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Xerox University Microfilms 300 North ZM b Road Ann Arbor, Michigan 48100 74-24,296 BARNHART,_ Ph . Jl1p Everett, 1930- PHOTOELECTRIC SOLAR LIMB SCANS FOR DETERMINING MEAN CHROMOSPHERIC STRUCTURE. The Ohio State University, Ph.D., 1974 Astronony
University Microfilms, A XEROX Company, Ann Arbor, Michigan
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. PHOTOELECTRIC SOLAR LIMB SCANS
FOR DETERMINING MEAN CHROMOSPHERIC STRUCTURE
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Philip Everett Barnhart, B. A., M. A. * # ★ * *
The Ohio State University
1974
Reading Committee: Approved By
Walter E. Mitchell, Jr Geoffrey Keller Qtojtiui-i. Adviser (IAdviser De part ment of Astr onom yGerald Newsom Department of AstronomyGerald ACKNOWLEDGMENTS
It is not a difficult task to express my gratitude to the many people who have come together directly and
indirectly to make this effort possible. Some, like the inspirational teachers along the way who were able to keep my interest alive, will have to settle for the general, nameless, "Thank You" to which 1 must resort in the interest of space utilization. Their numbers are legion.
Others deserve special mention because they have contributed so meaningfully that this work would not have been completed without them.
Inspiration for the whole thing grew out of the op portunity I have had over the years to work with Walter
E. Mitchell, Jr. He was willing to let me do it my way and when he pointed out the better way to do it he made it seem as if I had done it all myself. For this I shall always be grateful.
Enough can never be said about the warm, generous and always competent receptions I received from the Kitt
Peak Observatory staff. In the Tucson headquarters or on the mountain I was made to feel welcome and was afforded the best of help. I greatly value the untiring efforts
ii of Chuck Slaughter and Dick Aikens for putting together an efficient data acquisition program. As if that was not enough they provided valuable assistance and encouragement at the telescope. I also appreciate the stimulating dis cussions with A. Keith Pierce, William Livingston and Jim
Brault. They make being a member of the astronomical community a pleasure.
Being faced with such a volume of data 1 was led to conclude that I would never wade through it without invaluable help from the masters of the machines. I am deeply indebted to the staff of the Otterbein College
Data Center and that of the Battelle Memorial Institute for their patience in enduring the seemingly interminable outpouring of solar data. In particular I must acknowledge the tremendous help given me by Dennis Lohr who turned some of my vague, fuzzy ideas into a beautifully workable data processing achievement. There is much of him in these limb scans.
Among several who helped me work up the 1500 plots necessary to display what I thought I needed to see I must take particular note of my dear wife, Esther. She decided that if I was ever going to finish the job, she would have to do the dirty work.
iii A whole student generation has seen less of me them we would like. For that I apologize. For four years now my children have claimed to be fatherless. Starting this year they may see that it is really all for them.
iv VITA
September 2, 1930 . . B o m - Indianapolis, Indiana
1952...... B. A., Manchester College, North Manchester, Indiana
1955...... M. A., Indiana University, Bloomington, Indiana
1955 - 1964 ...... Research Associate, Research Foundation, The Ohio State University, Columbus, Ohio
1959 - 1962 ...... Instructor (part time) Dept. of Physics, Otterbein College, Westerville, Ohio
1962 - ...... Assistant Professor, Department of Physics and Astronomy, Otterbein College, Westerville, Ohio (Chairman, 1962 - 1970)
PUBLICATIONS
"Direct Observation of Element Motion in Stellar Shadow Patterns," Barnhart, P. E., Protheroe, W. M. and Galli, J., Jour. Opt. Soc. Amer. 46, 904, 1956.
"The Photoelectric Determination of the Direction and Velocity of Motion in the Scintillation Layer," Barnhart, P. E., Astron. Joum., 62, 3, 1957.
"Design of a Photoelectric Photometer for Observing the Distribution of Light Intensity in Telescopic Images," Protheroe, W. M., Barnhart, P. E. and Galli, J., Chapter 10, Final Report Contract AF 19(704) - 1409, AFCRC, Elec tronics Directorate, Laurence G. Hanscom Field, Bedford, Mass. 1956.
v "Description of a Device for Computing Statistical Proper ties of Stellar Shadow Pattern," Keller, G., Barnhart P. E. and Angelone, A., Scientific Report 1, Contract AF 19(604)-1954, AFCRC Geophysics Research Directorate, Laurence G. Hanscorn Field, Bedford, Mass. 1957.
"Investigation of Upper Air Turbulence by the Method of Analysing Stellar Scintillation Shadow Patterns," Barnhart, P. E., Keller, G., and Mitchell, W. E. Jr. Final Technical Report, Contract AF 19(604) - 1954, AFCRC, Geophysics Directorate, Laurence G. Hanscom Field, Bedford, Mass. 1959.
"A Program of Stellar Narrow Band Infrared Photometry," Barnhart, P. E. and Hynie, W. H., Mem. Soc. Roy. Sci. Liege, cinguieme serie, Tome IX, 425, 1964.
"Infrared Stellar Photometry," Barnhart, P. E. and Mitchell, W. E., Jr., Contributions from the Perkins Observatory, Series II No. 16, 1966.
FIELDS OF STUDY
Major Field: Astronomy
Studies in Atmospheric Seeing. Professors G. Keller and W. E. Mitchell, Jr.
Studies in Infra-Red Stellar Irradiances. Professor W. E. Mitchell, Jr.
Studies in Solar Chromospheric Structure. Professor H. E. Mitchell, Jr.
vi TABLE OP CONTENTS
Page
ACKNOWLEDGMENTS...... ii
VITA ...... V
TABLE OF CONTENTS...... vii
LIST OF T A B L E S ...... ix
LIST OF F I G U R E S ...... X
LIST OF SYMBOLS ...... xiv
I. INTRODUCTION ...... 1
Early History of Chromospheric Study .... 1 Discovery and Use of Flash Spectrum .... 2 Chromospheric Structure ...... 8 Chromospheric Spectral Analysis ...... 9 Mean Structure Outside Eclipse ...... 10
II. THE NEED FOR CHROMOSPHERIC INTENSITY MEASUREMENT 15
Proposed Technique of Observation .... 24 Magnitude of the Observing Problem .... 26
III. DESCRIPTION OF THE OBSERVING P R O G R A M ...... 32
Results of Preliminary R u n ...... 34 Description of Apparatus...... 45 Geometry of the Solar Limb ...... 51 Technique of Observation ...... 52 Method of Data Analysis ...... 62 The Search for Invariant Parameters . . . 76 Determination of Seeing Half-Width .... 92 Technique for Locating Limb Points .... 94 Status of the Solar L i m b ...... 99
vii Page
Presentation of Observed D a t a ...... 101 Observations of the Balmer Lines .... 104 Effects of Defocussing ...... Ill Metal Lines ...... 116 Helium L i n e s ...... 147
IV. CONCLUSIONS ...... 163
Value of the Mohler Technique...... 163 Specific Proposals ...... 167
APPENDIX
1. Normalization Procedure...... 173
2. Scan Rate Calibration ...... 185
3. Two Dimensional Scattering Function .... 192
BIBLIOGRAPHY...... 196
viii LIST OF TABLES
Page
Table 1 Theoretical Emission Source Heights 16
Table 2 Chromospheric Limb Heights 19
Table 3 List of Proposed Chromospheric Lines 33
Table 4 Lines Added at the Telescope 33
Table 5 Data Relevant to August 1970 Observing Run 46
Table 6 Status of Observed Limb Positions 100
Table 7 Limb Scan Data - Hg 105-6
Table 8 Hg Chromospheric Heights 117
Table 9 Limb Scan Data - Ha 123
Table 10 Limb Scan Data - Selected Balmer Lines 132-5
Table 11 Chromospheric Heights of Selected Balmer Lines 137
Table 12 Limb Scan Data - Ca II 138
Table 13 Limb Scan Data - Na I 142
Table 14 Limb Scan Data - Fe II 145
Table 15 Limb Scan Data - Sr II, Ti II 148
Table 16 Limb Scan Data - He I 157
Table 17 Summary of Chromospheric Data 159
Table 18 Data Obtained From Full Disc Scans 179
Table 19 Sample Computer Output for a Single Limb Position 180-4
Table 20 Image Scale Data 191 ix LIST OF FIGURES
Page
Figure 1 Source Height of Continuum Radiation 22
Figure 2 Schematic Representation of Segments of Solar Disc Scans 25
Figure 3 Components of Coronal Light 27
Figure 4 Strip Chart Record of Slow Limb Scan 37
Figure 5 Placement of Slit on Limb for Making Spectral Scans 39
Figure 6 Spectral Scans Hg 40
Figure 7 Spectral Scans Ha 41
Figure 8 Spectral Scans La II X4429 42
Figure 9 Spectral Scan, H12 43
Figure 10 Principle of Operation of the Rocking Arm Scanner 48
Figure 11 Full Disc Scans, Hg, 27 August, 7:30 a.m. 57
Figure 12 Full Disc Scans, Hg, 27 August, 3:30 p.m. 58
Figure 13 Full Disc Scans, Ha , 27 August, 2:38 p.m. 59
Figure 14 Full Disc Scans, Ca II, 28 August, 8 s 56 a>m. 60
Figure 15 Full Disc Scans, Fe II, 28 August, 8:16 a.m. 61
Figure 16 Integrated, Unshifted Limb Scans Ha 65
Figure 17 Integrated, Shifted Limb Scans Ha 66
x Page
Figure 18 Limb Scans of Figures 16 and 17 Superposed 67 Figure 19 Standard Deviations of Limb Scans Illustrated in Figures 16 and 17 69
Figure 20 Number of Channels Shifted in Integration Program 70
Figure 21 Expanded Scan in Hg — Good Seeing 74
Figure 22 Expanded Scan in Hp -- Poor Seeing 74
Figure 23 Theoretical Continuum Limb Profile - X4888 79
Figure 24 First Derivative Theoretical Limb Profile 79
Figure 25 Theoretical Line-Core Profile for Hg 83
Figure 26 First Derivative Theoretical Line Core Profile 83
Figure 27 Scale Heights as a Function of Radial Distance in Theoretical Limb Profiles 86
Figure 28 Comparison Between Two Assumed Line Core Profiles 88
Figure 29 Scale Heights in Revised Theoretical Limb Profile 89
Figure 30 Comparison of Observed Scale Heights with Theoretical Scale Heights for Revised Limb 90
Figure 31 First Derivatives of Limb Profiles Reflecting Deterioration of Seeing 93
Figure 32 Typical Limb Scans 95
Figure 33 First Derivative of Scans of Figure 32 97
xi Page
Figure 34 Height Above Chromospheric Limb at Which Smeared Profile Has a Value of of Central Intensity 108
Figure 35 Observed Extent of Ho Emission Above Chromospheric Limb 110
Figure 36 First Derivatives of Limb Profiles, Focussed and Defocussed 113
Figure 37 Comparison of Thomas and Athay's Hg Data With a Scan From This Work 120
Figure 38 Direct Comparison of Barnhart Data to Full Run of Thomas and Athay 1952 Eclipse Data 122 Figure 39 Observed Lxtent of Ha Emission Above the Chromospheric Limb 124
Figure 40 Ha Limb Scan Showing Possible Limb Brightening 126
Figure 41 Prominence Obtained on Scans 22 Augiist 129
Figure 42 East Limb Prominence Observed in Four Lines 130
Figure 43 Two Ca II Scans With and Without Prominence Nearby 139
Figure 44 Observed xtent of Ca II Above Chromosph aric Limb 141
Figure 45 Observed : Ixtent of Na I Emission Above the Chromospheric Limb 143
Figure 46 Observed : Ixtent of Fe II Emission Above the Chromospheric Limb 146
Figure 47 He I Intensity Scan With Photo- spheric Limb Indicated 150
Figure 48 He I Intensity Scan for Four Limb Positions, X5875, 28 August 151
xii Page
Figure 49 He I Intensity Scans for Four Limb Positions, X5875, 27 August 1970 153
Figure 50 He I Intensity Scans for Four Limb Positions, X4471 154
Figure 51 He I Intensity Scans for Four Limb Positions, X6678 156
Figure 52 Observed Limb Heights of Balmer Series Lines Compared With Chromospheric Models 161
Figure 53 Plot of Limb Scan and Portion of a Full Disc Scan Illustrating How They Can Be Related 174
Figure 54 Graph of the Position of a Scanned Spot as a Function of Time 189
Figure 55 Geometry of Two-Dimensional Scattering Function 193
xiii LIST OP SYMBOLS
The reciprocal of the Standard Deviation in a Gaussian spread function.
Radiation in a spectral line coming to the observer from the entire chromosphere above the limb of the moon.
The unsmeared run of intensity as a function of distance from the disc center: -- the "object function."
The intensity scale height, equivalent to the reciprocal of the logarithmic gradient of I(r).
Scale heights published by Thomas and Athay (1961).
Maximum height above photospheric limb to which the chromospheric radiation can be detected.
Mean source height of emission, i.e. the elevation for which ■ 1 at the disc center.
Height above photospheric limb at which helium emission attains its maximum intensity.
Maximum height to which the chromospheric radiation was detected and reported by S. A. Mitchell (1947).
Height of the chromospheric limb above the continuum limb.
Seeing half-width -- derived as the width in arcseconds of the first derivative of the limb intensity profile at one- half the peak value. 1(h) Intensity distribution as a function of height above the lunar limb at a solar eclipse.
K r ) The convolution of an object function and a spread function — the "image function."
IC
Il (P * o) Intensity of line-core radiation at the center of the solar disc.
I(o) Intensity at disc center.
I (P) Intensity at a radial distance p from the center of the solar disc.
«o Solar radius * 695#500 km. S(x) A spread function. The variables h, r, x and p are in the same units.
X Wavelength in Angstroms.
4> (sun) or Heliographic latitude.
P Radial distance from center of solar disc, in kilometers.
Radial optical depth.
Tt Tangential optical depth. t5000 Optical depth for continuum radiation at X5000, measured either radially or tangentially. x, r Dummy variables for distance in the radial directiohifrom the sun's center.
xv I . INTRODUCTION
(The chromosphere) . . . resembles a sheet of
scarlet fire. The appearance . . . is as if countless
jets of heated gas were issuing through vents and spira
cles like the blaze of a conflagration.
— C. A. Young, 1896
The Early History of Chromospheric Study. Young's
(1896) fiery description of the structure and appearance
of the solar chromosphere culminated a century and a
half of discovery relating to the relatively narrow region
of the solar atmosphere directly overlying the visible photosphere. From Berne, Switzerland, one Captain
Stannyan reported that he observed during the eclipse of 1706 the appearance of a blood-red streak of light six or seven seconds prior to the reappearance of the bright solar disc at the western limb at the end of the total phase of the eclipse. Hailey and Louville saw the same thing in 1715. Prominences, which appeared like distinct extensions of the chromosphere region into the lower corona, were reported in 1733, by Vassenius, a Swedish astronomer, 1 2
A sort of rediscovery occurred at the eclipse of
1842 in France, Italy, and Austria. Great surprise was expressed at the presence of the prominences observed indicating most of the previous observations had been forgotten or not taken into account. Following the eclipse of 1851, the general view, though not unanimous, was that the sun was completely surrounded by a continuous layer of some substance different from the main visible body represented by the photosphere.
The first successful application of photographic techniques to prominence activity was carried out in 1860 by Secchi and de la Rue. The sequential nature of the photographs indicated once and for all that the prominences were solar phenomena and not attached to the moon nor were they optical illusions. The eclipse of 1868 in India added one more important dimension to the study of prominences and the chromosphere.
Discovery and Use of Flash Spectrum. The newly in vented spectroscope revealed the fact that the prominence spectrum consists of emission lines dominated by the lines of hydrogen. All of the observers made essentially the same report - even to identifying a bright yellow line with sodium. It was after this eclipse that Janssen went one step further. Noting how bright the emission lines appeared he concluded it may be possible to detect them
in full sunlight. Clouds prevented him from checking his
idea the day of the eclipse but the next morning he ob
served the same bright lines and found that there was no
difficulty in lJcating them quite accurately in comparison with the dark lines in the Fraunhofer spectrum of the disc.
His pioneering visual observations marked the beginning of the study of the solar envelope outside the limited
times of total solar eclipse.
Young (1873) pointed out that to observe any of the
Fraunhofer lines reversed depends only upon instrumental power and atmospheric conditions. It is interesting to note that this ability to observe the chromospheric emission at the limb witJout the occurrence of solar eclipses has been largely ignored by workers interested in the physical structure of thJ chromosphere. This may be due in part to the glamour of eclipse chasing and in part to the complexities introduced into the reductions by scattered light in the optical systems and turbulence in the terrestrial atmosphere.
Athay (1965) points out that existing data obtained from flash spectrum observations have not been fully ex ploited. This is especially unfortunate due to the great effort put forth in obtaining the data. He emphasizes 4 that limitations on the use of chromospheric data (obtained at eclipse) primarily arise due to the incompleteness of the data rather than inaccuracies in the observations.
Observation of the flash spectrum is undoubtedly very popular because of the ease with which the observation can be made. By using essentially a camera with only a dispersing element at the entrance aperture one may obtain a spectrum of the chromosphere just outside the times of second and third contact of the lunar disc with the solar photospheric disc. Monochromatic images of the solar chromosphere are obtained without additional imaging optics nor particularly accurate driving or guiding mechanism.
For this reason the complexity of instrumentation needed on an eclipse expedition is greatly reduced. Unfortunately, data obtained in this manner yield total line intensities integrated over wavelength as well as over the entire chromosphere exposed above the lunar limb. This combines in each image the effects of spectral broadening of the line as well as geometrical spread of the image due to the finite thickness of the solar chromosphere.
Many of the eclipse observations of chromospheric characteristics have not been standardized. In particular, intensities of different lines in the chromospheric spec trum have been estimated visually. The vertical extent of the regions of the chromosphere containing the material producing each line is determined by measuring the lengths of the chromospheric arcs and the geometry of the lunar disc with respect to the center of the sun. This technique is sensitive to wavelength-dependent emulsion speed.
An attempt to overcome the ambiguity of flash spectrum measurements is found in the moving plate method proposed and used by Campbell. A very small portion of the flash spectrum is allowed to reach the photographic plate through a long slit oriented with its length along the direction of dispersion. The plate is then moved continuously at right angles to the dispersion during the period of time represented by the second and third contacts of the lunar limb. The resulting series of lines of different lengths and intensities is then used as a measure of the thickness of the emitting layer in the chromosphere. This technique requires that the position on the solar limb occupied by the spectrograph exit slit must be selected prior to the time of observation with the chance that the sampled region might include a prominence or region of abnormal chromospheric activity leading to the possibility of a determination of unusual chromospheric conditions. Further more, a very small sample of the total chromosphere is observed and effects which might be latitude dependent or more nearly of average characteristic could be overlooked.
Due to the rather long interval between individual flash spectrum exposures and the lack of intensity calibra tion! the data concerning mean elevations of formation and scale heights of chromospheric emission tend to be rather inexact. In attempting to overcome the disadvantages of the single spectrogram observations Henzel (Menzel and
Cillie! 1937) devised a "jumping plate" technique. In this method the total flash spectrum was recorded but in a series of short exposures between which the photographic plate was moved in much the same way a moving picture film is moved between exposures. This produces several spectro grams during each occurrence of the flash.
Menzel obtained spectrograms at the 1932 eclipse with height resolution of a little over 800 kilometers. In 1936 he had reduced the exposure interval a bit and obtained a 700 kilometer height resolution. These height intervals for observations are shown by Athay (1961) to be inadequate for the determination of emission scale heights.
Determination of chromospheric intensity profiles from flash spectrum exposures involves a differentiation of the observed data. This introduces a marked decrease in the signal to noise ratio. Unless the integrated intensities are known with great precision the resulting solutions for intensity as a function of height may contain
large uncertainties.
Later attempts to obtain spectrograms at much shorter
time intervals with much smaller height resolution by
Kristensen (1955) suffered from the need to reduce the
dispersion drastically, limiting the data to only the
strongest lines. Data from the 1952 eclipse were analyzed
by Thomas and Athay (1961) using spectrograms taken at *
intervals of 0.4 seconds giving a height resolution of
110 kilometers.
A further problem occurs for observation of chromo
spheric features lying low in the chromosphere. It is generated by the very short time that these elements are available for detection. The moon moves approximately 0.44 seconds of arc per second which translates to a covering or uncovering of a slice of solar chromosphere approximately
310 kilometers thick every second. Lines which are found within 500 kilometers of the photosphere are available for less than 2 seconds at each eclipse while lines up to approximately 14,000 kilometers above the photosphere may be observed up to 40 seconds. The majority of these lines occurring in the flash spectrum lie in the region below
700 to 1000 kilometers. Timing is alBO very important.
If a photographic exposure requires 1 second to record. the moon will smear across a 300 kilometer slab during
this time, further reducing the geometric resolution obtain
able from the flash spectrum. The repetition rate of flash
spectrum exposures is of the order of a second so
that at best, data for only the outer regions of the chromo
sphere will have much coherence.
Another complication is pointed out by Wildt (1947).
Since the moon moves continuously with respect to the sun,
different levels in the chromosphere will be recorded on
the same flash spectrum plate with different exposure
times. The discrepancy will be most noticeable in the
regions of greatest intensity due to the fact that they have small extent and contribute most to the integrated
intensity above a given level in the atmosphere.
Chromospheric Structure. Studies of the chromospheric structure have been carried out in a variety of ways.
Historically, the earliest discoveries were made visually, both of the physical appearance of the chromosphere at the limb and the spectroscopic nature of the chromosphere.
Early direct observations of the solar limb led to such descriptive phrases as Secchi's "burning prairie" and
Airy's name "Sierra" (after the geological name for a ridge of mountains whose peaks make a jagged outline.)
Later, the features visible in the chromosphere were called by Lyot and Mohler simply "jets." Roberts elected to call
the transitory features characterizing the upper chromo
sphere "spicules."
Motion picture and time sequence photography have
demonstrated the dynamic nature of the upper chromospheric
structure. Used in conjunction with coronographs and
narrow band interference filters such techniques yield
typical spicule lifetimes of the order of minutes or tens
of minutes. The spicules seem to rise above and fall back
into a region of generally uniform intensity distribution.
The uniformly illuminated component of the chromosphere may lie within the boundary of the chromospheric limb.
Many difficulties arise in trying to make a detailed
study of the structure of the chromosphere at times of
total eclipse due in part to the rugged conditions under which observations need to be made and in part to the very short period of time during which the relevant data may be obtained. S. A. Mitchell (1951) describes very well the rigors of eclipse chasing and the many difficulties in obtaining meaningful flash spectrum observations.
Chromospheric Spectral Analysis. Observations of the spectral characteristics of the chromosphere outside of eclipse were begun by Hale and Adams (1909) who photographed the chromospheric spectrum at the 60 foot tower on Mt. 10
Wilson. Adams and Burwell (1915) published a list of over
1000 chromospheric lines observed outside of eclipse with the 60 foot tower telescope. Increased image size avail able with the 150 foot Mt. Wilson telescope allowed Hale to obtain improved chromospheric spectra. More recently, important catalogs of chromospheric emission lines have been compiled, most notably the 1968 catalog of over
11,000 lines compiled by Fierce (1968) using the McMath
Solar Telescope at Kitt Peak National Observatory.
Several attempts have been made to photographically observe chromospheric line profiles outside of eclipse.
There are observations of HQ by Keenan (1932), de Jager
(1957), and E. V. P. Smith (1957), Hg and by Keenan
(1932a) and of metal lines by H. Smith (1957) and Parker
(1957). In particular these observations outside of eclipse probably contain large errors in the determination of the height to which the observations refer. Athay
(1961) maintains that the heights deduced for a given observation made outside of eclipse may not be known to within the order of tlOOO km. Athay (1965) generally discounts these data because of the poor height resolution and spectral contamination due to atmospheric scattering.
Mean Structure Outside Eclipse. Only modest attempts have been made to assess mean chromospheric structure outside eclipse. * Abetti (1955) summarized 25 years of chromospheric height measurements at Arcetri by pointing out the mean elevation of the emission from the chromosphere ( ** 7700 km) does not seem to change with time, but the heights at the pole relative to the equator fluctuate with the 11 year sunspot cycle. He reports that the distribution varies from a uniform distribution (heights equal at pole and equator) at times of sunspot maximum to a condition be tween maxima where the height of the chromosphere is greater at the poles than at the equator.
Notable by a scarcity of reported efforts is the attempt to determine intensity data in and around the chromosphere by photoelectric means. Mohler (1960) de scribes a technique of solar disc scans using a photo electric cell in the focal plane of a spectrograph to obtain intensity distributions in the continuum and in the cores of strong chromospheric lines. This idea had been suggested earlier by Pettit (1951) as a method to obtain an accurate measurement of the apparent solar dia meter. The Pettit technique has been recently applied to diameter measurement by Wittmann (1973). Due to the extension of line emission into the chromospheric region the scans in the line core should appear to reach farther 12 from the center of the solar disc than scans obtained In continuum light.
In 1967 and 1968 a modification of the Mohler tech nique was attempted by W. Mitchell (1969) at the Snow telescope of the Mount Wilson Observatory. In this method an Image sllcer consisting of two movable mirrors and a fixed reflecting 90° prism focused opposite limbs of the sun simultaneously a few millimeters apart on the slit of a spectrograph. A rotating prism scanned the Image across the slit and a single phototube monitored the out put at one position at a time in the spectrum as the oppo site limbs were scanned across the slit. Scans made in light of a chromospheric line and a nearby continuum point yielded mean heights of the chromospheric limb above the continuum limb.
Wilson and White (1966) performed a similar type of analysis on a particularly good Ha photographic spectro gram made at the Sacramento Peak Observatory.
Of considerable importance, therefore, is the question of whether it is possible to obtain useful data on the distribution of intensity as a function of height above the continuum limb outside eclipse. Framed in another way, we ask, can high spectrographic and optical resolution be utilized to measure average chromospheric structure 13
4 or reveal the average heights within the solar chromosphere at which the cores of the strong Fraunhofer lines are formed? II. THE NEED FOR CHROMOSPHERIC INTENSITY MEASUREMENT
In recent years considerable uncertainty has arisen about the determination of the mean effective height of emission of radiation in the cores of strong Fraunhofer lines. Conflicting estimates from various workers leave considerable doubt as to how one is to interpret the con ditions under which chromospheric emission occurs. Some disagreement exists as to the vertical structure of the atmospheric layers which produce the different features seen on spectroheliograms and in the stronger Fraunhofer lines. Different models of the chromosphere predict dis tinctly different values for the height above the photo sphere at which the cores of strong absorption lines originate. Chromospheric models are generally constructed to predict the appearance of the cores of strong spectral lines. A variety of assumptions are available to the theoretician. The complexity of the structure of the chromosphere makes the choice of assumptions to use quite difficult.
Wildt (1947) analyzed the estimated maximum emission heights obtained by S. A. Mitchell (1947) from flash spec trum chromospheric arcs. He used the argument that the
-14- 15
observed sharpness of the solar continuum limb could not
occur if the chromospheric density gradients were to extend
below the level of the point in the atmosphere where the
tangential optical depth xt ■ 1. He concludes from this
that the chromospheric density gradients must undergo
a sudden transition, probably in the region between 200
and 500 kilometers above the level of the photosphere.
The model rests upon density gradients obtained from
eclipse observations and is therefore an averaged model
representing a homogeneous chromosphere.
Another homogeneous model of the chromosphere is the
one produced by Bohm-Vitense (1955). This model differs
markedly in calculated densities from one due to Waltjer
(1954) which assumes geometrical structure consisting of
hot spicules embedded in cooler interspicular gases. Den
sity predictions from both models were used by de Jager
(1957) to calculate mean heights of emission for various wavelengths in the line cores for the first four members
of the Balmer Series. See Table 1. The Woltjer model is
not representative of the real chromosphere but does seem
to represent emission height predictions typical of in-
homogeneous chromospheric models.
Athay and Thomas (1958) arrive at a chromospheric
model based upon empirical source function data. This
model also predicts a range of possible heights from which 16
TABLE 1
Theoretical Emission Source Heights for Strong Fraunhofer Lines
h* (kilometers)
Woltjer Bohm-Vitense Athay and Thomas de Jager Line (1954) (1955) (1958) (1957)
5500 3200 2000 - 4900
Hp 3500 1700 950 - 4250
liy 2800 1200 400 - 3600
Hfi 2200 700 0 - 2150
Ca II K 3900 17 line core emission might arise. The limiting values of their emission heights are widely separated. The extremes as well as the midpoint of the range for each line are listed in Table 2. In addition to the predicted emission heights their model also predicts a distinct limb bright ening for Hgf Hyr and Hg, but not for Ha .
It is evident from Table 1 that predicted heights * of emission depend strongly upon the model chosen.
Wilson and White (1966) derived a relationship between the height of emission of radiation in the solar atmosphere and a corresponding height above the solar limb. They show for the case of a simple exponential atmosphere that an observed height at the limb can be related to an emission height by the expression: T— Roff h(Tt> « H{ln ^ + ln(^) } + h(Tr) (1) where h(xt) is the height above the photospheric limb at which the tangential optical depth is h(*r) is the emission height for which the radial optical depth is tr ;
H is the' emission scale height appropriate to the radiation in question and is the solar radius.
If Equation (1) is applied to the values of the emission heights in Table 1 using values of the emission scale heights published by Thomas and Athay (1961) and 18 assuming Tt *■ Tr * 1, values of geometrical heights for the chromospheric lines can be derived. The first part of Table 2 contains these values for all models included in Table 1. There is wide diversity in the predicted heights at which the chromosphere as viewed tangentially becomes opaque.
The assumption that a chromospheric limb will occur is not necessarily obvious. Wildt (1947) seems to indicate that the shallow density gradients observed in the chromo sphere speak for a very soft chromospheric limb. Examina tion of spectroheliograms or filtergrams reveals a rather ragged but sharp demarcation between the Ha emission in the chromosphere and the background of sky and corona. Thus one might well be justified in looking for a mean elevation above the photospheric limb where the tangential optical depth xt ■ 1. This location could then be called the chromospheric limb.
Attempts to measure directly such limb heights have not been numerous. Observations of spectroheliograms indi cate an elevation of a chromospheric limb in HQ which seems to be about 6000 kilometers above the photospheric limb.
Using such data obtained by D'Azambuja (1930) de Jager
(1957) calculated emission heights for Ha and Ca II (K).
Wilson and White (1966) obtained an emission height TABLE 2
Chromospheric Limb Heights
Calculated Limb HclrJits Observed LIr.b Heights Scale Limb Wilson and Line Height h* Kclcht de .Tnger White Hlttinann Mohler Mitchell
Ha 770 5500 (w). 7*100 3200 (bv) 5100 2000 (ta)min 3900 6000 4800 4900 7000 3500 (ta) 5^00 4900 (ta)aax 6800
HB 625 3500 (m) 5100 9000 1700 (bv) 3300 cguat. 950 (ta)mln 2600 2700 (ta) 4300 2400 4200 (ta)max 5900 pole
Hy 555 2e00 (w) 4300 1200 (bv) 2700 400 (ta)uin 1900 2000 (ta) 3500 ? (bv) - Bohm-Vitense (1955) 3600 (ta)max 5100 (ta) - Athay and Thomas (1958) C
H« 555 2200 (w) 3700 (w) - Woltjer (1954) 700 (bv) 2200 0 (ta)mln 1500 1100 (ta) 2600 2150 (ta)max 3700
Ca II (750) 3900 5300 4900 7600 10,150 (K) (K) (in
Na Dx 435 300 1500 1500 1200 20
for the core of HQ from measurements of a particularly
good spectrogram taken with the slit placed across the
limb of the sun. Their value of emission height was just
half that obtained by de Jager. Mohler (1960) obtained
heights from full disc scans in the cores of Ha , Ca II
(K) and Na D^. W. Mitchell (1969) measured limb heights
for Hjj and Ca II (H) . More recently Wittmann (1973) obtained a limb height for Ha using a full disc scan.
These measurements are all included in the second part of Table 2.
Where measured heights are available they are nearly as divergent as the theoretical values. There is obviously a scarcity of data relating to this type of analysis.
A recent photospheric model is the Harvard-Smithsonian
Reference Atmosphere (HSRA) constructed by Gingerich,
Noyes, Kalkofen and Cuny (1971). It is a model that is averaged over inhomogeneities that might be present in the atmosphere. It assumes that the solar atmosphere is static, that it varies only with height and is uniform over any given horizontal plane. Such models are useful in making predictions about the behavior of radiation observed from the sun, but do not describe in detail the surface phenomena one is able to observe. In parti cular, the solar atmosphere presents much evidence of 21
non-uniform dynamic structure.
Among the specific predictions of the HSRA is a
very sharp temperature minimum around 550 kilometers
above the level in the atmosphere where t ,.q q 0 ° In
this model the region of the atmosphere from the level
at which = 1 to the temperature minimum is defined
as the photosphere. Figure 1 is a plot of the source
height of the continuum radiation as a function of wave
length predicted by this model. The graph is taken from
Gibson (1973). The level of the temperature inversion
is indicated by the dashed line at 550 kilometers. At
lower levels than this in the atmosphere the temperature gradient is negative so emission arising in this region
should display limb darkening. At higher levels the temper ature gradient is positive. In fact it must rise at a very large rate to go from about 4300° K. at the minimum point to 1060 K. at an elevation of only a few thousand kilometers. Emission arising above the level of the tem perature minimum should display limb brightening. It is seen that radiation in the continuum from about 2000
Angstroms to about 200 microns should display limb darkening.
Outside these limits we should observe limb brightening because the continuum radiation is originating in a region having a positive temperature gradient. If one observes Height for t , = 1 (km. Figure 1 Source height of continuum radiation emission from HSRA from emission radiation continuum of height Source 1 Figure 1000 1200 600 200 400 800 10 10 s oe htshr. rp ae rmGbo (1973). Gibson from taken Graph photosphere. model Temperature Gradient Negative Gradient Temperature eprtr Gain Positive Gradient Temperature aeegh Angstroms Wavelength, 10 *
23 at wavelengths of absorption or emission lines, the situa tion may be greatly altered. In particular the values for emission heights of practically all the lines repre sented in Table 1 are above the level of the temperature inversion. Why these lines do not show marked limb brightening is one of the puzzles involved with the struc ture of the chromosphere.
If the emission heights obtained from the models represented in Table 1 are indicative of what occurs in the chromosphere, the fact that spectroheliograms do not show a limb brighter than adjacent regions of the solar disc may mean that much of the radiation from strong
Fraunhofer line cores somehow gets out between spicules from layers far deeper in the chromosphere where the temperature gradient is not so steep. Alternatively, if the temperature gradient along the lengths of the spicules is very small one might expect radiation arising from the spicules to show little limb brightening even up to 3000 or 4000 kilometers above the photospheric limb.
To try to fill in some of the gaps in the collection of observed chromospheric heights I suggested an observing program designed to assess the feasibility of obtaining intensity and height data for the chromosphere outside of an eclipse. Observations would be made at various locations 24 along the solar limb in the cores of strong chromospheric lines.
Proposed Technique of Observation. I proposed adapt ing the technique of Mohler (1960) as revised by W. Mitchell
(1969) to scan a single limb of the sun. One sweeps an image of the solar limb across a spectrograpTPShtrance slit aligned tangentially to the solar limb. A detector placed behind a slit in the focal plane of the spectrograph camera will record an intensity profile corresponding to a monochromatic image of the limb. If the exit slit is located in a wavelength corresponding to radiation from the continuum of the solar spectrum the resulting intensity scan will be appropriate for the sharp photo spheric limb and might appear as the curve labelled
"Continuum" in Figure 2.
If one places a second detector behind another exit slit so located that it records the radiation from a strong Fraunhofer line an intensity scan will occur similar to the curve labelled "Line" in Figure 2.
If these two curves are then sampled simultaneously in two data channels a point by point comparison of the intensity profiles can be obtained. If one locates the position of the continuum limb then all measures on the scan may be compared to that position. In this way 1.0
Approximately 99% of solar radius missing Region of I(P) Disc Center 1 (0) Sky 0.5 Region of Limb
Continuum Ir(P-O)
Line 0.0 ■ m 0
Figure 2 Schematic representation of segments of solar to disc 3cans made In line core and continuum light 26 heights of identifiable features in the chromosphere are obtained with reference to the location of the photospheric limb.
Magnitude of the Observational Problem. In seeking to answer the question "Should we be able to photoelec- trically observe average chromospheric structure outside of eclipse?" we may gain some insight from consideration of the nature of the distribution of various types of radiation in the immediate vicinity of the solar limb.
As one scans across the solar disc and off into the region beyond the photospheric limb, there are several distinct sources of illumination which prevent the observed inten sity from going to zero and rendering dark the sky adjacent to the solar image. Some of these are conveniently dis played by van de Hulst (1953) and in Figure 3, and one may infer characteristics of the rest by studying center to limb variations of Fraunhofer line intensities.
Following van de Hulst, we see that the coronal contribution to near limb intensity is very much less than all but the most transparent sky light.
Atmospherically scattered light from all regions of the sun contribute to the light level at very great distances from the solar limb. This component is selectively scattered, being more effectively scattered in the blue 27
disc -1
-2
Clear sky with haze
pure .blue" sky
K corona (max)
F corona
E corona -10
0 1 2 3 . 5 P/Re
Figure 3 The three components of coronal light and contribution of sky light to the off-limb Intensity distribution of the sun. This plot is taken from van de Hulst (1953)* 28 than in the red and on typically clear days amounts to from about a tenth to a half of one percent of the central intensity.
Instrumentally scattered light due to diffraction effects in the optics, dust or particulate matter within the optical train and spectral scattering due to irregu larities in the grating contribute to a redistribution of radiation within the final image of the optical system which has a very definite effect upon the geometrical interpretation of observations made at the extreme edge of the solar disc. Such phenomena as the "second limb" reported by Cragg, Howard and Zirin (1963) can be shown to be of this type. The magnitude of the instrumental redis tribution of light within the solar image is hard to assess theoretically. Information relating to such effects must come from empirical determinations.
Finally, the chromosphere itself provides two com ponents of radiation at the solar limb. First are the emission lines which occur immediately at the limb with an intensity that is a few percent of the central disc intensity in the nearby continuum and drop off in intensity with scale heights of the order of several hundred kilo meters reaching in some cases to heights of 10,000 or
15,000 kilometers. There is also a chromospheric continuum radiation. In analyzing data from the 1952 eclipse Athay
(1955) finds that the chromospheric continuum intensities at an elevation of 900 kilometers is less than one-half of one percent the intensity of strong chromospheric lines at approximately the same height. It seems evident that continuous radiation from the chromosphere itself will not be a disturbing factor in the analysis of seems made in the light of emission lines at the immediate limb.
The intensity of the continuous chromospheric emission changes very slowly with wave length so would tend to contribute equally to two spectral regions closely spaced in wavelength.
The problem is thus one of determining how much of the chromospheric line radiation it is possible to measure off the limb of the sun in the presence of radia tion scattered by the atmosphere and the optical apparatus into the same region of the focal plane of the telescope- spectrograph system. If indeed the chromospheric lines observed at the limb are as much as 20 percent of their monochromatic disc center intensity and scattered light
(or sky brightness) is only Jj% to 1% of this intensity, then chromospheric line emission will be observable to a distance off the continuum limb of the sun at which 30 the chromospheric intensity drops to about the level of sky intensity at the same wavelength, that is, having a dc signal to noise ratio of 1. The photographic survey of chromospheric lines made by Pierce (1968) with the
McMath Solar Telescope indicates the fact that chromospheric radiation can be easily detected off the limb of the sun.
In order to test the proposed procedure of making chromospheric photoelectric scans several basic require ments seem to be desirable. These include the following:
(1) A solar telescope in a location with promise
of at least some fraction of the available time
possessing good to excellent seeing conditions.
(2) The ability to detect and record radiation reach
ing two different wavelengths in the focal plane
of the spectrograph.
(3) A technique for repetitively scanning a region
of the solar limb across the spectrograph slit,
or some other technique to enhance the S/N ratio.
(4) A convenient data acquisition and storage system.
The requirement for an existing solar instrument with extensive data handling capability led immediately to consideration of the McMath Solar Telescope on Kitt Peak.
This instrument possesses the longest primary focal length of any solar telescope. It also has as part of its 31 available Instrumentation a matching spectrograph and existing data acquisition equipment.
A request was submitted for observing time with this telescope and attempts were made to locate or prepare auxiliary apparatus and an observing program that could be used with the instruments at Kitt Peak. III. DESCRIPTION OF THE OBSERVING PROGRAM
In order to assess the technique of simultaneous
sampling in line- and continuum-wavelength regions for the
purpose of measuring mean chromospheric structure and emis
sion I requested an opportunity to use the McMath Solar
Telescope of the Kitt Peak National Observatory. I proposed that attempts be made to measure this mean structure in
the cores of some of the strongest chromospheric lines at
a variety of heliographic latitudes.
A number of chromospheric lines selected from the
Pierce (1968) catalog on the basis of large observed in tensity was suggested as possible candidates. The proposed
list of 26 lines is shown in Table 3. Of the original
lines proposed only two were not observed. In addition ten lines were added to the observing list at the telescope.
These additions are listed in Table 4.
It was my intention to make observations simultaneously
in the central peak of a chromospheric feature and a con tinuum point selected as close as possible to the position of the chromospheric line. I originally proposed making
scans every 10° of heliographic latitude but later revised
this to every 30°. 32 TABLE 3
List of Proposed Chromospheric Lines Limb Scan Program
Intensity In Pierce Catalog (1968) >100 >8q >50
*3256 Fe II 1373** Si 3 *3277 Fe II *3750 ''12 *3933 Ca II(K) *3770 »n *3889 *3968 Ca I K K ) *3797 »10 *1102 »6 *3970 Hc *9930 La ZI *1315 Hy *1129 Sm II *9971 He I *1861 *1110 Ce II Fe II *5875 He I*9629 *959o Fe II *6563 »o *6678 Ho I *9593 Ce II *9620 Fe II *9666 Fe II *5019 Fe I, II
TABLE
Lines Added to the Observing Procran at the Telescope
Line * Intensity
H15 3712 90 H11 3722 60 H9 3835 100 Ha 1 5890 20 Ha I 5896 20 Fe II 9389 100 Fe II 9629 100 Fe II 9921 57 Sr II 9077 99 Ti II 9533 50
Intensities from Pierce (1968) 34
In response to this proposal a block of observing times was scheduled for me on the McMath Telescope from December
16, 1969 to December 22, 1969.
Preliminary discussions indicated existing data acquisition programs might be directly applicable. My selection of an existing rocking mirror scanner designed by Livingston (1968) meant that no auxiliary apparatus would need to be constructed as the spectrograph already was equipped with an adjustable, dual detector output. The
Livingston scanner was originally designed to scan short segments of the solar disc across the entrance aperture of the spectrograph. It seemed ideally suited to the task of scanning the limb region and was intended to be used without modification.
Results of Preliminary Run. The December observing run yielded little usable data, but was of great importance to the success of the entire program. In the midst of thunderstorm activity about 10 hours of observing time were utilized. Some spectral scans around regions of interest both on and off the limb were obtained. A few slow drift scans using the dual detector arrangement were made to assess the possibility of observing the differences between the continuum and core scans. It was found at the beginning of the December run that the one-revolution per 35
second scanner-motor had burned out and a new gear motor had to be ordered. The new motor arrived on the last day of the observing run so actual limb scans were obtained only on the final day and then under conditions of very high wind and extensive image motion.
During five days at the telescope and over coffee at the Tucson offices, Charles Slaughter, Dick Aikens and I decided attempts to use unmodified existing data handling programs would prove too cumbersome and time consuming. A second run was scheduled for August 1970 to allow time to write a new data acquisition program and develop some modifications to the observing technique.
Probably most valuable of the gains made in the
December observing run was the opportunity to accumulate experience and appreciation for the McMath Solar Telescope and allied instrumentation. Many valuable suggestions and much needed help were very generously offered by the observing assistants. The opportunity to work around the telescope while it was being used by other observers greatly increased my level of confidence and competence in using the instrument.
The information brought back to Ohio at the completion of the December run provided much needed real data for the development of the data analysis program which was finally 36 adopted. The data were not deemed suitable for the evaluation of the technique. It did provide an opportunity to write and test data analysis programs which proved very useful when the August 1970 data finally became avail able.
Some data acquired during December provided strong qualitative support for the value of the proposed ob serving program. On December 21 I made a series of slow scans of the east limb of the sun. The scan was generated by slowing the heliostat drive rate slightly so that the solar image would drift westward at the rate of about 3 seconds of arc per minute. Feeding the two output channels to a Bristol dual pen strip chart recorder I obtained tracings of Ha and the nearby continuum simultaneously as a function of position with respect to the solar limb.
A section of the original recorder chart is reproduced in
Figure 4.
The scan rate was sufficiently slow that rapid image excursions averaged out. To check the reproducibility the chart drive was turned back and a second scan super posed upon the first. The two scans possess similar detailed features indicating that methods which average out seeing effects will maintain the overall gross features of the limb intensity profile. This lent support Figure 4 Original strip-chart record of slow limb scans two in the core of Ha and one in a nearby continuum wavelength. 38 to the idea that the method might work, at least for the
stronger chroroospheric lines.
During the December 1969 observing period on Kitt
Peak a number of line profiles were obtained photoelectri- cally with the spectrograph slit oriented parallel to the limb at various heights above the photospheric limb and compared with the line profiles obtained with the slit placed well onto the solar disc. The purpose of this was to assess the feasibility of locating chromospheric features by setting the spectrograph exit slit on a spectral feature located using the spectral scanning program already available with the McMath spectrograph. A number of these line profile scans are illustrated in Figures 6 through 9*
Figure 5 identifies the approximate locations of the entrance slit of the spectrograph with respect to the solar limb at which the various scans were made. The letters correspond to the identifying letters on the individual scans in Figures
6 through 9. In the third profile where the distinct double peak of H shows up, traces of nearby photospheric emission can also be detected. Vertical intensity scales are quite different for each trace. The reduction program utilized with the spectral scan routine for the McMath spectrograph arbitrarily scales the entire scan between zero intensity and the maximum intensity recorded over the entire scan. SOLAR DISC
SOLAR LIMB (r • 16.5 inches)
Figure 5 A scale drawing of the solar limb indicating the approximate placement of the spectrograph slit to obtain the spectral scans in Figures k through 7. Position "E” was always at least 6 mm. outside the solar limb. 40
H6
(A)
(B)
(D-E) .
(E)
Figure 6 Spectral scans made in. the region of HO at various locations near the limb. Geometrical placement in the solar image is identified in Figure 3. 41
Ha
(A)
(B)
(C)
CD)
(E)
Figure 7 Spectral scans of Ha made at limb positions Indicated In Figure 3* (A)
(B)
La II
Figure 8 Spectral scans around A M 29 showing chromospheric feature due to La II. Geometrical placement In the solar Image is identified In Figure 3« (A)
(B)
(C) 12
Figure 9 Spectral scans of H12 which Is Indistinguishable on the disc scan, (A). Slit positions are those of Figure 3« 44
Thus, the scans are all essentially normalized to the brightest intensity obtained at the particular elevation.
This results in Figure 6 in an effective increase in gain of perhaps a factor of 100 or 200 from the top scan, taken on the solar disc, to the bottom scan which looks quite similar, taken entirely in the scattered sky light.
The scans of Ha seen in Figure 7 were not as care fully placed as those of Hp but a similar run of height is obtained from the top seem taken on the solar disc to the bottom which was recorded well off the solar limb.
Figure 8 is a spectral seem in the region of X4429 which illustrates the appearance of the chromospheric feature due to La II near the center of the scans. The top scan was taken on the solar disc. The middle seem was made with the slit on the solar limb and the bottom scan approx imately 1 mm off the limb. The emission features showing up on the bottom scan appear in the position of a not too noticeable spectral feature on the disc scan. In fact, scans of this sort taken with the slit just off the limb were used to set the spectrograph for observation of the chromospheric feature when no prominent Fraunhofer feature appeared in the disc scan. Figure 9 illustrates the ap pearance of the hydrogen line, t which is located in the wing of a very strong iron line and is essentially 45
indistinguishable on the disc spectra. The scan taken just
off the limb reveals a prominent emission feature which
persists for some distance away from the limb.
It seems from these observations that an image dis
secting device using multiple sensing techniques not unlike
the scanning program employed in this investigation might
provide image profile information of chromospheric lines
with somewhat greater quality than has been obtained here
tofore and is a program which would seem to warrant further
investigation.
A further observing period was scheduled for August
1970. A modified data handling program was prepared by
Slaughter and Aikens and was tested and revised during
the first few days of the run. A new drive cam for the
Livingston scanner was machined and put into operation just
before observations were begun on the second day. The
efficient data acquisition program and some long periods
of cloudless sky allowed collection of a large body of
data and the opportunity to terminate the run two days
prior to its scheduled completion.
Description of Kitt Peak Apparatus. Table 5 lists
the characteristics of the optical and mechanical features of the data acquisition system used in this investigation.
The image scanner consists of two flat mirrors TABLE 5
Data Relevant to August 1970 Observing Run -
McMath Splar Telescope Primary Aperture 160 cm (62 Inches)
Focal Length 90 m
Focal Ratio f/56.25 Imago Diameter 798 mm
Focal Plano Image Scale 17**0 km/mm
Spectrograph
Speed r/6o
Entrance Silt Width 100 microns
Length 2 0 mm Exit Slit Widths Continuum 100 microns
Line Core 60 microns Scattered Light Ghosts 5JC Approx. for 5th order
Oenoral 01
Orating Size 25 cm x 15 cm Grooves/mm 610 n 155000
Scanner
Linear Image Scan Rate 60.k mm/sec
Solar Scale Scan Rate 105.1 km/msec
Solar Scale per Sample Point 210.2 km/channel 47
mounted on a pivoted arm so arranged that as the arm is driven through a short arc a light ray incident upon the mirror system will be swept nearly linearly through suc cessive positions along the base of the scanner. Figure 10 is a schematic representation of the principle of the rocking arm scanner.
Livingston (1968) describes the scanner in detail.
Used over its full range it displays a non-linearity near the ends of the scans of about 0.11%. Using a cam newly fabricated for this program the total scan was about
2/3 that used by Livingston and the principal source of non- linearity iB the figure of the cam. The quality of the image scan is evaluated in Appendix II.
Pierce (1964) describes the McMath Spectrograph. He indicates the intensity of ghost images in the single pass amounts to approximately 5% of the central peak intensity in the 5th order and that there is perhaps 8% general scattered light within the spectrograph itself making it desirable to utilize a system to double pass the grating for photometric studies. The requirement that observations be made at two wavelengths simultaneously means however, that two separate detectors be mounted side by side in the focal plane of the spectrograph. It was thus necessary to use the photographic port in the McMath PIVOT PIVOT ✓ POINT ' POINT Mi
ROCKING ARM
INCIDENT INCIDENT SOLAR SOLAR RAY RAY
Front View
DIRECTION OP SCAN
SLIT SLIT
POSITION POSITION "B"
Figure 10 The principle of operation of the rocking arm scanner, after Livingston (1968). 49
Spectrograph. Also, the Intermediate slit in the double
pass optical train does not admit a wide enough spectral
band to include the total range of wavelengths necessary
to be available simultaneously. Observations thus had to
be made with only a single pass of the spectrograph grating.
As a result considerable quantities of spectrally scattered
radiation could be expected in the limb scans obtained in
this work.
The entrance slit to the spectrograph was a 100 micron by 2 centimeter aperture while the defining exit
slits mounted in front of the photoelectric cells were
100 microns wide for the continuum detector and 80 microns
for the line core. These slits were just under 2 centime ters long. The average dispersion in the 4th, 5th and
6th orders is approximately 0.15 AngBtroms/mm, so the
scans were made in segments of the solar spectrum approx
imately 10 or 20 milliangstroms wide.
The detection of radiation in the spectrograph focal
plane was accomplished by two uncooled photomultipliers with S-20 photocathode coatings. The two detectors were operated off separate bias supplies and the output amp
litudes could be individually controlled either by adjust
ing the bias potential or by step attenuators in the
preamplifier stages. 50
Signals from the photomultipliers were simultaneously sampled for one microsecond at preselected time intervals.
By combining the scanner rate with the number of sample points desired across the limb, a sampling rate can be selected. For the extreme limb scans of 300 sample points a sample rate of one point every 2 milliseconds was chosen and utilized throughout the observing run.
The individual pairs of sampled intensity were fed to an analog-to-digital converter, then to an SDS data handling computer which counted, timed, controlled the data acquisition sequence and recorded the data and ap propriate identification blocks on magnetic tape. The tapes generated at the telescope were in 256 BPI octal format. These tapes were then carried to the Tucson offices of KPNO where they were translated and packed into 800 BPZ binary coded decimal format. During the transfer, it was possible to eliminate blocks of data which had been recorded on the mountain but for various reasons (such as clouds or a wrong gain setting) were not suitable for reduction.
Thus only those data which were not affected by serious problems or obvious maladjustment were brought back to Ohio for reduction.
Data processing equipment at Tucson and Columbus are fortunately quite compatible. The machine at KPNO 51 in Tucson is a CDC 6400. The terminal at Otterbein College through which the unpacking and seem integration routines were run is tied into the Battelle Memorial Institute
CDC 6400. This minimized the problem of removal and trans lation of the data written by the Observatory computer.
Much of the exploratory computations and many of the plot programs in this work were carried out on the Wang
700B/702 programable calculator at Otterbein College.
This machine was easy to manipulate, had a desirable plot format for discrete points, was usable by untrained assistants and was almost always available when I needed it.
Geometry of the Solar Limb. During the time of observation the radius of the solar image was just over
399 mm. The length of the spectrograph slit was 20 mm.
By the theorem of Pythagoras the distance of the limb to the top of the slit centrally tangent to the limb is found to be 0.1253 mm. This distance is effectively reduced because the entrance slit of the predisperser is curved by an amount just sufficient to produce a straight spectral image at the output of the prismatic dispersing element.
This slit has a curvature of 2150 mm. In effect, this brings the top of the spectrograph slit 0.0232 mm. closer to the solar limb when it is centrally tangent to the limb. 52
Care was taken during all observations to assure that the curved predisperser slit was properly placed with respect to the curvature of the limb to take advantage of this slight gain in height resolution.
Over the entire length of the slit a smearing of the geometrical resolution results amounting to 0.10203 mm., equivalent to 177.5 km on the solar disc. This is the same order of magnitude as the width of the spectrograph slit (.1 mm.) whose projected width is 174 km. The separa tion of levels in the chromosphere sampled by the scan program is 210.2 kilometers. Thus the effective width of the spectrograph slit including the effect of the curvature of the solar limb is 351 km. while the distance the slit is moved between sample points is 210.2 km. The net result of these conditions is that the intensity samples of successive layers of the solar atmosphere over lap by about 40%.
Technique of Observation. 'With the rocking arm scanner turned off a number of spectral scans (that is, scans along the direction of dispersion covering approxi mately 10 angstroms) are obtained with the detector normally used for monitoring the line core. The purpose is to locate the desired line core on the appropriate detector.
The spectral scan program utilized at the McMath Solar
Telescope allows accurate setting of the position of a 53 spectral feature on the exit slit of the photometer.
This is accomplished simply by setting a fiducial mark on the desired spectral feature on the display oscilloscope at the control console and initiating a scan sequence.
The data acquisition program then automatically centers the subsequent scans on the position indicated by the fiducial mark.
Once the line core has been centered the spectral scan program is switched to accept the output of the second detector, separated from the first by approximately 20 angstroms, and the position of the second detector is physically moved relative to the detector centered upon the chromospheric feature until a region of relatively clear continuum is located on the fiducial mark of the monitor scope. This is done without moving the line core detector and without shifting the spectrum with respect to the line core detector. This leaves the dual detectors in a configuration in which one photometer will record a scan of the limb in the light of the line core while the second detector will record a similar scan in precise geometrical relationship but using light of continuum radiation not far from the line core.
When the detectors are properly Bet in position within the spectrum the program is switched to the scan sequence 54
and the scanner is turned on. The number of scans and
the time interval between sampling is then set on the
control panel and the limb of the sun is set so that it
lies at approximately the middle of the total throw of
the scanner. The entrance slit is set parallel to the
limb of the sun. The orientation of the slit thus deter mines the position along the limb or the latitude on the
sun. The orientation of the slit is varied by changing
the orientation of the spectrograph tank. The whole tank
rotates to maintain a fixed position relative to the sun
as the sun moves across the sky.
No attempt was made to match the sensitivity of the
two photocells nor to try to adjust one intensity to match the other intensity for the center of the solar disc. Either one of these procedures would be convenient
to carry out in making future observations of this type.
In view of this oversight it was necessary to write
a program to normalize the line core scans to the con
tinuum scans at the center of the disc. In a number of
instances full disc scans were made which included in
tensity data at the extreme limb as well as near the disc
center. In a few cases gain changes or dynode voltage
changes had been made and the full disc scans did not
provide the necessary normalization data. A description 55 of the normalization and seem integration program is included in Appendix I.
Actual data were in the form of individual sampled intensities in 50 pairs of 300 point scans. This meemt that each observed limb position yielded a total of
30,000 individual intensity points all of which were recorded on magnetic tape for processing in Ohio.
The full disc scans were conveniently made by driving the solar image across the spectrograph slit using the slow slewing rate of the declination drive.
At this rate the solar disc traversed the slit in about
28 seconds. By decreasing the sampling rate to once every 100 milliseconds the entire disc could be covered in 280 channels with about 10 channels off each limb into the sky. Some representative disc scans are presented in Figures 11 through 15. The representative scans were made on 27 and 28 August 1970. In all cases the plots are normalized to the maximum value of the continuum scan. The line core scan was then allowed to fall where the gain setting arbitrarily placed it. This results in the line core seem appearing in some cases above the level of the continuum, sometimes below*
A distinct asymmetry is noted in the line core scans of Ha and Hg, Figures 11, 12, and 13. This asymmetry apparently results from the fact that the full disc scans 56 were made along the north-south diameter of the sun and not along the direction of the sun's polar axis. The position of the line core detector was set in the spectrum at the south limb. The axis of rotation of the sun was inclined to the north-south direction by about 19° on these days and the solar rotation results in a Doppler shift sufficient to move the line core detector out of the center of the line as it approaches the north limb. This results in a slight increase in intensity for this detector as the scan proceeds north.
Figure 11 is a scan taken in Hg during the morning of 27 August and may be compared directly with Figure 12, a scan of Hp made in mid afternoon of the same day. It is noted that a sunspot appears near the central meridian of the sun in both scans and is associated with the same sunspot region seen in Ha , Figure 13. Evidence of a bright plage region adjacent to the sunspot appears in the Ha scan.
By the following day, the sunspot observed on the
Ha and H£ traces has evidently moved from the north-south meridian of the sun to be replaced by two spot groups, one nearly centered on the north-south meridian, the other about 30° south. Both spot groups are evident on the Ca II scan, Figure 14, as evidenced by very noticeable enhance ment of the line core emission in the region of the spots. Line Core
Continuum
a 35
Figure 11 Full disc scan, HB, 27 August 1970, 7:30 A. M. 27 Ault 1970 Set on South LIKb South to North
Line Core
Continuum
Figure 12 Full disc scan, HB, 27 August 1970, 3 = 30 P. M. m « h o . 90 31 Aur. 1970 l»:38s0? Set on South Llab South to North
Continuum
Line Core
Figure 13 Full disc scan, Ha, 27 August 1970, 2:38 P. M. Continuum
Line Core
Figure 14 Full disc scan, Ca II (H), 28 August 1970, 8:56 A. M. n i a it fa it II «■«•» 1*10 Itlltll Sat oa Soath LlaS loath ta l a n k
Continuum
Line Core
Figure 15 Full disc scan, Fe II, 28 August 1970, 8:16 A. M. 62
The same spot regions are evidenced by increased emis sion in the light of Fe II as seen in Figure 15. The scans taken on 28 August, 1970, were made about 40 minutes apart*
The way in which the data obtained from the single scans were utilized in the reduction of the extreme limb scans is described in Appendix 1.
The multiple scan limb observations and the single full disc scans were recorded together with appropriate identification blocks for transport back to Ohio. The ID blocks contained information which allowed identification of the associated data: Date, Time of Observation, Number of Scans, Points per Scan and whether it was a leading or trailing ID block. Each set of scan data was set off by similar leading and trailing ID blocks.
By 31 August I was ready to travel home with a tightly sealed box of five magnetic tapes tucked under my airline seat. My only worry was the possibility of passing through a magnetic metal detector and wiping out the whole run.
Fortunately, out of the entire collection of taped data only two files of a total of 380 contained poorly recorded data and could not be used.
Method of Data Analysis. Actual reduction of the raw data was carried out in a gradual manner over an extended 63 period of time. In the early stages of analysis it was not clear how effective the integration procedure might be. There was also some doubt about which characteristics of the limb profiles might be most productive in revealing information about the chromosphere.
The data reduction program has undergone modifica tion and editing during the entire analysis. Most of the changes have served to streamline the procedure and eliminate steps no longer necessary to the solution of the problem. The basic process of reading the individual
scans from the tapes, integrating them and plotting the
integrated limb scans has remained essentially unchanged
from the start.
Raw data obtained at the telescope for every limb position observed consist of 50 individual scans across the limb of the sun each made up of pairs of sampled
intensities separated from one another in time by two milliseconds. The scans cover a range of about 3.7 centi meters in the focal plane of the telescope corresponding to about 63,000 kilometers at the sun's distance.
In addition to the limb scan data calibration scans were made on two nights during the observing run. These were for the purpose of calibrating the image scan rate.
Typical reduction procedure for chromospheric features
having full disc calibration data available was carried 64
out in the following way. The sampled data points in the
two wavelength regions are geometrically coherent (i.e. .
they represent a one to one correspondence of intensity measurement at the same geometric point with respect to
the limb). It is thus necessary throughout whatever trans
formations are made to handle both the line core and con
tinuum scans as complete coherent units. This means that
if one scan of a pair is to be shifted geometrically with
respect to a succeeding or preceding scan in order to bring
corresponding elements of the sequential scans together
the corresponding paired scan muBt be shifted by the same
amount to maintain the geometric coherence inherent in
the scans. A Fortran program was written for the CDC6400
designed to remove the effects of slow image drift that might
arise if the telescope drive rate is not precisely adjusted.
The fifty individual scans should be summed after
removing as much as possible relative shiftB due to gross
image motion. This will reduce the smearing of the limb
by an amount which depends upon how steady the image was
in the 50 seconds during which the scans were made. Figure
16 is a plot of such summed scans, each consisting
of 400 sample points, added directly, with no relative
shifts between individual scans. Figure 17 was obtained 65
I(P)
Line Core
Continuum
P
Figure 16 Integrated, unshifted limb scans of Ha and the nearby continuum obtained December 28, 1969. Fifty scans, each containing 400 data points are integrated. The vertical intensity scale is arbitrary. 66
I(P)
Line Core
Continuum
P
Figure 17 Integrated, shifted limb scans. The data are the same used for Figure 16. Note the smoother line core scan with enhanced disc detail. 67
I(P)
Line Core
Continuum
P
Figure 18 Plots of Figures 16 and 17 superposed. The darker trace represents the unshifted integrated data of Figure 16. The change in vertical scale between the two line core scans was Introduced in the computer plot routine. The increase in the slope of both limb scans resulting from the shift routine is quite evident. by integrating the same data using the scan shift routine to compensate for gross motions. A casual comparison of these two plots reveals no startling differences. An over lay of the two, however, shows immediately that both the chromospheric and photospheric limbs are steeper in the shifted curves. Figure 18 is a direct overlay of the two set8 of curves just considered. The scans are made to coincide near the point of maximum slope on the continuum curve. The heavier lines correspond to the scans that were integrated without use of the shift routine.
To gain some idea of the magnitude of the improve ment brought about by the scan shift routine I arranged to calculate a standard deviation for each point of the integrated scans. To try to maintain numbers that were comparable in size on opposite sides of the limb
I divided the standard deviation by the value of the sum of the intensities.
Figure 19 illustrates plots of the standard devia tion per unit intensity for the unshifted (A) and shifted
(B) integrated seems. Since the values of the summed intensities are comparable in the two cases these plots may be compared point by point. Shifting of the indi vidual scans before summing reduces the stemdard deviation by nearly a factor of four. Any residual stemdard devia tion that remains etbove that of the adjacent flatter regions a
(A) (B)
-000 20.000 6.557 <0 CHRNNELSIX10 l > CHflNNELStXIO U UNSHIFTED RND UNSMOOTHED SHIFTED AND UNSMOOTHED
Figure 19 The reduction in the standard deviation of each integrated datum point produced by the shift routine. The values for the shifted integrated scans (B) of « Figure 17 are compared with the unshifted integrated scans of Figure 16. (A) 70 probably arises from higher frequency fluctuations of
the solar limb and would not easily be removed by a simple process of shifting complete scans an integral number of channels.
One piece of information printed out routinely in
the integration program is the number of channels each
seem is shifted before being added to the total scan.
Early in the morning of 28 August the first set of scans were noticeably drifting as I monitored the display screen.
I adjusted the drive rate and repeated the scans. Figure
20 is a plot of the number of channels shifted as a func
tion of the sample time while the image was drifting.
The same 1b plotted for the scans after the drive rate
had been adjusted to compensate. In the first case the
image is drifting an equivalent rate projected to the
solar distance of 50 km/sec or about one channel every
four seconds. If no shift routine were applied to the
integration program a smearing effect 12 channels wide
would occur. This alone is equivalent to 3.5 seconds of
arc. Even when the drive rate is maintaining the limb
in a fixed position large scale image fluctuations oc
curred over about a six channel range. Left uncompensated
this results in a smearing due to image motion alone
of about 1.8 seconds of arc.
Similar analysis of other scans leads to a range 71
+12
a>c +6 § JG U (A)
0 0 50 Sample Time (sec.)
+4
0 o G § A O (B)
0 50 Sample Time (sec.)
Figure 20 Plots of the number of channels shifted as a function of the sample time or channel number for a drifting image (A) and a non-drifting image (B). 72 of image shift from two channels up to 15 or 18 channels.
Left unshifted these scans would be smeared from 0.5 second to over 5 seconds of arc.
I decided the differences between the line core scans and continuum scans would be more noticeable if they were plotted to very nearly the same scale. I devised a program subroutine which would normalize both scans to the central disc intensity# X(p*o)# so that in effect I would be able to display plots of X(p)/X(o) as a function of radial distance# p# from the solar image center.
Included as a part of the integration-normaliza- tion computer program was the generation of a hard copy of the raw integrated intensities# the normalized in tegrated intensities# data about the amount of shift accomplished for each scan and a tabulation of the first differences of alternate channels for the purpose of lo cating critical portions of the limb seems. An example of the complete printout for a single limb position in one wavelength is included in Appendix X.
After the full scans were plotted and printed out# selected sections were examined in greater detail using a Wang 700 in conjunction with a Model 702B plotter.
An example of an expanded limb scan is illustrated 73 in Figure 21* The scans were made in the core of Hg at X4862 and a continuum point near X48B8 on the east limb at a solar latitude of 10° South. The time was
7:03 a.m. on 28 August 1970. The plot covers 60 channels, each corresponding to a separation from its neighbor equivalent to 210.2 km radial distance in the solar atmosphere.
Examination of the continuum scan reveals a smeared limb dropping essentially below the *5% level approxi mately ten channels outside the steepest portion of the intensity curve. Selection of the 0.5% point (0.005 in I(p)/I(o)) is based upon the ability to detect the rise of intensity of this order on the original plot.
Comparison of the line core plot with the continuum plot reveals a slightly shallower slope in the region
I(p)/I(o) - 0.15. Radiation is also detectable to nearly double the extent beyond the line core "limb." In addition a second hump occurs in the line core scan in a position corresponding to that of the continuum limb.
This second hump corresponds to the "second limb" described by Cragg, Howard and Zirin (1963). The double limb shows up in the light of all strong chromospheric lines in the present program at times of good seeing. The magnitude of the hump (about 8%-10% of the continuum intensity) 74
10,000 5000 P - R, km. Figure 21 Expanded scan in Hg — good seeing.
0.4 ~ m
0.0 - 10,000 5000 km. Figure 22 Expanded scan in H0 — poor seeing. 75 as well as the exact location in all scans coincident with the continuum limb argues very strongly for inter* pretation of this feature as scattered continuum light
into the wavelength domain of the line core. Zn discussions with Livingston concerning this matter I was able to ex* amine numerous high quality photographic spectrograms
taken in H0 showing very strikingly the occurrence of
continuum light scattered at the extreme limb. Livingston's
photographs were also taken in the single pass and show
convincingly the intrusion of continuum light into the
line core when seeing becomes good.
Figure 22 illustrates a scan in Hg taken late in
the morning of 29 August, also at 9° south latitude, when the seeing had deteriorated markedly. There is only slight indication of the "double limb" and a con*
siderably extended smearing. The overall effects of
atmospheric smearing of the solar image limb will be
examined in greater detail below.
Z made some attempts to remove the effects of this
scattered light, but for the purposes of this study it
introduces no spurious results. Zt even provides, in
some cases, a handy indicator of the position of the
continuum limb when only the line core scans are being
examined. 76
I examined the behavior of typical limb profiles which are smeared by simple spread functions. I hoped to find characteristics of the smeared profiles which would provide information about the chromosphere. Z thus devoted some effort to the search for quantities which remain invariant under image distortions due to simple smearing functions.
The Search for Invariant Parameters. Image profiles measured in open telescopes exhibit distortions which arise from turbulence both inside and outside the tele scope optical train. Sources of this distortion are described by Keller et al. (1956). Methods of de- convolution of smeared star images have been discussed by
Keller and Galli (Keller et al. (1956)). David and Elste
(1962) and Staveland (1972) have treated solar images, and
Perrin (1960) analyses optical images in general.
If one treats the unsmeared solar limb intensity run with distance from the disc center, F(r), as the object function, then the image function, I(r), resulting from a convolution of the object function with some spread function, S(x), will be: +«• I(r) ■ / S(x)F(r-x)dx (2)
In this expression, r is the radial coordinate from 77 disc center of the object function and x is the coordi nate in the same direction associated with the spread function. I have assumed for the purpose of this analysis a one dimensional scattering function. See Appendix III.
It is shown there that the scattered profile of the immediate limb is indeed very little different when calculated using either a one-dimensional or a two-dimensional scattering function. I did not extend the analysis to very broad spread functions which would require departure from the assumption of a nearly straight limb.
To examine the effect of different amounts of random agents of smearing I subjected several arbitrarily as sumed limb intensity profiles to convolutions with a range of Gaussian spread functions,
S(x> - e“**bx>2 (3) in which b is the reciprocal of the standard deviation, and serves to define the reciprocal of the breadth of the
Gaussian function.
The operation represented by Equation (2) was carried out numerically.
The limits of the integral must be taken formally to be ® and -® because the spread function trails off indefinitely. In the numerical integration the limits 78 are selected to be those for which the ordinate equals the smallest significant figure in the computation.
This value was selected arbitrarily to be at the level of relative intensity 0.005 or the one-half percent point. It introduces no appreciable error because this value of relative intensity approximates very closely the level to which the chromospheric limb scans can just be distinguished from the shy background. The convolution program was written for the Wang 700 so that only the value of b, the dispersion factor, needed to be entered followed by the numerical values of the "unsmeared" limb. The output 'Image' function was then available as a plot of l(r) and in tabular form. By selecting Ax in the numerical calculation to equal the observed sample interval in the solar scans I could then compare directly the computed image functions with observed limb profiles.
In this way I continually varied the object function and dispersion parameter until the convolution yielded an image function which corresponded to an observed limb profile at every point to better than 1%. The object function derived in this way was then used as an arbitrary
"unsmeared" limb profile to assess the effect of the various
Gaussian spread functions. The unsmeared continuum profile is plotted as solid points in Figure 23. This figure is plotted to the same scale as the expanded scans of most 79
K p )
Figure 23 Theoretical limb profile for X4888. Solid points — unsmeared. Open points — smeared with a Gaussian spread function with b “ 0.3 chan"1
R ♦ P Figure 24 First derivative of intensity profiles of Figure 23. Vertical scales for the two curves are not the same. 80
of the observed profiles. I then used the resulting
intensity profile to assess the effects of various amounts of atmospheric smearing upon the object function. A plot of the first derivative of the smeared and unsmeared limb profiles of Figure 23 is displayed in Figure 24.
The vertical scales of the two plots differ by about a factor of four. Several characteristics of the smeared profiles may be noted.
First, only the light in the neighborhood of a steep slope seems to be noticeably redistributed. Thus, steep discontinuities located in gradually sloping portions of the intensity scans, such as in the disc distribution, tend to be smoothed out. The principle effect is noted in the immediate vicinity of the limb.
The basic result is to move the position of the knee of the curve toward the center of the disc while producing outside the object limb a toe trailing off into the sky background. If one examines the first derivative of the unsmeared and smeared profiles it is found that the position of the peak (indicating the inflection point in the intensity tracing) does not shift. It is found that this inflection point does not shift when a smearing function is convolved with an already smeared limb profile indicating that for limbs having appreciably more gradual 81 object slopes the position of the inflection point is not affected by smearing with a Gaussian-type spread function.
It is thus demonstrated that for intensity profiles that are smeared with symmetric smearing functions the loca tion of the inflection point will not be affected (by more than a channel width) and in a series of comparative limb scans the relative positions of the inflection points in the continuum radiation and the line core radiation will not be shifted with respect to each other. The separa tion of these two points will provide one measurable invariant parameter that may be used to describe a mean height in the chromosphere.
A further possibility exists with regard to the suggestion by Wilson and White (1966). They suggest using the knee of the curve corresponding to a tangential optical depth t*. of 2.6 to specify a limb position for determining mean heights of formation in the atmosphere.
Provided the line core profile and the continuum profile have nearly the same slope, the relative position of the two knee points will not be changed more than one channel by a simple smearing function.
As a further check on the effect of application of smearing function to a limb profile I constructed a theoretical intensity profile to represent the Hp 82 chromospheric limb. I simply applied to the unsmeared continuum limb profile (obtained above) intensity distri butions which fall off from the steep portion of the continuum profile with various scale heights. I finally selected an "off limb" scale height of 1200 kilometers to use for this theoretical limb profile because it produced a maximum extent of emission more nearly repre sentative of the total extent beyond the sharp limb in
Hfj. I further assumed that this extended region of in tensity would meet the sharp limb profile at a value of approximately 0.1 di,)0 *
Using this theoretical chromospheric profile I then applied the smearing function and produced a theoretical smeared limb scan shown in Figure 25. Figure 26 illustrates the first derivative of the unsmeared and smeared theoret ical profiles. The peaks of the two curves coincide indicating that the smearing does not affect the position of the inflection point. The relative heights of the two peaks differ by a factor of about four. It is in teresting to note in Figure 26 that in the case of the smeared profile there is a noticeably greater amount of radiation outside the limb not found in the case of the unsmeared profile. However, beyond about 10 channels outside the inflection point the smeared and unsmeared Figure 25 Theoretical line-core profile for Ho. An arbitrary intensity distribution (with a scale height of 1200 km.) was matched to the assumed continuum distribution of Figure 23 at I(p)/I(0) » 0.1. Open circles represent the profile _ smeared by a spread function with b ■ 0.3 chan .
Al Ap
Figure 26 First derivative of intensity profiles of Figure 25. Vertical scales for the two curves are not the same. 84 profiles present essentially the same slopes.
I felt it might be instructive to see what effect the smearing function would have on measured scale heights.
If we define the scale height in terms of the expression:
X(x) « I0e“x/H (4)
Where I(x) is the intensity at a point x km. from the position where X0 is recorded and H is the scale height, equal to the reciprocal of the logarithmic gradient of
X, i.e.: 1 H (5) it is possible to calculate a scale height between ad jacent points in an observed image profile intensity scan using the relationship:
Ax H " lnl0-lnl • (6
For intensity points separated by fixed distances,
Ax, it is only necessary to enter the two intensities observed at the points separated by Ax and obtain a scale height.
X applied Equation (6) to the data points repre sented by the theoretical line-core limb-scan of Figure
25 and a series of smeared limb profiles having different values of the Bmearing parameter b. The results for the 85 cases b ■ 0.5, 0.4, 0.3 and 0.2 are shown in Figure 27.
The unsmeared profile is represented by a continuous line.
Xt is instructive to note that the points outside the position of the limb lie on a very nearly straight line at the level of 1,200 kilometers. This is the value assumed in the theoretical profile for the off-limb scale height. Just inside the limb, in the region of the knee of the curve, the scale height increases very rapidly as the intensities move up onto the disc* Xt should be noted that thiB is not a true scale height for the run of physical parameters as one moves into the sun but represents an effect brought about by the fact that the solar atmosphere has become opaque. Generally, points lying on this steeply rising portion of the scale height curve are of little importance. There seems to be an elevation of the smeared profile scale heights in the immediate vicinity of the limb.
Xf the off-limb intensity extends far enough at a nearly constant scale height the smeared scale heights approach and run concurrently with the unsmeared scale heights for some distance. It would thus seem, in some cases, that it might be possible to determine a scale height for the off-limb intensity that extends to consider able distances from the chromospheric limb.
After examining a number of observed limb scans Figure 27 Scale heights plotted as a function of radial of function a as plotted heights Scale 27 Figure
Scale Height 1200 distance In the theoretical limb profile of Figure of profile limb theoretical the In distance smeared intensity profile. intensity un smeared the of line solid representative The points the connects functions. spread various 25with 0 10,500 km +++ ,+ + «■p R o T+ — profile — unsmeared
86
87 for the run of scale heights X noticed very few indicated any depression at all below a general run of values near the chromospheric limb. X therefore generated another set of smeared profiles using a theoretical unsmeared limb at which the constant scale height ran up onto the limb to a point just above the value of X(p)/X(p»o) * 0.3.
This produced a slight change in the appearance of the theoretical unsmeared and smeared profiles, but made a profound difference in the run of scale height right at the limb. Figure 28 illustrates a comparison between the two assumed chromospheric limbs. Figure 29 is a plot of scale heights for the smeared and unsmeared limb pro files. A comparison of the run of scale height of the theoretical line core limb with radial distance with that of observed scale heights is shown in Figure 30* Xt would seem from this that the large scale height indeed extends inward to a point below the level at which the chromospheric limb occurs. Otherwise a dip would appear in the scale heights in the immediate vicinity of the limb.
Also, in the case of the observed data, it seems evident that there occurs a distinct increase in scale height well off the limb.
Because of the rapid increase in opacity of the at mosphere at the limb, data relating the scale height to lower chromospheric layers are not available from line 88
Matched at Ko)/I(0)
Matched at
Ho)/I(0)
Figure 28 Comparison between the two assumed chromo spheric limb profiles for the HB line core. Figure 29 The run of scale height as a function of function a as height scale of run The 29 Figure
Scale Height 3 4800 6000 1200 2400 3600 km. b ■ b ()I0 « .) hoeia lm intensity limb theoretical at 0.3) (matched « I(p)/I(0) revised the for distance radial itiuin Sldpit dnt te un the denote points Solid distribution. smeared with a Gaussian spread function with function spread Gaussian data a same with the smeared circles open profile, smeared 6000 0.3 ca" . chan"1 LIMB 0 •»- p km. p - R,- p
89 3600 * «
• SCALE HEIGHT • • _ • • 2400 • • 0 • • • • • • • (km.) • • • * t • O « • # to_ _ • *o • * Theoretical 1200 ™ •••••••••»••■•* o Smeared Limb ^ * Observed H0 Limb *
- 0 — + 5700 km. LIMB Height In Chromosphere
Figure 30 Theoretical Hg scale heights for a spread function with b * 0.3 chan-1 compared with observed scale heights under conditions of good seeing. 91 core observations. This problem could be approached
effectively if one were to make scale height measurements
in different regions of the absorption line profile.
As one observes farther from the line core he should find
the chromospheric limb occurring closer and closer to
the continuum limb and would thus have a method for deter mining intensity scale heights deep) into the chromospheric
region, ultimately reaching essentially to the photo
sphere in the extreme wings of the line.
The relative insensitivity of the position of the
inflection point, that is, the location of the maximum
in the first derivative, is found to hold over a wide
range of values of the breadth of the spread function.
This breadth (or half-width) of the spread function
is reflected in the first derivative of the continuum
limb scan in each observation. Perrin (1960a) has shown
that the microphotometer edge trace of a knife edge is
simply the integral of the spread function. Assuming
the solar continuum limb to be a good approximation to
a knife-edge object function, the first derivative of
the image intensity profile should reflect the form of
the spread function. Indeed, if we look at the first
derivative of three different continuum limb scans we
can see a systematic change in the form of the first de- 92 riyative. See Figure 31. As the quality of the image decreases the breadth of the spread function increases and the peak value of the spread function (corresponding to the slope of the limb profile) tends to decrease.
Most spread function plots display a slight asymmetry, bulging a bit toward the direction of the disc of the sun, due to the fact that the intensity at the solar limb is not a true knife edge, or step function, but a somewhat more gradually increasing function when it gets onto the image of the disc. In this first order analysis, extensive wings on the spread function have not been considered.
This is a refinement which presumably should be included if this technique is extended.
Determination of Seeing Half-Width. It is easy to obtain measures of the half-width, that is, the number of channels or kilometers between corresponding points on opposite slopes of the spread function having a value one-half that of the peak value. All that is necessary is to plot the first derivative of the continuum limb intensity profile and read off the number of channels separating the values that are half the peak value of the first derivatives. This separation may also be expressed in terms of seconds of arc.
Examination of the Gaussian function (Equation (3)) * • Continuum
• -./
• • •
Line •
Core • •
V\.• • • • • . • A • ^• • • • • * • * .••• •• , • • • • • 1* *• * • • • • • < (A) / ’ (B) (C) • • * • • « 3 arcseck • * • • 2100 km. • + +
Figure 31 First derivatives of three different H« limb profiles; (A) good seeing, (B) fair seeing and (C) poor seeing. 94 indicates that the width at any particular height on the curve iB directly proportional to b"l. This quantity is commonly referred to as the dispersion or standard deviation of the Gaussian distribution. A determination of the half-width of the observed first derivative should provide a measure of the dispersion of the spread function. Variations in the half-width will result from changes in the atmospheric seeing and focus of the telescope.
Technique for Locating Limb Points. Figure 32 illustrates an expanded plot of the core and continuum scan for Hg obtained at 7:01 a.m. on 28 August 1970.
The horizontal separation of each point from its im mediate neighbor is equivalent to 210.2 km. The horizontal scale is thus 10,510 km. between the two plus signs.
There is a slight vertical offset between the continuum scan and the line core scan. Both scans appear to be perfectly flat at the left end of the plot. In reality both were still falling off into the general sky background.
With the plotted scale used the rate of decline of intensity in this region is not evident.
Indicated on the plots are three significant loca tions: the point where the chromospheric profile begins to rise above the sky background, the location of the 95
o.*»
0.3
I(p)/I(0)
0.2
0.1
' 0.0
CHANNEL NUMjJ£R
Figure 32 A typical limb scan showing the location of the continuum limb, the chromospheric limb and the point above the limbs at which the emission Just becomes evident. There is a vertical shift between the two scans to separate the points at the left end. 96 chromospheric limb, and the location of the continuum limb. Examination of the direct scans does not allow precise determination of any of these points. The loca tion of the limbs (i.e., those points for which the line of sight optical depth is unity or xt ■ 1), is not evident
from the direct intensity profile. However, as shown by
Wilson (1966) this point corresponds to the condition:
lIjKr) - 0 (7) or the position where the first derivative of I is a maximum.
A plot the first derivative of the intensity pro files of Figure 32 is shown in Figure 33. The location of the peaks in the continuum and line core graphs allow determination of the location of the limb inflection point to within about one half sample interval, or channel number. It is in fact from this plot that the locations of the two limbs indicated in Figure 32 were obtained.
Examination of the direct profile in Figure 32
indicates the first sample point that obviously rises above the sky background occurs at channel 178. Exam
ination of Figure 33 reveals that the first obvious departure of the chromospheric feature above the sky level occurs in channel 174, fully 840 km. higher above 97
2081s
19 Hi
0.03 Continuum S
Line Core AI/Ah
17^
0.0 I 170 180 190 200 210 220
CHANNEL NUMBER
Figure 33 First derivatives of the intensity profiles of Figure 32. Location of the three significant points are easier to determine. 98 the continuum limb than evidenced by the direct intensity scan.
Wilson (1966) demonstrated that the knee of the limb profile corresponds to a tangential optical thick ness Tt ■ 2.6. It is found that the separation of the knee of the chromospheric limb from the continuum limb inflection point decreases a channel or two as the seeing deteriorates. The inflection point of the chromospheric limb, corresponding to unit optical thickness, does not undergo such a shift. For this reason I have elected to use the inflection points to define the continuum and line core limbs. I have in most cases obtained the sep aration of these points from the plots of the first de rivative of the intensity profiles. Similarly I have read the location of the maximum extent of the chromospheric radiation above the continuum limb from the same plots.
In some instances plots of the second derivative have proven useful in distinguishing relative limb positions.
In summary, about the only invariant factors found to remain in the observed limb profiles after a convolu tion with Gaussian smearing functions seem to be* 1) the total amount of radiation distributed about the limb and 2) the position of the maximum in the first derivative corresponding to the position of the unBmeared limb in both the continuum and the relatively sharp line-core 99 profiles. One feature showing relatively minor modifica
tion in the smeared profile is the off“limb scale height
for emission lines extending to considerable distances above the line-core limb.
Status of the Solar Limb. MoBt of the limb scans were obtained in the south-east quadrant of the solar
image. In two instances when the rotating spectrograph encountered the tank limit a sequence of sceuis was made in the south-west quadrant of the disc. One set of scans was made in the north-eaBt quadrant.
The northern extremity of the polar axis of the sun was inclined about 19° to the north-south direction and tilted 7° toward the earth. This placed the east limb of the sun at a solar latitude of about 19°N. The south point of the disc was at about 68°S.
The Fraunhofer Institute Maps of the Sun (1970)
indicate relatively little prominence activity in the limb positions used for the limb seems. Table 6 lists the limb conditions for the days during which the observa tions were made. Distinct prominences were detected in the equatorial regions in either Ha , Hg or the H- and
K-lines of Ca II on all four observing days. The possi bility that off-limb intensities of these lines might
reflect the presence of disturbed regions elsewhere in
the chromosphere cannot be disregarded. Only five limb TABLE 6
Status of Observed Llnb Positions at Tines of Observation, South East Quadrant
(Fraunhofer Institute Solar Maps) Date Solar Reported Observed (1970) Latitude 1 Disturbances 1 Disturbances 1 ' “I 22 Aug. 0° +19° none - 330° -11® Dlst. on Disc. Prom. H. S S. Prominence In Htt, Call (M) and (K) Very faint In Hg 300® -HO® none 270° -68® none —
27 Aug. 0° +21® Disturbance on disc 330° - 9° Prominence 1® M Prominence In Ka and Hr 300® -38° Prominence 3® S — 270° -68® none ——
28 Aug. 0® +21® Disturbance on limb Prominence Call (H) and (K), HB Absent In Hg 330® - 9® Prominence 300® -38® Prominence 5° N 270® -68® Prominence 2® 11 “
29 Aug. 0® +21° Prominence 330® - ■ Disturbance on limb Prominence Ha and Hg 300® -38® Prominence 3® M —— 270® -68® none 101 positions during the run exhibited freedom from prominence activity or obvious nearby disturbances on the disc or in the chromosphere. Limb profiles taken in these regions might provide information about a "quiescent" chromosphere.
On the other hand, the very nature of the phenomenon known as the chromosphere argues strongly for the expectation that no region along the solar limb can be referred to as quiet or undisturbed.
Presentation of Observed Data. In the paragraphs that follow I have grouped observations more for con venience of evaluation than any significance that might be attached to the particular atomic species or physical condition in the chromosphere. Thus the hydrogen lines are not treated as one block of data, but are considered in groups roughly according to frequency of observation.
Similarly, helium is considered separately because of the need to analyze it differently from the other constituents of the chromosphere.
For each line observed I have determined the values of the following five quantities at each limb position:
1. Heliographic Latitude: ($ Sun^ • T^is is ob
tained from the position angle of the spectro
graph tank and the orientation of the solar
axis of rotation in the sky. At the start of 102
each day's observation the spectrograph slit
was aligned tangent to the east limb. This is
accomplished by driving the heliostat north and
south while rotating the spectrograph until the
slit is just tangent to the east limb. A dig
ital counter, calibrated in tenths of a degree,
was set to 0.0 in this position. This counter
then monitored the position angle of the spectro
graph tank with respect to the east point of the
solar disc. By matching the position to the
tilted polar axis of the sun's rotation it is
possible to obtain the solar latitude of each
observation. The tabulated heliographic latitude
is most likely not more accurate than 14.
2. The height of the chromospheric limb above the
continuum limb: h(xt * 1)* This quantity is
obtained from the number of channels separating
the two peaks corresponding to the maxima in
the graphs of the first differences of intensity.
This difference in number of channels is converted
to kilometers by means of the scan rate calibra
tion (Appendix XI).
3. The maximum height to which the chromospheric
radiation can be detected: (h). This quantity
is obtained by locating the channel separation 103
of the continuum limb and the first channel in
the chromosphere which displays distinctly a
positive slope greater them the comparable channel
in the light of continuum radiation. (See Figure
33 page 97.)
4. The seeing half width: (h.w.). This is obtained
by converting the width in channels of the con-
tinuum first derivative peak at the half peak
value to seconds of arc.
5. The intensity scale height: (H). This is
obtained by applying Equation 6 to the run of
intensities just outside the limb. In most
cases the values of H are averages of the several
values over an eight or ten channel range.
Included in each data table are the approximate wave
length of the chromospheric line, the wavelength of the continuum point observed, the date of observation and the maximum height above the continuum reported by S. A.
Mitchell (1947) from flash spectrum observations.
A check of the Pierce catalog (1968) in the wave
length positions chosen for the continuum scans reveals no strong chromospheric emission features within ±2
Angstroms of the continuum wavelength for most observa
tions. The continuum point for He I 15875 was about 2 104
Angstroms from the D2 line of Na X. Some involvement
with moderate intensity chromospheric emission in the
continuum channel might occur for Fe II 13256, Hi5 13712
and H10 13798. The continuum scan for H$ is almost certain**
ly contaminated by strong chromospheric light around
14123. There is a complex band structure at 14123.251
with an estimated intensity of 22 and a line at 14123.871
of intensity 40 due to Ce XX or Nd II. This contamination
• was not evident at the time of observation.
Observations of the Balmer Lines. More scans were
made in the light of lines arising from hydrogen than in
all the other elements combined. This resulted in part
from the fact that the Balmer Series lines are very
prominent in the chromospheric spectrum, also in part
because X selected Hg as a control or standard line to
be observed on all days of the observing run. Much of
my ability to interpret other limb profiles resulted
from my attempts to put together the Hg results.
Table 7 lists the results obtained from scans
in Hg.
Each observing day was begun with a series of scans
in Hg. Thus some of the best seeing was encountered
for this line. Scans made later in the day provided
results under similar limb conditions with considerably
worse seeing conditions. Examination of the seeing half- TABLE 7: LIP© SCAN DATA - Hg
Line A4862 Continuum X4888 hm = 9000 km.
"'’s u n h(x h h.w. H Motes ( °) chan km. chan km. arc sec. km. -22 August 1970, 7:30 a.m.
+19 15-5 3270 40 0430 1.59 1200 -11 16.5 3480 42 8850 2.45 1300 Ha prominence -40 13.5 2850 37 7800 2.88 1300 -68 14.5 3060 37 7800 3.17 2000
-27 August 1970, 8:15 a.m.
-38 21.5 4530 41 8640 3.75 950 -68 17.5: 3690 40 8430 5.48 950 Poor Pocus -38 19.5 m i o 43 9060 4.32 1220 - 9 111 2950 32-5 6850 5.19 1200 Prominence observed +21 12.5 2640 37 7800 3-75 1100
-27 August 1970, 3:16 p.m.
-68 13-5 2840 39 8220 3.32 1150 -38 17.5 3690 35 7380 2.16 1200 - 9 19 4000 34 7170 2.74 1700 Prominence Observed + 9 in 2950 39 8220 2.31 1400
-27 August 1970, 3:36 p.m.
-68 16-. 5 3480 42 8850 4.32 1200 -82 in 2950 38 8010 4.18 1500 Very Broad Chrom. limb -51 19 4000 40 8430 4.18 1400 -21 12 2530 41 8640 3.17 1200 South-west Quadrant 105 TABLE 7: (Continued)
vsun4 h(T h h.v. H Notes (°) chan km. chan km. arc sec. km.
-28 August 1970, 7:04 a.m.
+21 18 3790 30 6320 1.73 1300. Call Prominence, Prominence +21 17 3580 32 6740 1.73 1000 Prominence - 9 14 2950 33 6960 1.87 1100 Prominence Suspected -38 14.5 3060 35 7380 2.16 1000 -68 15 3160 37 7800 1.B7 1450
-?B August 1970, 1:02 p.m.
+21 13-5 2840 41 8640 4.61 1150 Call Prominence - 9 9 1897 40 8430 4.76 1300 Prominence suspected -38 14 2950 46: 9700: 6.63: 1000 Focus Poor -68 17 3580 46: 9700: 6.92: 1200 Prominence: Poor Focus -68 12.5 2630 35 7380 4.75 1200 Hcfocusscd. Prominence
-29 August 1970, 7:02 a.m.
- 9 19 4000 38 8010 3.25 1200 Prominence observed -38 16 3370 35 7380 3.03 1100 -68 13 2740 36 7590 2.45 1500
-29 August 1970, 11.12 a.m.
-68 18: 3790 45: 9490: 6.49 1100 Poor Focus -38 13 2740 45: 9490: 4.co 1300 - 9 20.5 4320 48: 10120: 4.61 1150 Prominence observed +21 16 3370 47: 9910: 4.33 1100 107 widths in all wavelengths indicates the best seeing each day occurs from two to three hours after sunrise. The half-widths then increase to a maximum around noon followed by a slight improvement as the afternoon progresses.
Consideration of the seeing effects becomes important when we assess the extent of measurable radiation above the chromospheric limb. If one considers the smearing of a relatively sharp limb, as was done in Figure 23
(page 79), by various spread functions a linear relation is found to exist between the value of the half-width and the extent to which the smeared light cam just be detected. If we plot height of the >s% point of the smeared intensity distribution against the half-width of the seeing spread function we obtain the solid line seen on Figure
34.
Then, if we observe a chromospheric line which extends some distance, h, above the limb where it is just detectable above the sky background we would expect that this height would apparently increase quite gradually as the seeing worsened due to the slight spreading that would occur as the spread function operates on the very gradual slope of the outer region of the chromospheric intensity distribu tion. When the seeing finally deteriorates sufficiently the light will be spread from the sharp limb to beyond Figure 34 Height above the chromospheric limb at which at limb chromospheric the above Height 34 Figure
Height Above Chromospheric Limb 2000 4000 6000 km. 0 * normally can be traced traced canbe normally intensity an possess will profile limb smeared a hi w hoopei limbs. chromospheric own their lines represent examples o f line radiation that radiation f line dashed o The examples represent lines half-width. seeing the of function 4 fteslrds eta nest s a as intensity central disc solar the *of 0 2 4 seeing half-width seeing 1000 and and 6 5000 r seconds arc k. above km.
108
109 the maximum extent radiation would be observed without smearing. When this occurs the measured value obtained may be characterized as entirely determined by the poor quality of the seeing. This trend is illustrated by the two dashed lines in Figure 34. The upper one represents a line of moderate extent (5000 km.) above its chromospheric limb. The other represents a line that extends only a few hundred kilometers above its own limb.
In the case of Hg the heights above the chromospheric limb measured at times of good seeing average about 5100 km. Figure 34 indicates that measured heights of this magnitude are not seriously affected by seeing until the seeing half-width approaches nearly 5.5 seconds of arc. Seeing conditions this poor were not encountered very often during this run. A plot of all Hg heights measured above the chromospheric limb as a function of seeing half-width is shown in Figure 35. It is seen that four of the measured points lie below the sloping line corresponding to the location of the >s% points of the smeared chromospheric limbs. Several more lie very closely above or directly on it. Chromospheric intensities which extend to heights of only 1000 km. above their chromospher ic limb will be artificially raised when the spread func tion half-width exceeds 1.0 arc second! iue 5 bevdetn fH msinaoete chromo the above emission HB of extent Observed 35 Figure
Height Above Chromospheric Limb 6000 2000 km. spheric limb as a function of seeing half-width. seeing of function a as limb spheric 2 Seeing Half-Width Seeing 6 arc Seconds arc 6 110
Ill
While the selection of the *j% point for the limit - of detectability is strictly arbitrary it does not seem to be too unreasonable. In examining the first derivative plots it is found that differences as small as about 0.1% can easily be detected at the start of the chromospheric emission. Even smaller values may be detected from the tables printed out for the first derivatives. If one were to pick the 0.1% point the solid line would display a slightly greater slope and lie just above the one cor responding to the ]j% point.
Effect of Defocussing. If the arguments in the preceding paragraphs are correct it should be impossible for any points to lie below the line corresponding to the level of detectability assumed. I therefore examined the data represented by the points lying below the seeing limited level of detectability. In all four cases for Hg it was found that the points correspond to observations made with a defocussed image£ During the observing run there were a few inevitable occasions, when through over sight I did not continuously monitor the condition of the telescope focus. The scanner introduces an increase in optical path of about 30 inches for a very small segment of the solar image. If, as it should be, this scanned segment is in focus on the observing table the rest of 112 the solar Image is necessarily out of focus with the plane of optimum focus about 30 inches below the observing table.
Almost the entire solar image visible on the observing table was thus very badly out of focus. Only a strip of solar limb about 3 centimeters long falling on the slit was in focus. It was typically difficult to view this segment through the hole in the base of the rocking arm scanner, and even then I could check the focus only by stopping the scanner.
On several occasions I noted a definite defocussing of the image, corrected it, and made note of the fact in the observing log. This alerted me to the fact that scans obtained immediately prior to such adjustments were probably not made with the sharpest possible focus.
Consequently, I have collected some limb scan data using defocussed images. Examination of the direct scans and first derivatives of these images led me to the realization that a defocussed image can be recognized quite readily from the appearance of the first derivative of the continuum limb profile. Figure 36 illustrates the contrast between a focussed image and a definitely defocussed image obtained at times of comparable seeing. It is evident that the defocussed image yields a broader, flat-topped (A)
(B)
(C)
4220 km.
Figure 36 First derivative of two limb profiles obtained at nearly the same time under conditions of comparable seeing with a well focussed image (A) and a de focussed image (B). A well focused image under conditions of good seeing is included for comparison (C). 1X4
first derivative profile. This seems to be an effect simi
lar to one mentioned by Keller, et al.(1956) for out-of-
focus stellar images. Recognition of this characteristic
of defocussed images led to a thorough examination of
all first derivative plots made in this program. As a
result several seemingly discordant observations were found
to have flattened first derivative plots and were then
assumed to be affected by a lack of sharp focus. These
observations are noted in the tables as being accompanied
by poor focus.
When a defocussed image is used to determine the
height of the chromospheric limb some ambiguity occurs
as to the exact location of either limb because of the
difficulty of deciding where the maximum slope really
occurs.
It seems evident that the apparent lowering of the maximum height of emission above the chromospheric limb
occurs as a consequence of a decrease in contrast brought
about by a defocussed smearing of both the continuum
limb and the chromospheric limb. This results in a
trailing off of the chromospheric emission at a rate
similar to that of the continuum sky background at a
lower elevation above the limb than would occur in the
case of a sharply focussed image. 115
Relative heights to which a given line may be ob served at different times will most likely reflect changes both In local structure In the chromosphere and variation
In the scattering properties of the earth's atmosphere.
A slightly hazy terrestrial atmosphere will produce a marked decrease In contrast and a resulting lowering of maximum height to which the emission can be detected.
Thus the vertical scatter in points on Figure 35 can arise from actual changes in the mean chromospheric structure, variations in the scattering characteristics of the terrestrial atmosphere, or effects due to variation in the location of the focal plane of the telescope with respect to the plane of the entrance slit of the spectro graph .
As demonstrated above,the measured height of the chromospheric limb above the continuum limb is not sensi tive to changes in the spreading effects produced by the terrestrial atmosphere. Variations in this height will reflect more readily actual changes in the chromosphere that might occur in disturbed regions. Chromospheric limb height data in Table 7 indicate a slight increase in limb heights at those latitudes and times at which
Ha , Ca II or Hg prominences are observed. There is con siderable spread at all observed latitudes for observations 116 made at different times. The measured heights to the
chromospheric limb In location where prominences are
also observed tend to be much more divergent. From the
chromospheric limb data of Table 7, I have calculated mean values with standard deviations for three classes of observation: 1) limb positions with no observed pro minence activity combined with reasonably good focus,
2) limb positions with observed prominence activity, and 3) limb positions with poor focus. The results are
shown in Table 8. From this I conclude that in August
1970 the mean elevation of the chromospheric limb above the continuum limb is just over 3000 km. The value
is not affected much by the presence of active regions, but the spread in values is decidedly greater. This would seem to indicate active regions tend to lower as well as raise the level of the chromospheric limb. The principal effect of defocussing the image is to produce an increase in apparent limb height in the light of the chromospheric line. The increased standard deviation
in this latter case is probably due to the presence of
local activity in some of the regions having defocussed
images.
The maximum heights to which emission can be
detected in this program show similar variations. The 117
TABLE 8
Hg Chromospheric Limb Heights
Averaged over Heliographic Latitudes
Limb condition n h ± s.d.
No Prominence 17 3080 ± 286 km. Good Focus
Prominence 10 33^8 ± 752 km. Observed
Poor Focus 6 3775 ± 530 km. 118 average value at 31 limb positions is 8600 1cm. with a standard deviation of 1000 km. If I disregard those five heights that seem most likely to be elevated by seeing effects the mean is (7920 ±570) km.
When examining the maximum heights at different heliographic latitudes there appears to be no noticeable effects that can be described as latitude dependent.
Plots of maximum height as a function of seeing half- width at each latitude yields similar scatter diagrams.
Mean values at all four latitudes are the samer well within the standard deviations.
Determination of the off-limb scale heights leads to a typical value in the absence of close prominence activity of about 1100 km. This value is approximately twice the value reported by Thomas and Athay (1961) from eclipse observations. Their value determined for
Hg at the 1952 eclipse (obtained at a chromospheric height of about 6000 km., H <= 630 km.) was made near the upper limit of their height determination.
Following Thomas and Athay (1961) if we take E(hQ) to represent the radiation in a spectral line coming to the earth from the chromosphere above the limb of the moon during eclipse (or from above a given elevation in the present program) and if we take I(h) as the intensity 119
distribution over the same region, then:
E(h ) - I (h) dh (8) o
where hQ Is the lower boundary of the exposed chromosphere.
In trying to differentiate Thomas and Athay's data
to plot on the same scale as one of my direct Intensity
scans I encountered some difficulty because of the scatter
In their published values of E. Specifically, direct
differentiation leads to negative intensities at some
heights and rather large scatter on the line core disc.
It turns out that for the 1952 eclipse only four of the
points tabulated for are located outside the chromo
spheric limb. Figure 37 shows my attempt to compare
their outer-most points to one of my direct intensity
scans. The remainder of the points all lie on the portion of the limb profile corresponding to a gently sloping disc distribution characteristic of high opacity. It
is this region of the limb profile that yields the small emission gradients in the early Balmer lines noted by
Thomas and Athay.
In view of the large scatter of the differentiated points I decided to reverse the procedure and integrate one of my intensity scans and plot the two sets of data on a graph of log E vs. h. I included an arbitrary 0.4 + Thomas and Athay 1952 Eclipse
• • ♦ • Present Work August 1970 • • •
• • I(p) • • 1(0) • Continuum _
• Limb
• + il •
9
9 •
•+* P • •
0.0 ..... + \m— 3000 km. -*
Figure 37 Comparison of Thomas and Athay’s H8 data (+) from the 1952 eclipse with a direct intensity scan from the present investigation. I scaled their data to match mine at the fifth point in toward the photosphere from their maximum height measured. 121 factor to shift the two sets of data to agree at about
700 km. Figure 38 shows a distinct difference in slope between the two sets of data as well as a much less abrupt change in slope around 3000 km. in the 1970 data as com pared to the 1952 eclipse data. This elevation seems to correspond with the chromospheric limb position for
H„ in both cases. There also seems to be a marked increase p in scale height at about 8000 km. in my data.
It does not seem likely that this difference in scale height between the 1952 and 1970 data can be entirely due to seeing. My observation that simple spread func tions do not appreciably affect the off-limb scale heights in times of good seeing indicates that there are probably intrinsic differences in chromospheric structure measured at these different times.
The effects of seeing seem to be considerably less troublesome in the red region of the spectrum. Observa tions of Ha were made on three occasions and the seeing half-width ranged from very narrow to moderately broad.
Table 9 lists the data for Ha .
Figure 39 is a plot of the extent of emission above the Hq chromospheric limb as a function of seeing half width. It seems evident that the extent of radiation above the limb is not affected by the smearing function log E - k
5.0 • Barnhart (1970 data) + + + * •* . + Thomas and Athay (1952 + * • •. eclipse data) 4.0
e
• , 3.0 + • . + ' • 2.0 • •
1.0
0 2000 4000 6000 8000 10000 12000 km. Height Above Continuum Limb
Figure 38 Direct comparison of 1952 eclipse data (+) with
an Integrated limb scan for HP from this work. 122 The ordinate has an arbitrary zero point. Both sets of data are scaled to match at h = 700 km. TABLE 9: LIMB SCAN DATA - H a Line A6563 Continuum A6580 hjjj * 12,000 km.
h(T ’’sun tal) h h.w. K Notes (°) chan kn. chan km. arc sec. ka.
-22 Aucust 1970, 7:55 a.m.
-68 23 4850 47 9,910 2.45 1200 -68 21-5 4530 53 11,170 2.16 1200 -40 25-5 5380 6° 12,650 2.74 . 1000 -11 25 5270 243 51,000+ 2.16 2100 Proeinence +19 26 5480 . 71 14,970 1.68 1350
-27 August 1970, 2:30 p.m.
-68 19*5 4110 64 13,490 1.44 1050 -38 17 3580 65 13,700^ 1.87 1500 - 9 22 4640 230+ 48,300* 3.03 — Prominence +21 22.5 4740 49 10,330 1.95 1250
-28 August 1970, 9:46 a.m.
-68 29 6110 63 13,380 3.60 1150 -38 23 4850 52 10,960 4.04 1150 - 9 22 4640 48 10,120 3.03 850 Sllcht prominence +21 22 4640 138 28,980 2.16 850 Prominence 123 iue 9 bevdetn o aeiso bv te chromo the above emission Ha of extent Observed 39 Figure
Height Above Chromospheric Limb 6000 2000 km. spheric limb as a function of seeing half-width. seeing of function a as limb spheric 4 ac sec. arc 6 4 2 Seeing Half-Width Seeing 124
125 to the H% point. The fact that the lower boundary of the plotted points parallels the *s% seeing smeared limit is probably just a chance distribution of points. I have treated the Ha data as if they are not seeing influ enced .
If we ignore the limb positions in which a promi nence is evident the average maximum extent to which the
H line can be observed is (12,070 ±1780) km. The mean ct height of the chromospheric limb in Ha at those limb positions without prominence activity is (4830 ±710) km.
If we include the three limb positions with prominence activity the mean is (4830 ±635) km. It seems evident that prominences well off the limb do not affect the height of the Ha chromospheric limb. Measured scale heights range from 850 to 1500 km. in regions not exhib iting prominence activity.
One particular scan of HQ stands out. At 8:04 a series of scans was made at heliographic latitude +19°.
The seeing half-width was 1.68 seconds of arc - as steady as any noted during the run. Just outside the continuum limb there is seen a dip in the chromospheric profile indicating either an active region just off the disc or a slight ridge indicative of a possible limb brightening in Hq. Figure 40 is an intensity scan with 10% of the 0.6
• • • • • •
ICp ) 1(0)
0.0 —
10000 ' 5000 0 R km
Figure 40 Limb scan In the core of Ho with "second" limb
removed. The dip in the line core scan just 126 outside the position of the continuum limb may be indicative of limb brightening in Ha. 127 continuum value removed from each corresponding chromo
sphere channel. This procedure tends to remove the effect of the scattered light limb and reveals a more nearly representative profile of the line core limb. A nearly flat plateau is observed on some other chromospheric profiles in Hq and Ca II H and K, but the spread function is usually somewhat broader and may cover up any tendency the run of intensity might have toward a slight dip.
The profile at heliographic latitude - 11° on the same day appears as if it would show a dip under better seeing conditions. This is a phenomenon which might bear further examination in future observing programs.
The fact that chromospheric limb heights at a given limb position are found to differ by as much as 30% from day to day indicates the chromosphere undergoes rather rapid fluctuations in mean structure. The presence of prominence activity in the immediate vicinity seems to have little effect upon the height of the chromospheric limb. On the other hand it may not always be possible to distinguish prominences from the chromospheric limb.
Prominences are quite noticeable when limb scans are made in the light of H or the H- and K-lines of a Ca II. On 22 August a very noticeable prominence was recorded in H . Enhanced intensity in this prominence 126 extended more than 50,000 km. above the continuum limb.
Figure 41 Is a plot of data points covering nearly 78,000 km. at the limb In solar latitude -11°. The two plots are not normalized to disc center because there was no full disc scan made at this time. The line core scan
Is therefore about 25% lower than if it were normalized to the center of the disc. The main portion of the promi nence is about 21,000 km. wide and centered about 34,000 km. above the continuum limb. Enhanced radiation extends all the way from the continuum limb to the limit of the scans. It seems evident that radiation might have been observed at even higher elevations, had the scanner a longer throw. The same prominence appeared about 2h hours later in the light of both the H- and K-lines of ionized calcium. Examination of and the Na D-lines observed on the same day indicates that the enhancement of intensity did not occur close to the limb and neither nor the sodium lines were scanned far enough from the continuum limb to reach the main body of promi nence on 22 August.
On 28 August a prominence was observed in helio- graphic latitude +21. No attempt was made to observe it in particular but it was close enough to the limb to show up on the regular scans. Figure 42 is a plot !«* Line Core *•** i (p )
Continuum
tlltl
50,000 25,000 km. - (P - R0)
Figure 4l Extended limb scan showing the prominence ob served on 22 August. The line core scan is not normalized to disc center so is about 25J5 lower
than if it had been. Each point is separated 129 from its neighboring point by about 2100 km. 130
— J r A CaII(H) \J Vs* // Ha
I(P) 1 (0)
l '— /
30,000 15.000 0 - 15,000 km. * (p - R.)
Figure k2 The region of the east limb ( (H) and Ca II (K). The separation in time of all four scans is less than 3% hours. It is interesting to note that the strength of the emission from the prominence is directly related to the range of brightness fluctua tion observed for these lines on the disc. There seems to be a plage region on the disc about 10,000 km. from the limb, which shows an enhancement in intensity com parable to the intensity of the prominence in each wave length. Prominences projected very close to the solar limb could seriously affect chromospheric limb height measurements. Table 10 lists the data obtained for the remainder of the Balmer lines observed. These data represent a single observation at each limb position for each line. Examination of the Pierce Catalog reveals some very strong chromospheric lines in the position of the continuum wavelength used for the Hg observation. If the continuum detector happened to fall on one of these features a distinct lowering of the derived chromospheric limb height would occur. It seems evident that this was the case. I therefore discount the low limb height recorded for I have averaged the limb heights for each line over TABLE 10: LIMB SCAN DATA - SELECTED BALMER LINES $sun h(Tt-1) h h.w. H Motes (°) chan km. chan km. arc sec. 1 km. 8000 km & •*Y 14340 Continuum 14362 -27 August 1970, 11:30 a.m. +21 5 1050 41 8640 4.76 1600 - 9 13-5 2850 41 8640 4.32 1500 Prominence in Hn and Hg -38 12.5 2640 35 7380 2.45. 1100 Signs of double limb -68 10 2110 39 8220 3.75 1000 * 8000 km "6 14102 Continuum X4iplt -27 August 1970, 12:45 p.m. -68 6 1260 31 6530 3.46 1600 -38 3.5 740 27 5690 3.17 1500 - 9 6 1260 39 8220 3-32 2000 Prominence in HU . H« M +21 4 840 42 8850 2.74 1900 hn ” 8000 km He 13970 Continuum 13993 -28 August 1970, 1:42 p.m. -68 9 1900 32 6750 5.19 1100 -38 10 2110 32 ' 6750 5.48 1100 - 9 10.5 2210 29 6110 3.75 350 +21 4 840 37 7800 3-02 1320 Prominence in Ca II TABLE 10: Continued ♦sun h(Tt=1) h h.w. K Notes (°) chan km. chan kn. r.re sec. kn. hn = 8000 km Hc 13389 Continuum "13913 -27 August 1970, 12:57 p.m. +21 6.5 1370 33 6960 6.49 1700 Poor Focus - 9 9 1900 35 7380 6.92 1600 ' Prominence In H0 and Hg -38 10 2110 33 6960 6.49 1900 Poor Focus -67.9 3 630 33 6960 5.19 1600 hra ■ 7000 to Hg 13835 Continuum 13862 -27 August 1970, 1:26 p.m. -68 8 1690 34 7170 7-78: 1500 Bad Focus -38 7 1480 37 7800 8.60: 1600 Bad Focus -38 4 ■840 29 6110 3-32 1500 Refocussed - 9 5.5 1160 34 7170 2.83 1200 Ha and Kg Prominence +21 9 1900 32 6740 4.18 1400 hn " 6000 to H10 *3798 Continuum 13322 -27 August 1970, 1:56 p.m. -68 5 1050 32 6740 2.88 1140 -38 5 1050 34 7170 2.74 1200 - 9 6 1260 34 7170 4.32 1220 Htt and Hg Prominence +21 4 840 33 6960 4.32 1250 133 TABLE 10: Continued $sun H (°) chan km. chan km. arc sec. km. hjn “ 6000 km Hn 13770 Continuum 13789 -22 August 1970, 10:53 a.m. -68 19 4000 44 9280 6.63: Poor Focus -no 12 2530 42 8850 4.61 — -11 20.5 4320 42 8850 4.76 —- * +19 16 3370 41 8640 4.32 H0 and Ca II Prominence bin “ 6000 km % 2 *3750 Continuum 13775 -27 August 1970, 2:11 p.m. +21 4.0 840 26 5480 3.75 940 - 9 3.0 630 29 6110 4.61 1250 Ha and fig Prominence -38 3.0 630 24 5060 3.09 990 -68 2.5 530 21 4430 3-03 990 bja " 6000 km H13 13734 Continuum 13752 -28 August 1970, 7:27 a.m. -68 3.0 630 20 4220 2.16 1000 -38 3.5 740 22 - 4640 2.59 1100 - 9 2.5 530 33 6960 1.87 1100 +21 1.5 320 24 5060 1.87 1200 Ca II Prominence 134 TABLE 10: Continued $aun htxt-l) h h.w. H Notes (°) chan km. chan te. arc sec. km. ‘ 5500 km Hl4 *3722 Continuum 13740 August 1970 -68 *1.5 950 18 3900 2.7*1 700 -38 2.5 530 21 4430 2.31 820 - 9 1.0 210 20 U220 2.31 920 +21 1.0 210 17 3580 1.73 870 Ca II Prominence hD “ 5000 km H15 13712 Continuum 13730 -28 August 1970, 8:00 a.m. +21 -1 -210 18 3790 2.**5 840 Ca II Prominence - 9 0 0 19 *4 000 2.7*) 1040 -38 0 0 19 4000 2.7*) 980 -68 0 0 20 *1220 2.88 - 980 135 136 heliographlc latitude/ being careful not to include data for which the focus is definitely bad. These averaged values appear in Table 11. Values for defocussed images are included in Table 10. seems to have been consis tently observed with a defocussed image. seems to display discordant heights. Observations of Metal Lines. Table 12 contains the results for the H- and K-lines of ionized calcium. Both the H- and K-lines were observed on two occasions. Ob vious prominences occurred in 3 of the 6 individual limb scans in each line. The prominence of 22 August at -11° heliographic latitude very noticeably increased the maximum extent of the K-line emission. The limb scan in the H-line did not extend to the limit of emission so it provided no value for maximum height. These prominences seemed to distinctly alter the appearance of the chromospheric limb. Figure 43 shows a K-line limb scan in the presence of a prominence and a second limb scan without a prominence. Mean values for the limb heights of the H- and K-line chromospheres are 5060 km. and 5780 km. respectively. These are obtained from only those limb positions showing no prominence activity. Inclusion of those positions with evident prominences increases each average about 100 km. The average maximum extent of detectable 137 TABLE 11: CHROMOSPHERIC HEIGHTS OP SELECTED BALMER LINES Line Wavelength Chromt>3phoric Limb Maximum “m Angstroms Height Extent. km km km »a 6563 4830 l 635 12.0G8 t 1784 12000 He 4862 3080 l 290 6,600 i 1000 9000 h y 3*10 2160 8,220 8000 ■h 5 4102 1020: 7,320 . 8000 He 3970 1760 6,350 8000 Hc 3SB9 1500 7,060 8000 Hg 3835 1300 6,670 7000 H10 3798 1050 7,010 6000 H11 3770 2950: 8,780 6000 h12 3750 660 5,270 6000 “13 3734 550 5,220 6000 3722 470 4,030 5500 1115 3712 -50 4,000 5000 TABLE 12: LIMB SCAN DATA - Ca II ♦sun h(Tt-1) h h.w. H Kote3 • (°) chan km. chan km arc sec. kn. hm " 14,000 km (K) 13934 Continuum 13957 -22 August 1970, 10:26 a.n. +19 24 5060 62 13,070 6.63 1300 Poor focus -11 36 7590 270 57,320 5.48 1300 Pronlnence -40 30 6320 60 12,650 5.76 1300 -68 29 6110 55 11,590 5.19 1400 -28 August 1970, 8:50 a.m. +21 26 5480 148 31,000 2.01 2000: Pronlnence - 9 25 5270 139 29,100 2.25 2000: Pronlnence -33 22 4640 47 9,910 3*17 1250 -68 32 6750 56 11,800 3.BO 1250 hra " 14,000 kn (H) 13968 Continuum 13992 -22 August 1970, 10:12 a.n. -68 28 5900 47 9,910 5.19 1150 -1(0 28 5900 58 12,230 6.05 1200 -11 31 6530 239+ 51,000+ 6.05 1500 Prominence +19 25 5270 57 12,020 4.90 1200 - -28 August 1970, 9:12 a.m. -68 21 4430 56 11,800 3.46 1300 -38 18 3790 48 10,120 4.50 1250 Poor Focus - 9 21 4430 157+ 33,100+ 2.74 1900 Prominence +21 22 4640 160 33,730 2.01 1100 Pronlnence 138 139 K p > 1(0) 0.2 CONTINUUM • • LIMB * • t • 0.0 10,5^0 km. Figure 43 Two limb scans in the core of Ca II (K-line). The filled points were obtained at a time when a prominence was located above the chromoopheric limb out of the range of this plot. The open circles represent the intensity profile for a region of the chromosphere displaying no apparent prominence. 140 line radiation Is 11,200 km. for the H-line and 11,800 km. for the K-line. The prominences extended the measurable radiation to distances of the order of 30,000 km. to 55,000 km. above the photospheric limb. Figure 44 is a graph of the extent of the H- and K-lines above the chromospheric limb as a function of seeing half-width for those limb positions without prom inence activity or obvious focus difficulties. The D-lines of neutral sodium have figured prom inently in the chromospheric spectrum ever since the earliest visual observers of the flash spectrum mistook the neutral helium line at A5875 for the sodium doublet. Sodium displays a departure from the expected maximum extent based upon S. A. Mitchell's value determined from the lengths of the flash spectrum arcs. S. A. Mitchell reports 1500 kro. to be the height limit recorded for both sodium D-lines. Thomas and Athay record sodium emission up to about 2500 km. at the 1952 eclipse. Table 13 lists the measurements from this program and Figure 45 shows the sodium emission height above the chromospheric limb as a function of seeing half-width. The mean value of my well focussed maximum heights above the continuum limb is 6650 km. ± 730 km., about four times that reported by S. A. Mitchell. Examination Figure M Observed extent of the Ca II H- and K-lines and H- II Ca the of extent Observed M Figure Height Above Chromospheric Limb 2000 6000 km. above the chromospheric limb as a function of function a as limb chromospheric the above seeing half-width. seeing 2 Seeing Half-Width Seeing ac sec arc 6 141 TABLE 13: LIMB SCAN DATA - Na I ¥sun6 h{tfc-l) h h.w. H Notes (°> chan km. chan Jen. arc sec. km. Line >5890 Contlnuuio 15927 ha " 1500 km -22 August 1970, 9:45 a.m. +19 10.5 2210 30 6320 3.03 750 -11 7 1480 34 7170 4.00 900 H0 Ca II Prominence -40 i) 840 35 7380 4.IB 1150 -69 6 1260 32 6750 6.20 780 Poor Focus -68 5 1050 34 7170 4.90 850 Recentered -68 0 0 24 5060 4.04 IN VINO -29 August 1970, 10:54 a.m. -68 l 210 26 5480 5.76 -38 l 210 34 7170 4.18 1300 - 9 5.5 1160 36 7590 6.05 1200 Ha and Hg Prominence +21 2 420 36 7590 4.32 1100 1500 km -22 August 1970, 8:47 a.m. Lino X5896 Continuum 15933 hm " +19 8 1690 27 5700 2.16 700 -11 5 1050 26 5480 2.45 800 Ha Prominence -DO 6 1260 27 5700 3.89 850 -68 5 1050 34 7170 3.89 950 -68 5 1050 33 6960 4.61 925 -68 5.5 1160 29 6110 3.80 800 -DO i).5 950 31 6540 2.58 880 -11 l) 840 35 7380 3*17 1200 Ha Prominence -19 5 1050 34 7170 2.88 1100 — 29 August 1970, 11:04 a.m. +21 0.5 100 27.5 5797 3.02 1050 - 9 • 6 1260 6956 1000 33 4.75 H_U and Ha P Prominence -38 4.5 950 33 6956 5-76 850 -68 1 210 28 5900 5-76 850 iue4 Osre xet fN eiso bv the above emission I Na of extent Observed 45 Figure Height Above Chromospheric Limb 2000 4000 km. 6000 width. chromospheric limb as a function of seeing half seeing of function a as limb chromospheric Seeing Half-Width Seeing 6 arc arc 6 Bee 143 144 of Figure 45 Indicates that very few of the sodium scans are affected by poor seeing. The values that lie below the >5% point seeing limit are the result of poorly focussed images as was noted in connection with the Hg data. This kind of enhanced chromospheric height does not seem to be present in any of the other lines observed in this program. Neither does there appear to be any latitude dependence involved. The only connection that seems to be possible to make is that the latest eclipses reported by S. A. Mitchell (1947) were 1941 and 1945, both near sunspot minimum; Thomas and Athay report their height for the 1952 eclipse, again near minimum and my observations in August 1970 are just past maximum in the relative sunspot numbers. It may therefore be that the Na I D-line heights are sensitive to the sunspot cycle. Further observations will be needed to verify this sup position. Table 14 lists the limb scan data for four lines of ionized iron. All of these lines are found by S. A. Mitchell to terminate at 2000 km. or below. Figure 46 indicates all of the lines are elevated by the seeing spread function. Thus only the recorded limb heights have validity in describing the mean chromospheric con ditions for Fe II. The measured scale heights are TABLE 1*1: LIMB SCAN DATA - Fe II ^sun h (Tt’»1) h h.w. H Notes <°) chan kn. chan km. arc sec. km. Line 13256 Contlnuua 13272 hn « 120 3 -28 August 1970, 8:35 a.m. -68 5.5 1160 21 4230 3.75 1200 -38 4 ■ 840 16 3370 2.88 800 - 9 5 1050 20 4220 4.32 800 +21 3 630 18 3790 3.46 850 Ca II Prominence Line 13277 Continuum 13294 hn - 1200 -28 August 1970, 8:14 a.m. -68 3 630 20 4220 3.46 2100 -38 6 1260 21 4430 3.60 1850 - 9 6 1260 19 4000 2.74 1700 +21 6 1260 21 4430 2.88 1700 Ca II Prominence Line 14629 Continuum 14659 h_2k ” 1200 -28 August 1970, 3:34 P.m. -68 0 0 19 4000 4.32 800 -82 1 210 23 4848 3.75 950 -51 3.0 639 21 4430 3-75 850 S. V. Quadrant -21 3-0 630 26 5480 4.33 980 -68 0 0 19 4000 4.04 700 Line 15018 Contlnuua 15047 ha - 2000 -28 August 1970* 9:27 a.m. +21 1.0 210 16 3370 2.88 600 Ca II Pronlnence - 9 0.5 100 18 3790 3.03 700 -38 2.5 530 23 4843 4.61 700 -68 0 0 17. 5 3690 3.89 650 iue4 Osre xet fF I msinaoe the above emission II Fe of extent Observed 46 Figure Height Above Chromospheric Limb 6000 4000 2000 km. width. All points seem to be established by established tobe seem points All width. the seeing spread or by defocussing effects. defocussing by or spread seeing the chromospheric limb as a function of seeing half seeing of function a as limb chromospheric 4 ac sec. arc 6 4 2 Seeing Half-Width Seeing 146 147 generally smaller than those of the lines whose chromo spheric limbs are considerably higher in the chromosphere than Fe II. The scale heights probably reflect the shape of the smearing function rather than the run of Fe II intensity. Table 15 lists the data for Strontium II X4078 and Titanium II 14534. Both are characterized by relatively poor seeing. S. A. Mitchell quotes a chromospheric arc height of 6000 km. for Sr II X4078. My measures give a value very near the *j% height for all seeing half-widths for this line. The same is true of my measured heights for Ti II X4534. Mitchell gives 2500 km. as the extent of this radiation above the photosphere. I therefore conclude the maximum chromospheric heights derived in this study are probably affected by seeing. Helium Lines. Finally, three lines of neutral helium were observed. Some difficulty was encountered in setting on these chromospheric features. In parti cular, during times of poor seeing I had difficulty finding the chromospheric feature in the wavelength scanning mode with the spectrograph slit placed just off the limb. I discovered after several frustrating attempts that the roost effective technique involved scanning the spectrum with the slit somewhat farther from the limb than is TABLE 15: LIMB SCAN DATA - Sr II, T1 II ♦sun h(xt-l) h h.w. H Notes chan km. chan km. arc sec. km. Sr IX Line 14078 Contlnuun 14104 hn " 6000 -29 August 1970, 9:17 a.m. -6B 9 1900 30 6320 6.63 1300 -38 3 630 24 5060 4.76 1100 - 9 5 1050 31-5 6640 3.32 1050 H_ and H» Prominence +21 8 1690 23 4850 3.75 1100 Ti II Line 14534 Continuum 14573 hm ’ 2500 -29 August 1970, 10:34 a.m. -68 5 1050 35 7380 5.48 1100 -38 7 1480 28 5900 6.92 1000 - 9 l) 840 27 5700 5.19 950 H_a and Hn B Prominence +21 3 630 23 4850 4.61 900 149 customary for other lines. This is because the helium lines all peak in intensity at some distance from the limb. Helium does not ordinarily appear in absorption in the undisturbed disc spectrum. The only exception is the weak line at 110,830. If we assume the line scan and the continuum scan will normalize to the disc center in the same manner then they should be identical on the disc very near to the limb. The appearance of helium emission just off the limb will be the only feature to distinguish the scan made in chromospheric light. If we then subtract the continuum scan from the chromospheric scan we should be left with a measure of the helium emission intensity in terms of the intensity of the disc center. Figure 47 is a plot of the He I A5875 line intensity at a heliocentric latitude of +14.3° on 28 August 1970. Included on the plot is the first derivative of the continuum limb scan to indicate the location of the photospheric limb. The helium line peaks some distance outside the continuum limb as reported by Athay and Menzel (1956). When we examine the intensity traces similarly obtained at four different latitudes, as illustrated in Figure 48, we note a variation in height of the maximum 150 in o A\- Firot Derivative • Continuum . t* • ••• 6220 km. \ Figure lJ7 He I intensity scan (upper curve) 15875* 28 August 1970, heliographic latitude +1^?3. Plotted to the same horizontal scale and in the same geometric configuration to locate the photo* spheric limb is the first derivative of the continuum limb scan (lower curve). 151 lio If> o 0 1 Figure 48 He I 15875 intensity scans for four limb pos itions. All scans are aligned so that the con tinuum limb positions match. Scans are shifted vertically to avoid overlap. (28 August 1970) 152 intensity above the limb and the maximum extent to which the emission can be detected. This seems to be the only latitude dependent effect b o far detected in this program. In two of the curves , corresponding to heliographic latitude +14.3° and -9°, the helium emission seems to extend slightly onto the disc. However, at latitudes -38° and -68° the curves interestingly go negative right at the position of the limb as if one should expect to observe faint absorption very close to the limb in these two limb positions. The spectrograph was originally set on the wavelength of the line in the position at which the top scan was obtained. The scans were made in order from top to bottom. Since the maximum intensity occurs in a latitude nearly 50° away it seems the Doppler shift is not likely to be the cause of the dis crepancy. Another set of scans was made of the X5875 chromo spheric feature on 27 August. These are illustrated in Figure 49. Again the variation from latitude to latitude is seen. This time the maximum height occurred at the northern-most latitude observed. In all four limb positions on the 27th an absorption dip was recorded. The He I X4471 line (Figure 50) displays a lower intensity than X5875 but shows a similar effect at the limb. The var iation in maximum height of emission is considerably 153 T LIMB in oC l o 1 -38 7800 km Figure ^9 He I (15875) Intensity scans for four limb positions. (27 August 1970) 154 CO LIMB \ o o o • o +21 7800 km.------*-| +• p Figure 50 He I (XU471) Intensity scans for four limb positions. (27 August 1970) 155 greater, ranging from 3400 km. to 8800 km. The seeing for this set of scans was generally quite poor. Finally, Figure 51 illustrates the effect for He I X6678. This line has about 25% the relative intensity of X5875 but shows a much deeper absorption on the limb than either of the other lines. Table 16 summarizes the pertinent data obtained for the helium lines in this investigation. In general, the following conditions might be pointed out. X4471 does not seem to extend as far above the limb as the flash spectrum measures would indicate. The seeing for my He I scans on 27 August was notably poor. The D3-line, X5875, comes more nearly in agreement with the flash spec trum extension above the photospheric limb. The scans in X6678 display good seeing and con siderably higher extent than the flash data. With an average height of 8620 km. the points seem comfortably above the %% limit of seeing disturbance. It seems evident the average helium emission struc ture above the photosphere undergoes fluctuations in periods of the order of days or fractions of days. Also, observations with an image slicer or successive scans rastered in wavelength might provide line profile data for X6678, both in emission off the limb and ab sorption just on the limb. 156 LIMB +21 -38 -68 9500 0 km. *■ (P - Rq ) * Figure 51 He I (A6678) intensity scans for four limb positions. (28 August 1970) 157 TABLE 16: LIMB SCAN DATA - He I Inax Imln Seeing ♦sun h h.w. Notes h^max) 1(0) 1T0T >m ■ 7500 km X5875 27 August 1970, 7:30 & * in« +21° 1900 6960 0.0X72 -0.0039 Poor Pocus - 9° 26X0 6530 0.031X -0.0023 Poor Focus -38° 2320 67X0 0.01X6 -0.00X2 Poor Focus -68° 2950 7590 0.0192 -0.0030 Poor Focus 28 August 1970, 3:01 p.m. « y 2110 66X0 0.0505 3.89 1370 7590 0.0950 x.ox -380 1790 5900 0.0237 -0.0192 3.89 -68° 1790 X850 0.0326 -0.0178 X .90 hm • 7500 km XXX71 27 August 1970, 10:00 ft » HI • ♦21° 27X0 8220 0.0068 -0.00X3 X .33 - 9° 1530 6320 0.003X -0.0015 x .90 -38° 1X70 3370 0.0020 -0.0018 6.92 Poor Focus -68° 3060 B850 0.0027 -0.0035 6.92 hm ■ 2200’ km X6678 . 28 August 1970, 10:10 a.m. ♦ 21° 2320 9380 0.0119 -0.0356 2.B8 - 1900 8X30 0.010X -0.0272 2.X5 -36° 1690 8220 0.0109 -0.0127 3.60 -68° 3370 8X30 0.0127 >X.00 158 Table 17 summarizes the results of this investiga tion along with values determined by other investigators. Comparison of values of heights of barely detectable radiation obtained on this program with the chromospheric heights published by S. A. Mitchell (1947) indicates a good correlation. The only exceptions are Fe II, for which the maximum extent of radiation from the limb is determined largely by seeing, and Na I, the values for which seem quite independent of seeing and may reflect a real variation with solar cycle of chromospheric struc ture for these lines. Of the 27 lines measured on this program I have found only five which have had measured limb heights published for them. These five are included in Table 2 and again in Table 18 along with my values. There seems to be close agreement between my determination of the Ha limb height and those of Wilson and White (1966) and Wittmann (1973). The measurement given by de Jager (1959) is from a spectroheliogram and may not be represen tative of the same point I define in the chromosphere as the limb. Mohler's value is much larger than those obtained later. The only previous measurement listed for is due to Mitchell (1969). His equatorial limb height is nearly 159 TABLE 17 SUMMARY OP CHROMOSPHERIC HEIGHTS 11 LINE X h(Tt - 1 ) h hn »ta R km km km km km (This Work) (Others) 770 »o 6563 4830 l 635 4800 ww 12,070 12,000 4900 wl 6000 dj 7000 mo h b ml 8,600 9,000 1200 625 P 4862 3080 t 290 ooooe 2400p ml HY 4340 2160 8,220 8,000 1300 555 Hi 4102 1020;: Z'320 8,000 1700: 555 He 3970 1760 6,850 8,000 1100 Hr 3089 1500 7,060 8,000 1700 H§ 3835 1300 6,670 7,000 1300 665 H10 3798 1050 7,010 6,000 1200 640 h i t 3770 2950; 8,780 6,000 1200 620 HI 2 3750 660 5,270 6,000 990 595 1113 3734 550 5,220 6,000 1100 595 H14 3722 470 4,030 5,500 850 590 1115 3712 0 4,000 5,000 980 575 Ca II 3968 5060 10150 ml *11,200 14,000 1200 Ca II 3934 5780 4900 dj 11,800 14,000 1250 7600 mo Na I 5896 817 1500 dj 6,450 1,500 840 435 1200 mo Na I 5890 982 6,960 1,500 850 476 Fe II 5018 210 2,000 650 345 Fe II 4629 370 1,200 840 Fe II 3277 1100 — 1,200 1850 Fe II 3256 920 — - 1,200 850 Sr II 4078 1320 5720 6,000 1100 665 Ti II 4534 1000 5,980 2,500 975 He I 6678 -315 4,740 2,200 He I 5876 0 7,270 7,500 4,930 7,500 He I 4471 0 # :: Continuum light contaminated by chroraospherlc line. : Uncertain ww - Wilson and White (1966) wl - Wittroann (1973) dj - de Jager (1959) mo — Mohler (I960) • ml - Mitchell (1969) ta - Thomas and Athay (1961) Emission scale heights, Hta 160 6000 km. higher than mine while the polar elevation ia more in line with the values 1 obtained for the same line. Furthermore, his measurement at the equator for the H-line of Ca II is 5000 km. greater than the value I obtained. Taken together these two equatorial limb heights lead me to conclude Mitchell observed a region of the equatorial limb upon which was projected a pro minence . My value for the Na limb height is generally lower than others. This, along with the enhanced maximum height of emission, would seem to indicate a rather ex tensive spreading of the Na I chromosphere. Figure 52 combines the predictions of the chromo- spheric models presented in Table 2 and my limb height measurements for the Balmer Series. My plotted value for Hg is interpolated between those of He and Hy. The points representing the Woltjer and Bohm-Vitense models are connected by lines for clarity. The hatched area represents the range of heights predicted by the Athay and Thomas (1958) model based on the assumption of a spherically symmetric atmosphere. The upper and lower boundaries correspond to combined limits upon the assumed number of absorbing atoms in the line of sight at an elevation of 1500 kilometers above the photospheric Figure 52 Limb height predictions of chromospheric models chromospheric of predictions height Limb 52 Figure * Chromospheric Limb Height kilometers 1000 2000 3000 4000 00 - 5000 6000 00 - 7000 compared with heights measured on this program. this on measured heights with compared * 5 7 9 0 1 12 11 10 9 8 7 6 5 ** 3 Upper level quantum number quantum level Upper ■ . ote (195*1) Woltjer .. Bh-ies (1955) Bohm-Vitense + Observed — Present Work Present — Observed ta n hms (1958) Thomas and Athay 161 162 limb and the scale height for this number. These values are not independent of each other. For the upper boundary the number of atoms is 101€ and the scale height is 2000 kilometers. The lower boundary corresponds to 10*5 atoms with a scale height of 500 kilometers. Athay and Thomas proposed the true model would be intermediate to the two sets of limiting values. Even though Woltjer assumed a different temperature relationship between spicules and the interspicular regions than we presently believe to be the case, it seems evident that columns of gas with transparent regions between lead to predictions of higher chromospheric limbs for the Balmer lines than the homogeneous model of Bohm-Vitense. The run of limb heights measured in this investigation correspond more closely to the predictions of the homo geneous model and would seem to indicate a line-of-sight number of atoms and scale height value well within the Athay-Thomas prediction. It would seem that whatever might be the detailed structure of the chromosphere its limb masquerades quite well as that of a homogeneous, spherically symmetric atmosphere. IV. CONCLUSIONS The value of any Idea lies not in its truth but in its ability to successfully predict behavior of the world or to open new paths for exploration. The attempt to observe mean chromospheric structure outside of eclipse has opened some interesting avenues. Value of the Mohler Technique. It seems evident that an average distribution of light due to the chromo spheric emission can be displayed in limb profiles that may be related to observationally identifiable points associated with the solar photosphere. In particular, the ability to detect and locate a relatively sharp chromospheric limb makes it possible to survey the solar chromosphere on a continuing basis for short term fluc tuations in average structure, latitude dependent effects or secular variations in chromospheric structure related to the cycle of solar activity. Indeed, the technique utilized in this program should work just as well with much smaller optical systems with matched spectrograph and modest data handling equipment. The sharpness of the chromospheric limb enhances 163 164 the ability to determine a precise height of this limb above the continuum limb. At times of good seeing the slope of the chromospheric limb in most cases is between 60% and 80% of the slope of the photospheric limb. As the seeing deteriorates the ratio of limb slopes approaches unity. Previous knowledge of even rudimentary geometric structure of the chromosphere was very uncertain. This uncertainty arose mainly due to the inability to measure a reliable reference point from which to make geometric measures. Wilson and White (1966) used the knee of the limb profile for such a reference. I have succeeded in obtaining accurate reference to the inflection point of the intensity profile. Wilson (1966) points out that very little is known about the relationship between the height structure of a model atmosphere and the corresponding limb intensity profile. The present program offers an opportunity to measure a geometric parameter of the chromosphere which is related to an optical depth (t ^. ■ 1) in the radiation of a given spectral line. It would be hoped that this capa bility can lead to a way to assess the average run of temp erature and pressure at lower heights where the spicules are seen to overlap. Good observed intensity profiles can define limits for chromospheric models. 165 In determining the extent of chromospheric emission above the photospheric limb this technique seems to match quite well the ability of flash spectrum observations to yield maximum heights. There is good correspondence between heights measured by S. A. Mitchell from the tips of chromospheric arcs in the flash spectra and the maximum heights to which emission is detectable in this program. It may be possible with this technique to increase the signal to noise ratio in the region far above the limb where the intensity approaches the level of sky background in order to extend the heights to which radiation can be detected. This might be accomplished by increasing the number of scans to increase the integration time, or by applying to the off-limb data a difference technique similar to that used to obtain the helium intensities in this program. The distribution of intensity with height is obtained directly by means of this multiple-scan technique. There is no need for photographic sensitometry followed by dif ferentiation of the primary run of data. The present work provides a much more satisfactory definition of the location and structure of the chromospheric limb than does flash spectrum analysis. Photoelectric scans of the extreme limb have long 166 provided an opportunity to measure quickly and accurately the effects of atmospheric seeing and image defocussing. Indeed the possibility exists to construct a simple on-line seeing/focus monitor which can generate from a sequential series of scans of the limb in a narrow con tinuum band a visual display of the first derivative of the intensity profile. Focus may be adjusted continuously while watching the visual display for a maximum peak height corresponding to optimum sharpness of the photo- spheric limb. A calibrated scale of half width could then be read to provide immediately a numerical expression of a seeing-related parameter. Staveland (1972) has shown how accurately measured intensity scans are quite useful in determining the image spread function and thus provide valuable data for analysis of the redistribution of solar radiation in the telescopic image. At the present time it seems evident that measured scale heights from the direct intensity chromospheric scans are compatible with the extent to which the chromo spheric light is observable above the photospheric limb. The smaller scale heights reported by Thomas and Athay (1961) for the 1952 eclipse were also in agreement with the lower extent to which their intensities were measured. 167 My values of off-limb scale height seem internally con sistent, but are considerably larger than those quoted by others from eclipse observations. Specific Proposals. Several proposals for extend ing this work seem to be in order. Some of these pro posals deal with the problem of further interpretation of direct intensity scans in conjunction with the large body of flash spectrum data that presently exists. Other proposals are made in terms of the application of this technique to study phenomena not heretofore examined. In the former category I would suggest a coordinated effort be made to observe a number of chromospheric spectral features using this technique on the days just before, during and after the next total solar eclipse at which flash spectrum plates are taken. This would enable us to directly compare the two methods at the same limb positions and chromospheric conditions. This could serve the twofold purpose of providing supplementary calibration for the flash spectrum data and directly assessing the comparison between the two techniques for - measuring scale heights of the chromospheric emission. Some new proposals that seem in order include the exploration of two unexpected effects observed during 168 this work. The first of these is the possible occurence of limb brightening in Ha and the H- and K-lines of ionized calcium. A search for this effect could be made with modest instruments at sites possessing periods of extremely good seeing. All that would be required for such obser vations is the capability to scan the solar limb across the entrance slit of a spectrograph while monitoring the intensity in the core of one of the appropriate spectral lines. The requirement for excellent seeing arises from the fact that such subtle details become quickly smeared out when the seeing begins to deteriorate. A second interesting phenomenon to explore is the appearance of absorption in the light of He I at the ex treme limb. Image motion washes out the very localized absorption features in this region of the Bolar disc. An application of the technique of successive scans, which may then be summed with a partial removal of the effects of image motion, will indicate those positions along the solar limb where helium absorption occurs. Repeating the process at evenly spaced wavelengths across the helium line would provide absorption line profiles on the disc and emission line profiles at well defined distances from the level of the continuum limb off the solar disc. The advantage 169 of geometrical height resolution to within a hundred kilometers should not be overlooked. With the facilities used in this program such an observation would involve about 30 minutes observing time at each limb position for each line investigated. Requirements on the quality of seeing do not seem too stringent although relatively consistent seeing quality throughout the sequence of scans would seem to be desirable. It seems evident that this program would lend itself to application of a much smaller optical system. Data aquisition should be easily handled by means of a modest mini-computer. Routine monitoring of mean chromospheric structure could then be easily conducted as weather permits. Further studies of the effects of seeing upon the ^determination of direct intensity scale heights should be undertaken. In particular, the effects of scattered continuum light can be relatively easily assessed using the presently available data from this program. Another important aspect of the scale height problem would be to attempt to probe the lower layers of the chromosphere by a multiple-detector technique or rastered scan in wavelength with a single detector. 170 Typically, when one observes radiation having wavelengths further removed from the center of a Fraunhofer line he is seeing more deeply into the atmosphere of the sun. However, Zirin (1966, page 227) notes that for hydrogen the chromo spheric lines are temperature broadened and thus make some higher-elevation chromospheric structures more readily detected in off-band spectroheliograms than in spectro- heliograms made in the line core. Translated to the limb these overlying spicular regions do not produce chromospher ic limbs that are higher above the continuum limb than the limb observed at line center. Limb scans made at a series of wavelengths separated from each other by small amounts within the line will yield chromospheric limbs closer to the photospheric limb as the observed wavelengths approach continuum wavelengths. This technique ought to yield information about mean structure and scale heights in lower regions of the chromosphere. Good to excellent i seeing conditions would be required. Since the quality of the seeing seems generally better at longer wavelengths and a strong line with considerable range in height within the chromosphere is desirable the logical choice for such a depth probe is Ha . There exists in the present observational routine a source of smearing that can be simply reduced in fur ther applications of this method. This smearing results 171 from the fact that the entrance slit to the spectrograph Is not curved sufficiently to match the curvature of the solar limb. As a consequence there occurs a general overlap of adjacent sampled regions of the chromosphere. This overlap amounts to about 40% of the width of the slice of the chromosphere sampled. This overlap may be reduced without seriously reducing the signal to noise ratio by using a slit width equal to the sample point separation. Xf this is accompanied by a considerably reduced slit length to eliminate effects due to curvature of the solar limb such an aperture would be ideally 120 microns wide and 5 mm long. This would result in a reduc tion in admitted light by a factor of only 3, well within the usable range of signal to noise ratio obtainable with the McMath Telescope spectrophotometric system. A refinement in the scan shift routine will allow, using interpolation procedures, the accomplishment of fractional channel shifts in the summation program. Further analysis in terms of small scale intensity fluctuations on the solar disc might allow variable shift amounts to be included to remove effects in the scan due to rapid, non-coherent image excursions. It may be possible to evaluate this procedure using data presently available. 172 Since the placement of the entrance slit may be accurately defined in terms of its distance from the photospheric limb at all points in the scan, the principal objection raised against previous determination of chromo spheric line profiles is overcome using multiple seems. If limb scans are made in many wavelengths throughout the spectral line, a series of line profiles can be constructed at many distances from the continuum limb. Only the light scattered from the disc needs to be sub tracted. Need for consideration of incursions of the disc spectrum due to image motion is greatly reduced. Finally, it seems possible that one may be able to detect and analyse faint spectral features close to the photospheric limb using a technique similar to the one devised herein to isolate the helium emission and absorp tion. As long as the limb darkening curves in the con tinuum and the line are not too dissimilar, the differences between the two scans should yield chromospheric intensity data very close to the continuum limb. APPENDIX I Normalization Procedure Raw intensity data obtained from the individual scans at the solar limb bear no particular relationship to each other in the two wavelength regions. Gain setting and dynode voltage control on the photomultipliers were both arbitrary adjustments and were generally set to provide a display on the data monitoring screen which could be relatively easily compared. While it might be instructive to have a plot of relative Intensities which would match the central Intensity of the Fraunhofer line with the intensity of the nearby continuum at some point Just inside the solar limb it was felt that a more convenient way to display the limb intensities would be to normalize both scans to the central Intensity of the solar disc. The relationship between the central Intensities and the limb profiles are not available from the extreme limb scans alone. It is necessary to get these data from solar disc scans which Include both the limb and the center of the disc. Figure 53 illustrates those sections of the full disc scans appropriate to determining conditions at the extreme limb. By assuming that the full disc scans were made along an image diameter the scale in kilometers per channel is 173 Points from Full Disc Scan Limb Scan N-2 0 N + 250 Figure 53 Plot of a region of the solar limb illustrating the manner in which full disc scans are associated with the extreme limb scans allowing normalization of the limb scans to disc center. The plot con taining 250 data points is a continuum scan (X^888) observed along with a scan in the core of HB. The crosses (+) represent the data points from a full disc scan. Labelled points are described in Table 18. 175 obtained by dividing the solar diameter by the number of channels between Inflection points on the limbs on opposite sides of the solar Image. Specific data obtained from the full disc scans are listed In Table' 18. The reason for adopting the primed factors, the so-called contingency data, In this tabulation Is that some of the limb scans were made with the limb too close to the end of the 300 point scan sequence to be able to use a 92 point channel separation to tie the limb position to a disc position. Therefore, an option was made which would allow normaliza tion using a smaller separation between the limb and the on-dlsc Intensity points In case there was not sufficient separation In the recorded data. In some cases, particular ly those in which the observation was carried some distance off the limb to include a prominence, the normalization procedure did not work even In the contingency case. The procedure used in the data removal from the storage tape Is as follows: 1. The appropriate tape file Is accessed In the tape reading subroutine. Each file is numbered serially and contains 50 Individual limb scans containing 300 data points in two different wavelengths. 2. The first set of paired scanB are read Into storage and an arbitrary limb point is selected on the scan made In continuum light. This scan Is selected because of the generally steeper slope and larger signal to noise ratio. The limb point is selected as that channel for which the intensity (arbitrary units) is midway between the average of the first ten channels of the scan and the average of the last ten channels of the scan. The limb point selected is then labelled "Shift Channel." The next set of paired scans is read from the tape. The "Shift Channel" is similarly located on the continuum scan. If it agrees with the shift channel on the first scan the second pair of scans is added, channel by channel to the first pair of scans. If the shift channel numbers do not agree the second set of scans is Bhifted the appropriate amount and direction to bring the shift channels into agreement. Then the second set of scans are added, channel by channel to the first. This process is repeated for all remaining pairs and the resulting shifted, summed scans are read out as raw integrated limb scans. Examination of single scans provides Information to match the two scans at disc center. The entire line core Intensity scan Is multiplied by the ratio dc^ c/^L^o to brlnB t0 the same central Intensity level as the continuum scan. To establish the relative Intensity scale for the extreme limb, comparable values of Intensity must be found for specific locations on the full dlBc scans and the limb scans. To do this, the single, full disc, continuum scan was searched for the first channel containing an Intensity value distinctly rising above the sky level. This value was easily distinguished and usually very near the Inflection point of the Intensity trace because the limb covered only one or two channels In the full disc scans. This Intensity was then divided by the Intensity In the off limb channel two channels away. In this way two channels were established for which a unique ratio of Intensity exists. Since one channel on the full disc scan was found to correspond to 23 channels in the limb scans a search for the two intensities separated by 46 channels having the same intensity ratio 178 In the Integrated continuum limb scan located the corresponding channel on the limb. I chose to establish the scale of relative intensity further onto the disc where the intensity gradient is smaller. Having once established one point on the scan any other points in multiples of 23 channels on the extreme limb may be correlated to the full disc scan. Thus, the corresponding values of intensity for 92 and 69 channels from the limb are recorded. Occasionally, disc features not present on both the full disc scan and the integrated scans created normalizations that were not in the correct ratios. These data could still be used to obtain geometrical structure information because the limb positions are most easily obtained from the first derivatives, the peaks of which are not sensitive to the scale of the intensity scans. 7. With these values of intensity and location with respect to an identifiable point on the limb the Integrated scans can be normalized to disc center and scaled in relative intensity. i « Values of R, Pq , F^, Fc and PL are entered on each con trol card with the identifying file number in the data re duction program. A sample print-out of data is shown in Table 19. TABLE 18: DATA OBTAINED FROM FULL DISC SCANS Measured Values from "cnn3 Derived Quantities for Calculation O TC / *C (IC )G - Continuum "Intensity" at disc center s * tN f - Line core "Intensity" at disc center c - (ic jo / (iL)0 Hd - Channel Number correspondinr to first continuum point "obviously" above the sky. Usually about 10* to ?55 of the L * ILf»j)C disc center Intensity r IjJ - Value of continuum "Intensity" for ?C ” Jc^Hd^ * ^C^o channel, H IC(N.J- Value of continuum "Intensity" for Contingency Data: channel »d + ft I. (!!*)- Value of line core "Intensity" Tor l ' = T^tr;*3c channel Nd + t V Ir (Hj)- Value of continuum "Intensity" for * ' c * ^ * < V o channel :id + 3 Value of line core "Intensity" for - l ' / ic Oi*) channel !!d + 3 TABLE 19: SAMPLE COMPUTER OUTPUT FOR A SINGLE LIMB POSITION SHIFTED, INTEGRATED AND NORMALIZED IS p t V M M r#»vr.*( T ■, t »• » t !' •**STr» S“ |Ff “ I- ;«r. S*MM €►* *V L TS TS IS ^ w t n OU'JVFL r. 11* S m TF T f«i‘r *i ts 1 t- i r IS •f* *1 '.•rrt r**»* IS f« IS HACTra snirr ts 1 snirf fMi'f.rf 1* t.1. i t 1 - Is ts IS ** r s m |« T Ci».rTt i% 1 i*» *iHTT I r m v - n t • t ♦ * t ? t *, *1 r T r«* IS rs TS «* • t •* S **|t f t U l f T L i'* 1 Shjl 1 f * v * H 1 1 * * *' 1 - T< ts TS *: N ^ T F U VMM TS t n : i **&•,-•« r ts '** • . HV.t ^ .-■T* * r*»* v rt IS ts ts t • •%** FT »*, * * f VMM C M V ^ L IS I *'* THl'f * ». f* I> ts IS V.1* ntST* e '.m KT Th **ATL IS 1 4<> ^ M | M IS 11* * T T* ?r - '..■JfT r*4*v *1 IS TS TS * * T IS 1 Vt Ch ]» 1 IS Ts " V , ?» « ■*-U | rs IS IS | v » Ci« Mjcfra e^irr C H t T ^ L IS 1 11 s - M M IS * T I'. ••A* *l "» •’ •I* T is TS TS HA*T* ° NACfra SMfrT IS HQ SiT* 1 C h Iv r1 »s s»« M IS TS ts IS HASTr t> %*MM CHA*r*TL TS 114 V » K | C*nv.fj. ♦S fl fT IS **1S fr-» s«l* T :h * .*■»'. ts TS IS »A?Tf# V M M C«r*I*€L TS P« W l d « ‘r n_ vs *i r*t|rr TS *s IS TABLE 19: Continued r»i r v iT jM M M 1 Jf.M r.HAVJCL ^ frt .'.*7 W * 0 AM. ft T lJ .A 7ft4»* P i s . " N l . f l i i n . b 7ss,ft 7 9 1 .^ W . o 90P.0 •H.O *07. ft 7 0 , 4 ilH A . A -4*1.0 «% 7.4 -s O .ft • 4 ® . 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O.oini?*# ?s> 34* r.f*.-* t /I* t/in* ■* > 3 *1 7 3 , H %/tr,>L t *4 * 4 1 1 . * 0 0 , O f ) ? 4 | * 0 .0 0 4 * 1 ? > * 7 3 4 *i 0 . 0 0 3 4 '* 7 O.oi-"**'-.* A s Q . 0 O U 4 ? P . O ^ I W # > V % /'*? 0 . 0 0 1 ',44 3 * 4 *■ t * 0 . 0 0 1 / 7 0 3 S T o . o r * ? * -* e . w n / s o > 4 0 *'« 0 h / > i i i «U 7/7O wav- > %#s T>*»t '' * -*.(•»!» urn###jn, r«i*rrfro •HH 184 APPENDIX II Scan Rate Calibration The decision to use the Livingston (1968) linage scanner was based upon the knowledge that It had been used to geometrically Bean sections of solar Images across the spectrograph slit and Its mechanical characteristics seemed to fulfill the requirements for scanning at the solar limb. I was unable to discover a published Bean rate calibration for the device so on two occasions during the December run and with somewhat greater effort during the August run I was able to obtain scan rate calibration data for the optical scanner. The earliest attempts Involved measuring the total throw of the scanner and determining from the sampling rate In the measurement program the time required for the scan. This led to a reasonable mean speed of image across the Blit but failed to indicate In any way possibilities of variations during the scan. I also tried using a double aperture placed over the slit and scanning the solar limb along the direction of the slit. This allowed me to make point by point velocity determinations between points separated by the separation of the two aperture holes. This would ultimately lead to a complete scan picture of the whole slit length were It not for the fact that the limb was 185 186 not sufficiently sharp to produce a step function that would allow determination of the timing of the passage of the limb over each aperture. It was during discussions with Charles Slaughter that the possibility arose to use an IBM punch card with a column or row of holes punched on a standard keypunch machine. The suggestion was that the keypunch Is In effect a precision instrument and the holes punched In an IBM card are quite accurately separated. I punched a series of holes In IBM cards and devoted a period of time on one of the rainy afternoons to the measurement of the variation In hole size and hole spacing using a Qaertner traveling microscope. I found that indeed the hole size and spacing Is quite uniform and such punched cards thus make ideal, precisely repeatable aperture plates. It was decided to place the IBM card over the spectro graph slit and scan along the slit with a discrete source of light rather than an extended source such as the sun. On the night of 21 August, 1970, Slaughter, W. Mitchell, and I rigged a helium neon laser with a long focus lens to produce a spot that could be swept across about 1/3 of the length of the spectrograph slit. The IBM card aperture plate was placed over the length of the slit. A series of scans was then made with the laser beam scanned along the 187 length of the slit. Intensity was sampled In the same way the solar data was sampled to give an accurate time base with the different sections of the slit scanned In overlap ping segments. The data were transferred back to Ohio on the same tapes that contained the limb scan data. The spectrograph was adjusted so the sharp emission line from the laser was centered In the output Blit In front of the detector typically used for line core measurements In the limb scans. Great care was taken not to affect the settings of any of the apparatus while scans were measured. In particular we were careful not to move the IBM card mask nor the rocking arm scanner. In all, three cams were used and all three were calibrated using two or more aperture plates in front of the spectrograph slit. The majority of the data were taken with the cam which was fabricated in the shop at the McMath Solar Telescope during the day of August 20 while obser vations were being attempted with the available camB. The new cam was built because there appeared to be Image bounce when the long throw cam completed its flyback. It was also felt an intermediate throw would be more appropriate for display of the limb profiles. The new cam was used to obtain all data from August 22 through the end of the ob serving run. Thus It Is this cam we are most Interested 188 In calibrating. The actual measurements were Intended to show the positions of the edges of the holes In the IBM card and measurements were to be made In terms of the Intensity as a function of time using the locations of the hole edges as the positions or displacements from which the velocities of the image across the slit could be determined. Unfortu nately the laser produced sharply peaked lmage& with rather broad wings. Scans of the holes displayed profiles with poorly defined edges but with a sharp peak in the center of each hole. Therefore I decided to use the hole center as the location for the location of the measured displace- ment. I took the time of each displacement directly from the time base in the data sampling routine. The measured separation of corresponding positions of the successive IBM card holes was found to be 0.2211 centimeters. Thus the centers of successive punched holes will be separated by this amount. The times required for the scan to reach each of these positions in sequence were plotted against the displacements, and the velocity of the spot across the slit was calculated. ThlB graph is shown in Figure 54. A least-squares fit of a straight line to these data yields a velocity of 6.0*i cm/sec. There is a slight non-linearity apparent in the plot of the measured 189 y » 0,0018 + 0.00604x .... Cm. measured points + + + + + 3 .* .+ 2 .+ t t* V 1 y *• 0 6 I______I______L 0 200 400 600 msec. Time from start Figure 54 Graph of the position of’a scanned spot as a function of time. The equation Is derived from a least-squares fit to the measured points. The y-intercept is in centimeters. The slope is in centimeters/millisecond which yields a scan rate of 60.4 millimeters/second. 190 points. The value of the velocity Is slightly higher at the extremities of the scan. Since' most of the data used In the actual limb scans were taken from near the center of each scan I decided not to try to correct for the slight non-linearity in the ends of the scans. The coefficient of correlation in the linear regression analysis was O.998. If one takes as the solar radius 695*500 kilometers and the Image radius of 399 millimeters the Image scale is approximately 17*10 kilometers per millimeter. A measured scan rate of 60.4 mm/sec in the image plane can then be converted to scan rates in kilometers in the solar atmosphere per unit time. Knowing the time interval between each sample point it is then possible to specify the number of kilometers separating each data channel in the Bean program. These data are included in Table 20 for the days upon which observations were made. In most cases in this work the value of 210.2 was adopted to determine the horizontal scales of the scan plots and to evaluate the separation of specific points at the limb. 191 TABLE 20 Image Beale Data McMath Solar Telescope Date Image Radius Sean Rate 1970 Aro Sec. mm km/mBee km/channel 20 Aug 950.1 399.0 179.19 179.19 22 Aug 950.5 399.2 105.23 210.06 27 Aug 951.5 399.6 105.125 210.25 28 Aug 951.7 399.7 105.09 210.18 29 Aug 951.9 399.8 105.07 210.10 Single scan drift Rate ■ 5112 km/channel APPENDIX III Two Dimensional Scattering Function The choice of a one-dimensional scattering function rests upon the inability of a two-dimensional scattering function to yield significantly different limb profiles when convoluted with an assumed object intensity distribu tion. If we assume the image smearing occurs from distances not exceeding several arc seconds we may treat the limb as a straight edge. In Figure 55, light scattered to a point, P, from the surrounding regions will be represented by an expression such as: + 0 0 + 0 0 I (x* ,y') « / / S If we confine the points, P, to the x-axis, this becomes: I(x‘,o) - / / S(x,y) F(x-x\y)dxdy (10) — 00 — 00 In the two-dimensional case the value of S(x,y) for the Gaussian spread function will be: S(x,y) « e - ^ ^ t ^ + y 2)**)2 (11) 192 193 Limb To DIbo Center . obj obj Figure 55 Geometry for calculating the Intensity distribution using a two-dimensional scattering function. 194 In the case of one-dimensional scattering the value of S(x,y) becomes S(x) - e~*(bx>2 the same as Eq. 2 on Page 77. Comparison of scattered profiles computed on the basis of one dimensional and two dimensional smearing should reveal how serious might be the errors introduced by the assumption of one dimensional spreading. Table 21 contains a listing of the assumed object profile, the one dimensional and two dimensional scattered profiles with b ■ 0.3, and the difference between the two scattered profiles expressed in percent of the intensity at the center of the disc. It is evident that at all points in the vicinity of the limb the differences between the one- and two-dimensional scattering cases are all less them 0.04% of the disc central intensity. The additional time required to perform the two-dimensional scattering integration (amounting to a factor of about 35) does not seem to be justified by these figures. 195 TABLE 21 Comparison of One- and Two-dimensional Scattering Function Intensity Distributions I(r)obj I i(r) I2(r) 1*2 .000000 .000258 .000240 .00182 .000000 .000963 .000960 .00022 .000000 .002529 .002521 .00082 .000000 .005634 .005643 -.00082 .000000 .011341 .011287 .00542 .000000 .020857 .020893 -.00362 .000000 .035462 .035423 .00392 .000000 .055975 .055957 .00182 .000000 .082396 .082495 -.00982 .000000 .113647 .113715 -.00682 .200000 .147615 .147818 -.02032 .261000 .181611 .181801 -.01892 .277000 .213006 .213262 -.02562 .285000 .239858 .240160 -.03012 .291000 .261262 .261534 -.02712 .298000 .277304 .277625 -.03202 .301000 .288747 .289032 -,02852 .303000 .296696 .297078 -.03812 .306000 .302230 .302602 -.03712 .308000 .306227 .306564 -.03372 .310000 .309317 .309446 -.01282 .312000 .311804 .311848 -.00432 • 314000 .314061 .314009 .00512 .316000 .316188 .316171 .00172 .318000 .318258 .318212 ,00462 .321000 .320256 .320253 .00032 .323000 .322211 .322175 .00362 • 324500 .324109 .324096 .00132 .326000 .325949 .325897 .00512 .327750 .327746 .327698 .00472 .329500 .329471 .329500 -.00282 .331250 .331210 .331181 .00292 .333000 .332878 .332862 .00152 •334600 .334516 .334543 -.00262 .336200 .336083 .336104 -.00202 .337750 .337593 .337185 .04072 .339300 .339016 .338025 .09902 BIBLIOGRAPHY Abetti, G. 1955, In "Vistas in Astronomy," 1^ Ed. by Beer, A. 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