.57 5048 2
24 144 85852 DR Dra 160538 WD/K0­2III 905.9 31.05 ­/2.78 ­/4602 1
25 147 87965 Z Her 163930 F4V­IV/K0IV 3.992801 3.962 3.98/3.57 5048 2
26 152 88848 V815 Her 166181 G5V/M1­2V 1.809837 1.819 4.49/­ 5542 2
27 156 91009 BY Dra 234677 K4V/K7.5V 5.975112 3.827 4.57/4.62
28 159 92512 o Dra 175306 G9III 138.42 142.8 2.92 4291 1
29 163 94013 V1762 Cyg 179094 K1IV­III 28.5895 28.5895 2.78 4569 1
30 165 95244 V4138 Sgr 181809 K1III 13.048 60.23 2.78 4613 1
31 167 96003 V1817 Cyg 184398 A2V/K2III­II 108.854 108.854 4.16/2.63 8970 1
32 179 103833 ER Vul 200391 G0V/G5V 0.698095 0.6942 4.49/4.49 5948/5678 2
33 187 107095 42 Cap 206301 G2IV 13.174 3.77 5738 2
34 190 109002 HK Lac 209813 F1V/K0III 24.4284 24.461 4.27/2.89 4692 2
35 191 109303 AR Lac 210334 G2IV/K0IV 1.98 1.98 3.77/3.57 5616/5048 2
36 194 111072 V350 Lac 213389 K2III 17.755 2.63 4393 1
37 195 111802 FK Aqr 214479 dM2e/dM3e 4.08322 4.39 4.69/4.71
38 196 112997 IM Peg 216489 K2III­II 24.65 24.39 2.63 4534 1
39 202 114639 SZ Psc 219113 F8IV/K1IV 3.965866 3.955 3.89/3.55 6500/5500 1
40 204 116584 – And 222107 G8IV­III 20.5212 53.952 2.89 4842 2
41 206 117915 II Peg 224085 K2­3 V­IV 6.724183 6.718 3.20 4842 2
Notes: 1 Barrado y Navascues, D. et al. (1998), 2 Gunn, A. et al. (1997)
results than those based on Strasmeier et al. (1993) cat­
alogue. In the final section of the paper we compare the
result from the observational data with Mg ii k line profiles
as calculated with multi for a range of gravities, effective
temperatures, column mass in the transition region and
column mass at the temperature minimum.
2. Observational data and its reduction
We have searched the IUE Data Archive for the entire
CABS (Strasmeier et al. 1993). Mostly only LWP data was
reduced, although sometimes data from the LWR camera
was also used. Related parameters are given in Tables 1
& 2, e.g. the CABS number, hipparcos number, Star
Name, HD number, spectral type, V­band magnitude, (B--
V) color, P (orb) , P (rot) , log g, T eff , ú in milli arc second
from hipparcos, d in pc, absolute magnitudes and radius.
In Table 2, M v is calculated by
M v = V \Gamma 5logd(pc) + 5 \Gamma A v (1)
where A v is the correction for interstellar absorption ex­
pressed in V magnitude. The corrections were obtained
using
A v = 3:2 \Lambda E(B \Gamma V ) (2)

F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's 3
Table 2. The individual parameters for the stars in the sample (see text for description).
NO Star Name VCABS VHIP (B­V)CABS (B­V)HIP ú(mars)HIP d(pc) Mv Mv HIP
R ref
1 AP Psc 6.07 6.32 1.38 1.366 3.25 307.69 ­0.1 ­2.00 41 1
2 13 Cet 5.2 5.32 0.57 0.567 47.51 21.05 3.9/ 4.00 1.3 2
3 i And 4.06 4.25 1.12 1.100 17.98 55.62 1.9 0.49 0.7 1
4 CF Tuc 7.41 7.74 0.735 1.561 3.51 284.9 [4.4/3.1:] ­2.32 3.32 2
5 HD6286 8.4 8.36 [0.63] 0.960 4.64 215.52 [4.7] 0.64 1.02 3
6 AY Cet 5.47 5.58 0.9 0.888 16.08 62.19 /1.32 1.14 15 1
7 HD12545 8.11 8.56 1.21 1.107 5.08 196.08 /0.13 1.78 8 1
8 VY Ari 6.9 7.08 0.96 0.956 22.73 44.0 5.2 3.91 0.76 3
9 V711 Tau 5.7 6.04/8.90 0.92 0.885 34.52 28.97 4.2/3.2 3.13/6.93 1.3/3.9 1
10 BM Cam 6.1 6.24 1.12 1.112 5.22 191.57 0.2 ­0.49 16 1
11 YY Gem 9.07 ­.-- 1.35 ­.--- ­.-- ---.-- 9.14 0.62 1 /0.54 3
12 TY Pyx 6.835 7.02 0.72/0.76 0.695 17.91 55.83 3.9/3.8 3.30/3.30 1.59/1.68 1
13 IL Hya 7.25 7.52 1.02 1.012 8.36 119.62 0.15 2.38 12 2
14 GT Mus 5.08 5.18 0.79 0.804 5.81 172.41 0.3 ­0.14 16.6 3
15 BM CVn 7.21 7.48 1.16 1.157 9.00 111.11 0.2 2.03 16 2
16 V851 Cen 7.81 7.78 1.067 1.068 13.13 76.16 3.5 3.67 3.5 1
17 V841 Cen 8.5 ­.-- 1.069 ­.--- --.-- --.-- 4.6 3.12 3.16 3
18 HD131511 5.97 6.14 0.84 0.841 86.69 11.54 6.1 6.09 0.78 3
19 UZ Lib 9.3 ­.-- 1.06 ­.--- --.-- --.-- [/0.7] ­.-- 21 1
20 TZ CrB 5.7 5.71/6.74 0.47 0.599 46.11 21.69 4.1 3.65/5.06 1.22/1.21 1
21 WW Dra 8.22 8.75/9.71 0.6 0.714 8.67 115.3 3 3.07/4.87 2.12/3.9 2
22 ffl UMi 4.23 4.37 0.89 0.897 9.41 106.27 0 ­2.67/­0.75 1.7/12 1
23 V824 Ara 6.63 7.01 0.835 0.798 31.83 31.42 4/5.2 4.21/4.72 1.61/1.25 2
24 DR Dra 6.55 6.77 1.05 1.043 9.68 103.31 ­0.1 1.86 10 3
25 Z Her 7.23 7.37 0.59 0.602 10.17 98.33 2.9/3.5 1.76/3.39 1.85/2.73 1
26 V815 Her 7.66 7.83 0.72 0.728 30.69 32.6 5.2 7.64 0.97 2
27 BY Dra 8.07 8.28 1.221 1.265 60.90 16.42 7.6/8.6 6.36/7.48 0.7/0.6 3
28 o Dra 4.64 4.79 1.19 1.185 10.12 98.81 0.5 ­0.84 14.3 2
29 V1762 Cyg 5.81 6.05 1.09 1.086 14.24 70.22 1.67 1.83 9.2 2
30 V4138 Sgr 6.57 6.89 1.03 1.032 11.40 87.72 0.15 2.36 11.22 3
31 V1817 Cyg 6.32 6.52 1.16 1.123 3.10 322.58 ­1.1 ­1.15 62 1
32 ER Vul 7.27 7.46 [0.95] 0.614 20.06 49.85 4.62/4.74 3.93/4.18 1.07/1.07 1
33 42 Cap 5.17 5.29 0.65 0.672 30.73 32.5 3 2.50 3 2
34 HK Lac 6.52 7.09 1.08 1.052 6.62 151.06 3/0.8 1.06 15 2
35 AR Lac 6.09 6.25 0.72 0.763 23.79 42.0 3.5/3.3 2.74/3.13 1.52/2.72 2
36 V350 Lac 6.38 6.57 1.17 1.166 8.18 122.25 2.2 1.12 12.7 2
37 FK Aqr 9.05 9.13 1.5 1.466 115.71 8.6 9.5 9.46 0.5/0.44 3
38 IM Peg 5.6 6.03 1.12 1.132 10.33 96.81 2.0 1.10 7 2
39 SZ Psc 7.2 7.55 0.44/1.00 0.788 11.34 88.2 3.3/2.3 3.28 5.1 2
40 – And 3.7 3.97 1.01 0.984 38.74 25.81 2.2 1.61 7 2
41 II Peg 7.51 7.61 1.01 1.007 23.62 42.3 5.4 4.96 2.2 2
Notes: 1 Strassmeier et al. (1993), 2 Gunn et al. (1998), 3 Straizy & Kuriliene (1981)
E(B \Gamma V ) = (B \Gamma V ) observed \Gamma (B \Gamma V ) intrinsic (3)
The intrinsic (B--V) colours were taken from Fitzgerald
(1970). For conversion to surface flux, the radius was taken
from CABS, Gunn et al. (1997) or StraiŸzys & Kuriliene
(1981).
To analyse the IUE images we used the STARLINK
package dipso (Howarth et al. 1996). The widths and the
emission line fluxes of the Mg ii h&k lines were measured
using a least squares Gaussian fit (Table 3). Some stars
have more than one spectra, in this situation the resultant
values are given as a mean value in Table 3. All derived
line widths are corrected for the instrumental broadening
using a square correction
W 2 = W 2
observed \Gamma W 2
instrumental (4)
where W instrumental = 21 km s \Gamma1 (Turnrose & Thom­
son 1984). In Table 3, the FWHM of the Mg ii h&k lines,
logW h , logW k and the fluxes for each line are presented.
3. Observational Results
In Fig. 1 we plot P orb versus the P rot . With the excep­
tion of a few objects, there is a strong correlation between

4 F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's
Table 3. Spectroscopic results for the RS CVn stars in the sample.
NO Star Name FWHMh \Sigmaoe log Wh \Sigmaoe log Fh FWHMk \Sigmaoe log Wk \Sigmaoe log Fk
( š A) (km s \Gamma1 ) ( š A) (km s \Gamma1 )
1 AP Psc 1.639 0.112 2.244 0.029 5.919 1.716 0.045 2.265 0.011 6.077
2 13 Cet 0.490 0.205 1.720 0.169 6.468 0.611 0.072 1.817 0.049 6.466
3 i And 1.253 0.008 2.128 0.003 8.713 1.399 0.012 2.177 0.004 8.863
4 CF Tuc 1.282 0.279 2.137 0.094 7.524 1.655 0.055 2.249 0.014 7.607
5 HD6286 1.274 0.121 2.135 0.041 8.251 1.616 0.050 2.239 0.013 8.339
6 AY Cet 0.799 0.111 1.932 0.059 5.665 0.930 0.035 1.999 0.016 5.785
7 HD12545 1.105 0.188 2.073 0.073 6.663 1.092 0.077 2.069 0.030 6.663
8 VY Ari 0.704 0.057 1.877 0.034 7.571 0.756 0.033 1.909 0.019 7.622
9 V711 Tau 1 0.882 1.975 6.889 0.982 1.975 7.055
10 BM Cam 1.219 0.041 2.116 0.014 6.553 1.662 0.026 2.251 0.007 6.648
11 YY Gem (Pri.) 0.639 0.012 1.835 0.008 0.617 0.017 1.821 0.011
YY Gem (Sec.) 0.368 0.011 1.596 0.012 0.565 0.017 1.782 0.013
12 TY Pyx 2 (Pri.) 0.860 0.060 1.965 0.030 6.921
TY Pyx 2 (Sec.) 0.850 0.030 1.959 0.015 6.869
13 IL Hya 0.891 0.047 1.979 0.022 5.890 1.022 0.027 2.040 0.011 5.953
14 GT Mus 1.512 0.196 2.209 0.056 6.793 1.802 0.106 2.286 0.026 6.896
15 BM CVn 1.076 0.059 2.062 0.023 5.606 1.057 0.024 2.055 0.010 5.730
16 V851 Cen 0.769 0.012 1.915 0.007 6.575 0.780 0.011 1.923 0.006 6.749
17 V841 Cen 0.883 0.051 1.975 0.025 6.258 1.088 0.033 2.067 0.013 6.250
18 HD131511 0.513 0.027 1.740 0.021 6.261 0.541 0.020 1.764 0.015 6.310
19 UZ Lib 1.190 0.141 2.105 0.051 1.850 0.133 2.298 0.031
20 TZ CrB (Pri.) 0.551 0.065 1.771 0.048 6.480 0.699 0.031 1.875 0.018 6.593
TZ CrB (Sec.) 0.568 0.071 1.784 0.051 6.452 0.761 0.032 1.912 0.018 6.563
21 WW Dra(Pri.) 1.084 0.206 2.065 0.081 6.061 1.293 0.191 2.261 0.063 6.214
WW Dra (Sec.) 0.807 0.084 1.936 0.044 5.793 0.931 0.066 2.080 0.030 5.933
22 ffl UMi 1.173 0.076 2.099 0.028 6.452 1.373 0.047 2.168 0.015 6.580
23 V824 Ara(Pri.) 0.537 0.018 1.760 0.013 6.236 0.689 0.014 1.869 0.008 6.357
V824 Ara(Sec.) 0.516 0.022 1.742 0.017 6.320 0.595 0.018 1.805 0.013 6.389
24 DR Dra 0.815 0.063 1.941 0.033 6.084 0.955 0.025 2.011 0.011 6.118
25 Z Her 0.811 0.109 1.938 0.057 6.484 0.865 0.039 1.968 0.019 6.569
26 V815 Her 0.535 0.016 1.758 0.012 6.449 0.670 0.030 1.857 0.019 6.605
27 BY Dra (Pri.) 0.303 0.035 1.511 0.043 6.077 0.326 0.017 1.544 0.019 6.157
BY Dra (Sec.) 0.245 0.046 1.419 0.064 6.049 0.310 0.022 1.521 0.026 6.159
28 o Dra 1.170 0.196 2.098 0.072 5.894 1.131 0.105 2.084 0.040 6.068
29 V1762 Cyg 0.992 0.098 2.026 0.042 6.184 1.180 0.050 2.103 0.018 6.286
30 V4138 Sgr 0.807 0.038 1.936 0.020 5.840 0.823 0.019 1.946 0.010 5.912
31 V1817 Cyg 1.866 0.311 2.301 0.072 5.613 1.950 0.131 2.321 0.029 5.763
32 ER Vul(Pri.) 1.358 0.329 2.162 0.104 6.688 1.396 0.092 2.176 0.028 6.775
ER Vul(Sec.) 1.368 0.322 2.166 0.101 6.689 1.483 0.118 2.202 0.034 6.803
33 42 Cap 0.604 0.037 1.810 0.025 5.999 0.644 0.044 1.840 0.028 6.184
34 HK Lac 1.306 0.044 2.145 0.014 6.199 1.404 0.048 2.178 0.015 6.271
35 AR Lac (Pri.) 1.084 0.067 2.065 0.027 6.824 1.295 0.036 2.143 0.012 6.972
AR Lac (Sec.) 0.752 0.078 1.906 0.044 5.981 0.965 0.053 2.015 0.023 6.086
36 V350 Lac 1.347 0.148 2.159 0.047 6.128 1.521 0.071 2.213 0.020 6.201
37 FK Aqr (Pri.) 0.153 0.015 1.214 0.027 5.416 0.203 0.016 1.338 0.025 5.609
FK Aqr (Sec.) 0.241 0.011 1.412 0.016 5.826 0.302 0.014 1.511 0.017 5.963
38 IM Peg 3 1.305 2.145 6.810 1.464 2.196 6.922
39 SZ Psc 1.658 0.058 2.249 0.015 6.360 1.842 0.047 2.296 0.011 6.466
40 – And 0.838 0.056 1.953 0.028 6.367 0.974 0.005 2.019 0.002 6.459
41 II Peg 0.697 0.015 1.873 0.009 6.599 0.827 0.004 1.948 0.002 6.647
Notes: 1 Dempsey et al. (1996), 2 Neff et al. (1996), 3 Ol'ah et al. (1998)
them (r = 0:95) implying tidally locked systems. From
Table 3 we note that the surface fluxes are more than log
F surface;k = 5:2 which was given as an activity measure­
ment by ElgarÜy et al., (1997). Fig. 2 shows the M v ­
log W (km s \Gamma1 ) relation of Mg ii k for our sample of RS
CVn's. In this figure, we have also plotted the points for

F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's 5
DR Dra
Fig. 1. logProt versus logPorb for the stars in Table 1.
II
III
IV
V
Fig. 2. The Wilson­Bappu relation for the Mg ii k line. The
solid line only shows our relation for the RS CVn's only, the
dashed line shows the relation for all objects. Active & quiet
single stars (un­filled symbols), RS CVn's (filled symbols),
while the dotted line shows the relation for only the active
and quiet single stars.
the active and quiet stars as given by ElgarÜy (1997) for
Mg ii k. The Mg ii k least squares fit for all the objects in
Fig. 2 is
M v = \Gamma15:50(\Sigma0:67)log W MgIIk + 32:45(\Sigma1:28) (5)
ER Vul(p)
ER Vul(s)
HD 6286
SZ Psc
WW Dra(p)
CF Tuc
III
IV
V
Fig. 3. Surface gravity versus log W (km s \Gamma1 ) for the group of
RS CVn stars.
with a correlation coefficient of r=0.82, while that for only
the RS CVn's is
M v = \Gamma12:01(\Sigma0:89)log W MgIIk + 26:41(\Sigma1:82) (6)
with a correlation coefficient of r=0.80. This relation is
somewhat different from the relation for single stars with
the RS CV objects showing a larger variation in the line
width. It is however clear that stars ranging from lumi­
nosity i to luminosity v can have a similar line width but
differing in absolute magnitude by a factor of seven. This
therefore reflects the growing importance of the radius and
effective temperature in the super­giants and giants, sug­
gesting that log W versus M V are not the best parameters
to attempt a correlation if objects of differing luminosity
classes are involved.
Fig. 3 shows the surface gravity versus log W(km s \Gamma1 ).
It is immediately clear that a very good correlation exists
although there are exceptions which are probably due to
the method of deriving log g. The present values were de­
rived by using the spectral type as given by StraiŸzys &
Kuriliene (1981). This figure shows that different luminos­
ity classes have different line widths with the higher lumi­
nosity objects showing broader lines (see also discussion
by Lutz & Pagel 1982, Neckel 1974 and Reimers 1973).
In an attempt to understand the various parameters in­
volved in the formation of Mg ii, we constructed (see x4)
a series of model atmospheres varying T eff , log g, the col­
umn mass at the temperature minimum and the column
mass at the transition region.

6 F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's
Fig. 4. The adopted atmospheric structures ­ electron densities (upper panel) and electron temperatures (lower panel) vs.
column mass for an effective temperature of 4500K and log g = 4.
4. Atmospheric models
We have calculated a grid of models representing the ac­
tive component of RS CVn stars in order to investigate
in more detail the dependence of the Mg ii k line width
on effective temperature (varied between 3750 and 5000
K), stellar surface gravity (between log g = 2:5 and 4:5),
position of the temperature minimum (log mmin from --1
to 0) and position of the transition region (log m TR =--4.5
to --2.7). We adopted this particular range of values to
cover both the active and very active stars as Short et al.
(1998) have shown that the transition region in the RS
CVn system II Peg is at a very deep position (­2.8).
A total of 420 atmospheric structures were calculated
with the photospheric models of Kurucz (1992). Following
Ayres (1979), all models have T (mTR ) equal to ú 8500 K,
the temperature at the top of the chromosphere. Because
the atmosphere below T min is close to radiative equilib­
rium (RE), the choice of T min fixes the value of m min . We
assume that the atmosphere is in radiative equilibrium up
to the temperature minimum. With the chosen position of
the temperature minimum and the position of the tran­
sition region we then built a series of simple models by
keeping dT
dlogm constant in the chromosphere (e.g. Short
et al. 1998, Short & Doyle 1997). The grid of typical at­
mospheric structures (temperature and electron density

F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's 7
Table 4. Parameters used in the modelling: effective temperature (Teff ), surface gravity (log g) in cm s \Gamma2 , position of the
transition region (log mTR ) in g cm \Gamma2 and position of the temperature minimum (log mmin ) in g cm \Gamma2 . All possible combinations
of parameters were explored.
Teff log g log mTR log mmin
3750, 4000, 4500, 5000 4.5, 4.0, 3.5, 3.0, 2.5 --4.5, --4.0, --3.5, --3.0, --2.9, --2.8, --2.7 --1.0, --0.5, 0.0
Fig. 5. Full width at half maximum (log W ) of the Mg ii k line versus log g and log mTR for four different effective temperatures.
Note that for each log mTR , we have three separate lines for the column mass (log mmin) at Tmin .
distribution) for T eff of 4500K and log g = 4:0 are
shown in Fig 4, further details are given in Table 4.
With this range of parameters, we solve the hydro­
static equilibrium equation and NLTE problem for Hy­
drogen using the radiative transfer code multi version
2.2 (Carlsson 1986). This solution gives us the populations
levels for Hydrogen and the correct distribution of electron
densities in the structures. After that we solve the NLTE
problem for the Mg ii atom using a model atom with 18
levels. We converge the population levels of Mg ii until
changes are less than 1% .
Short & Doyle (1997) and Andretta et al. (1996) have
shown that for models of cooler stars it is necessary to
incorporate a better treatment for background opacities.
We did not follow their treatment of background opacities
mainly because of the huge computational requirements

8 F.F. ¨
Ozeren et al.: The Wilson­Bappu Relationship in RS CV's
for our number of models. However, since we deal with
larger effective temperatures than that considered by the
above authors, this effect should not be major, of the order
of 0.1--0.2 dex.
5. Discussion
In Fig. 5 we show four plots of the dependence of the
FWHM of the Mg ii k line on stellar gravity and position
for the transition region for different effective tempera­
tures. For each position of the transition region, three val­
ues are plotted corresponding to different positions of the
temperature minimum. The gravity dependence is clearly
visible, however the dependence on effective temperature
is small as seen by the similarity of the plots. In summary
the calculations show that (i) for a higher transition region
column mass the line width is smaller scaling as m \Gamma1=4
TR ,
(ii) with increased effective temperature there is a greater
dependence of the line width on the column mass at the
temperature minimum, (iii) with increasing column mass
at the temperature minimum there is an increase in line
width scaling as m 0:1
min and (iv) increasing line width as
the surface gravity decreases scaling as g \Gamma1=4 .
In his analysis, Ayres (1979) gave a qualitative descrip­
tion of the dependence of the FWHM of the resonance
lines of single ionized Magnesium and Calcium. For Mg ii k
the base line width was given by
\Delta– \Lambda ¸ ~
F 1=4 ~
g \Gamma1=4 ~
T 7=4
eff (7)
and thermalization width by
\Delta– \Lambda ¸ ~
F \Gamma1=4 ~ g \Gamma1=4 ~
T \Gamma5=4
eff ¸ 1=2 (8)
where ~
F , ~ g and ~
T eff are the chromospheric heating, sur­
face gravity and effective temperature expressed in solar
units and ¸ is the chromospheric Doppler width. Both of
these widths have the same gravity dependence but op­
posite sensitivity on chromospheric heating. For the ther­
malization width there is only a weak dependence on the
chromospheric velocity fields. This suggested that log W
is mainly sensitive to surface gravity (W ¸ g \Gamma1=4 ) but
insensitive to effective temperature and heating. This is
also clear from our calculations and also from the empir­
ical data analysed. Also from Fig. 5 it is clear that there
exist a qualitative dependence of width on position of the
temperature minimum ­ i.e. a deeper temperature mini­
mum generally gives wider lines.
Acknowledgements. Research at Armagh Observatory is grant
aided by DENI while support for software and hardware is
largely provided by the STARLINK Project which is funded by
the UK PPARC. FF ¨
O wished to thank the Turkish Scientific
and Technical Research Council for a grant which enabled a
visit to Armagh. This work was supported in part by a grant
(PPA/G/S/1997/00298) from the UK PPARC.
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