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As discussed in Section 3.2, the Mount Wilson program was initially established to answer the long-standing question of whether there were stellar analogs of the solar activity cycle. At the same time, the theoretical basis was developing for understanding activity cycles as manifestations of a magnetic dynamo driven by differential rotation and the convective envelopes of Sun-like stars. Increasingly detailed observations of the Sun’s magnetic field also revealed its organization into magnetic structures of varying size, from larger active regions to smaller network components. A fundamental astrophysical motivation for observations of stellar chromospheric activity, therefore, is the broader understanding of the operation of stellar dynamos and, with the advent of very high-resolution observations and analysis techniques such as Doppler imaging, the distribution of the magnetic structures responsible for activity around the stellar surfaces. Understanding the nature and evolution of dynamo processes in the cool half of the Hertzsprung–Russell diagram, and their effect on stellar output in various wavelength regimes and over the evolutionary history of the stars, remains an essential impetus for this work.
Observations of chromospheric activity developed an additional motivation with the launch of
space-based observatories and the realization that the Sun (i) did not have constant luminosity and (ii)
exhibited increasingly large variations over its activity cycle toward shorter wavelengths, particularly in the
X-rays. Combined with the renewed awareness and interest in Maunder Minimum episodes (Eddy, 1976
),
the obvious possibility that solar variations might have some impact on terrestrial climate created a keen
interest in identifying genuine twins of the Sun, whose chromospheric activity would ostensibly
be the most nearly valid proxy for assessing the likely envelope of solar variability. The solar
analog hunt was begun by Hardorp (1978), and in the best tradition of astronomical research, it
grew into a cottage industry (see, e.g., Friel et al., 1993 and previous papers in the series, the
exhaustive review by Cayrel de Strobel, 1996, and the “Top Ten” solar analogs of Soubiran and
Triaud, 2004). Understanding the so-called “solar-stellar connection” through high-resolution
solar observations and proxy stellar observations remains an important focus of stellar activity
work today, especially given the apparent paucity of real solar twins (see Section 5 for further
thoughts).
Our understanding of the long-term behavior of stellar chromospheric activity comes primarily
from the 40-year HK Project at Mount Wilson Observatory (MWO), which operated from
1966 through 2003; major summaries of the observations are given by Wilson (1978), Duncan
et al. (1991), and Baliunas et al. (1995). Observations from the HK Project are expressed in
terms of the dimensionless index S, the ratio of emission in the H & K lines cores to that in
two nearby pseudocontinuum reference bandpasses (see Section 4.2 for details). The HK data
have been used to explore a variety of stellar properties; in this section, I summarize the major
observational programs and the general stellar ensemble properties and periodicities present in the data
sets.
Baliunas et al. (1998) found that 60% of stars in the MWO survey exhibited periodic, cyclic variations,
25% showed irregular or aperiodic variability, and 15% had flat activity records (see Figure 9
). Within these
broad classifications are stars that also show evidence for multiple periodicities (Baliunas et al., 1995). This
general distribution of cycle characteristics is also found in the complementary long-term Solar-Stellar
Spectrograph (SSS) program at Lowell Observatory, but in a target set more closely clustered on the most
nearly Sun-like stars than in the MWO sample (Hall et al., 2007b). In general, in the MWO stars
both the amplitude and the mean level of chromospheric activity decrease with increasing cycle
length, and cycles shorter than about 6 yr in Sun-like stars are not observed (Baliunas and
Soon, 1995).
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In addition to identifying cycle durations, the MWO series can be used to identify rotation periods and
even differential rotation via drifts in rotation-timescale periodicities in S, assuming that the emergence
sites of stellar active regions migrate in latitude as do their solar counterparts, and if their evolution does
not obscure the signal. An initial attempt to extract the rather weak differential rotation signal from the
MWO series had limited success (Baliunas et al., 1985), but Donahue and Baliunas (1992)
reported detection of a drift in the apparent rotation period in β Com = HD 114710. The
sense of the change, however, was opposite that of the Sun, with longer periods late in the cycle
(from the familiar “butterfly” progression of active region latitudes over the solar cycle, we find
shorter periods as late-cycle active regions migrate toward the solar equator). Obviously, the
more active the star, the more likely such detections will be. Photometric Doppler imaging
techniques have been usefully applied to a number of very active stars (e.g., Strassmeier, 1996 and
subsequent papers in the series), but Hempelmann (2003) argues that the HK proxy and similar
diagnostics such as Mg ii and Ly α are more fruitful avenues for this work in low-activity,
Sun-like stars, since they are not affected by the cancellation of active region brightening and spot
darkening.
The MWO and Lowell data sets are magnitude-limited in their high-priority target list to about mV < 7 due both to instrumental limitations and the necessity of maintaining a relatively high observing cadence on samples of ≈ 100 stars, and they have been supplemented by a number of complementary programs that both reach somewhat fainter, as well as providing broad snapshots of patterns in chromospheric activity.
Wright et al. (2004) used the Carnegie Planet Search data set to derive S, R’HK, chromospheric ages,
and rotation rates for the largest survey sample presented to date, with results for over 1200
F-M stars.
A library of flux-calibrated spectra of 91 southern Sun-like stars has been published by Cincunegui and Mauas (2004); as I will discuss in Section 4.2, such libraries are certainly a desirable trend and should be expanded.
Giampapa et al. (2006) surveyed the Ca ii H & K emission of a sample of F-K stars in the open
cluster M67, probing a roughly solar-age group of dwarfs at much fainter magnitudes than the MWO or
Lowell programs. The chromospheric activity of the M67 stars was comparable to that observed in modern
solar cycles, though ≈ 25% of the stars were found outside the modern solar cycle excursion. About
15% of these were found to have activity levels below the present solar minimum, which is
comparable to the frequency of flat activity stars in the MWO and Lowell surveys. It is not clear,
however, if these are truly in non-cycling states, or merely represent the minima of cycling
stars.
Henry et al. (1996) surveyed the Ca ii H & K activity of over 800 southern Sun-like stars, a sample
mostly independent of the synoptic northern hemisphere programs. The general characteristics of
the ensemble appear in Figure 10, and they are typical of the activity-color appearance of
samples of Sun-like stars. Henry et al. (1996) identified four qualitative activity classes ranging
from “very active” to “very inactive,” as shown in the left panel of Figure 10. They also found
that (1) there was a deficiency in stars at intermediate levels of activity and that (2) this led
to a bimodal distribution of activity (right panel of Figure 10) that could be explained by a
double Gaussian distribution of active and inactive Sun-like stars, but which also revealed a very
low-activity excess (log R’HK < –5.1) which they suggested might be stars in Maunder Minimum-like
states.
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A more recent survey undertaken as part of the NStars project is discussed by Gray et al. (2003) and
Gray et al. (2006). In their analysis of their northern sample, Gray et al. (2003) obtained a
bimodal activity distribution essentially identical to that of Henry et al. (1996), including a
significant excess of possibly Maunder Minimum stars at R’HK = –5.1. Further work (Gray
et al., 2006) revealed that the apparently ubiquitous bimodal distribution was in fact a function of
metallicity (see Figure 11). Metal-poor stars of [M/H] < –0.2 do not exhibit a bimodal activity
distribution. Although the interpretation is complicated by the presence of a number of active stars
in the metal-poor sample, Gray et al. (2006) speculate that the pronounced break between
bimodal and unimodal activity distributions at [M/H] = –0.2 may reflect a physical change that
allows the presence of active chromospheres for solar-metallicity stars, while suppressing them in
metal-deficient stars. Further aspects of the “break” between active and inactive stars are noted in
Section 4.3.
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The glut of space-based observations of chromospheric activity from IUE were calibrated in absolute flux units, which had important consequences. Estimates of energy balance in the chromosphere naturally emerged in physical units from the models, but determining the analogous quantities from the ground-based observations is notoriously more difficult. Absolute flux calibrations rely on the primary spectrophotometric standards Vega and 109 Vir (Hayes and Latham, 1975; Tüg et al., 1977) or a handful of secondary standards (Hayes, 1970), and are especially vexing to relate to heavily blanketed continua such as the blue and near UV regions of Sun-like stars. Additionally, the usual measures of Ca H & K and Hα contain significant photospheric flux leaking into the filter bandpasses, and determining exactly what to remove is non-trivial. This difficulty heavily influences the characterization of ground-based observations of chromospheric activity the reader will find in the literature.
Absolute Ca K chromospheric fluxes for cool main-sequence stars were computed by Blanco
et al. (1974) and Blanco et al. (1976), but Linsky and Ayres (1978) showed that their method
underestimated the chromospheric radiative losses in the K line. Linsky et al. (1979) created absolute
Ca H & K flux profiles of F-M dwarfs and giants by deriving empirical relations giving the λ 3950 surface
flux as a function of Johnson V–R. This work was the most extensive absolute flux reference against which
the initial space-based observations were compared, and other workers have adapted the same procedure to
produce absolutely calibrated data sets for both H & K (e.g., Pasquini et al., 1988) and Hα (Pasquini and
Pallavicini, 1991).
In Sections 3.2 and 4.1, I discussed the origin and principal results of the four-decade Mount Wilson Observatory (MWO) survey of chromospheric activity in late-type stars. The HK photometer used in the initial MWO survey (Wilson, 1978) was replaced in 1977 by a successor instrument, the “HKP-2,” but both instruments measured activity in the same way and were satisfactorily cross-calibrated in terms of the nearly ubiquitous activity index S (Vaughan et al., 1978). This is a dimensionless ratio of the emission in the line cores to that in two nearby continuum bandpasses on either side of the H and K lines:
This has led a number of authors to explore the conversion of S to physical units. Middelkoop (1982)
developed a method to remove the color term from S, and Noyes et al. (1984) extended this work to create
the dimensionless index R’HK, which essentially gives the fraction of a star’s bolometric luminosity radiated
as chromospheric H and K emission. Nearly as common in the literature as S, R’ is typically expressed in
log units and ranges from about –4.4 to –5.1 for very active to highly inactive stars. To some extent,
however, even R’ is unsatisfactory due to luminosity and metallicity effects, and Rutten and
Schrijver (1987) found that the surface flux density was the optimum unit to use for deriving relations
between activity proxies (e.g., soft X-rays and Mg ii h & k), as well as relationships between activity and
rotation.
The calibration of S to flux has been primarily achieved using empirical approaches (e.g., Linsky
et al., 1979; Hall, 1996), but such methods are unlikely to achieve better than about 15 – 20% accuracy.
The S-flux calibration, using flux-calibrated spectra rather than the empirical flux scale approach of Linsky
et al. (1979) and others, has been examined by Cincunegui et al. (2007); while the available flux-calibrated
data are limited, this seems the more desirable approach.
The overall distribution of chromospheric HK fluxes in the MWO sample also revealed an interesting
bifurcation in the activity level, shown in Figure 12 (Vaughan and Preston, 1980) and now
known as the Vaughan–Preston Gap. Vaughan and Preston (1980) speculated that this could
result either from a fundamental property of dynamo evolution in cool stars, or a statistical
artifact.
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The MWO time series clearly show that the young, high-activity stars exhibit predominantly
irregular cycles, while older, Sun-like stars (i.e., those below the gap) have more well-defined cycles
(Vaughan, 1980; Baliunas et al., 1995). Durney et al. (1981) argued that this was a manifestation of a
rapid change in dynamo number from large, multiple-mode values to small, single mode values, without
requiring any sudden spindown of the star. Some subsequent studies argued against that interpretation
(Noyes et al., 1984), or suggested it was merely a statistical effect created by intrinsic upper and lower
bounds of the S index arising from photospheric background and chromospheric saturation (Hartmann
et al., 1984), but the gap appears in surveys employing both R’ (Henry et al., 1996; Gray et al., 2006)
and absolute flux (Hall et al., 2007b) and does appear to be a real aspect of chromospheric activity in
Sun-like stars.
The twin issues of whether the Vaughan–Preston gap is real, and if so, what it implies for the evolution
of the magnetic dynamo that drives chromospheric activity, have been fruitfully studied in terms of
quantities like the Rossby number Ro = Prot / τc (the ratio of the rotation period to the
convective turnover time, e.g., Noyes et al., 1984), or the ratio of cycle and rotation periods
Pcyc / Prot (e.g., Soon et al., 1993). Brandenburg et al. (1998) and Saar and Brandenburg (1999)
explored relationships between the ratio of the cycle and rotational periods and R’HK, finding that
most MWO stars fall in two distinct parallel samples which they called the active (A) and
inactive (I) branches, suggesting that a rapid increase in Prot / Pcyc by about a factor of 6
occurs at ≈ 2–3 Gyr, switching stars from the A to the I branch. Böhm-Vitense (2007) has
suggested that this means different dynamos operate at different times in a star’s life, since
I-branch stars of given mass require many more rotations to generate an activity cycle than
A-branch stars; she also notes that the Sun lies squarely between the A and I branches (see also
Section 5).
A color-flux diagram of the Mount Wilson stellar sample reveals a clear, color-dependent lower limit to the
Ca ii H & K flux. A lower limit here is not surprising, since the triangular bandpass of the MWO
photometer admits light from the photospheric line wings unrelated to the chromospheric activity; however,
IUE observations of the Mg ii h & k fluxes for 30 of Wilson’s original survey stars revealed the same lower
limit (Doherty, 1985), suggesting the presence of a non-radiative equilibrium, non-cycle related source of
heating. Schrijver (1987) showed that log linear power law relations between the flux densities in
various chromospheric, transition region, and coronal line fluxes were significantly tightened by
the removal of a color and luminosity class-dependent basal flux φi from each set of fluxes,
e.g.,
A detailed examination of the various sources of the flux in the MWO instrumental bandpass confirmed
that stars have “basal chromospheres” responsible for at least part of the observed activity (Schrijver
et al., 1989b). Solar observations showed that the Sun’s basal emission was as inhomogeneous as its
magnetic activity, with basal intensities being observed in field-free regions near the centers of supergranules
(Schrijver, 1992); this also agreed with the basal emission’s being of acoustic rather than magnetic origin.
The acoustic explanation for heating of the non-magnetic chromosphere was until recently considered the
most viable (e.g., Schrijver, 1995; Buchholz et al., 1998; Fawzy et al., 2002), though Schrijver (1995)
noted in his review of the subject that weak turbulent magnetic fields “could not be ruled out
entirely”.
Judge et al. (2003) have argued that this last caveat may be the case: based on hydrodynamic simulations of the chromospheric Ca ii λ 1335 multiplet, they conclude that the observed basal emission, at least in this line, is magnetic in origin, possibly arising from weak internetwork fields such as observed by Lites (2002). Using a specially uniformly timed sequence of Transition Region and Coronal Explorer (TRACE) observations, Fossum and Carlsson (2005, 2006) measured the acoustic flux in the solar chromosphere and concluded that the high frequency acoustic flux is a full order of magnitude less than the net radiative chromospheric losses, and that activity of the middle and upper chromosphere is dominated by the magnetic field. This has led to the idea of magnetoacoustic portals (Jefferies et al., 2006) allowing propagation of low-frequency magnetoacoustic waves via “leakage” through inclined flux tubes into the lower chromosphere. This interpretation also fits naturally with the formation of spicules via photospheric p-mode shocks propagating upward through flux tubes, driving the formation of the relatively short-lived spicules (de Pontieu et al., 2004).
The most likely scenario at present accommodates both acoustic and small-scale magnetic mechanisms. As noted above, ample evidence for acoustic contributions has emerged, but a “multiscale magnetic carpet” (Schrijver and Title, 2003) of surface fields unrelated to the dynamo is strongly suggested by the recent, high-resolution solar observations. This latter component will have important implications when we consider the nature of Maunder Minimum stars in Section 4.8.
The high temperature of outer stellar atmospheres means that most useful spectral diagnostics will lie in the UV beyond the ozone cutoff, EUV, and X-ray portions of the spectrum. The initial rocket and satellite observations of the late 1960s and early 1970s confirmed the existence of these indicators of chromospheric, transition region, and coronal activity in the solar UV spectrum (Goldberg et al., 1968) and for a few bright stars (e.g., McClintock et al., 1975; Evans et al., 1975; Dupree, 1975). The launch of IUE opened the spectrum from λλ 1150 – 3300 Å to near-continuous observation; likewise, the HEAO, ROSAT, and XMM-Newton X-ray observatories have allowed investigation of the evolution of stellar coronal activity unobservable from the ground.
The priorities and scheduling of these observatories has largely precluded extensive synoptic observing,
but we are nevertheless beginning to develop a multiwavelength picture of long-term stellar variations.
Hempelmann et al. (1996) compared MWO HK data with ROSAT survey and pointed observations of a
large set of Sun-like stars and found that the three broad types of stellar variability in the MWO sample
(see Figure 9) corresponded to distinct levels of X-ray emission, with irregular stars having the
highest X-ray fluxes and flat activity stars the lowest. While this is not unexpected, it does
create an additional method of checking for cycle minima versus true Maunder Minimum states
(cf. Section 4.8). From statistical arguments, Hempelmann et al. (1996) also showed that we
should expect to see coronal cycles in Sun-like stars if a sufficient X-ray time series could be
gathered.
This proposition has been borne out by more recent work. A synoptic observing program of the binary
HD 81809 with XMM-Newton begun in 2001 shows evidence for a coronal activity cycle; interestingly, the
cycle appeared to be shifted in phase by about one year from the HK data (Favata et al., 2004). In
contrast, Hempelmann et al. (2006) have identified a clear coronal activity cycle, using XMM-Newton
observations combined with earlier ROSAT observations, in 61 Cygni A = HD 201091 (see Figure 13).
The cycle is only 1/3 the amplitude of the solar coronal cycle variation, although 61 Cyg A has a much
higher S index than the Sun, and unlike HD 81809, the chromospheric and coronal cycles are tightly in
phase.
These results provide a fascinating first look at the link between chromospheric and coronal cyclic activity, although the observational perspective is where Olin Wilson was in about 1970. The first two good results show us coronal cycles both in phase and offset with the chromospheric emission, and synoptic observations of additional stars will no doubt turn up additional surprises.
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High resolution observations of the Sun provide a crucial conceptual and theoretical basis for interpreting
stellar activity, but unresolved, “Sun-as-a-star” observations are essential for comparing solar activity
directly with the unresolved stellar proxies. Ground-based observations of chromospheric and photospheric
proxies since 1974 from the National Solar Observatory (NSO) at Kitt Peak (KP) and Sacramento Peak
(SP) are reported in a number of papers (e.g., White and Livingston, 1981; Livingston and
Holweger, 1982; Keil and Worden, 1984; Worden et al., 1998, and references therein), and Livingston
et al. (2006) have provided a thorough summary of these synoptic observations from 1974 through
2006.
Figure 14 shows representative long-term solar observations from the NSO program (from Livingston
et al., 2006, Figure 18). The roughly 25% variation in Ca K is apparent; identical Ca K records are
obtained via lunar observations from Mount Wilson (Baliunas et al., 1995) and direct solar observations at
Lowell (Hall et al., 2007b). More surprising (and unexplained) is that the central intensities of the
photospheric lines deepened at the 1986 minimum but failed to do so for the 1996 minimum (see center data
series of Figure 14). This is particularly unexpected in light of evidence that line blanketing rather than
continuum variations are predominantly responsible for cycle-timescale irradiance variations (Mitchell Jr
and Livingston, 1991; Unruh et al., 1999). Livingston et al. (2006) suggest that there is a
hint of a 22-year cycle in the data, but that is clearly an issue that further observation must
decide.
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As discussed in Section 3.5, stellar chromospheric activity is related to the star’s magnetic structure and
therefore to the presence of photospheric features, such as spots and faculae, that modulate luminosity.
Nimbus-7 began the first long-term observations of the total solar irradiance (TSI), initiating a data set
now of critical importance in assessing the relationship between chromospheric activity and
solar and stellar luminosity. Radiometers aboard Nimbus-7 (launched in 1978) and the Solar
Maximum Mission (1980) revealed that the solar “constant” was variable in a manner that
appeared directly correlated with the activity level (e.g., Fröhlich, 1987, see Figure 4), consistent
with expectations that modulation of facular area by magnetic fields should lead to luminosity
variations (Foukal and Vernazza, 1979). Models of solar irradiance variability typically apply a
two-component model of facular brightening and sunspot darkening to reproduce the ≈ 0.1% cyclic
variability in the solar irradiance record (Chapman, 1987; Foukal and Lean, 1990), although
disagreement persists about the composite irradiance record and the presence or absence of a secular
increase in brightness from the cycle minimum of 1986 to that of 1996 (Willson, 1997; Fröhlich
and Lean, 1998). Non-facular sources of brightness changes have been postulated (Kuhn and
Libbrecht, 1991), but Lean et al. (1998) find that magnetic sources, both from active regions
and the active network, can explain the observed solar output variations, and recent work has
employed sunspot-faculae-network models to satisfactorily reproduce irradiance variations (Krivova
et al., 2007).
The relationship between solar luminosity and chromospheric activity has spurred complementary stellar
studies, the most extensive of which combined the Mount Wilson HK activity observations with 11 years of
Strömgren b and y photometry taken at Lowell Observatory of a sample of Sun-like stars
(Lockwood et al., 1997; Radick et al., 1998). The essential results appear in Figure 15. The two
panels at left are color-activity plots, and Radick et al. (1998) found that on cycle timescales,
more active (and hence younger) stars with log R’HK < –4.7 display, with few exceptions,
inverse correlations of chromospheric activity and brightness, while older (including solar-age)
stars displayed direct activity-brightness correlations (as of course does the Sun itself). An
initial interpretation is that stars switch from spot-dominated to facular-dominated brightness
variations at ≈ 2 Gyr. Equally interesting are the activity-variability plots on the right side of
Figure 15; the Sun has a vigorous chromospheric cycle relative to its closest stellar analogs
(upper right) but is photometrically sedate (lower right). Radick et al. (1998) found that this
discrepancy could not be due to inclination effects (i.e., that a sample of randomly inclined stars
might appear more photometrically variable than the Sun), a result corroborated by Knaack
et al. (2001).
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The Lowell photometric program ended in 1998, but observations of an expanded Sun-like star sample
continued at the Fairborn Observatory, using high-precision robotic photometric telescopes, in southern
Arizona (Henry, 1999). Observations from this program have been combined with the Lowell photometry
and the MWO data to provide a 20-year examination of chromospheric activity and brightness
variations for bright solar analogs (Lockwood et al., 2007). The conclusions from this study are not
significantly different from those of Radick et al. (1998) (a point I shall return to in Section 5),
but the photometric quiescence of the Sun remains a nagging issue. Lockwood et al. (2007)
point out that the Sun’s apparently low photometric variability may simply stem from their
small sample size, but also that the issue bears further investigation. Along those lines, the star
widely considered to be an excellent solar twin, 18 Sco = HD 146233 (Porto de Mello and
da Silva, 1997), has been found to have chromospheric activity similar to or slightly exceeding
that of the Sun, a Sun-like cycle amplitude (though of somewhat shorter length) and similarly
low photometric variability of about 0.09% over a full activity cycle (see Figure 16, from Hall
et al. (2007a)). Whether this similarity exists for other solar twins obviously remains to be seen.
Recently, Meléndez and Ramírez (2007) have found that the star HIP 56948 is a better
solar twin than 18 Sco, on the basis of its lower Li abundance. This is a good indication that a
larger sample of good solar analogs and twins, as we would statistically expect, will emerge once
surveys are pushed to fainter magnitudes than the MWO and Lowell programs have been able to
achieve.
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An intriguing aspect of chromospheric variability has been its absence in a number of Sun-like stars, including the Sun itself. Eddy (1976) created renewed interest in the period of solar inactivity from 1645 – 1715 which he called the Maunder Minimum, after the British astronomer who first noted it in the 1890s, during which the solar activity cycle did not shut down entirely, but operated at a greatly reduced level (Beer et al., 1998; Ribes and Nesme-Ribes, 1993). The solar activity-irradiance correlations described in Section 4.7 raised interest even further in so-called “grand minima”, especially in regard to estimating solar contributions to terrestrial climate change. Creation of solar irradiance reconstructions has proceeded along two fronts: (i) modeling cycle-timescale irradiance fluctuations via the cyclic evolution of bright faculae, active network and plage, and dark sunspots, and (ii) examining possible secular changes in the minimum activity level via evolution of the quiet network. I concentrate on point (ii) here.
A key initial problem was to estimate the Sun’s brightness in the absence of a quiet network. Mount
Wilson observations of the S indices of selected non-cycling stars suggested their Ca ii H & K emission
lay well below that of the contemporary solar minimum (Baliunas and Jastrow, 1990), from
which White et al. (1992) deduced that the K emission from the Sun during the Maunder
Minimum may have been as little as 11% that of current cycle minima. On this basis, Lean
et al. (1992) estimated that the Sun may have been 0.24% fainter during the Maunder Minimum, a
figure that guided subsequent irradiance reconstructions that included both cyclic and secular
components (e.g., Lean et al., 1995). Further examination of the activity records and S values of flat
activity stars yielded estimates of long-term solar variability as much as 0.4% (Baliunas and
Soon, 1995) or 0.6% (Zhang et al., 1994). However, Hall and Lockwood (2004) were unable
to recover the bimodal cycling versus non-cycling star activity distribution of Baliunas and
Jastrow (1990) using a larger sample, and Wright (2004) argues that previously identified Maunder
Minimum stars are actually evolved. Recent irradiance reconstructions have employed small
secular components to the solar activity trend since 1715 (e.g., Wang et al., 2005; Krivova
et al., 2007).
Renewed efforts to identify Maunder Minimum candidates demonstrably on the main-sequence have
been undertaken by Judge et al. (2004) and Judge and Saar (2007). Two leading candidates are
τ Ceti = HD 10700 and HD 143761, and Judge and Saar (2007) used UV and X-ray observations of these
stars to detect the presence of transition region and coronal emission, concluding that magnetic activity for
at least these two flat activity stars is not significantly reduced below a cycle minimum state. We
therefore presently have a tentative view of flat activity stars as having small-scale magnetic
fields and, technically, chromospheric activity, while lacking the large-scale active region fields
characteristic of cycling stars. The sample on which this is based remains small, and continued
studies of low-activity stars will help clarify matters. The Holy Grail in this area is a convincing
observation of a star entering or leaving a Maunder Minimum; the star HD 3651 in the MWO
program may have done this, and the star ψ Ser = HD 140538 makes an excellent case for
the end of a Maunder Minimum state in the Lowell data (see Figure 17). Essential adjunct
observations, of course, are the luminosity variations of such stars as their activity characteristics
change.
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Section 4.1: An unavoidable aspect of all the stellar time series is their uneven sampling, which manifests itself both on yearly (due to the stars’ observing seasons) and intraseason (due to telescope scheduling and weather vagaries) timescales. A widely used technique for handling the MWO data is an adaption of the Lomb–Scargle periodogram to unevenly sampled data described by Horne and Baliunas (1986). More recently, Frick et al. (1997) have developed an improved technique, using a similar extension to standard wavelet analysis.
I must also note in passing that the intentional focus of this review on Sun-like stars has completely ignored an important set of the most chromospherically active stars we know of: close binaries with cool components. The fundamental introduction in the modern literature is Hall (1976), introducing, among others, the archetypal active close binaries, the RS CVn systems, which typically include a G or K subgiant and a late F or G dwarf with orbital periods from a few days to a few weeks. Since such systems typically are synchronous, both components are greatly spun up and exhibit greatly enhanced chromospheric emission relative to field stars. They are thus excellent test cases for exploring the limits of activity as the atmospheres approach saturation, as well as Doppler imaging techniques (e.g., Vogt et al., 1987; Strassmeier, 1996) to map the rough distribution of surface features. The reader may find numerous texts on the subject (e.g., Hilditch, 2001), and the recent literature contains a number of surveys and catalogs of the brighter systems (Strassmeier et al., 1993; Montes et al., 2000).
Section 4.2: Interpreting the ground-based observations of stellar chromospheric activity in terms of
absolute flux has caused, as J.R.R. Tolkien put it, “a gorgeous row”. The Mount Wilson S index itself is in
reasonably good shape; the various other programs that have either replicated S or created S-like quantities
are in reasonable agreement (e.g., Hall and Lockwood, 1995; Gray et al., 2003; Wright et al., 2004; Hall
et al., 2007b), despite its shortcomings for physical interpretation. However, fine points in color corrections
and flux calibration have led to discrepant formulations of log R’HK and absolute surface flux from a
given S measurement, as well as difficulty reconciling solar and stellar observations (Noyes
et al., 1984; Rutten, 1984; Schrijver et al., 1989a). Duncan et al. (1991) wrote that “in general the
agreement [of S/flux calibrations] is good”, though the continued ruffling of feathers in the
literature suggests this assessment was generous. Hall et al. (2007b) have revisited the issue, and
while the S/flux and solar/stellar calibrations seem to be in good agreement, the empirical
determination of fluxes still has distressingly large errors of 15 – 25%, stemming largely from
uncertainties in the quantities needed to derive flux scales in the manner of Linsky et al. (1979). The
uncertainties are aggravated for low-activity stars that are currently of particular interest (see
Section 4.8), since most of the flux in the typical measurement bandpasses does not arise from
dynamo-related activity and must be removed to obtain R’ (see Noyes et al., 1984) or the excess flux 
(see Schrijver et al., 1989b; Hall et al., 2007b). Using carefully flux-calibrated spectra as a starting point
(Cincunegui et al., 2007) may be a promising approach to resolving some of these issues. Beyond all these
issues, the flux-calibrated space-based data also require careful treatment; for a thorough discussion, see
Judge (1990).
Section 4.6: Not surprisingly, the NSO HK records correlate well with other measures of the Sun’s overall level of activity, such as the 10.7 cm flux and the sunspot number. The latter, because of its 400-year baseline, is fundamental to the irradiance reconstructions described briefly in Section 4.7, and has also led to extensive work on an ancillary topic, the prediction of solar activity via application of various dynamo, statistical, and in some cases numerological models (for a review see Hathaway et al., 1999) to replicate the observed sunspot records. Predictions for solar cycle 24, which should last from ca. 2008 – 2017, indicate that it should be either very weak (Schatten, 2005;