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The study of stellar chromospheric activity has evolved steadily, but has hinged on several “cusps” that have led to fundamental advances. The first of these is discussed in this section: a set of critical theoretical advances that provided a solid basis for the synoptic ground-based programs that soon followed.
In the low photosphere, plasma conditions can be determined under the simplifying assumption of local thermodynamic equilibrium (LTE), wherein the source function
Spectral lines arise via both radiative and collisional processes, and Thomas (1957
) demonstrated that
in the conditions typical of a Sun-like chromosphere, the source functions of ionized metals should in general
be dominated by the collisional terms, while those of neutral metals should be dominated by the
radiative terms. Collisionally dominated lines such as Ca ii H & K reflect the local plasma
conditions since collisional processes are obviously tied to the local electron temperature. This is
manifested in the familiar emission reversal at the line cores, which for the opaque H and K
lines are formed high in the chromosphere (see Figure 3
); the H and K lines, therefore, have
long been the obvious choice for long-term, ground-based surveys of stellar activity. Neutral
metals in general reflect the continuum radiation via the control of their source functions by
radiative terms, and show no such reversal. The strong Hα line, whose core is formed high in
the chromosphere, is marginally photoelectrically controlled in Sun-like stars (Jefferies and
Thomas, 1959; Fosbury, 1974); in the hot, high density conditions that occur during flares (or
in extremely active stars) the collisional terms become increasingly important and it begins
to fill in or goes into emission. The essential point to glean from all this is that the radiative
versus collisional distinction is a useful first-order tool for understanding how and in which lines
we might track stellar chromospheric activity, but the formation and nature of the lines of
interest is complex and depends on the conditions over a possibly large range of depths in the
atmosphere.
The extensive work on the line source function in the presence of a chromosphere, along with the
“advantage of large electronic machines” as Schwarzschild (1958) quaintly but presciently put it, led to the
development of non-LTE (NLTE) chromospheric models (e.g., Auer and Mihalas, 1969 and subsequent
papers in that series, Athay, 1970, Vernazza et al., 1973 and subsequent papers culminating in the “VAL3”
models of Vernazza et al., 1981); the models variously approached the problem of chromospheric activity
analytically (i.e., calculating an emergent spectrum from first principles) and empirically (by iteratively
adjusting parameters of a model to match its output to an observed temperature distribution). Among
other things, these models made it apparent that significant mechanical heating was necessary to
sustain observed chromospheric conditions (Athay, 1970). An important (but understandable)
shortcoming of these models was their temporal and spatially-averaged nature; these shortcomings
and further details about the development of chromospheric modeling are discussed in Section
3.4.
The strongest spectral features observable from the ground are those dubbed H and K by Fraunhofer
in 1814, arising from singly ionized calcium. Eberhard and Schwarzschild (1913) noted the
presence of pronounced emission cores in these lines in spectra of Arcturus and other stars, and
sensibly wondered (1) whether the emission arose from processes analogous to solar activity and
(2) if the emission varied periodically in a manner analogous to the sunspot cycle. Perhaps
no researcher pursued these questions with such patience and perseverance as Olin Wilson at
the Mount Wilson Observatory (MWO; the confluence of names is a coincidence). Wilson’s
initial synoptic observations revealed that the chromospheric activity of main-sequence stars
decreases with age (Wilson, 1963; Wilson and Skumanich, 1964); this result was eventually
synthesized in the famous paper by Skumanich (1972), in which the stars’ Ca ii emission (and by
inference, the mean surface magnetic field) was shown to decay as the inverse square root of the
age.
The early MWO observations also revealed a curiously linear relation between the absolute
magnitude and the log of the K line emission widths for G and later stars, dwarfs, and giants alike:
Mv = 27.59 – 14.94 log Wo(K) (Wilson and Bappu, 1957). Relationships similar to the “Wilson–Bappu
effect” were subsequently found for other resonance lines, such as Mg ii k λ 2796 and Ly α λ 1216
(McClintock et al., 1975; Weiler and Oegerle, 1979). Numerous explanations were advanced, but
Ayres (1979), using scaling laws for the extent and density of the chromosphere, argued that the
Wilson–Bappu width is “a stellar barometer, not a tachometer”; i.e., rather than arising from details of
chromospheric flows, it is primarily a hydrostatic equilibrium acting in concert with the partial ionization of
hydrogen and resonance line cooling to postpone the onset of the sharp thermal instability that gives rise to
the corona. Pace et al. (2003) suggested that the Wilson–Bappu relationship can be used to
infer cluster distances, though it contains too much scatter to be useful for individual stellar
distances.
In 1966, Wilson undertook a systematic program of Ca ii H & K observations of main-sequence stars,
and in a seminal paper (Wilson, 1978) posed the question Does the chromospheric activity of main-sequence
stars vary with time, and if so, how? In that paper he concluded that all stellar chromospheres were variable
to one extent or another, that cyclical variations very likely did exist, and that they should be considered
to be generated and dissipated by processes and structures analogous to those observed on
the Sun until proven otherwise. Following Wilson’s retirement, the so-called “HK Project”
continued under the direction of S. Baliunas until the end of 2003, and it remains today the
fundamental observational data set of stellar chromospheric activity. Further details about the
program and its major results, as well as other stellar cycles investigations, are presented in
Section 4.1.
Complementing the stellar cycles programs are long-term HK observations of the Sun, both resolved and
full disk (i.e., “the Sun-as-a-star”). Wilson observed the Moon as a solar proxy with the MWO
spectrometer, and early observations of the solar Ca K line suggested that the central K2 emission peak
varied by as much as 40% over the solar cycle (Sheeley Jr, 1967). Direct, long-term H & K
observations of the Sun began at the National Solar Observatory (NSO) in 1974 using the McMath
solar telescope at Kitt Peak (White and Livingston, 1978), and in 1976 at Sacramento Peak
(Keil and Worden, 1984). By the peak of solar cycle 21, it was apparent that the “HK index,”
the total emission in a 1 Å rectangle centered on the line cores, closely tracked the sunspot
number, plage index, and 10.7 cm flux (White and Livingston, 1981). The NSO workers also
monitored a number of photospheric features (e.g., C i λ 5380 and several iron lines) to study
the relationship between chromospheric activity, photospheric structure, and solar and stellar
luminosity (Livingston et al., 1977; Livingston and Holweger, 1982; White et al., 1987); see also
Section 4.6.
The second cusp in our understanding of stellar chromospheric activity occurred beginning in 1978, with the deployment in rather rapid sequence of a number of space-based observatories, especially the International Ultraviolet Explorer (IUE) and the Einstein X-ray observatory; although certainly not the first observational ventures into space, they were far more capable than their predecessors. The advent of these satellites had two effects: (1) continuous access to the UV and X-ray spectrum where most outer atmosphere diagnostics lie, and (2) a steadily growing data set of flux-calibrated spectra. Thus, although the nature of IUE and similar missions precluded the kind of long-term observations Olin Wilson was able to carry out, a watershed of observations of outer stellar atmospheres rapidly accumulated.
A critical early result was the discovery of tight power law correlations between emission in
chromospheric, transition region, and coronal lines (e.g., Ayres et al., 1981). A few quotations from
that paper loom large in the present-day literature; Ayres et al. (1981) suggest that “the very
existence of the correlations argues that coronae and chromospheres are physically associated,” and
later in their paper, discussing chromospheric and coronal heating mechanisms, they write
that “the small-scale magnetic flux tubes thought to comprise the major component of the
solar surface field [may] serve as conduits of wave energy (acoustic or Alfvén) into the outer
atmosphere…While magnetic fields very likely provide the structure of stellar chromospheres, they
may be responsible only indirectly for the heating”. This is a fundamental shift in thinking
from the time averaged, spatially averaged nature of the “first generation” models discussed
above.
Subsequent work demonstrated that similar power laws applied for numerous diagnostics for normal
dwarfs to binaries and even bizarre objects such as FK Comae stars (Oranje, 1986). Wilson’s
Ca ii H & K measurements also were shown to be similarly related to transition region and coronal
emission (Oranje and Zwaan, 1985; Schrijver, 1987), solidifying the idea of a tight physical relationship
between the “layers” of the outer stellar atmosphere. For an exhaustive treatment of progress in the early
IUE years, see the review by Jordan and Linsky (1987).
Progress during this period was not limited to the stars. Within months of the commissioning of IUE,
the Nimbus-7 satellite was launched, initiating what is now a three-decade record of space-based
measurements of the total solar irradiance (TSI). The extended TSI composite appears in Figure 4; this
figure is widely reproduced but of sufficient importance to the interpretation of stellar activity and
luminosity that I include it here. Further arguments are deferred to Section 4.7; suffice to say here that the
discovery that the solar constant isn’t, as Figure 4 clearly shows, created an important new dimension to
the study of stellar activity, and is a pivotal part of the radical transformation of the field circa
1980.
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), since these were at that time the only stars other than
the Sun with high resolution, absolutely calibrated atlases suitable for creating absolute flux
profiles of the Ca ii lines. In subsequent papers, these models were refined and extended to
dwarfs spanning the right half of the HR diagram (Ayres et al., 1976; Kelch, 1978; Giampapa
et al., 1981).
These early models provided a number of fundamental insights on the broad characteristics of stellar atmospheric structure; perhaps most significantly, evidence was found for non-radiative heating in the photosphere as well as the chromosphere, and both the temperature gradient and the radiative loss rates were found to be higher for active chromosphere stars than for “quiet” stars. These modeling efforts also necessitated the development of methods for creating absolutely (if approximately) flux-calibrated profiles of a large number of cool stars (see Section 4.2). However, they also had some critical limitations, and Ayres and Linsky (1975) acknowledge these explicitly in their work on Arcturus: “A more detailed model [of the upper photosphere and low chromosphere] could be devised, but we feel that such an approach is not justifiable until we have a reliable estimate of the extent to which our assumptions of a homogeneous, static, plane-parallel chromosphere are valid for Arcturus …”.
This turned out to be a wise caveat. The “simplicity” of the early models was driven, of course, by the limitations of the available observations, both in terms of resolution and wavelength. As new data gradually overcame these limitations, it became clear that one-component models could not explain the full complexity of the chromosphere, a classic example being Heasley et al. (1978), who demonstrated that the derived parameters in the Ayres & Linsky model could not replicate Arcturus’s CO and Ca K line wing spectrum. This provided compelling evidence for the inhomogeneous nature of the chromosphere summarized in Section 2.1, and served as a natural springboard for more advanced modeling (see, e.g., Uitenbroek, 2000).
As the IUE era got underway, the growing body of ultraviolet data permitted much more extensive investigation of stellar chromospheres and transition regions, spurring two additional important series of papers: Outer Atmospheres of Cool Stars (Linsky and Haisch, 1979 and subsequent papers), continuing the semi-empirical modeling efforts in the SMC series, and Magnetic Structure in Cool Stars (Middelkoop and Zwaan, 1981 and subsequent papers). The former series focuses extensively on individual stars modeled in the SMC era, while the latter provides arguably the most comprehensive examination in the literature of the Mt. Wilson H & K data with the space-based data, but a pervasive theme in both series is the continual discovery of structures in stars that appeared to be direct analogs of solar outer atmospheric structures.
Semi-empirical models remain the standard approach to understanding chromospheric structure today,
with the older “VAL” models having been supplanted by the “FAL” models (e.g., Fontenla et al., 1993).
First-principle, theoretical models of the chromosphere, incorporating the effects of magnetic fields, appear
to be the “next wave,” though their full 3D incarnations remain beyond current computational limits (see
the review by Carlsson, 2007 for a detailed discussion).
In the preceding sections, I have reviewed the development of ground-based observations and models for phenomena that are clear signatures of chromospheric heating via non-thermal mechanisms. In this section I review the physical arrangement of these phenomena in the Sun, as revealed by modern, high-resolution instrumentation, under the assumption that analogous structures are responsible for stellar chromospheric activity, and that a detailed view of solar features will provide a more visceral feel for the unresolved observations of their stellar analogs.
Stellar activity cycles have long been considered to be the result of a self-sustaining magnetic
dynamo, created by the combined action of turbulent convection and differential rotation
(e.g., Parker, 1955; Babcock, 1961), and are likely generated near the base of the convection zone (in the
Sun, ≈ 1.5 × 105 km below the visible surface; Parker, 1975). Chromospheric activity can be a useful
proxy for luminosity variations, since the structures responsible for both are dependent on the extent and
distribution of this magnetic field. The total solar irradiance varies by ≈ 0.1% over the activity cycle
(Fröhlich and Lean, 1998), primarily as a result of darkening by sunspots but brightening by emission from
faculae and network. At left in Figure 5, the familiar sunspots (regions of intensely concentrated magnetic
flux emerging from the solar interior) and faculae (in visible light best seen near the limb, where their
warmer high altitude layers are more evident due to the oblique viewing angle, see Keller et al., 2004) are
apparent. Spruit (1977) gives a classic treatise on these phenomena, describing spots as “shadows”
on the solar surface arising from the suppression of convective heat transport by the intense,
concentrated magnetic fields. These elements permeate the chromosphere, and are apparent in the
Ca ii K image at right in Figure 5; numerous bright chromospheric emission regions, or plage, are
present.
The “quiet Sun” away from active regions is also permeated by magnetic features. High resolution
images of the quiet photosphere appear in Figure 6, obtained by the Dutch Open Telescope
(DOT, left) and the Swedish Solar Telescope (SST, right). The photospheric granulation is
obvious in the patterns of bright granules and dark intergranular lanes, as is the filamentary
structure of the sunspot penumbra. The SST observations near the limb at oblique viewing
angles (e.g., Lites et al., 2004) clearly reveal the granules, which are buoyant convective bubbles
arriving at the solar surface, as three-dimensional “hills;” they release their energy once the gas is
sufficiently optically thin, and the cooled plasma then sinks back into the interior in the dark lanes.
Myriad tiny magnetic flux tubes emerge in the granule centers, are swept up by horizontal
flows, and collect in the intergranular lanes (e.g., Spruit and Roberts, 1983), often appearing
as bright points in CH (“G band”) images: their lower internal gas densities suppresses the
molecular formation and allows radiation from hotter deeper layers to escape (see Figure 7,
left).
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The images in Figure 8 provide an exquisite view of the solar atmosphere from photosphere to
chromosphere, obtained with the Dutch Open Telescope and the Transition Region and Coronal Explorer
(TRACE). At top left is the photosphere, showing the very large active region AR10486, marked by a
number of spots and associated faculae. The simultaneous image of the chromosphere at top right clearly
reveals the greatly enhanced emission in the magnetically active areas near the active region, as well as the
general manifestation of the chromosphere as a seething mass of narrow, magnetically confined structures.
In this image, the Ca ii H primarily samples vertically-oriented flux tubes that have been called straws
(Rutten, 2007a) extending into hot transition region and coronal regimes; an Hα image reveals somewhat
different but still discrete structures variously termed mottles, fibrils, and spicules (e.g., Suematsu
et al., 1995). This is therefore a highly resolved version of what the long-term activity cycle
programs discussed in Section 4.1 “see” in the various chromospheric activity indices. Finally, at
the bottom in Figure 8 is an image taken by TRACE of AR10486 shortly after an enormous
X-class flare that erupted two days after the images at top were taken. An arcade of cooling,
post-flare loops is present; these delicate, croquet wicket structures are found not only in the active
corona, but also in “quiet” regions (see Schrijver et al., 1999 for an overview of initial TRACE
observations).
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Figure 8 represents what we may call a third cusp in our view of solar and stellar chromospheres. So far, we
have little evidence that stellar active chromospheric structures are substantially different from the Sun’s,
and the data from TRACE, SOHO, Hinode, SORCE, and comparable missions must strongly guide stellar
activity research over the next 15 years.
The earliest TRACE data revealed the highly confined nature of the outer solar atmosphere (Schrijver
et al., 1999), and have bolstered a “dynamical” view of the chromosphere that contrasts sharply with the
“layered” view alluded to in Section 2, and as modeled by the workers of the 1960s and 1970s (Section 3.1).
Carlsson and Stein (1995) even asked “Does a non-magnetic solar chromosphere exist?”, arguing that in the
internetwork regions, the temperature rise is merely an artifact of time-averaged modeling, with
evanescent pulses of high temperatures occurring from periodic heating by wave dissipation. This
view is supported by the presence of cool CO 4.7 μm emission at chromospheric heights, the
amusingly named CO-mosphere (Wiedemann et al., 1994). This interpretation has met with
criticism (Kalkofen et al., 1999; Kalkofen, 2001), but Ayres (2002) argues that much of what was
classically considered the chromosphere is indeed quite cool, and Rutten (2007b) goes so far as to
suggest that the chromosphere comprises merely the Hα mottles and fibrils – which leads us
full circle to the beautiful pink annulus of Figure 1, though with a far different conceptual
basis.
With this somewhat revised view to a chromosphere, I review in Section 4 the principal results from long-term observations of solar and stellar chromospheric activity.
Section 3.1: The size of the literature makes any statement like this rather subjective, but I believe the student interested in the development of stellar atmospheres theory can profitably use the beautiful trio of papers by Thomas (1957), Jefferies and Thomas (1958), and Jefferies and Thomas (1959) as an essential node both for researching subsequent developments as well as the early work by Milne, Eddington, Chandrasekhar, and others. These papers are singularly illuminating and readable. The early models have of course been thoroughly superceded; the classic VAL (Vernazza et al., 1981) models may be compared, for example, with Anderson and Athay (1989), the “FAL” stars (Fontenla et al., 1993 and previous papers in the series), and fully 3D models of “dynamic” chromospheres that are coming within the reach of current computing power (for a recent review, see Carlsson, 2007).
Section 3.2: Olin Wilson’s early explorations of the relationship between stellar rotation,
chromospheric activity, and age used observations of clusters (the Hyades, Pleiades, Praesepe, and
Coma, Wilson, 1963), but were soon extended to field stars (Wilson and Skumanich, 1964), many of which
would end up on his long-term stellar cycles program. The concept of “chromospheric ages” as deduced
from the Ca ii H & K activity proxy has since received a great deal of attention; an important synthesis is
presented by Soderblom et al. (1991), and Wright et al. (2004) give a large set of chromospheric ages for
stars observed as part of the Carnegie Planet Search Project. Wilson’s long-term observations of stellar
chromospheric activity commenced in March 1966 with 139 stars selected not for any particular “Sun-like”
nature, but by virtue of noticeable HK emission in spectrograms he had previously obtained (this point will
return when I discuss solar analogs later in this article). Even after over a year of observing,
Wilson was evidently not sanguine about the results of the program, noting that “If Sheeley’s
[Sheeley Jr (1967), who found the solar K line central intensity varied by 40% over the activity
cycle] results are correct …the observational problem of finding stellar cycles should not be too
difficult. However, the experiences of Popper and myself suggest a more pessimistic outlook”
(Wilson, 1968).
Section 3.5: Details of dynamo research and its numerous outstanding questions are outside the scope of this review; for a recent evaluation see Charbonneau (2005), and for summaries of the long-term observational programs within the dynamo context, see Baliunas et al. (1996) and Strassmeier (2005).
Section 3.6: In several places in this review, I make note of the evanescent nature of the chromosphere that these recent observations clearly support. I thank one of the referees for suggesting a comparison in this regard that should be useful for both researchers and students: despite the volume over which it is distributed, the mass of the solar chromosphere is only about the mass of Earth’s atmosphere; moreover, the mass of the photosphere down to τ = 1 in the continuum is only about that of the Indian Ocean!
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