DOES THE SUN HAVE A FULL-TIME COmosphere? Thomas R. Ayres 1

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1 The Astrophysical Journal, 575: , 2002 August 20 # The American Astronomical Society. All rights reserved. Printed in U.S.A. DOES THE SUN HAVE A FULL-TIME COmosphere? Thomas R. Ayres 1 Center for Astrophysics and Space Astronomy, University of Colorado, 389 UCB, Boulder, CO ; ayres@casa.colorado.edu Received 2001 November 19; accepted 2002 April 25 ABSTRACT Off-limb emissions of solar 4.7 lm rovibrational bands of carbon monoxide, recorded under excellent observing conditions with the Infrared Imaging Spectrograph at the McMath-Pierce telescope, are compared with theoretical translimb CO simulations based on time slices from the Carlsson & Stein dynamical model of chromospheric K grains. In the Carlsson-Stein view, the solar outer atmosphere in nonmagnetic internetwork regions is a spatially and temporally intermittent wave-driven phenomenon, yielding an average thermal profile in the classical low chromosphere that is cool, not hot. Recent papers by Kalkofen and collaborators have criticized the dynamical model in favor of traditional layered stratifications, in which temperatures vary smoothly with altitude and are warm throughout the chromosphere. The present work sharpens the controversy by reiterating that traditional models with warm thermal profiles in the altitude range km fail two key infrared CO tests. The same tests reveal that the Carlsson-Stein dynamical model which Kalkofen et al. argue is too cool in the low chromosphere is not cold enough. Equally important, there need not be any contradiction between the existence of cool gas above the classical temperature minimum and observations of ubiquitous ultraviolet emission from the solar outer atmosphere, a central criticism by Kalkofen and collaborators of a full-time cold COmosphere. Subject headings: molecular processes Sun: chromosphere Sun: infrared Sun: photosphere 1. INTRODUCTION 1 Visiting Astronomer, National Solar Observatory, operated by the Association of Universities for Research in Astronomy (AURA), Inc., under cooperative agreement with the National Science Foundation. 2 By convention, altitudes are measured positive outward relative to the layer in which the radial continuum optical depth at 0.5 lm is unity, i.e., the visible surface, or see level Until recently, the solar atmosphere was thought to be well characterized, based on a wealth of ultraviolet, optical, and submillimeter diagnostics (see review by Anderson & Avrett 1991). Standard reference models traced a smooth decline in temperature with increasing altitude 2 through the several hundred kilometer thick, radiation/convection controlled photosphere, a temperature minimum region bottoming out at 4400 K near 500 km, segueing into a 1500 km thick, 7000 K plateau in the mechanically heated chromosphere, and concluding with a sharp jump into the million degree corona at 2000 km (Vernazza, Avrett, & Loeser 1981). Disturbing that neatly layered view of the solar outer atmosphere, however, are infrared spectra of the carbon monoxide molecule. For one thing, strong lines of the 2143 cm 1 (4.7 lm) Dv ¼ 1 rotation-vibration bands of CO display very cool brightness temperatures (T B 3700 K) at the extreme edge of the solar disk, where the slanted line of sight probes into the low chromosphere (Noyes & Hall 1972; Ayres & Testerman 1981, hereafter AT81). For another, remarkable off-limb CO emissions protrude hundreds of kilometers into the chromosphere, an environment supposedly too hostile for molecules to exist (Solanki, Livingston, & Ayres 1994, hereafter SLA94). A straightforward, but somewhat controversial, proposal is that the low chromosphere is not hot at all but is instead permeated by COcooled clouds (Ayres 1981), 3 a COmosphere, if you will (Wiedemann et al. 1994). Subsequently, Carlsson & Stein (1995, 1997, hereafter C-S) invoked a purely dynamical process as an alternative explanation for cool gas at high altitudes: low-t rarefaction phases of large-amplitude acoustic waves passing through the low chromosphere, which ultimately shock and light up Ca ii K 2v grains at higher altitudes (see Rutten & Uitenbroek 1991 for a description of the phenomenon). In the Carlsson-Stein picture, the solar chromosphere is spatially and temporally intermittent, and the time-average thermal structure in the classical chromospheric layers is cool, not hot. In two recent papers, Kalkofen, Ulmschneider, & Avrett (1999, Does the Sun Have a Full-Time Chromosphere? ) and Kalkofen (2001, The Case against Cold, Dark Chromospheres ) have sharply criticized the Carlsson-Stein dynamical model and, by implication, have also called into question the existence of a cool part-time COmosphere, one possible consequence of the wave model. The controversy over the existence of cool gas in the low chromosphere bears on the question of how well the atmospheric stratification of our nearest stellar neighbor can be established by remote sensing. For if the solar atmosphere cannot be understood successfully, how can any other cos- 3 CO is an effective radiative coolant high in the atmosphere where its strong IR bands become transparent. As molecules begin to form in a cooling gas, they enhance the cooling, making more molecules, more cooling, and so forth, until the gas collapses to a relatively cold equilibrium in a molecular cooling catastrophe. The cold phase can be disrupted, however, by acoustic or magnetic heating of sufficient strength, yielding a complementary hot phase. The thermal bifurcation bistability mechanism proposed analytically by Ayres (1981) was later verified numerically by Anderson & Athay (1989).

2 FULL-TIME COmosphere? 1105 mic body be explored confidently by spectroscopic means? Furthermore, deriving accurate chromospheric models is at the heart of long-standing efforts to dissect plasma energy balance and ferret out elusive heating mechanisms (Vernazza et al. 1981; Anderson & Athay 1989, hereafter AA89). The controversy over the COmosphere focuses precisely on the high-density layers at the base of the chromosphere where small departures from radiative energy balance can signal large inputs of mechanical energy. This is exactly the regime of the solar atmosphere where kinetic control in the photosphere gives way to magnetic control in the corona the magnetic transition zone, a crucial site to seek unambiguous signatures of heating processes. This paper calls attention to a serious weakness in arguments presented by Kalkofen and collaborators, namely, the failure of uniformly hot chromospheric models to pass two key spectral tests based on the CO rovibrational bands. At the same time, the seeming contradiction between the existence of substantial amounts of cool gas well above the classical temperature minimum, and observations of ubiquitous warm ultraviolet line and continuum emission from the solar outer atmosphere, might not be a contradiction at all. 2. ATMOSPHERIC MODELING In their two papers, Kalkofen and collaborators presented numerous objections to the Carlsson-Stein model, mostly involving perceived failures of the radiation-hydro simulation to replicate other spectral diagnostics beyond its intended objective: plasma dynamics associated with Ca ii K grains. The authors then argue that because the C-S simulation is invalidated, hot layered models must be correct (because they successfully match the invalidating observations by design), and any cold regions responsible for the CO anomalies must be submerged in the photosphere itself, because there is no room in the chromosphere for them. Figure 1 attempts, in a cartoon way, to depict the differences between classical layered models and the new structure-based paradigm, of which the dynamics associated with K grains would be considered a key component. The many detailed criticisms by Kalkofen et al. of the C-S simulation with respect to traditional layered models could be addressed individually and specifically, but there is no need because the authors have ignored the fundamental philosophical distinction between an ab initio simulation, such as that of C-S, and semiempirical models, of E. H. Avrett and collaborators, for example Ab Initio Models An ab initio calculation begins with fundamental physics, modified by a series of assumptions to facilitate the numerics, and compares results with a target observation in an effort to test the simulated physical processes. It is very much a mechanism-based approach. In the case of the C-S study, the target observation was a detailed time sequence of Ca ii 3968 H-line spectra, which displayed a complex, quasi-repetitive combination of core profile shifts and brightness changes. The model itself was a one-dimensional radiation-hydrodynamics simulation, with self-consistent hydrogen and calcium ionization and cooling, driven by a deep-seated acoustic piston whose behavior was slaved to Doppler shifts measured in the same time series in a weak Fe i absorption in the H-line wing. The simulation successfully reproduced Doppler shifts and brightness changes in the higher-lying Ca ii core, with the conclusion that K grains must have an origin in atmospheric dynamics (rather than, say, a purely magnetic phenomenon). The model was never intended to be a complete description of the entire quiet chromosphere, which includes, in addition to K grains, magnetic elements of the supergranulation network, and the crucial canopy layer that derives from a tangled merger of network fields in the zone above the shock formation Fig. 1. Two cartoons of outer solar atmosphere, encompassing alternative views of key magnetic transition zone ( is the ratio of gas to magnetic pressure). Left: Classical layered paradigm. Right: More modern structured picture (implicitly also time-dependent). Diamonds indicate approximate formation altitudes for different species, UVc is the far-uv (1500 Å) continuum, IRc is the 4.7 lm thermal infrared continuum, l ¼ 1 refers to disk center, and l ¼ 0 is the extreme limb.

3 1106 AYRES Vol. 575 height of K grains (Giovanelli 1980; Solanki & Steiner 1990). Legitimate criticisms of an ab initio model concern how well it matches the target observation and whether good agreement is fortuitous because of overly restrictive assumptions. The idea behind such models is to test specific physical processes, not necessarily to devise a model-ofeverything. As far as describing the physical origin of K grains, the C-S dynamical simulation is unquestionably superior to one-dimensional static models, because, after all, acoustic disturbances are highly time-dependent. From that perspective, and given the excellent match to the Ca ii time series, the C-S model successfully accomplished its ab initio objective Semiempirical Models Semiempirical models are conceptually different. Here one begins with as many complementary observations as possible and attempts to conjure up a stratification of TðhÞ that satisfies all the diagnostics to the extent practical. The final model is, in a very real sense, a remapping of observed spectral brightness temperatures onto a thermal profile, although the NLTE synthesis by which the conversion is accomplished can be quite sophisticated (Vernazza, Avrett, & Loeser 1973, 1976, 1981, hereafter VAL). Once a universal temperature structure is established, it could then be used for subsidiary purposes, such as detailed calculations of radiative losses with altitude for comparisons with predictions of heating models (VAL). However, because semiempirical models are derived directly from observations, and are fundamentally a reexpression of those observations, the validity of such models must be held to a different standard than an ab initio simulation. In particular, if a semiempirical model claims to represent a universal thermal profile, then any spectral signature that is inconsistent with that profile must be considered a potential flaw of the model. Ideally, the conflicting diagnostic then would be reconciled in a new model that restored the desired universality. For example, the exploratory onedimensional homogenous average thermal models of the early 1970s were replaced by multicomponent models in the 1980s to reflect the fact that the solar surface is not a bland and featureless terrain but instead is composed of a wide diversity of structures, each possessing its own internal temperature stratification (VAL) The Infrared CO Tests Although current state-of-the-art, multicomponent, semiempirical models are crafted to match a remarkable collection of spectral diagnostics, there are at least two key tests such models are known to fail: (1) center-to-limb behavior of 4.7 lm CODv ¼ 1 fundamental rovibrational bands (AT81) and (2) off-limb emissions of the same species (SLA94). One might be tempted to dismiss the CO tests as unexplained hopefully insignificant anomalies, but the history of science teaches that oddities are oftentimes crucial signals that something is amiss in the conventional wisdom. By that measure, the failure of traditional single-component thermal profiles to fulfill the CO tests must be considered a potentially serious deficiency. It is important to note, in this regard, that just because a one-dimensional TðhÞ stratification successfully reproduces spatially average spectra of a particular diagnostic does not necessarily mean that the model is realistic or useful. One might argue that the importance of a model is to predict, for example, the correct amount of emission from a chromospheric species, so that ultimately one could estimate the amount of heat that must be deposited as a function of altitude in order to power the excess radiative cooling. It is not just the average emission that is important, however; it is also essential to know the spatial character of the sources on the surface. If the spatially average spectrum is dominated, say, by a sparsely distributed population of overheated bright points, any conclusions regarding the power source will be quite different than if the emission is smoothly spread over the surface. This is not a trivial point to establish by direct imaging, for two reasons: first, high spatial resolution spectral mapping of the solar surface, at 0>1 scales where much of the action is believed to occur, is technically challenging, and second, a distribution of very fine scale emission regions could appear to have a much more diffuse morphology in a diagnostic, such as Ca ii K, for which large scattering halos can develop because of horizontal transport effects. In the next section, the CO tests, and recent efforts to improve them, are discussed in more detail. 3. OBSERVATIONS The basis for the two CO tests, and key evidence for a cool COmosphere, are the center-to-limb behavior of CO Dv ¼ 1 bands and their off-limb emissions. As far as limb darkening of the CO 4.7 lm bands is concerned, the most useful data set is from the p-mode oscillation study of Ayres & Brault (1990), using the large 1 m Fourier transform spectrometer (FTS) on the McMath solar telescope (now McMath-Pierce) of the National Solar Observatory (NSO). The FTS has substantial advantages in terms of very high spectral resolution and signal-to-noise ratio (S/N), negligible scattered light, and broad frequency coverage compared with the latest generation of long-slit IR grating instruments. These advantages are crucial for center-to-limb work in the CO bands, where central depths of a wide range of narrow Dv ¼ 1 lines must be measured accurately at each l position. 4 Because infrared CO source functions scale roughly linearly with temperature, an error of only a few percent in line depths, due to under-resolving line profiles or presence of scattered light, can translate to an overestimate of hundreds of degrees in core brightness temperatures (which are a direct diagnostic of local kinetic temperatures; AT81). Therefore, the Ayres & Brault FTS center-to-limb measurements will define the first CO test. The second CO test involves off-limb emissions of the Dv ¼ 1 bands. Here the FTS has clear disadvantages. Because it can record only a single spatial point at a time and requires at least 40 s to accumulate a full interferogram, the FTS is poorly suited to document rapidly variable, spatially inhomogeneous phenomena over large fields of view. The off-limb CO emissions fall into that category by virtue of image shake and seeing fluctuations that would seriously hinder any attempt to trace the sharp continuum edge, say, 4 l cos, where h is the heliocentric angle measured radially from disk center. ¼ 0 (l ¼ 1) refers to disk center, and ¼ 90 (l ¼ 0) is the continuum edge.

4 No. 2, 2002 FULL-TIME COmosphere? 1107 by sequentially stepping an FTS aperture across the limb. 5 Long-slit stigmatic spectrograms, recorded in short exposures with a two-dimensional format camera system, is the preferred technique to explore translimb phenomena (Uitenbroek, Noyes, & Rabin 1994, hereafter UNR94). This study focuses on a series of translimb observations of CO bands obtained 1996 May 6 10 with the Infrared Imaging Spectrograph (IRIS) at the McMath-Pierce facility. It was clear and dry with good to moderate seeing for the entire week of the run. The Sun was relatively quiet during the period, which occurred near sunspot minimum. IRIS, commissioned in 1993, utilizes a Amber Engineering InSb camera, and the control system of the Near Infrared Magnetograph (Rabin 1994). The McMath- Pierce 1.5 m main telescope largest in the solar world is diffraction-limited at 0>8 at 4.7 lm, comparable to the seeing experienced during early morning hours under good observing conditions at Kitt Peak. Several groups have exploited IRIS for detailed studies of different aspects of the outer solar atmosphere seen in CO Dv ¼ 1 bands (UNR94; Ayres & Rabin 1996, hereafter AR96), including a fortuitous partial eclipse over Kitt Peak, where the lunar edge served as an external occulter to permit, in principle, 0>1 resolution at the limb, independent of seeing and the diffraction limit of the McMath-Pierce (Clark et al. 1995). To minimize surface scattering, the telescope mirrors were washed prior to the run. In addition, a cylindrical lens was removed from IRIS transfer optics that ordinarily compresses the stigmatic spectrum in the spatial direction to maximize field of view. The minifying lens introduces low-level distortions into images, however; and without it one obtains 2 times denser spatial sampling, an important consideration because the CO off-limb emissions are a comparatively subtle effect and finer sampling assists differential measurements of it. The theoretical resolving power of the large IR mosaic grating in second-order single pass is!=d! 1:1 10 5, but the apparent resolution in our earlier single-pass work (AR96) was significantly lower (with respect to FTS scans for which instrumental broadening and stray light are negligible). Suspicion was that scattered light was simulating a decrease in resolution. An effective way to control scattered light in a grating instrument is double-pass mode: two bounces off the disperser with an intermediate slit to chop wings and ghosts of the point-spread function after the first pass and diffuse scattered light monitored with the intermediate slit shuttered. Unfortunately, the internal slit allows only a single frequency to be recorded at a time, thereby negating the multiplex advantage of the two-dimensional format camera. In order to preserve spectral coverage, the Main spectrograph was operated in double pass with a broad slot replacing the narrow internal slit. In this setup, the singlepass line-spread function essentially is convolved with itself, thereby suppressing outer wings of the instrumental profile, noticeably improving apparent spectral resolution and reducing stray light compared with single pass (but not to the full extent possible in normal double-pass mode). 5 It should be noted, however, that discovery of CO off-limb emissions by W. Livingston, as reported by SLA94, was made in essentially that way: using a slow single-channel scanning system on the McMath-Pierce Main spectrograph, and stepping a parallel slit incrementally across the limb. The observation was successful largely due to the skill of the observer and superb atmospheric conditions during the measurements. In the 1996 run, translimb experiments were conducted in early morning hours when visible seeing was best. A whitelight scintillometer (Seykora 1993), operating on top of the McMath-Pierce, allowed a qualitative evaluation of atmospheric conditions during each translimb sequence. For the hour or so of best seeing each morning, a string of 1000 frames was recorded with a fixed slit normal to the visible limb. The integration time was 0.4 s, and the exposure cadence was 3 s (dictated by data transfer overhead). The objective was to persistently sample the translimb spectrum in hopes that a few occasions of excellent image stability and minimal atmospheric blurring would be captured. A 205 lm wide entrance slit collected as much light as possible without degrading the double-pass resolution (a 160 lm slit normally is used in single-pass work). A 1.2 cm 1 interval of spectrum near 2143 cm 1 was recorded, relatively free from terrestrial absorption and containing several CO Dv ¼ 1 transitions spanning a wide range of line strength. Sampling was cm 1 pixel 1 in the dispersion direction and 0>219 pixel 1 in the spatial direction. The field of view along the slit was slightly less than 1 0.An80 cm 1 bandpass cold filter inside the camera dewar isolated the second order and blocked broadband thermal noise from outside the designated spectral window. Instrumental profiles in the spectral and spatial directions were carefully determined by comparing disk-center spatially average IRIS spectra to the NSO FTS atlas (Wallace et al. 1996), and by evaluating, with respect to model predictions, apparent roll-offs of 4.7 lm continuum edges in translimb frames collected during periods of excellent seeing. The empirical instrumental profiles, which could be represented by Voigt functions, are crucial to ensure realistic comparisons between observed off-limb extensions of CO lines and model simulations. Translimb images were graded according to a limb sharpness test applied numerically to each frame (AR96). By that criterion, the 1 hr sequence on the morning of May 9 (beginning at 09:00 local time) was rated best. During that period, the sky was clear and the wind moderate; the airmass was 1.5. The slit was located just east of the geocentric north pole of the Sun, very close to radial. From the sequence of 1000 frames, the five best (in limb sharpness) were co-added after carefully registering the apparent continuum edges. Because of stochastic image drifts, ultimately corrected by limb guiders, the continuum edge in one frame might be displaced by several pixels from that in another. Combining several frames improves the S/N by increasing the effective exposure and averaging over any fixed pattern remaining after flat fielding, and allows an empirical assessment of noise levels due to photon counts and background statistics, and fluctuations of solar origin. In practice, each (already oversampled) image was expanded by a factor of 2 in the spatial direction and registered to the first by shifting an integral number of resampled pixels to an accuracy of 0>05. Prior to co-adding, intensities were normalized to an average disk spectrum in the range inside the measured continuum edge, after subtracting a low-level diffuse sky component accumulated in the range outside the continuum edge. The normalization suppresses telluric absorptions and equalizes intensities over the spectrum so that differential changes across the limb are emphasized. Translimb roll-offs of intensity in each wavenumber bin were determined by fitting a high-order polynomial to the

5 1108 AYRES Vol. 575 spatial profile, then interpolating the position where the normalized intensities fell to 50% of the on-disk value (i.e., the half-power point). Results of the procedure are illustrated in Figure 2. The strongest CO emissions reach about 0>7 beyond the continuum edge. The actual width of the limb is larger because of diffraction (even if seeing were perfect), but spatial displacements between, say, a line core frequency and a continuum frequency are measured as a differential effect and thus can be determined to a small fraction of an arcsecond. When comparing synthetic translimb spectral frames to observed off-limb extensions, the same normalization procedures and measurement methodology were applied to minimize systematic errors. Earlier efforts to measure the off-limb CO emissions in the 4.7 lm region include the following: 1. The discovery paper by Solanki et al. (1994), who did not publish a specific value, but an extension of 0>55 for the strong 3 2 R14 transition can be read off their Figure 2 (continuum half-power point to line half-power point). Fig. 2. Bottom: Spectrally resolved off-limb emissions in 2143 cm 1 region from the sum of five long-slit IRIS spectrograms. The slit runs from top to bottom, dispersion from left to right (as indicated by abscissa). The two-dimensional frame was normalized by dividing by a one-dimensional average on-disk spectrum (see text) to remove the influence of telluric absorptions and equalize intensities across the image. Each hump of emission projected against the dark sky background is an individual CO feature. Top: Shaded area outlined by dots indicates a trace of off-limb extensions (in arcseconds) of the spectrum point by point, measured at the 50% intensity level, where 0 refers to the continuum edge. Estimated photometric uncertainties, based on local standard deviations through the five-image set, are smaller than the symbol sizes. Extensions are less than the diffraction limit of the McMath-Pierce but are measured as a differential effect. Upper absorption spectrum (on a relative intensity scale from 0.0 to 1.0) illustrates appearance of the disk-center interval (Wallace et al. 1996). Prominent CO features are marked along the top of the panel: Larger fonts refer to 12 C 16 O, smaller fonts to 13 C 16 O (solar 13 C/ 12 C abundance ratio is only 1%). Notice that several of the weak absorptions on the disk become relatively much stronger in translimb regime. 2. Uitenbroek et al. (1994), who cited an extension of 0>5 for 3 2 R14, but a value closer to 0>7 is suggested by their Figure Clark et al. (1995), who reported 0>56 0>04 for the same line in their 0>1 resolution partial eclipse measurements, with no detectable CO emission beyond 1>1 above the IR continuum limb. 4. Ayres & Rabin (1996), who found an extension for the equally strong 2 1 R6 (see their Fig. 9) nearly identical to the Clark et al. result for 3 2 R14. The slightly smaller extensions (by 0>1) obtained in the previous work can be attributed to lower spectral resolution in those studies, all of which utilized the McMath-Pierce Main spectrograph in single-pass mode (see AR96, Fig. 11, for an illustration of the influence of spectral resolution on the off-limb emissions). 4. ANALYSIS Simulations of off-limb CO emissions were carried out using the modeling approach described by AR96. Key improvements in the present work are better knowledge of instrumental spatial and spectral smearing functions, and higher quality of the observations themselves (owing to both excellent conditions during the 1996 May run, as well as use of the double-pass mode with clean mirrors). Figure 3 illustrates the two-dimensional geometry of the simulated inhomogeneous solar atmosphere. The radiation transport was solved along one-dimensional rays, as depicted in the figure. LTE formation was assumed for the Dv ¼ 1 bands as well as the background continuum (dominated by H f f ), an excellent approximation in both cases (Ayres & Wiedemann 1989; Uitenbroek 2000b). Figure 4 depicts the range of thermal models used in the over-the-limb simulations. VAL C 0 is the standard reference model described by Maltby et al. (1986; with heritage of the VAL series). COOL 0 and COOL 1 are cool cloud models designed to reproduce center-to-limb behavior of CO lines under different assumptions concerning surface mixing fractions of the cool component with respect to a warm background atmosphere defined by VAL C 0 (see AR96). COOL 0 is appropriate if the cool component dominates spatially, while the more extreme thermal profile of COOL 1 is appropriate if it is only a minor constituent. Note that both COmosphere models have transitions to hotter temperatures at about 1000 km, to simulate the presence of the magnetic canopy in the middle chromosphere (see SLA94). The hot, molecule-free canopy would set a natural upper boundary for any translimb CO emissions. But if cold material persisted beyond that altitude, say through a gap in the canopy, the natural outward hydrostatic decrease in density would prevent even the strongest CO lines from achieving significant tangential optical depths. That in itself would render molecular gas difficult to detect above about 1000 km. The jumble of lighter-shaded temperature distributions labeled C-S represent 20 temporal snapshots from a segment of the Carlsson-Stein (1997) radiation-hydro simulation (kindly provided by M. Carlsson). The models document the upward propagation of an acoustic wave train that grows in amplitude and ultimately shocks above 800 km. These particular time slices represent a complete cycle of a relatively strong disturbance, showing well-devel-

6 No. 2, 2002 FULL-TIME COmosphere? 1109 Fig. 3. Cartoon depiction of two-dimensional geometry used to simulate solar atmospheric inhomogeneities on disk and over the limb. Individual TðhÞ models were arrayed in radial columns occupying a specific horizontal footprint (usually 1 Mm = 1000 km) in a pattern repeating across the surface. Formal solution of the radiation transport equation was obtained along a series of one-dimensional sightlines through the periodic structure, as indicated by rays in the diagram. Fig. 4. Schematic illustration of solar models used to simulate effects of atmospheric inhomogeneities on disk-center and translimb spectra. Notice that the cool phases of the C-S time slices in the low chromosphere ( km) trace out a lower temperature envelope similar to that defined by the COOL 0 and COOL 1 test models. oped cool phases and pronounced hot zones. Note, however, that the mid- and deep photospheres of the snapshots are relatively unaffected, owing to large densities and strong radiative damping at low altitudes. Also note that thermal profiles of the theoretical models are flatter than semiempirical VAL C 0 in the upper photosphere (h km). That is a consequence of a computationally expedient simplification in the radiative energy budget describing the deeper near-equilibrium layers of the C-S model: only continuum radiation transport was treated, ignoring the complex line blanketing, with its backwarming and surface cooling, which otherwise would steepen the photospheric temperature gradient relative to the continuum-only case. Figures 5a 5d depict disk-center and translimb simulations conducted with thermal models illustrated in the previous figure. Figure 5a is for the VAL C 0 reference model, uniformly distributed over the hypothetical solar surface. The left-hand portion of the figure contains three simulated long-slit spectrograms, analogous to that shown in Figure 2. The lower segment illustrates the appearance at disk center, here a simple absorption spectrum (light shading indicates higher intensities; dark shading indicates lower intensities), featureless along the slit because the input model is spatially homogeneous. The middle panel depicts the behavior at the extreme limb, at 4 times spatial magnification compared with the disk-center scene. Note the weak off-limb extensions of strong CO lines (the dark sky off limb has been rendered white in this visualization to highlight fine structure in the translimb regime). In the lower and middle images, the frames are displayed at full numerical resolution in space (50 km 0>07) and frequency (0.005 cm km s 1 ; turbulent broadening in the models is t 1:5 2kms 1 ). The uppermost image illustrates convolution of the resolved simulation with empirical spatial and spectral line-spread functions deduced for IRIS, normalizing the spectra in the same way as the observed translimb frames in Figure 2. Here the dark sky has been retained. Two representative Dv ¼ 1 transitions are marked: strong low-excitation 2 1 R6 and weak high-excitation 7 6 R67. Contribution functions for these features are illustrated in Ayres & Brault (1990) for VAL C 0 and a prototype cold COmosphere model based on CO surface-cooling simulations published by AA89. VAL C 0 exhibits some off-limb CO emission because the 2143 cm 1 continuum edge corresponds to an altitude (400 km) on the lower side of the classical T min, and modest amounts of CO survive even in the warm model for several scale heights above C tang ¼ 1. The upper right-hand panel compares predicted centerto-limb behaviors of the two reference CO line cores with observed values from the Ayres & Brault study. The VAL

7 1110 AYRES Vol. 575 Fig. 5a Fig. 5. (a) Results of over-the-limb radiative transfer simulation for uniform atmosphere consisting solely of VAL C 0 reference model. The synthetic spectral images have same geometry as Fig. 2; slit direction is from top to bottom, and dispersion direction is from left to right. (b) Periodic inhomogeneity consisting of 1 Mm of COOL 1 plus 4 Mm of VAL C 0. In center-to-limb panel (upper right), thick error bars under observed core T B values at l ¼ 1 and dots limbward of l ¼ 0:2 indicate full range of calculated brightness temperatures for inhomogeneous scene at numerical resolution. Contrast between darkest and brightest areas in 2 1 R6 at disk center is 1500 K, although much smaller in 7 6 R67. Latter forms deeper in atmosphere and has little contribution from the high-lying cool clouds. (c) Periodic inhomogeneity consisting of 4 Mm of COOL 0 plus 1 Mm of VAL C 0. Notice that T B spatial contrast in 2 1 R6 at l ¼ 1 is much reduced compared with previous scenario. (d ) Inhomogeneous scenario constructed using 20 temporal snapshots from Carlsson-Stein radiationhydro simulation, randomly distributed spatially in 1 Mm segments within a 20 Mm swath of surface, which was then repeated over computational domain. Height-dependent radial Doppler velocities of C-S model were incorporated in the line formation. C 0 reproduces the center-to-limb behavior of weak, deepseated 7 6 R67, indicating that the low-altitude ( km) temperature profile satisfies the first CO test; but is too hot in the upper photosphere to match strong, higher lying 2 1 R6 at either disk center or extreme limb. Indeed, it predicts that 2 1 R6 should display a chromospheric emission reversal limbward of l ¼ 0:1. The lower right-hand panel compares predicted and observed translimb extensions in the 2143 cm 1 interval. The spatial and spectral smearing, and normalization methodology, tend to accentuate the off-limb extensions of the reference model more than might be expected from the full resolution roll-off, but the traces clearly fall short of the observed behavior. Thus, the reference model fares poorly in both CO tests, at least for strong Dv ¼ 1 lines that probe the altitude range above 500 km. Figure 5b illustrates a spatially inhomogeneous model consisting of 20% COOL 1 in an 80% background of warm VAL C 0, arranged in a periodic 5 Mm pattern across the surface. Such a model might be invoked to explain the COmosphere as a spatially intermittent phenomenon, still within the context of static one-dimensional stratifications. The ultracold fingers of COOL 1 shadow the otherwise dominant warm components near the limb in strong CO lines, leading to a center-to-limb behavior in better accord with observations. At disk center, small-scale dark spots from COOL 1 counterbalance warmer core temperatures from VAL C 0, mimicking the observed T B ðl ¼ 1Þ. However, at 1 Mm (1>4) sizes and 1500 K cooler than their surroundings, such cold spots would be readily visible in existing CO thermal maps, but nothing so extreme is seen. 6 Furthermore, even though COOL 1 has cold gas reaching 500 km into the low chromosphere, the simulated translimb emissions still fall short of the empirical traces. Evidently, the sharp reduction in tangential opacity of strong CO lines, 6 Quiet-Sun spatial histograms of CO line core brightness temperatures, in strong transitions like 2 1 R6, are approximately Gaussian with a FWHM of only 150 K, with no obvious low-t tail (AR96; Ayres 2000). Uitenbroek (2000a) reports detecting occasional small-scale CO dark spots at disk center, under exceptional seeing conditions, but these are relatively rare and the apparent DT is only 400 K.

8 No. 2, 2002 FULL-TIME COmosphere? 1111 Fig. 5b owing to intermittence of the cold structures, is sufficient to weaken the off-limb extensions in degraded translimb spectra, despite full-resolution profiles extending 0>8 beyond the continuum edge. The inhomogeneous model with smallscale cold spots represents an improvement over homogeneous VAL C 0 as far as the first CO test is concerned but still is not a good match to the second (nor to the spatial morphology of disk center CO surface maps). Figure 5c depicts a second inhomogeneous model, this time with 80% COOL 0 and 20% VAL C 0, again arrayed in a pattern with 5 Mm repetition period. The disk-center scene is dominated by the majority cool component, not so cold as the dark spots of COOL 1, and shows intermittent bright points contributed by VAL C 0, a few hundred degrees warmer than the cooler background. That morphology is consistent with the overall bland appearance of diskcenter CO thermal maps, in which apparent mild thermal fluctuations are dominated by p-mode oscillations, and only occasional persistent small-scale bright spots are seen (related to magnetic fragments in the network; AR96; Uitenbroek 2000a). This is a crucial, somewhat paradoxical, aspect of the CO problem: If one does see a sprinkling of small-scale very dark (i.e., cold) points, then the cool clouds must be only a minor component of the low chromosphere and thus not very important; but if one does not see distinct CO dark spots, then the cool clouds must be pervasive (i.e., they dominate the scene and are thus not separately distinct) and therefore a key constituent of the lower chromosphere. In the limb image of Figure 5c, the warm columns become progressively more compressed toward the continuum edge by cool-zone shadowing, but their influence on center-tolimb behavior or translimb emissions is minor since the cool component completely dominates. Above the limb, strong CO lines display flat-topped profiles with square sides indicating optical depth saturation. Truncation of the translimb emissions is controlled by the (somewhat lower) altitude where COOL 0 rejoins the chromospheric thermal profile of VAL C 0. This version of the inhomogeneous model accurately reproduces center-to-limb behavior of strong CO lines and their translimb emissions, thus passing both CO tests. Of course, COOL 0 was designed by AR96 to do precisely that, in conjunction with 20% coverage by the warm component; but the point here is that the class of models that satisfy both CO tests must be quite different from the standard reference model in the km altitude range. At the same time, the simple two-component inhomogeneous model shares important similarities with the reference temperature distribution: the same TðhÞ profile in middle and deep photosphere and pervasive hot gas at canopy altitudes. The important difference is the presence of cool clouds in much of the low chromosphere. The final figure in the sequence, Figure 5d, is based on the Carlsson-Stein dynamical model. The 20 slices were arrayed

9 1112 AYRES Vol. 575 Fig. 5c in 1 Mm segments 7 randomly over a 20 Mm swath, which was then repeated as necessary to cover the computational domain. The pattern simulates an instantaneous average over a tangential cut through a collection of oscillating spatial points at random phases of their motion. The projected height-dependent Doppler shifts of each column were fully taken into account in the line formation ray solutions. Because the computed velocities in the one-dimensional C-S model are purely radial, shifts are most pronounced at disk center and minimal near the limb. Previously, Uitenbroek (2000b) described the temporal influence of Carlsson-Stein time slices on strong and weak CO transitions at disk center (including NLTE effects, although he verified the essentially LTE nature of the molecular excitation). The particular time series represented here is a relatively dynamic one, like that used by Uitenbroek, which not only has a large impact on the chromospheric layers but also produces significant brightness temperature fluctuations in cores of strong CO lines at l ¼ 1. Calculated time-dependent T B variations are much larger than seen in high-quality CO movies (Uitenbroek 2000a; Ayres 2000), an effect that Uitenbroek attributes to chemical disequilibrium in the real dynamic atmosphere. Furthermore, even though the Carlsson-Stein model has, in a time-average sense, significant amounts of cool material above the classical temperature minimum, off-limb CO emissions experience the same low-altitude truncation as in intermittent cold component models. Simulations with a quieter slice of the dynamical model, corresponding to something much less intense than a bright K grain, show substantially smaller CO brightness fluctuations at disk center but still a low-altitude cutoff of translimb emissions. Nevertheless, for an ab initio model that was not designed with CO in mind, the C-S simulation does surprisingly well on both CO tests, keeping in mind that the center-to-limb comparison is strongly influenced by the continuum-only radiative energy balance in the upper photosphere. Significantly better agreement on that account could be obtained by introducing a more realistic treatment of line blanketing. 8 My conclusion is that the C-S simulations which Kalkofen et al. argue are too cool in the low chromosphere are, in fact, not cold enough. A similar conclusion was reached by Uitenbroek (2000b) in his study of the influence of C-S time slices on disk center CO spectra. A plausible explanation is that the dynamical model does not include CO surface cooling, which is known to be a potent force in latetype stellar atmospheres in general (Johnson 1973) and the Sun in particular (Ayres 1981; AA89). CO cooling at midal- 7 Approximately the size of K bright grains observed in high spatial resolution Ca ii filtergrams (Rutten & Uitenbroek 1991). 8 This would be a cosmetic improvement, only, because ordinary lineblanketing is not very important in the key km range of the dynamical simulation, particularly when NLTE effects are considered.

10 No. 2, 2002 FULL-TIME COmosphere? 1113 Fig. 5d titudes in the dynamical model, where strong 4.7 lm rovibrational bands become transparent, might serve as a radiative damping force limiting growth of the acoustic waves, driving temperatures lower in the dynamic medium, and pushing shock formation heights outward. Cooling effects would be most pronounced for weaker wave trains where the H continuum, alone, would force an equilibrium near 4900 K (Ayres 1981), but the molecular RE boundary temperature could be below 3000 K (AA89). Incorporating CO cooling in the simulation would be relatively straightforward (see Ayres 1981), except that time-dependent gas phase chemistry is likely important for CO formation and destruction (AR96; Uitenbroek 2000a, 2000b) but is more difficult to treat than an instantaneous chemical equilibrium. 5. DISCUSSION In addition to undermining the C-S dynamical model, in order to negate one explanation for cool gas above the classical T min, Kalkofen et al. further argue that cold gas cannot even exist in the low chromosphere because SOHO Solar Ultraviolet Measurement of Emitted Radiation (SUMER) ultraviolet spectral images (e.g., Carlsson, Judge, & Wilhelm 1997; Ayres 2000) show persistent warm emission in chromospheric lines everywhere, at all times. They conclude, The type of chromospheric model advocated in this paper requires the strong infrared lines of CO to be formed in the upper photosphere and the temperature minimum region and is incompatible with models in which the CO lines form at chromospheric heights. 9 However, invalidating one possible explanation for a phenomenon (cold phases of the C-S model to explain COmospheric behavior of IR CO bands) does not invalidate the original observed phenomenon itself. As solar oscillation pioneer Robert Leighton once said: If it does happen, it can happen! The Carlsson-Stein model might well be incomplete in some respects, but the COmosphere has an independent basis in observations, specifically, the off-limb emissions of CO. What could be more emphatic evidence that molecular gas must exist well up into the altitude range usually considered to define the low chromosphere? Furthermore, arguing that ubiquitous UV emission seen in SUMER images is evidence against existence of the COmosphere is like citing pervasive X-ray emission from the corona as evidence against existence of an underlying cool photosphere (which is invisible at 1 kev). Far-UV emissions recorded by SUMER arise mostly in the warm canopy zone. The COmosphere exists beneath the optically 9 Perhaps the whole disagreement is merely semantics. Physically, the cool cloud model only requires that over significant areas of the surface, the upper photosphere extend several hundred kilometers higher than in conventional models, and T min is 10 3 K cooler. A chromosphere is still present but sets in at higher altitudes.

11 1114 AYRES Vol. 575 Fig. 6. Comparison of similar stretches of spectra in visible region (left: NSO FTS atlas) and thermal infrared (right: from shuttle flight of ATMOS FTS instrument), on a brightness temperature scale to remove intensity bias described in text. Terrestrial absorptions were removed in the visible atlas by comparing observations at different air masses and were negligible in the space-borne FTS measurements, an important consideration because otherwise the solar thermal IR spectrum would be totally dominated by telluric contamination. thick Å emission continuum, so it would not be expected to be accessible to SUMER in the first place. 10 In the visible, the continuum opacity is small, and the entire low chromosphere and upper photosphere are, in principle, accessible to view. The only diagnostics that are optically thick at those altitudes are resonance lines of abundant species, such as Ca ii, Nai, Mgi, and so forth. These are all strong scattering lines, however, so photons emitted by hot regions, where collisional production of radiation is efficient, can scatter freely either vertically or horizontally through colder regions where thermal emission is reduced severely. Thus, cool clouds having minimal internal UV thermal emission need not be dark but could be lit up by adjacent hot regions (such as bright points of the supergranulation network or the K grains themselves, shining back on the lower atmosphere). This is the bedevilment of NLTE effects: nonlocality of photon scattering can make the local source function appear to be much higher than the local thermal excitation possibly could support and cause one to infer a higher temperature than truly is present. Thus, the most reliable diagnostics of the low chromosphere are species that not only become opaque in those 10 At any vertical transition between hot material on the topside and colder material beneath, ionized gas will recombine and strongly boost the opacity of important neutral absorbers in the UV: Mg i, Al i, and especially Si i. Ci is also an important UV absorber but will be depleted, ironically enough, by CO formation. layers but also experience minimal scattering effects. The best example is CO and its Dv ¼ 1 bands. Other possibilities are few in number and generally suffer from one or more difficulties. The submillimeter f f continuum, for example, cannot be observed with high spatial resolution, intensities are difficult to calibrate, and heights of formation are tricky to assign given the exponential sensitivity of the ¼ 1 level to temperature via the electron density when hydrogen is partially ionized. One might be tempted to ignore the CO tests because the Dv ¼ 1 bands could be viewed as a somewhat unorthodox diagnostic, stuck as they are in the relatively unexplored spectral backwater of the long-wavelength infrared. But succumbing to that temptation would be a mistake. Figure 6 depicts comparable stretches of the visible region (left; Wallace, Hinkle, & Livingston 1998) and thermal infrared (right; Farmer, Norton, & Geller 1989). Spectra are displayed on a brightness temperature scale to avoid the intensity bias due to the much greater sensitivity of the Planck function to temperature in the blue than infrared. 11 In the visible segment, prominent Fraunhofer lines are marked. Note the great strength of the Ca ii doublet compared with other major absorption features. Nevertheless, the Ca ii lines are only minor contributors to the overall 11 The effect makes a visible absorption line appear stronger deeper in intensity than an infrared line formed in exactly the same atmospheric layers.

12 No. 2, 2002 FULL-TIME COmosphere? 1115 spectrum in that interval. Furthermore, many of the narrow features in the visible region are scattering lines that appear stronger (lower core brightness temperatures) than they would in LTE. In contrast, broad stretches of the thermal infrared are completely dominated by the CO Dv ¼ 1 bands. Thus, CO is not a spectral lightweight to be casually dismissed. A final fallacy of the Kalkofen (2001) paper is stated in his abstract: The same conclusion [the solar chromosphere...is never cold and dark] applies for stellar chromospheres. Even if the author is correct in the case of the Sun and I hope I have provided compelling evidence that he is not extending such a sweeping generalization to other late-type stars is unfounded. There are examples, such as the red giant Arcturus ( Boo; K1 III), where very cold (1000 K) gas sits in close proximity to hotter chromospheric material (diagnosed by far-uv fourth-positive bands of CO radiatively pumped by the strong O i 1305 emission multiplet), while the stellar transition zone (T 10 5 K) apparently lies beneath the cool absorber in which the fluoresced CO bands arise: C iv 1550 is seen longward of the Si i 1525 edge, but no hot lines are seen shortward (Ayres 2000). This topsy-turvy atmospheric arrangement is far from what anyone would dare suggest for the Sun. There is, however, one statement by Kalkofen and collaborators with which this author can agree: This conflict can be resolved only by further high-resolution observations and numerical simulations of a dynamical atmosphere that includes the formation of the CO lines in detail. This work was supported by grant AST from the National Science Foundation. I thank D. Rabin, C. Plymate, and D. Jaksha for their help with the observations at the McMath-Pierce. Anderson, L. S., & Athay, R. G. 1989, ApJ, 346, 1010 (AA89) Anderson, L. S., & Avrett, E. H. 1991, in Solar Interior and Atmosphere, ed. A. N. Cox, W. C. Livinston, & M. S. Matthews (Tucson: Univ. Arizona Press), 670 Ayres, T. R. 1981, ApJ, 244, , Sol. Phys., 193, 273 Ayres, T. R., & Brault, J. W. 1990, ApJ, 363, 705 Ayres, T. R., & Rabin, D. 1996, ApJ, 460, 1042 (AR96) Ayres, T. R., & Testerman, L. 1981, ApJ, 245, 1124 (AT81) Ayres, T. R., & Wiedemann, G. 1989, ApJ, 338, 1033 Carlsson, M., Judge, P. G., & Wilhelm, K. 1997, ApJ, 486, L63 Carlsson, M., & Stein, R. F. 1995, ApJ, 440, L , ApJ, 481, 500 Clark, T. A., Lindsey, C. A., Rabin, D. M., & Livingston, W. C. 1995, in Infrared Tools for Solar Astrophysics: What s Next?, ed. J. Kuhn & M. Penn (Singapore: World Scientific), 133 Farmer, C. B., Norton, R. H., & Geller, M. 1989, A High-Resolution Atlas of the Infrared Spectrum of the Sun and Earth Atmosphere from Space: A Compilation of ATMOS Spectra of the Region from 650 to 4800 cm 1 ( lm) (Washington: NASA) Giovanelli, R. G. 1980, Sol. Phys., 68, 49 Johnson, H. R. 1973, ApJ, 180, 81 Kalkofen, W. 2001, ApJ, 557, 376 REFERENCES Kalkofen, W., Ulmschneider, P., & Avrett, E. H. 1999, ApJ, 521, L141 Maltby, P., Avrett, E. H., Carlsson, M., Kjeldseth-Moe, O., Kurucz, R. L., & Loeser, R. 1986, ApJ, 306, 284 Noyes, R. W., & Hall, D. N. B. 1972, BAAS, 4, 389 Rabin, D. M. 1994, in IAU Symp. 154, Infrared Solar Physics, ed. D. M. Rabin, J. T. Jefferies, & C. Lindsey (Dordrecht: Kluwer), 449 Rutten, R. J., & Uitenbroek, H. 1991, Sol. Phys., 134, 15 Seykora, E. J. 1993, Sol. Phys., 145, 389 Solanki, S. K., Livingston, W., & Ayres, T. 1994, Science, 263, 64 (SLA94) Solanki, S. K., & Steiner, O. 1990, A&A, 234, 519 Uitenbroek, H. 2000a, ApJ, 531, b, ApJ, 536, 481 Uitenbroek, H., Noyes, R. W., & Rabin, D. 1994, ApJ, 432, L67 (UNR94) Vernazza, J. E., Avrett, E. H., & Loeser, R. 1973, ApJ, 184, , ApJS, 30, , ApJS, 45, 635 Wallace, L., Hinkle, K., & Livingston, W. 1998, An Atlas of the Spectrum of the Solar Photosphere from 13,500 to 28,000 cm 1 ( Å) (NSO Tech. Rep ; Tucson: National Solar Obs.) Wallace, L., Livingston, W., Hinkle, K., & Bernath, P. 1996, ApJS, 106, 165 Wiedemann, G. R., Ayres, T. R., Jennings, D. E., & Saar, S. H. 1994, ApJ, 423, 806