Lower Solar Chromosphere Research Articles

Observations of pores and surrounding regions with CO 4.66 μm lines by BBSO/CYRA

Context. Solar observations of carbon monoxide (CO) indicate the existence of lower-temperature gas in the lower solar chromosphere. We present an observation of pores, and quiet-Sun, and network magnetic field regions with CO 4.66 μm lines by the Cryogenic Infrared Spectrograph (CYRA) at Big Bear Solar Observatory. Aims. We used the strong CO lines at around 4.66 μm to understand the properties of the thermal structures of lower solar atmosphere in different solar features with various magnetic field strengths. Methods. Different observations with different instruments were included: CO 4.66 μm imaging spectroscopy by CYRA, Atmospheric Imaging Assembly (AIA) 1700 Å images, Helioseismic and Magnetic Imager (HMI) continuum images, line-of-sight (LOS) magnetograms, and vector magnetograms. The data from 3D radiation magnetohydrodynamic (MHD) simulation with the Bifrost code are also employed for the first time to be compared with the observation. We used the Rybicki-Hummer (RH) code to synthesize the CO line profiles in the network regions. Results. The CO 3-2 R14 line center intensity changes to be either enhanced or diminished with increasing magnetic field strength, which should be caused by different heating effects in magnetic flux tubes with different sizes. We find several “cold bubbles” in the CO 3-2 R14 line center intensity images, which can be classified into two types. One type is located in the quiet-Sun regions without magnetic fields. The other type, which has rarely been reported in the past, is near or surrounded by magnetic fields. Notably, some are located at the edge of the magnetic network. The two kinds of cold bubbles and the relationship between cold bubble intensities and network magnetic field strength are both reproduced by the 3D MHD simulation with the Bifrost and RH codes. The simulation also shows that there is a cold plasma blob near the network magnetic fields, causing the observed cold bubbles seen in the CO 3-2 R14 line center image. Conclusions. Our observation and simulation illustrate that the magnetic field plays a vital role in the generation of some CO cold bubbles.

Plausibility of ultraviolet burst generation in the low solar chromosphere

Context. Ultraviolet (UV) bursts and Ellerman bombs (EBs) are small-scale magnetic reconnection events taking place in the highly stratified, low solar atmosphere. The plasma density, reconnection mechanisms, radiative cooling and transfer processes clearly differ from one layer of the atmosphere to the next. In particular, EBs are believed to form in the upper photosphere or the low chromosphere. It is still not clear whether UV bursts have to be generated at a higher atmospheric layer than the EBs or whether both UV bursts and EBs can occur in the low chromosphere. Aims. We numerically studied the low β magnetic reconnection process around the solar temperature minimum region (TMR) by including more realistic physical diffusions and radiative cooling models. We aim to find out whether UV bursts may occur in the low chromosphere and to investigate the dominant mechanism that accounts for heating in the UV burst in the chromosphere. Methods. We used the single-fluid magnetohydrodynamic (MHD) code NIRVANA to perform the simulations. The time-dependent ionization degrees of hydrogen and helium are included in the code, which lead to a more realistic magnetic diffusion caused by electron-neutral collision and ambipolar diffusion. A more realistic radiative cooling model is also included in the simulations. The initial mass density and temperature are 1.66057 × 10−6 kg m−3 and 4400 K, respectively, values that are typical for the plasma environment around TMR. Results. Our results in high resolution indicate that the plasmas in the reconnection region are heated up to more than 20 000 K if the reconnecting magnetic field is as strong as 500 G, which suggests that UV bursts can be generated in the dense low chromosphere. The dominant mechanism for producing the UV burst in the low chromosphere is heating, as a result of the local compression in the reconnection process. The thermal energy occurring in the reconnection region rapidly increases after the turbulent reconnection mediated by plasmoids is invoked. The average power density of the generated thermal energy in the reconnection region can reach over 1000 erg cm−3 s−1, which is comparable to the average power density accounting for a UV burst. With the strength of the reconnecting magnetic field exceeding 900 G, the width of the synthesized Si IV 1394 Å line profile with multiple peaks can reach up to 100 km s−1, which is consistent with observations.

Onset of Secondary Instabilities and Plasma Heating during Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Atmosphere

Abstract We numerically study magnetic reconnection on different spatial scales and at different heights in the weakly ionized plasma of the low solar atmosphere (around 300–800 km above the solar surface) within a reactive 2.5D multifluid plasma–neutral model. We consider a strongly magnetized plasma (β ∼ 6%) evolving from a force-free magnetic configuration and perturbed to initialize formation of a reconnection current sheet. On large scales, the resulting current sheets are observed to undergo a secondary “plasmoid” instability. A series of simulations at different scales demonstrates a cascading current sheet formation process that terminates for current sheets with width of 2 m and length of ∼100 m, corresponding to the critical current sheet aspect ratio of ∼50. We also observe that the plasmoid instability is the primary physical mechanism accelerating the magnetic reconnection in this plasma parameter regime. After plasmoid instabilities appear, the reconnection rate sharply increases to a value of ∼0.035, observed to be independent of the Lundquist number. These characteristics are very similar to magnetic reconnection in fully ionized plasmas. In this low-β guide-field reconnection regime, both the recombination and collisionless effects are observed to have a small contribution to the reconnection rate. The simulations show that it is difficult to heat the dense weakly ionized photospheric plasmas to above 2 × 104 K during the magnetic reconnection process. However, the plasmas in the low solar chromosphere can be heated above 3 × 104 K with reconnection magnetic fields of 500 G or stronger.

Magnetic reconnection in the low solar chromosphere with a more realistic radiative cooling model

Magnetic reconnection is the most likely mechanism responsible for the high temperature events that are observed in strongly magnetized locations around the temperature minimum in the low solar chromosphere. This work improves upon our previous work [Ni et al., Astrophys. J. 852, 95 (2018)] by using a more realistic radiative cooling model computed from the OPACITY project and the CHIANTI database. We find that the rate of ionization of the neutral component of the plasma is still faster than recombination within the current sheet region. For low β plasmas, the ionized and neutral fluid flows are well-coupled throughout the reconnection region resembling the single-fluid Sweet-Parker model dynamics. Decoupling of the ion and neutral inflows appears in the higher β case with β0=1.46, which leads to a reconnection rate about three times faster than the rate predicted by the Sweet-Parker model. In all cases, the plasma temperature increases with time inside the current sheet, and the maximum value is above 2×104 K when the reconnection magnetic field strength is greater than 500 G. While the more realistic radiative cooling model does not result in qualitative changes of the characteristics of magnetic reconnection, it is necessary for studying the variations of the plasma temperature and ionization fraction inside current sheets in strongly magnetized regions of the low solar atmosphere. It is also important for studying energy conversion during the magnetic reconnection process when the hydrogen-dominated plasma approaches full ionization.

Magnetic Reconnection in Strongly Magnetized Regions of the Low Solar Chromosphere

Abstract Magnetic reconnection in strongly magnetized regions around the temperature minimum region of the low solar atmosphere is studied by employing MHD-based simulations of a partially ionized plasma within a reactive 2.5D multi-fluid model. It is shown that in the absence of magnetic nulls in a low β plasma, the ionized and neutral fluid flows are well-coupled throughout the reconnection region. However, non-equilibrium ionization–recombination dynamics play a critical role in determining the structure of the reconnection region, leading to much lower temperature increases and a faster magnetic reconnection rate as compared to simulations that assume plasma to be in ionization–recombination equilibrium. The rate of ionization of the neutral component of the plasma is always faster than recombination within the current sheet region even when the initial plasma β is as high as . When the reconnecting magnetic field is in excess of a kilogauss and the plasma β is lower than 0.0145, the initially weakly ionized plasmas can become fully ionized within the reconnection region and the current sheet can be strongly heated to above K, even as most of the collisionally dissipated magnetic energy is radiated away. The Hall effect increases the reconnection rate slightly, but in the absence of magnetic nulls it does not result in significant asymmetries or change the characteristics of the reconnection current sheet down to meter scales.

Slender Ca ii H Fibrils Mapping Magnetic Fields in the Low Solar Chromosphere

Abstract A dense forest of slender bright fibrils near a small solar active region is seen in high-quality narrowband Ca ii H images from the SuFI instrument onboard the Sunrise balloon-borne solar observatory. The orientation of these slender Ca ii H fibrils (SCF) overlaps with the magnetic field configuration in the low solar chromosphere derived by magnetostatic extrapolation of the photospheric field observed with Sunrise/IMaX and SDO/HMI. In addition, many observed SCFs are qualitatively aligned with small-scale loops computed from a novel inversion approach based on best-fit numerical MHD simulation. Such loops are organized in canopy-like arches over quiet areas that differ in height depending on the field strength near their roots.

Transverse Oscillations in Slender Ca ii H Fibrils Observed with Sunrise/SuFI

Abstract We present observations of transverse oscillations in slender Ca ii H fibrils (SCFs) in the lower solar chromosphere. We use a 1 hr long time series of high- (spatial and temporal-) resolution seeing-free observations in a 1.1 Å wide passband covering the line core of Ca ii H 3969 Å from the second flight of the Sunrise balloon-borne solar observatory. The entire field of view, spanning the polarity inversion line of an active region close to the solar disk center, is covered with bright, thin, and very dynamic fine structures. Our analysis reveals the prevalence of transverse waves in SCFs with median amplitudes and periods on the order of 2.4 ± 0.8 km s−1 and 83 ± 29 s, respectively (with standard deviations given as uncertainties). We find that the transverse waves often propagate along (parts of) the SCFs with median phase speeds of 9 ± 14 km s−1. While the propagation is only in one direction along the axis in some of the SCFs, propagating waves in both directions, as well as standing waves are also observed. The transverse oscillations are likely Alfvénic and are thought to be representative of magnetohydrodynamic kink waves. The wave propagation suggests that the rapid high-frequency transverse waves, often produced in the lower photosphere, can penetrate into the chromosphere with an estimated energy flux of ≈15 kW m−2. Characteristics of these waves differ from those reported for other fibrillar structures, which, however, were observed mainly in the upper solar chromosphere.

Morphological Properties of Slender Ca H Fibrils Observed by Sunrise II

Abstract We use seeing-free high spatial resolution Ca ii H data obtained by the Sunrise observatory to determine properties of slender fibrils in the lower solar chromosphere. In this work we use intensity images taken with the SuFI instrument in the Ca ii H line during the second scientific flight of the Sunrise observatory to identify and track elongated bright structures. After identification, we analyze theses structures to extract their morphological properties. We identify 598 slender Ca ii H fibrils (SCFs) with an average width of around 180 km, length between 500 and 4000 km, average lifetime of ≈400 s, and average curvature of 0.002 arcsec−1. The maximum lifetime of the SCFs within our time series of 57 minutes is ≈2000 s. We discuss similarities and differences of the SCFs with other small-scale, chromospheric structures such as spicules of type I and II, or Ca ii K fibrils.

MULTI-WAVELENGTH HIGH-RESOLUTION OBSERVATIONS OF A SMALL-SCALE EMERGING MAGNETIC FLUX EVENT AND THE CHROMOSPHERIC AND CORONAL RESPONSE

State-of-the-art solar instrumentation is revealing magnetic activity of the Sun with unprecedented resolution. Observations with the 1.6m New Solar Telescope of the Big Bear Solar Observatory are making next steps in our understanding of the solar surface structure. Granular-scale magnetic flux emergence and the response of the solar atmosphere are among the key research. As part of a joint observing program with NASA's IRIS mission, the NST observed active region NOAA 11810 in photospheric and chromospheric wavelengths. Complimentary data are provided by SDO and Hinode space-based telescopes. The region displayed a group of solar pores, in the vicinity of which we detect a small-scale buoyant horizontal magnetic flux tube causing abnormal granulation and interacting with the pre-existing ambient field in upper atmospheric layers. Following the expansion of distorted granules at the emergence site, we observed a sudden appearance of an extended surge in the HeI data. IRIS catched ejection of a hot plasma jet associated with the HeI-surge. The SDO/HMI data reveal emerging magnetic looplike structures. Hinode/Ca II H and IRIS filtergrams detail the connectivities of the newly emerged magnetic field in the lower solar chromosphere. From these data we fid that the orientation of the emerging flux tube was almost perpendicular to the overlying ambient field. Nevertheless the interaction of emerging magnetic field lines with the pre-existing overlying field generates high-temperature emission regions and boosts the surge/jet production. The localized heating is detected before and after the first signs of the surge/jet ejection. We compare the results with previous observations and theoretical models, and propose a scenario for the activation of plasma jet/surges and confined heating. Such process may play a significant role in the mass and energy flow from the interior to the corona.

The energy of waves in the photosphere and lower chromosphere

We investigate the statistics of the intensity distributions as function of the wavelength for Ca II H and the CA II IR line at 854.2 nm to estimate the energy content. We derived the intensity variations at different heights of the solar atmosphere as given by the line wings and line cores of the two spectral lines. We converted the observed intensities to absolute energy units employing reference profiles calculated in NLTE. We also converted the observed intensity fluctuations to brightness temperatures assuming LTE. The rms fluctuations of the emitted intensity are about 0.6 (1.2) W/m2 ster pm near the core of the Ca IR line (Ca II H), corresponding to intensity fluctuations of about 20% (30%). For the line wing, we find rms values of about 0.3 W/ m2 ster pm for both lines, corresponding to relative fluctuations below 5%. The rms shows a local minimum for wavelengths forming at about 130 km height, but otherwise increases from the wing to the core. The rms brightness temperature fluctuations are below 100 K for the photosphere and up to 500 K in the chromosphere. The skewness of the intensity distributions is close to zero in the outer line wing and positive throughout the rest of the spectrum. The skewness shows a pronounced maximum on locations with photospheric magnetic fields for wavelengths in between the line wing and the line core, and a global maximum at the very core for both magnetic and field-free locations. The energy content of the intensity fluctuations is insufficient to create a similar temperature rise in the chromosphere as predicted in most reference models of the solar atmosphere. The enhanced skewness between photosphere and lower solar chromosphere on magnetic locations indicates a mechanism which solely acts on magnetized plasma.

Chromospheric anemone jets and magnetic reconnection in partially ionized solar atmosphere

The solar optical telescope onboard Hinode with temporal resolution of less than 5 s and spatial resolution of 150 km has observed the lower solar atmosphere with an unprecedented detail. This has led to many important findings, one of them is the discovery of chromospheric anemone jets in the solar chromosphere. The chromospheric anemone jets are ubiquitous in solar chromosphere and statistical studies show that the typical length, life time and energy of the chromospheric anemone jets are much smaller than the coronal events (e.g., jets/flares/CMEs). Among various observational parameters, the apparent length and maximum velocity shows good correlation. The velocity of chromospheric anemone jets is comparable to the local Alfvén speed in the lower solar chromosphere. Since the discovery of chromospheric anemone jets by Hinode, several evidences of magnetic reconnection in chromospheric anemone jets have been found and these observations are summarized in this paper. These observations clearly suggest that reconnection occurs quite rapidly as well as intermittently in the solar chromosphere. In the solar corona (λi > δSP), anomalous resistivity arises due to various collisionless processes. Previous MHD simulations show that reconnection becomes fast as well as strongly time-dependent due to anomalous resistivity. Such processes would not arise in the solar chromosphere which is fully collisional and partially-ionized. So, it is unclear how the rapid and strongly time-dependent reconnection would occur in the solar chromosphere. It is quite likely that the Hall and ambipolar diffusion are present in the solar chromosphere and they could play an important role in driving such rapid, strongly time-dependent reconnection in the solar chromosphere.

STATISTICAL STUDY OF CHROMOSPHERIC ANEMONE JETS OBSERVED WITHHINODE/SOT

The Solar Optical Telescope on board Hinode has revealed numerous tiny jets in all regions of the chromosphere outside of sunspots. A typical chromospheric anemone jet has a cusp-shaped structure and bright footpoint, similar to the shape of an X-ray anemone jet observed previously with the Soft X-ray Telescope on board Yohkoh. The similarity in the shapes of chromospheric and X-ray anemone jets suggests that chromospheric anemone jets are produced as a result of the magnetic reconnection between a small bipole (perhaps a tiny emerging flux) and a pre-existing uniform magnetic field in the lower chromosphere. We examine various chromospheric anemone jets in the solar active region near the solar limb and study the typical features (e.g., length, width, lifetime, and velocity) of the chromospheric anemone jets. Statistical studies show that chromospheric anemone jets have: (1) a typical length {approx}1.0-4.0 Mm, (2) a width {approx}100-400 km, (3) a lifetime {approx}100-500 s, and (4) a velocity {approx}5-20 km s{sup -1}. The velocity of the chromospheric anemone jets is comparable to the local Alfven speed in the lower solar chromosphere ({approx}10 km s{sup -1}). The histograms of chromospheric anemone jets near the limb and near the disk center show similar averages andmore » shapes of distributions, suggesting that the characteristic behavior of chromospheric anemone jets is independent of whether they are observed on the disk or at the limb. The observed relationship between the velocity and length of chromospheric anemone jets shows that the jets do not follow ballistic motion but are more likely accelerated by some other mechanism. This is consistent with numerical simulations of chromospheric anemone jets.« less

MORPHOLOGY AND DYNAMICS OF THE LOW SOLAR CHROMOSPHERE

The Interferometric Bidimensional Spectrometer (IBIS) installed at the Dunn Solar Telescope of the NSO/SP is used to investigate the morphology and dynamics of the lower chromosphere and the virtually non-magnetic fluctosphere below. The study addresses in particular the structure of magnetic elements that extend into these layers. We choose different quiet Sun regions in and outside coronal holes. In inter-network regions with no significant magnetic flux contributions above the detection limit of IBIS, we find intensity structures with the characteristics of a shock wave pattern. The magnetic flux elements in the network are long lived and seem to resemble the spatially extended counterparts to the underlying photospheric magnetic elements. We suggest a modification to common methods to derive the line-of-sight magnetic field strength and explain some of the difficulties in deriving the magnetic field vector from observations of the fluctosphere.

The Energy of High-Frequency Waves in the Low Solar Chromosphere

High-frequency acoustic waves have been suggested as a source of mechanical heating in the chromosphere. In this work the radial component of waves in the frequency interval 22 to 1 mHz are investigated. Observations were performed using 2D spectroscopy in the spectral lines of Fe i 543.45 nm and Fe i 543.29 nm at the Vacuum Tower Telescope, Tenerife, Spain. Speckle reconstruction has been applied to the observations. We have used Fourier and wavelet techniques to identify oscillatory power. The energy flux is estimated by assuming that all observed oscillations are acoustic running waves. We find that the estimated energy flux is not sufficient to cover the chromospheric radiative losses.

Observing the Modification of the Acoustic Cutoff Frequency by Field Inclination Angle

We use observations of a sunspot from the Transition Region and Coronal Explorer (TRACE) spacecraft to demonstrate observationally the modification of the acoustic cutoff frequency in the lower solar chromosphere by the changing the inclination of the magnetic field as first predicted theoretically by Bel & Leroy.

Determination of the Acoustic Wave Flux in the Lower Solar Chromosphere

ABSTRACTHigh-cadenceobservationsof thequietSunhavebeenobtainedwiththe TransitionRegionAndCoronalExplorer(TRACE)satelliteintwoUVpassbandsaround1600and17008.Theobservationalprogramhasbeenoptimizedforthe detection ofhigh-frequency acoustic waves: the cadence is strictly regular, there is no data compression,andtheexposure time is optimized for quiet-Sun regions. Significant intensity variations are detected up to 40 mHz fre-quency. Non-LTE radiation hydrodynamics simulations are performed in order to calculate the acoustic energy fluxthat the observed intensity variations correspond to. The derived acoustic energy flux spectrum at the formationheightoftheUVcontinua(about400km)isdecreasingwithfrequency.Forfrequenciesabove40mHzwederiveanupper limit. The integrated acoustic energy flux is 255 W m 2 in the frequency range 5–50 mHz. This is lower thanwhat is needed to balance the radiative losses from the quiet-Sun chromosphere by at least a factor of 10. The majoruncertainty in the analysis is the possibility of high-frequency power with spatial scales smaller than the resolutionelement of TRACE. We make estimates of this effect and find it unlikely that it is larger than a factor of 2. In theconvection zone, where the waves are generated, the energy spectrum is rather flat and may have a peak at highfrequencies. We also show that the sensitivity of the observations to high-frequency waves is directly given by theFourier transform of the response function.Subject headinggs: Sun: chromosphere — waves1. INTRODUCTIONOneofthemainunansweredquestionsinsolarphysicsiswhythe solar outer atmosphere is hotter than the surface. Acousticwaves were suggested by Biermann (1948) and Schwarzschild(1948) to play an important part in the heating of the solar chro-mosphere and corona. The theory that the dissipation of shocksheats the outer atmosphere was further investigated by variousauthors, e.g., Schatzman (1949).Theamountofenergyavailableinacousticwavesfortheheat-ing of the outer atmosphere could, in principle, be estimated ontheoreticalgroundsfromatheoryof howacousticwavesaregen-erated by the turbulent motions in the convection zone. Theoriesoriginallydeveloped for the soundgenerationfromsmall regionsof turbulent flow embedded in an infinite homogeneous medium(Lighthill 1952) have been modified to estimate the sound radi-ationfromhomogeneous,isotropicturbulence(Proudman1952).TheweaknessoftheLighthill-Proudmantheoryisthatitonlydealswith homogeneous media and treats turbulence as isotropic, ho-mogeneous, and statistically steady over the time it takes for thesound to cross the turbulent region (Musielak et al. 1994). Noneof these assumptions are likely to be valid in stellar convectionzones.Followingtheworkof UnnoKBohn1981,1984;Musielak1987,1991;Ulmschneider1990). The theory has been revisited by Musielak et al. (1994),who found thattheturbulent energyspectrumchoseninpreviouswork was not very realistic. With their modified turbulent spec-trum theyfound that the emergingacousticwavepower from thesolarconvectionzonerisessmoothlyfromtheacousticcutofffre-quencytoaflatpeakaround16mHz.ThetotalacousticpowerfortheSunusingthistheoryis(1 3) ; 10

Dynamics of the solar chromosphere IV. Evidence for atmospheric gravity waves from TRACE

We study the low-frequency brightness modulation of internetwork regions in the low solar chromosphere using simultaneous ultraviolet and white-light image sequences from the Transition Region and Coronal Explorer(TRACE). The ultraviolet sequences exhibit a slowly varying brightness pattern in internetwork regions on which the more familiar acoustic three-minute oscillation is superimposed, with about half of the peak brightness reached in internetwork grains contributed by the low-frequency background. We address the nature of the latter, applying two-dimensional Fourier filtering to isolate it from the acoustic modulation. Spatio-temporal comparisons and selective time-delay scatter correlations between the ultraviolet and white-light low-frequency sequences establish that reversed granulation constitutes at most a minor part of the ultraviolet background. Fourier analysis shows that the meso-scale contribution dominates and consists of atmospheric gravity waves.

Flare heating and ionization of the low solar chromosphere. II - Observations of five solar flares

Two neutral Mg spectral lines formed in the temperature-minimum region and the low chromosphere, at 4571 and 5173 A, are used to quantify the changes in the atmospheric structure as a function of time during five solar flares. Eight proposed flare heating and ionization mechanisms and predictions of the effects of each on the temperature minimum region are discussed. Two Mg spectral observations made at the National Solar Observatory (Sacramento Peak), along with observations of hard and soft X-rays from the SMM and GOES satellites, are compared to the predictions of the eight proposed mechanisms. The initial effects in all five flares are consistent with backwarming by enhanced Balmer- and Paschen-continuum radiation originating in the upper chromosphere. Extended heating observed in two of the flares is most likely due to UV irradiation. In all cases heating by the dissipation of nonreversed electric currents, collisions with an electron or proton beam, irradiation by soft X-rays, and dissipation of Alfven waves are eliminated.

Flare heating and ionization of the low solar chromosphere. I - Inversion methods for MG I 4571 and 5173

Various methods of inverting solar Mg I 4571 and 5173 spectral line observations are examined to find the best method of using these lines to calculate the vertical temperature and electron density structure around the temperature minimum region. Following a perturbation analysis by Mein (1971), a Fredholm integral equation of the first kind is obtained which can be inverted to yield these temperature and density structures as a function of time. Several inversion methods are tested and compared. The methods are used to test data as well as to a subset of observations of these absorption lines taken on February 3, 1986 before and during a solar flare. A small but significant increase is found in the temperature and a relatively large increase in the electron density during this flare. The observations are inconsistent with heating and ionization by an intense beam of electrons and with ionization by UV photoionization of Si I.

Scaling-law equilibria for calcium in canopy-type models of the solar chromosphere

Scaling laws for resonance line formation are used to obtain approximate excitation and ionization equilibria for a three-level model of singly ionized calcium. The method has been developed for and is applied to the study of magnetograph response in the 8542 A infrared triplet line to magnetostatic canopies which schematically model diffuse, nearly horizontal fields in the low solar chromosphere. For this application, the method is shown to be efficient and semi-quantitative, and the results indicate the type and range of effects on calcium-line radiation which result from reduced gas pressure inside the magnetic regions.