Author name code: edmonds ADS astronomy entries on 2022-09-14 author:"Edmonds, Frank N." ------------------------------------------------------------------------ Title: A Statistical Analysis of NAID1 Profile Fluctuations at the Center of the Solar Disk - Part One - Data Reduction and Resolvable Velocities Authors: Edmonds, F. N., Jr.; Hsu, J. -C. Bibcode: 1983SoPh...83..217E Altcode: Three radial-velocity fluctuation arrays V(Δλ, Y) and line-formation fluctuation arrays L(Δλ, Y),where Δλ is wavelength displacement from the center of NaI D1 and Y is displacement on the Sun's surface along the spectrograph slit, were obtained from Sacramento Peak Observatory spectrograms. The variations of these line profile fluctuations are qualitatively described. The RMSυ's, coherences, and power spectra shapes for V(Δλ, Y) fluctuations are examined at different Δλ with the corresponding effective heights of formation calculated with Mein weighting functions. Title: A statistical analysis of resolvable velocities obtained from solar Na I D1 profile fluctuations. Authors: Edmonds, F. N., Jr.; Hsu, J. -C. Bibcode: 1983BAAS...15..615E Altcode: No abstract at ADS Title: A feasibility study of calibrating stellar photographic equivalent widths against solar photoelectric equivalent widths. Authors: Edmonds, F. N., Jr. Bibcode: 1978PASP...90..322E Altcode: The feasibility of reducing average systematic-plus-random errors in stellar photographic equivalent widths to S 5% by a direct calibration method is examined. Solar and stellar 2.5 A mm ' spectrograms covering the same wavelength range are exposed, developed, and reduced as similarly as possible, and the calibration of the solar equivalent widths against those obtained from A High-Resolution Spectral Atlas of the Solar Irradiance from 380 to 770 Nanometers is used to correct the stellar equivalent widths for systematic errors. The effects on overall accuracy of the procedure due to collimator (slit) illumination, development uniformity, density-to-intensity calibration, fixing continuum, width of profile measured, and filtering of noise are investigated. Overall procedure accuracy is estimated by comparison of calibrated (i.e., corrected) equivalent widths for Arcturus with those obtained from A Photometric Atlas of the Spectrum of Arcturus, and from reticon spectra taken at McDonald Observatory. The 5% average accuracy upper limit is feasible. The study also produces several cautions and recommended improvements for the procedure. Its potential for standardizing stellar equivalent widths is briefly discussed. Key words: equivalent widths-photographic spectra Title: A Feasibility Study of Calibrating Stellar Photographic Equivalent Widths against solar Photoelectric Equivalent Widths. Authors: Edmonds, F. N., Jr. Bibcode: 1977BAAS....9..635E Altcode: No abstract at ADS Title: Spectral analyses of solar photospheric fluctuations. V: A two-dimensional analysis of granulation at the center of the disk. Authors: Edmonds, F. N., Jr.; Hinkle, K. H. Bibcode: 1977SoPh...51..273E Altcode: Successful subtraction of instrumental background variations has permitted spectral analyses of two-dimensional measurement arrays of granulation brightness fluctuations at the center of the disk, arrays obtained from Stratoscope I, 1959B-flight, high-resolution frames B1551 and B3241. RMS's, uncorrected for instrumental blurring, are 0.0850 of mean intensity for B1551 and 0.0736 for B3241, somewhat higher than other determinations. These between-frame and between-investigation differences probably result from a combination of calibration errors, frame resolution differences, and, most likely, granulation pattern differences. Title: A Two-Dimensional Spectral Analysis of Solar Granulation at the Center of the Disk Authors: Edmonds, F. N., Jr.; Hinkle, K. H. Bibcode: 1976BAAS....8..311E Altcode: No abstract at ADS Title: Spectral Analyses of Solar Photospheric Eluctuations. IV: The Low-Wavenumber Power of Granulation Brightness Eluctuations Authors: Edmonds, F. N., Jr. Bibcode: 1975SoPh...44..293E Altcode: Synthetic one-dimensional scans of brightness fluctuations are generated from intergranulegranule profiles (IGP), which approximate observed scans of granulation fluctuations except that the local (i.e. IGP) mean intensity is kept constant. Comparing the power spectrum of such scans with the power spectrum of observed scans shows that nearly two thirds of the low-wavenumber (k < 0.0025 km-1) granulation power is due to this variable mean effect. This result favors the interpretation of granulation as turbulent thermal convection but cannot rule out the laminar convection interpretation. Title: Convective Flux in the Solar Photosphere as Determined from Fluctuations Authors: Edmonds, F. N., Jr. Bibcode: 1975BAAS....7..362E Altcode: No abstract at ADS Title: Convective Flux in the Solar Photosphere as Determined from Fluctuations Authors: Edmonds, F. N., Jr. Bibcode: 1974SoPh...38...33E Altcode: The fractional convective flux πFc(xc/πF) is computed for the effective level xc= logτc = 0.125, using bi-dimensional co-spectra for relative continuum-brightness fluctuations ΔI and radial velocity fluctuations ΔV measured for the CI 5052.16 spectral line. A more uncertain flux for xFe ≈ - 0.9 is obtained for the FeI 5049.83 line. Since the results (Figure 1) incorporate current uncertainties in RMSΔI, RMSΔV and RMSΔT(x), where ΔT are photospheric temperature fluctuations, they must be considered qualitative until these uncertainties are appreciably reduced. The requirement that the fractional convective flux < 1, places restrictions on these uncertainties which suggest that current RMSΔT(x)'s are too large. Title: Statistical Line Blanketing in Arcturus. I. Blanketing-Coefficient Description of Observations Authors: Edmonds, Frank N., Jr. Bibcode: 1973PASP...85...24E Altcode: A statistical description of line blanketing is presented for Arcturus (a Boo, K2 IlIp, V = +0.06) which is based on equivalent widths and identifications of roughly 10,000 spectral lines within the wavelength region AA3600-25,000 A. Equivalent-width contributions or blanketing coefficients for lines grouped as to equivalent width and identification are given for 100 A wavelength intervals for A < 9000 A and 500 A intervals for A> 9000 A (Tables I and II). Strong lines are listed individually (Table III), and the variation or scatter of blanketing within intervals is described. Corrections to this description for limitations in the observations and their analysis are discussed. Key words: line blanketing - statistics of spectral lines - spectroscopy Title: Spectral Analyses of Solar Photospheric Fluctuations. III. Bi-Dimensional Power, Coherence and Phase Spectra of Deep-Seated Radial Velocity and Photometric Fluctuations Authors: Edmonds, Frank N., Jr.; Webb, Carol J. Bibcode: 1972SoPh...25...44E Altcode: Fluctuations measured from a time sequence of high-resolution, high-dispersion Sacramento Peak Observatory spectrograms and previously analyzed by computing one-dimensional temporal and spatial spectra (Edmonds et al., 1965), are re-analyzed using bi-dimensional (temporal and spatial) power, coherence and phase spectra computed by fast-Fourier-transform techniques. The fluctuations measured are radial velocity for the FeI 5049.83, CrI 5051.91 and CI 5052.16 spectral lines, continuum brightness, and equivalent width and central intensity of the CI line. The bidimensional spectra, particularly those of coherence and phase, allow isolating different components of the fluctuations to a degree not possible in the one-dimensional analyses. Title: Line Blanketing in Arcturus - Statistical Descriptions of Observations. Authors: Edmonds, F. N., Jr.; Morgan, T. E. Bibcode: 1972BAAS....4..236E Altcode: No abstract at ADS Title: Spectral Analyses of Solar Photospheric Fluctuations. II. Profile Fluctuations in the Wings of the λ 5183. 6 MgI b1 Line Authors: Edmonds, Frank N., Jr. Bibcode: 1972SoPh...23...47E Altcode: Residual intensity fluctuation measurements within the wings of the λ5183.6 MgI b1 line, obtained from two, high-resolution, high-dispersion, Sacramento Peak Observatory spectrograms, have been subtracted from intensity fluctuations in the adjacent continuum in order to isolate fluctuations associated exclusively with line formation. The useable spectral range for studying these lineformation fluctuations is restricted to wavelengths between 1040 and 7170 km because the subtraction increases the relative importance of noise and large-scale photographic variations across the spectrograms could not be completely removed. Power and cross-power (coherence and phase) spectra proved to be valuable diagnostic tools in isolating line-formation fluctuations. Title: Spectral Analyses of Solar Photospheric Fluctuations. I: Power, Coherence and Phase Spectra Calculated by Fast-Fourier-Transform Techniques Authors: Edmonds, Frank N., Jr.; Webb, Carol J. Bibcode: 1972SoPh...22..276E Altcode: The application of the fast-Fourier-transform (FFT) algorithm to calculating one-dimensional and bi-dimensional (temporal and spatial), power and cross-power (coherence and phase) spectra is examined for solar photospheric fluctuations. Alternative methods for smoothing raw spectra, direct averaging (employing various weights) and indirect truncation of the correlation function, are compared, and indirect smoothing is compared with spectra calculated by mean-lagged-product (MLP) methods. Besides providing the raw spectrum, FFT techniques easily allow computing a series of spectra with varying amounts of smoothing. From these spectra a range of satisfactory compromise between resolution and stability can be determined which helps in the interpretation of spectral trends, and in identifying more clearly the existence and significance of spectral features. For bi-dimensional spectra presented as contour plots, this range of satisfactory smoothing can be restricted, particularly when spectral trends must be represented by small-scale contours. Equivalent spectra (i.e. comparable equivalent degrees of freedom) computed or smoothed by different methods have minor, but not negligible, differences. Examination of these differences favors computing of FFT spectra smoothed by averaging for photospheric fluctuations. Title: Line Blanketing in Arcturus - Statistical Descriptions of Observations. Authors: Edmonds, F. N.; Morgan, T. E. Bibcode: 1971BAAS....3..454E Altcode: No abstract at ADS Title: Profile Fluctuations in the Wings of the λ5183.6 Mg b Line Due to Solar Photospheric Inhomogeneities Authors: Edmonds, Frank N., Jr. Bibcode: 1971BAAS....3....6E Altcode: No abstract at ADS Title: Bidimensional (Spatial and Temporal) Power, Coherence, and Phase Spectra for Solar Photospheric Spectral Lines Authors: Edmonds, Frank N., Jr.; Webb, Carol Jean Bibcode: 1970BAAS....2..311E Altcode: No abstract at ADS Title: A Comparison of the Statistical Stability and Spectral Resolution of Power Coherence and Phase Spectra of Solar Photospheric Fluctuations as Evaluated by Fast-Fourier-Transform Techniques and by the Mean-Lagged-Product Method Authors: Edmonds, Frank N., Jr.; Webb, Carol Jean Bibcode: 1970BAAS....2Q.312E Altcode: No abstract at ADS Title: The Radial Velocity of Arcturus Determined from Interferometric Spectra Authors: Bopp, Bernard W.; Edmonds, Frank N., Jr. Bibcode: 1970PASP...82..299B Altcode: From high-resolution, infrared, interferometric spectra, the radial velocity of Arcturus is deterrnined by simple measurements between superposed spectral tracings of the star and the sun. A velocity of -5.47 1 0.07 km/sec obtained from metal lines is comparable to a highly accurate result obtained by Petrie and Fletcher (1967) using standard methods. A velocity of -5.82 1 0.18 obtained from CO lines is interpreted in terms of a differentially expanding atmosphere. Title: The Infrared Spectrum of Arcturus Authors: Montgomery, Earl F.; Connes, Pierre; Connes, Janine; Edmonds, Frank N., Jr. Bibcode: 1969ApJS...19....1M Altcode: Equivalent widths of 1036 stellar lines have been measured from high-resolution interferometric spectra of Arcturus covering the spectral range 876&3978 (1 129 A). Approximately 60 percent of these lines have been identified. Title: The Infrared Spectrum of Arcturus Authors: Montgomery, Earl F.; Connes, Pierre; Connes, Janine; Edmonds, Frank N., Jr. Bibcode: 1969BAAS....1R.201M Altcode: No abstract at ADS Title: The McDonald Coudé Sensitometer Authors: Edmonds, Frank N., Jr. Bibcode: 1969BAAS....1..150E Altcode: No abstract at ADS Title: Radiative transfer within a stellar absorption line. The contribution curves of fine-analysis methods. Authors: Edmonds, F. N., Jr. Bibcode: 1969JQSRT...9.1427E Altcode: No abstract at ADS Title: Contribution Curves in the Fine Analysis of Stellar Spectral Lines. Authors: Edmonds, Frank N., Jr. Bibcode: 1967AJ.....72R.793E Altcode: Three methods for the fine analysis of spectral lines are: (1) a straightforward combination of formulas arising from pertinent formal solutions to the equation of radiative transfer; (2) the Planckian-gradient method developed by Mugglestone; (3) the weight- saturation method developed by Pecker and others. These three methods are equivalent in that the formulas for one method can be obtained from those of another by simple integration by parts. In each of the three cases the formulas allow the computing of contribution curves which presumably show the relative contribution to line formation of the different layers of the model atmosphere used in the fine analysis. Computer programs have been developed for the three methods which compute the equivalent width and profiles of spectral lines under the assumption of formation by pure absorption. These programs have been designed to give contribution curves as well. The contribution curves for the same line abundance-model atmosphere situation are quite different for the three methods, and many of the properties of contribution curves which have been determined previously, using the weight saturation method, are not found in those for the formal solution or Planckian-gradient methods. These results lead to the conclusion that contribution curves are critically method dependent and do not provide information about the depth dependence of line formation. Previous determinations of effective depths of line formation based on or related to contribution curves are therefore suspect. The differences in the contribution curves of the three methods are such that the weight-saturation method weights more heavily the contribution from the upper layers of the atmosphere, while the Planckian-gradient method gives the least weight to these layers. One might expect, therefore, differences in equivalent widths and profiles computed by the different methods because of this difference in weighting. In particular, a method which weighted the most reliably determined layers of a model atmosphere would be preferable. Calculations testing these possibilities are under way, but results obtained so far indicate that differences between the methods are small, except when layer-dependent factors, such as the damping constant, critically affect equivalent widths. Title: Amplitude Distributions of Solar Photospheric Fluctuations Authors: Edmonds, Frank N., Jr. Bibcode: 1967SoPh....1....5E Altcode: Amplitude distributions, which are nearly Gaussian, have been calculated for radial velocity, continuum brightness, spectral line equivalent width and spectral line central residual intensity fluctuations measured from high-dispersion high-resolution spectrograms taken at the center of the solar disk. The RMS and skewness S for each distribution have been calculated in a manner which allows testing of the homogeneity of the granulation pattern (i.e. variations in its statistics across the solar disk and with time). Pattern inhomogeneity across the disk is strongly indicated, and further evidence suggesting appreciable pattern persistence over time intervals ≳ 15 minutes is presented. The possibilities for investigations of S and its associated bi-spectrum are discussed. The qualitative values of S obtained are shown not to be due to unusually bright, rising granules (though a statistical tendency towards such granules is possible). An attempt to explain S for continuum brightness fluctuations in terms of the nonlinear effects of Planckian emission and opacity fluctuations in a stratified photosphere, leads to contradiction with the measured amplitude distributions, a contradiction which is probably due to an oversimplified treatment of radiative transfer in an inhomogeneous photosphere. Title: Hydrogen-line Stark broadening functions Authors: Edmonds, Frank N., Jr.; Schluter, Hans; Wells, Donald C. Bibcode: 1967MmRAS..71..271E Altcode: 1967MmRAS..70..271E No abstract at ADS Title: A Spectrophotometric Analysis of Procyon. II. The Continuous Spectrum and Line Blanketing Authors: Talbert, Freddie D.; Edmonds, Frank N., Jr. Bibcode: 1966ApJ...146..177T Altcode: Photoelectric spectral scans of Procyon (F5 IV-V), obtained at McDonald Observatory, are combined with monochromatic magnitudes obtained by other observers to determine a measured continuous spectrum extending over the wavelength range X 3390-7460 and corrected for line blanketing measured from high-dispersion spectrograms. Line-blanketing measurements over the wavelength range X 3025- 4100 are also given. An attempt is made, with partial success, to correct further the continuum in the ultraviolet for blanketing by Balmer lines and unresolved lines, using primarily a straight-line extrapolation method which assumes that variations of color temperature with wavelength are small. Comparisons made between the measured continuous spectrum and the emergent flux predicted by a set of model atmospheres lead to the selection of a model atmosphere for the star. Title: The Evidence for an Oscillatory Component in Solar Granulation Brightness Fluctuations Authors: Edmonds, Frank N., Jr.; McCullough, James R. Bibcode: 1966ApJ...144..754E Altcode: The evidence for an oscillatory component of continuum brightness fluctuations, secondary maxima in temporal autocorrelation functions and power spectra, is examined critically with the provisional conclusion that such a component is theoretically possible and probably does exist. This component, with periods distributed about 5 min, constitutes between 0.5 and 2 per cent of the total fluctuation power. The results from one analysis (725) suggest the coexistence of a second oscillatory component with periods distributed about 10 min, but the evidence is quite uncertain. There are also indications that the effects of spectral windows may be masking a stronger concentration of power of continuum brightness fluctuations to lower frequencies Title: A Coherence Analysis of Fraunhofer-Line Fine Structure and Continuum Brightness Fluctutations Near the Center of the Solar Disk. II Authors: Edmonds, Frank N., Jr. Bibcode: 1966ApJ...144..733E Altcode: Spatial cross-correlation analyses between fluctuations in radial velocity, V, and continuum brightness, I, have been carried out for four high-resolution spectrograms of the center of the solar disk obtained by Michard at the Pic-du-Midi Observatory. These analyses employed a coherence technique, and the results are quite similar to those recently obtained from an analysis of Sacramento Peak Observatory spectrograms by Edmonds, Michard, and Servajean. These results suggest that the V fluctuations contain a large-scale oscillatory component poorly correlated with the I fluctuations, and a smaller-scale convective component sigiiificantly correlated with the I fluctuations. An improved method for determining confidence limits for the results of a coherence analysis is presented in the Appendix, and these limits are applied to the results of four spatial coherence analyses. It is shown that these and other estimates of random errors of the statistical analysis cannot explain the differences between the different analyses. Whereas instrumental and atmospheric blurring may be important causes of these differences, it appears that for the most part they are real differences between different samples of photospheric inhomogeneities. The effects of the possible inclination of inhomogeneities found by Evans are also discussed. Confidence limits estimates further show that small variations with wavenumber k1 of power spectra and coherences cannot be considered significant. Title: The Determination of the Ultraviolet Continuum of Procyon from Balmer Line Profiles Authors: Edmonds, F. N., Jr. Bibcode: 1966IAUS...26..159E Altcode: No abstract at ADS Title: Observational studies of macroscopic inhomogeneities in the solar atmosphere. VII. A statistical analysis of photometric and kinematic inhomogeneities in the deep atmosphere Authors: Edmonds, F. N.; Michard, R., Jr.; Servajean, R. Bibcode: 1965AnAp...28..534E Altcode: No abstract at ADS Title: Asymmetry in the Brightness Fluctuations of Solar Granulation. Authors: Edmonds, Frank N., Jr. Bibcode: 1965AJ.....70Q.674E Altcode: Recent determination of the amplitude of solar photospheric temperature fluctuations as a function of optical depth (Edmonds, F. N., Jr., Astrophys. J. 139, 1358) has been combined with the empirical model atmosphere of Pierce and Waddell (Mem. Roy. Astron. Soc. 68, 89) to calculate the skewness of source-function fluctuations and of emergent intensity fluctuations for assumed Gaussian and skew Gaussian-like distributions of the temperature fluctuations. These calculations show the skewness introduced into the emergent intensity fluctuations by the Planckian nature of the source function emission and by the stratification of the continuum contributing layers. This skewness is calculated as a function of position on the solar disk and is compared with that determined from a statistical analysis of solar granulation (Edmonds, F. N., Jr., Astrophys. J. Suppl. 6, 357). This photometric asymmetry of the granulation pattern is distinguished from the topological asymmetry (bright blobs surrounded by dark lanes) which is a manifestation of the upper boundary of the solar hydrogen convection zone. Title: The Continuous Spectrum and Line Blanketing for Procyon. Authors: Talbert, F. D.; Edmonds, F. N., Jr. Bibcode: 1965AJ.....70Q.332T Altcode: Low-dispersion photoelectric spectrum scans coupled with high-dispersion coude' plates have been used to construct an empirical continuum of Procyon corrected for line blanketing. Blanketing factors for 25 A intervals in the range XA30254100 have been determined. The straight-line extrapolation method of Canavaggia and Chalonge has been used to determine the continuum in the near ultraviolet, ~x3650#000, and concordant results have been obtained from a determination based on matching observed and computed profiles of the Balmer lines in this wavelength range. Comparison of the empirical continuum with that predicted by several model atmospheres calculated for Procyon indicate moderate discrepancies in the ultraviolet. Possible causes for these discrepancies are discussed. Title: A Set of Non-Gray Model Atmospheres for Procyon. Authors: Edmonds, Frank N., Jr. Bibcode: 1964ApJ...140..902E Altcode: A set of eight non-gray model atmospheres has been calculated for the subgiant Procyon (F5 IV) using the Str6mgren-Swihart method for determining a temperature-optical depth relation which maintains constant flux. The eight models correspond to two values each of the parameters Te (effective temperature), A (hydrogen-to-metal ratio), and p (helium-to-hydrogen ratio). These models are compared with respect to the variation with optical depth and/or wavelength of the following properties: 0 = 5040/T, log Fe, log Pg, hydrogen convection zone, limb darkening, and emergent flux with associated continuum contribution functions. The problem of model selection (and parameter determination) is discussed in general terms. The parameter Te can be obtained from the observed continuous spectrum, but the parameters A and p cannot, as would be expected for the spectral class F5 IV. The parameters A and p cannot be determined effectively from the observed strengths of weak spectral lines or from the Stark of the Balmer lines. Conversely, the determination of these two parameters does not seem to be necessary for a spectrophotometric analysis of weak lines. Title: Source-Function and Temperature Fluctuations in the Solar Photosphere. I. The Isotropic Approximation. Authors: Edmonds, Frank N., Jr. Bibcode: 1964ApJ...139.1358E Altcode: Measurements of power spectra and RMS's for granulation brightness fluctuations across the solar disk, as obtained from 1957 Stratoscope photographs by Edmonds (1962), are used to determine source- function and temperature fluctuations as a function of optical depth in the solar photosphere. This involves the solving, by the Laplace-transform method employing polynomials, of integral equations which are based on an approximation of isotropy and which are quite similar to the formal solution of the equation of radiative transfer. Limitations imposed on the results by the measurements and the method employed are discussed. Source-function and temperature fluctuations are presented in Tables 2,3, and 4 and in Figures 3 and 4. These fluctuations increase with optical depth r, this increase becoming more gradual or leveling off around optical depth 1.5 as the result of the maximum in the granulation brightness fluctuations which occurs at 0 500 on the disk. The best determined RMS of temperature fluctuations at the same opticat depth is approximately 880 K at r = 0.32, 2720 K at r = 0.80, 4540 K at r = 1.28, and 5140 K at r = 2.08. For the first three of these optical depths, the RMS's at the same geometricat tevet are 880 K, 3600 K, and 7400 K. Title: On the Calculation of Equivalent Widths from Spectral-Line Profiles. II. Authors: Edmonds, Frank N., Jr. Bibcode: 1964ApJ...139.1017E Altcode: No abstract at ADS Title: Cross Correlation between Continuum Brightness and Radial Velocity Fluctuations in the Solar Photosphere. Authors: Edmonds, Frank N., Jr. Bibcode: 1964AJ.....69Q.540E Altcode: Spatial coherence and phase analyses of the cross correlation between continuum brightness and radial velocity fluctuations in the solar photosphere have been completed for four bigh-resolution spectrograms obtained by R. Michard at the Pic-du-Midi Observatory, and from a time sequence of 60 spectrograms taken by J. W. Evans at Sacramento Peak Observatory. The latter set includes the low-lying CI line N5052.16, and its analysis is a joint effort with Dr. R. Michard and Dr. R. Servajean at the Observatoire de Paris Meudon. The results give mean cross-correlation coefficients for each set of 0.35 and mean, nearly anti- phase coherences which are significant (>0.5) in wavenumber ranges that lie between 10- and 2.5 X 1O-i km-'. These results, together with earlier analyses (Edmonds, Astrophys. J. 136, 507,1962), indicate first that, in general, significant cross correlation does exist between continuum brightness and radial velocities fluctuations with scales less than 8000 km. Therefore, thermal- driven convection is an appreciable physical cause of the fluctuations. Secondly, there is considerable variation in behavior between different samples of solar photospheric inhomogeneities, these differences appearing in other statistical properties and in the tracings of the fluctuations. That stronger cross correlation is not found is possibly understandable in terms of the recent discovery by Evans (to be published in A strophysica Norvegica; also see abstract by J. W. Evans) that photospheric inhomogeneities may be strongly inclined to the radial direction. There are problems with this interpretation which arise from the small separation ($ 200 km) between layers of continuum formation and of line formation. An analysis of the effects of random shifts in position on the solar disk between radial velocity and continuum brightness fluctuations predicts that orientation could reduce the cross-correlation coefficient only to about 0.75 and reduce coherence correspondingly in a manner which increases with wavenumber. Also, temporal coherence and phase analysis (Evans Michard, and Servajean, Ann. d'Astrophys. 26, 368,1963), provides a clearer picture as to the role played by oscillations (with periods around 300 sec) which are an important component of the radial velocity fluctuations but not of the contiuum brightness fluctuations. These results, together with more recent power spectra computed by Michard and Servajean suggest that whereas the oscillatory component is dominant for optical depths &0.01, it is still appreciable in continuum- forming depths >1.0. Title: On the Calculation of Equivalent Widths from Spectral-Line Profiles. Authors: Edmonds, Frank N., Jr. Bibcode: 1963ApJ...137..470E Altcode: The determination of equivalent width from a line profile in terms of Hjerting functions requires knowledge of the scale factor = A /V, where AX is the displacement in wavelength from the line's center and V is the Hjerting function argument. Tables are given in Section II which will allow the determination of p for a profile Pk(AXk) evaluated only at three values of AX,. Necessary factors to compute the equivalent width, based on fitting a Hjerting function to these points, are also tabulated. More general numerical integration formulae for determining the equivalent width, based on Hjerting functions, are discussed in Section III, and the weights and divisions V, are tabulated As shown in Section IV, these formulae will give greater accuracy for fewer divisions than methods now in use. For computed profiles, this should effect a worthwhile reduction in computational effort. Title: A Coherence Analysis of Fraunhofer Line Fine Structures and Continuum Brightness Fluctuations Near the Center of the Solar Disk. Authors: Edmonds, Frank N., Jr. Bibcode: 1962ApJ...136..507E Altcode: Cross-correlation analyses between fluctuations in radial velocity V and continuum brightness I have been carried out for four sets of measurements made near the center of the solar disk: those obtained from a McMath-Hulbert spectrogram (w18), those of Richardson and Schwarzschild (1950) (RS), those of Plaskett (1954) (P), and those of Servajean (1961) (S). in addition, cross-correlation analyses between fluctuations in line equivalent width W and fluctuations in V and in I have been applied to the w18 measurements. These analyses employed a coherence technique which gives the coherence or cross- correlation between the Fourier components of the same wavelength for each set of fluctuations and the phase difference (across the solar disk) between these Fourier components (Figs. 4 5 6 8 10 12). The analyses also computed power spectra (Figs. 3, 7, 9, 11), r.m.s. `5, and filtered and unfiltered cross-correlations (Table 2). A significant VI coherence with 180 phase difference was found in the wavelength range km (on the surface of the sun) for the RS measurements; no VI coherence was found for the w18 measurements; and the S and P measurements gave inconclusive results. A significant 1W coherence with 1800 phase difference for wavelengths > 5000 km, and no VW coherence was obtained for the w18 measurements. These results cannot be explained in terms of differences in the solar atmosphere levels making an appreciable contribution to line formation and to continuum formation. The negative nature of the 1W cross-correlation seemingly can be explained only in terms of 4-10 per cent increases in the level of microturbulence for dark areas on the solar surface, with corresponding decreases for the bright areas The inconsistent picture presented by the four VI coherence analyses can be explained in terms of a negative VI cross-correlation existing for wavelengths < 5000 km plus certain differences in instrumental and atmospheric resolution for the four sets of measurements. However, an explanation in terms of a heterogeneous convection pattern at the sun's surface seems more reasonable. The nature of the radial-velocity power spectra and the effects producing a low cross-correlation are also discussed. Title: A Coherence Analysis of Fraunhofer Line Radial Velocity Fine Structure and Continuum Brightness Fluctuations near the Center of the Solar Disk. Authors: Edmonds, Frank N., Jr. Bibcode: 1962AJ.....67Q.271E Altcode: Cross correlation analyses between fluctuations in radial velocity V and continuum brightness I have been carried out for four sets of measurements made near the center of the solar disk; those obtained from a McMath-Hulbert spectrogram (w18), those of R. S. Richardson and M. Schwarzschild (Astrophys. J. 111, 351, 1950) (RS), those of H. H. Plaskett (Monthly Notices Roy. Astron. Soc. 114, 251, 1954) (P), and those of R. Servajean (Ann. Astrophys. 24, 1, 1961) (S). These analyses employed a coherence technique which gives the coherence or cross correlation between the Fourier components of the same wavelength for each set of fluctuations, and the phase difference (across the solar disk) between these Fourier components. The analyses also computed power spectra, RMS's and filtered and unfiltered cross correlations. A significant VI coherence with 180~ phase difference was found in the wavelength range 1200-5200 km (on the surface of the sun) for the RS measurements, no VI coherence was found for the w18 measurements, and the S and P measurements gave inconclusive results. These results cannot be explained in terms of differences in the solar atmosphere levels making an appreciable contribution to line formation and to continuum formation. The inconsistent picture presented by the four VI coherence analyses can be explained in terms of a negative VI cross correlation existing for wavelengths ~ 5000 km plus certain differences in instrumental and atmospheric resolution for the four sets of measurements. However, an explanation in terms of a heterogeneous convection pattern at the sun's surface seems more reasonable. Title: A Statistical Photometric Analysis of Granulation across the Solar Disk. Authors: Edmonds, Frank N., Jr. Bibcode: 1962ApJS....6..357E Altcode: Twenty-five microphotometer scans from Stratoscope granulation photographs distributed across the solar disk have been analyzed statistically to yield amplitude distributions, power spectra, and related quantities. Power spectra have been calculated for twenty additional scans of the center of the disk obtained by Schwarzschild (1959). A difference in calibration procedures in part explains RMS's that are nearly twice those obtained by sChwarzschild. The range of wave numbers k1 for which power-spectra calculations yield quantitative results is limited by uncertainties in low-wave-number filtering to k1 > 0.001 km-' and by what is probably instrumental noise in the photographs to k1 < 0.008 km-'. This upper limit is further reduced to k1 < 0.004 km-' or less by instrumental corrections, using the method of Uberoi (1955b) generalized for foreshortening. These corrections account for the instrumental profile of the Stratoscope (determined from the limb of the solar disk),for focus of the photographs, and for the analyzing spot and focus of the microphotometer. The variation in the relative brightness fluctuation RMS across the solar disk (Figs. 4 and 9) is characterized by an increase from 0.14 for the central regions of the disk (out to 0 20 , to 0.20 at 0 50 and then a sharper decrease, which levels off and reverses itself at 0 70 . Ezamination of limb photographs attributes this reversal to the emerging photometric importance of a large-scale, essentially unforeshortened, pattern which does not seem to be instrumental or telluric aild may not be part of the normal photosphere granulation. Scatter in the RMS of adjacent scans can be attributed to statistical inhomogeneities in the granulation pattern. The amplitude distributions are approximately Gaussian (Fig. 3) with moderate positive skewness. The power spectra (uncorrected, Tables 3 and 4 and Figs. 2 and 5; corrected, Table 8 and Fig. 10) are characterized by a rapid decrease with increasing k,. A steepening of this falling-off toward the limb is probably due to the large-scale pattern. The variation in the brightness fluctuation RMS across the disk has been converted to the RMS of temperature fluctuations as a function of optical depth, using the Eddington-Barbier approximation (Fi . 11). The maximum of brightness RMS at 0 50 becomes a maximum in temperature RMS of 290 K at r 0.65. An inhomogeneous model solar atmosphere based on these temperature fluctuations has been constrncted (Table 9), and, using the&etical results of Ledoux, Schwarzschild, and Spiegel (1961), an associated velocity spectrum and convective transport have been roughly determined. Scans of two special regions have been analyzed: a region at the center of the disk, which is characterized by a low RMS and a flattened spectrum, and a facular region, which shows the normal spectrum and ouly a slightly higher RMS. Title: On Solar Granulation. Authors: Edmonds, Frank N., Jr. Bibcode: 1960ApJ...131...57E Altcode: From the examination of high-quality stratoscope photographs of solar granulation it has been determined that the fading of the granulation pattern occurs primarily in the region 60 < 0 < 78 and that the fading granulation is replaced by a larger, low-contrast pattern observable out to 0 87 . Inhomogeneities in the granulation pattern have also been observed. These consist of low-contrast regions which seem to persist for periods longer than 10 minutes and small-scale regions which seem to evolve with the normal pattern Title: Letters to the Editor CA II Emission in the Spectrum of Procyon. Authors: Kraft, Robert P.; Edmonds, Frank N., Jr. Bibcode: 1959ApJ...129..522K Altcode: No abstract at ADS Title: The Coefficients of Viscosity and Thermal Conductivity in the Hydrogen Convection Zone. Authors: Edmonds, Frank N., Jr. Bibcode: 1957ApJ...125..535E Altcode: The coefficient of viscosity, , the coefficient of thermal conductivity by conduction, X , and the coefficient of the thermal conductivity by radiation, X , have been calculated for stellar material (85 per cent hydrogen, 15 per cent helium) over temperature and pressure ranges which should include the hydrogen convection zones of most stars. Title: The DEBYE-HÜCKEL Effect and Statistical Theories for Collision Broadening. Authors: Edmonds, Frank N., Jr. Bibcode: 1956ApJ...123...95E Altcode: The theory of Debye and for electrolytes is shown to be valid and pertinent for ionized gases of astrophysical interest Corrections to statistical theories of collision broadening due to the effect are shown to be negligible in the cases of linear and quadratic Stark broadening of the spectral lines of ions In Appendix I, Debye- effect corrections are calculated for the related problem of the average distance to the nearest charged particle. Title: Noncoherent Scattering due to Collisions. I. Zanstra's Ratio of Coherent to Uncorrelated Noncoherent Scattering. Authors: Edmonds, Frank N., Jr. Bibcode: 1955ApJ...121..418E Altcode: A quantum-theory formulation of the problem of noncoherent scattering due to collisions is presented in a general form and then made equivalent to Zanstra's classical oscillator formulation by a set of assumptions. These assumptions are examined critically as an indirect method of determining whether Zanstra's results are correct for statistical broadening. It would seem that Zanstra's ratio of coherent to uncorrelated noncoherent scattering is too large by at least a factor of 20, and the coherent component is not strictly coherent. The validity of evaluating Zanstra's results for impact broadening by this method is bnefly discussed. Title: Compton Scattering by Electron Atmospheres. II. Problems with Incident Normal Flux. Authors: Edmonds, Frank N., Jr. Bibcode: 1954ApJ...119..425E Altcode: The problem of the transfer of radiation in an atinosphere of free electrons is solved in the first approximation for two sets of boundary conditions involving an incident normal flux, that of the planetary nebula problem and that of no incident diffuse radiation field. In the solution, account is taken of the noncoherent character of the electron scattering due to the Doppler shifts arising from a Maxwellian distribution of thermal velocities, the red shift of the Compton effect, and a non-Doppler blue shift arising from thermal motions and first pointed out by Dirac. The latter two effects, designated as "Compton scattering," are shown to produce asymmetries in spectral lines which would be very difficult to detect for very high temperatures, as they are much smaller than the thermal broadening. In an appendix, application of the solutions obtained to multiple Compton scattering of low-energy gamma radiation is considered. Title: Compton Scattering by Electron Atmospheres. I. The Schuster Problem. Authors: Edmonds, Frank N., Jr. Bibcode: 1954ApJ...119...58E Altcode: The problem of the transfer of radiation in an atmosphere of free electrons is solved in the first approximation under the conditions of the standard Schuster problem of line formation. In the solution, account is taken of the noncoherent character of the electron scattering due to the Doppler shifts arising from a Maxwellian distribution of thermal velocities, the red shift of the Compton effect, and a non-Doppler blue shift arising from thermal motions and first pointed out by Dirac. The latter two effects, designated as "Compton scattering," are shown to produce asymmetries in spectral lines which would be very difficult to detect for stellar temperatures, as they are much smaller than the thermal broadening. Title: Compton Scattering by Electrons with a Maxwellian Distribution of Thermal Velocities. Authors: Edmonds, Frank N., Jr. Bibcode: 1953ApJ...117..298E Altcode: The theory of the Compton effect is applied to the problem of scattering of radiation by electrons with a Maxwellian distribution of thermal ; and a spectral distribution function for scattered radiation is obtnined in the second approximation. This function, equation (26), is asymmetric, and the frequency shift of scattered radiation corresponding to this asymmetry is given by - cos 0 - t m0 c2 (kv-3kT), where p is the incident frequency, p' the scattered frequency, 0 the angle of scattering, and the other symbols have their usual meaning. The red shift in this expression is due to the Compton effect, while the blue shift is a result of the thermal motions of the electrons, as first pointed out by Dirac. Title: Scattering by a Moving Electron Atmosphere and its Effect on Spectral LINES.I. the Schuster Problem. Authors: Edmonds, Frank N., Jr. Bibcode: 1950ApJ...112..307E Altcode: The problem of the transfer of radiation in an atmosphere of free electrons undergoing differential expansion is solved in the first approximation under the conditions of the standard Schuster problem of line formation. It is further assumed that electron scattering is in accordance with the frequency-independent Thomson scattering coefficient, the Rayleigh phase function, and a Maxwellian distribution of thermal velocities. In the solution, account is taken of the noncoherent character of the scattering due to velocities arising from the thermal and mass motions of the electrons. The solution for radiation emerging from the atmosphere contains terms for unscattered and scattered radiation. The latter contains a function which represents the spectral distribution of scattered radiation for incident monochromatic radiation. The shape of this function, which is due to the thermal motions of the electrons, produces broad spectral lines characterized by a shallow center and extended wings. Further, a shift of this spectral distribution function resulting from the differential expansion of the atmosphere produces asymmetries in spectral lines. Two numerical examples of these effects have been calculated. Title: Scattering by a Moving Electron Atmosphere and its Effect on Spectral Lines. II. The Planetary Nebula Problem. Authors: Edmonds, Frank N., Jr. Bibcode: 1950ApJ...112..324E Altcode: The problem of the transfer of radiation in a planetary nebula undergoing differential expansion and consisting of free electrons in thermal motion is solved in the first approximation for the emergent radiation. In the solution, account is taken of the noncoherent character of the scattering, which is due to the thermal and mass motions of the electrons. The solution for the emergent radiation represents radiation of the incident flux from the central star, which has suffered scattering by electrons in the nebula. The solution contains a function which describes the spectral distribution of scattered intensity for incident monochromatic flux. The shape of this function produces in the solution a broadening of spectral lines characterized by a shallow center and extended wings. A shift of this function, due to the differential expansion of the nebula, produces shifts in the lines. A numerical example has been worked out.