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R i n s l a n d , C u r t i s P h il ip
SPECTRA OF LATE-TYPE STARS IN THE ONE TO FOUR MICRON REGION
The Ohio State University Ph.D. 1980
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University MicroTiims international 30C \ 13 = 3 30 4=1 SQ 4 VI! 43'06 '313! 761-4700 SPECTRA OF LATE-TYPE STARS IN THE ONE TO FOUR MICRON REGION
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Curtis Philip Rinsland, B.S., M.S.
*****
The Ohio State University
1980
Reading Committee: Approved By
Professor Stanley J. Czyzak
Professor Geoffrey Keller
Professor Robert F. Wing
Department of Astronomy ACKNOWLEDGMENTS
My deepest gratitude goes to my adviser, Professor Robert F. Wing, for his encouragement and guidance during the course of this research project. His knowledge, insight, enthusiasm, and patience were indispensable in every phase of this work. If I am ever put in the role of advising graduate students, I only hope I can perform a small fraction as well as he has. His influence x^ill be appreciated long after this manuscript has gathered dust.
I am particularly grateful to Professor K. Narahari Rao for his assistance and encouragement during my many years as a graduate student.
The many beneficial ideas contributed throughout the pursuit of this work are greatly appreciated. His continued financial support has helped to sustain me during these lean times.
I am indebted to Dr. Sergio Ghersetti for making available the facilities of the Institute of Organic Chemistry in Venice, Italy. The hospitality extended to the author during his two visits to Venice is greatly appreciated.
Special thanks to Dr. Agostino Baldacci who introduced me to the mysteries of acetylene. It has been a pleasure to work with him both at The Ohio State University Infrared Molecular Spectroscopy Laboratory and in Venice, Italy. Without his advice and assistance, the analysis of acetylene reported in this work would not have been possible.
I would like to thank Drs. John H. Shaw and Robert J. Nordstrom of the Ohio State University for guidance to the literature of the atmospheric sciences.
I would also like to express my sincerest gratitude to the following people, places, and things for their contributions to this experiment and/or my life: Drs. S. Ridgway, D. Hall, and P. Connes
(for FTS data), Dr. C. Sneden (for MOOG), Kitt Peak National Observato ry (for the observing time), AUDREY (the rather cold and sometimes temperamental InSb detector of KPNO), Dr. R. Joyce (AUDREY'S father),
Dr. S. Giorgianni (whose wine cellar is one of the great landmarks of Italy), Dr. Z. Gastone (useful discussions), and Y. Gardner and
R. Bowman (great friends and neighbors).
Finally, I would like to thank my parents who have always encour aged me to do my best, offered understanding and support in all my decisions, and, above all, given me their love. VITA
December 5, 1950 . . . Born - Allentown, Pennsylvania
1972 ...... B.S. in Physics, The Pennsylvania State University, University Park, Pennsylvania
1972-1975...... Research Associate, The Ohio State University Radio Astronomy Observatory, Department of Electrical Engineering, The Ohio State University, Columbus, Ohio
1975 ...... M.Sc. in Astronomy, The Ohio State University, Columbus, Ohio
1975-1978...... Teaching Associate, Department of Astron omy, The Ohio State University, Columbus, Ohio
1978-197 9 ...... Teaching Associate, College of Mathemati cal and Physical Sciences, The Ohio State University, Columbus, Ohio
1979-198 0...... Research Associate, The Ohio State University Infrared Molecular Spectroscopy Laboratory, Department of Physics, The Ohio State University, Columbus, Ohio
PUBLICATIONS
"Ohio Survey VII", with R.S. Dixon, M.R. Gearhart, and J.D. Kraus, Astronomical Journal, 79, 1129 (1974).
"The Ohio Radio Sky Survey: Supplement 2", M.Sc. thesis, The Ohio State University, Columbus, Ohio (1975).
"Ohio Survey Supplement 2", with R.S. Dixon and J.D. Kraus, Astronomical Journal, 80, 759 (1975).
"Observations of First-Overtone Silicon Monoxide Bands in Cool Stars", with R.F. Wing and R.R. Joyce, in Symposium on Recent Results in Infrared Astrophysics, ed. P. Dyal, NASA TM-X-73, 190, 23 (1977). iv "Observations of First-Overtone Silicon Monoxide Bands in Cool Stars", with R.F. Wing and R.R. Joyce, in Symposium on Recent Results in Infrared Astrophysics, ed. P. Dyal, NASA TM-X-73, 190, 26 (1977).
"Scans of the 4-p SiO Bands in Late-Type Stars", with R.F. Wing, Bulletin American Astronomical Society, 10, 408 (1978).
"Atmospheric Extinction and Photometric Reductions near Four Microns", Bulletin American Astronomical Society, 10, 408 (1978)
"A Comprehensive Analysis of the Errors Affecting the Measurement of Intensities in Infrared Spectra", with D.W. Chen, K. Narahari Rao, W.C. Braun, and B. Fridovich, Thirty-third Symposium on Molecular Spectroscopy, Columbus, Ohio (1978).
"Strengths of 13C 150.? and 12C 1E,0?_ Lines at 4.3-4,5 pm", with W.C. Braun, B. Fridovich, G.R. Smith, E.E. Champion, D.W. Chen, and K. Narahari Rao, Thirty-third Symposium on Molecular Spectroscopy, Columbus, Ohio (1978).
"Aspects of Line Strengths and Half Widths for some the the V2 band lines of 12C 150 2 ", with V.M. Devi, P. Das, IC. Narahari Rao, and B. Fridovich, Thirty-fourth Symposium on Molecular Spectroscopy, Columbus, Ohio (1979).
"Acetylene Spectra Observed in N-type Stars: A Laboratory Study", with K. Narahari Rao, A. Baldacci, and S. Giorgianni, Thirty-fourth Sympo- ium on Molecular Spectroscopy, Columbus, Ohio (1979).
"Measurements of Atmospheric Extinction near 4 pm", with R.F. W.ng, Thirty-fourth Symposium on Molecular Spectroscopy, Columbus, Ohio (1979).
"Atmospheric Extinction in the 4 pm Region", with R.F. Wing, Astronomical Journal, 84, 1235 (1979).
"Strengths of 13C 1502 Lines at 4.3 pm", with A. Baldacci and K. Narahari Rao, Journal of Molecular Spectroscopy, in press.
v TABLE OF CONTENTS
Page ACKNOWLEDGMENTS ...... ii
VITA ...... iv
LIST OF T A B L E S ...... viii
LIST OF F I G U R E S ...... xiv
Chapter
I. INTRODUCTION ...... 1
1. General Comments ...... 1 2. Overview of the Program...... 9
II. SCANNER OBSERVING PROGRAM...... 14
1. Introduction...... 14 2. Instrumentation and Observing Procedure...... 17 3. Selection of Stars ...... 19 4. Data Reduction ...... 28
III. MEASUREMENTS OF ATMOSPHERIC EXTINCTION IN THE 4 ym REGION ...... 34
IV. OBSERVATIONS OF THE FIRST-OVERTONE SiO BANDS NEAR 4 ym . . 41
1. Introduction...... 41 2. Description of the Spectral Region ...... 43 3. Observations and Reduction Procedure ...... 49 4. Derived Quantities...... 52 5. Normal Oxygen-rich Giants and Supergiants...... 59 6 . Observations of Peculiar Supergiants ...... 65 7. Observations of Mira Variables...... 72 8 . Computation of Synthetic 4 ym Spectra...... 82 9. Comparison between Observed and Synthetic Spectra. . . 92
V. INTERPRETATION OF INFRARED COLORS...... 98
1. Introduction...... 98 2. Description of the Bandpasses...... 102
vi TABLE OF CONTENTS (CONTINUED)
Page 3. Observational D a t a ...... 107 4. Computation of Synthetic Colors...... 131 5. Comparison between Observed and Synthetic Color Temperatures for Giant and Bright Giant Stars...... 142
VI. LABORATORY STUDIES OF THE INFRARED SPECTRUM OF ACETYLENE . 158
1. Introduction...... 158 2. Theory of Vibration-Rotation Spectra of Linear Molecules...... 159 3. Measurements of Line Intensities of Linear Molecules . 165 4. Experimental Details ...... 176 5. Partition Function of 12C2H 2 ...... 185 6 . Analysis of the Spectrum at 3 p m ...... 188 7. Results of the 3 ym Intensity A n a l y s i s ...... 243 8 . Intensities of the Vi + V 51 and V 2 + V 51 Combination Bands and the Acetylene Column Density in IRC +10216 . 267
VII. CONCLUDING REMARKS ...... 275
APPENDIXES
A. Atlas of 4 ym Scans...... 278
B. Acetylene Line Positions in the 3 ym Region...... 294
LIST OF REFERENCES...... 315
vii LIST OF TABLES
Table Page
1. 17-point Scanner Program ...... 16
2. Program Stars...... 21
3. Vega Colors Computed with ATLAS...... 31
4. Comparison of Model Colors ...... 31
5. Summary of Observational Data...... 33
6 . Model Atmosphere Parameters...... 37
7. 4 ym Scanner Results for Non-Miras ...... 55
8 . Mean Relation between W(SiO) and MK Spectral Type for Giant and Bright Giant Stars ...... 61
9. Blackbody Indices in the 4 ym R e g i o n ...... 71
10. 4 ym Scanner Results for Miras ...... 78 o 11. Synthetic SiO Equivalent Widths (A)...... 93
12. Comparison of 2.1 ym Bandpass Depressions and 8-color CN I n d i c e s ...... 106
13. Narrow-band Magnitudes and Color Temperatures for Non-Miras...... 110
14. Error in Temperature Resulting from a 0.02 mag grror in the Color Index taken with respect to 10395 A . . . . 127
15. Effect of Reddening on Color Temperatures...... 129
16. Synthetic Colors and Blackbody Temperatures...... 133
17. Relations between Color, Color Temperature, Spectral Type, and Effective Temperature for Giant and Bright Giant Stars...... 147
viii LIST OF TABLES (CONTINUED)
Table Page
18. Classification of Vibrational States of Linear Molecules . 160
19. Infrared Selection Rules for Linear Molecules...... 164
20. Nuclear Spin Statistical Weights for Acetylene Isotopes of Point Group D ...... 164 “h 21. Experimental Details in Recording Acetylene Spectra. . . . 177
22. Experimental Conditions for 3 ym ^2^2 ^os-*-t:*-on Spectra • • 178
23. Ro-vibrational Constants (cm--*') and Statistical Weights for Lower Levels of 12(^2**2......
24. 12("2^2 Fartition Function...... 187
25. 12(^2^2 FartFtion Function Polynomial Coefficients...... 189
26. Calculated Unperturbed Energies for Several Diads and Triads of 12C2H 2 in Fermi Resonance (cm--*-)...... 193
-1 i ? 27. Molecular Constants (cm ) of i,iC„H Derived from Bands at 3 ym...... 194
28. Molecular Constants (cm ■*) of *-2C 13CH2 Derived from Bands at 3 ym...... 196
29. Observed and Calculated Wavenumbers (vac.cm--*) of the 0010°00-000000° Band of 12C 13CH2 ...... 198
30. Observed and Calculated Wavenumbers (vac.cm ^) of the 10011 0°e-0000°l1e Band of 12C2U2 ...... 199
31. Observed and Calculated Wavenumbers (vac.cm ^) of the 100110°f-0000°l1f Band of 12C2H 2 ...... 200
32. Observed and Calculated Wavenumbers (vac.cm ^) of the
0010000-000000° Band of 12C2H2 ...... 201
ix LIST OF TABLES (CONTINUED)
Table Page
33. Observed and Calculated Wavenumbers (vac.cm ) of the 001110°e-000110°e Band of 12C2H2 ...... 202
34. Observed and Calculated Wavenumbers (vac.cm of the 0011100f-000110°f Band of 12C2H2 ...... 203
35. Observed and Calculated Wavenumbers (vac.cm of the 0010°l1e-0000°l1e Band of 12C2H2 ...... 204
36. Observed and Calculated Wavenumbers (vac.cm of the 0010°l1f-0000°l1f Band of 12C2H2 ...... 205
37. Observed and Calculated Wavenumbers (vac.cm of the 010(ll)°+-000000° Band of 12C2H2 ...... 206
38. Observed and Calculated Wavenumbers (vac.cm of the 010(21)1e(TI)-000110°e Band of 12C2H2...... 207
39. Observed and Calculated Wavenumbers (vac.cm 2) of the 010(21)1f (II)-000110°f Band of 12C2H2 ...... 208
40. Observed and Calculated Wavenumbers (vac.cm 2) of the 010(12)1e(II)-0000°l1e Band of 12C2H2 ...... 209
41. Observed and Calculated Wavenumbers (vac.cm of the 010(12)1f(II)-0000°l1f Band of 12C2H9 ...... 210
42. Observed and Calculated Wavenumbers (vac.cm of the 0012°00-0002°00 Band of 12C2H2 ...... 211
43. Observed and Calculated Wavenumbers (vac.cm of the 001220°e-000220°e Band of 12C2H2 ...... 212
44. Observed and Calculated Wavenumbers (vac.cm of the 001220°f-000220°f Band of 12C2H9 ...... 213
X LIST OF TABLES (CONTINUED)
Table Page
45. Observed and Calculated Wavenumbers (vac.cm of the 001(11)°+-000(11)°+ Band of 12C2H2 ...... 214
46. Observed and Calculated Wavenumbers (vac.cm 2) of the 001(11)°_-000(11)°_ Band of 12C2H2 ...... 215
47. Observed and Calculated Wavenumbers (vac.cm of the 001(ll)2e-000(ll)2e Band of 12C2H? ...... 216
48. Observed and Calculated Wavenumbers (vac.cm 2) of the 001(ll)2f-000(ll)2f Band of 12C2H2 ...... 217
49. Observed and Calculated Wavenumbers (vac.cm 2) of the
0010°20-000002° Band of 12C2B2'’ ■•••••••••••• 218
50. Observed and Calculated Wavenumbers (vac.cm of the 0010°22e-0000°22e Band of 12C2H 2 ...... 219
51. Observed and Calculated Wavenumbers (vac.cm of the 0010°22 f-0000°22f Band of 12C9H2 ...... 220
52. Observed and Calculated Wavenumbers (vac.;cm of the 010(31)°+-0002°0° Band of 12C2H2 ...... 221
53. Observed and Calculated Wavenumbers (vac.cm of the 010(31)2e(II)-000220°e Band of 12C2H2 ...... 222
54. Observed and Calculated Wavenumbers (vac.cm of the 010(31)2f(II)-000220°f Band of 12C2H2 ...... 223
55. Observed and Calculated Wavenumbers (vac.cm 2‘) of the 010(22)°_-000(11)°- Band of 12C2H2 ...... 224
56. Observed and Calculated Wavenumbers (vac.cm of the 010(22)2e(II)-000(ll)2e Band of 12C2H2 ...... 225
xi LIST OF TABLES (CONTINUED)
Table Page
57. Observed and Calculated Wavenumbers (vac.cm of the 010(22)2f (II)-000(ll)2f Band of 12C?H2 ...... 226
58. Observed and Calculated Wavenumbers (vac.cm of the 010(13)°+-0000°2° Band of 12C2H2 ...... 227
59. Observed and Calculated Wavenumbers (vac.cm '^) of the 010(13)2e(II)-0000°22e Band of 12C2H2 ...... 228
60. Observed and Calculated Wavenumbers (vac.cm of the 010(13)2f (II)-0000°22f Band of 12C2H2 ...... 229
61. Observed and Calculated Wavenumbers (vac.cm 2) of the 0110000-010000° Band of 12C2H2 ...... 230
62. Observed and Calculated Wavenumbers (vac.cm of the 0011100e-000110°e Band of 12C 13CK2 ...... 231
63. Observed and Calculated Wavenumbers (vac.cm of the
001110°f-000110°f Band of 12C 13CH2 ...... 232
64. Observed and Calcualted Wavenumbers (vac.cm of the 0010°l1e-0000°l1e Band of 12C 13C1I2...... 233
65. Observed and Calculated Wavenumbers (vac.cm of the 00100l1f-0000°l1f Band of 12C 13CH2 ...... 234
66. Observed and Calculated Wavenumbers (vac.cm of the 010(ll)°+-0000°0° Band of 12C 13CH2 ...... 235
67. Observed and Calculated Wavenumbers (vac.cm 2) of the 1000000-000000° Band of 12C 13CHr ...... 236
68. Some Vibrational Term Values (cm of 237
xxi LIST OF TABLES (CONTINUED)
Table Page
69. Ground State Combination Differences for 12C 13CH2 . . . . 239
70. Observed Wavenumbers (vac.cm in the P Branch of the 100(11)2+-0000°2 ° Band of 12C2H2 ...... 244
-2 -1 71. Observed and Calculated Line Intensities (cm atm at 300 K) in the 0010°0°-0000000 Band of 12C2H2 ...... 246
-2 -I 72. Observed and Calculated Line Intensities (cm atm at 300 K) in the 010(11)2+-0000°0° Band of 12C2H2 ..... 247
-2 -1 73. Observed and Calculated Line Intensities (cm atm at 300 K) in the 001110°-0001100 Band of 12C2D-2 ...... 248
74. Observed and Calculated Line Intensities (cm —‘-atm 9 — ] ' at 300 K) in the 0010°11-0000°11 Band of 12C2H2 ...... 250
, -2 -1 75. Observed and Calculated Line Intensities (cm atm at 300 K) in the 010(21)1 (II)-000110° Band of 12C2H2 . . . . 252
76. Observed and Calculated Line Intensities (cm — 9 zatm — 1 at 300 K) in the 0 1 0 U 2 )1 (ID-OOOO0!1 Band of 12C2H2 . . . . 254
77. Observed and Calculated Line Intensities (cm — 9 ^atm — 1 at 300 K) in the 0010°00-0000°00 Band of 12C 13CH2 ...... 256
78. Summary of Acetylene Intensity Parameters Measured at 3 y m ...... 265
79. Comparison of 3 ym Integrated Intensity Values for Acetylene...... 266
-2 -1 80. Calculated Line Intensities (cm atm at 300 K) . . . . 270
xiii LIST OF FIGURES
Figure Page
1 . Comparison of observed and calculated extinction coefficients. Dots are the values measured at Kitt Peak on 1977 October 28 from observations of 12 standard stars. The smoothed curves show the calculated extinction coefficients for pressure- induced absorption by , far-wing absorption by CO2 , discrete line absorption by N90 , and continuous absorption by H 90. The level of the contribution by aerosol, wich is nearly constant throughout the spectral region, is indicated by the line segment in the lower right. The sum of the five components is also shown. This diagram has been taken from Wing and Rinsland ( 1 9 7 9 ) ...... 38
2 . Comparison of an observed 4 ym spectrum of atmospheric transmittance with calculated monochromatic trans- mittances at 10 cm-1 wavenumber intervals. The observed spectrum has been derived from an observation of the carbon star IRC+10216 on 21 October 1977 at Kitt Peak with a resolution of 0.05 cm 1 and a time averaged air mass of 1.085. The observed and calculated transmittances (solid circles) have been normalized so as to agree at 2500 cm-1 (4 ym). Con tinuous absorption by the molecules CO2 , and H2O has been included in the calculation of the synthetic transmittances also with aerosol extinction. The Vi + 2v2 band of N2O (center=2462.0 cm-1) is prominent in the observed spectrum...... 40
Kitt Peak Fourier transform spectrum of a Ori in the spectral interval 2442 to 2510 cm-1. The upper (reference) spectrum is of IRC+10216 which is feature less in this spectral interval except for telluric lines. The interference pattern present in the ref erence and stellar (middle) spectra is caused by a blocking filter. The lower spectrum is the ratio of the upper two and shows stellar features only. The locations of the R branch (2,0), (3,1), and (4,2) band- heads of 28SiO are labeled...... 46
xiv LIST OF FIGURES (CONTINUED)
Figure Page
4. Kitt Peak Fourier transform spectrum of a Ori in the spectral interval 2376 to 2445 cm-1. The format is the same as Fig. 3. The (5,3) and (6,4) o o bandheads of SiO are identified as well as the region affected by high J lines of the atmospheric V 3 band of CO2 . Beyond 2388 cm-1 the atmosphere is completely opaque...... 43
5. Smoothed 4 ym transformation coefficients ob tained on 28 Oct 77 (upper), 26 Oct 77 (middle) and 8 Nov 77 (lower) plotted vs. wavelength in air microns. The transformation coefficients are expressed on a magnitude scale per unit wavelength and have been smoothed using a Gaussian of half-width equal to the resolution (88 8 )...... 53
6. The relation between W(SiO) and MK spectral type for K and M stars. The peculiar supergiants discussed in Section 4.6 and Mira variables have been excluded. Luminosity class II and III stars are shown as solid circles, lab and lb supergiants as open circles, la and Ia-Iab supergiants as solid triangles, and MS stars as plus (+) symbols. The solid line represents the mean relation for luminosity class II and III stars...... 60
Scanner observations of 8 Gem (K0 Illb), ot Tau (K5 III), and 6 Oph (MO.5 III). The MK spectral types are indicated below the star name as well as the calculated I(104)-L(400) blackbody temperature. The wavelength scale is in air microns. The fluxes are on a magnitude scale per unit wavelength subject to arbitrary normalization. The bandpass (88 8 ), an 0.1 mag flux interval, and the positions of the OH and SiO features are shown below. Each scan is accompanied by a blackbody curve (solid line) of the temperature corresponding to the I(104)-L(400) color. The wavelength interval used to define the L(400) magnitude and to set the height of the blackbody curve is shown above the spectrum of a Tau...... 63 xv LIST OF FIGURES (CONTINUED)
Figure Page
8 . Scanner observations of (3 Peg (M2.5 II-III) , XY Lyr (M4-M5 II), and RX Boo (M8 :e) are shown on the same format as Fig. 7 ...... 64
9. Scanner observations of the M supergiants W Cep (M2 Iaep), 119 CE Tau (M2 Iab-Ib), and RW Cyg (M3-M4 Ia-Iab) are shown on the same format as Fig. 7...... 66
10. Scanner observations of the very luminous supergiants S Per (M4e la) and RW Cep (K0 O-Ia) are shown on the same format as Fig. 7. SiO emission may be present at the location of the SiO (2,0) and (3,1) bands...... 67
11. Scanner observations of the peculiar M supergiants NML Cyg, VX Sgr, and VY CMa are shown on the same format as Fig. 7 ...... 68
12. Scanner observations of the Mira variables R And (phase 0.77), o Get (phase 0.88), and IK Tau (phase 0.5) are shown on the same format as Fig. 7 ...... 73
13. Scanner observations of the Mira variables R Aur (phase 0.79), U Ori (phase 0.16), R Cnc (phase 0.87), and W Aql (phase 0.20) are shown on the same format as Fig. 7 ...... 74
14. Scanner observations of the Mira variables R Cyg and X Cyg are shown on the same format as Fig. 7. Upper observation was obtained at phase 0.34, middle at 0.31, and lower at 0 . 1 7 ...... 75
15. Scanner observations of the Mira variables x Cyg (phase 0.17) and R Cas (phase 0.68 and 0.63) are shown on the same format as Fig. 7...... 76
xv i LIST OF FIGURES (CONTINUED)
Figure Fage
16. A portion of a synthetic spectrum generated with MOOG. The model atmosphere used was on opacity-sampling log g = 1.0, T = 3200 K model. Solar elemental abundances, terrestria? isotope ratios, and a microturbulent velocity of 2 km/s were assumed in the calculations. The positions of atomic, SiO, OH and CN lines are indicated above and below. Molecular lines of the terrestrially most abundant isotope are indicated with arrows while short lines mark features from less abundant isotopes. The 20SiO bandhead at 2467.2 cm-1 is weakly visible in the computed spectrum...... gg
17. Continuation of the synthetic spectrum shown in the previous figure. The 28SiO (3,1) bandhead is at 2472.9 cm- 1 . The 29SiO bandhead at 2481.7 cm-1 is weakly visible in the computed spectrum ...... 37
18. Continuation of the synthetic spectrum shown in the previous figure. Most of the strong lines are due to the (2,0) band of 28SiO...... 88
19. Continuation of the synthetic spectrum shown in the previous figure. The (2,0) 28SiO bandhead occurs at 2497.2 cm-1. The region shortward of the (2,0) head is nearly free of line blanketing...... 89
20. Continuation of the synthetic spectrum shown in the previous figure. Most of the strong lines are due to OH. 90
21. Synthetic 4 pm scanner spectra are shown on the same format as Fig. 7. All spectra have been computed with solar elemental abundances, terrestrial silicon, oxygen, and carbon isotope ratios, and a 2 km/s microturbulent velocity. The effective temperature and surface gravities of the models are indicated to the left of the spectra. The uppermost model is from the grid of Bell _et _al. (1976a) . All other models are from Johnson, Bernat, and Krupp (1980) ...... 91
xvii LIST OF FIGURES (CONTINUED)
Figure Page
22. Plot of W(SiO) in Angstroms vs. effective temperature for solar-composition opacity-sampling models with different surface gravities and a fixed microturbulent velocity of 2 km/s. The positions of models with log g = 0 .0 , 1 .0 , and 2.0 are indicated with "x", "o", and "+" symbols, respectively. Sets of models with the same surface gravities have been connected with dashed lines. The solid line is the mean giant and bright giant relation taken from Table 8 . The effective temperature scale of Ridgway ejt al. (1980) has been used to convert from spectral type to effective temperature...... 95
23. Plot of W(SiO) in Angstroms vs. effective temperature for solar-composition opacity-sampling models of log g = 1.0 showing the effect of microturbulence. Open rectangles indicate the results obtained with a micro turbulent velocity of 2 km/s while solid rectangles represent values computed with 4 km/s. Sets of models with the same microturbulent velocity have been connected with dashed lines. The solid line is the mean giant and bright giant relation taken from Figure 22...... 96
24. Kitt Peak FTS spectrum of e Tau in the region of 2.101 pm bandpass of the infrared colors program. The top spectrum is a solar spectrum, the middle spectrum is the stellar spectrum, and the lower spectrum is the ratio of the two. Line positions are from the Hall (1970) a t l a s ...... 104
25. Comparison of an observed spectrum of a Ori (solid line) with a synthetic spectrum (+ symbols) in the region of the 2.101 ym bandpass of the infrared colors program. The region scanned was from approximately 4751 cm-1 (2.104 ym) to 4765 cm-1 (2.098 ym). Telluric absorption features are indcated below the spectrum. The synthetic spectrum was computed with CN lines only, ...... 105
xviii LIST OF FIGURES (CONTINUED)
Figure Page
26. Kitt Peak FTS spectrum of e Tau in the region of the 2.285 ym bandpass of the infrared colors program. The format is the same as in Fig. 24. The *2C0 (2,0) bandhead can be seen at 4360 cm- * ...... 108
27. Comparison between the continuous energy distribution of the Bell et_ _al. (1976a) solar composition T = 3750 K and log g = 2.25 model atmosphere (dotsf and a 3750 K blackbody energy distribution. The fluxes are on a magnitude scale per unit wavelength, normalized to the 1.0395 ym reference wavelength. Arrows mark the wavelengths of the infrared colors program and the continuum points of the Wing 8-color system. The peak in the continuum caused by the H- opacity minimum is clearly visible at 1.65 y m ...... 138
28. Absorption coefficient of H- (cm-* per neutral hydrogen atom) plotted against wavelength for a temperature of 3835 K and an electron pressure of 6.71x10“* dynes/cm2 . The solid line is the total H- absorption coefficient; the dashed line indicates the free-free component only. The conditions correspond to a level in the Bell et_ al. (1976a) Te = 3750 K and log g = 2.25 solar composition model close to continuum optical depth unity at 1.0395 y m ...... 139
29. The relation between T (104-210) and T (104-400). Stars of luminosity classes 5l and III are sfiown as + symbols and dots, respectively. Large open symbols represent models from the grid of Bell_et_al. (1976a), large solid symbols models computed by Johnson, Bernat, and Krupp (1980). All models were computed with solar abundances. Solid lines connect models with the same surface gravity. The dashed line is defined by the relation T (104-210) = T (104-400). The arrow indicates the approximate slope ofcthe reddening line...... 143
xix LIST OF FIGURES (CONTINUED)
Figure Page
30. The relation between T (104-400) and T (8c) for models and stars of luminosity class II and I?I, shown in the same format as Fig. 29. The dashed line is T (104-400) = T c(8c)...... 144
31. T (104-129) plotted against effective temperature. T^e solid line is defined by the luminosity class III relations in Table 17. The corresponding spectral types (+ symbols) are indicated. Opacity-sampling solar-composition model atmosphere results (Johnson, Bernat, and Krupp 1980) are indicated by solid symbols; open symbols mark values obtained with the solar-composition models of Bell _et _al. (1976a) . The dashed line defines the locus of points where the color temperature is equal to the effective temper- acure. . . . 148
32. T (104-210) vs . effective temperature is shown in the same format as Fig. 31. . 149
33. T (104-228) vs . effective temperature is shown in the same format as Fig. 31. . 150
34. T c (104-400) vs . effective temperature is shown in the same format as Fig. 31. . 151
35. Eight-color near-infrared color temperature vs. effective temperature is shown in the same format as Fig. 31...... 152
36. Correction for experimental loss. The singly cross- hatched region indicates the area under the line profile used to measure the equivalent width. Be cause of the residual line absorption near the ends of the integration interval, the 100% transmittance level will be underestimated. The additional area (doubly cross-hatched region) must be included to determine the true equivalent width...... 172
xx LIST OF FIGURES (CONTINUED)
Figure Page
37. Curves of growth. The data were taken from the tables of Jansson and Korb (1968)...... 175
38. Comparison of pressure gauge readings obtained with the NOAA/NESS and the Ohio State Baratrons. The data shown here were taken with the Ohio State 0-100 torr head and the NOAA/NESS 0-1 torr head. The percentage difference between the readings of the two gauges has been plotted vs. the pressure in pm Hg ...... 181
39. Profile of an absorption line obtained with the Ohio State University 10-m focal length Czerny-Turner vacuum grating spectrometer. The data were digitized with a Bendix Datagrid digitizer. Arrows mark the limits of integration used to determine the equiva lent width...... 184
40. Acetylene spectrum between 3290.1 and 3291.3 cm recorded at room temperature with a pressure of 3.05 torr and a path length of 96.95 cm. The stronger features are identified. The effect of nuclear spin statistics can be seen for rotational levels split by £-type doubling. The intensity ratio is 3:1 for lines of 12C2H 2 - ...... 190
41. Comparison between acetylene spectra recorded at 12.0 mm Hg pressure and 160 C (upper) and at 3.5 mm Hg pressure and room temperature (lower) in the region 3207 to 3211 cm- 1 ...... 192
42. Square of2the vibration-rotation matrix element I Rv 5 £' j ^ Pl°ttec^ against the integer m in the 0010°0°- 0000°0° band of 12C2H 2 . Error bars represent the standard deviation of the measure ments of an individual line. The horizontal . T a 1 t * I o dashed line is the mean value of Rv ~ 4 ...... 258 1 v £ J 1
xx i LIST OF FIGURES (CONTINUED)
Figure Page
43. Square of the vibration-rotation matrix element |RV n ^ 1^ vs< m in tbe 010(11)° -0000°0° band of 12C H . v £ J z z Error bars represent the standard deviation of the measurements of an individual line. The horizontal v » £»j? 2 dashed line is the mean value of |Rv | ...... 259
44. Square of the vibration-rotation matrix element IRv'£'J' I 2 VS’ m in the 010(21)1(II)-000ll°0 band of ^^C2^2' Error bars represent the standard deviation of the measurements for an individual line. The horizontal dashed line is the calculated value of ,v' £' J ’ 12 , ^ i^v' £ ,2 |R I obtained with the values of [Rr . [ and A "V A; J "V ~ listed in Table 78 ...... 260
45. Square of the vibration-rotation matrix element
\T? Z j '|2 vs. m in the 010(12)1 (II)-00000!1 band of 1 ? 2b2 ' Error bars represent the standard deviation of the measurements for an individual line. The horizontal dashed line is the calculated value of I _v ' £' J' 12 , . , . , , . £ ij't' 12 , . R „ , obtained with the values of R . and A 1 v £ J 1 ' v £ listed in Table 78 ...... 261
46. Square of the vibration-rotation matrix element |RV ln ? I2 vs. m in the 001110°-0001100 band of v £ J 1 C2b2 * Error bars represent the standard deviation of the measurements for an individual line. The horizontal dashed line is the calculated value of l^v'Ji'J’ ^ , . , .. , . |_v^ £ ^ 12 R . T obtained with the values of R . and A 1 v £ J 1 1 v £ 1 listed in Table 78 ...... 262
xxii LIST OF FIGURES (CONTINUED)
Figure Page
47. Square of the vibration-rotation matrix element i v ' f' T' 12 0 1 0 1 R I vs. m in the 0010 1 -0000 1 band of ' v £ J 1^C2H2 « Error bars represent the standard deviation of the measurements for an individual line. The horizontal dashed line is the calculated value of |RV ^ ^ obtained with the values of |RV „ and A 1 v £ J 1 1 v £ 1 listed in Table 78...... 263
48. Spectrum of the vj + V 5I band of 12C2H 2 near 4091 cm- 1 . The solid line is the laboratory spectrum measured with a pressure of 2.00 torr and a path length of 96.95 cm. The synthetic spectrum (+ symbols) has been con volved with a 0.030 cm-1 gaussian instrumental profile. Line positions and alternation of intensities are indicated below...... 271
49. Observed and synthetic spectra of the V 2 + V 51 band of 12C2H 2 near 2701 cm-1 are shown in the same format as Fig, 48. The laboratory spectrum was measured at a pressure of 5.00 torr and a path length of 96.95 cm. . . . 272
50. Scanner observations of a Lyr, a Ari, and S Oph are shown on the same format as Fig. 7 ...... 279
51. Scanner observations of a Boo, e Peg, and 6 And are shown on the same format as Fig. 7 ...... 280
52. Scanner observations of y Aql, p Per, and 8 Cnc are shown on the same format as Fig. 7 ...... 281
53. Scanner observations of £ Aur, a Lyn, andT 1 Aur are shown on the same format as Fig. 7 ...... 282
54. Scanner observations of u Gem, HR 1009, and y Eri are shown on the same format as Fig. 7 ...... 283
xxiii LIST OF FIGURES (CONTINUED)
Figure Page
55. Scanner observations of HR 8726, u Aur, and a Cet are shown on the same format as Fig. 7 ...... 284
56. Scanner observations of a Ori, tt Leo, and HR 1155 are shown on the same format as Fig. 7...... 285
57. Scanner observations of KQ Pup, 119 CE Tau, and y Cep are shorn on the same format as Fig. 7...... 286
58. Scanner observations of AD Per, p Per, and y Gem are shown on the same format as Fig. 7...... 287
59. Scanner observations of p Gem, tt Aur, and o 1 Ori are shown on the same format as Fig. 7...... 288
60. Scanner observations of SU Per, 51 BQ Gem, and HR 8621 are shown on the same format as Fig. 7...... 289
61. Scanner observations of p Per, XY Lyr, and RS Per are shown on the same format as Fig. 7...... 290
62. Scanner observations of 71 Peg, R Lyr, and HD 11961 are shown on the same format as Fig. 7...... 291
63. Scanner observations of a Her, EU Del, and 45 RZ Ari are shown on the same format as Fig. 7 ...... 292
64. Scanner observations of HD 207076 and HR 1105 are shown on the same format as Fig. 7...... 293
xx iv CHAPTER I
INTRODUCTION
Section 1.1 - General Comments
The multitude of phenomena present in the atmospheres of red giant and supergiant stars make them fascinating and particularly important sources of astrophysical information. If we adopt the most general definition of a stellar atmosphere as the region that connects the core of a star to the interstellar medium, red giant atmospheres reveal diverse processes such as variability, grain formation, shock waves, and mass loss which are of interest to theoreticians and observers alike.
In recent years the study of red giant stars has been advanced to a large extent by studies in the infrared spectral region. Although the observed IR spectra of many cool stars are complex, the infrared reveals important processes inaccessible by visual spectroscopy.
The purpose of this section is to discuss the difficulties connected with the interpretation of cool star spectra and to point out the role that IR studies can play in promoting an understanding of cool stars.
Many of the valuable contributions that have been made by IR investiga tors will be mentioned. An exhaustive review is not intended here since excellent review articles have appeared in the literature (Spinrad and
Wing, 1969; Merrill and Ridgway, 1979). Instead, since the region 1.5 to 4 ym has been investigated in this thesis , problems related to the interpretation of cool star spectra in this region will be emphasized. The formation of molecules at the low temperatures of the atmos
pheres of late-type stars has numerous effects on both observation and
interpretation. The dissociation equilibrium for most observable mole
cules is greatly affected by the carbon to oxygen abundance ratio. In
spectral appearance, stars with carbon-to-oxygen ratios less than one
are dramatically separated from stars with carbon-to-oxygen ratios
greater than unity. This effect is due to the very high dissociation
energy, 11.1 eV, of the CO molecule. If carbon is less abundant than
oxygen, all the carbon is bound in CO and the excess oxygen forms oxides
producing the "oxygen-rich" K and 15 star sequence. If carbon is more
abundant than oxygen, all the oxygen is tied up in CO and the left-over
carbon forms molecules such as CN, CH, and C2 , resulting in typical
carbon star spectra.
An important advantage of the presence of molecules is that isotope
shifts for both vibration-rotation and electronic transitions are much
larger than the shifts in atomic spectra. Frequently, these shifts are
sufficient to separate isotopic bandheads even in low resolution scans
(cf. Fay, et al. 1974). The 12C/13C ratio, which is a quantitative measure of the amount of nuclear-processed material reaching the surface
has been studied with several different approaches in the infrared.
High-resolution photoelectric scans of the red and near-infrared CN bands have been interpreted with curves of growth to derive 12C/13C
ratios in a large sample of G, K, and M type giant and supergiant stars
(Tomkin and Lambert, 1974; Tomkin, Lambert, and Luck, 1975; Dearborn,
Lambert, and Tomkin, 1975; Hinkle, Lambert, and Snell, 1976; Tomkin,
Luck, and Lambert, 1976). The observed values have been directly 3 compared to stellar evolution predictions. Although values of 12C/13C in the range 25 to 30 can be understood in terms of mixing as a star ascends the giant branch, problems remain in explaining some of the lower values observed (Dearborn, Eggleton, and Schramm, 1976; Scalo and
Miller, 1978). For fainter stars crude measurements of 12C/13C can be obtained rapidly with photoelectric scanner measurements of CN between
7820 and 9048 X (Wing, 1974).
The carbon monoxide vibration-rotation bands provide an important check on the 12C/13C ratios obtained from other molecules. Generally three sequences of CO bands are visible in the infrared spectra of cool stars. In order of decreasing strength, these are the fundamental
(Av=l) near 4.7 pm, the first-overtone (Av=2) near 2.3 pm, and the second-overtone (Av=3) near 1.6 pm. The greatest difficulty usually encountered in using the CO bands for isotope studies is the problem of severe line saturation. Carbon monoxide is fully associated in stars later than about K 3 , and very large CO column densities exist in many late type stars. The large line strengths observed in the first-over- tone region have lead to difficulty in extracting the 12C/13C ratio
(Thompson, 1973). The second overtone line oscillator strengths are two orders of magnitude weaker than the first overtone lines, and this sequence should be used when sufficient column density exists for the
13C0 lines to be observable. Spectral synthesis has been used in this region to derive the 12C/'3C ratio for a Ori (Lambert, Dearborn, and
Sneden, 1974; Gautier, jrt al., 1976) and a lower limit for 12C/13C in a Her (Thompson and Johnson, 1974) , although the results of the two a
Ori studies are contradictory. The discrepancy may be due to the assumed value of microturbulence (7 km/s by Lambert, Dearborn, and
Sneden, 1974; 2 km/s by Gautier, et_ a_l. , 1976), inadequacies in the model atmosphere structure, and/or errors in locating the continuum in the lower resolution (0.5 cm-1) spectrum of Gautier, et_ a\_. (1976). Use of curve of growth techniques has been found to give consistent results from the Av=2 and Av=3 bands of CO and CN lines near 8000 % for a Ori,
6 Peg, x Cyg, a Her, and a Boo (Hinkle, Lambert, and Snell, 1976).
Carbon isotope ratios derived for carbon stars are frequently con tradictory [compare, for example, the values of Fujita and Tsuji (1977) with the results of Climenhaga, et_ al.. (1977)], although it is encourag ing that Dominy, et a_l. (1978) obtained consistent values from CO and
CN. Other elements whose isotopes have been studied in the infrared include titanium (Lambert and Luck, 1977), silicon (Beer, Lambert, and
Sneden, 1974; Ridgway, Hall, and Carbon, 1977), and oxygen (cf. Maillard,
1974).
The quantitative measurement of molecular band strengths by means of a scanner or narrow-band filters has proved to be a very effective method of spectral classification. The most widely used and best cali brated system in use today is the 8-color system of Wing (1971). This system measures five quantities in the 0.7 to 1.1 qm region: the 1(104) magnitude, the continuum color, and the strength of TiO, V0, and CN.
This system has been applied to the classification of M supergiants
(White, 1971; White, 1972; White and Wing, 1978), carbon stars (Baumert,
1972) and M dwarfs (Wing, 1973). A modified 8-color system which measures ZrO, TiO, LaO, CN, 1(104), and continuum color has been devel oped by Piccirillo (1977) to classify and interpret S star spectra. 5
At longer wavelengths, quantitative classification is not as well
developed. Classification at wavelengths longer than 1.1 pm has been
discussed in two recent articles (Wing, 1979; Merrill and Ridgway, 1979).
Narrow-band photometry can also be used to derive atmospheric
abundances. Hartoog, Persson, and Aaronson (1977) have used intermediate
bandwidth filters to measure CO band strengths in weak G-band stars.
Their results confirm that these stars are deficient in carbon by a
large factor. The system of Piccirillo (1977), besides classifying
S-stars, has been calibrated with model atmospheres to derive 0/C abun
dance ratios.
The existence of strong blanketing by both atomic and molecular
lines creates severe difficulties in the computation of model atmo
spheres. In order to account properly for the bound-bound opacity,
literally millions of lines must be included in the. computations. The major opacity sources must be identified, accurate line lists with the
correct oscillator strengths must be assembled, and the opacity must be
accounted for properly and in a manner suitable for calculation in a
reasonable amount of computer time.
Considerable progress has been made in treating molecular line
opacities. Early model atmospheres (cf. Tsuji, 1967, 1969; Auman, 1969)
represented the opacity within a wavelength interval by a single number,
either a straight mean or a harmonic mean of the opacity. The straight mean introduces serious error in that the averaging process fills in the
low opacity windows between strong spectral lines where mujh of the
stellar flux emerges in a real stellar atmosphere. The harmonic mean,
computed from the average of the reciprocal opacities over a spectral 6 interval, is a better representation but the opacity is systematically underestimated and serious errors may result near the surface (Carbon,
1974).
Two methods are in current use which represent the opacity much more accurately. The opacity distribution function (ODF) method uses a series of numbers to approximate the distribution of the opacity within a wavelength interval. The advantages and disadvantages of this technique have been thoroughly discussed (Carbon, 1974; Van Paradijs and Vardya, 1975). An alternative and particularly flexible method called opacity sampling (OS) statistically samples the opacity at a set of points. Given a large enough grid of points, the computed model structure will approach the correct value (Peytremann, 1974; Johnson and
Krupp, 1976; Sneden, Johnson, and Krupp, 1976).
Current line lists used in the computation of model atmospheres include several million lines. Despite the large number, it is an impor tant observational task to determine if the computed models can correct ly reproduce the observed energy distributions. Accurate comparisons are required at both low and high resolution with spectroscopic and photometric techniques. Such studies should reveal if any important opacity sources have been omitted from the models. For many molecules, accurate laboratory data is needed for both model computations and spectral synthesis studies.
The infrared contains many important indicators of the CNO abun dance of late-type stars. Most of the molecules observed contain carbon, nitrogen, or oxygen; and the relatively low density of lines compared to the visible region in many stars makes the infrared potentially very useful. In oxygen-rich stars the molecules CO, CN, H 2 , OH, NH, SiO, HF,
and H20 have been identified while HCN, C2H 2 , CH, CN, CO, CS, and C2
have been detected in carbon stars. Many of the molecules seen in the
IR cannot be observed in the visible (a.g. CO, SiO), and hence the infra
red can provide unique information useful for CNO abundance studies.
In order to compute a synthetic spectrum to match a given star, the
effective temperature and surface gravity of the star must be accurately
known. For the K and M field giants, two recent studies have suggested
considerable revision of the effective temperature scale. Ridgway, et al.
(1980) have used angular diameters from lunar occultations and measured bolometric magnitudes to derive a temperature scale considerably warmer
than the one given by Johnson (1966), which has been in general use. The
revised scale is consistent with the results of Tsuji (1978a) based on a
comparison of observed and synthetic energy distributions. This agree ment suggests that (at least for the oxygen-rich giants) the effective
temperature scale may now be considered established. Although the sur
face gravities of the warmer late-type stars are sufficiently well known
to permit detailed spectrochemical studies (cf. Clegg, 1977; Lambert and
Ries, 1977), fundamental determinations of log g become extremely diffi
cult for the coolest stars owing to their vanishingly small parallaxes
and the absence of suitable binary star systems to derive stellar masses.
The astrometric measurements planned with the Hipparchus satellite and
the Space Telescope should improve the situation.
Measurements of energy distributions of celestial objects are
derived from comparisons with standard stars whose energy distributions
are known. The standard stars must be distributed throughout the sky and their flux distributions expressed on a uniform scale of absolute fluxes. Furthermore, the monochromatic flux differences between the standard stars must be accurately known if one is to use them to derive magnitudes or evaluate the stability of one's equipment.
No such data exist at wavelengths longer than 1.1 pm. The magni tudes which are available are essentially all wide-band measurements which include entire atmospheric windows. These data are of limited use for spectrophotometric reduction and in general do not have the photometric accuracy of fluxes at shorter wavelengths. The absolute fluxes of the wide-band magnitudes are not well established, and the extinction coefficients that have been measured with wide filters cannot provide the detailed knowledge of atmospheric extinction that is required for spectrophotometric calibrations.
Many additional difficulties exist in the interpretation of cool star spectra. Stratification effects, deviations from plane-parallel geometry and local thermodynamic equilibrium, micro- and macroturbulence, circumstellar shells, mass loss, and variability are just a few of the problems not completely understood. Despite what remains, considerable progress has been made recently and will no doubt continue to be made in the future. It is hoped that the results presented in this disserta tion will add to our understanding of cool stars. Section 1.2 - Overview of the Program
The purpose of this section is to discuss the objectives of this study and to describe briefly both the observing program and the methods used to interpret the data.
This investigation is primarily directed towards a study of the normal "oxygen-rich'' giant and supergiant stars of spectral types G, K, and M in the spectral region 1.2 to 4.1 pm. The infrared was selected because it is close to the energy maximum of these stars, is relatively free of line blanketing, and contains molecular bands of several of the most abundant molecules in stellar atmospheres, including CO, H 20, OH, and SiO. Meaurements of these bands are particularly useful for the determination of the elemental abundances of H, C, N, and 0, and their isotopes, and they may be helpful in the classification of extremely cool or heavily reddened stars not detectable at shorter wavelengths.
The objectives of this investigation are the following: (1) to mea sure the strengths of infrared bands of molecules containing carbon, nitrogen, or oxygen in a large sample of late-type stars to determine their suitability for classification purposes; (2 ) to study the energy distributions of late-type giants and supergiants by measuring narrow band magnitudes at a series of widely spaced continuum points throughout the infrared; (3) to compare the observed band strengths and continuum colors with the predictions of model atmospheres; and (4) to investigate the accuracy to which narrow-band photometry with a scanner can be done in the IR by making repeated measurements of a series of standard stars. 1 0
These objectives required the use of both low and high resolution
data. The Kitt Peak InSb grating spectrometer AUDREY has been used to measure molecular band strengths1 and narrow-band continuum magnitudes
in a large sample of late-type stars. This instrument offers flexi bility in the selection of wavelengths and bandwidths to be measured, moderate resolution (AA/A about 500), high speed, and good photometric accuracy. Observations were obtained during observing runs in Septem- ber-October 1976 and October-November 1977 with the Kitt Peak 1.3-m telescope.
The selection of program wavelengths requires a fairly detailed knowledge of the spectra of a series of representative stars. High- resolution Fourier transform spectrometer (FTS) spectra obtained with
the Kitt Peak 4-m telescope (Ridgwav and Hall 1978) and the M t . Palo- mar 5-m telescope (Connes and Michel 1974) were used, in combination with published observations, to select the program bandpasses. In addition, the FTS data have been used to study features requiring higher resolution than could be obtained with the scanner.
The observations have been compared to synthetic fluxes computed with model atmospheres and the synthetic spectrum program M00G (Sneden,
1974). The recently published grids of Bell, et_ aJ. (1976a) and John son, Bernat, and Krupp (1980) have been adopted and are believed to be the most realistic models currently available.
MOOG has been described in detail in the Ph.D. dissertation of
Sneden (1974) so that the procedure used to calculate the synthetic spectra will only be discussed briefly. The basic assumptions of MOOG are local thermodynamic equilibrium, plane-parallel geometry, and the 1 1
formation of lines in pure absorption. The model atmosphere parameters
(optical depth, temperature, gas pressure, and electron density) and
microturbulent velocity must be provided as input to MOOG along with
the relative abundances of the elements. With these parameters the
continuous opacity and molecular dissociation equilibrium can be calcu
lated at each layer in the atmosphere. A line list specifying wave
lengths, excitation energies, and gf values is required to evaluate the
line opacity at each depth in the atmosphere and at each wavelength in
the spectrum. From the continuum and line-plus-continuum optical depth
scale, MOOG computes the spectrum depths by integrating the second Milne
equation assuming the source function is the Planck function.
In addition to the studies of stellar spectra and energy distribu
tions, results of a laboratory analysis of the molecule C2H 2 are reported
in this dissertation. Acetylene has recently been detected in the
spectra of cool carbon stars in the 3 pm region (Ridgway, Carbon, and
Hall, 1978) and in the circumstellar spectrum of IRC +10216 (Ridgway,
_et _al. , 1976). The 3 pm depression is very strong in all cool carbon
stars and is due almost entirely to HCN and/or C2H2 . It is likely that
acetylene is an important opacity source in the upper atmosphere of many
of these stars and should therefore be included in model atmosphere cal
culations. To obtain the basic laboratory data required, the 3 pm bands
have been recorded with The Ohio State University 10-m focal length
Czerny-Turner vacuum grating spectrometer. Line identifications and
molecular constants are reported as well as measurements of the absolute
strengths of 101 lines in the seven strongest bands. The integrated
strengths of the + V 5 1 and v 2 + V 5 1 bands have also been measured and 1 2 have been used to derive a revised column density of acetylene molecules in the circumstellar shell of IRC +10216.
The results of this dissertation are presented in the following sequence. In Chapter II the scanner observing program is described in cluding the observing procedure and methods used to reduce the data.
In Chapter III are presented results of a study of atmospheric extinc tion in the 4 pm region. The extinction coefficients are the first narrow-band measurements reported in this spectral region. The observed extinction coefficients are compared to synthetic values generated with laboratory data and a model terrestrial atmosphere. Although the laboratory data were already available in the literature, they had not previously been assembled to calculate the effect of extinction on astronomical measurements in the 4 pm region and to determine the physical processes giving rise to this extinction. In Chapter IV scanner measurements of the 4 pm SiO bands are reported for 77 stars and are used to study the behavior of SiO strength with respect to spectral type and luminosity class. The SiO strengths observed in luminosity class II and III stars are compared to calculated values obtained with recently published model atmospheres. Previous studies of the SiO bands were limited to a much smaller number of stars. In
Chapter V the first narrow-band continuum color temperatures measured longward of 1 pm are reported and compared to model atmosphere pre dictions. The results of the high-resolution laboratory study of acetylene are presented in Chapter VI. The analysis at 3 pm is considerably more extensive and at higher resolution than previous studies and the observed line positions and absolute intensities 13 should be useful for quantitative studies of these bands in cool carbon star spectra. In Chapter VII the major results of this work are summarized, and a few concluding remarks are presented. CHAPTER II
SCANNER OBSERVING PROGRAM
Section 2.1 - Introduction
The Kitt Peak InSb grating spectrometer AUDREY has been used to study a sample of G, K, and M giant and supergiant stars in the 1.2 to
4.1 ym region. The observations have been reduced to yield measurements of the equivalent widths of the SiO first-overtone bands and narrow-band magnitudes at four widely spaced wavelengths nearly free of stellar blanketing.
The usefulness of narrow-band scanner measurements of cool stars in the near infrared has been amply demonstrated in the dissertation of
Wing (1967a). He used measurements at 27 carefully selected wavelengths between 0.7 and 1.1 ym to derive an infrared continuum magnitude (1(104)), a near-infrared color temperature, and band strength indices of the molecules TiO, VO, ZrO, and CN for over 300 stars. This system was later modified to be used with narrow bandpass filters by reducing the number of wavelengths to eight. The 8-color system (Wing, 1971) has been particularly useful for classifying stars of spectral types K, M, and C. Other applications have been discussed by Wing (1974).
Since narrow-band photometry of cool stars has proved to be so useful in the near infrared, measurements at longer wavelengths with the same procedure should also provide important information. The infrared beyond 1 ym is broken up by regions of very strong telluric
14 15
absorption, mostly by H 2O. Within the atmospheric windows, numerous bands of molecules containing H, C, N, and 0, and their isotopes, are observable. Measurements of these bands are of interest for CNO abund ance studies and may also be useful for classification in the IR. In addition, since there are spectral intervals which are nearly free of stellar line blocking in even very cool stars, narrow-band continuum magnitudes can be measured.
The original objective of these observations was to study the behavior of the molecular bands of CO, CN, SiO, OH, H2O, C2 , and SiO by making integrations at a relatively small number of wavelengths.
A 17-point photometric system (Rinsland, Wing, and Joyce, 1977) designed for this purpose was developed for the Kitt Peak scanner.
Unfortunately, flexure problems, described in Section 2.2, caused wave length shifts too large to be tolerated, and this program could not be carried out. Since any future system developed to study these molecules at a similar resolution will have to measure many of the same features, the wavelengths and bandpasses of the 17-point system are given in
Table 1. Measurements of these bands should prove useful for both classification work and for studies of CNO abundances.
Although measurements of spectral features cannot be made reliably with a single wavelength when the wavelength scale is uncertain, useful indices can still be derived from continuous scans over spectral fea tures. This procedure is less efficient but was necessary under the circumstances. Continuous scans have been obtained of the SiO first- overtone region, the first-overtone CO bands including the (2,0) 1 3C0 TABLE 1
17-POINT SCANNER PROGRAM
Central Central Wavelength Bandwidth Primary Wavenumber (cm-^-) in Air (ym) (cm"l) Order Feature* Contaminants
2493.7 4.0090 5.5 1 SiO (2,0) Atm. N2O 2496.0 4.0053 5.5 1 SiO (2,0) head Atm. N 2O 2502.0 3.9957 5.5 1 Continuum Atm. N 2O 4232.0 2.3623 7.9 2 ^ C O (4 >2) l3C0, Atm. H20 4263.0 2.3451 8.0 2 }3C0 (2 ,0 ) 12 C0, Atm. H 20 4354.0 2.2962 8.4 2 12 C0 (2,0) Atm. H 2O 4386.0 2.2794 8.5 2 Continuum -- 4518.5 2.2125 9.0 2 Continuum -- 4757.0 2.1016 10.0 2 Continuum -- 5647.0 1.7704 14.0 2 c2 Atm. H 2O 5713.0 1.7499 14.4 2 Continuum Atm. HoO, CO 5956.0 1.6785 10.4 3 Continuum CO 6253.7 1.5986 11.4 3 12C0 (5,2) Atm. CO2 6273.5 1.5936 11.5 3 Continuum Atomic lines, CO 6470.0 1.5452 12.4 3 Continuum CN 6501.0 1.5378 12.4 3 OH (4,2) CN 6512.0 1.5352 12.4 3 CN --
* In some bandpasses H2O will dominate in stars later than about M6 . 17 bandhead, the (5,2) CO bandhead, and the OH (A,2) R branch head. In this dissertation results of the SiO scans are reported.
For many program variables, concurrent observations on the 8-color system were obtained by R.F. Wing on a 0.4-m telescope at Kitt Peak.
These data were used to derive 1(104) magnitudes and spectral types.
Section 2.2 - Instrumentation and Observing Procedure
The infrared scanner observations were made at Kitt Peak National
Observatory with the 1.3-m telescope and a grating spectrometer (AUDREY).
The InSb photovoltaic detector was operated in the recommended zero bias setting and the liquid-nitrogen filled dewar was pumped to about 30 torr pressure to cool the system to 63 K to reduce detector Johnson noise.
Background subtraction was accomplished by square-wave modulation of the secondary mirror. For all observations the chopping frequency was
20 Hz and the chopping distance was usually set at 30 arcsec. Beam switching was used to eliminate, to first order, zero point drifts.
The entrance aperture used was quite large (18 arcsec) so that the photometric accuracy would not be limited by seeing fluctuations.
Scanning was accomplished by driving the grating with a stepping motor. The 0.5 mm exit slot employed for all measurements produced a band pass of about 88 R in first order. Observations were made in first order between 3 and 4 pm, in second order in the 2 pm region, and in third order at wavelength points shortward of 1.5 pm. A series of filters, cooled to liquid-nitrogen temperature, were used to block light from unwanted orders. For the brighter stars a series of two 18
or three integrations were taken at each wavelength with typical inte gration times of 10 seconds.
The operation of the scanner was computer-controlled. Observations were made in either a discrete wavelength or a continuous scan mode.
Continuous scans required as input a starting step position, a final step position, the separation in steps between each wavelength point,
and the number of integrations at each point. In the discrete wave length mode, the scanner performed integrations at a specified set of wavelengths, in both forward and reverse directions. Stepping motor position was calculated from the wavelength, the order, the stellar radial velocity, and two grating constants which were derived from calibration lines.
To calibrate the wavelength scale, hydrogen lines of the Paschen and Brackett series were observed in A-type stars. Unfortunately, during the first observing run in September 1976 it was discovered
that flexure in the scanner would cause uncontrollable wavelength shifts amounting to 10-20 percent of the widths of the bandpasses.
Wavelength shifts could be minimized by working in limited regions of
the sky and carefully centering the star with respect to the entrance aperture, but it was not possible to eliminate the problem. Observa tions of spectral features were therefore restricted to continuous scans, but continuum points in clean spectral regions could be observed on the discrete point program.
Although the majority of the data was obtained at night, some observations were made in the daytime. Since most of the stars 19
observed are bright visually, it was usually possible to see the stars
through the telescope. Stars fainter than about V=4 could be seen only under exceptional seeing conditions and acquisition had to be made by offsetting from bright stars and peaking up on the infrared signal of
the program star. Data acquisition was considerably slower for the invisible stars since scans had to be interrupted frequently to check
the centering. Another problem encountered in daylight observing was poor seeing. Generally, the seeing would begin to deteriorate seriously by 10 a.m. and remain poor until late afternoon. During times of poor seeing light would be lost outside the entrance aperture and observing had to be terminated. Some days of. good seeing did occur, and the photometric quality of these data was as good as obtained at night.
Section 2.3 - Selection of Stars
The selection of stars was governed by several factors. First, it was decided that the primary emphasis of the observing program would be to study normal oxygen-rich giant and supergiant stars of spectral types
G, K, and M. The observing list contained a large number of these stars well distributed in both spectral type and luminosity class between
G2 and M8 . Second, the stars selected for observation had to be relatively bright. AUDREY is a rather high resolution infrared scanner
(88 1 in first order with an 0.5 mm exit slot), and only for stars brighter than K~ 2 could scans be made within a reasonable amount of 2 0 telescope time. Third, it was felt that program stars should have well determined MK spectral types so that the dependence of the derived quantities with respect to temperature and luminosity could be accurately studied. And fourth, preference was given to stars that have been measured on the Wing 8 -color system. This was considered to be important since the 8-color system would provide narrow-band near-infrared measure ments of both color and color temperature that could be combined with the infrared scanner data to study the energy distributions of stars over a large wavelength interval (0.7 to 4.0 pm).
Fortunately, it proved to be possible to assemble an extensive observing list of stars which meet these criteria. For variable stars, whenever possible, simultaneous 8-color observations were made with a
0.4-m telescope at Kitt Peak. However, since 8-color measurements could not be made for daytime objects, not all of the variables have concurrent 8-color data.
In addition to normal oxygen-rich stars, some peculiar supergiants,
Mira variables, and chemically abnormal stars have been observed.
Several "infrared" stars such as NML Cyg and VY CMa were measured.
Since the observing time available at Kitt Peak was limited, it was not possible to study the variation of the derived quantities with phase in the Miras. A few MS, S, SC, and carbon stars were included in the program.
Table 2 lists the stars which have been observed with the scanner, in order of right ascension. In the first five columns the following information is contained: (1) the HD or BD number; (2) the HR or BS 2 1
Table 2
Program Stars
Variable Program ) or BD HR=BS Name Name Type Spectrum Col 4ym 8-c Notes
1013 45 X Peg M2+ III S X
1967 90 R And M S4, 6 e XX P=409.Od
3627 165 6 And K3 III X XX
3712 168 a Cas cst ICO- Ilia X X
4128 188 6 Cet 100058 K1 III X
6860 337 3 And 100088 M0 Ilia XX X
9927 464 51 And K3 III X
11961 M5 III XX
12929 617 a Ari 100163 IC2 11 lab S s X
14270 AD Per SRc M2.5 lab X X h&x Per
14386 681 0 Cet o Cet M M5 .5e XX P=331.6d
14469 SU Per SRc M3-4 lab X h&x Per
14488 RS Per SRc M4.5 lab X h&x Per
14528 S Per SRc M4e la X X h&x Per
17506 834 0 Per K3- Ib-IIa XX
18191 867 45 Ari RZ Ari I? M 6- III: XX X
18884 911 a Cet Ml.5 III S s
19058 921 P Per p Per SRb M4 Ilb-IIIax XX
20797 1009 M0+ Ila X X
22049 1084 e Eri K2 V X
22649 1105 328 S5,3 XX X 2 2
Table 2
Program Stars
(cont1d.)
Variable Program HD or BD HR=BS Name Name Type Spectrum Col 4ym 8 -c Notes
23475 1155 343 M2+ Ilab XX X
NHL Tau IK Tau M M9 X P=470d
25025 1231 Y Eri M0 III XX
27371 1346 Y Tau 102439 K0- Illab X
28305 1409 £ Tau K0 III XX
29139 1457 a Tau K5 III S s X
30959 1556 0 1 Ori 448 M3S XX X
32068 1612 ? Aur t, Aur EA K5 II+B XX
GP Ori SR SC X
32736 1648 W Ori SRb C5,3 X
34019 1707 R Aur M M6.5e X P=458.4d
36389 1845 119 Tau CE Tau SRc M2 Iab-Ib X X
38944 2011 u Aur 100686 M1+ Ilia X
39801 2061 a Ori a Ori SRc Ml-2 Ia-Ib X
39816 2063 U Ori M M 6 . 5e X P=372.4d
40239 2091 7T Aur 700 M3 II X X
42475 2190 TV Gem M0-1 lab X XX
42543 2197 6 Gem BU Gem Ic? Ml-2 Ia-Iab XX X
42995 2216 n Gem r) Gem SRb M3 III X X 23
Table 2
Program Stars
(cont1d.)
Variable Program I or BD HR=BS Name Name Type Spectrum Col 4pm 8-c Notes
44478 2286 y Gem 740 M3 Illab XX
44537 2289 Aur V 1 Aur Ic? K5--MOIab-Ib X
48329 2473 £ Gem 100759 G8 lb X
55383 2717 51 Gem BQ Gem M4 III XX
58061 VY CMa M5 I X x
60414 2902 KQ Pup M2 Iabep+B XX
60522 2905 U Gem M0 III XX
62509 2990 e Gem 100892 K0 Illb S s
69243 3248 R Cnc M M 6 ,5e X P=361.7d
69267 3249 6 Cnc K4 III XX
76827 3576 P UMa M3 Illb X
78712 3639 RS Cnc SRc M 6<2 (S) X
80493 3705 a Lyn 101039 K7 Illab X X
81797 3748 a Hyd 101049 K3 II-III X
82308 3773 X Leo 101056 K5 III X
84441 3873 £ Leo G1 II X
85503 3905 y Leo K1 .5 III XX CN1, Ca Str.
86663 3950 TF Leo M2-- Illab XX
90432 4094 y Hyd K5 III X 24
Table 2
Program Stars
(cont* d.)
Variable Program HD or BD HR=BS Name Name Type Spectrum Col 4ym 8-c Notes
95689 4301 a UMa 101174 K0-- Ilia S
96833 4335 UMa K1 III X
97778 4362 72 Leo 101191 M3 III X
100029 4434 X Dra 101207 M0 III X
108849 BK Vir lb M7- X
112300 4910 6 Vir M3 III X High vel.?
113226 4932 e Vir 101352 G8 Illab X
119228 5154 83 UMa 101398 M2 Illab X
124897 5340 a Boo 101433 K2 nip s s
126327 RX Boo SRb M 8 XX
127665 5429 P Boo K3 in X
131873 5563 B UMi 101477 K4 in X
132813 5589 RR UMi SR? M5 in X
140573 5854 a Ser K2 in X CN1.5
146051 6056 6 Oph M0,,5 III s
148387 6132 n Dra G8 III X
148783 6146 30 Her g Her SRb M 6-- Ill X
148856 6148 B Her 101593 G8 III X
156014 6406 a 1 Her SRc M5 Ib-II X
156283 6418 IT Her 101640 K3 Ilab X 25
Table 2
Program Stars
(cont'd.)
Variable Program HD or BD HR=BS Name Name Type Spectrum Col 4ym 8-c Notes
154143 6337 M3- III X
159181 6536 8 Dra G2 Ib-Ila X
161096 6603 8 Oph K2 III X X
164058 6705 y Dra K5 III X
165674 VX Sgr M4e X
167006 6815 104 Her 3895 M3 III X
i701^7 f' n X/XXVt /UU1 a Lyr 101745 A0 V o o X
172380 7009 XY Lyr lb M4-5 II X XX
175588 7139 62 Lyr 8 2 Lyr 1 M4 II X X
175865 7157 13 Lyr R Lyr SRb M5 III X X X
W Aql M S3 s9e X P=490.2d
185456 R Cyg M S3,9e XX P=426.3d
186791 7525 Y Aql K3 II s s X
187796 7564 X Cyg X Cyg M S7,2e X XX P=406.8d
+39°4208 RW Cyg SRc M3-4 Ia-Iab X XX
196610 7886 EU Del SRb M 6 III L-l X X High vel.
197989 7949 £ Cyg K0- III X X
IRC+40448 M 6 X NML Cyg
206778 8308 e Peg 102124 K2 lb X X
206936 8316 y Cep y Cep SRc M2 la X X X 26
Table 2
Program Stars
(con'd.)
Variable HD or BD HR=BS Name Name Type Spectrum Col 4ym 8-c Notes
207076 5468 M7 III: XXX
208816 8383 VV Cep EA M2 Ia-Iab XXX
210745 8465 X, Cep 102155 K1.5 lb X
212466 RW Cep Ic ICO 0-Ia XX
213310 8572 5 Lac 102179 M0 Iab+B X X
214665 8621 102195 M4 III XXX
216946 8726 102221 M0- lb XX
217476 8752 GO la XX
217906 8775 B Peg B Peg lb M2.5 II-IIIx XX
221615 8940 71 Peg 5749 M5- Ilia XXX
224427 9064 ip Peg M3 III XX
224490 9066 R Cas M M7e X X 27
number; (3) the Bayer or Flamsteed name or an alternate designation;
(4) the variable star name; and (5) the type of variability. Numerical designations in column 4 have been taken from the Catalogue of Stars
Suspected of Variability (Kukarkin, et al. , 1951), while the variability type refers to the designations of the General Catalogue of Variable
Stars (Kukarkin, et al., 1969). The spectral types listed in column 6 are from several references. For the G, K, and M stars the revised types of Morgan and Keenan (1973) have been used in preference to those given elsewhere. The spectral types of Mira variables except IK Tau refer to their normal maxima as given in the catalogue of Keenan,
Garrison, and Deutsch (1974). The spectral type of IK Tau is the mean maximum value derived by Wing and Lockwood (1973) on the basis of eight years of photometric measurements in the 1 pm region. Other references for spectral types were Buscombe (1977), the Catalogue of Bright Stars
(Hoffleit, 1964), Keenan (1954, 1963), Wildey (1964), Humphreys (1970), and Humphreys, Strecker, and Ney (1972). The columns headed "Col",
"4 pm", and "8-c" refer to the infrared colors program, the 4 pm con tinuous scans, and simultaneous 8-color measurements which were made
for the program variables, respectively. An "x" in these three columns means that data were obtained on the program while an "S" means that the star has been used as a standard in the reduction procedure.
The final column contains notes including the periods for all the Mira variables in days. 28
Section 2.4 - Data Reduction
In the reductions, all observations of standard stars obtained during any continuous observing period, corrected if necessary for wavelength shifts, were used in a least squares solution for the extinc tion and transformation coefficients for that period. The extinction was assumed to increase linearly with air mass, and fluxes have been expressed on a magnitude scale per unit wavelength interval.
The reduction programs of Wing have been used with minor modifica tions to reduce the data. Since the reduction procedure has been described in detail elsewhere (Wing, 1967a) , it will only be outlined here.
If the bandwidth of each measurement is sufficiently narrow that its effective wavelength is the same for all stars, and if the atmos pheric extinction depends linearly on the air mass, the flux per unit wavelength of star s at wavelength A and time t can be expressed on a magnitude scale by
F(s,A,t) = -2.5 log10 c(s,A,t,n,z) - k(A,n)X(z) + T(A,n) (2.4-1) where c(s,A,t,n,z) is the average counts per unit time (or the average d.c. signal) observed on night n at zenith distance z corrected for background; lc(A,n) is the extinction coefficient in mag per air mass;
X(z) is the air mass of the star; and T(A,n) is the transformation coefficient on a magnitude scale. In the reduction procedure X(z) has been approximated by sec z. 29
The transformation coefficient, which includes an arbitrary con stant, should be a smooth function of wavelength since it is a product of several functions that change slowly with wavelength: the detector sensitivity, the reflectivity of the optics, the efficiency of the grating, the transmittance of the filter, and the dispersion of the grating. An exception to this statement can occur in regions of large atmospheric extinction where features saturate and hence do not vary linearly with air mass. In those regions, the coefficients k(A,n) and
T(A,n) are no longer independent of z, but Eq. 2.4-1 still serves as a good first approximation since the lower atmospheric transmittance appears in the T(A,n) term.
In order to find lc(A,n) and T(A,n) a linear least-squares solution of Eq. 2.4-1 is performed with the observed readings c(s,A,t,n,z) for each standard star of known flux F(s,A,t), observed at air mass X(z).
For nights of lower photometric quality or for nights for which too few standard stars were observed for a reliable determination of the extinc tion and transformation coefficients, minimum and maximum permissible values of k(A,n) were specified. The assumed values of k(A,n) in these cases were based on nights where the observed coefficients were parti cularly well determined.
The absolute fluxes for the bandpasses used in the infrared colors program were derived with the model atmosphere program ATLAS (Kurucz,
1970) and the model structure computed for Vega by Schild, Peterson, and
Oke (SPO, 1971). The emergent colors computed with the OSU version of
ATLAS agreed to about 1% in the infrared with the published values of 30
SPO. The calculated monochromatic flux differences between each wave- o length and 10395 A, expressed on a magnitude scale per unit wavelength, are tabulated in Table 3. For the reduction of the continuous SiO scans a somewhat different procedure, discussed in Section 4.3, was used because of uncertainty in the hydrogen line strengths which affect the spectrum of Vega in the 4 pm region.
Recently Kurucz (1979) and Dreiling and Bell (1980) have published revised model atmospheres for Vega. Although the adopted model para meters differ (1^=9400 K, log g=3.95 for Kurucz; 1^=9650 K, log g=4.00 for Dreiling and Bell) , the computed infrared colors are very similar
to SPO. Dreiling and Bell (1980) note that their Vega model is about
2% fainter than SPO between 1 pm and 2 pm and agrees to within 1% for
2 pm < X < 10 pm. Model atmosphere predictions of infrared monochromatic
flux difference in magnitudes between 1.04 and 4.00 pm are compared in
Table 4. The models are designated in column 1 by their effective
temperature and surface gravity. The current status of the Vega calibra
tion problem has been discussed by Lange and Wing (1979).
The fluxes of the standard stars were obtained by iteration. The procedure was begun by reducing the nights of highest photometric quality on which Vega had been observed using mean extinction coeffi cients. By averaging the computed standard star fluxes for several nights, a preliminary standard star deck was assembled. These fluxes were then used to reduce the observations anew, without forcing mean
extinction coefficients. After assigning weights to the standard star
fluxes based on the quality of the night, several iterations were Table 3
Vega Colors Computed with ATLAS
Wavelength (£) 12870 0 . 8 6 8 21010 2.705 22850 3.052 33965 5.344 Table 4 Comparison of Model Colors Parameters Reference I (104)-L(400) 9000/4.0 1 5.322 9400/3.9 1 5.353 9400/3.95 1 5.353 9400/4.0 1 5.349 9500/3.9 1 5.359 9500/4.0 1 5.356 9650/4.05 2 5.344 9650/4.0 3 5.370 ^Kurucz (1979) 2 Computed with ATLAS using SPO parameters 3 Dreiling and Bell (1980) 32 required to minimize the residuals. To make all the program fluxes internally self-consistent, the final standard star deck was used to reduce all of the observations. The probable errors in the magnitudes for the infrared colors program and the 4 pm scanner observations were 0.016 and 0.015 mag, respectively. The accuracy of the colors obtained in both programs was 0.008 mag. These values are typical of the errors quoted in the literature for photoelectric work and indicate that the Kitt Peak InSb detector is as stable against sensitivity changes as a good photo multiplier. The observational data are summarized in Table 5. 33 Table 5 Summary of Observational Data IR Colors 4 ym Scans No. of Standard Stars 10 11 No. of Standard Star Observations 42 48 N o . of Nights Used 5 6 No. of Days Used 2 3 No. of Stars Observed 1 1 1 * 77 Probable Error of Magnitudes 0.016 mag 0.015 mag Probable Error o.f Colors 0.008 mag 0.008 mag *34 stars observed at 1.29, 2.10, 2.28 ym only; 27 stars observed at 4 ym only; 50 stars observed at all four wavelengths of the infrared colors program CHAPTER III MEASUREMENTS OF ATMOSPHERIC EXTINCTION IN THE 4 ym REGION The Kitt Peak grating spectrometer AUDREY has been used to record stellar spectra from 3.98 to 4.07 ym. Although the primary purpose of the program was to study the behavior of the SiO first-overtone vibra- tion-rotation bands in a sample of late-type stars (Chapter IV), atmospheric extinction was measured by making repeated observations of a series of non-variable, standard stars. The extinction at 4 ym was found to be larger than expected and strongly wavelength dependent. The results of this study have been published (Wing and Rinsland, 1979) and will be summarized here. The region studied is near the long-wavelength edge of the photo metric L band. Inspection of high-resolution solar spectra of this region revealed only weak telluric lines of N 2O so that atmospheric extinction was expected to be small. The observations, however, revealed that the extinction in this region was suprisingly large, increasing from about 0.05 mag per air mass at 3.98 ym to 0.25 mag per air mass at 4.07 ym. The weak N2O bands did not have the proper distribution or sufficient strength to account for the general increase in extinction to longer wavelengths observed in this region. To account for the measured extinction the following sources of atmospheric opacity were considered: continuous absorption by the 34 35 molecules N 2 , CO2 , and H2O; discrete line absorption by N 2O; and aerosol extinction. Absorption by N 2 in this region is caused by pressure-induced transitions in the fundamental vibration-rotation band. The pressure in the terrestrial atmosphere is sufficient to induce a dipole moment, and measurable absorption occurs because of the high concentration of nitrogen in the earth's atmosphere. Continuous absorption by CO2 is from the wings of distant lines from the v3 fun damental and its associated "hot" bands near 4.3 pm. Although the region observed is far from these bands, the superposition of the extreme wings of these very intense lines produces a strongly wave length-dependent extinction. Weak continuous absorption by water vapor has been observed in this region in the laboratory (Burch, Gryvnak, and Pembrook, 1971; Watkins, et al., 1979), but its nature is unclear. The same process as for CO2 is likely to occur, although absorption from water vapor dimers is suspected and may dominate in some spectral regions. Absorption and scattering by small particles (aerosol extinc tion) produces only a small contribution in the infrared. The observed extinction coefficients have been compared to synthe tic extinction coefficients calculated from absorption coefficients measured in the laboratory and a model terrestrial atmosphere. A mid latitude Spring-Fall model (U.S. Standard Atmosphere Supplements, 1966) was adopted. Water vapor content as a function of altitude was approximated by scaling the mean annual mid-latitude mixing ratios of Gutnick (1965) so as to agree with the observed water vapor content at Kitt Peak at the time of the observations. The adopted model 36 parameters are tabulated in Table 6 . Absorption from N2 O was evaluated from the atmospheric lines appearing in the interferometric spectrum (resolution=0.05 cm-1) of IRC +10216 (Ridgway and Hall, 1978) Aerosol extinction was estimated from the extinction observed at Kitt Peak in the 1 ym region (which is believed to be due almost entirely to aerosols) and theoretical calculations of the wavelength dependence of aerosol extinction (Elterman, 1964). The comparison of observed and computed extinction coefficients is shown in Figure 1. The calculations indicate that the primary com ponent of extinction in the region observed is N 2 . The N2O lines, primarily from the + 2v2 band, also produce considerable absorption in the region. The C02 absorption is small in the region observed, but it rises rapidly at wavelengths longer than 4.10 ym and reaches equality with the N 2 absorption at 4.17 ym, just before the onset of C02 line absorption from the v 3 fundamental band. The contributions of water vapor and aerosol are small throughout this region and nearly independent of wavelength. Considering the many sources of error in the laboratory data, the synthetic extinction coefficients are in good agreement with the observations. Since the photometric measurements of extinction were limited to a rather narrow wavelength interval (3.98 to 4.07 ym), it is of interest to compare the calculated coefficients with observations made over a larger spectral region. Ridgway (1979) and his associates have used a high-resolution (0.05 cm-1) spectrum of IRC +10216 to obtain measure ments of atmospheric transmittance in the 4 ym region. The observation 37 TABLE 6 MODEL ATMOSPHERE PARAMETERS ALTITUDE TEMPERATURE , PRESSURE H_0 MIXING RATIO (1cm) (K) (mb) 2.00 275.15 795.0 0.01160 2.25 273.53 770.6 0.01079 2.50 271.90 746.8 0.01002 2.75 270.28 723.7 0.00927 3.00 268.65 701.1 0.00856 3.25 267.03 679.1 0.00788 3.50 265.40 657.6 0.00723 3.75 263.78 636.8 0.00661 4.00 262.15 616.4 0.00602 4.25 260.53 596.6 0.00547 4.50 258.90 577.3 0.00494 4.75 257.28 558.5 0.00445 5.00 255.65 540.2 0.00399 5.25 254.03 522.4 0.00356 5.50 252.40 505.1 0.00316 5.75 250.78 488.2 0.00280 6.00 249.15 471.8 0.00246 6.25 247.53 455.9 0.00216 6.50 245.90 440.3 0.00189 6.75 244.28 425.3 0.00165 7.00 242.65 410.6 0.00144 7.25 241.03 396.4 0.00127 7.50 239.40 382.5 0.00 1 1 2 7.75 237.78 369.1 0.00 1 0 1 8.00 236.15 356.0 0.00093 8.25 234.53 343.3 0.0 8.75 231.28 319.0 0.0 9.25 228.03 296.2 0.0 9.75 224.78 274.6 0.0 10.25 221.53 254.4 0.0 11.50 216.65 209.2 0.0 14.00 216.65 141.0 0.0 16.00 216.65 102.9 0.0 17.00 216.65 87.87 0.0 18.50 216.65 69.36 0.0 20.00 216.65 54.75 0.0 21.50 218.15 43.25 0.0 23.00 219.65 34.22 0.0 24.00 220.65 29.30 0.0 26.50 223.15 19.94 0.0 28.50 225.15 14.70 0.0 31.00 227.65 10.08 0.0 35.00 237.05 5.589 0.0 39.00 248.25 3.182 0.0 47.00 270.65 1.109 0.0 MAGNITUDE PER AIR MASS 0.4 0.3 0.2 0.5 0.0 0.1 which is nearly constant throughout this spectral region, region, spectral this throughout constant nearly is which en ae fo igadRnln (1979). Rinsland and Wing from taken been CO by absorption by H^O. The level of the contribution by aerosol, aerosol, by contribution the of level The H^O. by absorption extinction calculated and observed of Comparison 1. Figure is indicated by the line segment in the lower right. The The right. lower the in segment line the by indicated is The stars. standard 12 of observations from 28 October 1977 sum of the five components is also shown. This diagram has diagram This shown. also is components five the of sum coefficients extinction calculated the show on curves Peak smoothed Kitt at measured values the are Dots coefficients. for pressure-induced absorption by N _ , far-wing absorption absorption , far-wing _ N by absorption pressure-induced for 2 , discrete line absorption by N^O, and continuous continuous and N^O, by absorption line , discrete 2500 xicin Coefficients Extinction bevd s Calculated vs. Observed .00 W AVELENGTH AVELENGTH W VNME ( 1) " m (c AVENUMBER W 2450 (^m) 4.10 TOTAL CO. 4.15 2400 Aer. 38 39 was made at Kitt Peak National Observatory on 21 October 1977, with a Fourier transform spectrometer and the 4-m telescope. The time averaged air mass was 1.085. IRC +10216 is a late-type carbon star heavily obscured by a dust shell, and its 4 pm spectrum is continuous except for telluric lines. Corrections have been applied for the variation of the response function of the interferometer with wavelength by observing a blackbody source of known temperature. The variation of stellar flux with wavelength has been corrected for by dividing the observed spectrum by a blackbody having the photometric color tempera ture of IRC +10216. The resultant transmittance spectrum has arbitrary normalization. The Kitt Peak spectrum is compared with synthetic extinction cal culations in Figure 2. The 100% transmittance level has been derived by requiring the observed and synthetic transmittances agree at 2500 cm-1 (4.0 pm). Calculated monochromatic transmittances (solid circles), shown at 10 cm-1 intervals, have been computed as previously described except that N2O line absorption was not included. The observed and calculated transmittances are in excellent agreement throughout the interval. rmnn i teosre spectrum. theobserved in + Viprominent The extinction. aerosol with along themolecules by absorption ’ anc* transmittances Continuous C02 synthetic ^2* the of t>een ^as ^2® calculation the in (4 been ym).Included have cm-1 2500 (solid circles)at to agree as so transmittances normalized calculated and observed The airmass 1.085. averaged timeof a and cm-1 0.05 of resolution a with Peak Kittat 1977 October pcrmhs endrvd rma osraino tecro sa IC126o 21on IRC+10216 star carbon the ofobserved The observation an from derived been has spectrum intervals. wavenumber cm-1 10 at transmittances monochromatic calculated Figure 2. Comparison of an observed 4 ym spectrum of atmospheric transmittance with with transmittance atmospheric of spectrum 4ym observed an of Comparison 2. Figure sraA2g»“9“«— 3 1 f ■ 1 m m CHAPTER IV OBSERVATIONS OF THE FIRST-OVERTONE SiO BANDS NEAR 4 pm Section 4.1 - Introduction The infrared spectra of many late-type stars exhibit absorption bands due to the first-overtone vibration-rotation sequence of the free radical silicon monoxide (SiO). Since SiO is predicted to be an abundant molecule in cool oxygen-rich giants and supergiants (cf. Johnson, Beebe, and Sneden, 1975) and the first-overtone bands are conveniently placed for measurement in the L-band window, scanner observations were made to study the behavior of SiO with respect to spectral type, luminosity class, and chemical composition. The first-overtone bands of 2 8 Si160 were first observed by Cudaback, Gaustand, and Knacke (1971) in a Ori (M2 lab). At their resolution of 2 cm-1 the longward degrading R branch bands are clearly visible starting with the (2,0) head at 2497.2 cm-1. Crude synthetic spectra were used to show the SiO absorption was photospheric in origin. Observations of the region of the (3,1) bandhead of 2 8 Si160 were made by Wollman et. al. (1973) using a Fabry-Perot interferometer mounted at the coude focus of the Lick 120-inch. At a resolution of 0.6 cm-1, absorption was detected in 9 M giants and supergiants and in the mild S-type Mira x Cyg (S7,le-SlO,le). Negative detections were 41 42 reported for the cool carbon stars Y CVn and V Cyg, the prototype long period variable o Ceti (M5-M8), the semiregular variable W Hya (M8 e), two peculiar M supergiants (NML Cyg and VX Sgr), and a Boo (K2 IIIp). The first high resolution observations (0.1 cm-1) of SiO were reported by Beer, Lambert, and Sneden (1974). Their Fourier transform spectrum of a Ori fully resolved the rotational structure and confirmed that SiO was the dominant absorber in the region. A few stellar OH lines from the P branches of the fundamental bands were also identified. A model atmosphere (Johnson, 1974) and spectral synthesis were used to estimate the SiO abundance and upper limits to the silicon isotope ratios. The dependence of SiO strength with phase has been studied in the spectra (resolution 0.5 cm-1) of several long period Mira variables (Hinkle, Barnes, and Lambert, 1976). In the three stars observed — o Ceti (M5-M8), R Leo (M7-M9e), and y Cyg (S7,le-S10,le) — the SiO bandheads are not detectable at maximum light. Near minimum the band- heads of 28SiO were observed in all three stars. The shape of the continuum was also noticed to change with phase, although this effect may be due to the wavelength dependent extinction noted in this spectral region (see Chapter III). The hydrogen line Ba which lies near the (3,1) SiO bandhead was observed in emission in some of the spectra obtained near maximum light. The isotopic bandheads of 2^SiO and 30SiO were detected in y Cyg, and crude spectral synthesis indicated a near terrestrial ratio of the silicon isotopes. 43 A number of stars have been observed near 4 ym at high resolution with the Kitt Peak FTS (Ridgway, Hall, and Carbon, 1977). The 30SiO bandheads are faintly visible in some stars and indicate a 2 8 Si/30Si abundance ratio consistent with the terrestrial value of 30. SiO has been seen in emission in some Mira variables. The SiO bands are relatively weak features. SiO absorption cannot be seen in the low resolution spectra of Merrill and Stein (1976) and Noguchi et al. (1977). Merrill and Stein (1976) did note a sharp rise in flux to longer wavelengths in the spectra of S Per (M4e la) and IRC+ 60370 (K4.5 la) at the location of the SiO bands. Their suggestion of SiO emission in some highly luminous stars is supported by the results obtained in this study. Preliminary results of this study have been reported previously (Wing, Rinsland, and Joyce, 1977; Rinsland and Wing, 1978). A discus sion of the SiO results was also included in a review paper on classi fication by photometric measurement of molecular bands (Wing, 1979). Section 4.2 - Description of the Spectral Region The Kitt Peak grating spectrometer has been used to scan the spectral interval 3.98 to 4.07 ym in a sample of late-type stars at a - 1 0 resolution of 5.5 cm 1 (88 A). Of primary interest was to study the first-overtone vibration-rotation sequence of the silicon monoxide free radical. Within this interval are located the R branch bandheads of the (2,0) and (3,1) bands of the primary isotope 2 8 Si160 at 2497.2 cm-1 (4.003 ym) and 2472.9 cm-1 (4.043 ym), respectively. In addition, the 44 isotopic (2,0) heads of both 29 Si160 and 30Si16O occur in this region. The (2,0) 2 9 Si160 bandhead is favorably located at 2481.7 cm-1 (4.028 ym) between the main isotope bandheads. The (2,0) 30Si15O head occurs at 2467.2 cm 1 (4.052 ym) and is difficult to separate from the 2 8 Si150 (3,1) bandhead at the resolution used. The terrestrial isotope abun dance ratios of 2 ®Si:23Si : 3^Si are 92.2:4.7:3.1. Also of interest were the hydrogen lines in this spectral interval. The Brackett a line occurs at 2467.8 cm-1 (4.051 ym), very close to the location of the (3,1) 2 8 Si150 bandhead. Absorption from this line can be expected in early type stars (Dreiling and Bell, 1980) and was ob served on this program. Paschen and Brackett lines have been seen in emission in Mira variables in the 1 to 2 ym region (cf. Johnson, et al., 1968; Johnson and Mendez, 1970) and Ba emission has been reported in x Cyg (Hinkle, Barnes, and Lambert, 1976). Detection of Brackett a emission is difficult with low-resolution scans because of the coinci dence of the (3,1) 2 0 Si16O band. The hydrogen line Humphreys 14 at 2487.0 cm-1 (4.020 ym) can also been seen in the infrared spectra of Sirius and Vega calculated by Kurucz (1979). The published spectrum of a Ori (Beer, Lambert, and Sneden, 1974) and Kitt Peak spectra of a Tau, y Gem, and a Ori (Ridgway and Hall, 1978) were used to examine the spectral region at high resolution. The Kitt Peak spectrum of a Ori is reproduced in Figures 3 and 4. In all three stars SiO is the dominant absorber with a small number of OH fundamen tal band P branch lines occurring throughout the region. Shortward of the onset of SiO absorption only a few OH lines are observable, and the Figure 3. Kitt Peak Fourier transform spectrum of a Ori in the spectral interval 2442 to 2510 cm-^. The upper (reference) spectrum is of IRC+10216 which is featureless in this spectral interval except for telluric lines. The inter ference pattern present in the reference and stellar (middle) spectra is caused by a blocking filter. The lower spectrum is the ratio of the upper two and shows stellar features only. The location of the R branch (2,0), (3,1), and (4,2) bandheads of 28SiO are labeled. 45 tfflVELEKGTH (BJ r c kavtfac3£R its? ) 46 Figure 4 Kitt Peak Fourier transform spectrum of a Ori in the spectral interval 2376 to 2445 cm-'*'. The format is the same as Fig. 3. The (5,3) and (6,4) bandheads of 28SiO are identified as well as the region affected by high J lines of the atmospheric v 3 band of CO2 . Beyond 2388 cm”*- the atmosphere is completely opaque. 47 KSWELEKCTH (f5> KSVEKUXEER 5 48 49 scanner magnitude observed at 3.996 ym has been used as a continuum point in the reduction procedure and in the program of infrared colors (Chapter V). The telluric spectrum has been discussed in detail as part of a study of atmospheric extinction in the 4 ym region (Wing and Rinsland, 1979; Chapter III). A high resolution spectrum of atmospheric trans mittance near 4 ym is shown in Figure 2. Section 4.3 - Observations and Reduction Procedure Continuous scans between 3.98 and 4.07 ym have been obtained of o _. 77 late-type stars at a resolution of 88 A (5.5 cm 1). Measurements u were made at 51 spectral points separated by a step size of 16 A (=0.0016 ym) or 1 cm- 1 , corresponding to about 5 data points per resolution element. Observations were made during observing runs in September-October 1976,and in October-November 1977. During the latter run, near simultaneous 8-color observations were made with the //3 Kitt Peak 0.4-m telescope of most of the brighter program variables accessi ble during nighttime. These measurements provided concurrent 1(104) magnitudes and 8-color spectral types. The basic scanner data reduction procedure has been described in Section 2.4. Flexure in the scanner caused the wavelength scale to shift from star to star by amounts up to several steps. However, the presence of SiO features in the data allowed the step positions to be re-numbered, and the uncertainty in the wavelength scale was reduced to approximately one step (1 cm-1). 50 The reductions were first attempted with an absolute flux distri bution of Vega calculated with ATLAS and the model atmosphere parameters of Schild, Peterson, and Oke (1971). The spectrum was computed in non- LTE and included hydrogen line absorption due to Brackett a and Humphreys 14. The calculated fluxes were placed on a magnitude scale per unit wavelength and convolved with the scanner bandpass to obtain the standard values needed to initiate the reductions, which proceeded as described in Section 2.4 until a total of 11 stars had been tied together as standards. The reduction made in this manner proved to be unsatisfactory for two reasons. First, since a Lyr is rather faint at 4 pm, all of the measured scans for this star are noisy. Since the point-to-point scatter in the a Lyr data was not sufficiently averaged out in the small number of available observations, it reappeared in the calculated trans formation coefficients and hence also in all of the reduced spectra. Second, the calculated transformation coefficients, besides being noisy, showed a wavelength dependence that was not smooth. This effect could not be attributed to telluric absorption, which is relatively small in this region (Chapter III), and it was concluded that the calculated energy distribution for Vega was in error in the regions of the hydrogen lines. An alternative approach was therefore tried. Instead of basing the reductions on a model energy distribution for a Lyr, it was decided to try assuming blackbody energy distributions for the three warmest standard stars: 3 Gem (KO Illb), a Ari (K2 Illab), and a Boo (K2 IIIp). These stars are of relatively early type, bright 51 at 4 ym, and no spectral features were apparent in the raw data. In addition, synthetic spectrum calculations (Section 4.8) indicated that stars in this temperature range have featureless 4 ym spectra at the resolution of the scanner with neither SiO bands nor hydrogen lines present. The color temperatures measured on the Wing 8-color system were adopted. Since 4 ym is several times the wavelength of the energy maximum for these stars, the computed blackbody energy distribu tions are closely approximated by the Rayleigh-Jeans law (FAaX-1*) and are insensitive to the adopted temperature (see Table 9 below). To account for the relative brightness of g Gem, a Ari, and a Boo, a constant was added to the blackbody fluxes of each star in the standard deck to minimize the residuals in the scanner data. The remaining 8 standards were then added to the standard deck and the final values of the standard stars were determined by iteration. The final fluxes were scaled so that the magnitude of a Lyr at 3.996 ym was 0.0. At this point the wavelength dependence of the transformation coefficients was again examined and was found not to show any features, although small (0.01 mag) point-to-point differences existed because of noise in the standard star data. To reduce further the scatter in the transformation data, a gaussian of full half-width equal to the bandpass o (88 A) was convolved with the measured transformation coefficients. This procedure preserves the wavelength dependence of the transformation data and decreases the point-to-point scatter. Smoothed transformation coefficients were now used to iterate the standard deck. The final values for the program stars were computed from a self-consistent set 52 of standard star fluxes and smoothed transformation coefficients. The smoothed transformation coefficients obtained on 26 October 1977, 28 October 1977, and 8 November 1977 have been plotted against wavelength in Figure 5. Section 4.4 - Derived Quantities Blackbody color temperatures were computed from a two point index formed from the 8-color magnitude at 1(104) and the observed scanner flux at 3.996 pm. The latter wavelength lies shortward of the onset of SiO absorption and represents a point of minimum absorption in most of the stars observed. Continuum magnitudes measured at 3.996 pm (averaged over three scanner data points) will henceforth be referred to as L(400). The measured fluxes were transformed to an absolute flux scale by the procedure described in Section 2.4. The I (104)-L(400) color index has been used in the study of infrared colors (Chapter V ) . Equivalent widths of both the (2,0) and the (3,1) 2 8 Si160 bands have been derived. Since in many stars SiO absorption occurs at all program wavelengths longward of the (2 ,0 ) bandhead, the continuum level had to be extrapolated into the SiO-depressed region. The continuum level was calculated using L(400) as a continuum point and the 1(104)- L(400) color index to derive a blackbody slope. For temperatures warmer than about 3000 K the computed continuum slope is insensitive to errors in the blackbody temperature caused by reddening and photometric errors since the blackbody distributions in this region can be closely approxi mated by the Rayleigh-Jeans law (FAaA-t+). MAG 26 OCT 77 8 NOV 77 1 ' BANDPASS a i 8______» » " « » 4.00 4.05 Figure 5. Smoothed 4 )Jm transformation coefficients obtained on 28 October 77 (upper), 26 Oct 77 (middle), and 8 Nov 77 (lower) plotted vs. wavelength in air microns. The transformation coefficients are expressed on a magnitude scale per unit wavelength and have been smoothed using a Gaussian of half-width equal to the resolution (88 54 The (2,0) band equivalent width was computed by integrating between the wavelengths 3.998 and 4.016 ym, and the (3,1) band equivalent width was integrated from 4.038 to 4.058 ym. The total Si0 equivalent width W(SiO) was defined to be the sum of these two terms. Errors in the measured values of W(SiO) can result from errors in the photometry at the wavelengths used to integrate the SiO equivalent width and from errors in the computed continuum level in this region. Since the blackbody slope has been shown to be insensitive to the adopted temperature for most stars, the largest source of error in determining the continuum is likely to be the L(400) magnitude. This wavelength has been assumed to be free of stellar blanketing in all stars. Both the synthetic spectrum calculations (Section 4.8) and the Kitt Peak FTS spectra of a Ori, a Tau, and y Gem indicate this assump tion is likely to be valid for most stars, but it is possible that water vapor or some unknown absorber could depress both the L(400) continuum point and the SiO region in the cooler stars or in peculiar objects. Since H 2O absorption occurs in the 2 ym region in giants later than M 6 (Baldwin, Frogel, and Persson, 1973), the measured values of W(SiO) are likely to be less accurate because of water vapor absorption in the coolest stars. The uncertainty in the measured value of W(SiO) resulting from errors in the photometry can be estimated from the repeated measurement of the standard stars. The probable error of 0 W(SiO) for the standards is 5 A. The 4 ym scanner results for all stars except Mira variables are summarized in Table 7. The first three columns are self-explanatory. 55 Table 7 4 ym Scanner Results for Non-Miras # of W(SiO) HD HR=BS Name Spectrum Scans L(400) A Notes 3627 165 6 And K3 III 1 0.340 2.8 3712 168 a Cas K0- Illb 1 -0.342 -2.4 1 6860 337 6 And M0 Ilia 1 -2.033 21.4 11961 M5 III 1 -0.090 46.7 12929 617 a Ari K2 Illab 4 -0.748 1.1 14270 AD Per M2.5 lab 1 1,744 25.6 2 14469 SU Per M3-M4 lab 1 1.103 30.6 2 14488 RS Per M4.5 lab 1 1.270 36.1 2 14528 S Per M4e la 1 0 .010 -28.5 2,3 17506 834 r) Per K3 Ib-IIa 1 0.003 3.8 18191 867 45 RZ Ari M 6- III: 1 -1.270 40.0 18884 911 a Get Ml.5 III 6 -1.884 25.1 19058 921 p Per M4 Ilb-IIIa 1 -2.213 31.1 20797 1009 M0 II 1 0.246 23.0 22649 1105 S5,3 1 -0.071 28.3 23475 1155 M2+ Ilab 1 -0.867 32.4 25025 1231 y Eri M0 III 1 -1.125 18.1 29139 1457 a Tau K5 III 10 -3.020 15.4 30959 1556 o 1 Ori M3S 1 -0.787 29.7 32068 1612 C Aur K5 II + B 1 -0.039 13.9 GP Ori SC 1 1.699 4.7 1 56 Table 7 4 ym Scanner Results for Non-Miras (cont'd.) # of W(SiO) HD HR=BS Name Spectrum Scans L(400) A Notes 32736 1648 W Ori C5 s 3 1 -0.927 7.9 36389 1845 119 CE Tau M2 Iab-Ib 1 -1.228 39.3 38944 2011 O Aur M1+ Ilia 1 0.440 21.8 39801 2061 a Ori M1-M2 Ia-Ib 3 -4.519 40.9 40239 2091 7T Aur M3 II 1 -1.069 40.4 42475 2190 TV Gem M0-M1 lab 1 0.569 43.9 42543 2197 6 BU Gem Ml-M2 Ia-Iab 1 0.482 18.4 42995 2216 n Gem M3 III 1 -1.654 31.6 44478 2286 y Gem M3 Illab 1 -2.106 29.5 44537 2289 ip1 Aur K5-M0 Iab-Ib 1 0.250 24.7 55383 2717 51 BQ Gem M4 III 1 -0.383 30.9 58061 VY CMa M 1 -3.172 -24.0 60414 2902 KQ Pup M2 Iabep+B 1 -0.254 37.0 60522 2905 U Gem M0 III 1 0.103 19.4 62509 2990 6 Gem K0 Illb 4 -1.174 -1.0 69267 3249 e Cnc K4 III 1 -0.005 10.9 76827 3576 p UMa M3 Illb 1 0.217 28.2 78712 3639 RS Cnc M 6e(S) 1 -1.979 32.4 80493 3705 a Lyn K7 Illab 2 -0.772 14.4 85503 3905 y Leo K1.5 III CN1 1 1.146 0.5 57 Table 7 4 pm Scanner Results for Non-Miras (cont'd.) # of W(SiO) HD HR=BS Name Spectrum Scans L (400) A Notes 86663 3950 TT Leo M2- Illab 1 0.345 — 5 108849 BK Vir M7- 1 -1.298 36.2 1 124897 5340 a Boo K2 IIIp 5 -3.128 1.7 126327 RX Boo M 8 2 -2.407 39.6 146051 6056 6 Oph M0.5 III 2 -1.423 19.7 156014 6406 a 1 Her M5 Ib-II 2 -3.785 40.8 161096 6603 3 Oph K2 III 1 0.126 2.5 165674 VX Sgr M4e 1 -1.842 — 172167 7001 a Lyr A0 V 4 -0.003 15.5 4 172380 7009 XY Lyr M4-5 II 1 -0.505 49.0 175865 7157 R Lyr M5 III 1 -2.319 39,1 186791 7525 Y Aql K3 II 3 -0.759 8.5 RW Cyg M3-M4 Ia-Iab 2 -0.021 20.2 196610 7886 EU Del M 6 III 1 -1.393 38.3 NML Cyg M 6 1 -1.874 — 206778 8308 £ Peg K2 lb 2 -0.977 6.8 206936 8316 y Cep M2 la 4 -2.292 18.9 207076 M7 III: 1 -1.907 27.3 208816 8383 W Cep M2 Ia-Iab 1 -0.435 22.4 212466 RW Cep K 0 O-Ia 2 1.461 -18.3 3 58 Table 7 A ym Scanner Results for Non-Miras # of W(SiO) HD HR=BS Name Spectrum Scans L(AOO) A Notes 21A665 8621 MA III 1 -0.A12 3A.6 2169A6 8726 MO- lb 1 0.58A 29.1 217A76 8752 GO la 1 1.126 0.6 217906 8775 3 Peg M2.5 II-III 3 -2.AA3 22.6 221615 89A0 71 Peg M5- Ilia 1 -0.A27 36.6 Remarks concerning stars in Table 1 One or more noisy scans. Somewhat higher errors. 2 Supergiants near the h and x P®r cluster. 3 SiO in emission? A Calculated value of W(SiO) not meaningful. 5 Missing data. W(SiO) could not be calculated. 59 Column 4 is the published spectral type repeated from Table 2 in Chapter II. Column 5 lists the number of scans made for each star. Column 6 contains the mean observed scanner flux at 3.996 pm, on a magnitude scale normalized so that L(400) for a Lyr is 0.0. Column 7 is the average observed SiO equivalent width in Angstroms. The last column refers to notes which immediately follow the table. Section 4.5 - Normal Oxygen-rich Giants and Supergiants In Figure 6 the total SiO equivalent width W(SiO) is plotted against MK spectral type for non-variable and low-amplitude variable stars of spectral types K and M. In the figure luminosity class II and III stars are shown as solid circles while supergiants of types lab and lb are indicated with open circles. Solid triangles refer to stars classified as la or Ia-Iab on the MI system. MS stars are indicated with a plus (+) symbol. The relationship between band equivalent width and spectral type is well-defined for the giant and bright giant stars. The SiO bands have no appreciable strength in the early K stars, but they are defi nitely present at K5 and continue to increase in strength until at least M 6 . The data can be satisfactorily represented by a straight line, which has been drawn in Figure 6 . The two MS stars observed, o 1 Ori (M3S) and RS Cnc (M6 S), have SiO strengths similar to normal giants of the same spectral type. The mean giant and bright giant relation is listed in Table 8 . The effective temperature scale of Ridgway, et al. 6 0 50 TV Gam 40 119 To 30 W(SiO) O A AD Per 20 ERROR KO Kl K2 K3 K4 K5 MO Ml M2 M3 M4 M5 MS M7 MS MK SPECTRAL TYPE Figure 6. The relation between W(SiO) and MK spectral type for K and M stars. The peculiar supergiants discussed in Section 4.6 and Mira variables have been excluded. Luminosity class II and III stars are shown as solid circles, lab and lb super giants as open circles, la and Ia-Iab supergiants as solid triangles, and MS stars as plus (+) symbols. The solid line represents the mean relation for luminosity class II and III stars. 61 Table 8 Mean Relation between W(SiO) and MK Spectral Type for Giant and Bright Giant Stars T W(SiO) MK eff Spectral Type (Ridgway et al. 1980) K1 4610 0.0 K2 4450 2.0 K3 4270 6.0 K4 4095 10.0 K5 3980 14.0 MO 3895 18.0 Ml 3810 22.0 M2 3730 26.0 M3 3640 30.0 M4 3560 34.0 M5 3420 38.0 M6 3250 42.0 62 (1980) has been included in the table to facilitate comparisons with the model atmosphere calculations in Section 4.8. A sequence of scans of K and M giant stars is shown in Figures 7 and 8 . Each scan begins and ends at slightly different wavelength points because of shifts in the wavelength scale caused by flexure (see Section 4.3). The nearly straight line with each spectrum is a blackbody curve of the temperature corresponding to the I(104)-L(400) color and passes through the mean of the data points used to define L(400). In B Gem the SiO bands are not apparent and the spectrum is fea tureless apart from noise. In K5 to M2 stars the SiO bands are defi nitely present but sufficiently weak that the spectrum nearly reaches the continuum just shortward of the (3,1) head. In cooler stars the bands are much stronger, and all points longward of the (2 ,0 ) head are significantly depressed. It is noteworthy that in all spectra the (3,1) band is stronger than the (2,0) band. This is in agreement with synthetic spectra calculations (Section 4.8). For the supergiants it is evident from Figure 6 there is a consid erable dispersion in SiO strength at a given MK type. Three of the supergiants identified in Figure 6 , 119 Tau (M2 Iab-Ib), a. Ori (M1-M2 Ia-Ib), and TV Gem (M0-M1 lab), have SiO equivalent widths nearly twice as large as giant stars of the same spectral type. Other M supergiants, notably RS Per (M4.5 lab), AD Per (M2.5 lab), and SU Per (M3-M4 lab) of the h and x Per cluster, have SiO strengths similar to those on the mean giant relation. The four la or Ia-Iab M supergiants observed, RW Cyg 63 . BETA GEM KO II IB >1860 1(400) ALPHA TAU 1-1 K5 III 3618 . DELTA OPH MAG 12,0) (3, n .00 U.05 WAVELENGTH (MICRONS) Figure 7. Scanner observations of 6 Gem (KO Illb), a Tau (K5 III), and 6 Oph (MO.5 III). The MIC spectral types are indicated below the star name as well as the calculated I(104)-L(400) blackbody temperature. The wavelength scale is in air microns. The fImres are on a magnitude scale per unit wavelength subject to arbitrary normalization. The band pass (88 $)„ an 0.1 mag flux intervals and the positions of the OH and SiO features are shown below. Each scan is accompanied by a blackbody curve (solid line) of the temperature corresponding to the I(104)-L(400) color. The wavelength interval used to define the L(400) magnitude and to set the height of the blackbody curve is shown above the spectrum of a Tau. . BETfi PEG 3262 XT LYR 3052 . RX BOO 2563 ■V' HRG BRNDPfiSS a U U *814.05 • U J WAVELENGTH (MICRONS) Figure 8. Scanner observations of B Peg (M2.5 II-III), XY Lyr (M4-M5 II), and RX Boo (M8:e) are shovm in the same format as Fig. 7. 65 (M3-M4 Ia-Iab), p Cep (M2 la), W Cep (M2 Ia-Iab), and BU Gem (M1-M2 Ia-Iab), ail lie below the mean giant relation. Supergiant scans of three stars are shown in Figure 9. Although a large variation of SiO strength among supergiants of the same spectral type is indicated by the data, further measurements are needed to show whether this is caused by actual differences in SiO abundance. Observations over a wider wavelength region or at higher resolution are needed to check that the region just shortward of the (2,0) SiO bandhead is a clean continuum region in all stars, as has been assumed. Also, higher resolution is required to detect any emis sion which could fill in and weaken the bands as observed with the scanner. Section 4.6 - Observations of Peculiar Supergiants Five unusual, high-luminosity supergiant stars were observed on the program. Scans of these objects are reproduced in Figures 10 and 11. S Per. The 8-color spectral type at the time of observation was M4.7 la. The 4 pm data show a sharp rise in flux at the location of both the (2,0) and the (3,1) bandheads suggesting that SiO was in emis sion at the time of observation. Emission in the 4 pm SiO bands has been previously suspected by Merrill and Stein (1976), whose low-reso- lution measurements at two epochs indicated a sharp upturn in the spectrum at the location of the SiO features. Vibrationally excited SiO has been detected in emission in the microwave region (Kaifu, Buhl, and Snyder, 1975). . VV CEP M2 IA-IAB 3091 ECL. BIN. 119 CE TAU M2 IAB-IB 3066 . RW CYG H3-U IA-IAB 2386 HAG U.00 H.05 WAVELENGTH (MICRONS) Figure 9. Scanner observations of the M supergiants W Cep (M2 Iaep), 119 CE Tau (M2 Iab-Ib), and RW Cyg (M3-M4 Ia-Iab) are shown on the Bame format as Fig. 7. . S PER M4E m 2238 H £ CHI RW CEP KO O-IR 3396 MRC (2,0) BflNDPfiSS U.00 WRVELENGTH (MICRONS) Figure 10, Scanner observations of the very luminous supergiants S Per (M4e la) and RW Cep (KO O-Ia) are shown on the same format as Fig. 7. SiO emission may be present at the location of the SiO (2,0) and (3,1) bands. NML CYG . VY CHfl H I 1422 HRG 12,0) BfiNDPfiSS WAVELENGTH (MICRONS) Figure 11. Scanner observations of the peculiar M supergiants NML Cyg, VX Sgr, and VY CMa are shown on the same format as Fig. 7. 69 RW Cep. The scanner data for this object also suggest that the (2,0) and (3,1) bands of SiO are in emission. This result, if confirmed, is surprising in view of the early spectral type of this object (KO O-Ia). However, it is possible that the emission at the SiO bands is only a feature of the most luminous supergiants since both S Per and RW Cep are generally considered to be among the most luminous late-type stars known. RW Cep is also well known for its abundance of emission lines in the violet (Merrill and Wilson, 1956) and a large infrared excess (cf. Dyck, et al., 1971). Again, observations at higher resolution are needed to confirm the presence of SiO emission. Also because the spectrum is peculiar and quite noisy, it is difficult to know that the wavelength scale is correct. VX Sgr, NML Cyg, and VY CMa. All three of these objects are well known for their excess radiation at infrared wavelengths (cf. Merrill, 1977). The present observations at 4 pm indicate that the region scanned is void of stellar absorption or emission features. The peculiar energy distributions observed strongly suggest that any photospheric SiO pre sent in these stars has been veiled by circumstellar emission. This result is consistent with the 4-5 pm observations of Geballe, Wollman, and Rank (1973) and Wollman, et al. (1973). No photospheric 4.7 pm CO lines were observed in VY CMa or NML Cyg despite strong first-overtone CO absorption at 2.3 pm. The SiO (3,1) band was absent in their data for both VX Sgr and NML Cyg. Although the blackbody continua shown in Figures 7 to 9 all have about the same slope, this is no longer true at very cool temperatures. 70 Table 9 shows how the blackbody magnitude changes over the width of the interval scanned as a function of temperature. Only at temperatures below 1500 K does the slope show noticeable change. For temperatures less than 720 K the blackbody flux increases to longer wavelengths. Blackbody fits to the general trend in the spectra yield temperatures of about 700 K, 1500 K, and 400 K for VX Sgr, NML Cyg, and VY CMa, respectively. In Figure 11 the blackbody curve indicated for VY CMa is based on the simultaneous measurement of 1(104). The difference between the observed and calculated 4 ym slopes clearly documents the presence of excess emission in this spectral region. No blackbody curves accompany NML Cyg and VX Sgr because simultaneous 8-color photometry could not be obtained. The nature of the infrared flux distributions of highly luminous cool supergiants has been the subject of much controversy. Humphreys (1974) and Gilman (1974) have suggested that the reported weakening of absorption lines in the near infrared is due to chromospheric H- bound- free emission, and that optically thin free-free radiation is responsi ble for the observed 3-8 ym energy distributions. The results of Fawley (1977) indicate that the identification of H- bound-free emission is erroneous and that the excess can be explained by overcorrections for interstellar extinction and TiO opacity. Fawley identifies the 3-8 ym excess with thermal reradiation from the circumstellar shell. The presence of thermal circumstellar water vapor emission (Tsuji, 1978b) may further complicate the interpretation of the observed energy distri butions in the 5-8 ym region. Table 9 Blackbody Indices in the 4 ym Region THETA TEMPERATURE (K) L(400)-L(406) 0.1 50400 0.065 1.0 5040 0.061 1.5 3360 0.056 2.0 2520 0.052 2.5 2016 0.047 3.0 1680 0.043 5.0 1008 0.022 10.0 504 -0.035 20.0 252 -0.151 L(400) = magnitude per unit wavelength at 3.9965 ym L(406) = magnitude per unit wavelength at 4.0576 ym 72 Section 4.7 - Observations of Mira Variables The observations of Hinkle, et al. (1976) indicate that the SiO strengths in Mira variables vary markedly with phase. Unfortunately, it was not possible to follow individual stars with phase on this pro gram. A total of ten Miras were observed, two of which were scanned a second time after an interval of about one year. Although the behavior with respect to phase is not well defined in these data, the strongest SiO absorption was observed in stars near minimum light while SiO was weak or absent in stars near maximum light. Both of these results are consistent with Hinkle, et al. (1976). Scans of the Mira variables are presented in Figures 12 to 15. The I(104)-L(400) blackbody temperatures and calculated 4 ym continuum levels have been indicated. In four cases the simultaneous 1(104) magnitudes observed with the 0.4-m Kitt Peak telescope have been used in this cal culation. For the other SiO observations, 1(104) magnitudes have been estimated from published infrared light curves (Lockwood and Wing, 1971; Wing and Lockwood, 1973) and unpublished scanner (Wing, 1967a) and 8- color data. Most of the Miras observed show rather strong absorption at the positions of both SiO bands so that there can be little doubt regarding the identification of this molecule. However, some of the spectra have a different character. In some cases the SiO bands seem to be absent, and it's not clear at this resolution if this is due to a deficiency of SiO molecules in the atmosphere, or the presence of additional absorp tion in this region (e.g.^O), or to a filling in of the SiO features . R RND S6.6E 2128 3444.852 0M1CRON CET GM6E 2802 ’ 3142.959 IK TRU H8.0-H10 1364 ’ 3417.911 13,1) 4.05 WAVELENGTH (MICRONS) Figure 12. Scanner observations of the Mira variables R And (phase 0.77), o Cet (phase 0.88), and IK Tau (phase 0,5) are shown on the same format as Fig. 7. U OR I M8E 2572 3455.942 R CNC M6E-H8E 2811 3456.060 . U ROL S3.9E 3036.727 OH BflNDPRSS U.00■ UU 4.05 1•UJ WAVELENGTH (MICRONS) Figure 13. Scanner observations of the Mira variables R Aur (phase 0.79), U Ori (phase 0.16), R Cnc (phase 0.87), and W Aql phase 0.20) are shown on the same format as Fig. 7. R C T G S3.9E-S6.8E 2070 - 3447.675 '1 . CHI CTG S7,1E-S10 2325 3036.745 DH WAVELENGTH (MICRONS) Figure 14. Scanner observations of the Mira variables R Cyg and x Cyg are shown on the same format as Fig. 7. Upper observation was obtained at phase 0.34, middle at 0.31, and lower at 0.17. . CHI CTG S7.1E-S10.1E 2268 34414.699 R CflS M6E-H8E 1899 3036.990 . R CHS M6E-H8E 1971 3 W 2 . 9 3 1 HRG (2.0) U.00U.00 11.05 WAVELENGTH (MICRONS) Figure 15. Scanner observations of the Mira variables x Cyg (phase 0.17) and R Cas (phase 0.68 and 0.63) are shown on the same format as Fig. 7. 77 by emission by the molecule itself. Furthermore, the hydrogen line Bae which is nearly coincident with the location of the (3,1) head, may appear in emission at phases near maximum light. At high resolution SiO emission has been noted in Miras (Ridgway, Hall, and Carbon, 1977), but it is not known if this is a common occurrence. Line doubling has been noted for CO (Hinkle, 1978) and other features and may also occur for SiO at some phases, further complicating the interpretation of the SiO band strengths. The observations are summarized in Table 10. The first three columns contain the HD number, the HR=BS number, and the variable star name. Column 4 is the spectral type determined by simultaneous 8-color photometry. Column 5 is the Julian date (+2440000) of observation. Column 6 contains the phase counted from visual maximum. Phases reported here are based on observations made by the American Association of Vari able Star Observers (Mattei, 1978) except for IK Tau for which the elements of Wing and Lockwood (1973) were used. Columns 7 and 8 are the 1(104) and L(400) magnitudes derived from 8-color and scanner data, respectively. The calculated 8-color and I(104)-L(400) color tempera tures (discussed in Section 5.3) are in columns 9 and 10. For stars which do not have simultaneous 8-color data, the magnitudes and color temperatures in columns 7 and 10 are enclosed in parentheses. The final column contains the calculated SiO equivalent width in Angstroms. These values have been calculated in the same manner as for the non-Mira stars. Because of the peculiarities of the 4 ym spectra sometimes observed and because of the problems of interpretation rioted earlier, Table 10 4 vim Scanner Results for Miras 8-color W(SiO) HD HR=BS Name Spectrum JD Phase 1(104) L(400) T(8-c) T(l-4ym) A 1967 90 R And 3444.85 0.77 (3.2) -0.279 (2128) 19.3 14386 681 o Cet M 6.8 3442.96 0.88 -1.087 -3.434 2659 2802 (-11.5) IK Tau (M10) 3447.91 0. 5±0.1 (4.1) -2.050 (1384) 59.5 34019 1707 R Aur 3455.99 0.79 (1.52) -1.313 (2462) 15.0 39816 2063 U Ori 3455.94 0.16 (0.95) -1.711 (2572) 17.6 69243 3248 R Cnc 3456.06 0.87 (1 .2 ) -1.136 (2811) -2.5 W Aql 3036.73 0.20 -1.705 185456 R Cyg 3034.72 0.34 (3.8) 0.283 (2 1 2 0 ) 74.7 185456 R Cyg 3447.68 0.31 3.780 0.165 1562 2070 76.3 187796 7564 X Cyg 3036.75 0.17 (0 .0 ) -3.112 (2325) 58.5 187796 7564 X Cyg M7.7 3444.70 0.17 -0.038 -3.221 1946 2268 34.7 224490 9066 R Cas (M10) 3036.99 0.68 (1.4) -2.615 (1899) 38.2 224490 9066 R Cas M9.5 3442.93 0.63 1.452 -2.414 1384 1971 42.1 79 the calculated values of W(SiO) may not be meaningful. In the case of o Cet the spectrum is so obviously peculiar that the value of W(SiO) has been enclosed in parentheses. Individual objects are discussed in the following paragraphs. R And. A single 4 ym scan of this strong S star was obtained during rising light. Both the (2,0) and (3,1) bands are clearly visible but only of a strength comparable to a K5 giant star. o Cet. A single observation was made shortly before maximum light, when the 8 -color spectral type was M 6 .8 . The spectrum is peculiar with no identifiable features. The excess above the continuum level in the longward half of the spectral region may be due in part to Ba emission. IK Tau (NML Tau) . Strong SiO absorption from both the (2,0) and (3,1) bands is evident in a scan obtained at phase 0.5+ 0.1. IK Tau was invisible at the 1.3-m, and unfortunately it was impossible to obtain a simultaneous classification from 8 -color photometry with the 0.4-m telescope. However, since IK Tau is the only star known to reach spectral type M10 consistently at every minimum, it may be assumed that the type was at or near M10 when this SiO scan was made. An 1(104) magnitude of 4.1 has been estimated from the light curves of Wing and Lockwood (1973). R Aur. A scanner observation obtained in November 1977 on the rising branch of the light curve shows a decrease in flux at the posi tion of the (2,0) bandhead. However, the (3,1) head is not visible in the scan. Perhaps the (3,1) band has been filled in by Ba emission. 80 Clearly, higher resolution measurements are required to interpret the spectrum properly. U Ori. A scan obtained shortly after maximum light is very similar to the R Aur observation. The (2,0) bandhead is present, but the (3,1) bandhead is not. R Cnc. A single observation of this star was obtained approaching maximum light. The (2,0) bandhead is absent and an emission feature, probably Ba, is observable near the location of the (3,1) bandhead. W Aql. This nearly pure S-type Mira was observed shortly after maximum light. No features are visible in the spectrum. R Cyg. This star, another nearly pure S-type Mira, exhibited the strongest SiO bands observed. Observations were obtained in September 1976 at phase 0.34 and in October 1977 at phase 0.31. Although the 1976 scan is noisier, both observations show similar SiO strengths. R Cyg was more than 0.1 mag fainter at 4 pm during the latter observa tion . X Cyg. Observations of this mild S star in September 1976 and October 1977 were both made at phase 0.17. The (2,0) and (3,1) bands are visible in both spectra but are weaker in the 1977 data. As in the case of TiO absorption in Miras (Wing, 1967a), the strength of the SiO features at a given phase may vary from cycle to cycle. At L(400), X Cyg was more than 0.1 mag brighter at the latter epoch. R Cas. Observations near minimum light (phase 0.68 and 0.63, respectively) were made in September 1976 and October 1977. The spectral type of this star at normal minimum has been adopted as the 81 definition of type M10 (Wing and Lockwood, 1973), and the type at the time of the 1977 observation was M9.5. The (2,0) and (3,1) bands are strong at both epochs. In addition, an absorption feature is visible in both spectra near the location of the 2^SiO bandhead. High resolu tion measurements are needed to confirm this identification and to derive silicon isotope ratios. L(A00) differed by 0.2 mag at the two epochs. Although only a relatively small number of observations were obtained some trends are evident. Among the M-type Miras, the strongest SiO bands were observed at the latest spectral types, which occur near minimum light. Near maximum light the bands are considerably weaker, and in fact are much weaker than normal M giant stars of the same TiO types (about M6 ) . A similar effect is observed in S-type stars whose SiO strength varied from vanishingly small to among the strongest ob served. Any systematic differences between the M and S stars are masked by the large changes with phase displayed by both. Since the two stars of latest type, R Cas and IK Tau, show strong SiO bands, it is evident that SiO absorption dominates over anything else in this region at the lowest temperature. This result would appear to argue against the idea that the SiO features in warmer Miras are obliterated by absorption, by water vapor, or some other temperature sensitive molecule. Likewise, since the nearly pure S star R Cyg, whose spectrum is full of unidentified bands in other regions, shows strong SiO and no evidence for other absorbers, it seems unlikely that the weakness of the SiO bands in other S stars (e.g.W Aql) can 82 be explained by absorption by other molecules. Thus, this indicates that there are no strong absorbers in this spectral region other than SiO in stars of any type. It seems likely, therefore, that the peculiar shapes of the spectra of some Miras are more the result of emission by SiO and/or Ba, rather than absorption by other molecules. Section 4.8 - Computation of Synthetic 4 pm Spectra The synthetic spectrum program MOOG was used to generate theoreti cal spectra to compare to the observed 4 pm scans. The line list in cluded the first-overtone SiO bands, the bands of the Av=-3 sequence of the CN red (A2 tt-X2 Z) system, the fundamental vibration-rotation bands of OH, and atomic lines. The computation of the synthetic spectra is discussed in this section. The vibrational and rotational constants used for the calculation of the SiO line positions were taken from Table 1 of Beer, Lambert, and Sneden (1974). These values were obtained from microwave data and the observed first-overtone line positions in a Ori. The standard isotopic relations (Herzberg, 1950) were used in the computation of the line positions for 29SiO and 3 0 SiO. The transition probabilities for SiO adopted here are those calcu lated by Hedelund and Lambert (1972). These values are based on a fit to the electronic dipole moment measurements of Raymonda, Muenter, and Klemperer (1970). A Morse potential function was assumed. The rota tional line oscillator strengths have been computed on the assumption of negligible vibration-rotation interaction. Beer, Lambert, and 83 Sneden (1974) have shown that the effect of vibration-rotation inter action is small for the first-overtone lines. Isotopic lines were assumed to have the same gf values as the corresponding lines of 2 8 SiO. The OH fundamental-band line positions were calculated from the constants derived by Maillard, Chauville, and Mantz (1976) with a computer program furnished by D. L. Albritten (see Albritten, et_ al., 1973, for a description of the program). A set1 of isotopic relations, also furnished by Albritten (1978) , was used to compute line positions for 170H and 180H. The accuracy of these positions is unknown since the isotopic lines have not been observed in the laboratory. The experimental OH oscillator strengths of Roux, d'Incan, and Cerny (1973) were used for the (1,0) and (2,1) bands. These values were determined from spectra of an oxyacetylene flame in thermal equili brium. In the calculations the rotational line strength formulae of Kovacs (1969) were used and the experimental polynomial fits for the Herman-Wallis factor were adopted. Since absolute strength measure ments have not been reported for the higher vibrational levels of this sequence, the relative transition probabilities of Murphy (1971) were scaled to the absolute values of Roux, d ’Incan, and Cerny (1973) and the Herman-Wallis factors were taken to be unity for these bands. The OH oscillator strengths must be regarded as quite uncertain. The adopted values differ considerably from the theoretical results of Mies (1974). The observed transition probabilities for the (1,0) atd (2 ,1 ) bands are approximately a factor of two smaller than the 84 theoretical values. Also, the theoretical values predict strong vibration-rotation interaction for the fundamental bands. The CN line positions have been calculated from the constants of Fay, Marenin, and van Citters (1971). These values are based on the measurements of Davis and Phillips (1963) in the visible and near in frared and cannot accurately reproduce the observed infrared line posi tions of Cerny, et a l . (1978). However, the calculated positions are accurate enough for the bandpass synthesis used in this study. Posi tions for both 32CN and ^3CN lines were calculated. For the oscillator strengths and dissociation energy of CN, I have adopted f = 1.0 x 10-3 and D = 7.89 eV (Carbon, 1973). The 00 0 Franck-Condon factors of Spindler (1965) based on RKR potentials have been used. The Hc5nl-London factors of Earls (1935) were normalized via the rules of Tatum (1967). The atomic line list and semi-empirical gf values of Kurucz and Peytremann (1975) were used in the computations. The line positions should be sufficiently accurate for bandpass synthesis. The solar composition atmospheres of Johnson, Bernat, and Krupp (1980) and Bell, et al. (1976a) were used to generate the synthetic spectra. The abundances of the elements adopted were those of Gustafsson, et al. (1975). Terrestrial values were used for the isotope ratios of carbon, oxygen, and silicon. In the dissociation equilibrium a total of 74 molecules were included. 85 A synthetic spectrum calculated with the Johnson, Bernat, and Krupp (1980) solar-composition opacity-sampling model of effective temperature 3200 K and log g = 1.0 is shown in Figures 16 to 20. A microturbulent velocity of 2 km/s was adopted. Virtually all of the features calculated to be visible are due to either SiO or OH. The isotopic (2,0) bandheads of 29SiO and 30SiO can be weakly seen in the spectra at 2481.7 and 2467.2 cm-1, respectively. Both isotopic band heads have been seen in some late-type stars (Hinkle, et al., 1976; Merrill and Ridgway, 1979). The calculated spectra have been convolved with the spectrometer bandpass to produce synthetic 4 pm scans. A sequence of synthetic scans is shorn in Figure 21. It can be seen that the region is pre dicted to be featureless in warmer stars (T > 4500 K ) . This result e supports the use of smooth energy distributions for 6 Gem (KO Illb) , a Ari (K2 Illab), and a Boo (K2 IIIp) in the reduction procedure. Both the OH and SiO depressions are weakly present in the 3800 K synthetic scan, and the strengths of both molecules are predicted to increase towards lower effective temperatures. The depression near 3.985 pm is caused by about a dozen strong lines of OH as can be seen from a comparison of Figures 3 and 20. The OH depression occurs at the short- wavelength edge of the region scanned. The downturn in flux due to OH can be seen in some of the stellar data in this chapter and in Appendix A. To calculate SiO equivalent widths from the theoretical scans, a procedure similar to the method used to treat the observations was 8 6 WAVELENGTH IN ANGSTROMS <106.20 <10600 <10580 wdsbo <105.40 <10820 ATOM ATOM SIO SIO OH OH D.O 3 2 0 0 / 1 . 0 / S HAVENUHBEA CN CN <10620 <10600 <10580 H0560 <10540 <10520 <10500 <10<160 <10<160 HPVELENDTH IN ANGSTROMS Figure 16. A portion of a synthetic spectrum generated with MOOG. The model atmosphere used was an opacity-sampling log g = 1.0, Te = 3200 K model. Solar elemental abundances, terrestrial isotope ratios, and a microturbulent ve locity of 2 km/s were assumed in the calculations. The positions of atomic, SiO, OH, and CN lines are indicated above and below. Molecular lines of the terrestrially most abundant isotope are indicated with arrows while short lines mark features from less abundant isotopes. The ^ S i O bandhead at 2467.2 cm is weakly visible in the computed spectrum. 87 WAVELENGTH IN ANGSTROMS 40440 40420 40400 4O3B0 ----40360 -- ATOM ATOM 0H 0H 0.0 0.0 3300 / 1.0 /5 HAVENUHBER CN CN 40440 40420 40400 40380 40360 40340 40320 40300 402B0 WAVELENGTH IN ANGSTROMS Figure 17. Continuation of the synthetic spectrum shown in the previous figure. The 28SiO (3,1) bandhead is at 2472.9 cm-l. The 28SiO bandhead at 2481.7 cm-^ is weakly visible in the computed spectrum. 8 8 WRVELENGTH IN RNGSTROMS 10260 102.10 10220 10200 MO 1.80 101,60 >101110 10120 RTOM IIII Ill 1 BI II II I II I II 1 I II I III I II II RTOM /N /Is /ts ''T' /tv/K/tv/^/tv/*v/f\/tv/ts./tv/N /^/ts/ts /N4v/K4v 'N't'* 'f'/tv / vK SIO SIO ' 1 N 7 \ 7 \y NKM7I 4*1' 44' OH OH ys , f w 3 2 0 0 / 1 . 0 / S sues1 ------M r HRVENUMBER A * s /txJ^m s /tXtv /tv /fv /TVKi^v /fv /fv /|v4»^\ /fvtxfvTtftv CN ^ ii inn CN VIW4I'' 4v 44* 1 1 1 1 I*/' 4444*1/ >10260 >102«10 10220 10200 101B0 10160 10110 10120 WRVELENGTH IN ANGSTROMS Figure 18. Continuation of the synthetic spectrum shown in the previous figure. Most of the strong lines are due to the (2,0) band of 28SiO. 89 WRVELENGTH IN RNGSTROMS 40040 ------399,GO39980 RTOM 51 III RTOM OH OH 0.0 3200/1.0/5 HRVENUMBER CN CN 40100 40080 40060 40040 40020 40000 399B0 39960 39940 WRVELENGTH IN RNGSTROMS Figure 19. Continuation of the synthetic spectrum shown in the previous figure. The (2,0) 28SiO bandhead occurs at 2497.2 cm--*-. The region shortward of the (2,0) head is nearly free of line blanketing. 90 WAVELENGTH IN ANGSTROMS 39920 39900 39880 39860 398,40 398,20 396,00 39780 39760 RTOM RTOM SIO OH OH 0.0 3200/1.0/S 2SiBr"~ MAVENUMBER CN CN 39920 39900 39880 39860 39820 39800 39780 39760 HAVELENG N ANGSTROMS Figure 20. Continuation of the synthetic spectrum shown in the previous figure. Most of the strong lines are due to OH. 91 4500/2.25 SOLAR 2 KM/SEC 3800/1. 0 SOLAR 2 KM/SEC 3600/1.0 SOLAR 2 KM/SEC 3400/1.0 SOLAR 2 KM/SEC 3200/1o 0 SOLAR 2 KM/SEC 3000/1.0 SOLAR 2 KM/SEC OH (2 . 0 ) BANDPASS WAVELENGTH (MICRONS) Figure 21. Synthetic k ym scanner spectra are shown on the same format as Fig. 7. All spectra have been computed with solar elemental abundances, terrestrial silicon, oxygen, and carbon isotope ratios, and a 2 lan/s micro- turbulent velocity. The effective temperatures and surface gravities of the models are indicated to the left of the spectra. The uppermost model is from the grid of Bell et al. (1976a). All other models are from Johnson, Bernat, and Krupp (1980). 92 adopted. For each model a synthetic color temperature was computed from a blackbody fit to the continuum fluxes at 1(104) and L(400). This color temperature was used then to calculate a blackbody continuum in the SiO-depressed region. The SiO equivalent widths were computed by integrating the synthetic scans over the same wavelength intervals used for the observational data. The calculated SiO equivalent widths are tabulated in Table 11. All models assume solar elemental abundances and terrestrial isotope ratios. For each model SiO equivalent widths have been computed for a range of microturbulent velocities. The calculated values are com pared to the observations in the next section. Section 4.9 - Comparison between Observed and Synthetic Spectra The observed line strengths are determined primarily by four quantities: effective temperature, surface gravity, chemical composi tion, and microturbulent velocity. It is impossible from low resolution observations to determine all of these simultaneously. However, the effective temperature can be determined independently from color measurements, and the models can be used to explore the effects of varying the other parameters. In this section solar-composition model atmospheres have been used to study the relation between W(SiO) and effective temperature for various values of surface gravity and microturbulent velocity. The effect of varying the composition could not be studied since realistic M star models are only available for solar composition (Johnson, Bernat, and Krupp, 1980). 93 Table 11 Synthetic SiO Equivalent Widths (£) W(SdO) in £ E, = 2 km/s £ = 4 km/s E, = 7 km/s Teff (K) log g 4500 2.25 -0.4 4000 0.0 4.8 1.0 4.6 4.9 2.0 4.6 3800 0.0 11.9 1.0 12.2 14.0 2.0 10.6 3600 0.0 23.9 1.0 22.0 27.5 2.0 16.5 3400 0.0 34.0 44.0 1.0 28.6 37.2 2.0 20.4 3200 0.0 41.9 1.0 32.6 43.0 2.0 22.9 3000 0.0 45.5 62.6 1.0 34.6 45.8 2.0 24.7 94 In Figure 22 the effect of varying the surface gravity is shown for a constant value of the microturbulent velocity (2 km/s). Models with log g = 0.0 are denoted by "x", open circles represent models with log g = 1 .0 , and plus (+) symbols indicate models with log g = 2 .0 . All models with the same value of log g are connected with dashed lines. The observed mean giant and bright giant relation is shown as a solid line. The temperature scale of Ridgway, et al. (1980) has been used to convert the abscissa of the observed relation from MK spectral type to effective temperature. The synthetic spectra predict a mono tonic increase in SiO strength to cooler temperature in accordance with the giant star data. For cooler stars the SiO bands are predicted to be stronger in stars of lower surface gravity. The importance of the choice of the microturbulence velocity has been tested for models with a surface gravity of log g = 1.0. In Figure 23 model results are shown for a microturbulent velocity of 2 km/s (open rectangles) and of 4 km/s (solid rectangles). At the warmer temperatures the synthetic SiO equivalent width is nearly inde pendent of microturbulent velocity, but it becomes increasingly sensi tive to microturbulence in the cooler models as the bands saturate. The calculated SiO strengths are for most cases weaker than the observed values. It is not clear what is the cause of the discrepancy. The possibilities include: (1) the Si and/or 0 abundances differ from the solar values, (2) the SiO oscillator strengths are in error, (3) the models do not accurately represent the atmospheric structures, and (4) non-LTE effects are important. However, the general increase 95 g / u@e ® v / fU-JL-Jt—rt— {L_J— fl n n fl a I— 5 0 0 0 :CTIVE Ti Figure 22. Plot of W(SiO) in Angstroms vs. effective temperature for solar-composition opacity—sampling models with different surface gravities and a fixed microturbulent velocity of 2 Ian/s. The positions of models with log g = 0.0, 1.0, and 2.0 are indicated with ' V , "o", and "+" symbols, respectively. Sets of models with the same surface gravities have been connected with dashed lines. The solid line is the mean giant and bright giant relation taken from Table 8. The effective temperature scale of Ridgway et_al. (1980) has been used to convert from spectral type to effective temperature. 96 rr=T-T- \ f 2 (cm/s ULU ’FECTBVE TEMPERATURE CK) Figure 23. Plot of W(SiO) in Angstroms vs. effective temperature for solar-composition opacity-sampling models of log g = 1.0 showing the effect of microturbulence. Open rectangles indicate the results obtained with a microturbulent ve locity of 2 km/s while solid rectangles represent values computed xjith k lon/s. Sets of models with the same micro turbulent velocity have been connected with dashed lines. The solid line is the mean giant and bright giant relation taken from Figure 22. 97 in strength with decreasing temperature is at least qualitatively the same. The small scatter in the observed relation for normal giants (as noted in Section 4.5) implies that for these stars there exists a relatively small range in the chemical and physical variables. For the cooler stars an enhancement in SiO strength can be brought about by either lowering the surface gravity or increasing the microturbulence. Unfortunately, it is impossible to distinguish between these two effects on the basis of these measurements alone. It will be important to study a sample of M stars at high resolution to determine the range of microturbulent velocity in the atmospheres. At present, the interpretation of the results is hampered by a lack of knowledge of the atmospheric parameters of M stars. These uncertainties are largest in the coolest stars where the model atmos phere results are most sensitive to both log g and the microturbulent velocity. For this reason, additional scanner measurements of SiO strengths in the cooler stars would not be useful at the present time for deriving elemental abundances. Also, abundance differences among the cooler stars may be masked by intrinsic differences in these parameters. The observed differences in SiO strengths among the M supergiants could, in part, result from these effects. The SiO bands may prove to be very useful for abundance studies of warmer stars (T > 3600 K) where the bands are weak and show little dependence on log g* CHAPTER V INTERPRETATION OF INFRARED COLORS Section 5.1 - Introduction The problem of determining the temperatures of late-type stars is an important one and has been the subject of much recent work. The fundamental parameter of interest is the effective temperature, which can be obtained directly from the angular diameter and bolometric mag nitude of a star. The number of direct measurements of effective temperature is increasing rapidly, and it is important to be able to calibrate the measured effective temperatures in terms of one or more temperature-sensitive parameters which can be conveniently, accurately, and quickly obtained. A valid system of relative temperature indices can be used to interpolate between the effective temperature data, and the calibration can provide a means of determining the effective tempe’rature of other stars. Color temperatures, obtained from a blackbody fit to the observed fluxes, expressed on an absolute scale, at any two wavelengths, are particularly useful for this purpose. However, color temperatures must be interpreted with care. Since the energy distribution of any star differs from a blackbody curve, different color temperatures will be obtained with different choices for the two wavelengths. Color 98 99 temperatures are affected by the line absorption and continuous opacity in both bandpasses. They are, of course, also affected by interstellar reddening. Despite these problems, color temperatures have been frequently used to estimate the effective temperatures of stars. Ideally, any system established for this purpose should have the following charac teristics. First, the two wavelengths used to form the color index must be widely separated in wavelength so as to be sensitive to changes in the slope of the energy distribution with respect to temperature. Second, since the spectra of most late-type stars are heavily blanketed in the visible region, bandpasses should be selected in the near infra red or infrared where continuum regions can be located. Narrow-band measurements are preferable, since even in the infrared, wide-band photometry cannot avoid molecular bands and atomic lines. The differ ence between the continuous opacities at the two wavelengths used to form the color index should be sufficiently small that the continuous fluxes will both originate from the same range of stellar layers. This will make the color temperatures insensitive to differences in the tem perature structure caused by composition variations among stars. Color temperatures obtained at wavelengths selected on the basis of these criteria will have values close to the effective temperature, and the remaining differences will be systematic and can be calibrated. The calibration of the color temperature in terms of the effective temper ature can be made either from direct measurements (angular diameters and bolometric magnitudes) or from calculations made with model atmos pheres. 100 A new effective temperature scale for luminosity class III K and M stars has been determined from angular diameter measurements and infrared photometry (Ridgway, et al., 1980). The new scale assigns systematically higher temperatures to M giants than previous scales (Johnson, 1966; Dyck, Lockwood, and Capps, 1974). The new calibration is given both in terms of the color temperature on ..the 8 -color system and also as a function of spectral type. According to the empirical results, the color temperatures measured on the 8 -color system are lower than the effective temperatures by 150 K at MO and by 650 K at M 6 . The implication of this result is that the 0.7540 pm shortward continuum point is affected by blanketing which increases to later spectral types. It is therefore of interest to test color temperatures that use differ ent continuum points to see if any of them are more direct indicators of the effective temperature. Extensive grids of line-blanketed, flux-constant models (cf. Bell, et al., 1976a; Johnson, Bernat, and Krupp, 1980) are available and can be used to calculate synthetic energy distributions and colors for comparisons with observations (cf. Gustafsson and Bell, 1979). The synthetic colors can be compared with the measured values to test the accuracy of the model atmosphere predictions and to calibrate color indices in terms of fundamental parameters including the effective temperature. The model atmosphere results, therefore, provide an independent test of the effective temperature scale derived from angular diameter measurements. 101 Detailed comparisons between observations and model predictions have proved to be difficult. Wide-band colors are important but have certain disadvantages since they involve complex integrations of stellar and telluric features with the telescope-photometer-filter sensitivity function over large wavelength regions. Since numerous atomic and molecular lines invariably occur in any wide spectral region of a cool star, the interpretation of wide-band colors is complicated by uncertainties in the line data (missing lines, errors in the dissocia tion energies and gf values) and by the sensitivity of line blanketing to changes in temperature, surface gravity, chemical composition, and microturbulent velocity. In addition, systematic discrepancies may arise if LTE is assumed in computing the spectrum. Since all of these parameters affect wide-band colors, it is difficult to use them to determine accurate values of effective temperature, surface gravity, and chemical composition. Narrow-band colors, however, can be measured at points nearly free of blanketing so that the comparison between observed and calculated colors is not subject to the large uncertainties mentioned above. In the present study narrow-band magnitudes were measured at four continuum points between 1.29 and 4.00 pm with the Kitt Peak grating spectrometer. For most of the stars observed, measurements are also available on the Wing 8 -color system so that color temperatures can be formed over an extended wavelength region. 102 Section 5.2 - Description of the Bandpasses The purpose of the infrared colors program is to provide narrow band measurements of infrared fluxes in oxygen-rich giants and super giants at a series of widely spaced continuum points in the infrared. To provide the widest possible wavelength coverage, data obtained with the Kitt Peak infrared scanner has been combined with measurements made with the Wing 8 -color system. The program wavelengths cover the interval from 0.7 to 4.0 pm. The 8-color photometric system has been described in detail else where (Wing, 1971). The continuum points for this system are at 0.7540 pm, 0.7810 pm, and 1.0395 pm. The 0.7540 pm point is used as a con tinuum point for K4 to M 6 stars while the 0.7810 pm serves as a con tinuum point for G and K stars. In the 8 -color reduction procedure corrections are applied at 0.7540 pm for slight contamination by CN (White and Wing, 1978). The 1.0395 pm bandpass is an excellent con tinuum point in a wide range of late-type stars, and absorption seldom exceeds 5% in any star (Wing, 1967b). The half power bandpasses for the 8 -color filters are 50 A (=0.005 pm), 40 R, and 50 R at 0.7540 pm, 0.7810 pm, and 1.0395 pm, respectively. For stars later than M 6 , V0 bands suddenly appear strongly at 0.7540 pm, contaminating the short- ward continuum point of the 8 -color system. The points measured with the Kitt Peak grating spectrometer (AUDREY) will now be discussed individually. 103 1.287 pm (7768 cm-1) . Magnitudes reported for this wavelength, referred to as J(129), represent an average of measurements made at three overlapping bandpasses centered at 1.286 pm, 1.287 pm, and 1.288 o pm, with an exit slot of 29 A (0.0029 pm) in third order. The effec- o tive bandpass of the resulting average is about 40 A. Inspection of high resolution spectra of a Ori, a Her, p Gem, and a Sco indicates this region is nearly free of both stellar and telluric features. 2.101 pm (4758 cm-1) . Magnitudes for this point, designated K(210), are the average value of measurements at five wavelengths between 2.098 pm (4766 cm-1) and 2.104 pm (4751 cm-1). Data were obtained in second o order (bandpass = 44 A ) , and the effective bandpass of the average is about 80 X. This region in e Tau is shown in Figure 24 and in a Ori in Figure 25. For the a Ori data (solid line), a synthetic spectrum (plus symbols) computed with only CN lines is also shown. Line positions used are from Cerny, et al. (1978) and CN strengths were computed fol lowing Carbon (1973) . It can be seen that many of the weak lines ob served in this region are due to CN. In Table 12 the mean depression in magnitudes across the bandpass as determined from high-resolution spectra has been compared with the CN index of the 8 -color system. The depressions are small but correlate well with the near-infrared CN data. To correct the photometry for CN contamination to a first approximation, the following quantity has been added to the observed fluxes at this wavelength: Absorption at 2.101 pm (mag) = 0.40 CN (8 c) (5.2-1) 104 WAVELENGTH ffl) 22850 22800 22750 Epsilon Tau K1 III 00 CO 4370 WAVENUMBER ( c m '1) Figure 24. Kitt Peak FTS spectrum of e Tau in the region of the 2.101 pm bandpass of the infrared colors program. The top spectrum is a solar spectrum, the middle spectrum is the stellar spectrum, and the lower spectrum is the ratio of the two. Line positions are from the Hall (1970) atlas. ______RLPHfl ORI I. 0 14755' 4760' 14765' U77b' HRVENUMBER Figure 25. Comparison of an observed spectrum of a Ori (solid line) with a synthetic spectrum (+ symbols) in the region of the 2.101 pm bandpass of the infrared colors program. The region scanned was from approximately 4751 cm""-*- (2.104 pm) to 4765 cm“l- (2.098 pm). Telluric absorption features are indicated below the spectrum. The syn thetic spectrum was computed with CN lines only. 106 Table 12 Comparison of 2.1 pm Bandpass Depressions and 8-color CN Indices 2.101 pm Bandpass 8-color Depression CN Index Star (mag) (mag) a Tau 0.032 0.086 p Gem 0.033 0.072 a Sco 0.069 0.190 a Ori 0.072 0.178 a Her O.O69 __ 107 where the 8 -color CN index is defined to be the mean of the depressions observed at filters 4 and 8 in magnitudes (White and Wing, 1978). 2.2850 pm (4375 cm-1). This bandpass is just.shortward of the (2,0) bandhead of 12C0 at 4360 cm-1. This region in e Tau is shown in Figure 26. Although a moderate amount of telluric absorption occurs in this region, only a few weak stellar features are observable at high resolution. Magnitudes reported for this wavelength are the average of scanner data obtained in second order at five points between 2.282 pm (4381 cm-1) and 2.288 pm (4370 cm-1). They are designated I<(228) and o have an effective bandpass of about 80 A. 3.996 pm (2502 cm-1) . Continuum magnitudes at this wavelength, referred to as L(400), were obtained from the 4 pm scans of the SiO first-overtone bands. This spectral region is discussed in Section 4.2. Section 5.3 - Observational Data A total of 111 bright late-type stars were observed at one or more wavelengths of the infrared colors program. Measurements at 3.996 pm were made as part of the SiO continuous scan program described in Chapter IV and at 1.287, 2.101, and 2.285 pm during 5 nights and 2 days in November 1977 with the infrared scanner. Data were obtained at all four infrared wavelengths for 50 stars. The spectral types of the "oxygen-rich" program stars range from G1 to M 8 with the majority being IC and M giants. Observations on the Wing 8 -color system have been used to provide 1(104) magnitudes and a near-infrared color temperature. The spectral region covered by the 108 WRVELENGTH (R) 21000 20950 Epsilon Tau K1 III o coo © oo © o o tip © © © co i I I s ] R ICR _i__l___ .___ I .___ . I l_ j .___ .___ I--- .--- 1--- .--- .--- 1--- 1--- 1--- 1--- 1--- 1--- 1--- 1--- 1--- 1--- 1--- L H7BD M770 4780 4790 WRVENUMBER Figure 26. Kitt Peak FTS spectrum of e Tau in the region of the 2.285 pm bandpass of the infrared colors program. The format is the same as Fig. 24. The 1 CO (2,0) bandhead can be seen at 4360 cm-^. 109 8 -color and infrared scanner data extends from 0.75 to 4.0 pm and includes the region where the majority of cool-star flux is emitted. The observational data for non-Miras are shown in Table 13. The observed fluxes are expressed on a magnitude scale, and the zero points have been established by arbitrarily setting the magnitude of Vega equal to zero at each wavelength. Infrared color temperatures are listed below the magnitudes at each wavelength and have been computed from a blackbody fit to the fluxes at each wavelength and the reference wavelength 1.040 pm assuming the model atmosphere absolute colors of Vega listed in Table 3. The color temperatures derived from the 8 -color data are listed in the second to the last column. The K(210) magni tudes have been corrected for CN contamination as described in Section 5.2. The bandpasses for both the infrared measurements and the 8 -color continuum points have been carefully chosen to avoid as well as possible the effects of line blanketing. Despite this, the observed color tem perature derived between any two wavelength can differ from the "true" stellar continuum color temperature for the following five reasons: errors in the observed color index caused by (1 ) photometric errors; or (2) stellar variability; (3) systematic errors in the calibration of the absolute color of the primary standard star Vega; (4) differential line blanketing within the bandpasses; or (5) interstellar or circum- stellar reddening. These problems will be discussed next. The photometric error in the 8 -color data should be very small (<0.01 mag) since most stars have been observed repeatedly: in fact, Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) T (8c) Notes 1013 45 X Peg M2 III 2.101 1.420 0.517 0.530 3623 3025 2921 3084 3627 165 6 And K3 III 1.551 1.012 0. 387 0.408 0.340 4270 3593 3566 3779 4260 3712 168 a Cas K0- Ilia 0.721 0.228 -0.326 -0.263 -0.342 4574 3843 3807 4139 4593 4128 188 B Cet K1 III 0.632 0.190 -0.290 -0.252 4799 4159 4109 4408 6860 337 3 And MO Ilia -0.405 -1.046 -1.963 -1.928 -2.033 3645 3166 2954 314 8 3557 9927 464 51 And K3 III 1.868 0.716 0.769 4297 3588 3871 11961 M5 III 1.931 1.168 0.103 0.083 -0.090 2623 2775 2651 2766 3095 12929 617 a Ari K2 Illab 0.416 -0.083 -0.693 -0.674 -0.748 4435 3810 3673 3891 4359 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras. (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) T (8c) Notes 14270 AD Per M2.5 lab 3.974 1.744 2802 h&x Per 2900 14469 SU Per M3-4 lab 3.394 1.103 2708 h&x Per 2848 14488 RS Per M4.5 lab 3.648 1.270 2482 h&x Per 2777 14528 S Per M4e la 3.254 0 .010 2141 h&x Per 2238 17506 834 T] Per K3- Ib-IIa 1.416 0.788 -0.053 -0.003 0.003 3589 3215 3071 3296 3884 18191 867 45 Ari M6- III: 0.747 -0.031 -1 .110 -1.128 -1.270 2606 2733 2623 2739 3099 18884 911 a Cet Ml.5 III- -0.195 -0.854 -1.768 -1.762 -1.884 3570 3101 2935 3089 3476 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8c) Notes 19058 921 p Per M4 Ilb-IIIa -0.296 -1.043 -2.045 -2.053 -2.213 3323 2820 2733 2862 3204 20797 1009 M0+ Ila 2.010 1.420 0.399 0.409 0.246 3354 2886 3043 3378 22049 1084 e Eri K2 V 2.478 2.089 1.665 1.657 5081 4557 4422 4599 22649 1105 S5,3 1.754 1.212 0.192 0.209 -0.071 3319 3579 2949 3118 3309 23475 1155 M2+ Ilab 1.051 -0.867 3198 3204 25025 1231 Y Eri M0 III 0.517 -0.150 -1.032 -1.020 -1.125 3690 3073 2965 3129 3538 27371 1346 Y Tau K0 IIlab 2.331 1.911 1.433 1.455 4897 4315 4174 4431 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J (129) K(210) K(228) L (400) 28305 1409 e Tau K0 III 2.198 1.767 1.296 1.327 4865 4235 4163 4446 29139 1457 a Tau K5 III -1.455 -2.065 -2.903 -2.898 -3.020 3737 3285 3099 3260 3647 30959 1556 o 1 Ori M3S 1.227 0.476 -0.573 -0.585 -0.787 3089 2806 2680 2803 3103 32068 1612 £ Aur K5 II+B 1.532 0.899 0.029 0.083 -0.039 3688 3196 3025 3252 3638 GP Ori SC 4.439 1.699 2247 2520 32736 1648 W Ori C5,3 2.028 -0.927 2889 2390 36389 1845 119 Tau M2 Iab-Ib 0.823 0.112 -0.991 -0.996 -1.228 2904 2928 2666 2796 3065 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont* d.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8c) Notes 38944 2011 U Aur M1+ Ilia 2.111 0.440 3576 3501 39801 2061 a Ori Ml-M2 Ia-Ib -2.679 -4.519 3235 3292 40239 2091 tt Aur M3 II 0.840 0.191 -0.834 -0.835 -1.069 3213 3137 2815 2955 3213 42475 2190 TV Gem M0-1 lab 2.919 2 .120 0.947 0.955 0.569 2673 2678 2516 2653 2799 42543 2197 BU Gem Ml-2 Ia-Iab 2.657 1.889 0.770 0.805 0.482 2943 2761 2594 2762 2948 42995 2216 ri Gem M3 III 0.156 -0.521 -1.500 -1.486 -1.654 3392 3039 2836 2995 3325 44478 2286 U Gem M3 Illab -0.273 -1 .000 -1.983 -1.972 -2.106 3385 2879 2775 2927 3298 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD KR=BS Name Sp.Type 1(104) J (129) K(210) K (228) L(400) T (8c) Notes c 44537 2289 ip1 Aur K5-M0 Iab-Ib 2.046 0.250 3350 3343 48329 2473 e Gem G8 lb 1.256 0.737 0.091 0.151 4311 3702 3564 3858 55383 2717 BQ Gem M4 III 1.517 0.765 -0.246 -0.272 -0.383 3205 2806 2718 2828 3223 58061 VY CMa M5 I 2.771 -3.172 2095 1422 60414 2902 KQ Pup M2 Iabep+B 1.727 0.989 -0.060 -0.062 -0.254 3168 2846 2693 2828 3136 60522 2905 U Gem M0 III 1.680 1.039 0.188 0.225 0.103 3757 3166 3039 3243 3629 62509 2990 8 Gem K0 Illb -0.217 -0.663 -1.145 -1.108 -1.174 4784 4133 4092 4388 4870 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) T (8 c) Notes 69267 3249 B Cnc K4 III 1.463 0.863 0.101 0.106 -0.005 3925 3326 3225 3392 3794 76827 3576 p UMa M3 Illb 1.745 0.217 3478 3703 78712 3639 RS Cnc M 6e(S) 0.216 -1.979 2404 2931 80493 3705 a Lyn K7 Illab 0.834 0.178 -0.671 -0.655 -0.772 3772 3111 3022 3194 3588 81797 3748 a Hyd K3 II-III 0.010 -0.563 -1.322 -1.284 4005 3442 3273 3497 82308 3773 X Leo K5 III 2.016 1.342 0.519 0.549 3816 3049 3033 3226 84441 3873 £ Leo G1 II 1.867 2.195 1.159 1.167 5307 4923 4781 5026 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8 c) Notes 85503 3905 U Leo K1.5 III 2.263 1.757 1.186 1.216 1.146 4419 3771 3740 3987 4464 86663 3950 it Leo M2- Illab 1.990 1.307 0.407 0.413 0.345 3574 3018 2922 3076 3534 90432 4094 U Hyd K5 III 1.696 1.092 0.295 0.311 3878 3310 3168 3348 95689 4301 a UMa K0- Ilia 0.317 -0.132 -0.719 -0.693 4517 4113 3831 4075 96833 4335 UMa K1 III 1.442 0.974 0.387 0.435 4514 3991 3789 4082 97778 4362 72 Leo M3 III 1.562 0.858 -0.106 -0.114 3421 2950 2822 2954 100029 4434 X Dra M0 III 1.345 0.669 -0.238 -0.215 3645 3042 2922 3098 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont’d.) MK Magnitudes and Blackbody Temperatures (K) ID or BD HR=BS Name Sp.Type 1(104) J (129) K(210) K(228) L(400) T (8 c) Notes c 108849 BK Vir M7- 1.060 -1.298 1922 2793 112300 4910 6 Vir M3 III 0.313 -1.306 -1.302 3437 High 2879 3028 vel. ? 113226 4932 e Vir G8 Illab 1.602 1.229 0.804 0.833 5009 4695 4468 4772 119228 5154 83 UMa M2 Illab 1.898 1.284 0.322 0.350 3539 3270 2931 3114 124897 5340 a Boo K2 nip -1.820 -2.382 -3.066 -3.048 -3.128 4175 3491 3416 3614 4069 126327 RX Boo M 8 0.267 -0.859 -2.031 -2.093 -2.407 1631 2043 2259 2333 2563 127665 5429 p Boo K3 III 1.808 1.240 0.527 0.566 4215 3464 3355 3588 118 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J (129) K(210) K(228) L(400) T (8 c) Notes c 131873 5563 6 UMi K4 III 0.028 -0.638 -1.425 -1.387 3944 3076 3093 3302 132813 5589 RR UMi M5 III 0.735 -0.053 -1.066 -1.070 3140 2707 2678 2811 146051 6056 6 Oph M0.5 III 0.221 -1.423 3678 3537 148387 6132 U Dra G8 III 1.486 0.587 0.589 4913 4170 4371 148783 6146 g Her M 6- III -0.191 -0.990 -2.088 -2.107 2495 2678 2584 2699 148856 6148 8 Her G8 III 1.493 1.075 0.628 0.697 5015 4329 4265 4680 156014 6406 a 1 Her M5 Ib-II -1.668 -3.785 2565 3003 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont' d.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8 c) Notes 156283 6418 it Her K3 Ilab 1.226 0.638 -0.095 -0.058 4038 3376 3291 3514 154143 6337 M3- III 2.055 1.352 0.431 0.436 3504 2953 2872 3023 159181 6536 6 Dra G2 Ib-IIa 1.507 1.210 0.748 0.761 4969 5051 4598 4853 161096 6603 6 Oph K2 III 1.213 0.675 0.125 0.168 0.126 4524 3605 3718 3992 4535 164058 6705 y Dra K5 III 0.042 -0.600 -1.413 -1.371 3858 3162 3090 3305 165674 VX Sgr M4e 2.302 -1.842 1592 1872 167006 6815 104 Her M3 III 1.981 1.231 0.277 0.279 3451 2811 2781 2924 120 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J (129) K(210) K(228) L(400) Tc (8 c) Notes 172167 7001 a Lyr A0 V 0.009 0.000 0.000 0.000 -0.003 8892 20102 12035 12356 1 2100 172380 7009 XY Lyr M4-5 II 1.560 0.744 -0.346 -0.369 -0.505 2792 2635 2576 2686 3052 175588 7139 6 2 Lyr M4 II 0.502 -0.259 -1.314 -1.316 3181 2780 2663 2797 175865 7157 R Lyr M5 III -0.323 -1.115 -2.165 -2.175 -2.319 2951 2696 2638 2762 3121 186791 7525 Y Aql K3 II 0.675 0.078 -0.703 -0.679 -0.759 3927 3339 3201 3397 3849 +39°4208 RW Cyg M3-4 Ia-Iab 2.981 1.906 0.499 0.454 -0.021 2069 2121 2136 2222 2364 196610 7886 EU Del M 6 III L-l 0.706 -0.124 -1.192 -1.225 -1.393 2462 2600 2584 2684 3019 121 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont1d.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) T (8 c) Notes 197989 7949 e Cyg K0- III 1.061 0.577 0.002 0.058 4640 3895 3779 4092 IRC+40448 M 6 7.189 -1.874 1015 1011 206778 . 8308 E Peg K2 lb 0.475 -0.183 -0.938 -0.884 -0.977 4098 3104 3149 3389 3820 206936 8316 U Cep M2 la -0.105 -0.924 -1.982 -1.953 -2.292 2747 2627 2603 2766 2938 207076 M7 III: 0.349 -0.559 -1.628 -1.687 -1.907 2158 2425 2512 2588 2877 208816 8383 W Cep M2 la-lab 1.591 0.866 -0.212 -0.199 -0.435 3017 2885 2676 2826 3090 210745 8465 C Cep K1.5 lb 1.319 0.730 -0.034 0.032 3879 3372 3240 3509 122 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8c) Notes 212466 RW Cep K0 0-Ia 3.214 2.749 1.887 1.923 1.461 3090 4010 3280 3502 3394 213310 8572 5 Lac MO Iab+B 1.662 1.025 0.052 0.094 3484 3181 2890 3088 214665 8621 M4 III 1.493 0.826 -0.224 -0.192 -0.412 3287 3073 2767 2944 3217 216946 8726 MO- lb 2.321 1.702 0.749 0.793 0.584 3456 3250 2937 3141 3414 217476 8752 GO la 2.585 1.126 3667 3810 217906 8775 3 Peg M2.5 II-lil -0.592 -1.349 -2.338 -2.340 -2.443 3408 2791 2736 2872 3278 221615 8940 71 Peg M5- Ilia 1.502 0.767 -0.284 -0.273 -0.427 3170 2855 2694 2843 3191 123 Table 13 Narrow-Band Magnitudes and Color Temperatures for Non-Miras (cont'd.) MK Magnitudes and Blackbody Temperatures (K) HD or BD HR=BS Name Sp.Type 1(104) J(129) K(210) K(228) L(400) Tc (8c) Notes 224427 9064 Y Peg M3 III 1.629 0.900 -0.071 -0.062 3494 2873 2786 2937 125 many are 8-color standards. However, some of the cooler stars, parti cularly the supergiants, are slightly variable in the near infrared. For many of these stars simultaneous 8-color observations were made in November 1977 with the 0.4-m Kitt Peak telescope. The simultaneous data have been used, when available, so that the observational results refer to a single epoch. Errors may be somewhat larger for the cooler stars for which simultaneous 8-color data could not be obtained. The probable errors of the infrared magnitudes are about 0,016 mag (Table 5). Unfortunately, because of the limited amount of observing time available, most stars were observed only once. The errors in the absolute colors of the fundamental standard star Vega are difficult to estimate. Since the absolute flux of Vega has been measured in the near-infrared (Hayes and Latham, 1975 ; Tiig, White, and Lockwood, 1977), the near-infrared colors are probably accurate to 0.02 mag. The situation at wavelengths longer than 1.1 pm is less satisfactory since the absolute energy distribution of Vega has not been measured and can only be inferred from model atmosphere computa tions. Despite the surprisingly large difference in the parameters deduced for Vega by Kurucz (1979) and Dreiling and Bell (1980), the infrared colors computed for their models are in good agreement and closely match the results of Schild, Peterson, and Oke (1971). It is therefore likely, but by no means certain, that the infrared absolute colors of Vega are accurate to ±0.03 mag. Additional discussion of this problem was presented in Section 2.4. 126 The occurrence of line blocking within the bandpasses used to com pute the color indices will cause the observed color temperature to differ from the continuum color temperature. As noted previously, the color temperatures on the Wing 8-color system are now believed to be systematically lower than the effective temperatures for all M stars because of some source of blanketing in the 0.7540 pm filter (Ridgway, et al. , 1980). The bandpasses of the infrared points have been examined at high resolution (Section 5.2) and are believed to be nearly free of line blocking in all but the coolest stars. Small corrections for CN contamination have been applied at 2.101 pm. For giants and supergiants later than about M6 it is important to remember that water vapor ab sorption occurs throughout the infrared and is likely to effect one or more of the program bandpasses. Table 14 has been constructed to show the effect of a given error in the photometry, arising from any cause, on the resulting color tem perature. The value 0.02 mag has been chosen as representative of errors in the relative photometry. The error AT in the computed black- body temperature is tabulated for the two shortward continuum points of the Wing 8-color system (0.7540 and 0.7810 pm) and the four wave lengths of the infrared colors program. As in Table 13 the reference wavelength for fitting the blackbody curve has been taken to be 1.040 pm. For relatively small errors in the color (<0.10 mag), the error in the calculated color temperature is nearly linearly proportional to the error in the color. As noted by Wing (1967a), the error A0 (6=5040/T) is nearly independent of temperature at each wavelength. 127 Table 14 Error in Temperature Resulting from a 0.02 mag Error in the Color Index taken with respect to 10395 X Wavelength AT for T (A) A0 2000 2500 3000 3500 4000 4500 5000 7540 0.018 14 22 32 45 59 77 88 7810 0.020 16 25 37 51 68 88 95 12870 0.038 28 45 66 92 124 162 140 21010 0.015 11 18 26 37 50 65 81 22850 0.014 10 16 24 34 46 61 77 39965 0.011 8 13 19 27 36 47 59 128 The value of A0 for each wavelength is also listed in Table 14. Errors in the color temperature are largest at 1.287 pm because of the rela tively short baseline used to fit the blackbody curve. The effect of reddening on the observed color temperatures has been calculated from the van de Hulst theoretical reddening curve #15 (Johnson, 1965). The absorption in magnitudes at each of the program wavelengths is related to the color excess in B-V by the relations A (0.7540 pm) = 1.84 E(B-V) A (0.7810 pm) = 1.72 E(B-V) A (1.0395 pm) = 1.05 E(B-V) A (1.287 pm) = 0.75 E(B-V) A (2.101 pm) = 0.31 E(B-V) A (2.285 pm) = 0.27 E(B-V) A (3.9965 pm) = 0.12 E(B-V). In Table 15 the change AT in the color temperature has been eva luated at the program wavelengths for color excesses in E(B-V) from 0.01 to 0.50. As expected from the wavelength dependence of inter stellar extinction and the Planck functions the largest changes occur at the shortest wavelength and for the warmest stars. Results from this table have been used to compute the slope of the reddening line in the color temperature vs. color temperatue plots presented in Section 5.5. 129 Table 15 Effect of Reddening on Color Temperatures Wavelength AT for T E(B-V) (A) 2000 2500 3000 3400 4000 4500 500( 0.01 7540 6 9 13 17 23 30 38 7810 5 8 12 16 23 29 37 12870 4 7 10 13 19 24 31 21010 4 6 10 13 18 24 30 22850 4 6 9 13 18 23 30 39965 4 6 9 11 17 22 27 0.05 7540 27 43 62 81 114 146 184 7810 27 42 61 79 111 143 179 12870 21 33 49 64 91 117 149 21010 20 32 47 62 90 116 147 22850 20 31 47 62 88 115 145 39965 18 29 43 57 81 106 134 0.10 7540 54 84 122 158 221 283 353 7810 52 82 119 153 215 276 345 12870 41 65 95 125 177 228 288 21010 39 63 93 122 175 226 285 22850 39 62 92 121 172 223 281 33965 35 57 85 111 159 206 260 0.20 7540 105 163 234 301 417 529 656 7810 102 159 228 293 407 517 641 12870 81 127 185 240 337 433 541 21010 77 123 180 235 333 428 536 22850 76 121 178 232 329 423 529 39965 69 111 164 215 305 393 492 0.30 7540 154 237 338 431 592 747 918 7810 150 231 329 420 579 730 898 128 70 119 185 268 346 484 616 765 21010 114 179 262 340 478 610 758 22850 112 177 258 335 471 602 749 33965 102 163 239 311 439 561 699 0.40 7540 200 306 433 550 751 940 1148 7810 195 298 423 537 734 920 1125 12870 155 241 346 445 618 782 965 21010 148 233 338 437 610 774 957 22850 146 230 334 432 602 765 946 33965 133 212 310 402 562 715 886 130 Table 15 Effect of Reddening on Color Temperatures (cont'd.) Wavelength (A) 2000 2500 3000 3400 4000 4500 5000 7540 244 371 522 660 894 1113 1352 7810 237 362 510 645 875 1091 1326 12870 190 294 420 538 741 933 1145 21010 182 284 410 528 731 924 1136 22850 179 280 405 521 723 913 1124 131 Section 5.4 - Computation of Synthetic Colors Since the continuum points were chosen in spectral regions nearly free of line blanketing, synthetic color temperatures and indices have been computed with only continuum opacity sources. The sources of con tinuous opacity included were H bound-free, H- bound-free and free-free, H£- free-free, H Rayleigh scattering, H2 Rayleigh scattering, He Ray leigh scattering, He- free-free, H2+ bound-free and free-free, and electron scattering. The algorithm to compute the absorption and scat tering coefficients was taken almost entirely from the synthetic spec trum program MOOG (Sneden, 1974). The calculated H2- coefficients of Somerville (1964) have been increased by 40% (John, 1975). Rayleigh scattering by H2 was approximated by the formula of Dalgarno (1962). The model atmospheres of Bell, et al. (1976a) and Johnson, Bernat, and Krupp (1980) were used to compute the emergent fluxes. In both grids the standard assumptions of plane-parallel stratification in homogeneous stationary layers in hydrostatic and local thermodynamic equilibrium were made. In the models of Bell, et al. (1976a) the line opacity was treated with opacity distribution functions whereas Johnson, Bernat, and Krupp (1980) have used the opacity sampling method. These models are believed to be the best currently available. Synthetic colors were also computed with several straight mean opacity models of Johnson (1974), but the calculated colors were found to be in poor agreement with the observational data. Models in the effective temperature range 2750 to 5000 K were con sidered. When the appropriate models were available, synthetic colors 132 were computed for a range of gravities and chemical compositions at each effective temperature. The calculated synthetic color temperatures and color indices are tabulated in Table 16. Both the indices and color temperatures have been computed with 1(104) as the reference wavelength. The color temperatures were computed by fitting a blackbody curve to the model fluxes between each wavelength and the 1.04 pm reference wave length. The color indices are magnitude differences expressed on a scale of absolute flux per unit wavelength. To illustrate the wavelength dependence of the continua in late- type stars, continuum fluxes have been computed between 0.6 and 4.0 pm with the solar composition T^ = 3750 K and log g = 2.25 model of Bell, et al. (1976a). In Figure 27 the emergent fluxes (dots) are expressed on a magnitude scale per unit wavelength, normalized to the 1.0395 pm reference wavelength. Arrows mark the wavelengths of the infrared colors program and the continuum points of the 8-color system. For comparison, a 3750 K blackbody energy distribution (solid line) normalized to 1.0395 pm is also shown. A peak in the continuous flux near 1.65 pm is clearly visible in the calculated continuum. The shape of the energy distribution can be readily explained by the wavelength dependence of the dominant infrared opacity source, H- (Figure 28). Absorption by H- at wavelengths less than 1.65 pm is primarily by the bound-free component. The bound-free cross-section is largest at 0.85 pm and falls to zero at wavelengths longer than 1.65 pm (Geltman, 1962). Free-free absorption occurs at all wavelengths: its cross-section increases to longer wavelengths but Table 16 Synthetic Colors and Blackbody Temperatures Blackbody Temperature (K) and Color ■ Index (mag) (reference wavelength 10395 A) T log g Model 7540 7810 12870 21010 22850 33965 A eff 5000 1.5 Bell (DBV=2) 4909 4863 4112 4266 4401 4994 Solar -0.540 -0.489 0.419 1.840 2.165 4.431 2.25 Bell (DBV=2) 4898 4852 4067 4214 4357 4966 Solar -0.537 -0.487 0.412 1.822 2.150 4.421 3.0 Bell (DBV=2) 4883 4837 4037 4178 4326 4939 Solar -0.534 -0.484 0.407 1.809 2.139 4.412 4500 0.75 Bell (DBV=2) 4441 4406 3662 3752 3871 4401 Solar -0.428 -0.392 0.341 1.633 1.953 4.200 1.5 Bell (DBV=2) 4424 4385 3658 3698 3828 4371 Solar -0.423 -0.387 0.340 1.607 1.933 4.186 2.25 Bell (DBV=2) 4406 4366 3624 3653 3788 4341 Solar -0.418 -0.382 0.334 1.586 1.913 4.172 2.25 Bell (DBV=2) 4347 4310 3607 3620 3751 4290 A/H=-l.0 -0.402 -0.369 0.330 1.569 1.895 4.149 2.25 Bell (DBV=2) 4376 4339 3626 3647 3779 4324 |_i A/H=-l.0 -0.410 -0.376 0.334 1.583 1.909 4.164 £ Table 16 Synthetic Colors and Blackbody Temperatures (cont'd.) Blackbody Temperature (K) and Color Index (mag) (reference wavelength 10395 A) T log g Model 7540 7810 12870 21010 22850 33965 X eff 3.0 Bell (DBV=2) 4386 4346 3602 3622 3758 4314 Solar -0.413 -0.378 0.329 1.570 1.899 4.160 0.75 Bell (DBV=2) 3902 3868 3220 3163 3279 3756 Solar -0.261 -0.245 0.241 1.301 1.621 3.852 1.50 Bell (DBV=2) 3886 3852 3190 3112 3236 3725 Solar -0.256 -0.240 0.233 1.266 1.590 3.832 1.50 Bell (DBV=2) 3835 3805 3185 3097 3215 3699 A/H=-l.0 -0.237 -0.225 0.232 1.255 1.578 3.816 1.50 Bell (DBV=5) 3860 3829 3199 3117 3236 3725 A/H=-l.0 -0.246 -0.232 0.236 1.269 1.592 3.833 2.25 Bell (DBV=2) 3869 3834 3173 3083 3205 3701 Solar -0.250 -0.234 0.229 1.245 1.571 3.816 2.25 Bell (DBV=2) 3834 3802 3174 3080 3198 3681 A/H=-1.0 -0.237 -0.223 0.229 1.242 1.565 3.804 3.0 Bell (DBV=2) 3854 3819 3162 3065 3188 3684 Solar -0.244 -0.229 0.226 1.232 1.558 3.805 Table 16 Synthetic Colors and Blackbody Temperatures (cont'd.) Blackbody Temperature (K) and Color Index (mag) (reference x^avelength 10395 A) T log g Model 7540 7810 12870 21010 22850 39965 1 eff 0.0 Johnson 3641 3615 3051 2973 3075 3496 Solar -0.162 -0.159 0.196 1.162 1.474 3.672 1.0 Johnson 3647 3617 3025 2903 3015 3471 Solar -0.164 -0.160 0.187 1.106 1.426 3.652 2.0 Johnson 3653 3623 3036 2898 3013 3474 Solar -0.166 -0.162 0.191 1.102 1.425 3.655 0.75 Bell (DBV=2) 3611 3581 2977 2860 2970 3425 Solar -0.149 -0.146 0.173 1.070 1.390 3.616 1.5 Bell (DBV=2) 3601 3569 2960 2823 2937 3400 Solar -0.145 -0.142 0.167 1.038 1.361 3.596 1.5 Bell (DBV=2) 3562 3534 2941 2786 2904 3386 A/H=-l.0 -0.128 -0.129 0.161 1.006 1.332 3.586 2.25 Bell (DBV=2) 3589 3557 2918 2804 2918 3383 Solar -0.140 -0.138 0.164 1.021 1.345 3.582 2.25 Bell (DBV=2) 3574 3543 2952 2803 2917 3376 A/H=-0.5 -0.133 -0.132 0.165 1.021 1.344 3.578 Table 16 Synthetic Colors and Blackbody Temperatures (cont'd .) Blackbody Temperature (K) and Color Index (mag) (reference wavelength 10395 X) T log g Model 7540 7810 12870 21010 22850 39965 X eff 0.0 Johnson 3430 3407 2892 2762 2862 3272 Solar -0.069 -0.078 0.146 0.983 1.295 3.489 1.0 Johnson 3467 3441 2911 2742 2850 3284 Solar -0.086 -0.092 0.152 0.965 1.284 3.499 2.0 Johnson 3502 3476 2948 2773 2883 3319 Solar -0.102 -0.106 0.164 0.994 1.314 3.530 0.0 Johnson 3275 3257 2813 2630 2728 3120 Solar 0.007 -0.013 0.119 0.855 1.166 3.348 0.5 Johnson 3293 3272 2810 2611 2713 3118 Solar -0.002 -0.020 0.118 0.836 1.151 3.346 1.0 Johnson 3324 3302 2835 2629 2732 3143 Solar -0.018 -0.034 0.126 0.854 1.171 3.370 2.0 Johnson 3385 3363 2892 2689 2794 3205 Solar -0.048 -0.060 0.146 0.914 1.231 3.429 Table 16 Synthetic Colors and Blackbody Temperatures (cont'd.) Blackbody Temperature (K) and Color Index (mag) (reference wavelength 10395 $) T log g Model 7540 7810 12870 21010 22850 39965 X eff 3200 0.0 Johnson 3125 3110 2719 2504 2598 2970 Solar 0.088 0.057 0.085 0.719 1.028 3.194 1.0 Johnson 3218 3199 2789 2557 2657 3043 Solar 0.037 0.014 0.110 0.779 1.092 3.271 2.0 Johnson 3292 3272 2854 2632 2732 3119 Solar -0.002 -0.020 0.133 0.857 1.171 3.347 3000 0.0 Johnson 3033 3020 2682 2442 2533 2886 Solar 0.142 0.103 0.071 0.647 0.952 3.098 1.0 Johnson 3129 3113 2753 2506 2602 2964 Solar 0.086 0.055 0.097 0.722 1.031 3.187 2.0 Johnson 3213 3195 2822 2590 2686 3048 Solar 0.040 0.015 0.123 0.814 1.123 3.276 2750 1.0 Johnson 3041 3028 2718 2468 2557 2888 Solar 0.138 0.099 0.084 0.677 0.980 3.102 138 0.0 .0 2.0 3.0 4.0 8.0 2.0 3.0 4.0 WAVELENGTH (§Jm) Figure 27. Comparison between the continuous energy distribution of the Bell e£ al. (1976a) solar composition T = 3750 K and log g 2.25 model atmosphere (dots) and a 3750 K blackbody energy distribution. The fluxes are on a magnitude scale per unit wavelength, normalized to the 1.0395 pm reference wave length. Arrows mark the wavelengths of the infrared colors program and the continuum points of the Wing 8-color sys tem. The peak in the continuum caused by the H- opacity minimum is clearly visible at 1.65 pm. 139 log k 1.0 2.0 3 .0 4 . 0 WAVELENGTH (pm) Figure 28. Absorption coefficient of H“ (cm per neutral hydro gen atom) plotted against wavelength for a tempera ture of 3835 K and an electron pressure of 6.71x10“^ dynes/cm^. The solid line is the total H~ absorption coefficient; the dashed line indicates the free-free component only. The conditions correspond to a level in the Bell et_ al. (1976a) Tg = 3750 K and log g = 2.25 solar composition model close to continuum op tical depth unity at 1.0395 pm. 140 is less accurately known (Geltman, 1965; John, 1979). The sum of the two components has a sharp minimum at 1.65 pm. The occurrence of the H- opacity minimum in combination with the location of the maximum of the Planck function at cool-star temperatures produces a sharp peak in the continuous flux at 1.65 pm. The "1.65 pm peak" can also be seen in the calculated continua of Tsuji (1978a). An examination of the calcu lated opacities indicates that H- is dominant in the deeper layers where the majority of the continuum radiation originates. From an examination of Figure 27 it is apparent that color tempera tures computed with the 1.0395 pm reference wavelength will be strongly wavelength dependent. For all wavelengths longward of about 0.7 pm the continuum color temperature is less than the effective temperature; the largest difference between the color temperature and effective tempera ture occurs at the II- opacity minimum. For the model illustrated in Figure 27 the color temperature between 1.04 and 1.65 pm is 1400 I< less than the effective temperature. From Table 16 it can be seen that these same conclusions are valid for all the cool star models. The color temperatures are very wave length dependent, and the largest difference between the effective tem perature and color temperature occurs at the program wavelengths near the H- opacity minimum. The temperatures from the 8-color and 1(104)- L(400) indices are predicted to be good indicators of the effective temperature. Surface gravity appears to have only a minor effect on the calcu lated colors. For a given effective temperature a difference of less 141 than 100 K in the color temperature is calculated to occur between gravities believed to be typical of giant and supergiant stars. The differences in the computed color indices is calculated to be on the order of the photometric accuracy of the data. Also, the effect of gravity is even smaller when the calculated colors are plotted against each other. Models of various surface gravities and effective tempera tures define nearly a single curve on all color-color plots. This result can be seen in Figures 29 and 30. This is very helpful since the observed colors can then be compared to a single theoretical rela tion independent of surface gravity. For the warmer temperatures (T > 3750 K) the grid of Bell, et al. (1976a) was used to study the effect of differences in the chemical composition on the model colors. The shift in the synthetic colors with a change of (A/H) from 0.0 to -1.0 was found to be small (typically 0.01 mag). As noted by Gustafsson, et al. (1975), the rather small sensitivity of the model structures to changes in (A/H) can be explained by saturation of spectral lines for near-solar compositions and the partial compensation for the increased line absorption by a corresponding increase in the continuous opacity. Although the chem ical compositions of late-type giants and supergiants are largely unknown, these calculations suggest that the infrared continuum colors should be only slightly affected by moderate differences in chemical composition, at least for near-solar-composition cases. Unfortunately, similar computations could not be carried out with models in the lower temperature range since only solar composition models were available. 142 The importance of the microturbulent velocity parameter was also examined. Continuum colors of models computed with a Doppler broaden ing velocity (DBV in Table 16) of 2 km/s and 5 km/s differed only slightly as can be seen in Table 16. It is important to recall that the model atmospheres used to compute the synthetic colors make the standard assumptions of plane- parallel geometry, local thermodynamic equilibrium, hydrostatic equili brium, and horizontal homogeneity. Departures from these assumptions are likely to produce errors in the calculated colors, particularly for stars of the highest luminosities and coolest temperatures. These effects have been discussed elsewhere (cf. Gustafsson, et al., 1975; Carbon, 1979) and will not be considered further here. Chromospheric free-free and bound-free emission (Humphreys, 1974; Gilman, 1974), thermal reradiation from circumstellar grains (Fawley, 1977), and/or H2O thermal emission (Tsuji, 1978b) may also occur in the infrared, but these effects are likely to be important only for the most luminous stars. Section 5.5 - Comparison between Observed and Synthetic Color Tempera tures for Giant and Bright Giant Stars In Figures 29 and 30 synthetic color temperatures generated with solar-composition model atmospheres are compared with the observed values for luminosity class II and III stars. Results obtained with the grid of Bell, et al. (1976a) are indicated with open symbols while filled symbols represent values obtained with the models of O ( S04-2I0) Figure 29. The relation between T (104-210) and T (104-400). Stars Stars (104-400). T and (104-210) T between relation The 29. Figure 2000 0 0 0 4 3000 I” 3000 models from the grid of Bell et_ al. (1976a)9 large solid solid large et_ (1976a)9 Bell of grid al. the from models T (104-400). The arrow indicates the approximate slope slope approximate the indicates arrow The = (104-210) T (104-400). relation T the by defined is line dashed The and dotSp respectively. Large open symbols represent represent symbols open Large respectively. dotSp sfiownsymbols and are + III as and 5l classes luminosity of symbols models computed by Johnson by computed models symbols Solid lines connect models with the same surface gravity. gravity. surface same the with models connect lines Solid o? the reddening line. reddening the o? (1980). All models were computed with solar abundances. abundances. solar with computed were models All (1980). 3000 3 0 0 0 EC 0 0 0 3 3 S 0 0 EC 0 0 S 3 Te 0 5 7 3 3 8 0 0 EC 0 0 8 3 C 104-400) EC 4000 „ Bernat, and Krupp Krupp and Bernat, 25 □ 5 .2 2 MODEL RESULTS Boll EC 0 0 5 4 Johnson SC 0 0 0 5 5000 143 t (104-400) 4000 - 4000 3000 - 3000 5000 - 5000 iue 30 Figure l_ o Terlto ewe c(0-0) n c(c frmdl ad tr of stars and formodels (8c) Tc and (104-400) Tc between relation The . h ahd ie s c(0-0) c(8c). Tc = (104-400) Tc is line dashed The uioiycass Iad I, hw i tesm fra sFg 29. Fig.as format same the in shown III, and II classes luminosity 2.25 □ 2.25 . O 3.0 . A 1.5 Bell MODEL logg + IT+ o HI RESULTS Johnson lo9 9 0.0 0.0 . 5000 145 Johnson, Bernat, and Krupp (1980). Solid lines connect models with the same value of log g. In the T (104-210) vs. 1^(104-400) diagram (Figure 29) the observed and synthetic relations are in close agreement for all temperatures. The two color temperatures are nearly linearly related to each other with T (104-210) between 500 and 800 I< lower than T (104-400). This c c indicates that the model atmospheres can satisfactorily reproduce the observed "excess" flux near the H- opacity minimum and confirms that H- is an important continuous opacity source in the cooler late-type stars. The observed and model-atmosphere results in the 1^(104-400) vs. Tc (8c) diagram (Figure 30) are in good agreement for the warmer stars but deviate systematically for the later spectral types. The devia tion begins in the early M stars and increases to cooler temperatures. The calculations indicate that the two color temperatures should be nearly equal, whereas the observed relation turns sharply leftward for Tc (8c) < 3300 K. The results for the other diagrams are similar. Mien color tem peratures formed between 1.0395 urn and the infrared wavelengths are plotted against each other, the observed and model atmosphere relations agree to within about 100 K. Model atmosphere calculations based only on continuous opacity sources, however, cannot reproduce the rapid decrease in Tc (8c) relative to the other color temperatures observed in the coolest stars. 146 Mean relations between color, color temperature, MK spectral type, and effective temperature are given in Table 17 for luminosity class III stars. The Ridgway, et al. (1980) calibration has been used to relate 8-color temperature to MK spectral type and effective temperature. The relations between the color temperatures are well-defined except for T (104-129). In this case, the separation between the two wave lengths used to form the color temperature is small, and the photome tric errors have a large effect on the calculated color temperature, particularly for the warmer stars (see Table 14). At the other wave lengths the color temperatures are sufficiently well determined to separate stars differing by one or two spectral subtypes in almost all cases. The few bright giants observed have color temperatures that are close to the mean giant-star relations. An important check on the temperature scale of Ridgway, et_ al. (1980) is to test if the calibration can be correctly reproduced by model atmosphere calculations. In Figures 31 to 35 the data of Table 17 are compared with results obtained with solar-composition model atmospheres. When the color temperatures formed between the 1.0395 pm reference wavelength and the infrared wavelengths are plotted against effective temperature, the observed mean giant-star relations (assuming the Ridgway, et_ al. , 1980, calibration) agree with the model atmosphere calculations to within about 100 K over the entire range of spectral types. The surface gravity has only a minor effect on the model atmosphere continuum color temperatures. Considering the uncertainties involved, the agreement must be considered excellent. When a similar Table 17 Relations between Spectral Type, Color Index, and Temperature for Class III Giant Stars Color Temperature (color index) Effective Sp. Type Tc(8c) (104-129) (104-210) (104-228) (104-400) Temperature G8 III 4900 4310(0.42) 4190(0.89) 4510(0.85) 4930 K K0 III 4760 4110(0.45) 4020(0.96) 4330(0.91) 4830(0.97) 4790 K1 III 4580 3910(0.48) 3820(1.04) 4100(1.00) 4600(1.06) 4610 K2 III 4400 3720(0.52) 3640(1.13) 3890(1.09) 4400(1.15) 4450 K3 III 4200 3520(0.55) 3450(1.23) 3650(1.21) 4160(1.26) 4270 K4.0 III 4000 3350(0.59) 3260(1.34) 3440(1.33) 3920(1.39) 4095 K5.0 III 3860 3250(0.62) 3120(1.43) 3300(1.42) 3750(1.50) 3980 M0.0 III 3750 3150(0.64) 3030(1.50) 3210(1.48) 3640(1.57) 3895 Ml.0 III 3640 3060(0.67) 2950(1.56) 3120(1.54) 3540(1.64) 3810 M2.0 III 3530 2980(0.69) 2880(1.62) 3030(1.61) 3430(1.72) 3730 M3.0 III 3400 2880(0.73) 2790(1.70) 2930(1.70) 3300(1.83) 3640 M4.0 III 3250 2800(0.75) 2710(1.77) 2850(1.77) 3220(1.90) 3560 M5.0 III 3000 2770(0.76) 2630(1.85) 2780(1.83) 3130(1.99) 3420 M6.0 III 2600 2730(0.78) 2600(1.88) 2720(1.89) 3100(2.02) 3250 m iue 1 T 1419 potdaant fetv tmeaue The temperature. effective against plotted (104-129) T 31. Figure ( ( 104-129) 4000 3000 - 3000 00 5000 0 0 0 4 3000 where the color temperature is equal to the effective effective the to equal is temperature color the where atmosphere results (Johnson, Bernat, and Krupp 1980) are are 1980) Krupp and Bernat, (Johnson, results atmosphere are indicated. Opacity-sampling solar-composition model model solar-composition Opacity-sampling indicated. are andwt te oa-opsto oes f el et_ Bell of al. models ob solar-composition the values mark with tained symbols open symbols; solid by indicated (+ symbols) types spectral corresponding The relations III 17. class Table in luminosity the by defined is line solid temperature. (1976a). The dashed line defines the locus of points points of locus the defines line dashed The (1976a). 2.25 3.0 MODEL 1.5 Bell log FETV TMEAUE (K) TEMPERATUREEFFECTIVE g . a 1.0 o □ A RESULTS Johnson . o 2.0 0.0 0.0 / • ogg / a / A Jvl 2 148 o (104-210) iue 2 T 1420 v. fetv tmeaue s hw i the in shown is temperature effective vs. (104-210) Tc 32. Figure 0 0 0 3 0 0 0 4 00 0 0 0 4 3000 - - _ - - ae omt sFg 31. Fig. as format same .5 . H 1.0 □ 2.25 MODEL . o 3.0 . A 1.5 o glg g log g log Bell » M 6 FETV TEMPERATUREEFFECTIVE RESULTS Johnson . o 2.0 . A 0.0 —I —r i— I— i— — 1 / ' / i r i (K) 5000 149 h* o (104 — 228) Figure 33. Tc (104-228) vs. effective temperature is shown in the in shown is temperature effective vs. (104-228) Tc 33. Figure 4000 3000 00 00 5000 4000 3000 ae omt s i. 31. Fig. as format same MODEL RESULTS FETV TMEAUE .( TEMPERATUREEFFECTIVE K) Johnson 150 iue 4 T 1440 v. fetv tmeaue s hw i the in shown is temperature effective vs. (104-400) Tc 34. Figure (104-400) 4000 5000 00 i 3000 00 4000 3000 ae omt s i. 31. Fig. as format same MODEL 4 .5 □ 2.25 3.0 3.0 Bell . A 1.5 i i i i i I i I i i i i ! •°g9 FETV TMEAUE (K) TEMPERATURE EFFECTIVE O RESULTS Johnson 0.0 0.0 . o 2.0 1.0a o g log a \ i l 5000 151 152 5000 — i— i— i— |— i— i— i— i— |— r A - MODEL RESULTS - Bell Johnson Tr(8c) — !°g g !°g g - 1.5 A 0.0 A 2.25 □ 1.0 a 3.0 O 2.0 o 4000 3000 3000 4000 5000 EFFECTIVE TEMPERATURE (K) Figure 35. Eight-color near-infrared color temperature vs. effective temperature is shown in the same format as Fig. 31. 153 plot is made with the 8-color data (Figure 35), agreement is excellent for the warmer stars (T > 3800 K ) , but again the models cannot repro duce the rapid drop in the 8-color temperature in the M stars. The dis crepancy between the observed and model atmosphere continuum color tem peratures is very large for the coolest stars (over 600 IC at T^ = 3250 K) . This effect has also been noted by Ridgway, et al. (1980), who compared the 8-color temperatures to effective temperatures determined from angular diameters. The lunar occultation data led to an effective temperature scale in the M stars considerably warmer than the corres ponding 8-c.olor temperature scale. It was proposed that there exists a source of blanketing in the 0.7540 pm region that increases moderately from M0 to M 6 . The present study provides additional evidence to support this hypothesis. The model atmospheres of Bell, et al. (1976a) and Johnson, Bernat, and Krupp (1980) predict relations between the color tempera tures close to the observed values for all the infrared wavelengths but not for the 8-color system. The rapid decrease in 8-color temperatures relative to the infrared color temperatures in the M stars also suggests that an additional opacity source is affecting the 8-color results. In addition, the infrared color temperatures predicted with the model atmospheres are consistent with the effective temperature scale of Ridgway, et al. (1980), whereas the computed 8-color temperatures are not. These discrepancies can only be resolved by assuming the 0.7540 pm region is affected by some source of blanketing. 154 The source of blanketing at 0.7540 uni is difficult to determine. A continuous opacity source seems unlikely since it would have to be moderately strong at 0.7540 um but negligible at 1.040 pm, since the infrared color temperatures computed with the 1(104) magnitude appear to be unaffected. Absorption by CN would act to lower the color tem perature but CN decreases in strength with decreasing, temperature in the M stars. The V0 molecule depresses the flux within the 0.7540 um bandpass in stars later than about M 6 , but its strong temperature dependence assures that the affect of V0 in the early M stars should be negligible. Model atmosphere calculations including TiO line-by-line as an opacity source have been carried out by A. Bernat, J. Piccirillo, and H. R. Johnson at Indiana University (as mentioned by Ridgway, et_ al., 1980). The results indicate that the 0.7540 um region is depressed by high-excitation lines of TiO. Although these lines have never been observed in the laboratory, their calculated intensities indicate these lines are the likely source of the 0.7540 um depression. A few supergiants and Mira variables were also observed, but the observational data are difficult to interpret. The supergiant colors are affected by interstellar reddening, and it is difficult to infer anything concerning their intrinsic colors. Also, many supergiants are known to be variable at 1(104) and in 8-color spectral type (White and Wing, 1978), and therefore are likely to vary in the infrared. A study of Mira variable colors would require observations at all phases and interpretation with dynamical models. 155 Of the color temperatures measured in this study, 1^(104-400) appears to be the best indicator of the effective temperature. The relation between T (104-400) and effective temperature is nearly c linear, and the model atmosphere calculations indicate that T (104-400) c should deviate from Tg by less than 300 K over the entire range of spectral types studied here. Since the opacities at 1.0395 and 3.9965 pm are nearly equal and of the same origin (predominately continuous absorption by H-), 1^(104-400) should be insensitive to differences in the stellar temperature structure caused by differences in composition. Also, 1^(104-400) is less affected by reddening than temperature indi cators measured in the visual part of the spectrum, such as B-V. Of course, the other color temperatures can also be calibrated for use as indicators of the effective temperature. The 8-color tem peratures are quite sensitive and are close to the Ridgway, et al. (1980) effective temperatures for the warmer stars. For cooler stars of abnormal composition, the 8-color temperatures should be used with caution since the uncertain origin of the 0.7540 pm opacity could make the observed values sensitive to gas pressure, microturbulent velocity, and/or chemical composition. Because of the large difference in con tinuous opacity between 1.0395 pm and wavelengths near the H- opacity minimum, the other infrared color temperatures should be regarded as less desirable temperature indicators. These color temperatures will be sensitive to differences in the atmospheric temperature structure. They may, however, be useful for other purposes. As noted by Bell, 156 et al. (1976b) , this sensitivity may offer an observational method of studying the effects of convective energy transport on the temperature structure of stellar atmospheres. Previous studies of the infrared colors of late-type stars have been made at lower resolution. The H-flux peak is a pronounced feature in the spectrum of a Tau obtained by Woolf, et al. (1964) with the balloon-borne Stratoscope II telescope and has been studied by Bahng (1969), Walker (1969), Lee (1970), Bell, et al. (1976b), and Persson, Aaronson, and Frogel (1977) with intermediate and wide-band photometry. The interpretation of the intermediate and wide-band results is complicated by line blocking, particularly in the 1,5-1.8 pm (H band) window, where the H- flux peak is expected to be largest. As noted by Bell, et al. (1976b), the effect of CO and CN lines in this region is of crucial importance in interpreting the luminosity dependence of the colors reported by some observers (cf. Lee, 1970), since both absorbers are known to increase in strength with higher luminosity. Inspection of Kitt Peak and M t . Palomar FTS data (Connes and Michel, 1974; Ridgway and Hall, 1978) confirms that this region is affected by numerous lines of CN and CO. In addition, absorption by atomic lines and OH is also present. The line blocking in this region increases rapidly to later types and exhibits a positive luminosity effect. In the dwarf stars absorption by H2O will occur in spectral types as early as about M2 (Mould, 1978) and should effect the wide-band colors of these stars. 157 Bell, et al. (1976b) have shown that line blocking must be included in the calculation of synthetic intermediate-band colors. The results of this study show that these problems can be avoided by mea suring at continuum points with narrow-band photometry, greatly sim plifying the interpretation of the observational data. CHAPTER VI LABORATORY STUDIES OF THE INFRARED SPECTRUM OF ACETYLENE Section 6.1 - Introduction Absorption bands of the molecule acetylene (C2H 2) have recently been detected in the infrared spectra of several cool carbon stars (Ridgway, et al., 1976; Ridgway, Carbon, and Hall, 1978). This chapter presents a laboratory analysis of the bands reported in these stars including measurements of intensities of some lines in the stronger bands. The laboratory data were taken in 1978 and 1979 with The Ohio State University 10-m focal length Czerny-Turner vacuum grating spectrometer in collaboration with Dr. K. Narahari Rao of The Ohio State University Department of Physics and Dr. A. Baldacci of the Institute of Organic Chemistry in Venice, Italy. This project was part of a ongoing study of molecules of astrophysical interest in the laboratory of Dr. Rao. Dr. Baldacci has studied the infrared spectrum of acetylene for a number of years, and references to his work on this molecule appear throughout this chapter. During the summer of 1979 and in January and February 1980 the author worked in Venice, Italy, with Dr. Baldacci to complete the analysis at 3 pm reported in this chapter. Acetylene is an important molecule in the atmospheres of many cool carbon stars. High-resolution spectra obtained at Kitt Peak indicate 158 159 that for some stars it is an important contributor to the strong 3 pm depression (Ridgway, Carbon, and Hall, 1978). Since polyatomic forma tion is favored at lower temperatures and 3 pm is close to the flux peak, it can be expected that acetylene will be an important opacity source in the upper atmospheres of the cooler carbon stars and should be included in model atmosphere computations. Also, since the v 3 band of 12C 13CH2 has been detected, the acetylene bands can be used to derive a value of the 12C/13C ratio in some stars. As emphasized in the recent review article on infrared spectro scopy of stars by Merrill and Ridgway (1979), there is an important need for laboratory data of many atomic and molecular species of astro- physical interest. This study was undertaken to provide some of the line data needed for the molecule acetylene. Section 6.2 - Theory of Vibration-Rotation Spectra of Linear Molecules In the first approximation the term values (cm-1) for the rota tional levels in a vibration-rotation band are given by V = = G (v, 2,, J) + F (2,, J) (6 .2-1 ) he v where G(v,2,,J) and F^(2,,J) are the vibrational and rotational term values, respectively. The rotational term value is given by F (2, J) = B fJ(J+l) - 22] - D [J(J+1) - 2,2 ]2 + H [J(J+1) - &2]3 V V V V - Lv [J(J+l) - l2]h + (6 .2-2) 160 where £ is the vibrational angular momentum quantum number which arises for degenerate vibrations (v^ and V 5 modes of acetylene). For each degenerate mode with vibrational quantum number v_^ the vibrational angular momentum quantum number can assume the values £. = v ., v . , v . ,...,1 , 0 1 1 1 - 2 1-14 In linear molecules the vibrational states may be classified according to the value of the quantum number £ as indicated in Table 18 below. Table 18. Classification of Vibrational States of Linear Molecules £ = I Ai Vibrational Species 0 E+ or Z~ 1 n 2 A 3 $ •• •• •• The existence of £ values greater than zero leads to an energy splitting called "£-type doubling". In II vibrational states the splitting is significant, but in A states the effect is usually small except when a I vibrational state lies nearby. Since the total angular momentum J must be equal to or greater than the vibrational quantum number £, rotational levels within a vibrational band are given by J = £, £+1, £+2, £+3, .... 161 Sublevels of II, A, $, ... states are designated as e or f depending on the symmetry of rovibronic eigenstates upon inversion. In this study the following convention is adopted for labeling e and f components: an e component is + if J is even and is - if J is odd and an f compon ent is - if J is even and + if J is odd. In the case of acetylene ^he individual vibrational states are £i £ c £ labeled as viv2v3vt v5 or V1V2V3(vtvs) • The latter designation applies to states involved in vibrational £-type resonance or doubling. If two states exist with the same designation, they are distinguished with the aid of Roman numerals I and II rather than by the values of £4 and £5 since they are no longer good quantum numbers. The interpretation of the vibrational energies of acetylene is complicated by the existence of £-type resonance and doubling effects in the degenerate modes. Pliva (1972a) has studied the degenerate modes of 12C2H2 and has obtained a set of molecular constants from the laboratory data of Pliva (1972b) and Palmer, Miclcelson, and Rao (1972). Energy expressions correct to the fourth order of approximation were required, and solutions were obtained as eigenfunctions of the vibra tion-rotation energy matrix. The total eigenfunction in zeroeth approximation can be written as a product of the electronic, vibrational, and rotational eigenfunc tions. Rotational levels of linear molecules are designated as having positive or negative parity depending on whether the total eigenfunc tion remains unchanged or changes sign for an inversion of all particles at the center of mass. If the electronic and vibrational eigenfunctions 162 remain unchanged, the symmetry character depends only on the rotational eigenfunctions and the even rotational levels are positive, the odd ones negative. This is the case for states of acetylene, while £ vibra tional levels have negative even rotational levels and positive odd rotational levels. In n, A, etc., vibrational levels both positive and negative components occur for each J, and the order alternates for successive rotational levels etc. or etc.). For linear molecules with a center of symmetry (point group D^), the total wavefunction can either be symmetric or antisymmetric with respect to a simultaneous exchange of all pairs of identical nuclei. All vibrational levels that are symmetric with respect to an inversion are subscripted g (gerade) while those that are antisymmetric are subscripted u (ungerade). The positive rotational levels are symmetric and the negative antisymmetric for "g" states. The reverse is true for rotational levels within a "u" subscripted vibrational state. These designations do not apply to linear molecules of point group C ^ , such as 12C13CH2 . The dipole selection rules for vibration-rotation transitions of linear molecules have been summarized in Table 19-. The symbol -e > indicates that the transition is allowed and -<— -j— ► means it is forbid den. In the case for which A£=0 but 5.^0, AJ=0 is allowed, but the corresponding (Q) branch is weak with the intensity decreasing rapidly to higher J. 163 Transitions for which AJ = J ’-J" = +1 are termed R branch transi tions, AJ = 0 transitions are Q branch transitions, and AJ = -1 are P branch transitions. The single primed values refer to the upper level and the double primed to the lower level. If a linear molecule belongs to point group D , that is, if it has “h a center of symmetry, alternate rotational levels have different statis tical weight due to nuclear spin. The ratio of the statistical weights of the symmetric and antisymmetric levels depends on both the nuclear spin and the type of statistics (Bose or Fermi) obeyed by the consti tuent nuclei. Statistical weights applicable to the various forms of acetylene of point group are summarized in Table 20. Since the rotational levels within a vibrational band are alternately symmetric and antisymmetric, successive lines in each branch of a molecular band of a D , molecule show a characteristic "alternation of intensities", °°h This alternation is very helpful in deciding the J numbering of a band and in identifying the vibrational states involved in a transition. The effect of nuclear spin statistics must also be included in computing the partition function (see Section 6,5). For isotopic forms of acetylene not listed in Table 20 the distinc tion between symmetric and antisymmetric levels disappears and there is no difference in the nuclear spin statistical weights of the even and odd rotational levels. These molecules are of the COT^ point group and intensity alternation does not occur in the spectra. 164 Table 19. Infrared Selection Rules for Linear Molecules 1. A& = 0, ±1 Vibrational Levels 2. X X 3. g <— p U, g ■*-/-+ g, U <5-7^ U 4. AJ = 0, ±1 (J=0 J=0) 5. + *—► + •»/❖ +, - - 6. s o— o s , a Table 20 Nuclear Spin Statistical Weights for Acetylene Isotopes of Point Group D . °°h - Statistical Weight Factors Resultant Symmetric Antisymmetric Molecule Statis tics Levels Levels 1 2 r h Fermi 1 3 2 2 13r h Bose 10 6 2 2 12C D Bose 6 3 2 2 13C D Fermi 15 21 2 2 165 Section 6.3 - Measurement of Line Intensities of Linear Molecules Consider a beam of radiation of intensity 1 (v) incident on a homp- o geneous gas sample in thermal equilibrium. The one dimensional equa tion of radiative transfer for pure absorption can be written (Arnold, Whiting, and Lyle, 1969) dlpX>dx') = a (vH 1-exP ( ^ B(v,T) -1- a(v) I(v,x) exp ( -a(v) I(v,x) (6.3-1) where a(v) is the absorption coefficient per unit length per unit pres sure at wavenumber v, I ( v jX) is the specific intensity at distance x measured from the boundary of the gas sample, and B(v,T) is the Planck function of the gas at temperature T. The first term on the right side corresponds to spontaneous emission, the second is induced emission and the last is absorption. For a slab of thickness L, the emergent intensity is given by I(v,L) = B(v,T) [l-exp(-k(v)pL)]+ Iq (v) [exp(-k(v)pL)] (6.3-2) where k(v) = a (v) [1-exp ^ J is the absorption coefficient (cm-1 atm-1) corrected for stimulated emission. In the case that B(v ,T)< T(v) = = exp(-k(v)pL). (6.3-3) •Lq l‘) 166 For room-temperature absorption experiments in the 3 pm region, Equa tion 6.3-3 applies since the incident intensity of the spectrometer beam is far larger than the magnitude of the Planck function. The line intensity or the integrated absorption coefficient is defined by the relation (Pugh and Rao, 1976) (6.3-4) For laboratory work the units in common use are cm 1 atm 1 at tempera ture T for k(v), atm for pressure, cm for path length, and cm-2 atm-1 at temperature T for the line intensity. Other units and conversion factors are given by Pugh and Rao (1976). The intensity of a rotational line will change with temperature in accordance with the Maxwell-Boltzmann distribution law. The line in tensity at temperature T can be converted to a reference temperature Tq from the expression (6.3-5) where E is the excitation energy of the lower level of the transition above the ground state and Q(T) is the total internal partition func tion at temperature T and is given by Q(T) 2 (f)(2J+1) exp[-E(v,J)/kT] (6.3-6) v J 167 where v represents the set of quantum numbers which define a vibrational state and cj> is the nuclear spin statistical weight (1 or 3 for 12C2H 2). The summation over all levels includes rotational levels split by £-type doubling. For molecules in which one atom is replaced by an isotopic atom, for example 12C33CH2, there is no difference in the statistical weights of even and odd levels and The line intensity (cm-2 atm-1 at temperature T) for a rotational level within a vibration-rotation band of a linear molecule is given (Penner, 1959) by 8tt3v N, o t v'i'J1 JJ,£ R sj (i) ' 3hcQ(T) 5J'£' J £ v£ J hcv 1-exp Tf~ (6.3-7) where is the total number of molecules per unit volume per unit JU' pressure, V is the wavenumber at line center. is the matrix J£ element of the dipole moment of the pure rotational transition, v 1 £1 J' R is the matrix element of the dipole moment of the vibrational v£J transition and gji^i the statistical weight of the upper state. Applying the proper summation rules and including the nuclear spin statistical weight factor, the following expressions can be derived from Penner (1959). 168 For A£ = 0 (parallel bands), J ' £1 (m2-£ 2) R and P branches, 3J'£' J£ [ml J' £' £2 (2J+1) U Q branch (6.3-8) 3J'£' J £ J(J+1) where the unprimed quantum numbers refer to the lower level of the transition and the primed quantum numbers refer to the upper level, In the above m = J+l for the R branch and m = -J for the P branch. For A£ = ±1 (perpendicular bands), J ' £' (J ± £+ 1) (J + £ + 2) U R branch, J£ 2 (J+l) (-J + £) (J + £ - 1) P branch. 2J (2J+1) (J + £) (J ± £ + 1) Q branch. (6.3-9) 2[J(J+l)] If the line strength is measured for an unresolved £-type doublet, the factors given in Equation 6.3-8 must be multiplied by 2. Because of the interaction of vibration and rotation, the matrix element of the vibrational transition is often written as: v ' £' J1 v ' £1 R R F(J) (6.3-10) v£ J v£ v ' £ 1 where R is referred to as the rotationless matrix element and v£ F(J) is a factor which accounts for the interaction of vibration and rotation (centrifugal stretching, Coriolis interaction, etc.). 169 Band strengths are frequently reported in the literature. In this analysis the band strength is defined as the sum of the line intensities of all lines in all branches in a band: Stot(T) = 5 3 SJ (T)* (6.3-11) band If degenerate levels are involved, the summation is taken to include the subbands split by Ji-type doubling. Equation 6.3-11 is convenient when comparing results with low resolution measurements. Unfortunately, under the experimental conditions used in this study, the line intensity cannot be directly computed with Equations 6.3-3 and 6.3-4. The Doppler half-width is approximately a factor of 10 smaller than the resolution of the spectrometer used in this study. Therefore, the observed line profile primarily reflects the instrumen tal profile function, and the absorption coefficient cannot be directly measured as a function of wavelength. It is therefore necessary to assume a knowledge of the broadening mechanism and use the method of equivalent widths. The measured equivalent width is defined by the relation ' Vo+n / (1 - T(v))dv. (6.3-12) V — T) 0 In the above v is the wavenumber at line center and the integration- o has been carried out to distance r| (cm-1) from line center where the absorption is negligibly small, From Equations 6.3-3 and 6.3-12 the 170 equivalent width can also be calculated over the same interval from the absorption coefficient with the relation W [1 - exp (-lc(v)pL) ] dv (6.3-13) c It has been shown theoretically (DePrima and Penner, 1955; Goody, 1964) that the equivalent width is independent of resolving power if Iq varies linearly with v, if the response function is symmetric, or if Iq is constant over the width of the response function. For most lines the dominant broadening mechanism is either colli- sional or Doppler broadening or a combination of the two. The usual approximation is to adopt the Voigt profile which is a combination of independent Lorentz and Doppler broadening mechanisms. It is given (Pugh and Rao, 1976) by (6.3-14) where M is the molecular mass, is Avogadro's number, and b^ and bp are the half-width at half height of the Lorentz and Doppler profiles, respectively. In the present analysis the numerical relations of Armstrong (1967) were used to evaluate the Voigt function. The compu ted values agree with the tabulated values of Hummer (1965) to eight decimal places. 171 It is generally assumed that collisional half-widths are linearly proportional to the pressure so that bL = Yop. (6.3-15) Although techniques have been developed to calculate theoretical colli sional half-widths (cf. Yamamoto, Tanaka, and Aoki, 1969), it is generally agreed that laboratory measurements are preferable because of inadequacies in the theory (Varanasi and Sarangi, 1974). It is important to note that the values of y q are a function of rotational quantum number and the temperature, and the values are different for each molecule and broadening gas. Under laboratory conditions it is not possible to carry out the integration of Equation 6.3-12 over all wavelengths. Instead the integrals in Equations 6.3-12 and 6.3-13 are carried out to a distance q (cm-1) from line center where the absorption is small and changing slowly over one spectral slit width. In this case it is necessary to apply corrections for experimental loss resulting from the slow decrease of the absorption in the wings of Doppler-Lorentz lines. The situation is illustrated in Figure 36. Here a line with line center at has a measured equivalent width (singly cross-hatched area) determined by integrating from v„ = v - n to v = v + n. The J b I o u o measured 100% transmittance level has been determined from data points near the ends of the integration interval and is less than the true 100% transmittance level because of residual absorption near the end points. The measured equivalent width and the true equivalent width 172 CORRECTION FOR EXPERIMENTAL LOSS 100% LxJ O z: < i- CO z < cr t- LU V (c m '1) W (TRUE) = [l- T ( 2 /g ) -AZ/+T(I/f)- W(MEAS) W(TRUE)=TRUE INTEGRATED ABSORPTION W(MEAS) = MEASURED INTEGRATED ABSORPTION Figure 36. Correction for experimental loss. The singly cross- hatched region indicates the area under the line profile used to measure the equivalent width. Be cause of residual line absorption near the ends of the integration interval, the 100% transmittance level will be underestimated. The additional area (doubly cross-hatched region) must be included to determine the true equivalent width. 173 are related by the expression (Fridovich, et_ a l ., 1980) Wt = [1-t(v£)]”Av + t (v £) Wm (6.3-16) The line strengths in the present analysis were determined by iteration. From a starting value of S a computer program determined W^ by integrating Equation 6.3-13 over the interval of measurement. Iterations continued until agreed with Wt within 1 part in 101*. For the conditions used in this study experimental loss corrections amounted to a change of only 0.5 to 2% in the calculated value of S. Measurements of line intensities are best made at high resolution and at low pressure. When the pressure is less than about 1 torr the line shape is almost a pure-Doppler contour which has a very sharp wing cutoff. The corrections for experimental loss are much smaller for a Doppler line than for a Voigt or Lorentz line. For a Lorentz line near the linear absorption region, integrations out to a total distance of 25 Lorentz half-widths (of the order of 2.5 cm-1 at atmos pheric pressure for many molecules) are required in order to keep corrections for experimental loss less than 10% or over a distance of 400 Lorentz half-widths to obtain corrections of 0.3% (Korb, Hunt, and Plyler, 1968). At these distances line overlap is likely to be a problem and any small error in the baseline level will cause serious errors in the measurements. Since is an experimentally determined parameter, an error in its assumed value will result in additional error in the measured intensity. In addition, there is 174 considerable evidence that the Lorentz profile is only an approxima tion to the collision-broadened line shape in the far wings (cf. Winters, Silverman, and Benedict, 1964), and this will introduce an additional error. The measurement of Doppler lines requires high resolution. In Figure 37 data from the tables of Jansson and Korb (1967) have been used to generate curves of growth for several values of a. For typical conditions in this study a = 0.05 and b^ = 0.004. From the figure it can be seen that for equivalent widths larger than about 0.01 cm-1, the curve of growth becomes strongly nonlinear. Small errors in the measurement of the equivalent width can cause large uncertainties in the derived line strength at large equivalent widths. It is therefore important to measure weak lines (W <0.01 cm-1) at m high resolution. The resolution of The Ohio State University 10-m focal length Czerny-Turner vacuum grating spectrometer is sufficient (0.03 cm’"1) to make such measurements. = 10.0 a = 0. 4 Figure 37. Curves of growth. The data were taken from the tables of 175 Jansson and Korb (1968). 176 Section 6.4 - Experimental Details All acetylene spectra reported in this thesis were recorded with the Ohio State University 10-m focal length C z e m y - T u m e r vacuum grating spectrometer in double-pass mode. The experimental details have been summarized in Table 21. The data recorded in the 3 pm region were obtained at both room temperature and at a temperature of 160 C. The elevated temperature was used to bring out "hot" bands which might be visible in stellar spectra. A heating blanket and control unit purchased from the Briscoe Manufacturing Company (Columbus, Ohio) were used for the high temperature runs. A total of 32 charts were recorded for the line position studies. The experimental conditions and regions covered by each chart are summarized in Table 22. Chart #5 has not been included since it was later determined to have been recorded in the wrong grating order. Line positions were measured relative to the (1,0) and (2,0) bands of carbon monoxide (Mantz, et al., 1975). A Michelson goniometer (Chen, 1975) eliminated most of the sources of systematic error, especially changes in the rate of the chart paper and grating drives. Most line positions were measured at least four times, and some were measured ten or more times. Line positions for the stronger unblended lines varied by no more than 0.005 cm” 1. The mean measured positions of all 3000 lines are tabulated in Appendix B. A 99.6% minimum purity acetylene sample supplied by the Matheson Company was used for the measurements. For the intensity calculations, the gas sample was assumed to be 100% pure with the distribution of the 12 12 isotopic varieties given by the terrestrial values of 97.81% C 177 Table 21 Experimental Details in Recording Acetylene Spectra (a.) Spectrometer and Accessories 10-m focal length Czerny-Turner vacuum grating spectrometer equipped with a 40 cm x 20 cm (16" x 8") Harrison-ruled echelle (Smith et_ a_l. 1978) Source — carbon rod furnace (Rao 1972) Spectral resolution — about 0.03 cm Scanning rate — 0.01 cm ^/min; Detector — liquid nitrogen cooled InSb; Signal-to-Noise ratio — 50:1 peak-t.o-peak with a 3 sec time constant. (b.) Absorption Cells For intensity measurements — Glass cells equipped with CaF^ windows. For position measurements — Glass cell of 1-m length with CaF^ windows. Steel cell of 1-m length and a heating jacket for elevated temperatures. (c.) Gas Pressure For intensity measurements — 0.20 to 5.49 torr measured with MKS Baratron gauges. For position measurements — 2.5 to 100 torr pressure. (d.) Temperature For intensity measurements cell temperatures were monitored with precision thermistor probes. (e.) Range of Equivalent Widths for Intensity Studies 0.003 to 0.010 cm ^ corresponding to near Doppler lines on the linear part of the curve of growth. 178 Table 22 Experimental Conditions for 3 pm Position Spectra 2 Region Pressure Calibration (cm~l) Order (mm Hg) Temperature-*- Standard 3198-3254 18 3.5 R Cl, C2 2 3201-3259 18 3.5 R Cl, C2 3 3251-3297 19 2.5 R C2 4 3297-3357 19 2.5 R Cl, C2 6 3290-3366 19 2.5 R Cl, C2 7 3350-3407 19 45.0 R C2 8 3347-3405 19 45.0 R C2 9 3160-3209 18 45.0 R C2 10 3163-3209 18 45.0 R C2 11 3353-3402 19 50.0 H C2 12 3297-3357 19 2.5 H C2 13 3292-3360 19 7.5 H C2 14 3254-3292 19 2.5 H C2 15 3251-3292 19 2.5 H C2 16 3198-3259 18 2.5 H Cl, C2 17 3201-3259 18 2.5 H Cl, C2 18 3146-3192 18 100.0 H C2 19 3139-3198 18 100.0 H C2 20 3135-3192 18 100.0 H C2 21 3363-3405 19 100.0 H C2 22 3366-3407 19 100.0 H C2 179 Table 22 Experimental Conditions for 3 pm Position Spectra (cont'd.) 2 Chart Region Pressure Calibration No. ( cm- ) Order (mm Hg) Temperature^ Standard 23 3317-3376 19 12.0 H C2 24 3305-3357 19 12.0 H C2 25 3353-3378 19 12.0 H C2 26 3183-3259 18 12.0 H Cl, C2 27 3177-3254 18 12.0 H Cl, C2 28 3251-3305 19 7.0 Ii C2 29 3249-3317 19 7.0 H C2 30 3254-3309 19 3.0 R C2 31 3309-3357 19 3.0 R C2 32 3189-3259 18 3.0 R Cl, C2 Notes: 1 R = room temperature; H = heated sample (160 C) 2 Cl = CO (1,0); C2 = CO (2,0) 180 2.18% 12Cl3CH ; and o.01% 13C 13CH2 (Barnes, 1972). Gas pressures have been measured with MKS Instruments (Burlington, MA) Baratron gauges. For pressures less than 1.0 torr a 0-1 torr head was used while pressures greater than 1.0 torr were measured with a 0- 100 torr head. A model 170M-26A meter unit, a 170M-7A electronics unit, and 170M-34B multiple head selector head were used. The calibration of the pressure readings was viewed as very impor tant. Both gauge heads were sent to the factory for calibration prior to beginning the measurements. Approximately midway through the inten sity measurements both heads were again sent to the factory to have the calibration checked. The readings of the two pressure heads were also intercompared throughout data acquisition. At pressures greater than 0.1 torr, the readings were always found to agree to within 0.5%. Pres sure readings were compared on several occasions with those obtained with Baratron gauges owned by the National Oceanic and Atmospheric Administra tion/National Environmental Satellite Service. Since the NOAA/NESS gauge was calibrated at the National Bureau of Standards, an independent check of the pressure readings was obtained. Within the range of pres sures used for the intensity measurements, the gauges agreed to within 1%. In Figure 38 pressure readings obtained with the Ohio State and NOAA/NESS Baratron gauges are intercompared at two epochs. The procedure used to fill the sample cells is as follows. Sample cells were pumped for two or more hours with a diffusion pump equipped with a liquid-nitrogen-filled cold trap. When the system pressure reached approximately 2 x 10 5 torr (as measured with a Varian model 524-2 cold cathode gauge and model 860 meter), the zero points on the DIFF (Pt.-Poso/Pt) x 100 .f o 2.of- -2 .L O l.0L Figure 38. Comparison of pressure gauge readings obtained with the the with obtained readings gauge pressure of Comparison 38. Figure - A O ° O OCTOBER 77 OCTOBER O ° O ° O ° A AU A A U A A A 0 20 0 40 0 60 0 80 0 1000 900 800 700 600 500 400 300 200 100 were taken with the Ohio State 0-100 torr head and the the and head torr 0-100 State Ohio the with taken were between the readings of the two gauges has been plotted plotted been has gauges two the of readings the between NOAA/NESS 0-1 torr head. The percentage difference difference percentage The head. torr 0-1 NOAA/NESS here data The Baratrons. State Ohio the and NOAA/NESS vs. the pressure in pm Hg. pm in pressure the vs. s O © G © O O ” s 5 P(/zmHg) RSUE AG COMPARISON GAUGE PRESSURE A 78 MAY A NOAA- OSU NOAA- A A 181 182 Baratron gauges were checked and adjusted, if necessary. The pumping system was then valved off, and the acetylene gas was allowed to flow slowly into the system until the desired pressure was reached. The system pressure was monitored for several minutes to assure that equili brium had been reached. At this point the pressure and cell temperature were recorded and the cell valve closed. The sample cell was immediately taken to the spectrometer to record the data. Cell temperatures were continuously monitored with precision ther mistor probes and a model 46 meter obtained from the Yellow Springs Instrument Company (Yellow Springs, Ohio). The YSI Series 400 probes have a quoted accuracy of ± 0.1 C while the meter accuracy was stated to be ± 0.15 C. Nine glass cells having path lengths ranging from 1.988 to 96.95 cm were used for the intensity runs. For the longest cell the path length was measured with a Pratt and Whitney 80-inch traveling microscope. Measurements were taken at 90 degree intervals along with circumference of the windows, averaged, and the CaF x<7indow thicknesses subtracted to obtain the gas path length. The readings at the four points agreed to within 0.01 cm. The path lengths of the shorter cells were measured to an accuracy of 0.003 cm with precision calipers. System linearity was tested by placing a sapphire window in the beam, and the fractional decrease in signal amplitude was measured as a func tion of source intensity. The fractional decrease in the recorded out put was found to be independent of the beam intensity. By comparing the signal level at the center of a saturated line with that obtained by blocking the beam at the exit slit and placing the prism between orders, 183 the amount of scattered light was found to be less than 0.3%. Scattered light corrections were not applied to the intensity data. Long term source-electronics stability was tested by running the chart recorder at a fixed grating position for about one hour. No drift was noted during that period. The analog records were digitized with a Bendix Datagrid Digitizer. Approximately 2000 data points were recorded per line by moving the cur sor along the spectral line profile. A linear least squares fit to the data points on both sides of the line was used to determine the zero absorption level. About 0.10 cm-1 of spectrum was included in the least squares fit. Successive measurements of the equivalent width of the same record agreed to better than 0.5%. Accuracy was limited primarily by the ability to follow the spectral profile manually with the cursor. A digitized scan is shown in Figure 39. A total of 709 intensity scans were made, all at room temperature. For each line four or more scans at between two and eight pressures were made. For each scan the zero level was measured prior to and after the run by moving the prism between orders. Calibration lines on both sides of the line being measured for intensity were included to calculate the dispersion. The use of goniometer fringes increased the accuracy of the dispersion measurements. The intensities reported are the mean values of all runs at 300 K. The pressures and path lengths were adjusted for each line so that the equivalent width was between 0.003 to 0.010 cm-1. For the experimen tal conditions this range of equivalent width is very close to the linear 0.0 0.0 0.2 0.3 0.4 CT m 0.5 x X 0.6 O.S.U. DIGITIZED OUTPUT: f LIMITS OF INTEGRATION 0.9 2320. 5 I 2320. 61 2 3 2 0 .GG2320.56 WAVENUMBER Figure 39. Profile of an absorption line obtained with the Ohio State University 10-m focal length Czemy-Tumer vac uum grating spectrometer. The data were digitized with a Bendix Datagrid'digitizer. Arrows mark the limits of integration used to determine the equivalent width. 185 part of the curve of growth. Pressures were kept as low as possible to minimize the effects of collisional broadening. 12 Section 6.5 - Partition Function for C2H2. In order to calculate the dipole moment matrix element from the observed line intensity, it is necessary to know the total internal partition function. This quantity allows the relative population of an individual rotational level to be calculated at temperature T under the conditions of thermal equilibrium. The partition function can be used to relate the observed line strength at one temperature to the line strength at any other temperature. All thermodynamic quantities can be expressed in terms of it (Herzberg, 1945). In the present study the total internal partition function has been 12 evaluated from a tabulation of the molecular constants of all ^ 2^2 -1 vibrational levels within 2200 cm of the ground state. The rotational and vibrational constants were assembled from several sources (Scott and Rao, 1965; Palmer, Mickelson, and Rao, 1972; Pliva, 1972a; Pliva, 1972b; Baldacci, et a l ., 1977) and are shown in Table 23 along with the appro priate nuclear spin statistical weight factors for the rotational levels of each vibrational band. The rotational constants for many of the vibrational levels listed in Table 23 must be regarded only as effective constants because of the effects of 5,-type resonance. The calculations were performed with Equation 6.3-6. For each vibrational state, rotational levels up to J = 100 were included. Values of Q(T) for the temperature range 200 K to 350 IC are tabulated in Table 24 at 10 K intervals along with the fractional population of Table 23 1 8 6 R0-VIBRATIONAL CONSTANTS (cm”1) AND STATISTICAL WEIGHTS FOR LOWER LEVELS OF 12C2H2 NSTATE SYMMETRYV 3 a J°EVEN J=0DD 0 D M 0 6 HMO 10 1 0000°0° l+ 0.000 1.17660810.000014 1.61010.007 0 1 3 g 01 O 1.17533910.000024 1.64010.015 1 3 o o o 2 O n 612.870i0.002 l g 1.18055810.000025 1.65410.017 3 1 1.17641210.000018 1.61010.009 3 1 3 0000°l1f n 730.3314±0.0016 l u 1.18111210.000019 1.65510.010 1 3 4 0002°0° z+ 1230.39i0.05 1.179510.0007 -8.514.1 0 1 3 g 1.177210.0003 7.410.8 1 3 2 0 5 0002 0 A 1233.5210.05 2 g 1.178410.0003 3 1 6 000(11) ° Z* 1328.073510.0017 1.1805010.00004 3.6210.03 3.0810.14 0 u 3 1 7 000(11)_° l" 1340.54710.003 1.1801010.00003 1.6910.02 0 u 1 3 1 e 1.1798510.00006 -0.20l0.Q5 -2.7+0.3 3 1 a 000(11)" A 1347.52410.005 u 2 1. 1798410.00005 1.6210.02 1 3 + 9 0000°2° I 1449.12110.003 1.1811010.00003 4.1010.02 4.9H0.05 0 1 3 g 1.1807410.00003 -1.07+0.04 -6.710.2 0 2 e 1 3 10 0000 2 A 1463.01310.003 2 g 1.18077+0.00003 1.6710.01 3 1 1 0 e 1.178 1 3 11 0003 0 n 1855.7210.05 g 1 1. 163 3 1 3 0 e 1.184 I 3 12 0003 0 1861.9310.05 g 3 1.184 3 1 1.1779510.00005 2.8710.12 1.810.9 3 1 13 000(21)1I1^ n 1941.17910.003 u 1 1.1856910.00005 3.1010.10 0.410.6 1 i 1.1826510.00008 3.4610.29 8.612.8 3 1 14 000 (2 l)11 6 n 1960.B7410.004 1 f u 1.1799010.00007 3.2210.25 5.912.3 1 3 1.186 3 1 15 000(21)3 ® 4* 1962.1 u 3 1.186 1 3 16 0100°0° Z+ 1974.31710.003 1. 1704010.00003 1.6510.03 g 0 1 3 1.1778310.00004 2.3510.04 0.910.1 1 3 17 000(12) 1ixe n 2049.05910.009 f g 1.1874910.00003 2.6610.04 1.010.2 3 1 1.183 1 3 18 000(12)1I e n 2066.998 f g 1.180 3 1 1.188 1 3 19 000(12)3 * 4 2085.5 g 3 1.188 3 1 0 1 G 1.1785810.00003 2.5110.09 1.510.6 3 1 20 0000 3 JI 2170.34310.002 u 1 1.1881510.00003 2.7010.08 -2.310.5 1 3 0 3 e 1.189 3 1 21 0000 3J 2198.1 u 3 1.189 1 3 TABLE 24 12c 2H2 ?ARTITI0N FUNCTION Vibrational Band 1 2 3 4 5 6 7 8 9 T Q(T) 10 11 12 13 14 15 16 17-21 200.0 245.4252 0.9657 0.0235 0.0100 0.0001 0.0003 0.0001 0.0001 0.0001 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 210.0 259.9259 0.9573 0.0287 0.0128 0.0002 0.0004 0.0001 0.0001 0.0002 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 220.0 274.9698 0.9479 0.0344 0.0159 0.0003 0.0006 0.0002 0.0001 0.0003 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 230.0 290.6077 0.9376 0.0405 0.0194 0.0004 0.0008 0.0002 0.0002 0.0004 0.0001 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 240.0 306.8898 0.9264 0.0469 0.0232 0.0006 0.0011 0.0003 0.0003 0.0006 0.0002 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 250.0 323.8649 0.9143 0.0537 0.0273 0.0008 0.0015 0.0004 0.0004 0.0008 0.0002 0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 260.0 341.5815 0.9015 0.0606 0.0316 0.0010 0.0020 0.0006 0.0005 0.0010 0.0003 0.0005 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 270.0 360.0871 0.8880 0.0677 0.0362 0.0013 0.0025 0.0007 0.0007 0.0013 0.0004 0.0007 0.0001 0.0000 0.0001 0.0001 0.0001 0.0000 0.0001 280.0 379.4288 0.8739 0.0749 0.0409 0.0016 0.0031 0.0009 0.0009 0.0017 0.0005 0.0009 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0002 290.0 399.6529 0.8593 0.0820 0.0458 0.0019 0.0038 0.0012 0.0011 0.0021 0.0006 0.0012 0.0002 0.0002 0.0001 0.0001 0.0001 0.0000 0.0002 300.0 420.8057 0.8442 0.0892 0.0507 0.0023 0.0045 0.0014 0.0014 0.0026 0.0008 0.0015 0.0002 0.0002 0.0002 0.0001 0.0001 0.0001 0.0003 310.0 442.9326 0.8287 0.0963 0.0558 0.0027 0.0054 0.0017 0.0016 0.0032 0.0010 0.0019 0.0003 0.0003 0.0002 0.0002 0.0002 0.0001 0.0005 320.0 466.0791 0.8129 0.1032 0.0608 0.0032 0.0063 0.0021 0.0020 0.0038 0.0012 0.0023 0.0004 0.0004 0.0003 0.0002 0.0002 0.0001 0.0006 330.0 490.2901 0.7969 0.1100 0.0659 0.0037 0.0074 0.0024 0.0023 0.0045 0.0014 0^0027 0.0005 0.0005 0.0003 0.0003 0.0003 0.0001 0.0008 340.0 515.6101 0.7807 0.1166 0.0709 0.0043 0.0084 0.0028 0.0027 0.0052 0.0017 187 0.0032 0.0006 0.0006 0.0004 0.0004 0.0004 0.0002 0.0010 350.0 542.0835 0.7644 0.1229 0.0758 0.0048 0.0096 0.0032 0.0031 0.0060 0.0020 0.0037 0.0007 0.0007 0.0005 0.0005 0.0005 0.0002 0.0013 188 each of the 16 lowest vibrational levels. Polynomial coefficients in T accurate to the seven significant figures over the same temperature range are presented in Table 25 (powers of 10 are in parentheses). Section 6.6 - Analysis of the Spectrum at 3 pm This section presents an analysis of the bands observed in the absorption spectrum of acetylene in the 3 pm region. The primary objec tive of this project was to identify "hot" bands arising from the 0002° ,20°, 000(11)°’2 and 0000°2°’2 levels which have sufficient intensity to be detectable in stellar spectra. In addition, corrections in the rotational assignments were made in a few instances for bands previously reported in the literature. 12 The strongest absorption in ^ i s from the bands and + (v. + vr)° , , which are in strong Fermi resonance and of comparable I a 3 /A- intensity. A total of five IT-H bands from the 0001°0° and OOOO0!1 levels were identifed and are of moderate intensity in the room-temperature spectrum. In the present work it has been possible to identify 14 12 additional "hot” bands of ar^s-‘-n§ from higher vibrational levels and 5 bands of 12C°3CH^ from the ground state, 0001°0°, and 0000° l1 levels. The 27 bands identified provide data on 41 different vibrational states. Figure 40 shows a short section of the 3 pm spectrum recorded at room temperature and a pressure of 3.05 mm Hg, with rotational assign ments given for the stronger lines. The strongest absorption features are from the v„ and v0 + (v, + v')?,. bands. Lines from several II—II 3 Z b 2,“}- bands are indicated and exhibit resolvable rotational L-type doubling. 189 Table 25 12 C2^2 Partit:*-on Function Polynomial Coefficients a = -1.8923462300 (+01) o 1.6578377395 (+00) al = -4.1672521882 (-03) a2 = 1.4106025215 (-05) a3 = 11 D3 D3 -9.4194026521 (-09) ■F* i ■F* 5.2942462726 (-12) a5 = Q(T) = aQ + a1 T + a2 T2 + a3 T3 + a^ T4 + a5 T5 ABSORPTION iue4. ctln setu ewe 39. n 39. cm 3291.3 and 3290.1 between spectrum Acetylene 40. Figure y -ye obig Te nest ai i 31 for 3:1 is ratio intensity The doubling. £-type by eodda ro eprtr ihapesr o 3.05 of pressure a with temperature room at recorded ie of lines stronger The cm. 96.95 of length path a and torr ttsis a e en o oainl ees split levels spin rotational for nuclear of seen be effect can The statistics identified. are features 3290.5 3291.0 190 191 Components with the same J value occur with an intensity ratio of 1:3 because of the effects of nuclear spin statistics. Although only a natural sample was used, rotational structure of the V3 band of is of moderate intensity in the spectrum. Short sections of spectra recorded at room temperature and at 160 C are compared in Figure 41. In addition to the strong resonance betx^een v and v (v + v )2., b 3 2 i+ 5 Fermi resonance is expected x^ithin a number of higer-energy diads and triads. Calculated unperturbed energies are presented in Table 26 for a number of resonating polyads expected as upper levels of transitions observable at 3 ym. From the data it can be seen that a very close resonance is expected between the levels in columns 1 and 3. Since the uncertainty in the unperturbed energies is likely to be large, it appears to be impossible to distinguish the ordering of the levels in columns 1 and 3 at the present time. In this analysis the convention has been adopted that the levels in column 1 (with v^ = 1) are assumed to have higher energies than those in column 3. In reality, a strong mixture of wave functions of the interacting levels will occur, owing to the extreme nearness of the unperturbed levels. Molecular constants reported in Table 27 and 28 were determined with the polynomial in "m" program of Palmer (1972). The errors quoted are the standard deviations in units of the last significant decimal place. Because many of the levels analyzed in this study are perturbed by A-type resonance and/or Fermi resonance, the rotational constants obtained for many bands are only effective values. For these transitions extrapolation to J values outside the range of the measured values will produce large errors. For two highly perturbed bands, systematic rather cfff' 3207.00 3208 00 320900 3270.00 Figure 41. Comparison between acetylene spectra recorded at 12.0 mm Hg pressure and 160 C (upper) and at 3.5 mm Hg pressure and room temperature (lower) in the region 3207 to 3211 cm-1. 193 Table 26 Calculated Unperturbed Energies for Several Diads 12 -1 and Triads of ^2^2 *n ^erm^ Resonance (cm ) Level G Level G Level G o o o 0010°0° 3288.AO 010(11)° 3288.34 001110° 3890.27 010(21)^ 3888.97 010(21)* 3908.66 00100!1 4007.84 010(12)^ 4007.76 010(12)* 4025.69 0012°0° 4496.79 010(31)° 4495.91 “T 001220° 4499.92 010(31)^ 4496.84 010(31)2 4524.99 001(11)° 4594.58 010(22)°IT 4594.24 010(22)°x 4630.26 001(11)° 4607.06 010(22)° 4607.41 OOl(ll)2 4614.03 010(22)^ 4612.37 010(22)2 4638.79 0010°2° 4715.74 010(13)° 4714.93 0010°22 4729.63 010(13)2X 4730.32 010(13)2 4752.63 T.iMi* ii Mtilucnl;ir Const.ints ( ) of lin Per I veil from the l'aruls .it 3 Urn .IMAX St. Dev. vo-i;1 v r r (n,-B")xin1 (n,-n")xio6 (ii'-iOxio10 (i.'-L")xio1A UPPER V R xlO3 0 010(11) o: '*> onoo°u° O' +) 11:81 .0020 i 6 -4.099 3- 4 0.853 3 7 1 . 92 ± 5 2.25 ± 9 52 51 2 .4 u g J269. 5399 ± 10 -4 . 676 3 5 0.515 -l 6 0.60 3 2 47 43 3.5 010(21)1 (IT) (II ) 0001!00 (II ) f-f 32 09. 3436 i 'J -3.127 ± 4 0.797 3 6 0.88 ±2 48 44 3.2 e-n 3272, 1050 ± 10 -5,164 t 6 0.457 - 8 0.56 15 46 42 3.9 010C12)1 (IT) (n ) 0000°1] (N ) f-f 3272. 1071 ± 10 -2.421 i 6 1.075 ± 7 1.33 ± 3 46 43 3.8 010(31)° (IT) O'. +) 0002°0° (E +) 3258.4594 i 35 -4.480 1 40 -2.138 ± 132 -21.62 ± 1.59 -64.51 i 6.46 39 33 8.0 e-e 3257. 2984 i 30 -3.071 2 41 3.977 ± 155 36.01 ± 2.26 143.71 ± 11.71 37 29 7.1 010(31) (TT) (A ) 000220° (A ) f-f 3257. 3180 i 18 -3.767 ± 8 0.489 ± 7 36 34 5.9 0 010(22) a B ) 000(h) - o; u ) 3259.2282 ± 15 -3.847 ± 9 0.493 ± 10 33 29 5.6 e-e 3260. 4 7 30 i 30 -3.639 3 36 -1.422 ± 102 -15.76 ± 78 31 28 7.2 010(22) (II) (A ) 000(11) (A(1) f-f 3260. 4755 1 19 -3. 625 9 0.548 ± 10 37 28 6.6 (110(1 3)^ (II) (r. +) noonn2° a 3 126].6321 3 22 -3.676 i 23 2.147 t 47 22 20 4.2 e-e 3262. 8331 ± 35 -3.738 ± 48 -1.916 ± 176 -16.36 ± 1.83 27 23 6.2 (A ) 0000°22 (A ) f-f 3262. 8332 ± 22 -3.682 ± 12 0.583 t 14 29 30 5.7 0 0 1 0 °0 ° (1 +) oooo°o0 O' +) 3294.8406 i 9 -4.213 ± 6 1.658 ± 10 4.65 ± 6 5.02 ± 12 53 51 3.5 e-e 3205 ,4715 ± 11 -4.662 1 6 0.900 ± 7 1.45 ± 2 47 46 3.9 oouV in ) onoi1 o° (ii ) f-f 3285 .4625 i 12 -4.082 ± 6 1.038 3 8 1.19 ± 3 46 46 4.4 194 Table 27 (cent inued) l.EVKLS JMAX St.Dev. ,v ,7 v0-n' v 2+n' ixlO1 (I)’-l)"]KlOr’ (H’-[lM)xl0lf} (L'-L*W 4 UPPER LOWER r R xlO3 e-e 3286.3846 t 10 -5.676 * 5 0.176 " 6 0.59 1 2 4 6 48 3.8 ooio0!1 ooooV (II ) u < V f-f 3286.3868 ± 11 -3.588 i 9 -0.316 ‘ 21 -5,06 " 17 -7.59 ± 42 46 44 3.5 nai 2non (T + ) n 002n 0° 32 77. 63RO J- 36 -5.184 i 63 1 .067 272 20.41 i 1.97 111.35 i 18.53 35 31 10.4 1) e-e 3275.704 7 ± 51 -3.311 ^ 69 1.046 ± 259 -3.01 ± 3.50 -32.13 37 32 12.6 2 0 ± 15.54 0012 0 (A ) 000220° 11 001(11)" a + ) 000(11)° 3281.2629 ± 21 -4.84 5 ± 32 2.081 ± 110 15.32 ± 1.00 28 26 5.7 g O a 3277.3741 ± 14 -4.485 ± 10 0.701 ± 12 30 28 4.8 001(11)° V 000(11)° u 3277.2561 ± 22 -4.901 ± 24 -1.560 1 65 -6.12 ± 47 30 30 5.0 001(11)2 000(11 )2 (A ) 11 0010°2° e-e 3239.7258 ± 14 -7. 728 ± 6 0.020 ± r» 38 28 4.8 inoiV (n ) nooo0!1 tn ) p. f-f 3239. 7295 ± 1 3 -7.115 ± 6 0.009 ± 5 38 3L 4.5 0110°0 ° (E +> 0100°0° (£ +) 3285.7058 ± 36 -5. 599 ± 3(1 -0. 350 + 71 25 19 6.8 195 Table 28 -1 12 13 Molecular Constants (cm ) of C CII^ Derived from the Rands at 3 pm LEVELS JMAX St.Dev. V o-B'£.'2+B''L"2 (B'-B")xl03 (D'-D")xl06 (U'-H")xl010 UPPER LOWER P R xlO3 0010°0° (Z+) 0000°0° (Z+ ) 3284.1904 ± 7 -5.499 ± 5 -0.015 ± 7 0.42 ± 2 42 44 3.1 e-e 3274.7079 ± 16 -5.554 ± 9 -0.109 i 10 31 30 3.8 0011l0° (n) oooi1o° (II) f-f 3274.7045 ± 19 -5.283 ± 15 -0.088 ± 27 30 19 4.2 e-e 3276.8239 ± 34 -5.550 ± 23 -0.121 ± 29 27 29 8.4 00100!1 (n> 00000 !1 (n> f-f 3276.8367 ± 33 -5.611 ± 22 -0.174 i 25 29 28 5.7 (01011)° (£+ ) 0000°0° (I+) 3250.4842 ± 20 -2.715 ± 16 1.361 ± 31 30 18 3.9 1000°0° a +) 0000°0° a+) 3361.5759 ± 20 -6.424 ± 30 -0.024 ± 104 16 20 5.8 196 197 than random differences exist between the observed and calculated values even with an eighth order polynomial. Observed and calculated line positions (cm "*) are presented in Tables 29 to 67. Vibrational term - 1 12 values (cm ) of C2H 2 obtained in this study are presented in Table 68. Transitions from the Ground State Bands of 12C2H2 : Both the v 2 and v 2 +(v^ + ^ 5) ^ bands have been measured up to approximately J = 50 in the present work. A satisfactory fit to the observational data required an eighth-order polynomial in both cases. The need for additional terms can be attributed to the effects of Fermi resonance and 5,-type resonance in the upper states. The lower-level combination differences were found to be in agreement with values com puted with the ground state constants of Palmer, Mickelson, and Rao (1972). Bands of 12C 13CH2 : Although only a natural sample was used in this study, it was possible to measure lines of the v ^ band up to J = 44 in the R branch and J = 42 in the P branch. A sixth-order polynomial was required to fit the data accurately. The values obtained are in agreement with the constants of Lafferty and Thibault (1964) and Ghersetti, et_ al. (1975). The ground-state constants of this molecule were calculated by fitting the AF''(J) values obtained in this study and in several other studies (Baldacci, Ghersetti, and Rao, 1973; Ghersetti, et al., 1975; Baldacci, Ghersetti, and Rao, 1977) to the standard expressions. 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5 3 5 2 o b 02 317 7o 147 3 1 7 7 o150 “ 0 o 3 38 3 3 3 4 o 74b 317 4o 4o0 6 A 7 4 o 4 6 1 “ Ool 3V 333bo 6 bC 3 35b o67 8 0 o 2 3 1 7 l o 734 3 1 7 i o 759 “Oob 40 3b5b o 392 3338 o392 “0 o 0 316 9 o 046 3 1 6 9oC43 0 a 3 4 A 33b0o46b 33b0o489 “ 0 o2 3 lb 6 o 3 lb 3166 o 314 0 o 4 *12 3362 o372 3 3o2 o3 7 0 0 o2 3163a 574 3i 63o 572 0 a 1 J 3364 o25? 5 364 o 284 0 o 3 316 0 o 822 3 l 60 o b17 Oob 4J.4* 3366 o 078 3 3ti6o 03 2 "0 o4 3 1 3 boObO 313bo04b 0 a 2 43 313 5o 2 b6 3 1 55o 266 ■“OoO 313 2 o 468 3132 o471 —0 o 3 4 S 3 A49o 661 3 l4 9ofob3 “ 0 o 2 4b 3 A4bo 842 3146 o b42 - 0 a 0 _ A 209 U b L c 40 0 UDSfc k\f t L AMD CAL6ULA TEL) rtAtf EMuMB fcKb i VAL oCM > 12 Uh THE 010(12) 1 (II) - 00000! 1 bAMU Oh e e L2 n 2 J M J 5 Ubb K 5 OSCALC 0-C P4 8 ) UBS SCALC U-C A100 A A 00 X 32 76 o 779 32?6o?b0 —0 0 A X 327 Vo 10 A 3 2790102 -O ol 326 Jo3bb 32o7 0 Bbb “ 0 0 3 3 32 b A o 410 3 2b1o 414 —0 0 4 326 5o 007 3265c 015 “0 o? 4 3 2 8 3 o if A6 3283 07 A3 0 0 2 32b 2 0 62 8 32 62 o631 “ 0 0 2 3 32 bb o007 32bOo003 0 0 2 326 0 0 241 3260o 236 0 0 3 6 52bbo2v3 32b8o2fct4 0 o9 3237c 832 7 3290o349 3290 o333 “ 0 o4 323 3 0422 32 5 5 0 417 Oob a 32V2 o 806 3292 ob10 “ 0 o4 3 2 3 2 0 993 32 32 0 992 Ocl y 3xV3 o053 3293 o 037 “0.3 325 0o 3b1 3250 0 357 0 o4 10 329 7 o289 3 297 o 29 A “ 0 0 3 324 bo 117 3248 0112 0 a 6 3299c313 324 3o 653 324 5 0 6 56 i l 0 “ 0 0 3 12 3 3 0 l o 731 330x o 726 0 3 2 4 3 0 lb7 3243o189 “ 0 0 2 A5 3303o92b 3 2 4 0 0713 14 3306 o113 3 306 oil'} -O ol 3238 o225 A 5 330b o2fc7 J30do 290 -00 3 3235o 727 lb 33i0o433 33x0 o433 Ool 32 33 o2 18 i 1 3 3 1 2 o o04 3 312 ob04 “ 0 cl 3230 0 698 lb 3314 o 7 44 3 3 a 4 o 7 4 2 Ool 322 8 0 A6 A 3228 0 167 -O 06 i.y 32 ibobbb 3 3 A 6 o 8 6 7 —0 0 2 322 60 629 322 5 o626 0 0 3 20 331b oV80 3 31 & o 9 7 9 Ool 3 22 3 0 ii73 3 2 2 3 oG72 Ool 21 3 3 2 1 o077 332lo07b -O ol 322 0o 30b 3 2 2 0 0 308 0 o0 22 332 3 o163 3323 o 16J OoO 3/,i 70936 3217ov32 Oob 23 3 32 3 o 2 4 I 3 32 3c2 34 Oo i 3 2 1 5o 344 3215 0 344 “0 o0 24 332? 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3 326 o003 -0o A 3183a10b 3 A 3328 o038 318 0o491 31b0o48? 0 o* 32 3 3 3 0 oOtoZ 3330o0bto O o b 3 17 7 obb4 3177 obb? “0 g 3 33 3332 oOtoV 3 A? bo223 31 lj o 2 i 5 Oob ! £ o 34 3334o 04 1 3334 o04to o 317 2 o b ? 3 3 a 72 o btoO 1 o 3 33 3 1 6 9 o 892 31to9o 893 “Ool 3o 3 ito $ » 204 316? o213 -OoB T AtiLE 55 * DESERVED AND LALCULa TED WAVENuMBEks ( VAC «LM ) DF THt 010(22)°- - 000(11)°- BAND OF 12 C ^ 2 a c M M B .e .a c==x= o- « cd■ — «=*. es» «» excmb . 3 K 4J HUBS R 1 *J) I CalO 0 -L AM 3 0 065 AM J J OALC o -c X100 Xl 00 0 3 2 6 1 o 38 I 1 3263o923 325 6 0 862 3256 0 068 “ 0 06 2 32b6oZ62 3254 0 509 32 54 o500 0 0 0 3 526bo 389 3268 o39 a “*0 Q 2 3 2 5 2 o l2 af 3252 0 125 -Ool •"* 3270o912 324Vo 733 3249 o742 —0 0 9 5 32 ? 3 o 22 i 32 7 3o223 —0 0 3 3247 c 357 3247 0 352 0 0 5 6 3 £.7 5 o529 3z75 o529 “ 0 0 1 3z44o945 3244 0 953 “0 0 9 7 / 7 o 827 52 77 0856 Ool 324 2o 542 3242 0 540 — 0 o 5 0 32bO o 112 5280 o l 14 —0 0 2 3 2 4 0 0 141 5 2 4 0 o 134 Oa? 9 3/82 o 393 3282c, 395 “0 o 0 323 7 0 711 3237o 713 “ 0 0 2 JlO 3£.b4c,662 5289 o664 - o a 3 2 3 5 o284 32 3 5 0 2 8 4 -OoO 11 32 06 a 92 9 32o6 o923 0 o4 323 2 0 848 3232 0 84 7 OoO Id 3 2 8 9 o A 8 / 3 2 8 9 0 1 7 8 0 o9 3230o413 3 2 3 0 0 40 3 1 oO 13 5 2 9 1 o428 3 2 9 1 04 2 1 Q06 3 /2 7 0947 3227 0950 —0 0 £. 14 5£93 o640 5293 o63 3 “ 0 0 7 322 5 o49b 3225 o489 0 0 9 15 32 95c 8 74 3 293 0 8 7 9 "0 0 6 322 3o 02 i 32 23o 020 OoO 16 5298 »08v 3298 o093 “ 0 0 5 3 / 2 Oo 545 3220 o543 0 0 2 i } 3 3 0 0 o29 0 3218 0 063 32 lb 0 057 0 0 6 18 3 3 0 2 o4 9 1 3 2 1 5o553 3 2 l 5 0 563 “ A o0 aV 5504 o 6 ?4 5504 0 67 4 0 o0 3 2 1 3 o062 3213 0 060 0 0 5 20 330o o 838 3 3 0 608 45 ““0 0 8 3210 c. 354 52 A 0o 54? 0 0 1 21 3309 o COfc 3 3 0 90006 0 0 2 320 8 0 02 b 3208 0 026 0 0 2 £.2 32ilo162 3311 015 5 O08 320 5 a 496 32 05 0 495 OoO 23 33l3o29fc 3 3i 3 c 29 / 0 0 6 3 /0 2 OF The 010(22)2e(H)--ooo(ii)2e BAND UF 12 C H 2 2 JiObb K ISO J)CALC 0 —c P«JDObS P 5 JPCALC U~C A100 JUOO 2 326 7 o b 10 3 2 6 7 obOV Ool 3 3,c69o89t 3 2 6 9o8 9 a 0 ob 32b 3o 369 32b3o 371 “ 0o7 3Z?2 o Ibi 3272oi6b “I o3 32buo983 32 b0o 99u “ Do ? b 327^ o9bZ 3 2 9 8 o 60 A 6 327 6o 7 93 3296 a 209 3296 o 2 Ob 0 ,3 i 32 79 o 097 329 3© b0b 3293 o b03 0 a 9 b 32b A » 39b 3Z9 A o 399 3Z91 o399 0 o 6 9 3z83 ©687 3 2 3 8 o. 9 7 3 3238o978 “ 0ob 10 3zbbo979 3 2 8 b o 9 l3 Oat) 323 6 o bbb 3z36obbb “OoO A 1 3ZbOoZoo 32bbc2b3 i o 3 3239c 126 32 39 o 12 8 "0 a 2 Iz 3290 o b2 7 3z3 A o 699 3 2 3 1 o6V5 “ Ool 13 3292 o79b 322 9o 269 3229o 2bb 0 o 9 19 329bo ObB 3226 o 619 32 26 o 810 0 Q 9 A b 3z97o 3 i4 322 9 o 3b9 3z2903b9 0ob 16 3z99 o b b 1 3z99ob69 “ A c. 3 3221©901 3z21 o 902 "Uo A 1? 3 3 0 1 &b0b 3ZA9o939 32 a 9 o 99 0 ”0 o 6 It 3309 oOnb 3216 o96b 32 16 o 97 1 “ 0 06 19 3306 oiiG 3 3 0 6 o2? 3 -0 o 3 32 i 9 o 98 8 3zA9o996 “0 o 8 20 330&G>99b 3308 Oo A 3zA £ o 009 32 1 2 o 019 -0 g b £ 1 3 3 a0 o704 320 9o b27 3209ob2b Ool 22 3312 o909 320 7 o 030 3207 o 028 0 o2 23 33 Ab oObb 3 3 ib o 0 9 l -0o5 3209c bZ9 62 09 o b2 1 0o 8 29 331?o2 7b 3317 o 2 6 9 1 o 2 320 2 o 000 3202 o009 “0 o 9 £ 6 33l9«,.9Z0 3A 99o970 3A99o 97b -0 o 9 l b 3321obbz 3321ob58 0 o9 319bo 93« 3196 <>932 0o 1 £ 1 33 12 OF The 010(22)2f (II)- 0 0 0 (ll)2f BAND CF c 2h 2 J KIJ )OdS R 11 3 5CALL U-C P{ jflGbb P5 JJCALC Lt-C X1C0 A100 2 32 to 1 o b 10 3 2 6 ? o b ll -0 * 0 $ 3 26V ob^b 3269 o 04 1 0 Q 8 32b3o 364 32 b3 0 37b “ 1 0 1 4 32 72 o 154 $ 2 1 2 o k 64 -loO 32b 0o9e3 3250&994 - l o l b 3 2 7 4 o4 ? 9 3248 0 606 to 3276 o786 3246 0 208 3246 0 210 “ 0 0 2 1 327 9 o 08b 3243o80b 32*o3 0 807 —0 0 1 8 32 8 lo 3 7 32blo3 (?7 “OoO 324Io399 324 10 397 0 0 2 9 3 2 B 3 o 6 6 1 32b2>o6b 0 Ool 323 bo 973 3238 o980 “~Q 0 i lo 32bb o V3fa 328bo93b 0 0 3 323bob56 3236 0 bbb Ool 11 32b& o 20 1 3234o126 3234o123 0 o3 4s.iL 329Go4bfc 32V0o4b9 “ 0 0 0 3231o694 3231 0 68 3 l o l 13 3292 o 7 Al 3292 o 707 0 0 3 322 9o 231 3229o 236 “0 0 4 14 3294o947 3226o781 lb 3297 ol77 3 2 2 4 0 32 0 32 2 4 0 3 17 0 0 3 io 3299 o397 322 io b49 3 2 2 1 0 846 0 ob 17 330 io t>07 3301o608 “0 0 1 3 21 90 380 3219 0 367 l o j IB 3303 o BO** 3303 o8Qti “0 0 4 32l6obbb 3 2 16 0 879 0o6 19 330o o 000 330bo 99b 0 0 2 3 2 l4 o 389 3 2 14o383 0 06 2 O 330b o 179 3 308 0 A1 1 0 0 2 321lo87b 3211 0 877 D 0 0 2 2 1 3310 o 347 33l0o 34 b 0 0 2 3 2 0 9 0 374 3209 0 363 l o l 2 2 331,2 o 49 1 3312 ob02 “loO 320 bo b3b 3206 0 890 “0 0 2 23 33 i “4o fcbC 3314o646 1 0 3 3204o311 3 2 0 4 o3 0 7 0 0 4 24 3 3 ib o 782 3316c ?79 0 0 3 3 20 1 0 7 b 8 32 0 1 c 76 5 “ 0 0 6 2b 331b ob99 3318 o899 “0 0 0 3l9Vo209 31990 212 —0 0 3 20 3 3^ 1 o 0 0 1 3a96o641 3196 0 649 -0 ob 2 1 332 3 o iOt 3323 0 101 0 0 b 3l9 4o06b 3l94o07b “0 0 8 2b 33^3 allO 332boiB1 “lol 3 1 9 10 492 29 318 8 0 893 318 8 0 897 -0 04 30 3 1 8 6 o288 3186 o290 -0 o2 31 3 18 3 0 toto 1 3 1 8 3 o67 1 “0 0 4 32 318 A o033 3A 8 i 0 040 “0o? 33 317 b ©4Qb 3176 ob97 Gob 3*4 3 l7bo 7b3 J i7 b o ? 4 l - 0 0 a 33 -3 17 3o 077 3173 0 071 0 0 to 36 3 1 7 0 a3b7 3 7 3 1 6 1 0698 3 lo7o 690 0 Q 8 CQ “ I lABLfc 58 e ObSfc RVfcD AMU CAtCULAlEU wAVENUMBEKS 8VACoCM I OF iMt 010(13)°+- 0000°2° BAND OF 12 C H *9 DBS K (U1CALC 0“C P3 3&0BS p u k a l c o-c XI00 X100 0 3263o981 1 3266o335 3259o265 3259o270 “0o4 2 3268 o67 3 325 6o90i 325bo900 Ool 3 32?lo007 32 54o 523 4 32?3o33Q 3252 o139 5 3275o645 3275o643 OoO 3249o ?48 6 32770953 327 7o 9 5 1 Ool 3247o 349 ? 3 2 8 Q o 245 3 2 8 0 o 2A8 ~0 o2 3244o942 8 3282o532 3 2 8 2 o 534 “ 0 o2 3 2 4 2 o328 9 3284o 813 J284o8 10 0o3 3240oll0 3240 o106 0 o4 10 3<£.87 o0?8 3287 o07 5 0 o3 3237o674 3237 o 676 “ 0 o 2 11 3289o333 3 2 8 9 o328 0o5 323 5o 236 3235 o 237 “ Ool 12 329lo563 3 2 9 1 o568 “ 0 o5 3232o 386 3232o789 “ 0 o 3 13 3293o803 3 2 9 3 o 796 Oo 8 3230o 337 3230 o331 0 o 6 14 3296 o009 3227ofa60 .>227 o863 -0o3 lb 3 z 9 8 o 199 3298 o 207 “■0 08 3225=>380 3226o384 “ 0 o 5 16 3300o389 322 2 o 895 3222 o 894 Ool 1? 3302o554 322Oo395 3220o392 0 =.3 9 O 18 3304o6§6 3304o70i 0 Ui 3217 o 87 8 19 3306 o82 9 O <.n ^2l5o350 20 3308 o 942 3308 o93J 0 3212o809 3 2 12o80d 0 o2 21 3 210o 299 32iO o 250 “0 oO 2 2 3 2 0 7 o 6?3 3207 o 676 “ Ool -1 228 1AtSLE 59 „ 0B8t RVE D Anl> LALCULA FEl) wAVFNUMBFKb t VACoCM J UF The 010 (13)2 (II)~0000°22 BA imD OF 12 C h e e / z J K J J 5 0 B i» R F j P CalL 0-C P1J }ObS P{J ) C ALL U-C XI00 X100 2 3269oB? 3 3 327 2 o zO 7 32? 2 oiO 8 “OoO 6233o724 *» 3 2 ? 4 0834 3 233a33b 328 3 o 3^0 -O ol 3 3z?6 o 8 3b 3 2?6o 832 “ 1 3zb0o954 32 30 09h8 0 o 6 6 3279 o 16t> 324 8 o 549 7 32 b 1 o 4 7 0 3246 o 144 a 3z b3 o 767 3 z 8 3 a 7 7 0 “0 a 3 3 29 3 o 736 3z43 o 7 32 0 o 9 9 32b6 o0?3 b>286 o069 0 o 9 8 2 4 1 o 319 32 9 A o 319 0 o 9 10 jzeboibO 32bbo332 0 ati 323 bo bb 9 ^2^8 o 890 -0 o 0 l i 3290o63aJ 3290 o63 3 “Ool 3236o<1>i>6 3z36 o 4 8 9 ■ 0oit 12 3 2 9 2 o921 3292 oVi 3 O o l 32 34 o 024 13 J /V 5 o 1b1 329 3 o18 6 “ 0 o 6 323 io 372 3 2 3 1 o683 "iaO 3z9 7 e431 3 2 9 7 o433 - 0 a4 3 2 2 9 o 137 13 oz 99 o 71 b .3299o 719 “Ool 322 6 a 683 322 6 o o 8 6 -Uo3 16 3 3 0 1 o9o 1 3 3 0 io 9 7 b 0o4 3 2 2 4 0 239 82 24© 230 0 o9 17 3 3 0 4 o 23C 3 304 o2 3 z “0 o 2 322 1o 763 3 2 2 1 o 769 — 0 o 6 lb 3306 o A-7 B 3306a 98 I “0 a 2 3 2 1 9o312 3219 o 303 0 o 9 19 330Bo ?26 330BO729 Oo 2 3216 o 823 3216o 832 —0 a 6 20 3 3 i0 o 9 6 2 3214 o 33 3 21 33 13 0 19 £ 3 3 1 3 o192 “0 o 1 3 2 1 1 o87b 32 i 1 o 872 U O 3 22 j 313 o*fiJ 3 a l3 o ^ I5 “0 o 2 320 9a 3 j 2 0 9o 38 2 -0 a b 23 33 i 7 o 6 31 331? 0629 0 o2 3 2 0 6 Q883 3206 o 8 34 Ool Z4* 33l9ob 32 320^0 3b2 3204o 377 0 o 6 23 332 2 o 02 z 320 io 869 320io 860 0 o 3 26 319 9o 323 3199o 330 -0.7 z7 3 l9t»o ?B7 3l96o7 86 Ool „! 229 7 AuLc 60o UBbhkVtD Al\)L> CALCULATfcD WAV fcNUMd EkS < VACoCM I 0 2 UF 1 nE -0000 2 BAND OF 12 C H 010 (13)2f (ID 2 2 J k 4 0 } UB8 KJ^PLAtC U“C EM 0 J) DB6 EM 0 JCAlC 0 - t Xl 00 X100 2 326 V o 8 ?4 3 32.7 2 o 207 3272 o 206 0 0 2 32 35a726 3274o330 323 3o338 3253a 342 “O 0 4 3 3 2 7 6 o b3b 3 21 bob*-) 6 “ 0 a 6 325Go 934 3230o 932 0 0 3 b 32 79 o13 3 3248o553 7 32b i o 463 32610^33 ” 0 0 2 3246 0 14b b 32&3o743 3263 o 7 *9-6 “ 0 o2 3 2 4 3 o? 3o 324 3 0 735 0 0 O 3 2 2 9 o099 14 3297 031b<■0 322 9 0 G9o “ 0 0 i. lb 02 99o 331 32 v 9 o 34b 0 3 2 2 6 o 641 3 2 2 6 o632 0 0 V Ao 3 3 0 io 7 6 ? 3224 0 157 A 7 33C3 o v?2 3303 oVJ6 “ 0 o4 322 I 0 660 3 2 2 1 0 674 *"i 0 ^ i a 33u6 o17 5 32i9olfcl 3219 o 182 “ 0 0 A IV 33Gb o 363 3 30b a 36 2 0o0 3216 0 6 b 1 2O 33 aG o332 3 3 10 o339 “ 0 0 7 321170 6 2 A4 0 172 “Ua 2 A i 3 3 i2 o 703 3 312 0 704 Ool 321 lo 632 32 110 633 -Ool 22 a 3 a ‘io Bo a 3 3 a 4 0 b 3 7 0 0 3 3 2 0 9 a 128 3209 0 123 0 0 3 23 3 31 7 o 003 3 3 a6 a999 Ool 3 2 0 60 390 3206 0 387 0 oJ 24 33 19 o A 2 1 3 3 a9 o12? 0o0 3^.0 4 0 033 3204o 039 -O 06 2 b 332 ^ o 243 332 1 0 2*9- 3 OoO 320 1 0 4»60 3 2 0 1 o4b1 °"lo5 2fc 33 23 o 3io£ 3323 0 34 3 —0 0 3 3 19 b092 A 319b 0 913 0 0 b 2 7 3 3 2 5 o433 3 19 6 a 3^6 3 1 9 6o334 1 0 3 2 « 3327 o 510 3327 O307 0 o 3 319 3 0 791 31 93a 74 3 —0 0 29 3329ob6 7 3191c139 3l91o i 4 A “ 0 0 30 3 3 3 1 o bU 7 333 A 0 6 1 A -0 0 4 -1 230 TABLE 61 e o b s e r v e d a n d c a l c u l a t e d wi a v e n u m b e r s 4v a C oC m j OF T m E o i i o °o ° - oioo°o° BAND OF 12 C2H 2 a Rt«j $ UBS HJ^SCALC O-C P4 J50B3 H J JCAl C 0 -C X 10 0 A 1 00 0 32b8o036 I 3290o354 3283 ©365 2 3292©6bl 328 Oo 999 32b1oO13 — I 0 3 3 3294o957 327 80648 3278 © 650 -Ool 4 3297©242 3276o289 3276o275 1 ©4 5 3299 ©5 lb 327 3o 890 3 2 7 3 o 890 OoO 6 3301o?7b 327lo4b8 3271©494 —0 06 7 33Q4o029 3269o095 3 2 6 9 0087 0 o8 8 330b o269 3266 0 669 9 3300©497 32b 4©2 3b 3264o240 “0 0 5 10 3310 o?l5 3 2 6 1 o80I 11 3312o922 325 9 0 352 32 59o352 Ool 12 3315©3L 17 3256o892 13 3317 0 302 3254©427 32 5 4 0422 0 ©5 14 33l9©47b 33l9o4 32 3 1 0 739 r® 22 O 23 322 Vo 203 3229ol96 0 24 3226 ©625 25 3224o045 3224o046 -Ool 231 -1 TAbLE 62 0 UbihKvED AND CALCULATED WA V ENuMB E Rb. ( VAC I 1 0 . 1 0 12 13 UP T HE 0011 0 - 0001 0 bAimD OF c ch2 e e J k I A 3220b 32b 2 0 2 73 Al 330 A o3b9 3 3 0 A o 3 6 9 “ 0 0 b 324 b 0 b 7*9 324b 0 b70 0 0 4 12 33G3o b 11 3 3 0 3 o b l2 "Ool 32 4 6 o4b ? 13 3 3 0 b o64b 3244o 032 3 2 4 4 © 033 -Ool A.1* 3307o?73 3 2 4 1 0 599 l b 3 3 0 9 o887 32 39 c. 1 54 i O 33 11 oVb? 3 32 1 o 9 90 "0 & 2 323 6 0 692 3236 o699 " 0 0 i 1? 33 14 <> 08 b 3 3 i ^ o0dA Oo'J 323“$ 0 23b 3234o 234 Ool i b 3316 o 160 3 23 lo 7b8 3 2 3 1 0 7 b9 "0 0 1 0 O 19 33 lb o 229 33A6 o 2 2 9 a 32 2 9 0.2 74 20 3320 02 86 3226 0 7 79 ll 3322 o332 32 2 4o 274 Cl 33 2“* o 366 3 3 2 4 o 3 6 6 “ OoO 32 21 0 7 59 23 3326o389 3219 0 2 3 7 3 2 19o23b 0 O 3 24 33 2 0 o 3 99 332.bo402 “ 0 0 2 321 to 701 3216 0 700 0 0 A 2b 3330 0 4 0 2 3214 0 157 ^ o 3332*392 3 2 1 1 0 604 i t 3 3 3 4 o 3 7 2 3334o37 A 0 0 2 3 20 9o 04 •' 3209o 042 0 0 2 10 3336o339 .3336 033b Ool 3206o 465 32 06 0 470 -u O b 2 9 3 3 3 b o OE THE 0 0 1 1 10 ° f - 0 0 0 1 10 ° f tJAND CE 12C1 3 CH2 €J» — — I 1 1 C C k (J ) Ubb k (JILALC U“C H J 5 Ubb E 4 J } 0 A LC o - c XI00 X100 1 327 9 o28 A 2 d2 b 1 o dd7 d281odb3 0 oJ 3270 o0&6 3 32o3 obid 326 7o 760 3267 o 761 “ 0 a i 4 3286e>066 326 d o42 d d 3 ^ 8 8 o306 326 3o 078 3^63o079 “ Ool to J290od36 2 2 6 0 o 723 i 32 9 2 o s d7 3292 o 7 d d 0 o 3 34dbo3d6 b o9d0 3294 o 96 3 - 0 o3 32d5o979 V 329? a A6 U 22d3cd92 i 0 3299o 340 3299 oi*4d ” 0 06 32d Ao19d 32d 1 a19d 0 © 1 i l 3301 o d 1** 330A o52I -0o7 329 b o790 3248 o 787 Oo 3 A 4 3303 o69 0 3303 o 68 6 0 o 4 3246o 369 3246 © 3 70 -OoO i3 330b o847 330da 840 O o l 324 3 o 940 3243 o 942 “0 o 2 3307 09b3 3 2 4 1 o dOd id 3 3 i0 o i i t 3310 oA1 d O o l 323 9 oObo 323 9o Cd 8 “ 0 & 2 It J ii^ o 23h 3 312 o 2 3t> -0 o2 32 36 o 601 A 7 3 3 1 9 o 390 3 2 3 4 0 I3d i b 33Abo49d 3 2 3 1 o6d8 A9 33ib od33 33A8 Q d34 - 0 o 0 3 2 2 9 o l7 3 cO 3 2 2 6 o b l l 21 3 2 2 4 o i7 3 O i.2. 322 1o 6o0 3 2 2 1 o bd9 0 23 3219 o13d 2 4 32 a6 o603 2 d 3214 a 034 32 2 4 © 062 “ Octi 26 3 2 1 1 odl7 321 I © d A A vi ® 6 27 320 b o9d7 32 08 o 9 d2 0 © d 2 b 3 2 0 6 a 383 3 2 0 6 o384 “Ool 320 3o 604 3 z 0 3 o b0? -0 o 3 30 3 2 0 l o a21 3 a 0 1 o 222 -OoO -1 233 f AbLfc UbitKVtU An d CALCULATED wAVENuMbEKS | VALoCM ) 0 1 ___ 0,1 12 13 UP 7 he. 0010 1 - 0000 1 BAND OF c ch2 e e ocooratB «=»a»«»«3»ea>cm»« s»«s» <»<»<»•»a o N 5 5 Ob S K flaDCALC 0 “ C P fJ JObS PJJ >CAlC D-C Xl 00 XI 00 1 l o ' s n 3281o389 “0 0 7 2 6283 o697 3272 0220 3 32b6o899 32b9 0 b 9b 3269o901 “ 0 o3 9 3 2 68 o190 326To 682 3267o 671 loO 6 32V0 o 366 329Qo369 —0 o9 3266 o23l O 32V2o387 32b2 0 879 7 3294o?99 3260 0 617 a 3296 o990 326 8 0 136 326 8 0 199 “ 0 o9 9 32W o Abb 3 2 9 9 o i? 9 “ 0 0? 32b 6 0 7b2 3266o7b0 0 »2 l 0 330 A o369 3 3 0 1 o 396 l o l 3 2b3o 369 3253o 366 ~0 0 2 A1 3303c 6 a! 3303 O609 0 a 2 3 2 5 0 o939 3260o961 “0 0 7 12 3303o660 3298 0 696 16 3307 o 799 32 96 0 119 3309o926 3293o683 16 3312 oO^V 3312 o09 3 0 0 6 329 A 0 269 3 2 9 10 236 lob A6 3 319 o 19 to 323 80 788 32 3 8 0 7 79 0 0 v 1 1 3316 o 290 3 3 l6 o 2 9 2 "-0 o2 323 b o 3 l6 3^36o312 0 o9 io 3318 o329 3233o830 3233o b36 ™“0 0 6 IV 3320o3Vi> 323 io 392 3 2 3 1 o39B “ 0 0 6 20 33e2 <>956 322 6 0 892 322 8 0 b 51 “ 0 0 9 21 3329 a 609 32 2 6 o396 22 33^.6 o 393 3326 0 692 Ool 3223o 828 23 3326 056b 3 2 2 l o 302 29 23 30 o 677 3330o 68 3 “ 0 06 321bo 772 3218 0 76 7 O06 26 333e <>682 3332 o587 ” 0 06 32 i6o222 2 b 3 3 6 9 o5b0 3e.l3 0 6 69 3 e 1 3 0668 “ 1 »9 2 7 3336 06&6 3336o6o2 0 o3 3 2 1 Ao11 6 32 A 10 106 1 0 i 2 t 333bo 633 e V 3.390 n't'h 3 3 9 0 a 9V 9 0 0 3 ~1 234 table 65 o observed and calculated i^avenumbeks &vac0cm i OF lHfc 0010°l1f - 0000°l1f BAND OF 12C13CH2 0 RUIQbS RUBC a LC 0“C PUSUbi . FJJKALC U”L XI00 Al 00 1 3 2 8 i 04>l^ 2 3283o686 3272o214 3 32t>5>o9^1 32o9o«98 3269o886 1q2 *t 3288o 196 326?o552 3267o5^7 0 ob 5. 3290 ©434 3265 a 190 326 5 c 197 -0o7 6 3292o660 32b2o836 7 3294o8?5 3260 B 3297 o079 3258 ©08 A 9 3299o271 3255 o 6B0 10 3301 ©452 . 3 2 5 3 o 2 75 3253o28*> ~Go9 11 3 3 0 3 o6 2 1 325 0o 8 66 3250o869 “0o 3 12 3305 o 773 3 3 0 5o7?9 -»0o6 32*<>8o443 13 330 if o927 3307o926 Ool 32‘ti>6o00? 14 3 3 1 0 o061 3243o36l 15 33i2old5 32^iol09 324io105 0^ 16 33A4o298 3238a&37 3238o638 -Ool 1? 33i6o398 3316 0399 “-Ool 3236»162 lb 3318 o492 3318 o48 9 0o3 32330675 19 3320 o568 3231ol79 20 3322ob36 3228 o672 21 33240692 3226 o157 22 332&o738 32230632 23 3328o?72 3 2 2 1 o 0 9 7 24 3330o795 3218o553 25 3 3 3 2 o 812 3332©8QB 0o5 3216o005 3216o001 0o5 26 3334o807 3334oB09 *“0 o 3 3213e>435 32A3o439 ”0o4 27 3336o80l 3336o800 Ool 3210 08 72 3210o868 0o3 28 3338 o 779 3358o?80 -Ool 3208o289 29 320 5 o 699 3205o?02 -0o2 -1 235 TAdLE 66® llbiEtWEu A (MU CALCULATED W A\/ENUMb EK3 JVACoCM ) OF lHt 010(11)^+ - 0000°0° bAND UF 12C13CH2 «»8> 0 K 4 J& U b 8 r\ ID i CALC 0 “-L F4 JJUbi> F I j }CA LC 0 —C Al00 A1 0 0 0 3 2 8 2 0 77 6 A 3233 o0b4 32 33 0 062 0 o3 3248 0 187 2 323 7 0 336 3 2 3 ? 0 34 2 “ 0 06 3245 O 885 3 3 2 3 9 o6 1 ? 3243 0 57 7 4 3 2 6 lo 8 8 3 3 2 4 1 0 26v 3 326V 0 lv3 326 V 0 1v 8 — 0 o5 32 38 O946 6 3 2 6 6 0v O v 3236 0 621 7 3268 0 63 4 32 34 0 292 a 3270 o897 3231 0 V56 9 32 i?3o 13V 3 2 7 3 0 133 0 a 6 322 Vo 611 32 2 9 0 6 i v — 0 0 2 10 32 7 8 0 3 6 1 322 7 0 268 32 27 0 266 “0 o 0 11 3 2 7 7 088 i 322 Vo 914 32 2 4 0 911 0 0 3 12 3 2 7 9 c 7 9 3 322 2 a 832 322 2 0 549 0.3 A3 3 2 b i o 9 9 7 3 2 8 1 cV 96 0 0 2 32 2 0 0 1 8 0 1*» 32 bv 0 188 3 2 8 V 0 1 b 9 "“0 0 2 32 i7o 8 04 ID 3286a3?3 321 3 0 4 2 0 lo 3288 0 3v9 3 2 8 8 ® 3v6 0 0 2 3 2 1 3 o 0 2 7 A? 3 2 9 0 o 709 3210 0 b26 ib 8292 o 83 # 3 2 9 2 0 80 0 -0.3 3206=, 213 3 2 O 8 0 218 Ool IV 3203 0 796 3205 0 794 0 0 2 2 C 2203 c. 363 0 <1 1 2 A 3 2 OO 0 918 3200 a 92 1 0 22 2 198 0 4 0 7 23 3 196 0 001 24 3iV3o 523 23 3191*030 2 6 3188 o525 27 3186 0 CO 1 2b 318 3045Y 3 18 3 01*b 3 “ 0 0 6 2 V 3l80o9i0 3lb0o 908 0 0 2 30 31 / 8 0 339 31/8o 336 0 o 3 236 -1 TAtsLt 67® Utl^tKVciJ And CALCULATED rtAVtNUMbEKS tVACoCM ) UF 1Ht 1000°0° - 0000°0° BAND UF 1 2 C 1 3 C H 2 «»-osr-«oa«-e» J K I J fCob K 4 j)CAlC U-C P< JIDt'S P4J JCAlC U-C X100 A1 0 C U 33b3 o b b b 3 3t»3 o bo 0 -0 a 3 1 bb6 6 o 1 IV 3 366 0 ib2 -lob 33bVo27V 2 3368 o3V 1 b 36b o3V a ~0 o0 33b 6 ® V / V 33 be © V6b lol 3 3370 o 63 b 3 b?Goobo “Ool 33bAo tbO b3bAo foA5 0© A H 2 3 7 2 o b 7 i 3372ob6V 0 a 2 33b2o 310 3 337b o Ova 3 3 ? b o C 6 V Oob 33a9 © 962 6 ^ 3 1 1 o^VV 3377 o2vb OoA b 3A 7 o cO1 33A7o60l 0,C 7 b37 V a H o i bb7V©Abb “ 0 O A. 33a 5 o227 b 33b1 066 ? b b b lo 6 6 S “ Ool b3A 2 o bA 2 v 3be 3 o ti 33 33o3o ai4 “Ool 3 3a 0 o *»3 2 33a0 o a A A “ 1 o 1 iO 3363oVbA 3 38b o V8 if “0 o 3 3 33 bo 03b 33380 033 0 0 2 11 33bb o 12 3 338bc&2 7 “0 oA 333 bo 6 AA 3 33b o6i0 OoB 1 Level Species Term Value 010(11)° I + 3281.902 u 0010°0° r + 3294.841 u (II) n 3882.407 010C21)1 u o o n 1o° n 3898.332 u 100110° 3 3970.051 g 010C12)1 (II) n 4002.433 g 00100!1 p 4016.712 ‘g 010(31)° (II) r + 4488.849 ”u £ 4490.817 010(31)2 u 0012°0° V + 4508.028 “u 001220° A 4509.233 u 010(22)° Z 4599.775 g 010(22)2 (II) A 4607.989 g 001(11)° Z + 4609.336 g 001(11)° Z 4617.921 g 0 0 1 (II)2 £ 4624.764 g 010(13)° (II) v + 4710.753 u 010(13)2 (II) A 4725.830 u 0010°2° Z + 4727.072 u ooio°22 A 4741.012 u 0110°0° I + 5260.023 238 (1964). The errors quoted in parentheses are the standard deviations in units of the last significant decimal place. The observed and calculated combination differences are listed in Table 69. The v 0 + (vu + Vir)®. and \)j bands were also observed but are much weaker than the v 3 band. Because many of the lines were covered by stronger features from other bands, the results obtained here are less extensive than reported in the enriched sample studies of Lafferty and Thibault (1964) and Ghersetti, et al_. (1975). 10 0 1 Transitions from 0001 0 and 0000 1 12 Bands of C2H2 : The five II—II bands for which molecular constants were determined are: 1 0 1 0 ooii o - oooi o (n u •<- n g' ) 0 1 0 1 ooio i - oooo i (n n ) g u i i o 010(21) (ii)- oooi o (n •<- n ) u g 1 0 1 010(12) (ii)- oooo i (n n ) g u 1 0 0 1 i o o i o - oooo i (n n ). g u The rotational assignments yield self-consistent combination differences for the lower levels in excellent agreement with the values calculated with the molecular constants of Palmer, Miclcelson, and Rao (1972). The present results modify the assignments made at lower resolution by Scott and Rao (1966). 1 0 1 Constants for the levels 0011 0 and 010(21) (II) have also been reported by Palmer, Mickelson, and Rao (1972), although the assignments would be reversed with the convention adopted here for designating Table 69 12 13 GROUND STATE COMBINATION DIFFERENCES FOR C CH AVE. STD. CALC. 3 a a k CN k a p J a (v[++v5) 0 0 b CO ^ 3 u5 v 3 V2 + (V4+V 5) ■ V l+v3 vl+v5 AF2" DEV. AF," 1 6 886 6 .892 6 900 6 .898 6 .909 6 .8 Q0 6.896* 0.008 6.890 2 11 490 1 1 .483 11 492 11 .493 11 .464 11.507* 11.490* 0.005 11.484 3 16 082 16. 076 16 066’ 16 .087* 16 .101 16.082* 0.013 16.077 4 20 674 20 672 2 0 .665 20 667 20 .671 20 .652 20.679 20.665 20.670 0.005 20.670 5 25 .263 25 .259 25. 259 25 .256 25 .263 25.226* 25.260 0.003 25.263 6 29 .858 29 .847 29 838 29 .856 29 .846 29.854 29.864 29.852 0.009 29.855 7 34 449 34 .453 34. 447 34 440 34 .437 34 .449 34.413* 34.443 34.445 0.006 34.447 8 39 040 39 037 39. 048 39 .044 39 .033 39.020* 39.039 39.040 0.005 39.038 9 43 635 43 .621 43. 653* 43 626 43 .635 43.594* 43.629 0.007 43.629 10 48 218 48 217 48. 242* 48 202 48 . 226 48 . 224 48.217 0.009 48.219 11 52 814 52 797 52. 824 52 801 52 .805 52 .816 52.804 52.805 52.808 0.009 52.808 12 57 396 57. 409 57 394 57 . 390 57 .401 57.400 57.398 0.007 57.396 13 61 988 61 983 61. 989 61 982 61 .980 62 .000 61.987 0.007 61.984 14 66 582 6 6 .548* 66 580 66 .578 66 .563 66.576 0.009 66.570 15 71 164 71. 131* 71 157 71 .161 '71.161 0.004 71.155 16 75 742 75 751 75. 745 75 726’' 75 .750 75 749 75.733 75.745 0.007 75.740 17 80 325 80 307 80 323 80 319 80 .316 80.324 80.319 0.007 80.322 18 84. 908 84 909 84 915 84 .892 84 .890’ 84.906 84.903 0.010 84.904 19 89. 491 89. 479 89. 497 89. 492 89 .473* 89 .458’ 89.497 89.488 0.011 89.484 20 94. 072 94. 079 94 .069 94.076 94.074 0.004 94.063 21 98. 648 98. 661 98. 656 98. 637 98 .633’ 98.647 0.012 98.640 22 103. 221 103. 224 103. 246* 103. 214 103 184’ 103.220 0.005 103.216 23 107. 792 107. 809 107. 806* 107. 777 107 .797 107.774 107.792 0.014 107.790 24 112 367 1 1 2 .345* 112 355 112 .353 112.351 112.354 0.012 112.362 25 116. 935 116. 930 116. 941 116 .923 116 .905 116.926 116.931 0.007 116.932 26 1 2 1 .506 1 2 1 .511 1 2 1 .507 121 .506 121 .513 121.509 0.003 121.501 27 126. 116* 126 066- 126 .056 126 .070 126.064 0.007 126.068 28 130. 640 130. 653 130 636 130 .614 130.643 0.009 130.632 29 135. 201 135. 185 135.193 0.011 135.194 239 30 139. 752 139. 790* 139. 760 139.756 0.006 139.755 Table 69 (CONTINUED) 12 13 GROUND STATE COMBINATION DIFFERENCES FOR C CH2 b a b„ b , j AVE. STD. CALC. J (vl,+v>5)0 yg V2+(vi4+V5)® V 3 + V 3 2v 3 v5 Vl+V5 AF2" DEV. a f 2" 31 144.309 144.308 144.309 0.001 144.312 32 148.883 148.860 148.872 0.016 148.868 33 153.408 153.408 153.421 34 157.974 157.959 157.967 0.011 157.972 35 162.529 162.515 162.522 0.010 162.520 36 167.079* 167.050 167.064 0.021 167.065 37 171.605 171.605 171.608 38 176.155 176.155 176.148 39 180.691 180.691 180.685 40 185.215 185.215 185.219 41 cl89.741* 189.750 a = enriched sample b = natural sample C = values not used for calculation NJ o 241 resonating Fermi polyads. The constants derived for the band designated by these authors as 010 (21)1 d (II) - 0000°0° appear to be in error. The 1001^0^ - 0000^1^ band was observed for the first time in this study. From this band and the vibrational constants of Palmer, Mickel- son, and Rao (1972), the anharmonic constant is calculated to have -1 a value of -15.67 cm The bands 010(21)1 (I) - OOOl3^ 0 and 010(12)1 (I) - 00000!1 also occur in this region. The failure to identify these transitions was not unexpected since the effect of Fermi resonance is small, and hence the bands are weak. Bands of 12C 13CHo:”i2: The bands 001110° - 000110° and 00100!1 - 00000!1 were observed. Despite the fact that many of the lines were blended, the molecular constants reported here should be of comparable accuracy to those obtained by Ghersetti, _et al. (1975) at lower resolution. Transitions from the 0002°s^0° Levels Of particular interest are the four bands assigned to transitions arising from 0002°5^0°: 0012°0° - 0002° 0° I + <- E + u g 010(31)° (II) - 0002°0° S + <- E + + u g 2 0 2 0 0012 0 - 0002 0 A <• A u g 010(31)2 (II) - 0002200 A <- A . u g The assignments of the first two bands were made on the basis of the observed vibrational term values of Plxva (1972a) for 0002°0° and Baldacci, Ghersetti, and Rao (1972) for the upper levels. The upper and lower state combination differences are in good agreement with data 242 obtained in other spectral regions (Baldacci, Ghersetti, and Rao, 1972; Baldacci, Ghersetti, and Rao, 1977). The loiter state combination 2 0 differences obtained for 0002 0 agree with results obtained at 1.5 pm (Baldacci, Ghersetti, and Rao, 1977). The present measurements greatly 0,2 0 extend the range of J values observed for 0002 0 . 0 0 2 0 The levels 0002 0 (£ +) and 0002 0 (A ) perturb each other through 2 0 strong £-type resonance while the 0002 0 (A )f level is unperturbed § t (Amat and Nielsen, 1958). In the upper levels £-type resonance occurs 0 + 2 between the 010(31)+ (II) (Eu ) and 010(31) (II) (A )£ states and 0 0 + 2 0 between the 0012 0(E) and 0012 0 (A ) states. In addition, Fermi u u e 0 + 0 0 + resonance occurs between the 010(31)_j_ (II) (E ) and 0012 0 (E^ ) states 2 2 0 and between the 010(31) (II) (A ) and 0012 0 (A ) states. The u e u e effects of these perturbations are evident from examining the anomolous 0 0 0 0 2 0 rotational constants in Table 27. For the 0012 0 - 0002 0 , 0012 0 - 20 0 00 2 20 0002 0 e-e, 010(31)+ (II) - 0002 0 , and 010(31) (II) - 0002 0 e-e transitions, systematic rather than random differences exist between the observed and calculated values even with an eighth order polynomial. 2 0 A fourth order polynomial was sufficient to fit the data for the 0012 0 - 2 0 2 2 0 0002 0 f-f and 010(31) (II) - 0002 0 f-f bands where no £-type reso nance occurs. Transitions from Higher Levels A number of these levels are also perturbed by £-type and/or Fermi resonance. The effects can be noted in the anomolous rotational constants obtained for a number of the bands. 243 0 0 The positions of rotational lines of the 100(11)„, -0000 2 band Z+ + + (£ E ) were calculated from constants obtained in other spectral u g regions (Baldacci, Ghersetti, and Rao, 1972; Palmer, Mickelson, and Rao, 1972). It was possible to identify lines between P(8 ) and P(25) in spectra obtained on the long-wavelength side of the 3 pm bands at high temperature (160 C) and high pressure (10 cm Hg). The proper alternation of intensities was noted. The R branch falls in a region recorded only at lower pressure, and the lines of this band were too weak to be identified, so that meaningful constants could not be obtained. The observed line positions are listed in Table 70. 0 0 0 0 A few lines of the 0110 0 -0100 0 band were observed, but this band is very weak even at 160 C because of the high excitation energy of the lower level. The constants for the upper and lower levels are in good agreement with those of Palmer, Mickelson, and Rao (1972). Section 6.7 - Results of the 3 ym Intensity Analysis The absolute intensities of 101 rotational lines in the seven strongest bands of C2H2 have been measured. The bands studied include 0 T9 the V3 fundamental and the V2 + (v^ + Vs)^ bands of C2H 2 which are in strong Fermi resonance and of similar strength. The other bands of 12C2H2 measured were the II-II "hot" bands x^+Vi^-Vi^, V 3+V 5^-V51, v2+2vi+2+V51-vlf1 and V2+V|J+2V52-V51 . The v 3 fundamental band of 12C13CH2 was also measured for intensity. 244 Table 70- Observed Wavenumbers (vac.cm in the P Branch of the 100(11)°+- 0000°2° Band of 12C2H 2 J P(J) OBSERVED 8 3205.248 9 3202.756 10 11 3197.778 12 3195.265 13 3192.738 14 3190.203 15 3187.653 16 17 3182.525 18 3179.938 19 3177.349 20 21 22 3169.480 23 3166.854 24 3164.209 25 3161.541 245 The measurement of intensities in the 3 pm region was complicated by the high density of lines in the spectrum. Fortunately, the posi tional analysis described in the previous section provided sufficient information to select unblended lines in clean spectral regions for the intensity program. However, it did prove to be necessary to restrict the measurements to J < 35. At room temperature high J lines could only be measured at high pressures (P > 10 torr for the "hot" bands). At high pressures the effects of collisional broadening create large uncertainties in the calculated line strength. The y q parameter affects the value of S in the curve of growth as well as in the corrections for experimental loss and line overlap. Also, it was difficult to be certain that the weak, high J lines were not blended with an unidenti fied feature of comparable intensity. The average values obtained for the line strengths are given in Tables 71 to 77. The strengths, expressed in units of cm-2 atm-1 at 300 K (powers of 10 are in parentheses), have been corrected for the presence of isotopes by dividing by 0.9781 for 12C2H 2 and 0.0218 for 12C13CH2 . The room-temperature, self-broadened collisional half widths of Varanasi and Bangaru (1975) have been adopted. The average line strengths are the unweighted means of the measurements at all pressures. The standard deviations of the measurements ranged from 8 to 15% for most lines. The standard deviations were systematically smaller for lines measured near the blaze of the grating where the signal-to- noise ratio was higher. 246 Table 71 -2 -1 Observed and Calculated Line Intensities (cm atm at 300K) in the 0010°00-000000° Band of 12C2H S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. ..ine Calc.. Mens. (300K) Line Calc. Meas. (300K) RO 3.00 -1) R1 1.78 K)) PI 8.89 -1) R2 8.72 -1) P2 5.79 -1) R3 3.37 +0) P3 2.52 +0) 2.76(10) 2.18(-1) R4 1.34 +0) P4 1.07 +0) R5 4.58 + 0) P5 3.79 10) R6 1.67 +0)P6 1.41 + 0) 1.60(10) 1.83(-1) R7 5.28 +0) P7 4.57 +0) R8 1.81 + 0) P8 1.59 + 0) 1.63(10) 1. 7 5(—1) R9 5.45 + 0) 5.51(+0) 1.93(-1) P9 4.84 +0) RIO 1.79 +0) P10 1.60 10) 1.76(10) 1.52(-1) Rll 5.17 +0) 5.24(+0) 3.20(-l) Pll 4 .66 1-0) R12 1.63 + 0) P12 1.48 + 0) 1.45(10) 1.4K-1) R13 4.56 +0) 4.70(1-0) 4.35(-1) P13 4.15 10) R14 1.39 +0) P14 1.27 +0) 1.33(10) 1.14(-1) R15 3.76 +0) 3.86(1-0) 2.83(-1) P15 3.45 10) 3.73(10) 4.43(-1) R16 1.11 + 0) P16 1.02 10) 1.18(10) 1.65(-1) R17 2.92 + 0) P17 2.69 10) R18 8.39 -1) P18 7.74 -1) R19 2.14 +0) P19 1.98 10) R20 5.98 -1) 5.96(-1) 3.69(-2) P20 5.53 -1) R21 1.48 +0) 1.15(1-0) 1.31(-1) P21 1.37 10) R22 4.04 -1) 3.45(-1) 1.85(-2) P22 3.74 -1) R23 9.76 -1) P23 9.05 -1) R24 2.59 -1) P24 2.40 -1) R25 6.10 -1) P25 5.65 - 1) R26 1.58 -1) P26 1.46 -1) R27 3.62 -1) 2.79(-1) 2.70(-2) P27 3.36 -1) 3.75(-1) 4.70(—2) R28 9.12 -2) P28 8.46 -2) R29 2.04 -1) P29 1.89 -1) 1.80(-1) 1.36(-2) R30 5.02 -2) P30 4.65 -2) R31 1.10 -1) P31 1.02 -1) 9.39(-2) 7.44(-3) R32 2.63 -2) P32 2.44 -2) R33 5.62 -2) P33 5.20 -2) 5.02(-2) 6.17(-3) R34 1.32 -2) P34 1.22 -2) R35 2.74 -2) P35 2.53 -2) 2.28(-2) 3.77(-3) 247 Table 72 -2 -1 Observed and Calculated Line Intensities (cm atm at 300K) in the 010(11)°4- -0000°0° Band of 12C2H2 S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Me as. (300K) Line Calc. Meas. (300K) R0 3.55 -1) R1 2.11 +0) PI 1.05 +0) R2 1.03 +0) 1.21(4-0) 6.19(-2) P2 6.84 -1) R3 3.99 +0) P3 2.97 +0) R4 1.59 +0) 1.57(4-0) 2.18(-1) P4 1.26 4-0) 1.06(4-0) 1.00(-1) R5 5.41 +0) P5 4.47 4-0) R6 1.97 + 0) P6 1.67 4-0) 1.56(4-0) 1•55(-1) R7 6.24 +0) P7 5.40 4-0) R8 2.14 +0) P8 1.88 4-0) 1.60(4-0) 2.43(-1) R9 6.64 +0) P9 5.72 4-0) RIO 2.11 +0) P10 1.89 4-0) 2.19(4-0) 3.74(-1) Rll 6.11 +0) 4.89(4-0) 6.51 (-1) Pll 5.51 4-0) R12 1.93 +0) P12 1.75 4-0) R13 5.38 +0) P13 4.90 4-0) R14 1.64 +0) P14 1.50 4-0) R15 4.44 +0) 4.39(4-0) 4.37(-1) P15 4.07 .4-0) R16 1.31 +0) P16 1.21 -10) R17 3.45 +0) 3.44 (-H)) 2.88(-1) P17 3.18 4*0) R18 9.91 -1) P18 9.15 -1) R19 2.53 +0) 2.33(4-0) 8.58(-2) P19 2.34 4-0) R20 7.07 -1) P20 6.54 -1) R21 1.75 +0) 1.74(+0) 8.13(-2) P21 1.62 4-0) R22 4.77 -1) P22 4.42 -1) R23 1.15 +0) P23 1.07 4-0) R24 3.06 -1) P24 2.84 -1) R25 7.20 -1) P25 6.68 -1) R26 1.86 -1) 1.83(-1) 8.97(-3) P26 1.73 -1) R27 4.28 -1) 4 .22 (-1) 3.24(-2) P27 3.96 -1) 4.38(-1) 3.73(-2) R28 1.08 -1) 1.26(-1) 7.66(-3) P28 9.99 -2) R29 2.41 -1) 2.34(-1) 1.6 3(—2) P29 2.24 -1) 2.33(-1) 1.98(-2) R30 5.93 -2) P30 5.50 -2) R31 1.30 -1) P31 1.20 -1) 1.22(-1) 1.17(-2) R32 3.11 -2) P32 2.88 -2) R33 6.64 -2) P33 6.14 -2) 6.64(-2) 4.47(-3) R34 1.56 -2) P34 1.44 -2) R35 3.24 -2) P35 2.99 -2) 248 Table 73 / -2 -1 Observed and Calculated Line Intensities (.cm atm at 300K) in the 1 0 12 o o n 1o°-0001 0 Band of C ^ S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) Rle 7.21(-2) f 2.40(-2) R2e 4.16(-2) P2e 2.40(-2) f 1.25(-1) f 7 .19(-2) R3e 1.69(-1) P3e 1.24(-1) f 5.62(-2) f 4.14(-2) R4e 6.84(-2) P4e 5.60(-2) f 2.05(-1) f 1 .68(-1) R5e 2 .35(-1) P5e 2.04(-l) f 7.82(-2) f 6.80(-2) R6e 8.55(-2) P6e 7.76(-2) f 2.56(-1) f 2 .33(-1) R7e 2.71(-1) P7e 2.54(-1) f 9,01(-2) 8.65(-2) 4.23(-3) f 8.46(—2) R8e 9.26(-2) P8e 8„94(-2) f 2.77(-1) f 2 .68(-1) R9e 2.78(-l) P9e 2 .75(-1) f 9.25(-2) f 9.14(-2) RlOe 9.07(-2) 9.52(-2) 8.47(-3) PlOe 9.15(-2) f 2.71(-1) f 2.74(-1) Rile 2.6K-1) Pile 2.69(-1) f 8.68(-2) f 8.92(-2) R12e 8.20(-2) P12e 8.58(-2) f 2.45(-l) f 2.56(—3) R13e 2.28(-l) P13e 2.42(-1) f 7.56(—2) 7.19(-2) 5.93(-3) f 8.04(-2) R14e 6.9K-2) P14e 7.47(-2) f 2.06(-1) f 2.23(-l) R15e 1.86(-1) P15e 2,04(-1) f 6.16(-2) 6.59(-2) 5.16(-3) f 6.75(-2) R16e 5.47(-2) P16e 6.08(-2) f 1.63C-1) f 1.81(-1) R17e 1.43(-1) P17e 1.61(-1) f 4.72(-2) 5.63(—2) 1.62(-2) f 5.32(-2) R18e 4.08(-2) P18e 4.66(-2) f 1 .21(-1) f 1.39C-1) R19e 1.03(-1) P19e 1.20(-1) f 3.41(-2) f 3.95(-2) 249 Table 73 (cont'd.) S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) R20e 2.87(-2) P20e 3.37(-2) f 8.53C-2) 8.11(-2) 8.35(-3) f 9 o 9 9(—2) R2Ie 7.08(-2) P21e 8.41(-2) 1.19(-1)* 1.52(-2) f 2.33C-2) f 2.77(-2) R22e 1.92(-2) P22e 2.30(-2) 9.30(-2)* 1.26(-2) f 5.68(-2) f 6.82(-2) R23e 4.60(-2) P23e 5.60(-2) 6 .86(-2)* 7.97(-3) f 1.51(-2) f 1.84(-2) R24e 1 .21(-2) P24e 1.49(-2) f 3.58C-2) f 4.4K-2) R25e 2.84(-2) P25e 3.54(—2) f 9.3K-3) 8.26(-3) 1.14(-3) f 1.16(~2) R26e 7.29(-3) P26e 9.19(-3) f 2.15(-2) 2.15(-2) 8.57(-4) f 2.7K-2) R27e 1 .66(-2) P27e 2 .12(-2) f 5.44(-3) f 6.94(-3) R28e 4.16(-3) P28e 5.38(-3) f 1.22(-2) f 1.58(-2) R29e 9.27(-3) P29e 1.21(-2) f 3.02(-3) f 3.95(-3) R30e 2.26C-3) P30e 2.990-3) f 6.64(-3) f 8.77(-3) R31e 4.92(-3) P31e 6.57 C—3) f 1.60(-3) f 2.14(—3) R32e 1.17(-3) P32e 1.58(-3) f 3.42(-3) f 4.63(—3) R33e 2.48(-3) P33e 3.40(-3) f 8.05(-4) f 1.10(-3) R34e 5.78(-4) P34e 7.99(-4) f 1.68(-3) f 2.33(-3) R35e 1.20(-3) P35e 1.67(-3) f 3.86(-4) f 5.40(-4) * Integrated strength of unresolved £-type doublet. 250 Table 7A -2 Observed and Calculated Line Intensities (cm atm ^ at 300K) in the 1 0 1 12 0010°:1-0000 1 Band of C H S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) Rle 1.62(-2) f 4 .86(—2) R2e 8.40(-2) P2e 4 .88(—2) f 2.80(-2) f 1.63(-2) R3e 3.78(—2) P3e 2.81(-2) f 1.13(-1) f 8.43(-2) R4e 1.38(-1) P4e 1.14(-1) f 4.59(-2) f 3.80(-2) R5e 5.24(-2) P5e 4.63(-2) f 1.57(-1) f 1.39C-1) R6e 1.72(-1) P6e 1.59(-1) f 5.72(-2) f 5.28(-2) R7e 6.03C-2) 6.42(-2) 9.08(-3) P7e 5 .78(—2) f 1.81(-1) f 1 .73(-1) R8e 1.85(-1) P8e 1.83(-1) f 6.17(-2) f 6.09(-2) R9e 6.17(-2) P9e 6 .26(—2) f 1.85(-1) f 1.87(-1) RlOe 1.81(-1) PlOe 1 .88C-1) f 6.02(-2) f 6.24(-2) Rile 5.78(-2) Pile 6.13(-2) f 1.73(-1) 1.79C-1) 1.72(-2) f 1.83C-1) R12e 1.63(-1) P12e 1.76(-1) f 5.42(-2) f 5.86(-2) R13e 5.03(-2) P13e 5.54(-2) f 1.50(-1) f 1 .66C-1) Rl4e 1 .37(-1) P14e 1.54(-1) 1.44C-1) 1.60(-2) f 4.55(-2) f 5.10(-2) R15e 4.09(-2) P15e 4.67(-2) f 1 .22(-1) f 1.39C-1) 1.58(-1) 2.07(-2) R16e 1.08(-1) P16e 1.25C-1) f 3.58(-2) 3.50(-2) 3.80(-3) f 4.16(-2) R17e 3.13(-2) P17e 3.69(-2) f 9.32(-2) 8.55(-2) 7.83(—3) f l.lO(-l) R18e 8.02(-2) P18e 9.62(-2) 1.09(-1) 1.69(-2) f 2 .66(-2) f 3.18(-2) R19e 2.26C-2) P19e 2.75(-2) f 6.71C-2) 6.53C-2) 5.17(-3) f 8.18(-2) 7.26(-2) 8.45(-3) 251 Table 74 (cont'd.) S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) R20e 5.63(-2) 5.69(-2) 3.57(-3) P20e 6 .97(-2) f 1 .86(-2) f 2.30(-2) R21e 1 .54(-2) P21e 1.94(-2) f 4.58(-2) f 5.75(-2) R22e 3.74(-2) P22e 4.77(-2) f 1.23(-2) f 1 .57(-2) R23e 9.97(-3) P23e 1.29(-2) f 2.96C-2) f 3.83C-2) R24e 2.36(-2) P24e 3.10(-2) f 7.76(—3) f 1 .02(-2) R25e 6.12(-3) P25e 8.17(-3) f 1.81(-2) f 2.42(-2) R26e 1.41(-2) 1.51(-2) 1.13(-3) P26e 1.91(-2) f 4.63(-3) f 6.27(-3) R27e 3.57(-3) P27e 4.91(-3) f 1.05(-2) f 1.45(-2) R28e 8.03(-3) P28e 1.12(-2) f 2.63(—3) f 3.67(-3) R29e 1.98(-3) P29e 2.80(-3) f 5.83(-3) f 8.25(-3) R30e 4.35(-3) P30e 6.24(-3) f 1.42(-3) f 2.04(-3) R31e 1.05(-3) P31e 1.52(-3) f 3.07(-3) f 4.47(-3) R32e 2.24(-3) P32e 3.31(-3) f 7.29(-4) f 1.08(-3) R33e 5.26(—4) P33e 7.88(—4) f 1.54(-3) f 2.31(-3) R34e 1.10(-3) P34e 1.67(-3) f 3.57(-4) f 5.42(-4) R35e 2.52(-4) P35e 3.88(-4) f 7.35(-4) f 1.13(-3) 252. Table 75 -2 -1 Observed and Calculated Line Intensities (cm atm at 300K) in the 010(21)1 (II)-000110° Band of U C2E2 S(300K) S(300K) St. Dev, S(300K) S(300K) St. Dev. Line Calc, Meas. (300K) Line Calc. Meas. (300K) Rle 6.86(-2) f 2.29(-2) R2e 3.95(-2) P2e 2.28(-2) f 1.19(-1) f 6.84(-2) R3e 1.60(-1) P3e 1.18(-1) f 5.35(-2) f 3.94(-2) R4e 6.51(-2) P4e 5.32(-2) f 1.95C-1) f 1.59(-1) R5e 2.23C-1) P5e 1.94(-1) f 7.43C-2) 7.19(-2) 8.22(-3) f 6.46(-2) R6e 8.13(-2) 7.47(-2) 5.21(-3) P6e 7.38(-2) 3.21(-1)* 5.48(-2) f 2,44(-1) f 2.21(-1) R7e 2.58(-l) P7e 2.42(-1) f 8.57(-2) f 8.04(-2) R8e 8.81(-2) 8.46(—2) 6.60(-3) P8e 8.49C-2) f 2.64(-l) f 2 .54(-l) R9e 2.65(-1) P9e 2 ,61(”1) f 8.80C-2) f 8 .68(-2) RlOe 8.63C-2) PlOe 8.69(-2) f 2.58C-1) f 2.60(-l) Rile 2.49C-1) Pile 2«55(-1) f 8.26(-2) f 8.47(-2) R12e 7.81C-2) P12e 8.15(-2) f 2.33C-1) f 2.44(-l) R13e 2.17(-1) P13e 2.30(-l) f 7.20(-2) f 7.63(-2) R14e 6.58C-2) P14e 7.09(-2) f 1.97(—1) f 2 .12(-1) 2.28(-l) 2.12(-2) R15e 1.77(-1) P15e 1.93(-l) f 5.87(-2) f 6.4K-2) R16e 5.21(-2) P16e 5.77(-2) f 1.55(-1) f 1.72(-1) R17e 1.36(-1) 1.39(-1) 2.04(-2) P17e 1.53(-1) 1.42(-1) 1.36(-2) f 4.50(-2) f 5.05(-2) 6.35(-2) 8.28(-3) R18e 3,88(-2) P18e 4.42(-2) 3.70(-2) 4.53(-3) f 1.16(-1) f 1.31(-1) R19e 9.85(-2) 1.07(-1) 9.92(-3) P19e 1.14(-1) 1.03(-1) 9.94(-3) f 3.25(-2) f 3.75(-2) 253 Table 75 (cont'd.) S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) R20e 2.74(-2) P20e 3.19(-2) f 8.13C-2) 9.01(-2) 7.37(-3) f 9.48(-2) R21e 6.75C-2) P21e 7.98(—2) 7.50(-2) 8.19(-3) f 2 .23(-2) f 2.63(-2) R22e 1.83C-2) P22e 2 ,18(-2) f 5.41C-2) f 6.47(-2) R23e 4.39(-2) 3.97(-2) 6.10(-3) P23e 5.31(-2) f 1.44(-2) f 1.75(-2) R24e 1.16(-2) P24e 1.42(-2) f 3.42(—2) f 4.19(-2) 4.13(-2) 4.21(-3) R25e 2.71C-2) P25e 3.36(—2) f 8.88(-3) f 1 .10(-2) R26e 6.95(-3) P26e 8.72(-3) f 2.05(-2) f 2.57(-2) 2.83(-2) 2.68(-3) R27e 1.59(-2) P27e 2.01(-2) f 5.19(-3) f 6.59(—3) R28e 3.97C-3) P28e 5.10(-3) f 1.17(-2) f 1.50(-2) R29e 8.84C-3) P29e 1.15(-2) f 2.89C-3) f 3.75(-3) R30e 2.16C-3) P30e .2.84 (-3) f 6.34(-3) f 8.32(-3) R31e 4.69(-3) P31e 6.23(-3) f 1.53(-3) f 2.03(-3) R32e 1.12(-3) P32e 1.50(-3) f 3.27(-3) f 4.39(-3) R33e 2.37(-3) P33e 3.22(-3) f 7.69(-4) f 1.04(-3) R34e 5.52(-4) P34e 7.58(-4) f 1.6K-3) f 2.2H-3) R35e 1.14(-3) P35e 1.59(-3) f 3.69(—4) f 5.12(-4) * Integrated strength of unresolved £-type doublet. 254 Table 76 -2 -1 Observed and Calculated Line Intensities (cm atm at 300K) in the 010(12)1 (II)-0000°11 Band of 12C2H2 S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) Rle 9.91(-3) f 2 .97(-2) R2e 5.14(-2) P2e 2.96(-2) f 1 .71(—2) f 9.88(—3) R3e 2.32(-2) P3e 1.71(-2) f 6.95(-2) f 5.12(-2) R4e 8.46(-2) 7.93(—2) 1.84(-3) P4e 6.91(-2) f 2.82C-2) f 2 .30(—2) R5e 3.22(-2) P5e 2 .e0 (-2) f 9.66(-2) f 8.40C-2) R6e 1.06C-1) P6e 9.59(-2) f 3.52 (-2) f 3.19(-2) R7e 3.72(-2) P7e 3.49(-2) f l.ll(-l) 1.10(-1) 9.48(-3) f 1.05(-1) R8e 1.14(-1) P8e 1.10(-1) f 3.81(-2) 4.40(-2) 6.00(-3) f 3.67(-2) R9e 3.82(-2) P9e 3.77(-2) f 1.14C-1) f 1.13(-1) RlOe 1.12(-1) PlOe 1.13(-1) f 3.73(—2) f 3.76(-2) Rile 3.59(-2) Pile 3.68(-2) f 1.07(-1) f 1 .10(-1) R12e l.Ol(-l) P12e 1.06C-1) f 3.37(-2) f 3.52(-2) R13e 3.13(-2) P13e 3.32(—2) f 9.35(-2) 9.24(-2) 1.22(-2) f 9.93(-2) R14e 8.55(-2) P14e 9.21(-2) f 2.84(-2) f 3.06(-2) 2.69(-2) 1.41(-3) R15e 2.55(-2) P15e 2.79(-2) f 7.62(-2) f 8.33C-2) R16e 6.76(-2) P16e 7.50(-2) f 2.24(-2) f 2.48(-2) R17e 1,96(-2) P17e 2 .20(-2) f 5.84(-2) f 6.57(-2) R18e 5.04(-2) 5.33(-2) 4.02(-3) P18e 5.74(-2) f 1.67(-2) f 1.90(-2) 2.11(-2) 3.35(-3) R19e 1.42(-2) P19e 1.64(-2) f 4.22(-2) f 4.87(-2) 255 Table 76 (cont'd.) S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) R20e 3 .55 (-2) 3.30(-2) 5.48(-3) P20e 4.15(-2) f 1.17(-2) f 1.37(-2) R21e 9.72(-3) P21e 1.15(-2) f 2.89(-2) f 3.42(-2) R22e 2 .37(-2) P22e 2.84(-2) f 7.80(-3) f 9.35(-3) R23e 6.31(-3) P23e 7.66(-3) f 1.87(-2) f 2.27(-2) R24e 1.50(-2) P24e 1.84(-2) f 4.92(-3) f 6.05(-3) R25e 3.89(-3) P25e 4 „83(-3) f 1.15(~2) f 1.43(-2) R26e 8.99(-3) P26e 1.13(-2) f 2.95(-3) f 3.71(-3) R27e 2.28(-3) P27e 2.90(-3) f 6.73(-3) f 8.55(-3) R28e 5.14(-3) P28e 6.61(-3) f 1.68(-3) f 2.16(-3) R29e 1.27(-3) P29e 1.65(~3) f 3.74(-3) f 4.86(-3) R30e 2.79(-3) P30e 3.67(-3) f 9.12(—4) f 1.20(-3) R31e 6.73(-4) P31e 8.96(-4) f 1.98(-3) f 2.63(—3) R32e 1.44(-3) P32e 1.94(-3) f 4.70(-4) f 6.33(—4) R33e 3.40(-4) P33e 4.63(-4) f 9.95(-4) f 1.36(-3) R34e 7.1K-4) P34e 9.80(-4) f 2.31(-4) f 3.18(-4) R35e 1.63(-4) P35e 2.28(-4) f 4.77(-4) f 6.65(-4) 256 Table 77 -2 -1 Observed and Calculated Line Intensities (cm atm at 300K) in the 0010°00-000000° Band of 12C13CH S(300K) S(300K) St. Dev. S(300K) S(300K) St. Dev. Line Calc. Meas. (300K) Line Calc. Meas. (300K) RO 1.15(+0) R1 2.27(+0) PI 1.13(4-0) R2 3.33(+0) P2 2.22(4-0) R3 4.30(4-0) 4.40(4-0) 2.72(-l) P3 3.21(4-0) R4 5.15(+0) P4 4.10(+0) R5 5.86(+0) P5 4.84(4-0) R6 6.40(4-0) P 6 5 .44 (4-0) 5.71(4-0) 1.13(4-0) R7 6.77(+0) P7 5.87 (4-0) 5.43(4-0) 8.5K-1) R8 6.98(4-0) 6.57(4-0) 9.38(-1) P 8 6.13(4-0) 6.94(4-0) 1.00(4-0) R9 7.03(4-0) P9 6.25(+0) 6 .44 (4-0) 1.15(+0) RIO 6.93 (4-0) P10 6.21(4-0) 5.74(4-0) 7.99(-1) Rll 6.70(4-0) Pll 6.05(4-0) 6.32 (4-0) 6.06(-1) R12 6 .37(+0) P12 5.78(4-0) 5.67(4-0) 9.65(-1) R13 5.95(4-0) P13 5.42(4-0) R14 5.47(4-0) P14 5.00(4-0) R15 4.95(4-0) P15 4.54(4-0) R16 4.41(4-0) 4.67(4-0) 5.18(-1) P16 4.06(4-0) R17 3.87(4-0) P17 3.57(4-0) R18 3.36(4-0) 3.21(4-0) 3.47(-1) P18 3.10(4-0) 3.30(4-0) 2.81(-1) R19 2.87(4-0) 2.78(4-0) 2.93(-l) P19 2.65(4-0) R20 2.42(4-0) P20 2.24(4-0) R21 2.01(4-0) 1.92 (+0) 2.00(-l) P21 1.86(4-0) R22 1.65(4-0) P22 1.53(4-0) R23 1.34(4-0) P23 1.24(4-0) R24 1.07(4-0) 1.02(4-0) 1.19(-1) P24 9.95(-1) R25 8.47(-1) P25 7-87(-1) R26 6.62(-1) P26 6.14(-1) R27 5.10(-1) P27 4.74(-1) R28 3.89(-1) P28 3.61(-1) R29 2 „93(-l) P29 2.71(-1) R30 2.17(-1) P30 2.02(-1) R31 1.60(-l) P31 1.48(-1) R32 1.16(-1) P32 1.08(-1) R33 8.32(-2) P33 7.71(-2) R34 5.90(-2) P34 5.46(-2) R35 4.14(-2) P35 3.83(-2) 257 For each line measurements were made at two to ten different pres sures. No systematic differences in the measured strengths at differ ent pressures were noted. By introducing the measured values of S and all known quantities into Equation 6.3-7, the square of the matrix element of the vibrational v'i'J' transition has been calculated for each line. Plots of R v£J expressed in units of Debye2 vs. m (defined in Section 6.3) are presented in Figures 42 to 47 for all six bands of 12C2H2. The error bars represent the standard deviation of the measurements. For the bands originating from the ground state (V3 and v ’r J' V2 + (vt, + v5)^+)no systematic dependence of R with m is v£ J apparent in the data. Evidently the effect of vibration-rotation interaction is small over the range of m measured. For the hot bands v ’£'J' arising from the and V5 degenerate levels, the values of R v£J are larger for lines in the P branch in comparision to lines in the R branch. For these bands, the effect of vibration-rotation interac tion has been described by the empirical relation v ' r j ' 2 _ v' V R R (1 + Am) (6.7-1) v£J v£ v * Z 1 where R is the "rotationless" dipole moment matrix element, m v£ is J+l for the R branch and -J for the P branch, and A is a constant determined from a linear least squares fit to the data for each band. 9 12C2H2 0010 0 -0000 0 8 7 6 5 U — -J— m 3 2 Figure 42. Square of the vibration-rotation matrix element v*1 ' J' |2 |R . , I plotted against the integer m in the 0010 0 - 0000^0*^ band of . Error t>ars represent the standard deviation of the measure ments of an individual line. The horizontal I v*£'J'i^ dashed line is the mean value of R „ , . ' v £ J 1 259 9 1 2 c 2 h 2 (01011)° -o o o o V 8 7 6 5 l T I I t U ■ H r * - ■ f t ! - 3 I 2 -30 -20 -10 0 10 20 30 M s» Figure 43. Square of the vibration-rotation matrix element |RV ^ ^ | vs. m in the 010 (11) %- 0 0 0 0 % ^ band of V A s »J Z» 1 0 C„H . Error bars represent the standard deviation of the measurements of an individual line. The i v * * J' | ^ horizontal dashed line is the mean value of R . , . 1 v H J 1 260 9 (Cl 021) -0001 0 8 7 6 5 4 1 I 3 2 Figure 44. Square of the vibration-rotation matrix element |RV I 'J | vs. m in the 010(21) 1-000110° band of V 36 J Error bars represent the standard deviation of the measurements of an individual line. The horizontal dashed line is the calculated value of I „v * A * J * |2 . . - I Dv' £' ,2 |R T I obtained with the values of |R ., | and V x. J V X- A listed in Table 78. 261 9 (01012) -0000 1 8 7 6 5 4 3 2 Figure 45. Square of the vibration-rotation matrix element I r V ^ t 1^ v s * 111 010(12)^-0000^1^ band of 1 v £ J 1 12C2H2 « Error bars represent the standard deviation of the measurements of an individual line. The horizontal dashed line is the calculated value of i v 15 * T'i2 i v ' i ’i2 R T obtained with the values of R and 1 v £ J ' v SL A listed in Table 78. Figure 46. Square of the vibration-rotation matrix element vs. m in the 001110°-000110° band of 1 v % J 1 12C2H2* Error bars represent the standard deviation of the measurements of an individual line. The horizontal dashed line is the calculated value of IrV f ^ I obtained with the values of |RV ^ | and 1 v £ J 1 v I A listed in Table 78. IR^'IMO'3 DEBYE* iue 7 Sur f h irto-oainmti element matrix vibration-rotation the of Square A7. Figure 2 il 6 8 3 5 7 9 -20 itd nTbe 78. Table in listed A oiotl ahd ie s h cluae au of value calculated the is line dashed horizontal f h esrmns f n niiul ie The line. individual an of measurements the of 12C ' v v1? 1 1 n 0 1 0 1 n ' v 1i v ?1 T1 12 . R R n R n v * 1 i 1 I 2 H J 1 a v 1 1 J Z J Z Jl 2 ' J ’ . T obtained with the values of values the with obtained . T - Error bars represent the standard deviation standard the represent bars Error - v. i the in m vs. T 1 , 2 v J , r uv'i' |2 uv'i' r , J v 2 - 1 0 0010 0010 1 1 0 0 0 0 - 1 0 ooio 12c 2h2 2h2 12c V- R ad of band 20 oooo and „ ° i ' 263 264 ,v'£' The values of and A have been tabulated in Table 78. v£ .0 For v3 and V2 + (v4 + v 5)^.+ the value of A has been taken to be zero, r,V'£' 2 v 1 £' J 1 2 and the computed value of R n is the mean value of R v£ v£J for each band. Since there were insufficient data on the energy levels of 12C13CH2, the partition function could not be computed and hence the v 1 £ values of R and A could not be found. The band strength was v£ computed assuming no vibration-rotation interaction. v ’ £ ’ J' From the measured values of R and A for each band, the v£J line intensities have been calculated with Equation 6.3-7. The calcu lated intensities are listed in Tables 71 to 77. Band strengths have been computed by summing the calculated strengths of all lines in all branches. The small contributions of the Q branch has been included for the n—II bands. The band strengths S t at 300 K are presented in the last column of Table 78. At room temperature, absorption by C2H2 in the 3 pm region is pre dominantly from the v 3 and V2 + (vt, + v s)^+ bands which are in strong Fermi resonance. The present measurements indicate that the v 2 + (V4 + v 5)^ band is slightly stronger than v 3 . In 12C13CH2, and 1 5 0 more so in 1 ^ 2^ , the lines of V2 + (v^ + v 5)^+ are wea^cer than those of v 3, indicating that Fermi resonance is much weaker in the isotopic varieties (Ghersetti, et al., 1975). A summary of previous determinations of the integrated strength of the 3 pm bands is given in Table 79. These studies were all made at low resolution, and the reported values have been converted to units 265 Table 78 Summary of Acetylene Intensity Parameters Measured at 3 ym Stand. Dev. S (300 K) 1i*vT V I i1 2 tot 2 -2 -1 Transition Debye A Debyer. , 2 cm atm *• ■» 010(11)°+-0000°0° 4.46xl0_3 - 4.83xl0~4 125,98 ooio°o°-oooo0o0 3.76xl0~3 - 3.99xl0_4 106.63 ooio0i1-oooo°i1 4.60xl0~3 -7.03xl0~3 4.24xl0~4 7.75 001110°-000110° 3.87xl0-3 -5.74xl0_3 3.21xl0~4 11.49 010(21)^I-000110° 3.70xl0~3 -5.64xl0~3 4.30xl0~4 10.92 010(12) ^-OOOO0!1 2.81xl0-3 -5.69xl0_3 2.89xl0~4 4.73 ooio°o0-oooo0o° 12 13 c c h 2 208.71 Table 79 Comparison of 3 pm Integrated Intensity Values for Acetylene S (300 K) -2 -1 Reference Reference Value cm atm Calloman, McKean and Thompson (1951) 835xlo'" cm ^sec ''atm ^ at STP 254 Kelly, Rollefson, and Schurin (1951) (976 t 49)xlo"' cm '"sec '"atm ^ at STP 296 ± 15 Eggers, Hisatsune, and Van Alten (1955) (925 ± 93)xlo'"" cm '"sec '"atm ^ at STP 281 ± 28 Weber (1957) 590 cm “'atm ^ at 300 K 590 Hunter (1967) 420 ± 29 cm "atm '" at STP 382 ± 26 -2 -1 Varansi and Bangaru (1974) 294 ± 6 cm atm at 300 K 294 ± 6 Mast and King (1976) 69.195 + 0.659 km mole '" 281 ± 3 Smit, Van Straten, and Visser (1978) 76.244 + 1.194 km mole ^ 310 ± 5 Kim and King (1979) 70.4 ± 0.4 km mole '" 276 ± 2 This study 272 ± 27 cm "atm ^ at 300 K 272 ± 27 266 267 of cm-2 atm'1 at 300 K with the conversion factors of Pugh and Rao (1976). It may be noted that the differences in the reported band strengths are considerably larger than the reported experimental errors An integrated 3 ym strength at 300 K has been computed by multiplying each of the band strengths in Table 78 by 0.9781 for the 12C2H 2 bands and 0.0218 for the V 3 12C13CH2 band and summing the values. An additional 5 cm-2 atm-1 has been added to the total as an approximate correction for the additional hot bands not measured. The majority of the additional absorption should be from the - V51 band. Most of the low-resolution determinations of the integrated 3 ym strength fall within the estimated error of the value measured in this study (±10%). Section 6.8 - Intensities of the + V5^ and v2 + Vg1 Combination Bands and the Acetylene Column Density in IRC +10216 Numerous molecules in the circumstellar shell surrounding the carbon star IRC+10216 have been detected in the microwave and infra red regions (cf. Morris, 1975; Ridgway, et a l ., 1976; Hall and Ridgway 1978) . Since grain formation and extensive mass loss of nuclear-pro- cessed material are occurring, it is important to use the observed molecular transitions to study the chemistry, dynamics, and physical conditions of the circumstellar envelope. Quantitative studies of the observed transitions have been hampered by a lack of laboratory data. In this section the first intensity measurements of the perpen dicular (A£=l) bands vj + V 51 and v2 + V 51 of 12C2H 2 are reported. 268 The measured intensities have been used to deduce a revised estimate of the circumstellar acetylene column density in IRC+10216. The experimental procedure has been outlined in Section 6.4. For the present measurements spectra were obtained in 15th and 23rd orders for the x>2 + V51 band (head at 2701 cm-1) and the vi + V 51 band (4091 cm-1), respectively. The dispersion was calculated using goniometer fringes and CO fundamental and first-overtone calibration lines. Since at a resolution of 0.03 cm-1 it was impossible to resolve the individual rotational lines near the bandhead, the integrated Q branch intensities have been measured. The line strength Sj(T) of a single rotational line in a Q branch of a 11—E band of a linear mole cule may be written (Penner, 1959) 8TWN 1 - exp (6 .8-1) The symbols in the above have the same meaning as in Section 6.3. In v ’Z'J' this analysis R is assumed to be independent of J. v£J The line intensities were derived using the method of equivalent widths. The line positions were calculated from Baldacci, et_ al. (1973) for vi + V 51 and from Palmer, et a l . (1972) for V2 + V51. The self-broadened, room-temperature collisional half-widths of Varanasi and Bangaru (1975) were adopted. Line strengths were computed with v'£’J' Equation 6.8-1 for a trial value of R The observed band viJ 269 equivalent width was compared to the calculated equivalent width over the same spectral interval computed using a synthetic spectrum program and the line list. A Voigt line shape was assumed. The value of v ' £1 J1 2 K was then adjusted until the observed and calculated equiva v£J lent widths were equal. Measurements were made at two pressures for each band. For the pressures were 1.000 torr and 2.000 torr, and for the weaker v2 + V 51 band data were taken at 3.078 and 5.000 torr. Measurements were made at relatively low pressure to minimize the effects of colli- sional broadening, and the equivalent widths were kept relatively small to stay close to the linear part of the curve of growth. The mean values for the square of the matrix elements were 0.0095 and 0.0025 Debye2 for + V51 and v2 + V 51 , respectively. The determinations at the two different pressures agreed to within 5% for both bands. For v2 + v 5* an additional line had to be included in the line list. It is identified as R7 of the V3-V4* band at 2701.731 cm-1 (Palmer, 1972). Since this line occurs near the bandhead and was unresolved, only a rough estimate of 0.0096 ± 0.0025 cm-2 atm-1 can be given for its strength at 300 K. Calculated line strengths at 300 K are presented in Table 80 (powers of 10 are in parentheses). Synthetic spectra, con volved with a 0.030 cm-1 Gaussian instrumental profile, are shown in Figures 48 and 49 along with the observed spectra of vj + V 51 at 2.00 torr and v2 + V 51 at 5.00 torr. 270 Table 80 -2 -1 Calculated Line Intensities (cm atm at 300 K) J vi + V 5 1 v 2 + V 5 1 J Vi + V 5 1 v2 + V 5 1 1 4.18(-2) 7.27(-3) 21 4.48(-2) 7.79(-3) 2 2.27(-2) 3.95C-3) 22 1.22 (-2) 2.12(-3) 3 9.23C-2) 1.60(-2) 23 2.95(-2) 5.12(-3) 4 3.78(-2) 6.-57C-3) 24 7.82(-3) 1.36(-3) 5 1.31(-1) 2.28(-2) 25 1.84(-2) 3.20(-3) 6 4.82(-2) 8.38(-3) 26 4.76(-3) 8.27(-4) 7 1.53C-1) 2.68(—2) 27 1.09C-2) 1.90(-3) 8 5.33(-2) 9.26(-3) 28 2.76(-3) 4.79(-4) 9 1.61(-1) 2.80(-2) 29 6.17(-3) 1.07(-3) 10 5.31(-2) 9.23(-3) 30 1.52(-3) 2.64(-4) 11 1.54(-1) 2.68(-2) 31 3.32(-3) 5.76(-4) 12 4.87(-2) 8.47(-3) 32 7.96(-4) 1.38(-4) 13 1.36(-1) 2.37(-2) 33 1.7 0(—3) 2.95(-4) 14 4.17(-2) 7.25(-3) 34 3.97(-4) 6.90(-5) 15 1.13(—1) 1. 9 6(—2) 35 8.27(-4) 1.44(-4) 16 3.34(—2) 5.81(-3) 36 1.89(-4) 3.29(-5) 17 8.79(-2) 1. 5 3(—2) 37 3.84(-4) 6.68(-5) 18 2.53(-2) 4.39(-3) 38 8.58(-5) 1.49(-5) 19 6.45(—2) 1.12C-2) 39 1.7 0(—4) 2.96(-5) 20 1.80(—2) 3.14(-3) 40 3.72(-5) 6.46(-6) TOTAL 1.67(+0) 2.90(-l) DEPTH 0.9 0.0 0.2 ;WT HRVENUHBER ^ band ^ of ^^2^2 near cm • s°lid line is 5 gaussian instrumental profile. Line positions and 9 0 9 0 . 0 0 c m - -'- length of 96.95 cm. The synthetic spectrum symbols) (+ has been convolvedalternation of intensities are indicated below. the laboratory spectrum measured with a pressure of 2.00 torr and a path with a 0.030 =2.00 TORR 1=96.95 CH T°29G.2K 0.2 o.o 0.0 0.9 0. 0.5 0.6 DEPTH Figure 48. + SpectrumV of the \>j N5 •'j DEPTH 0.6 0.6 0.2 o.o 0.30.3 2702.00 I band I of 5 + V 2 2701.50 WRVENUMBER . . The laboratory spectrumwas measured at a near 2701 cm are shown in the same format as 48 2701.00 ^ ^ 2 ^ 2 Fig. Fig. pressure of 5.00 torr and a path length of 96.95 cm. ^ P-5.00 T0RF1 L = 96.95 CM T°296.4K = P-5.00 T0RF1 L Figure 49. Observed and synthetic spectra of the V 0.0 0.2 0.5 0.6 DEPTH 273 The measured equivalent widths of the vj + V 51 and the V 2 + V 51 bands in IRC+10216 are 0.2 and 0.04 cm'1, respectively (Ridgway, et al., 1976; Ridgway, 1979). Since both bands are weak and the ratio of stellar equivalent widths is very close to the ratio of the measured laboratory intensities, the bands have been assumed to be optically thin. The profile of the + V51 band drops sharply longward of J=16, suggesting a rotational temperature of 200 to 300 K (Ridgway, et al., 1976). From a comparison of synthetic profiles convolved with the Kitt Peak instrumental function and the published observations, a rota tional temperature of 300 K was adopted. The v? + V 51 profile is consistent with this temperature, but the band is very weak and badly blended with a telluric line on the longward edge. From the stellar equivalent widths and the measured laboratory strengths, the C2H 2 column density is estimated to be 3±1 x 1018 mol cm-2. This revised value is a factor of 10 lower than estimated by Ridgway, et a l . (1976). Although the laboratory data have provided a more reliable estimate' of the acetylene column density, further studies are needed. The low density in the circumstellar shell and the strong infrared radiative flux suggest that non-thermal molecular populations exist. Accurate treatment of the circumstellar chemistry will require modeling of the geometric structure and treatment of the radiative transfer, dynamics, and molecular statistical equilibrium. Observations at a resolution sufficient to resolve the rotational structure provide important infor mation. For example, Betz, McLaren, and Spears (1979) have used the 274 profiles of infrared absorption lines of NH 3 to study the dynamics and distribution of ammonia and to estimate the ammonia rotational tempera ture and column density and the H2 density. For acetylene, laboratory studies of collision rates with H2 and stellar observations at higher resolution would be useful. CHAPTER VII CONCLUDING REMARKS The major results of this study can be briefly summarized as follows: (1) Measurements made with a grating spectrometer and InSb detec tor in the 1.2 to 4.1 pm region have yielded narrow-band magnitudes of an accuracy camparable with results obtainable with photoelectric detec tors at shorter wavelengths (± li5%) „ This system has proved to be useful for measuring narrow-band colors and band strengths in late-type stars and atmospheric extinction. (2) Atmospheric extinction between 3.98 and 4.07 ym is predom inantly caused by continuous absorption by N 2 with smaller contributions from continuous absorption by H20 and C02 , discrete lines (primarily N20 ) , and extinction by aerosol particles. Synthetic extinction coeffi cients generated with a model terrestrial atmosphere and absorption coefficients measured in the laboratory are in good agreement with the measured values. (3) Narrow-band colors measured at continuum points in the infrared have been compared with color temperatures measured on the Wing 8 -color near-infrared photometric system and with results synthesized with model stellar atmospheres. The infrared continuum colors of late-type stars are strongly affected by the wavelength dependence of the dominant infrared opacity source, H . For oxygen-rich giants the infrared colors 275 276 are in agreement with model atmosphere results, but supergiant colors are hard to interpret because of the effects of reddening. A calibra tion of the observed giant star infrared color temperatures with model atmospheres is in good agreement with the effective temperature scale of Ridgway, et al. (1980). (4) Measurements of SiO band strengths have been made for 77 stars, mostly oxygen-rich giants and supergiants, with the infrared grating spectrometer. For giant stars the relation between SiO strength and spectral type is well defined with the absorption increasing rapidly to later types until at least M 6 . The data indicate that a considerable range of SiO strengths exists for M supergiants at a given MK spectral type, although this conclusion should be verified at high resolution. Two highly luminous supergiants (RW Cep and S Per) may have the (2,0) and (3,1) bands of SiO in emission; spectra of the peculiar supergiants VX Sgr, NML Cyg, and VY CMa are featureless at the resolution of the scanner measurements (5.5 cm-1). (5) Laboratory measurements of a number of infrared bands of acetylene have been made at high resolution, mostly in the 3 pm region. Molecular constants and line assignments are reported for a total of 27 bands arising between 41 different vibrational states. Absolute intensities have been measured for 101 lines in the 7 strongest bands in the 3 pm region. Integrated intensities measured for the vj + V 5 1 and V2 + V 5 1 bands have been used to derive a revised column density of acetylene molecules in the circumstellar shell of IRC+ 10216, a peculiar cool carbon star with a thick, expanding gas and dust shell. 277 Finally, I would like to end with a few comments and opinions: (1 ) There is an obvious need for absolute flux measurements at wavelengths beyond 1.1 Pm. The results presented in this dissertation have had to rely on model atmosphere absolute fluxes which have not yet been compared with observations. A program of absolute flux measure ments is currently being carried out at Kitt Peak by D. S. Hayes, S. T. Ridgway, and R. R. Joyce. (2) Although accurate measurements of the strengths of infrared molecular bands can be obtained by scanning across features, this method is slow and inefficient. Indices of band strengths can be obtained more efficiently by measuring at a small number of carefully chosen wave lengths, but wavelength shifts have made this impossible at present with the Kitt Peak grating instrument. Future infrared scanners should be built with accurate shaft encoders to keep track of grating rotation to try to eliminate this problem. (3) Measurements of atmospheric extinction are needed throughout the infrared. The wavelength dependence of extinction in the IR is poorly known, and detailed comparisons of observed and synthetic extinc tion coefficients at relatively high resolution are needed to ascertain the physical processes giving rise to extinction within each of the atmospheric windows. APPENDIX A: Atlas of 4 ym Scans Figures 50 to 64 in this appendix present 4 ym scanner observa tions of a large number of late-type stars. The purpose is to illus trate the dependence of the observable features with respect to' temperature, luminosity, and chemical composition. Additional obser vations have been presented in Chapter IV. The spectra are arranged in order of decreasing temperature. The fluxes are on a magnitude scale per unit wavelength subject to arbi trary normalization. The wavelength scale is in air microns. The bandpass of the scanner, an 0.1 mag flux interval, and the positions of the OH and SiO features are shown below. The continuum level, deter mined from a blackbody fit between the fluxes at 1(104) and L(400) is indicated with a solid line. The MK spectral type and calculated blackbody temperature appear below the star name. Because of instru mental wavelength shifts, the starting and ending wavelengths vary from star to star by several points. 278 279 . RLPHfl LYR RO V 12068 . BETA OPH K2 I I I «536 HRG 12,0) BANDPASS 14.00 14.05 WRVELENGTH (MICRONS) Figure 50. Scanner observations of a Lyrj a Ari„ and 3 Oph are shown on the same format as Fig. 7. 280 . ALPHA BOO K2 H IP W02« EPSILON PEG K2 IB 3823 . DELTA AND K3 I I I M262 HAG (2,0) BANDPASS l£.00 WAVELENGTH (MICRONS) Figure 51. Scanner observations of a Boo, e Peg, and 6 And are shown on the same format as Fig. 7. 281 . GAMMA AOL K3 I I 3816 ETA PER K3- IB -I 3885 . BETA CNC 3795 MAG (2 ,0) BANDPASS IJ.DO *4-05 NRVELENGTH (MICRONS) Figure 52. Scanner observations of y Aql, n Per^ and 8 Cnc are shown on the same format as Fig. 7. 282 . ZETfl AUR K5 I I * I 3639 ALPHA LYN K7 IIIR B 3611 KS-MO IAB-IB 3343 HRG BANDPASS 13.1) 4 .DO 4.05 WAVELENGTH (MICRONS) Figure 53. Scanner observations of X, Aur, a Lyns Aur are shown on the same format as Fig. 7. 283 . UPSILON GEM MO I I I 3630 HR 1009 MO I I 3380 . GAMMA ERI MO I I I 3539 GH WAVELENGTH (MICRONS) Figure 54. Scanner observations of u Gem, HR 1009, and y Eri are shown on the same format as Fig. 7. 284 . HR 8726 MO- IB 3416 UPSIL0N RUR GUI 3501 . ALPHA CET Ml.5 in 3492 MRG BANDPASS WAVELENGTH (MICRONS) Figure 55. Scanner observations of HR 8726, u Aur, and a Cet are shown on the same format as Fig. 7. 285 . ALPHA OR I Ml-2 IR-IB 3292 PI LEO M2- 11IRB 3536 . HR 1155 M2* IIRB 3204 MAG BANDPASS 14.00 il .05 WAVELENGTH (MICRONS) Figure 56. Scanner observations of a Ori, it Leo, and HR 1155 are shown on the same format as Fig. 7. 286 . KQ PUP M2 IRBEP * 3136 BOSS 1985 119 CE TflU M2 IRB-IB 3017 . MU CEP M2 IR 2938 12, 0 ) BRNDPRSS il.OO U.05 NRVELENGTH (MICRONS) Figure 57. Scanner observations of KQ Pup, 119 CE Tau, y Cep are shown on the same format as Fig. 7. 287 . AD PER M2.5 IAB 2900 H I CHI RHQ UMA M3 11 IB 3703 . MU GEM H3 11IAB 3300 MAG (2.0) BANDPASS u.oo u.os NRVELENGTH (MICRONS) Figure 58. Scanner observations of AD Per, p Per, and p Gem are shown on the same format as Fig. 7. 288 ETfl GEM M3 III 3327 PI RUR M3 I I 3213 . OH ICRON 1 ORI M3S 3203 MRG 12,0) BRNDPflSS (3,1) 11,00 *4.05 WAVELENGTH (MICRONS) Figure 59. Scanner observations of n Gem,, n Aurs and o1 Ori are shown on the same format as Fig. 7, 289 . SU PER H3-U IRB 2848 H & CHI 51 80 GEM MU III 3223 . HR 8621 MU I I I 3218 HRVELENGTH (MICRONS) Figure 60. Scanner observations of SU Per, 51 BQ Gem, and HR 8621 are shown on the same format as Fig. 7. 290 . RHO PER m iIB-11 in 3205 XY LYR m »s ii 3052 . RS PER M4.5 IAB 2777 H 4 CHI (2.0) BANDPASS 81.00 81.05 WfiVELENGTH CHI CRONS) Figure 61. Scanner observations of p Per, XY Lyrs and RS Per are shown on the same format as Fig. 7. 291 . 71 PEG GM5 3191 R LYR M5 II 3121 . HD 11961 M5 III 3089 BANDPASS (3,n NflVELENGTH (MICRONS) Figure 62. Scanner observations of 71 Peg, R Lyr„ and HD 11961 are shown on the same format as Fig. 7. 292 . ALPHA HER M5 I B - ii 2981 EU DEL M6 III 3020 - WEAK LINES . US RZ HRI M6- IIIi 3100 MRG (2.0) BANDPASS o UU *0® U J WAVELENGTH (MICRONS) Figure 63. Scanner observations of a Hers EU Dels and 45 RZ Ari are shown on the same format as Fig. 7. 293 . HD 297076 2878 CSV 5468 HR 1105 S5.3 330S (2,0) 4.00 ll. 05 WAVELENGTH (MICRONS) Figure 64. Scanner observations of HD 207076 and HR 1105 are shown on the same format as Fig. 7. APPENDIX B : Acetylene Line Positions in the 3 ym Region This appendix contains the mean measured positions of all lines recorded in the laboratory in the 3 ym region. Although the spectra were recorded in vacuum, a few of the lines reported in Appendix B are from residual water vapor in the path rather than acetylene. 294 APPENDIX B ACETYLENE LINE POSITIONS IN THE 3 MICRON REGION SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 6300 3137.3148 6850 3153.5428 7280 3160.5077 6310 3137.4198 6860 3153.7226 7290 3160.5625 6320 3137.4793 6870 3153.8264 7300 3160.8220 6350 3139.7732 6880 3153.9266 7310 3160.8656 6360 3139.9912 6890 3154.1367 7320 3160.9419 6370 3140.0751 6900 3154.4058 7330 3161.1301 6380 3140.2237 6910 3154.4509 7340 3161.2050 6390 3140.3037 6920 3154.4902 7350 3161.2937 6400 3140.6292 6930 3154.7958 7360 3161.4881 6410 3141.1364 6934 3155.0396 7370 3161.5410 6420 3142.6893 6936 3155.1504 7380 3161.7086 6430 3143.0889 6938 3155.2658 7390 3161.8285 6440 3143.1620 6940 3155.3651 7400 3161.8617 6450 3143.3205 6944 3 155.6376 7410 3162.0271 6460 3145.2913 6960 3155.9702 7420 3162.2724 6470 3145.5617 6965 3156.0489 7430 3162.3147 64S0 3146.0210 6970 3156.1787 7440 3162.5406 64 oj 3146.4150 6980 3156.3687 7450 3162.5793 6490 3146.8421 6990 3156.3993 7455 3162.6441 6497 314 7.6495 7000 3156.5347 7460 3162.7414 6500 3147.8183 7005 3156.6586 7470 3162.8450 6520 3143.2931 7010 3156.7726 7480 3163.0214 6530 3148.4448 7018 3156.9389 7490 3163.0736 6540 3148.6563 7020 3156.9710 7492 3163. 1370 6545 3143.7719 7030 3157.1887 7500 3163.4261 6550 3148.8026 7040 3157.2844 7510 3163.5290 6560 3148.8439 7050 3157.4768 7520 3163.5736 6570 3143.9639 7060 3157.5451 7530 3163.8067 6580 3149.0393 7065 3157.6036 7540 3163.9645 6590 3149.4221 7070 3157.6889 7550 3164.0311 6600 3149.6610 7080 3158.0503 7560 3164.2088 6610 3149.8638 7090 3158.1030 7570 3164.2490 6620 3150.0837 7100 3158.1334 7580 3164.4442 6040 3150.6885 71 10 3158.3294 7590 3164.5340 6650 3150.7545 7120 3158.4262 7600 3164.5790 6660 3150.9274 7140 3158.5916 7610 3164.7288 6670 3151.075 1 7145 3158.6928 7620 3164.8286 6680 3151.2397 7150 3158.886 1 7630 3165. 1263 6690 3151 .2953 7160 3159.1206 7640 3165.2633 6700 3151.6107 7170 3159.2143 7650 3165.3632 6710 3151.6796 7180 3159.3080 7660 3165.4815 6730 3151.8904 7200 3159.7555 7670 3165.5150 6740 3151.9639 7210 3159.7896 7680 3165.6014 6750 3152.0044 7212 3159.8172 7690 3165.6533 6760 3152.0379 7220 3159.9037 7700 3165.7280 6770 3152.3330 7230 3159.9640 7710 3165.7589 6790 3152.4683 7240 3160.0738 7720 3165.8610 6810 3152.8296 7250 3160.1300 7730 3165.9435 6820 3152.9606 7260 3160.2343 7740 3166.0703 6830 3153.0237 7270 3160.4344 7750 3166. 1 105 APPENDIX B (CONTINUED) ERIAL WAVE SERIAL WAVE SERIAL WAVE LIMBER NUMBER NUMBER NUMBER NUMBER NUMBER 7760 3166.2734 8250 3170.5819 8730 3174.8887 7770 3166.3184 8260 3170.6773 8740 3174.9321 7780 3166.5310 8262 3170.7146 8750 3175.0490 7790 3166.6282 8270 3170.8546 8760 3175.1076 7800 3166.7066 8280 3170.8902 8770 3175.1693 7810 3166.7784 8290 3170.9266 8780 3175.2233 7820 3166.8535 8300 3171.0816 8790 3175.2564 7830 3167.0628 8310 3171.1201 8792 3175.3182 7840 3167. 1704 8320 3171. 1933 8800 3175.3755 7850 3167.2042 8330 3171.2267 8810 3175.4098 7860 3167.3680 8340 3171.2731 8820 3175.4957 7870 3167.4252 8350 3171.5074 8830 3175.6722 7880 3167.6195 8360 3171.5638 8840 3175.7328 7890 3167.6981 8370 3171.6532 8842 3175.7619 7900 3167.7556 8380 3171.7266 8850 3175.8400 7910 3167.9220 8390 3171.7536 8860 3175.8993 7920 3167.9582 8391 3171.7824 8870 3175.9439 7930 3168.0431 8400 3171.8300 8880 3176.0483 7931 3163.0719 8410 3171.9290 8890 3176.2042 7940 3168.1356 8420 3172.0708 8900 3176.2458 7950 3168.2025 8430 3172.1378 89 10 3176.3114 7960 3163.3484 8440 3172.1904 8920 3176.3597 7970 3168.3773 84o0 3172.2562 8930 3176.4554 7971 3168.4050 8460 3172.4156 8940 3176.5036 7930 3168.4427 8470 3172.5731 8946 3176.6779 7990 3168.5403 8480 3172.6200 8950 3176.7561 8000 3168.5940 8490 3172.7568 8960 3176.8485 8010 3168.6601 8500 3172.8413 8966 3176.9477 8020 3168.6900 85 10 3172.9145 8970 3176.9803 8030 3168.8391 8520 3173.0766 8980 3177.0984 8040 3168.9340 B530 3173.1528 8990 3177.1473 8050 3168.9705 8532 3173.1836 9000 3177.1845 8060 3169.0419 8o40 3173.2296 9010 3177.2850 8070 3169. 1053 8550 3173.3823 9020 3177.3487 8030 3169.1679 8560 3173.4644 9030 3177.4662 8032 3169.2072 8570 3173.5303 9040 3177.5333 8090 3169.3242 8580 3173.6287 9050 3177.7155 8100 3169.4481 8590 3173.7959 9060 3177.8279 8110 3169.4796 8600 3173.8202 9070 3177.8539 8120 3169.7093 8601 3173.8476 9080 3177.9530 8130 3169.7495 86 10 3173.9026 9090 3177.9970 8140 3169.8125 8620 3174.2066 9 100 3178.0486 8150 3169.8913 8630 3174.2747 9102 3178.0920 8160 3169.9307 8640 3174.3429 9110 3178.1189 8170 3170.0442 8650 3174.4235 9120 3178.3390 8180 3170.0965 8660 3174.4601 9130 3178.4046 8190 3170.1720 8670 3174.5025 9140 3178.4645 8200 3170.2307 8680 3174.6005 9150 3178.5191 8210 3170.2899 8690 3174.6242 9160 3178.5919 8220 3170.3455 8700 3174.6860 9170 3178.6316 8230 3170.3913 8710 3174.7372 9172 3178.7050 8240 3170.517S 8720 3174.8634 9180 3178.7911 297 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 9190 3178.8691 9650 3182.6981 10160 3186.654-0 9200 3178.9329 9670 3182.8934 10170 3186.7191 9210 3178.964S 9672 3182.9188 10180 3186.7611 9220 3179.0782 9680 3182.9530 10190 3186.8238 9230 3179.1098 9690 3183.0077 10200 3186.8911 9240 3179.1977 9700 3183.0786 10205 3186.9649 9248 3179.2877 9710 3183.1371 10210 3186.9950 9250 3179.3246 9720 3183.2732 10220 3187.1248 9260 3179.4353 9730 3183.3528 10230 3187. 194-6 9270 3179.4952 9740 3183.3937 10240 3187.2586 9272 3179.5357 9750 3183.4-594 10250 3187.3639 9280 3179.6295 9760 3183.5940 10260 3187.3986 9290 3179.6657 9770 3183.6672 10270 3187.4959 9300 3179.7027 9780 3183.7124 10280 3187.5409 9310 3179.8272 9790 3183.8027 10290 3187.6526 9320 3179.8830 9800 3183.8707 10300 3187.7787 9330 3179.9380 9810 3183.9265 10310 3187.8407 9340 3180.054 1 9820 3184.0097 10312 3187.8722 9350 3180.1279 9830 3184.0621 10320 3187.9194 9360 3180.2343 9840 3184.2038 10326 3187.9684 9370 3180.3126 9850 3184.2552 10330 3188.0193 9380 3180.3721 9860 3184.3289 10340 3188.0626 9390 3180.4572 9870 3184.3589 10350 3188.1767 9400 3180.4910 9880 3184.4548 10352 3188.1995 9410 3180.5892 9890 3184.5417 10360 3188.304-7 9420 3180.6704 9900 3184.6260 10362 3188.3932 9421 3180.7076 9910 3184.7038 10364 3188.454-0 9424 3180.795S 9920 3184.7385 10370 3188.4926 9430 3180.9171 9925 3184.8181 10377 3188.5228 9440 3181.0014 9930 3184.8836 10380 3188.5637 9450 3181.0331 9940 3185.0865 10390 3188.6409 9460 3181.1435 9950 3185.1402 104-00 3188.7612 9470 3181.214-5 9955 3185.2520 104x0 3188.7907 9480 3181.2981 9960 3185.2882 10420 3188.8931 9490 3181.3559 9970 3185.3555 10430 3189.0068 9492 3181.4065 9980 3185.4683 10432 3189.0288 9500 3181.4642 10000 3185.5403 10440 3189.1214 9506 3181.5819 10010 3185.6138 10450 3189.1659 9510 3181.6212 10020 3185.7139 10460 3189.1911 9520 3181.6559 10030 3185.7741 10470 3189.2635 9530 3181.7419 10040 3185.8274 10472 3189.2958 9540 3181.7705 10050 3185.8737 10474 3189.3521 9550 3181.8777 10060 3185.9632 10480 3189.3971 9560 3181.9203 10070 3186.0066 10490 3189.4453 9570 3182.0850 10080 3186.0723 10500 3189.4921 9580 3182.1631 10090 3186.1275 10510 3189.5545 9590 3182.2248 10100 3186.2435 10520 3189.6258 9600 3182.2598 10110 3186.2878 10530 3189.6629 9610 3182.4235 10120 3186.4256 10540 3189.7021 9620 3182.4912 10130 3186.4740 10550 3189.7799 9630 3132.5246 10140 3186.5242 10560 3189.8297 9640 3182.5631 10150 3186.5693 10570 3189.9001 298 APPENDIX B (CONTINUED) »ERI AL WAVE SERIAL WAVE SERIAL WAVE rUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 10580 3190.029-6 11030 3193.8456 11480 3197.8243 10590 3190.0897 11060 3194.0071 11490 3197.8501 10600 3190.2029 1 1070 3194-. 0679 11500 3197.9655 106 10 3190.3302 11080 3194.1433 11520 3198.1627 10620 3190.4061 1 1090 3194.2170 1000 3198.2162 10622 3190.4611 1 1100 3194.3522 1002 3198.3309 10630 3190.5225 1 11 10 3194.3914 1004 3198.3868 10632 3190.5684 1 1120 3194.5078 1006 3198.4164- 10636 3190.6695 1 1 122 3194.6030 1010 3198.4671 10640 3190.7373 1 1130 3194.6660 1020 3198.5859 10650 3190.7987 1 1140 3194.7015 1022 3198.6289 10660 3190.8851 11150 3194.7796 1023 3198.6513 10670 3190.9768 1 1 160 3194.8331 1024 3198.6993 106S0 3191.0269 1 1162 3194.8705 1026 3198.8075 10690 3191.0671 1 1 170 3194.9688 1030 3198.9210 10700 319 1 .1393 1 1180 3195.0512 1032 3199. 1212 10710 3191. 190S 1 1 190 3195.0851 1034 3199. 1678 10720 3191.2928 1 1195 3195. 1391 1036 3199.2090 10730 3191.3623 1 1200 3195.2271 1037 3199.2749 10740 3191.4553 1 1210 3195.2647 1038 3199.3230 10750 3191.5079 1 1220 3195.4-413 1040 3199.3936 10760 319 1.5730 1 1230 3195.4806 1050 3199.4704 10770 3191.6062 1 1240 3195.6241 1060 3199.5674 10730 319 1.7162 1 1242 3195.7010 1065 3199.6429 10790 319 1.7993 1 1250 3195.7738 1070 3199.7315 10794 3191.8979 1 1260 3195.8428 1072 3199.7746 10300 3191.9503 1 1270 3195.9438 1074 3199.8778 1C310 319 1 .9765 1 1280 3196.0049 1076 3200.0030 10312 3192.0359 1 1290 3196. 1142 1080 3200.0611 10320 3192.1195 1 1300 3196. 1901 1082 3200.1404 1CS30 3192.1952 1 1310 3196.3105 1090 3200.2502 10340 3192.3169 1 1314 3196.3463 1094 3200.3576 1 OooO 3192.4214 1 1320 3196.4283 1096 3200.4009 10360 3192.4578 11325 3196.4509 1100 3200.4833 10S66 3192.5695 1 1330 3196.4943 1 102 3200.5856 10370 3192.6240 1 1340 3196.6414 1 1 10 3200.7980 10S90 3192.6913 11350 3196.7058 1112 3200.8325 109C0 3192.7383 11360 3196.7870 1114 3200.9179 10910 3192.7877 11362 3196.8244 1116 3200.9931 10920 3192.8927 1 1370 3196.8946 11 IB 3201.1177 10930 3192.9730 1 13S0 3196.9381 1120 3201.1617 10940 3193.0217 1 1390 3196.9891 1 125 3201.2215 10950 3193.0933 1 1400 3197.0460 1130 3201.2844 10952 3193.1802 1 1410 3197.1180 1132 3201.3638 10960 3193.3279 1 1420 3197.2170 1 133 3201.4685 10930 3193.4101 1 1422 3197.2456 1 136 3201.5758 10990 3193.4600 1 1430 3197.3657 1 138 3201.6078 1 1000 3193.5206 1 1440 3197.4244 1140 3201.7585 1 1010 3193.5822 1 1446 3197.5645 1 144 3201.8105 1 1012 3193.6264 1 1450 3197.6155 1 150 3201.8645 1 1020 3193.7410 11460 3197.6636 1 152 3201.8951 1 1024 3193.7990 11470 3197.7777 1 158 3201.9997 299 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER I 160 3202.0673 1360 3205.4959 1564 3209.2391 1170 3202.1045 1362 3205.5569 1565 3209.2634 1172 3202.1425 1363 3205.5984 1570 3209.3741 1 180 3202.2250 1364 3205.6582 1580 3209.5267 1 182 3202.2784 1365 3205.6995 1582 3209.6027 1 184 3202.3233 1370 3205.7981 1590 3209.6516 1 190 3202.3750 1372 3205.8608 1592 3209.6985 1 192 3202.4631 1380 3205.9307 1600 3209.7496 1197 3202.4975 1390 3206.0721 1602 3209.8413 1198 3202.6257 1392 3206.1382 1610 3209.9466 1200 3202.6833 1394 3206.1916 1620 3210.0154 1210 3202.7555 1400 3206.2770 1622 3210.1028 1220 3202.8219 1402 3206.3832 1630 3210.1337 1222 3202.8685 1403 3206.4655 1633 3210.2495 1225 3202.8845 1408 3206.5898 1635 3210.2951 1230 3202.9501 1410 3206.6329 1638 3210.4163 1234 3203.0014 1413 3206.7610 1640 3210.4441 1236 3203.0706 1414 3206.8151 1650 3210.4822 1237 3203.1528 1415 3206.8381 1660 3210.5545 1238 3203.1971 1418 3206.8852 1670 3210.6372 1240 3203.2843 1420 3207.0298 1680 3210.7072 1250 3203.3632 1430 3207.1410 1690 3210.7855 1252 3203•4803 1432 3207.1927 1692 3210.8718 1253 3203.5468 1437 3207.2941 1694 3210.9251 1254 3203.5947 1440 3207.3839 1700 3211.0143 1260 3203.6632 1446 3207.4660 1704 321 1.0737 1270 3203.7252 1450 3207.5118 1706 3211.1162 1230 3203.8041 1452 3207.5630 1710 3211.2231 1232 3203.8951 1455 3207.6427 1712 3211.2563 12S4 3203.9693 1456 3207.6749 1720 3211.3388 12S6 3204.0330 1460 3207.7978 1721 3211.3811 1290 3204.1210 1470 3207.9001 1725 3211.5168 1296 3204.1946 1480 3207.9350 1730 3211.5984 1297 3204.2317 1482 3208.0285 1732 3211.6518 1291 3204.31 13 1484 3208.0315 1734 3211.7210 1292 3204.3514 1490 3208.1083 1736 3211.8192 1293 ’ 3204.3825 1492 3208.1761 1740 3211.8752 1295 3204.4745 1500 3208.2166 1742 3211.9780 1294 3204.5293 1502 3208.2855 1750 3212.0092 1293 3204.6275 1503 3208.3233 1752 3212.1091 1300 3204.7312 1510 3208.4752 1760 3212.1479 1305 32o4.80o4 1516 3208.5400 1762 3212.2329 1310 3204.S746 1520 3208.5899 1763 3212.3435 1312 3204.919 1 1522 3208.6314 1764 3212.4033 1315 3205.0015 1530 3208.7051 1766 3212.4747 1320 3205.0922 1532 3208.7512 1763 3212.5309 1330 3205.1771 1540 3208.8131 1770 3212.6383 1332 3205.2487 1550 3208.8420 1780 3212.7421 1340 3205.296 1 1554 3208.9573 1782 3212.8095 1341 3205.3649 1556 3209.0438 1784 3212.8562 1350 3205.3897 1560 3209.1276 1788 3212.9199 1352 3205.4393 1562 3209.1693 1790 3212.9742 APPENDIX B (CONTINUED) SERIAL NAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 1800 3213.0621 2095 3216.9653 2332 3220 5429 1810 3213.1574 2097 3217.0262 2334 3220 6076 1820 3213.2226 2 1 0 0 3217.0661 2336 3220 6484 1830 3213.2975 2110 3217.1389 2340 3220 7315 1836 3213.4347 2112 3217.2178 2342 3220 7749 1838 3213.4856 2114 3217.3351 2344 3220 8250 1840 3213.5428 21 16 3217.5629 2346 3220 9217 1845 3213.6537 2118 3217.6285 2350 3221 0263 1850 3213.7086 2120 3217.6667 2360 3221 0850 1860 3213.8582 2125 3217.7497 2370 3221 1366 1862 3213.9842 2130 3217.8053 2380 3221 2886 1864 3214.0536 2140 3217.8545 2390 3221 3662 1870 3214.1225 2150 3217.9384 2400 3221 49 10 1872 3214.1699 2160 3217.9660 2405 3221 6 135 1B74 3214.2234 2170 3218.0632 2406 3221 6602 1876 3214.2799 2172 3218.0905 2410 3221 7330 1880 3214.3425 2180 3218.1885 2412 3221 7630 1890 3214.3839 2190 3218.2965 2414 S221 8495 1892 3214.4878 2200 3218.4674 2415 3221 9014 ie94 3214.5796 2210 3218.5111 2420 3222 0477 1896 3214.6583 2 220 3218.5767 2430 3222 1065 1900 3214.6953 2230 3218.6839 2432 3222 1888 1910 3214.7753 2235 3218.7190 2434 3222 236 1 1912 3214.8423 2236 3218.7718 2435 3222 2706 1914 3214.9182 2240 3218.8292 2356 3222 3095 1918 3215.0000 2250 3218.8741 2358 3222 3992 1920 3215. 1015 2251 3218.9686 2440 3222 4681 1925 3215.1923 2252 3219.0108 2450 3222 5480 1930 3215.2536 2253 3219.1021 2452 3222 7040 1940 3215.3439 2254 3219.1423 2460 3222 7588 1950 3215.4370 2255 3219.1812 2462 3222 8191 1960 3215.4714 2256 3219.2374 2470 3222 8952 1970 3215.5126 2258 3219.3121 2472 3222 9336 1972 3215.5531 2260 3219.3801 2480 3223 0207 1930 3215.6501 2262 3219.4339 2490 3223 0732 1982 3215.6995 2264 3219.5091 2492 3223 1360 1984 3215.7571 2268 3219.5502 2494 3223 1662 1990 3215.8219 2270 3219.6214 2500 3223 2689 2000 3215.8795 2272 3219.6860 2502 3223 3564 2010 3215.9601 2275 3219.7250 2504 3223 3982 2020 3216.0675 2280 3219.7754 2506 3223 4736 2030 3216.1644 2290 3219.9539 25 10 3223 5760 2032 3216.2020 2292 3220.0050 2520 3223 6225 2040 3216.3345 2293 3220.0529 2530 3223 7274 2050 3216.3736 2296 3220.1357 2532 3223 7483 2052 3216.4417 2300 3220.1829 2540 3223 8475 2060 3216.5115 2310 3220.2168 2542 3223 8848 2070 32 16.5848 2312 3220.2678 2544 3223 9441 2 0 S0 3216.7014 2314 3220.3524 2545 3223 9800 2082 3216.7361 2318 3220.3951 2546 3224 0455 2085 3216.8254 2320 3220.4439 2550 3224 1420 2090 3216.8343 2330 3220.5084 2552 3224 1732 301 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 2554 3224.2393 2792 3227.8597 3100 3231.5725 2560 3224.2715 2800 3227.9475 31 10 3231.6595 2570 3224.3200 2802 3228.0710 3120 3231.6941 2572 3224.3641 2810 3228.1364 3130 3231.7584 2574 3224.4583 2820 3228.1615 3132 3231.8538 2576 3224.5434 2830 3228.2996 3140 3231.89 16 2580 3224.5832 2840 3228.3896 3150 3231.9465 25S2 3224.6956 2842 3228.4224 3160 3231.9907 2583 3224.747B 2850 3228.5267 8170 3232.0948 2590 3224.8098 2860 3228.6254 3180 3232.1670 2592 3224.8447 2870 3228.6624 3190 3232.2755 2596 3224.9159 2872 3228.7399 3192 3232.3234 2600 3224.9972 2880 3228.7824 3194 3232.3580 2605 3225.0836 2882 3228.8421 3195 3232.3908 26 10 3225.1441 2890 3228.9 164 3196 3232.4892 2620 3225.2953 2892 3228.9884 3200 3232.6012 2630 3225.3797 2894 3229.0214 3202 3232.6482 2631 3225.4981 2896 3229.0981 3204 3232.6926 2640 3225.5872 2900 3229.1547 3206 3232.7860 2650 3225.6287 29 10 3229.2315 3210 3232.8476 2660 3225.7164 2920 3229.2640 3212 3232.8801 2670 3225.79 15 2922 3229.2965 3214 3232.9432 2674 3225.8667 2930 3229.3788 3216 3232.99 10 2675 3225.9481 2932 3229.4282 3220 3233.0173 2676 3225.9949 2940 3229.5246 3230 3233.0812 2680 3226.0533 2942 3229.5552 3240 3233.2179 2690 3226.1270 2950 3229.6069 3250 3233.3006 2700 3226.1873 2954 3229.6978 3252 3233.3375 2705 3226.2521 2960 3229.8296 3260 3233.4017 2710 3226.3297 2970 3229.8857 3270 3233.4596 2714 3226.4404 2971 3229.9427 3272 3233.5149 2716 3226.5772 2974 3230.1435 3274 3233.5680 2719 3226.6407 2978 3230.1920 3280 3233.6187 2720 3226.6663 2980 3230.2167 3290 3233.7011 272 1 3226.6S2S 2982 3230.2952 3300 3233.8301 2730 3226.7696 2990 3230.3368 3305 3233.9245 2740 3226.8186 2992 3230.4126 3310 3234.0096 £745 3226.9359 3000 3230.4477 3320 3234.0603 2747 3227.0039 3010 3230.6110 3330 3234.1261 2750 3227.0568 3020 3230.6827 3332 3234.1580 2752 3227.1264 3030 3230.8044 3340 3234.2350 2754 3227.1578 3032 3230.6443 3350 3234.3060 2756 3227.2229 3036 3230.8987 3360 3234.4071 2760 322?!2633 3033 3230.9647 3370 3234.4365 276 1 3227.3255 3040 3230.9951 3372 3234.5131 2764 3227.4031 3050 3231.0436 3380 3234.5899 2770 3227.4599 3052 3231.1266 3382 3234.6206 2772 3227.4978 3060 3231.1882 3384 3234.6623 2774 3227.6130 3070 3231.2435 3386 3234.7031 2776 3227.6932 3072 3231.3420 3390 3234.8015 2780 3227.7597 3080 3231.3696 3392 3234.8413 £790 3227.8038 3090 3231.4911 3394 3234.8768 APPENDIX B (CONTINUED) 1 ■ ——' — — — — IRIAL WAVE SERIAL WAVE SERIAL WAVE IMBER NUMBER NUMBER NUMBER NUMBER NUMBER 3400 3235.0023 3640 3238.2949 3990 3242.1657 3401 3235.0399 3650 3238.3576 3995 3242.2461 3403 3235.1100 3660 3238.4071 4000 3242.3017 3402 3235.1666 3670 3238.5031 4005 3242.3481 3404 3235.2360 3680 3238.5793 40 10 3242.4060 3406 3235.2837 3682 3238.6374 4012 3242.4591 3410 3235.3550 3690 3238.7158 4020 3242.5423 3415 3235.4801 3700 3238.7884 4024 3242.6475 3416 3235.526 1 3710 3238.8892 4026 3242.7740 3420 3235.5774 3720 3238.9731 4030 3242.8293 3421 3235.6119 3730 3239.0563 4032 3242.8880 3430 3235.7063 3740 3239.1284 4040 3242.9334 3440 3235.7396 3750 3239.1607 4050 3243.0003 3450 3235.7744 3752 3239,2345 4060 3243.1201 3460 3235.8586 3760 3239.3178 4070 3243.1875 3470 3235.9 115 3770 3239.4111 4080 3243.2440 3472 3235.9516 3772 3239.4912 4090 3243.3739 3480 3236.0062 3776 3239.5734 4100 3243.4559 3490 3236.1408 3780 3239.6375 4110 3243.5606 3500 3236.2157 3790 3239.7059 4120 3243.6827 3510 3236.3164 3800 3239.7379 4130 3243.7365 351 1 3236.3368 3802 3239.8949 4140 3243.8065 3512 3236.3844 330t> 3239.9402 4 142 3243.8367 3520 3236.4559 3808 3240.0054 4150 3243.9405 3530 3236.5559 3810 3240.1105 4160 3244.0014 3540 32S6.6030 3820 3240.1444 4162 . A3 0 5 3550 3236.6313 3822 3240.2092 4170 3244!1008 3553 3236.6667 3824 3240.2873 4180 3244.1683 3554 3236.6922 3330 3240.3439 4190 3244.2159 3555 3236.7347 3832 3240.4112 4200 3244.3927 3553 3236.8176 3834 3240.4724 4201 3244.4109 3560 3236.8897 3840 3240.6766 4202 3244.4375 3570 3236.9218 3860 3240.7556 4206 3244.5366 3572 3237.0143 3870 3240.7866 4210 3244.6010 3o i 4 3237.0319 3880 3240.8841 4216 3244.7265 3580 3 2 3 7 .173S 3835 3240.9355 4218 3244.8034 3582 3237.2140 3390 3241.0157 4220 3244.8503 3oB4 3237.2650 3894 3241.1093 4230 3244.9447 3585 3237.3458 3900 3241.2045 4232 3244.9784 3586 3237.4230 3910 3241.2542 4234 3245.0317 3537 3237.4946 39 15 3241.3187 4235 3245. 1007 3590 3237.5758 3920 3241.3992 4240 3245.1866 3592 3237.6739 3930 6241.4997 4241 3245.2527 3600 3237.7103 3940 3241.6054 4250 3245.2996 3602 3237.7503 3950 3241.6555 4252 3245.3505 3610 3237.8521 3960 3241.6913 4260 3245.4070 36 12 3237.9393 3970 3241.7486 4270 3245.4570 3620 3237.9790 3972 3241.7831 4272 3245.5104 3622 3238.0180 3980 3241.9003 4280 3245.6208 3624 3238.0816 3982 3241.9753 4290 324 5.6533 3626 323S.1425 3983 3242.1004 4300 3245.7292 3630 3238.2534 3984 3242.1334 4320 3245.8506 303 APPENDIX B (CONTINUED) SERIAL NAVE SERIAL NAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 4330 3246.0110 4671 3249.6070 4935 3253.1764 434G 3246.0574 4672 3249.6639 4940 3253.2265 4350 3246.1457 4674 3249.7344 4941 3253.2747 4360 3246.2034 4676 3249.7997 4942 3253.3382 4362 3246.25S6 4677 3249.8326 4950 3253.3640 4370 3246.3695 4680 3249.9053 4960 3253.4865 4372 3246.4440 4682 3249.9460 4965 3253.5328 4380 3246.474B 4683 3250.0086 4970 3253.5584 4390 3246.5763 4684 3250.0765 4980 3253.6068 4400 3246.6703 4690 3250.2294 4990 3253.6599 4410 3246.7192 4692 3250.3035 499 I 3253.7083 4420 3246.8399 4693 3250.3424 4992 3253.8205 4422 3246.8898 4694 3250.4213 4994 3253.8867 4426 3246.9549 4695 3250.4479 5000 3253.9774 4430 3247.0235 4700 3250.4777 5002 3254.0687 4432 3247.0719 4710 3250.5608 5003 3254.0962 4434 3247.1693 4720 3250.6633 5010 3254.1200 4440 3247.263) 4730 3250.7712 501 1 3254.1609 4450 3247.3C6 1 4733 3250.8657 5020 3254.1802 4452 3247.3567 4740 3250.9197 5030 3254.2661 4460 3247.3811 4742 3250.9542 5032 3254.4275 4462 3247.4301 4744. 3250.9828 5033 3254.4565 4463 3247.5241 4750 325 1.05 18 5034 3254.5089 4464 3247.5775 4760 3251.0814 5036 3254.5541 4463 3247.6744 4770 3251.1954 5037 3254.6812 4470 3247.7661 4780 325 1.2654 5033 3254.7493 4480 3247.8361 4790 3251.339 1 5039 3254.8708 4490 3247.8971 4792 3251.4018 5040 3254.9179 4492 3247.9905 4800 3251.4339 5050 3255.0642 4500 3243.0592 4S10 3251.5281 5055 3255.0902 4510 3248.1173 4820 3251.6445 5060 3255.1373 4520 3248.2043 4830 3251.7049 5061 3255.1808 4530 3243.2627 4840 3251.7475 5062 3255.2180 4540 3248.3164 4850 3251.8615 5070 3255.2885 4542 3248.3896 4852 3251.9422 508O 3255.3278 4546 324S.4607 4853 3251.9775 5090 3255.4219 4550 3243.5099 4856 3252.0914 5100 3255.4693 4560 3248.5619 4860 3252.1237 51 10 3255.5642 4570 3248.5954 4862 3252.226 1 5120 3255.6210 4580 3243.7383 437" 0 3252.2800 5130 3255.6709 4590 3243.7898 4875 3252.3631 5140 3255.7620 4600 3243.8741 4880 3252.4179 5150 3255.8098 4610 3243.966S 4384 3252.4720 5155 3255.8665 4612 3249.0296 4838 3252.5992 5160 3255.9 1 10 4620 3249.0525 4890 3252.6893 5170 3256.0055 4630 3249.1605 4891 3252.7242 5171 3256.0478 4640 3249.2198 4892 3252.8335 5172 3256.0633 4650 3249.3003 4900 3252.8871 5180 3256.1116 4652 3249.3331 4910 3252.9935 5181 3256.2492 4654 3249.4030 4915 3253.0519 5182 3256.3450 4660 3249.4447 4920 3253.0742 5190 3256.4286 4670 3249.5364 4930 3253.1155 5192 3256.4585 304 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBERNUMBER 5200 3 2 5 6 .5 8 2 8 5470 3 2 5 9 .8 8 1 4 5792 3 2 6 2 .9 7 6 4 5210 3 2 5 6 .6 4 2 2 5471 3 2 5 9 .9 0 5 3 5798 3 2 6 3 .0 4 3 9 5211 3 2 5 6 .6 7 2 2 5480 3259.9344 5800 3 2 6 3 .0 7 8 2 5216 3 2 5 6 .7 3 4 7 5490 3 2 6 0 .0 1 8 3 5810 3 2 6 3 .1 2 5 8 5212 3 2 5 6 .8 6 1 8 5500 3 2 6 0 ,0 6 14 5820 3 2 6 3 .1 5 3 3 5213 3 2 5 6 .9 0 1 2 5501 3260.0920 5825 3 2 6 3 .2 3 8 0 5214 3 2 5 6 .9 4 1 9 55 10 3260.1981 5828 3263.3179 5215 3 2 5 6 .9 6 7 7 5520 3 2 6 0 .2 4 1 2 5830 3263.3519 5218 3 2 5 7 .0 6 5 9 5521 3 2 6 0 .2 7 4 8 5831 3 2 6 3 .3 7 7 7 5217 3 2 5 7 .0 9 0 5 5530 3260 .3 3 8 9 5832 3263.4560 5219 3 2 5 7 .1 4 3 0 5532 3260 .3 6 0 9 5834 3 2 6 3 .4 8 9 3 5212 3 2 5 7 .2 0 2 2 5534 3 2 6 0 .3 8 9 8 5840 3263.5619 5220 3 2 5 7 .2 2 0 7 5540 3 2 6 0 .4 2 4 9 5850 3263.6229 5230 3 2 5 7 .2 5 1 6 5550 3 2 6 0 .4 5 1 6 5860 3263.7036 5240 3 2 5 7 .2 9 0 0 5560 3 2 6 0 .5 2 3 8 5870 3263.8146 5241 3 2 5 7 .3 3 6 4 5562 3260.5775 5880 3 2 6 3 .8 6 4 3 5242 3 2 5 7 .3 7 3 6 5570 3 2 6 0 .6 6 2 0 5890 3 2 6 3 .9 186 5250 3 2 5 7 .4 0 7 6 5560 3260.7284 5900 3 2 6 3 .9 8 1 3 5252 3 2 5 7 .4 6 5 0 5590 3 2 6 0 .7 8 0 2 5903 3264.0244 5260 3257 .5 2 2 1 5600 3260.8934 5910 3264.1120 5270 3 2 5 7 .5 8 1 3 5602 3260.9370 5915 3264.1431 5275 3 2 5 7 .6 5 6 3 5610 326 1.0107 5920 3 2 6 4 .1 7 4 9 5280 3 2 5 7 .6 8 8 7 5620 326 1.0513 5925 3264.2358 5282 3 2 5 7 .8 1 9 0 5630 3 2 6 1 .0 8 8 3 5926 3264.3086 5290 3257.8411 5640 3261 .' 1298 5927 3 2 6 4 .3 4 1 4 5300 3 2 5 7 .B695 5643 3 2 6 1 .2 1 1 6 5928 3264.4245 5310 3 2 5 7 .9 4 2 4 5650 3 2 6 1 .2 8 4 7 5929 3264.4910 5320 3257.9984 5651 326 1.4382 5940 3264.5291 5330 3 2 5 8 .0 6 1 5 5660 3 2 6 1 .4 7 5 8 5950 3264.5775 5340 3258.1080 5670 3 2 6 1 .5 4 1 6 5955 3 2 6 4 .6 6 6 3 5342 3258. 135 1 5671 3261.6681 5960 3 2 6 4 .7 6 2 5 5350 3258.2373 5672 326 1.7242 5970 3 264.8101 5360 3 2 5 8 .32SG 5674 326 1.86 14 5980 3264.8713 5370 3258.3581 5676 3 2 6 2 .0 0 8 9 5990 3264.9111 5380 3258.4214 5680 3 2 6 2 .1 0 2 0 6000 3265.0073 5390 3258.4586 5682 3262.1428 6010 3 2 6 5 .0 3 6 5 5400 3258.5275 5683 3 2 6 2 .1 8 5 7 6020 3265.0900 5410 3 25 8 .5 5 7 1 5690 3262.2145 6021 3265.1114 5420 3258.6091 5696 3 2 6 2 .2 9 8 3 6027 3 2 6 5 .1 6 2 0 5422 3258.6488 5700 3 26 2 .3 4 5 6 6028 3265.1903 5425 3258.7856 5705 3 2 6 2 .3 9 6 6 6040 3265.2573 5430 3 2 3 8 .8 6 1 5 5710 3262.4497 6050 3265.3109 5440 3 2 5 9 .0 3 3 3 5720 3 262.5571 6060 3265.3615 5450 3259.0950 5730 3262.5973 6070 3265.4700 5452 3 2 5 9 .2 6 5 4 5740 3 2 6 2 .6 2 8 3 6080 3265.5066 5453 3259.3525 5750 3 26 2 .6 6 3 5 6085 3265.6274 5454 3 2 5 9 .4 1 2 2 5751 3 26 2 .7 1 3 6 6090 3265.7309 5458 3259.5955 5752 3 2 6 2 .7 7 7 8 6093 3265.7993 5460 3259.6625 5760 326 2 .7 9 4 5 6095 3265.8623 5462 3259.7023 5770 3 2 6 2 .8 4 2 6 6096 3265.8920 5463 3259.7583 5780 3 2 6 2 .BS27 6 100 326 5 .9 7 4 1 5469 3259.8536 5790 3 2 6 2 .9 4 8 6 61 10 3 2 6 6 .0 2 8 5 305 APPENDIX B (CONTINUED) iRIAL WAVE SERIAL WAVE SERIAL WAVE JMBER NUMBER NUMBER NUMBER NUMBER NUMBER 6120 3 2 6 6 .1 2 0 4 6440 3269 .5 4 7 1 6760 3 2 7 3 .1 4 0 5 6 1GG 3 2 6 6 .1 7 8 4 6450 3 2 6 9 .5 9 1 7 6770 3 2 7 3 .2 2 1 3 6 140 3266.2431 6460 32 6 9 .6 6 4 0 6775 3 2 7 3 .2 6 7 1 6150 3 2 6 6 .3 4 5 8 6470 32 6 9 .6 9 3 3 6780 3 2 7 3 .2 9 7 3 6160 3 2 6 6 .4 0 2 9 6471 3 2 6 9 .7 4 8 9 6790 3 2 7 3 .3 5 1 0 6 16 1 3 2 6 6 .4 6 5 3 6472 3 2 6 9 .8 0 9 2 6800 3 2 7 3 .4 2 4 7 6165 3 2 6 6 .4 9 4 0 6474 3 2 6 9 .8 4 8 5 6805 3 2 7 3 .4 6 5 4 6 176 3 2 6 6 .6 6 3 2 6476 3 2 6 9 .8 9 7 8 6810 3 2 7 3 .5 8 0 6 6 180 3 2 6 6 .7 4 3 0 6477 3 2 6 9 .9 7 3 6 6820 3 2 7 3 .6 1 9 8 6185 3 2 6 6 .8 1 4 5 6480 32 7 0 .0 0 2 3 6830 3 2 7 3 .7 6 5 2 6190 3 2 6 6 .836B 6490 3 2 7 0 .0 4 9 3 6832 3 2 7 3 .8 9 0 2 6200 32 6 6 .9 5 4 6 6500 32 7 0 .1 0 9 7 6834 3 2 7 4 .0 0 5 3 620B 3 2 6 7 .0 9 9 6 65 10 327 0 .1 4 0 5 6838 3 2 7 4 .1 5 4 9 6210 3 2 6 7 .1 8 4 3 6520 327 0 .2 4 6 9 6850 3 2 7 4 .2 1 4 6 6220 3267 .2 4 7 1 6522 3 2 7 0 .3 0 3 2 6860 3 2 7 4 .2 4 4 8 6230 3 2 6 7 .2S72 6524 3 2 7 0 .3 4 8 9 6864 3 2 7 4 .3 6 7 3 6231 3 2 6 7 .3 5 4 3 6530 327 0 .4 2 0 5 6865 3 2 7 4 .4 0 8 7 6240 3 2 6 7 .3 8 5 6 6540 3 2 7 0 .5 1 6 5 6870 3 2 7 4 .5 0 0 4 6242 3 2 6 7 .4 4 3 2 6550 3 270.5641 6875 3 2 7 4 .6 0 2 4 6244 3 2 6 7 .5 1 0 3 6553 327 0 .6 6 9 6 6876 3 2 7 4 .6 3 6 6 6245 3 2 6 7 .5 5 2 3 6555 3 2 7 0 .7 2 2 4 6880 3 2 7 4 .6 9 9 4 6246 3 2 6 7 .5 8 1 7 6560 3 2 7 0 .7 9 8 7 6890 32 7 4 .7 5 6 2 6250 3 2 0 7 .6 5 9 1 6570 3270.6436 6900 3 2 7 4 .8 1 6 2 625 1 3 2 6 7 .6 9 4 8 6580 3 2 7 0 .9 1 7 4 69 10 3 2 7 4 .8 6 9 9 6260 3 2 6 7 .7 5 9 6 6590 3 271.0159 6920 3 2 7 4 .9 3 4 8 6270 3267 .8 0 2 1 6600 3271 .0607 6922 3 2 7 5 .0 1 2 3 6280 3267 .8 3 4 1 6608 3 271.1119 6923 3 2 7 5 .0 4 7 2 6232 3 2 6 7 .9 2 1 4 6610 3 2 7 1 .1 4 2 6 6924 3 2 7 5 .1 2 3 0 6284 3 2 6 7 .9 8 5 4 6620 3 2 7 1 .1 7 7 8 6926 3275.1728 62S6 3 2 6 3 .0 8 5 5 6630 3 2 7 1 .2 2 3 8 6930 3 2 7 5 .2 5 5 8 6290 3 2 6 8 .1 1 1 0 6640 3 2 7 1 .2 9 2 2 6933 3 2 7 5 .3 2 6 8 6294 3 2 6 8 .2 2 9 2 6642 3 2 7 1 .3 3 7 0 6940 3 2 7 5 .3 6 2 7 6297 3 2 6 3 .3 1 3 9 6650 32 7 1 .4 8 7 7 6944 3 2 7 5 .4 5 4 0 6300 3 2 6 8 .3 7 1 4 6660 3 2 7 1 .5 5 2 5 6950 327 5 .5 2 8 9 6310 3268 .4 1 5 1 6668 32 7 1 .7 0 1 2 6960 327 5 .5 7 0 9 6320 3 2 6 3 .4 7 4 4 6670 32 7 1 .7 6 4 0 6965 3 2 7 5 .6 4 5 3 6330 3268 .5 8 9 1 6680 3271.8181 6970 3 2 7 5 .7 0 4 0 6340 3268.6420 6690 3 2 7 1 .8 9 8 2 6980 3275.7762 6350 3 2 6 3 .7 6 6 0 6700 3 271.9911 6990 3275.8874 6360 326 8 .8 2 1 1 6705 3 2 7 2 .0 5 0 6 7000 3 2 7 5 .9 7 7 6 6370 3 2 6 3 .8 9 0 2 6710 3 2 7 2 .1 0 0 0 7010 3 2 7 6 .0 1 0 4 6380 3 2 6 8 .9 9 0 2 6720 3272.1540 7015 3 2 7 6 .0 2 7 7 6382 3269.0411 6730 3272 .2 0 7 5 7030 3 2 7 6 .2 2 3 4 6386 3 2 6 9 .0 9 4 6 6738 3272 .3 4 8 9 7040 3276.2528 6390 3 2 6 9 .1 2 2 0 6739 3 2 7 2 .3 9 5 3 7042 327 6 .2 8 9 1 6400 3269.2430 6740 3 2 7 2 .4 3 7 6 7044 3 2 7 6 .3 6 3 0 6405 3 2 6 9 .2 7 1 2 6743 3 2 7 2 .4 9 1 8 7050 3 2 7 6 .4 8 3 0 6410 3269.3436 6750 3 2 7 2 .5 9 4 9 705 1 3 2 7 6 .5 0 7 0 6415 3269.3720 6752 32 7 2 .6 4 2 7 7060 3276.5290 6420 3269.4175 6754 3 2 7 2 .7 3 0 9 7070 3 2 7 6 .5 8 5 9 6430 3269.4804 6755 3 2 7 2 .7 7 7 2 7080 3276.6966 6435 3269.5114 6758 32 7 2 .8 9 3 7 7090 3 2 7 6 .7 7 9 3 306 APPENDIX B (CONTINUED) DUAL WAVE SERIAL WAVE SERIAL WAVE IMBER NUMBER NUMBER NUMBER NUMBER NUMBER 7100 3 2 7 6 .8 1 1 8 7422 3280.1121 7 7 3 5 3 2 8 3 .6 2 3 7 7105 3276.8381 7423 3 2 8 0 .1 5 3 3 7740 3 2 8 3 .6 6 1 3 7110 3276.9011 7425 3 2 8 0 .2 4 5 3 7750 328 3 .7 1 6 5 7115 3 2 7 6 .9 8 0 2 7427 3280.2931 7755 3283.7452 7120 3 277.0506 7430 3280 .4 3 3 9 7760 3 2 8 3 .7 6 7 4 7125 3 2 7 7 .0 7 4 5 7435 3280 .4 7 4 5 776 1 3283.8112 7130 3277.1021 7440 3280.5465 7770 328 3 .8 4 3 5 7132 3 277.1315 7450 32 8 0 .5 9 5 0 7780 3 2 8 3 .9 183 7140 3277.1867 7455 3 2 8 0 .6 3 1 8 7790 3284.1170 7145 3 2 7 7 .2 2 3 6 7460 3230.6801 7800 3284.1948 7150 3 2 7 7 .2 6 5 4 7470 3 2 8 0 .7 4 3 8 7810 32 8 4 .2 4 7 7 7160 3 2 7 7 .3 2 8 2 7480 3280.7761 7818 3284.2821 7165 3 2 7 7 .3 6 2 0 7490 3 2 8 0 .8 2 9 4 7820 32 8 4 .3 0 2 7 7180 3277.5779 7495 3 2 8 0 .9 9 9 3 7822 3 2 8 4 .3 7 6 4 7185 3 2 7 7 .6 0 9 4 7500 3281.1531 7823 3 2 8 4 .3 9 7 5 7190 3277.6791 7505 3281 .1 8 0 9 7826 3284.4995 7195 3 2 7 7 .7 4 7 3 75 10 3281.2530 782S 32 8 4 .5 7 9 4 7200 3277.8266 75 15 3281.2808 7829 3 2 8 4 .6 4 0 7 7205 3 2 7 7 .8 7 3 7 7520 3281.3766 7830 3 2 8 4 .6 6 2 5 7210 3 2 7 7 .9 2 8 0 7530 3 2 8 1 .4 0 9 8 7835 3 2 8 4 .7 0 7 0 7215 327 7 .9 5 2 6 7535 3281.4533 7840 328 4 .7 5 3 9 7220 3 2 7 7 .9 8 7 0 7540 3281 .5 0 7 5 7842 3284.8129 72S0 3278.1153 7545 3281.5569 7843 3284.9041 7240 3278.1838 7550 3281.6353 7850 3284.9381 7250 3 278.2365 7560 32 8 1 .6 6 1 7 7860 3 2 8 5 .0 0 7 3 7260 3 270.2599 7568 3281.8646 7868 3 2 8 5 .0 5 2 8 7270 3 2 7 8 .3 5 5 0 7570 3 2 8 1.89 16 7870 3285.0692 7280 3 2 7 8 .3 8 7 0 7574 3281.9249 7880 3285.1744 7290 3 2 7 8 .4 7 4 2 7560 3 2 8 1 .9 9 7 8 7890 328 5 .2 7 4 6 7292 3 2 7 8 .5 0 1 0 7590 3282.0711 7899 3285.3492 7294 3 2 7 8 .6 4 8 3 7593 3282.1144 7900 328 5 .3 8 0 6 7296 3 2 7 8 .6 9 0 2 7596 3282.2099 7910 3265.4073 7299 3278.8125 7600 3282.3115 7920 3285.4312 7300 3278.8493 7610 3282 .3 9 6 9 7930 328 5 .5 0 3 6 7301 3 2 7 3 .9 0 2 0 76 15 3282.5319 7940 3285.5211 7310 3 278.9229 76 17 3282.6492 7943 3285.5500 7314 3 2 7 8 .9 7 2 8 7620 3 2 8 2 .6 9 9 2 7944 3 2 8 5 .5 9 3 0 7320 3 2 7 9 .1 0 1 4 7630 3282.7500 7945 328 5 .6 2 9 6 7330 3279.1606 7635 3282.8131 7948 3 2 8 5 .6 8 0 4 7340 3 2 7 9 .1 9 2 3 7640 3282 .9 3 8 5 7950 3 2 8 5 .7 3 2 8 7350 3279.2811 7650 3282.9901 7960 3265.8019 7352 3279.3400 7660 3283.0576 7970 32 8 5 .8 4 1 4 7355 3279.39 11 7666 3283 .0 9 5 6 7980 3285.8943 7360 3279.5060 7668 3233.1451 7984 3 2 8 5 .9 3 7 8 7370 3279.5491 7670 3 2 8 3 .1 7 0 8 7985 3285 .9 6 7 5 7380 3279.5831 7680 3283.2662 7988 3 2 8 5 .9 7 8 8 7390 3 2 7 9 .6 3 6 4 7690 3283.3664 7990 3286.0069 7400 32 7 9 .7 8 4 0 7695 3283.4051 8000 3286.0731 7405 32 7 9 .8 2 4 0 7700 3 283.4496 8010 3286 .1 7 9 9 7410 3279.9041 7710 3283.4882 8020 3286.2628 7415 3279.9696 7720 3233.5451 8030 3286.3200 7420 323 0 .0 7 6 6 7730 3283.5764 8040 3 2 8 6 .3 6 8 8 307 APPENDIX B (CONTINTJED) SERIAL WAVE SERIAL WAVE SERIA.L WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 8050 3 2 8 6 .3 9 1 8 8241 3 2 8 9 .7 2 6 3 8475 3 2 9 2 .8 5 7 0 8060 3 2 8 6 .4 2 2 6 8243 3 2 8 9 .8 0 5 9 8480 3 2 9 2 .9 2 0 8 8070 3 2 8 6 .4 7 4 2 8244 3 2 8 9 .8 9 2 0 8432 3 2 9 2 .9 5 8 8 8075 3 2 8 6 .5 0 1 4 8247 3 2 9 0 .0 5 3 2 8484 3293.©244 8080 3236.5851 8250 3 2 9 0 .1 3 3 9 8486 3 2 9 3 .0 9 2 8 8082 3 2 8 6 .6 1 9 2 8260 3 2 9 0 .1 8 5 5 8490 3 2 9 3 .1 3 7 0 8 0 3 8 3 2 8 6 .6 8 3 6 8268 3 290.1981 8500 3 2 9 3 .2 6 8 9 8090 3286.7291 8270 3290.2699 8520 3 2 9 3 .3 7 4 9 8093 3 2 8 6 .7 8 3 2 8272 3290.3049 8530 3 2 9 3 .4 2 6 2 8097 3206.8661 8271 3290.3656 8540 3 2 9 3 .5 0 8 2 8100 3 2 8 6 .9 2 9 0 8279 3 2 9 0 .4 2 8 2 8550 3 2 9 3 .5 4 4 5 8110 3286.9741 8280 3 2 9 0 .4 5 8 4 855 1 3 2 9 3 .5 7 4 6 81 12 3 2 8 7 .0 0 3 7 8282 3290.4690 8555 3 2 9 3 .6 4 8 3 8114 3 237,0779 3290 3 2 9 0 .5 0 5 4 8556 3 2 9 3 .6 7 1 2 81 16 3237.1731 8300 3290.5493 8560 3 2 9 3 .8 0 3 5 8120 3 2 3 7 .2 6 6 4 8301 329 0 .5 7 9 5 8562 3 2 9 3 .8 8 7 5 8122 3 2 8 7 .3 1 9 0 8304 3 2 9 0 .6 0 6 6 8564 3 293 .9 6 4 1 812S 3 2 8 7 .3 4 7 2 8305 3 2 9 0 .6 3 4 5 8565 3 2 9 4 .0 0 7 3 8130 3 2 3 7 .3 8 9 7 8310 3290.7086 8567 3 2 9 4 .0 5 3 7 8132 3 2 3 7 .5 0 7 4 8320 3 2 9 0 .8 2 3 9 8570 3294.1302 8133 3 2 0 7 .5 5 4 2 8322 3290.8737 8580 3 2 9 4 .2 0 6 3 8134 3 2 3 7 .6 1 0 7 8328 3290.9560 8590 3 2 9 4 .2 7 6 3 8136 3 2 0 7 .6 8 9 G 8329 3290.9857 8592 3 2 9 4 .3 8 4 4 8140 3 2 3 7 .7 6 0 2 8350 3 2 9 1 .0 1 6 9 8594 3 2 9 4 .4 3 4 4 8142 323 7 .8 0 0 7 8340 3 2 9 1 .0 6 0 3 8596 3 2 9 4 .6 5 5 3 8143 3207.8699 83o0 3291.© 865 8597 3 2 9 4 .6 9 5 6 8144 3 2 8 7 .8 9 6 0 8355 329 1.16 18 8600 3 2 9 4 .7 7 5 7 8143 3 2 3 7 .9 6 6 0 8360 3291 .2 3 2 6 86 10 3 2 9 4 .8 2 9 4 8150 3 2 8 8 .0 1 0 7 836 1 329 1.2610 8612 3294.8591 8160 3 2 3 3 .2 0 6 0 8368 3291.2945 8620 3 2 9 4 .9 6 0 0 8166 3230.2659 8370 329 1.3512 8630 3 2 9 5 .0 5 3 4 8170 3233.2935 83S0 329 1.4277 8640 3 2 9 5 .0 8 0 0 8173 3253.3599 83 S3 329 1.5632 8649 3295.1809 8174 3238 .4 1 8 5 8390 3 2 9 1 .5 9 5 7 8650 3 2 9 5 .2 0 7 5 8175 3233.4o64 84G0 3 2 9 1 .7 3 9 0 8655 3 2 9 5 .3 5 5 6 8180 3288.5022 8410 3 2 9 1 .8 0 2 7 8656 3 2 9 5 .3 9 7 8 8190 3233.5512 8415 329 1.9 185 8660 3 2 9 5 .4 4 4 3 8190 3283.7136 8420 329 1.9885 * 8670 3 2 9 5 .5 1 0 0 8200 3288.7550 8422 3292.0623 8672 3 2 9 5 .5 5 3 2 8208 3288.B723 8423 3292.0972 8678 3295.6371 8210 32S3.9161 8424 3 2 9 2 .1 8 3 4 8680 3 2 9 5 .6 8 0 3 8212 3233.9618 8426 3 2 9 2 .3 0 3 8 8690 3 295.7641 8213 3 2 3 9 .048o 8427 3 2 9 2 .3 6 9 3 8700 3295.8462 8215 3239.1873 8428 3292 .4 0 3 9 8701 3 2 9 5 .8 7 3 6 8217 3239.3028 8430 3 2 9 2 .4 9 6 0 8710 3 2 9 5 .9 1 9 5 8218 3289.3323 8440 3 2 9 2 .5 166 8715 3 2 9 5 .9 8 7 8 8220 3289.3989 8446 3 2 9 2 .5 7 9 5 8720 3 2 9 6 .0 2 9 0 8230 3239.5037 8448 3292.5956 8728 3296.1170 8232 3239.5304 8450 3 2 9 2 .6 5 6 3 8730 3296.1747 8234 3 2 3 9 .5 7 5 3 8460 3 2 9 2 .7 1 0 6 8 7 3 2 3 2 9 6 .2 1 3 9 8236 3 2 3 9 .6 152 8468 3292.7575 8734 3 2 9 6 .2 7 6 5 8240 3239.6935 8470 3292.8065 8738 3 2 9 6 .4 3 2 3 308 APPENDIX B (CONTINUED) :r i a l NAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER ------IMBER ------ 8740 3 2 9 6 .4 8 1 9 9165 3 3 0 0 .1 3 7 6 9463 3 3 0 3 .8 0 4 4 8750 3 296 .5 4 7 6 9169 3 3 0 0 .2 2 3 4 9470 3303.9331 875 1 3296 .5 7 3 5 9170 3 3 0 0 .2 5 8 4 9472 3 3 0 3 .9 7 1 6 8755 3 2 9 6 .6 5 9 2 9 ISC 3 3 0 0 .3 0 7 4 9480 3304.0481 8760 3 2 9 6 .8 0 8 3 9185 3 3 0 0 .3 3 8 8 9490 3304.1621 8770 3 2 9 6 .8 7 2 5 9190 3 3 0 0 .4 2 3 2 9491 3 3 0 4 .2 2 9 6 8775 3296 .9 2 9 9 9191 3 300.4601 9492 3 3 0 4 .2 9 5 9 8780 3 2 9 6 .9 9 6 2 9200 3 3 0 0 .4 8 5 7 9500 3304 .3 6 3 6 8785 3297 .0 3 1 9 9210 3 300.5731 9508 3 3 0 4 .5 3 6 8 8790 3297.0781 9215 3 3 0 0 .6 0 6 0 9510 3 3 0 4 .6 0 7 4 8800 3 2 9 7 .1 4 3 7 9220 3 3 0 0 .7 0 1 2 9520 3304 .6 7 3 9 8810 3 297.1799 9225 3 3 0 0 .8 8 9 8 9521 3 3 0 4 .6 9 5 8 8820 3297.2886 9230 33 0 1 .0 0 3 6 9526 3 3 0 4 .7 5 0 6 8830 3 2 9 7 .3 5 8 7 9240 3 3 0 1 .0 6 12 9530 3 3 0 4 .7 9 7 4 8840 3 2 9 7 .4 5 0 8 9245 3 3 0 1 .0 8 6 3 9535 3 3 0 4 .8 5 7 4 8850 3 2 9 7 .5 0 5 8 9250 3 3 0 1 .1 2 0 8 9540 3304.9691 8860 3 2 9 7 .6 5 0 4 9260 3 3 0 1 .3 2 1 9 9550 33 0 5 .0 2 2 0 8870 3 297.7426 9261 3 3 0 1 .3 5 8 8 9552 33 0 5 .0 7 4 2 8872 3 2 9 7 .7 8 9 8 9270 3 3 0 1 .4 2 8 3 9560 3305 .1 8 7 5 8879 3297.9311 9275 3 3 0 1 .4 7 0 5 9570 3305 .4 7 4 5 8830 3 2 9 7 .9 7 7 2 9280 3 3 0 1 .5 1 4 5 9580 33 0 5 .5 3 9 2 8S90 3 2 9 8 .0 5 5 8 92B5 3301 .6068 9590 3 3 0 5 .5 9 5 7 9000 329 8 .0 3 3 6 9290 3 3 0 1 .6 5 8 5 9600 3 3 0 5 .6 5 3 9 9010 3298.1416 9300 3 3 0 1 .7 3 0 8 9602 3 3 0 5 .6 9 0 0 9020 329 8 .1 9 8 9 9310 3 3 0 1 .7 5 4 5 9610 3 3 0 5 .7 7 3 0 9022 32 9 8 .2 5 2 3 9320 3301.8481 9620 3305.8201 9030 3 2 9 8 .3 8 8 4 9330 3 3 0 1 .8 8 9 2 9630 3305.8471 9040 3 2 9 8 .4 3 9 7 9335 3 3 0 1 .9 8 1 4 9632 330 5 .8 9 5 9 9042 3 2 9 8 .5 8 2 0 9340 3 3 0 2 .0 4 5 3 9634 3 3 0 5 .9 6 6 2 9043 3 2 9 8 .6 8 9 0 9350 3302.1661 9635 3 3 0 5 .9 9 9 7 9045 3298.7503 9355 3 3 0 2 .2 0 5 3 9640 3306.1131 9049 3 2 9 8 .8 0 3 0 9359 33 0 2 .3 0 3 3 9642 3 3 0 6 .1 4 0 0 9050 3298.8276 9360 3 3 0 2 .3 2 4 4 9650 3 3 0 6 .1 9 5 8 905 1 3 2 9 8 .8 5 7 7 9370 3 3 0 2 .4 5 3 4 9655 3306.2701 9053 3293.9261 9380 33 0 2 .5 3 4 4 9660 330 6 .3 3 1 9 9054 3298 .9 9 8 0 9390 3 3 0 2 .5 8 9 7 9670 3306.3885 9055 3 2 9 9 .0 7 3 2 9400 3 3 0 2 .7 0 3 9 9680 3 3 0 6 .4 7 8 3 9060 3 2 9 9 .1 6 7 8 9401 3 3 0 2 .7 6 0 2 9690 3 3 0 6 .5 4 6 2 9070 3299.2166 9403 3 3 0 2 .7 8 5 5 9700 3 3 0 6 .6 9 9 7 9080 3299.2609 9405 3 302.8591 9705 3 3 0 6 .8 3 7 7 9090 3299 .3 4 0 0 9410 3 3 0 2 .9 5 1 0 9710 3 3 0 6 .8 7 7 8 9100 3 2 9 9 .3 7 5 2 9412 3 3 0 2 .9 8 3 9 9715 3 3 0 6 .9 9 4 4 91 10 3299 .4 5 6 5 9414 3 3 0 3 .0 5 7 9 9720 3307.0431 9120 32 9 9 .5 2 1 2 9418 3 3 0 3 .2 4 7 7 9730 3 3 0 7 .0 3 7 8 9130 3299.5509 9420 3 3 0 3 .2 9 9 9 9740 3307 .1 6 9 9 9140 3299.6291 9430 3 3 0 3 .3 4 9 5 9750 3 3 0 7 .2 2 3 6 9141 3299.6745 9431 3 3 0 3 .3 9 2 8 9760 3307 .3 2 0 6 9142 3 2 9 9 .7 1 7 8 9433 330 3 .4 2 7 1 9761 3307 .3 7 8 5 9143 3299.7794 9440 3 3 0 3 .5 1 1 2 9762 3307 .4 1 3 6 9143 3299.8940 9450 3 3 0 3 .6 2 8 4 9764 3 3 0 7 .5 8 7 7 9150 3 2 9 9 .9 5 6 0 9460 3 3 0 3 .6 9 0 2 9768 3307.6991 9160 3300.0375 946 1 3 303.7131 9770 3307.7661 309 APPENDIX B (CONTINUED) 'ERIAL WAVE SERIAL WAVE SERIAL WAVE [UMBER NUMBER NUMBER NUMBER NUMBER NUMBER 9780 3 3 0 7 .8 3 0 9 10075 3 3 1 1 .4 7 0 8 10443 331 4 .9 1 7 5 9781 3 3 0 7 .9 1 1 4 10080 3311.5091 10442 3 3 1 5 .0 2 1 7 9782 3 3 0 7 .9 2 7 4 10090 3311.5591 10446 3 3 1 5 .0 3 6 3 9790 3 3 0 7 .9 9 2 0 10100 331 1 .6393 10450 3 3 1 5 .1 4 4 7 9792 3 3 0 3 .1 1 1 0 10110 3 3 1 1 .7 1 1 6 10460 3 3 1 5 .1 7 7 0 9794 3 3 0 8 .1 7 9 2 10120 331 1.7742 10470 3 3 1 5 .2 7 1 3 980G 3 3 0 8 .2 8 7 1 10130 33 1 1 .8 3 1 3 10480 3 3 1 5 .3 6 3 8 9810 3 3 0 8 .3 1 5 8 10140 3 3 1 1 .8 9 6 8 10481 3 3 1 5 .4 1 3 2 9815 3 3 0 8 .3 5 6 4 10150 3311.9871 10482 3 3 1 5 .5 7 1 7 9820 3 3 0 8 .4 4 9 4 10160 3312.0491 10490 3 3 1 5 .6 2 3 7 9822 3 3 0 3 .4 9 4 7 1016 1 3 3 1 2 .0 9 5 4 10492 331 5 .6 7 8 9 9824 3 3 0 3 .5 3 1 2 10170 3 3 1 2 .1 7 8 4 10493 3 3 1 5 .7 1 0 2 9830 3 3 0 8 .6 1 6 5 10180 3 3 1 2 .2 3 3 8 10500 3 3 1 5 .8 0 4 2 9840 3 3 0 8 .6 9 5 5 10190 3 3 1 2 .2 7 2 2 10505 3 3 1 5 .8 5 5 3 9850 3 3 0 3 .7 2 5 8 10200 3312 .3 1 3 7 10510 3 3 1 5 .8 8 0 2 9860 330 3 .7 7 8 6 10210 331 2 .3 8 7 6 10520 3 3 1 5 .9 1 5 2 9870 330 8 .8 3 7 9 10215 3 3 1 2 .4 5 7 8 10530 3 3 1 6 .0 0 2 3 9872 33C3.B730 10220 33 1 2 .4 9 1 2 10532 331 6 .0 2 8 9 9876 3 3 0 8 .9 4 1 7 10230 3 3 1 2 .6 0 3 7 10540 3 3 1 6 .1 5 1 2 9830 3309.0080 10231 331 2 .6 4 0 9 10541 331 6 .2 0 4 5 9890 3 3 0 9 .0 8 8 5 10232 3 3 1 2 .7 0 5 0 10542 3316.2401 9900 3 3 0 9 .1 4 3 3 10234 3 3 1 2 .7 6 16 10543 3 3 1 6 .3 9 7 8 99 10 3 3 0 9 .2 4 2 4 10236 3 312.8479 10550 331 6 .4 3 7 5 9920 3 3 0 9 .2 7 4 2 10240 3 3 1 2 .9 2 5 1 10560 3316.5301 9921 3 3 0 9 .326S 10242 3 3 1 2 .9 5 9 3 10561 3 3 1 6 .5 5 1 9 9930 3 3 0 9 .3 7 3 3 10250 3 313.0399 10570 3 3 1 6 .5 8 2 4 993 1 3 3 0 9 .4 2 1 3 10260 3 313.0629 10580 331 6 .6 5 7 5 9940 3 309.4721 10270 3 3 1 3 .1 2 2 7 10581 3 316.7045 9950 3 3 0 9 .6 1 6 2 10230 3 3 1 3 .1 9 17 10582 3316.7821 9954 3 3 0 9 .7 2 5 8 10290 3 313.2595 10583 3 3 1 6 .8 0 9 3 9956 3 3 0 9 .8 5 9 0 10295 3 3 1 3 .2 9 8 0 10590 3 3 1 6 .8 6 5 7 9960 3 3 0 9 .9 0 2 0 10300 3 3 1 3 .3 5 4 2 10595 3 3 1 6 .9 1 1 2 9970 33C 9.9734 10310 3 313.4155 10591 3 3 1 7 .0 0 5 3 9980 3 3 1 0 .0 5 9 9 1031 1 3313 .5 1 2 5 10592 3 3 1 7 .0 6 8 3 9990 3 3 1 0 .1 1 5 7 10320 3313.5851 10593 3 3 1 7 .1 7 2 8 10000 3310 .1 6 1 5 10330 3 3 1 3 .6 4 8 0 10594 3317.2361 1000 I 3310 .2 2 7 1 10340 3 3 1 3 .7 1 7 3 10600 3 3 1 7 .3 0 9 7 10004 3 3 1 0 .2 7 6 9 10341 3313 .7 8 5 5 106 10 331 7 .3 5 0 6 10006 3 3 1 0 .3 4 7 0 10350 3 313.8425 10620 3 3 1 7 .4 6 2 9 10010 3 3 1 0 .4 5 4 8 10360 3 3 1 3 .9 3 7 2 10625 3 3 1 7 .5 3 5 4 10G20 3 3 1 0 .5 3 2 4 10370 3 3 1 4 .0 1 7 8 10630 3 3 1 7 .5 9 1 2 10025 3 3 1 0 .5 9 3 6 10380 3 3 1 4 .0 8 5 0 10631 3 3 1 7 .6 3 0 8 10030 3 3 1 0 .6 9 5 2 10390 3 3 1 4 .1 7 2 2 10632 331 7 .7 2 8 5 10031 3 3 1 0 .7 3 4 7 10400 3 314.2745 10640 3 3 1 7 .8 1 6 6 10040 3 310.8731 10405 3 3 1 4 .3 0 2 8 10650 3317.8841 10050 3 3 1 0 .9 8 3 9 10410 3 3 1 4 .3 5 9 7 10654 3 3 1 7 .9 3 4 9 10060 331 1.0731 10420 3 3 1 4 .4 5 7 3 10660 3318.0251 10062 331 1 . 1625 10425 3 3 1 4 .5 1 3 0 10670 3318.1049 10063 3 3 1 1 .1 9 0 7 10430 3 3 1 4 .6 2 4 2 10671 3318.1384 10064 3 3 1 1 .2 4 7 2 10432 3 3 1 4 .6 5 9 8 10680 331 8 .2 0 7 5 10068 3 3 1 1 .3 4 9 0 10440 3 3 1 4 .7 4 3 8 10681 331 8 .2 2 8 9 10070 3 3 1 1 .3 9 9 6 10441 3314 .8 6 0 9 10690 3318.3561 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 10691 3 3 I B . 4192 10920 3 3 2 2 .3 7 4 5 11162 3 3 2 6 .2 4 1 0 10692 3318.4921 10930 3322.4334 11170 3 3 2 6 .3 3 9 5 10694 3318.5331 10940 3 3 2 2 .5 2 6 4 1 1 180 3 3 2 6 .4 0 7 6 10693 3 3 1 8 .5 8 3 2 10950 3 3 2 2 .6 3 4 7 1 1 181 3 3 2 6 .4 3 7 6 10700 3 3 1 8 .6 9 9 2 10^60 3 322 .7 3 1 6 1 1 187 3 3 2 6 .4 5 9 3 10701 3 31 8 .8 2 9 9 1096 1 3 3 2 2 .8 3 6 7 1 1 182 3 3 2 6 .5 4 2 8 10702 3318.8991 10970 3 3 2 2 .8 8 9 6 11 183 3 3 2 6 .6 3 9 6 10710 3 3 1 8 .9 8 0 0 10980 3 3 2 3 .0 0 3 0 1 1 190 3 3 2 6 .7 1 8 8 1071 1 3319.0806 10981 3323. 1063 11200 3 3 2 6 .8 1 5 9 10712 3 3 1 9 .1 2 7 4 10990 3 3 2 3 .1 6 3 4 11210 3 3 2 6 .9 0 1 2 10713 3 3 1 9 .2 6 5 7 11060 3 3 2 3 .1 9 4 4 1 121 1 3 3 2 6 .9 7 2 8 10714 3 3 1 9 .2 8 1 6 1 1001 3 3 2 3 .2 5 0 0 1 1217 3 3 2 7 .0 1 4 5 10715 3 3 1 9 .3 5 3 5 11003 3 323.3181 1 1220 3 3 2 7 .0 5 6 9 10720 3 3 1 9 .4 2 4 4 11004 3 3 2 3 .3 4 2 0 1 1221 3 3 2 7 .1 2 5 3 10725 33 19.4756 11002 3 3 2 3 .5 1 1 7 11222 3 327.1841 10730 3319.5445 11007 3 3 2 3 .5 5 3 3 11223 3 3 2 7 .2 4 4 3 10740 3319.5687 1 1010 3 3 2 3 .6 2 3 9 1 1230 3 3 2 7 .2 9 1 6 10750 3 3 1 9 .644S 1 1020 3323 .6 6 3 9 11240 3 3 2 7 .3 4 6 2 10760 3319.7049 11024 3 3 2 3 .7 0 4 2 11242 3 3 2 7 .4 2 6 6 10770 3 3 1 9 .8 1 4 3 1 1021 3 3 2 3 .7 8 3 2 11243 3 3 2 7 .5 1 0 5 10771 3319.9991 11022 3 3 2 3 .6 7 0 6 1 1250 3 3 2 7 .5 8 3 9 10780 3320.1341 11030 3 3 2 3 .8 9 9 6 11260 3 3 2 7 .6 5 9 9 10781 3 3 2 0 .1 9 9 7 1 1040 3 3 2 3 .9 7 8 7 1 1270 3 3 2 7 .7 7 3 8 10790 3 320.2776 1 1042 3 3 2 4 .0 1 2 8 1 1277 3 327.8561 10S00 3320.3189 1 1046 3324 .1 4 8 6 1 1271 3 3 2 7 .9 2 8 8 10S02 3 3 2 0 .3 6 1 5 1 1050 3 3 2 4 .2 2 3 0 1 1272 3327.9781 10SO1 3 32 0 .4 1 9 6 11054 3 3 2 4 .2 6 8 0 11273 3 3 2 8 .0 6 0 8 10810 3320.5492 11055 3 3 2 4 .3 3 0 4 11274 3 3 2 8 .1 3 0 7 1031 1 3 3 2 0 .6 0 4 3 1 1051 3 3 2 4 .3 6 6 1 1 1280 3 3 2 8 .1 9 8 0 10312 3 3 2 0 .7 1 7 3 11052 3 3 2 4 .5 0 4 5 1 1290 3 3 2 8 .2 5 8 4 10320 3 3 2 0 .7 9 9 3 11060 3 3 2 4 .5 4 2 0 11291 3 3 2 8 .2 9 2 4 10321 3320.B534 11070 3324.5981 11292 3328 .3 9 9 5 1CS30 3 3 2 0 .9 5 13 11080 3 3 2 4 .7 1 8 7 11293 3328.4331 10840 3320.99 17 11081 3 3 2 4 .8 2 6 8 1 1296 3 328 .5 1 7 6 1C 3o0 3321.0773 1 1090 3324.9001 11300 3 3 2 8 .5 7 9 9 10S51 3321. 11 16 1 1 100 3 3 2 4 .9 6 2 3 11302 3 3 2 8 .7 7 2 6 10353 3 321.1646 11101 3 3 2 5 .1 2 2 9 11310 3 3 2 3 .8 4 1 6 10S5S 3321.2429 1 1 102 332 5 .1 7 0 5 11312 3 3 2 8 .8 7 9 0 10860 3321.2864 11110 3 3 2 5 .2 4 1 5 1 1318 3 3 2 8 .9 5 5 5 10S64 3321.3484 1 11 1 1 3 3 2 5 .2 9 1 2 11320 3 3 2 9 .0 1 9 2 10867 3321.4403 11112 3 3 2 5 .3 3 8 7 1 1330 3 329.0731 10870 3 3 2 1 .4 8 9 2 1 1120 3 3 2 5 .4 3 1 8 1 1332 3 3 2 9 .1 1 3 7 10830 3321.5297 1 1126 3 3 2 5 .6 2 2 2 11340 3329.2041 10832 3321.5622 1 1128 3 3 2 5 .6 6 1 7 11344 3 3 2 9 .2 5 8 6 10831 3 3 2 1 .6 4 1 7 1 1 130 3 3 2 5 .7 0 6 8 1 1350 3329.3341 10890 3321.7300 11131 3 3 2 5 .7 6 6 9 11357 3 329.4101 10900 3 3 2 1 .8 1 9 3 1 1 132 332 5 .8 3 9 9 11360 3 3 2 9 .4 5 0 4 10902 3 3 2 1 .8 4 9 0 1 1 133 3 3 2 5 .9 3 3 4 11362 3 3 2 9 .4 9 2 7 10901 3 3 2 1 .8 9 5 4 1 1134 3 3 2 6 .0 0 4 2 1 1361 3 3 2 9 .5 4 1 2 10910 3 3 2 2 .0 2 3 8 11 140 3326.0571 1 1370 3329.6411 10911 3322.0660 1 1150 3 3 2 6 .1 2 4 2 1 1375 3329.7194 109 12 3322.295S 11160 3 3 2 6 .2 2 6 8 1 1380 3 3 2 9 .8 3 6 1 311 APPENDIX B (CONTINUED) .RIAL WAVE SERIAL WAVE s e r i a l ' WAVE fMBER NUMBER NUMBER NUMBER NUMBER NUMBER 1390 3 3 2 9 .8 7 SB 11560 3 3 3 4 .2 9 4 7 1 1758 3 3 3 8 .5 6 1 0 139 1 3 329.9431 1156 1 3 334.3249 11760 3 3 3 8 .6 7 8 0 1392 3 3 3 0 .0 6 2 5 1 1567 3334.3725 11770 3 3 3 8 .7 1 2 6 1S93 3 3 3 0 .1 2 0 3 11562 3 3 3 4 .4 0 3 7 1 1 7 8 0 3 3 3 8 .7 3 9 8 1394 3 3 3 0 .1 Boo 11570 3334.5486 11781 3 3 3 8 .7 7 9 0 1395 3330.2771 1 1580 3 3 3 4 .5 8 1 8 11782 3 3 3 8 .8 3 2 5 1400 3 3 3 0 .3 3 0 ! 1 1590 3 3 3 4 .6 2 3 8 11783 3 3 3 8 .9 1 8 3 1410 3 3 3 0 .3 8 0 2 11592 3334.8066 11786 3 3 3 9 .1 0 3 6 1415 3 3 3 0 .5 7 7 3 1 1593 3334.8477 11787 3 3 3 9 .1 3 4 7 1420 3 3 3 0 .7 3 7 6 1 1594 3 3 3 4 .9 0 4 8 11788 3 3 3 9 .2 0 3 3 1423 3330.8001 1 1600 3 3 3 5 .0 1 8 0 11790 3 3 3 9 .2 4 1 2 1430 3 33 0 .8 1 6 9 11602 3335.0645 11792 3 3 3 9 .3 3 3 7 143 1 3 3 3 0 .8 7 4 5 1 16 10 3335. 1264- 11793 3 3 3 9 .4 4 1 6 1440 3 3 3 0 .9 4 7 2 1 16 1 1 3335.2041 1 1795 3 3 3 9 .5 0 6 7 1441 3 3 3 0 .9 7 9 0 1 16 12 3335.3006 11797 3 3 3 9 .6 3 0 9 1448 3 3 3 1 .0 5 4 2 1 1620 3 335.3784 11800 3339 .7 3 8 1 1450 3 3 3 1 .1 1 1 2 1 1630 3335.4981 1 1805 3 3 3 9 .8 2 6 6 1460 3 3 3 1 .2 0 9 0 1 1640 3335.5519 11807 3 3 3 9 .8 7 9 3 1470 3331 .3 3 7 9 1 1650 3 3 3 5 .6 138 11810 3 3 3 9 .9 5 8 0 1471 3331 .414-8 1 165 1 3335.6475 1 1812 3 3 4 0 .0 2 9 2 1472 3 3 3 1 .4 6 7 7 1 1653 333 5 .7 1 0 4 11815 3340 .2 4 0 1 1473 3 3 3 1 .5 2 6 3 11655 3335.8256 1 1816 3 3 4 0 .2 9 4 0 1474 3 3 3 1 .6 0 7 3 1 1660 3335.9430 11820 3 3 4 0 .4 0 3 6 1475' 3 331.6385 1 1662 3336.0205 11822 3 3 4 0 .4 3 1 7 1477 3331.7343 I 1663 3336.0985 1 1823 3 3 4 0 .4 9 6 8 14oO 3331 .8834 1 1665 3 33 6 .3 3 9 3 1 1824 3 3 4 0 .5 5 7 9 1481 333 1 .9277 1 1666 3 33 6 .4 0 0 2 11830 334-0.7696 1435 3 332.0101 1 1668 3336.4536 1 1831 3 3 4 0 .7 9 3 7 1490 3 3 3 2 .091B 11670 3 336.4886 11840 3 3 4 0 .8 5 12 149 1 3 332 .2 2 6 9 11675 3336.5651 1 1842 3 3 4 0 .9 0 1 5 1492 3 332 .3 3 7 5 11680 3336.6366 1 1844 3 3 4 0 .9 9 6 9 1493 3 332.3796 11681 333 6 .6 6 4 4 11846 3 3 4 1 .0 6 6 1 n n n o / < ~ 1 Q 0 O u O a - . T f l ' O H - J 1 1690 3336.7181 1 1847 3341. 1043 1501 3 3 3 2 ,4 8 5 4 1 1696 3336.8008 11849 3341 .2196 1503 3 3 3 2 .5 8 1 7 1 1700 3336.8469 1 1850 3 3 4 1 .2 7 4 3 1507 3 3 3 2 .8 1 2 4 1 1710 3337.1386 11860 3 3 4 1 .3 3 0 3 1510 3332.8898 11720 3 33 7 .1 8 4 2 1 1862 3 3 4 1 .3 8 6 3 15 15 3 3 3 2 .9 7 5 0 1 1723 3 3 3 7 .3 6 2 7 11865 3 341 .5 5 0 1 1520 3333.0384 1 1725 3 3 3 7 .4 4 6 8 11867 3 3 4 1 .6 2 6 2 1522 3 3 3 3 .1 2 7 4 1 1 7 2 6 3 33 7 .4 9 4 3 11868 3 3 4 1 .6 7 0 9 1527 3333.2155 11728 3337.6131 1 1870 3 3 4 1 .8 0 3 2 1523 3 333 .2 3 9 9 1 1730 3 33 7 .6 6 18 11880 3 3 4 1 .9 4 7 1 1524 3333.3016 1 1740 3 33 7 .6 9 2 3 11881 334-1.9875 1530 3 3 3 3 .3 8 2 4 11742 3337.7599 1 1882 3 3 4 2 .1 0 3 6 1540 3 3 3 3 .4 5 4 3 1 1745 3 3 3 7 .8 8 6 8 1 1883 3 3 4 2 .1 8 1 9 1541 3333.5484- 1 1750 3 337.9617 11884 3 3 4 2 .2 2 6 9 1542 3 3 3 3 .5 8 9 4 11751 3337 .9 9 9 4 1 1885 3 3 4 2 .4 6 5 4 1543 3 3 3 3 .6 5 7 4 11752 3338.0352 11836 3 3 4 2 .5 0 7 9 1544 3333.7409 1 1754 3338.1177 1 1887 3342.6121 1550 3 3 3 3 .9 1 9 7 11755 3338.2926 1 1833 3 3 4 2 .7 0 7 1 1552 3 3 3 4 .0 4 1 3 1 1756 3338.4-548 11890 3 3 4 2 .8 0 8 7 IS" .TO A. \J v> W 3 3 3 4 .0 6 9 2 11757 3338.5153 1 1892 3 3 4 2 .8 3 9 0 312 APPENDIX B (CONTINUED) IERIAL WAVE SERIAL WAVE SERIAL WAVE NJMBER NUMBER NUMBER NUMBER NUMBER NUMBER ------■— 11900 3343.01 1 1 12102 3 3 4 8 .2 8 3 8 12256 3 3 5 4 .1 0 0 9 1190S 3 3 4 3 .2 2 0 5 12103 3 3 4 8 .4 4 2 7 12257 3354.1953 11910 3 3 4 3 .2 9 8 5 12108 3 3 4 8 .7 5 3 7 12258 3 3 5 4 .2 4 5 8 11920 3 3 4 3 .4 0 2 5 121 10 3 3 4 8 .8 3 7 0 12260 3 3 5 4 .3 0 5 5 11924 3 3 4 3 .5 7 2 6 12115 3 3 4 8 .9 4 1 9 12261 3 3 5 4 .3 5 5 7 1 1926 3 3 4 3 .6 3 3 5 12120 3 3 4 9 .0 7 1 6 12262 3 3 5 4 .5 2 2 9 11927 3 3 4 3 .7 0 2 6 12130 3 3 4 9 .2 7 0 2 12269 3 3 5 4 .5 8 5 5 1 1928 3 343 .7 5 6 1 12132 3 3 4 9 .3 1 7 5 12279 3 3 5 4 .6 4 9 8 1 1930 3343.8541 12140 3 3 4 9 .4 3 7 0 12277 3 3 5 4 .6 9 9 4 11940 3 343 .9 3 7 1 12150 3 3 4 9 .5 164 12263 3 3 5 4 .7 2 4 9 1 1950 3 3 4 4 .0 4 6 0 12152 3349.5629 12264 3 3 5 4 .8 2 1 2 1 1953 3 3 4 4 .1 2 4 6 12160 3 3 4 9 .8 0 5 2 12265 33 5 4 .8 9 9 7 1 1956 3 3 4 4 .3 2 5 6 12170 3 3 4 9 .9 1 5 2 12275 3 3 5 4 .9 8 9 3 1 195S 3 3 4 4 .4 0 8 9 12172 3 3 5 0 .0 0 6 9 12266 3355. 1179 1 1960 3 3 4 4 .5 0 4 3 12178 3 3 5 0 .1 8 1 2 12278 3 3 5 5 .1 5 3 9 1 1964 3 3 4 4 .6 8 6 5 12180 3 3 5 0 .2 5 0 0 12272 3 355.2061 11965 3344.7321 12181 3 350.3001 12273 3 3 5 5 .2 6 5 8 1 1970 3 3 4 4 .8 3 3 2 12182 3 3 5 0 .3 7 0 4 12274 3 3 5 5 .3 0 2 2 1 1975 3 3 4 4 .9 4 5 8 12183 3 3 5 0 .4 2 5 0 12267 3 3 5 5 .4 7 5 8 1 1930 3 3 4 5 .1 6 5 4 12168 3350.6411 12268 3 355.5891 1 19S2 3 3 4 5 .2 0 4 7 12189 3 3 5 0 .7 6 8 9 12270 3 3 5 5 .7 0 4 7 11990 3 3 4 5 .2 9 9 0 12190 3 35 0 .8 1 6 1 12271 3 3 5 5 .7 5 3 7 1 1992 334 5 .3 3 8 5 1219 1 3 3 5 0 .8 7 4 7 12280 3 3 5 5 .8 5 0 7 1 1995 3 3 4 5 .3 8 9 9 12193 3 3 5 0 .9 3 8 4 12290 3 3 5 5 .9 3 9 4 12000 33 4 d . 4544 12195 3 3 5 1 .0 6 9 3 1229 1 3 3 5 5 .9 9 1 0 12003 3 3 4 5 .5 2 4 0 12196 3351 . 1199 12295 3 3 5 6 .1 9 4 4 12004 3S4o . 58*73 12200 3 3 5 1 .2 4 0 6 12296 3 3 5 6 .2 4 7 9 12005 3 3 4 5 .6 1 1 6 12205 335 1 .2944 12300 3 3 5 6 .3 0 4 7 12007 3 3 4 5 .7 9 0 5 12210 3 3 5 1 .3 6 0 3 12301 3 3 5 6 .3 6 1 7 12010 334;} ■ 883o 1221 1 3351 .4 1 2 9 12305 3356 .6 4 6 6 12012 334 5 .9 2 9 9 122 12 3 3 5 1 .4 4 5 7 12306 3 3 5 6 .6 8 0 3 12017 3 3 4 6 .0 4 0 3 12213 3 3 5 1 .5 2 2 3 12307 3356.7681 12020 3 3 4 6 .1 2 8 8 12214 3 3 5 1 .5 5 9 2 12308 3356 .8 8 1 6 12023 3 3 4 6 .4 6 2 4 12217 335 1 .7513 12309 3 3 5 6 .9 7 9 0 12024 334 6 .4 9 3 5 12220 3 3 5 1 .9 1 3 9 12310 3 3 5 7 .0 3 4 7 12025 3 3 4 6 .5 9 14 12224 3 3 5 2 .0 1 9 4 12312 3 3 5 7 .0 9 5 3 12030 3 3 4 6 .7 9 4 8 12226 3 3 5 2 .2 1 4 3 12315 3 357.4255 12040 3 3 4 6 .8 4 4 0 12230 3 3 5 2 .2 8 7 4 12316 3 3 5 7 .4 9 8 2 12045 3 3 4 7 .0 5 2 8 12231 3352.3668 12320 3 3 5 7 .8 0 0 8 12047 3 3 4 7 .1 8 9 0 12235 3 3 5 2 .4 1 3 4 12321 3 3 5 7 .8 2 8 8 12050 3 34 7 .3 0 0 5 12232 3 3 5 2 .5 0 3 6 12322 3357 .8 5 3 6 12051 3 3 4 7 .4 4 3 4 12233 3 3 5 2 .6 7 7 4 12323 3 357 .9 3 0 5 12060 3 3 4 7 .4 9 2 0 12234 3 3 5 2 .7 7 6 9 12324 3 357 .9 6 0 6 12070 3 3 4 7 .5 7 4 8 12239 3 3 5 3 .0 1 1 9 12327 3 3 5 8 .0 1 8 0 12071 3 3 4 7 .6 0 1 2 12236 3 3 5 3 .1 8 3 6 12329 3358 .1 6 8 9 12074 3 3 4 7 .7 7 7 4 12237 3 3 5 3 .33S5 12330 3358.2412 120S0 3 3 4 7 .8 6 0 3 12238 3 3 5 3 .5 0 9 4 12340 3358 .2 8 6 9 12090 3 347.9031 12240 3 3 5 3 .6 5 3 0 12331 3358 .3 3 9 9 12092 334 7 .9 7 3 9 12248 3 3 5 3 .8 0 0 7 12341 3 3 5 3 .3 8 7 7 12093 3 3 4 8 .0 4 5 ° 12250 3 3 5 3 .8 8 9 3 12342 3 3 5 8 .5 139 12094 3348.1015 12252 3353 .9 5 2 6 12343 3 3 5 8 .5 5 9 4 12100 3 3 4 8 .1 9 6 8 12255 3354.0099 12344 3 3 5 8 .5 9 1 9 313 APPENDIX B (CONTINUED) SERIAL WAVESERIAL WAVE SERIAL WAVE IUMBERNUMBER NUMBER NUMBER NUMBER NUMBER 12334 3358.6381 12479 3 3 6 4 .4 7 4 0 12583 3 3 7 0 .0 2 5 0 12345 3 3 5 8 .9 3 8 6 12472 3 3 6 4 .5 4 7 2 12584 3 3 7 0 .1 2 1 7 12346 3359.0050 12473 3 3 6 4 .8 2 5 6 12586 3 3 7 0 .5 0 9 7 12347 3359.0632 12474 3 3 6 5 .0 2 0 0 12587 3 3 7 0 .5 6 2 7 12343 335 9 .3 5 8 1 12475 3365 .1 0 8 6 12590 3 370 .6 3 5 1 12349 3 3 5 9 .3 9 6 0 12476 3 365.1409 12599 3 3 7 0 .9 2 2 0 12350 335 9 .5 1 7 9 12477 3365.2171 12600 3370.9651 12356 335 9 .6 5 6 9 12465 3 3 6 5 .3 3 2 4 12609 3 3 7 0 .9 8 9 9 12360 3359.7281 12478 3365 .4 1 5 6 12601 3 3 7 1 .0 2 9 7 12365 3359.8127 12481 3365.6359 12603 3 3 7 1 .1 7 9 3 12370 3 359.8865 12483 3365.7046 12610 3 371.3901 12371 3359.9561 12480 3365.7360 12612 3 3 7 1 .4 4 6 0 12380 3360 .2 5 0 6 12482 3 365 .8 1 6 6 12620 337 1.6437 12381 3 3 6 0 .3 1 6 0 12486 3 365.8899 12623 3371 .8214 12382 3360.4510 12488 3365.9456 12625 3 3 7 1 .9 2 1 3 12383 3360.4878 12490 3366.0239 12623 3 3 7 2 .0 1 0 0 12384 3 360.5336 12491 3 3 6 6 .0 7 8 0 12630 3 372.0991 12385 3360.5933 12492 3 3 6 6 .1 1 9 0 12631 3 3 7 2 .1 4 9 2 12386 3360.8241 12495 3366.3241 12632 3 3 7 2 .3 0 3 5 12377 3360.9369 12493 3 3 6 6 .3 9 2 3 12633 3 3 7 2 .3 5 9 4 12387 3 3 6 1 .2 3 3 0 12494 3366.5287 12634 3 3 7 2 .3 9 2 4 12383 3361.2632 12496 3 3 6 6 .8 7 0 8 12640 3 3 7 2 .7 7 7 0 12389 3361.5905 12497 3 3 6 6 .9 2 4 8 12650 3372.8713 12S9G 3 3 6 1 .6 2 7 7 12501 3366.9994 12655 3 3 7 3 .2 1 9 2 12400 336 1 .6480 12502 3367.1741 12656 3 3 7 3 .2 8 0 3 12401 3361.6789 12500 3 3 6 7 .2 8 3 7 12660 3373.4796 12402 3361.7337 12510 3367.459 1 12662 3 3 7 3 .5 9 7 9 12404 330 1.8200 12520 3367.5149 12664 3 3 7 3 .7 3 5 2 124C5 3361 .9233 12530 3 3 6 7 .6 4 3 4 12666 3 3 7 4 .0 7 0 7 12407 3362.06 16 12532 3367.7194 12667 3 374.1351 12408 3362.1139 12533 3367.8098 12668 3 3 7 4 .2 1 9 4 12410 3362.1936 12534 3367.8501 12670 3374.4272 12420 3362.2824 12540 3367.9217 12680 3 3 7 4 .5 7 5 2 12422 3362.3276 12543 3367 .9 7 2 5 12681 3 3 7 4 .6 1 9 9 12423 3362.3720 1254 1 3368.0570 12683 3 3 7 4 .8 0 7 4 12428 3362.6914 12542 3368.2152 12687 3 3 7 4 .9 7 2 9 12429 3362.7338 12544 3368.3907 12688 3 3 7 4 .9 8 3 0 12427 3362.7760 12545 3368.5613 12690 3375.0940 1243C 3 3 6 2 .8 3 5 2 12547 3368.6530 12692 3 3 7 5 .2 1 0 5 12431 3 3 6 2 .8 7 5 4 12546 3 3 6 8 .7 0 5 4 12700 3 3 7 5 .3 0 0 3 12432 3362.9372 12550 3 3 6 8 .8 1 5 7 12701 3375.3569 12435 3363.1503 12d55 3 3 6 9 .0 0 9 8 12702 3375.4306 12437 3363.4319 12560 3369.1338 12703 3 3 7 5 .6 2 5 8 12440 3363.5361 12562 3 3 6 9 .3 0 0 4 12704 3375.8250 12442 3363.7238 12563 3369.3440 12705 3 3 7 5 .8 6 10 12443 3363.8576 12565 3369.5004 12706 3 3 7 6 .0 4 7 9 12446 3363.9465 12567 3369.6052 12708 3 3 7 6 .3 5 3 8 12450 3364.1259 12570 3 3 6 9 .6 6 1 3 12709 3376.7159 12455 3364.1731 12580 3369.7917 12710 3 3 7 6 .7 6 0 4 12460 3364.2424 125S9 3369.8105 1271 1 3 3 7 6 .7 9 7 0 12470 3364.3398 12581 3369.8869 12712 3 3 7 6 .8 4 9 5 12471 3364.3710 12582 3369.9729 12718 3 377.0261 APPENDIX B (CONTINUED) SERIAL WAVE SERIAL WAVE SERIAL WAVE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER 12720 3 3 7 7 .0 9 8 6 12859 3385.6118 13160 3406.0108 1 2 7 2 2 3 3 7 7 .1 6 5 7 12860 3385.7016 13170 3406.7730 12729 3 3 7 7 .2 7 2 2 12365 3385.7404 12730 3 3 7 7 .2 9 8 7 12870 3385.B291 12733 3 3 7 7 .4 9 2 2 12875 3385.9158 12734 3 3 7 7 .5 5 1 2 12880 3385.9843 12739 3 3 7 8 .0 7 0 0 12890 3386.1461 12740 3 3 7 8 .1 1 4 4 12893 3386.6503 12745 3 3 7 8 .4 4 0 9 12900 3387.5260 12748 3 3 7 8 .8 2 7 1 12910 3388.1227 12750 3 3 7 8 .8 7 7 5 12912 3388.3006 12754 3 378.9291 129 14 3 3 8 8 .5 1 0 8 12755 3 3 7 8 .9 5 7 4 12919 3389.1747 12760 3 3 7 9 .0 9 8 0 12920 3389.2053 12762 337 9 .1 3 3 4 12930 3390.2540 12764 3 3 7 9 .2 5 9 9 12940 3390.8757 12766 3 3 7 9 .3 3 3 2 12950 3391.5601 12770 3 3 7 9 .4 8 6 9 12960 3392.3713 12772 3 3 7 9 .85oo 12970 3392.4279 12773 3 3 3 0 .0 0 2 2 129S0 3392.5093 12774 333 0 .1 4 0 6 12935 3392.5668 12775 3 3 3 0 .2 1 8 5 12990 3392.7271 12777 3330.4628 13030 3392.9415 12779 3 3 3 0 .5 5 7 5 13005 3393.0091 12780 3 3 3 0 .6 4 2 0 13007 3393.1416 12783 3 3 8 0 .9 5 7 0 13010 3393.2507 12785 3 o o l . locvo 13018 3394.1420 12789 3 3 8 1 .3 7 5 7 13020 3394.4653 12783 3381.4037 13030 3395.6242 12790 3 3 8 1 .4 4 0 5 13032 3395.7557 1 2 7 9 1 3 3 3 1 .5 1 IS 13040 3396.5517 12795 3331 .5 8 1 1 13047 3397.1059 12800 3 3 8 1 .6 6 6 7 13050 3397.2150 12802 3 3 8 1 .8 3 1 0 13051 3397.2726 12803 3332.2533 13052 3397.3464 12809 3 3 3 2 .3 2 3 9 13060 3397.9971 12810 3 3 3 2 .3 8 6 4 13062 3398.0531 12812 3 322.4691 13070 3398.6204 12813 3332. 6 li0 2 13072 3398.9360 12817 3 3 8 2 .9 1 4 0 13077 3400.3890 12820 3 3 3 0 .0 6 5 0 13080 3400.6311 12821 3 3 3 3 .0 9 1 0 13090 3400.6853 12822 3 3 8 3 .2 8 9 0 13093 3400.7884 12S24 3333.4934 13095 3401.0505 12828 3383.7341 13097 3401.1061 12830 3333.7889 13100 3401.4982 12840 3 3 8 3 .8 3 3 3 13105 3402.0580 12S42 3383.9335 13110 3402.7243 12846 3 3 3 4 .1 1 8 3 13130 3403.5818 12850 3 3 8 4 .3S32 13140 3403.7119 12E52 3 3 8 4 .6 0 5 1 13145 3404.1456 12355 3 3 8 4 .9 7 8 7 13150 3404.7535 LIST OF REFERENCES Albritten, D.L. 1978, private 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