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The Sun in Time: Activity and Environment 25
with respect to the ambient gas pressure, i.e., the field strength is primarily dependent on spectral
type, although a weak activity dependence is also present (e.g., Montesinos and Jordan, 1993). The
higher filling factors lead to less expansion of photospheric/chromospheric flux tubes because the
tubes merge with adjacent tubes (Cuntz et al., 1999). Therefore, toward more active stars, coronal
magnetic fields interact progressively more frequently due to their denser packing. A higher rate of
large flares is a consequence. Since flares enhance the electron density along with the temperature,
stars with a higher activity level should reveal a predominance of hotter structures (Güdel et al.,
1997b). Such a trend is observationally well supported; as further described in Section 5.5.2 below,
coronae at higher activity levels are systematically hotter.
4.3 Activity cycles in the young Sun
Records of sunspot numbers back over several hundred years show a near-cyclic modulation that
has turned out to be a central challenge for dynamo theories. The activity period between two
successive spot maxima is approximately 11 years; because the magnetic polarity reverses after
one period, the full magnetic cycle amounts to 22 yr. Activity cycles corresponding to the 11 yr
solar cycle have been found on many cool stars, mostly as a result of the Mount Wilson HK project
(Baliunas et al., 1995) that has collected a continuous data stream of the chromospheric Ca ii H
& K line flux diagnostic for many stars over several decades. A subset of stars appear to lack
such cycles, however, and very active stars tend to exhibit an irregular rather than a cyclic mode
of variability (Hempelmann et al., 1996). An alternative method for finding activity cycles on
magnetically active stars is the identification of cycles in the starspot coverage.
4.3.1 Starspot cycles of solar analogs
Messina and Guinan (2002) specifically studied starspot cycles of stars from the “Sun in Time”
program. Activity cycles are found in all of them, with periods ranging from 2.1 yr to 13.1 yr.
A comparison with the more comprehensive survey and the theoretical interpretations presented
by Saar and Brandenburg (1999) confirms the presence of two or three branches: i) inactive solar
analogs show cycles about 100 times longer than the rotation period, P ; ii) active stars reveal
cycles 200 – 600 times longer than P ; iii) and “super-active” stars show cycles about 4 order of
magnitude longer than P (Figure 7a). Among G-type stars, only EK Dra appears to be compatible
with the third class (Messina and Guinan 2002).
The brightness amplitude increases with increasing inverse Rossby number (i.e., increasing
rotation rate for constant turnover time), indicating that spots produce progressively more modulation
toward higher activity levels (Figure 7b). A plateau is suggested for the most active stars,
indicating a saturation effect when spots cover a large fraction of the stellar surface (Messina and
Guinan, 2002).
The standard near-ZAMS solar analog, EK Dra, has been an important target for cycle studies.
Dorren and Guinan (1994a) and Dorren and Guinan (1994b) showed that its long-term photometric
variations by ≈ 0.07 mag are consistent with a period of about 12 yr. Variations compatible with
this time scale are also found in Ca ii HK, Mg ii h and k, and the ultraviolet C iv, C ii, and He ii
fluxes (Dorren and Guinan, 1994a), and in X-rays (see Section 4.3.2 below). The spot periodicity
has been confirmed by Messina and Guinan (2002) although their best estimate for the period is
9.2 ± 0.4 yr (Figure 8). The star is optically faintest when chromospheric and transition-region
activity is highest. On top of this cyclic behavior, there is a long-term trend in the optical light,
namely a decline of the blue light by 0.0017 ± 0.0004 mag yr −1 for an investigated time span of
35 yr (Fröhlich et al. 2002; see also Messina and Guinan 2003 and Järvinen et al. 2005). Further,
two active longitudes shift in phase in concert with the activity cycles (Järvinen et al., 2005). The
dominant spot concentration switches between the two preferred longitudes with a “flip-flop” cycle
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