3 The Care and Feeding of a Chromosphere

In Section 2, I established working definitions of chromospheres and activity. I now review the development of the theory and observations that underlie the modern interpretation of chromospheric structure and activity, beginning with work of the 1960s and proceeding to the present state of affairs. The arrangement of the sections is pseudo-chronological, but the sections overlap and are otherwise not restricted in scope. The intent is to provide a general narrative describing how our picture of the energy balance and physical structure of active chromospheres has evolved since about 1960. The observational results of the long-term solar and stellar observing programs are presented in Section 4, and are linked from the sections below as appropriate.

3.1 Early theory and models of the chromosphere

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

𝒮 ν ≡ jν∕αν
(the ratio of emission to absorption within a given volume of plasma, or, equivalently, the emissivity per unit optical depth) saturates to the Planck function at the local electron temperature:
𝒮 ν = B ν(T ).
As one moves up through the photosphere, the plasma becomes optically thin and LTE no longer applies; long range multiple scattering effects cause the source function for a line to be affected by remote as well as local conditions, diluting to some degree the responsiveness of the line profile to sharp changes in atmospheric structure, such as the initial chromospheric temperature rise. The latter appears relatively feebly in the cores of the Ca ii H & K lines, but much more strongly in the analogous h & k cores of Mg ii (at 2800 Å); thanks to the 15 times higher Mg abundance, the h & k lines are much more opaque than H & K, and much less susceptible to departures from LTE at the base of the chromosphere, and thus display the temperature rise more crisply. Prior to the advent of space-based astronomy, insights about the nature of stellar chromospheric activity were therefore driven strongly by parallel theoretical and observational examinations of optical and near-UV resonance lines. The available set of lines was understandably limited, but fortunately the most prominent and best-studied of these – the H and K lines of singly ionized calcium (3933, 3968 Å), the D lines of neutral sodium (5889, 5895 Å), and Hα (6563 Å) – provided precisely the observational grist needed for essential theoretical advances.

Spectral lines arise via both radiative and collisional processes, and Thomas (1957Jump To The Next Citation Point) 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 3View Image); 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, 1959Jump To The Next Citation PointFosbury, 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, 1970Jump To The Next Citation Point, Vernazza et al., 1973 and subsequent papers culminating in the “VAL3” models of Vernazza et al., 1981Jump To The Next Citation Point); 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.

3.2 Long-term observations of Ca ii H & K

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, 1963Jump To The Next Citation PointWilson and Skumanich, 1964Jump To The Next Citation Point); 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., 1975Jump To The Next Citation PointWeiler 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, 1978Jump To The Next Citation Point) 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, 1967Jump To The Next Citation Point). 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, 1984Jump To The Next Citation Point). 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, 1981Jump To The Next Citation Point). 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., 1977Livingston and Holweger, 1982Jump To The Next Citation PointWhite et al., 1987); see also Section 4.6.

3.3 From ground to space

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., 1981Jump To The Next Citation Point). 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, 1985Schrijver, 1987Jump To The Next Citation Point), 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 4View Image; 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 4View Image 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.

View Image

Figure 4: The extended composite total solar irradiance (TSI) record since 1975, from the World Radiation Center (PMOD-WRC) in Davos, Switzerland (Fröhlich).

3.4 Semi-empirical models

Empirical chromospheric models, in which parameters are adjusted until a satisfactory fit with observations is obtained, began to emerge in earnest in the 1970s as logical outgrowths of extensive work on the solar Ca ii line. Initial efforts in this area began with the first of the papers in the important Stellar Model Chromospheres (SMC) series by Jeffrey Linsky and his ‘Cool Star Mafia’ (his term, not mine). Their early models focused on Procyon (Ayres et al., 1974) and Arcturus (Ayres and Linsky, 1975Jump To The Next Citation Point), 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., 1976Kelch, 1978Giampapa 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., 1993Jump To The Next Citation Point). 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, 2007Jump To The Next Citation Point for a detailed discussion).

3.5 The high resolution chromosphere

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, 1955Babcock, 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, 1998Jump To The Next Citation Point), primarily as a result of darkening by sunspots but brightening by emission from faculae and network. At left in Figure 5View Image, 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 5View Image; numerous bright chromospheric emission regions, or plage, are present.

View Image

Figure 5: Left: a well-known white light image of the Sun, illustrating sunspots and faculae, the latter being apparent as bright regions near the limb (image courtesy NSO/AURA/NSF). Right: Ca ii K image showing chromospheric emission from active regions and network (image courtesy Big Bear Solar Observatory/New Jersey Institute of Technology). The chromospheric extensions of the faculae (the so-called “plage”) are readily visible across the disk.

The “quiet Sun” away from active regions is also permeated by magnetic features. High resolution images of the quiet photosphere appear in Figure 6View Image, 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 7View Image, left).

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Figure 6: Left: A closeup of a sunspot, clearly showing the penumbral spot structure and surrounding photospheric granulation (image courtesy Dutch Open Telescope). Right: a sunspot, granulation, and faculae observed from a more oblique angle (image courtesy Goran Scharmer and Mats G. Löfdahl, Institute for Solar Physics of the Royal Swedish Academy of Sciences).
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Figure 7: Left: Observations of photospheric granulation in the CH G band (4300 Å) show the granulation and bright points in the dark lanes; these are where the line of sight intersects flux tubes whose rarefied interiors allow one to see to deeper, hotter gas. Right: the upper photosphere, viewed in the Ca ii H line, exhibits reversed granulation (images courtesy Dutch Open Telescope).

The images in Figure 8View Image 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 8View Image 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., 1999Jump To The Next Citation Point for an overview of initial TRACE observations).

View Image

Figure 8: Three contemporaneous views of the Sun. Top left: The solar photosphere, observed in the light of the λ 4300 CH G band on 2003 November 2. Active region AR10486 is apparent at center. Top right: The solar chromosphere in the same location and time, observed in Ca ii H (images courtesy Dutch Open Telescope). Bottom: A λ 171 Å image of an arcade of magnetic loops following a large flare that erupted from AR 10486 two days after the other images were taken (image courtesy Transition Region and Coronal Explorer).

3.6 The modern chromosphere

Figure 8View Image 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 µmemission at chromospheric heights, the amusingly named CO-mosphere (Wiedemann et al., 1994). This interpretation has met with criticism (Kalkofen et al., 1999Kalkofen, 2001), but Ayres (2002Jump To The Next Citation Point) 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 1View Image, 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.

3.7 Going further

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. (2004Jump To The Next Citation Point) 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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