PRICE, Stephan Donald, 1941- QUANTITATIVE INTERPRETATION OF THE INFRARED SPECTRA OF LATE-TYPE STARS. The Ohio State University, Ph.D., 1970 Astronomy University Microfilms, A XEROX Company, Ann Arbor, Michigan QUANTITATIVE INTERPRETATION OF THE INFRARED SPECTRA OF LATE-TYPE STARS 01SSERTATION Presented in Partial F u lfillm e n t of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State U niversity By Stephan Donald Price, A.B., M.Sc. ***** The Ohio State University 1970 Approved by Department of Astronomy ACKNOWLEDGMENTS I would lik e to acknowledge Dr. Robert F. Wing for many valuable discussions and c ritic is m which were essen- tial in defining and detailing this thesis topic. I would also lik e to thank Dr. Russel G. Walker, whose encouragement and assistance made the completion of this thesis possible. i i VITA 3 August 1941 . Born — Trenton, New Jersey June, 1963 . ■ > A.B,, University of California, Los Angeles, Los Angeles, California April 1966 . M.Sc., The Ohio State University, Columbus, Ohio t il TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii VITA lii LIST OF TABLES v LIST OF FIGURES vi Chapter I. INTRODUCTION 1 I I . ANALYSIS AND STATEMENT OF THE PROBLEM 6 111. DETERMINATION OF MOLECULAR ABSORPTION COEFFICIENTS 13 IV. H20 27 V. CO VIBRATION-ROTATION BANDS 32 VI. THE CN RED SYSTEM, A2TTj-X2£ 35 V II. C2 BALL IK-RAMSAY AND PHILLIPS BANDS 1*8 V I I I . TIO AND VO 62 IX. SYNTHETIC SPECTRA AND MOLECULAR BLANKETING 68 X. CONCLUDING REMARKS 112 BIBLIOGRAPHY 118 APPENDIX A 126 B 136 iv LIST OF TABLES TABLE Page 1. Wavenumbers of Rjj and Rj ^ Bandheads hi 2. Partition Functions for and C^c'^ 53 3. Wavenumbers of the P h illip s R Bandheads and Bal1ik-Ramsay R^ ^ Bandheads 60 *♦. Parameters of the Representative Stars 66 5. Blanketing in Magnitudes Due to H^O for Various Values of the Equivalent Width of the 1.38 Micron Band 85 6. Blanketing in Magnitudes Due to CO for Various Values of the Equivalent Width of the F irst Overtone 89 7. Blanketing in Magnitudes Due to CN for Various Values of the Depressions in the (0,0) Band 93 8. Blanketing in Magnitudes Due to C 2 for Various Assumed Carbon Abundance Classes 97 9. CalculatedBlanketing in Magnitudes Due to CN and C2 in Carbon Stars 103 10. Colors and Spectral Types for Some Carbon Stars 105 11. Blanketing in the 1 and J Filters Due to TiO+VO 110 V LIST OF FIGURES FIGURE 1. Log of the Mass Absorption Coefficients for H20 at 1008 and 3360°K 2. Log of the Mass Absorption Coefficients for CO at 1008 and 3360°K 3. Log of the Mass Absorption Coefficients for C120 and C130 at 3360°K 4. Log of the Mass Absorption Coefficients for C12N at 1008 and 3360°K 5. Log of the Mass Absorption Coefficients for C12N and C13N at 3360°K 6. Log of the Mass Absorption Coefficients for c j2 at 1008 and 3360°K 7. Log of the Mass Absorption Coefficients for C]22 and C,2 C13 at 3360°K 8. Calculated Residual Intensities Due to TiO+VO at 1500 and 3000°K and the Normalized Spectral Response of the 1 F ilt e r 9. The Calculated Residual Intensities Due to C2, CN, CO and H^O Plus the Transmission of the tar Atmosphere and the Normalized Response of the Johnson F ilte rs 10. The Observed and Calculated Normalized Energy Distributions for «Tau 11. The Observed and Calculated Normalized Energy Distributions foro-Ori 79 12. The Observed and Calculated Normalized Energy Distributions for^uCep 80 13. The Observed and Calculated Normalized Energy Distributions for R Leo 81 14. The Observed and Calculated Normalized Energy Distributions for o Ceti 82 v ii CHAPTER I. INTRODUCTION Stars with surface temperatures lower than about ^000°K radiate more than h alf of their flu x in the infrared at wavelengths longer than one micron. Black-body or grey- body extrapolation of their infrared fluxes from visual observations was shown by Barnhart and Mitchell (1966) to lead to very large errors. Therefore, to assure the accuracy of any calculated quantity related to the flux, such as effective temperature or bolometric correction, measurements in the infrared for cool stars must be made. Since the classic radiometric s te lla r measurements of P e ttit and Nicholson (1928), equipment and observational techniques have improved considerably and now the litera­ ture abounds with infrared observations on stars of all spectral classes. With some notable exceptions, these observations are wide band pass photometry obtained from the ground. As our atmosphere is completely opaque to incoming radiation in certain spectral regions, the principal absorbers being water vapor, carbon dioxide and ozone, ground based photometric systems are confined to the relatively transparent atmospheric "windows" centered at 1.25, 1.65, 2.2, 3.8, 5.0, 10 and 20 microns. The most extensive system currently being used, both in terms of number of observations and number of colors employed, is the 10 color photometry defined by Johnson (1965), which I has five "visual" colors (0.36 to 0.9 microns) plus filters at 1.25, 2.2, 3.8, 5.0 and 10 microns. Barnhart and Mitchell (1966) give an excellent review of other Infrared photometric and radiometric systems in use prior to 1965. Johnson's system does not make use of the 1.65 micron window, though model atmosphere calculations by Gingerich and Kumar (1964) and Gingerich, Latham and Linsky (1967) predict a flux excess at 1.64 microns for cool stars due to a minimum in the H~ opacity. Walker (1966) employs a 7 color system (from 0.35 to 2.21 microns) which s p e c ific a lly does include a 1.63 micron f i l t e r to attempt to measure this flux excess. Bahng (1967* 1969 a,b) also measured stars in three colors, 1.21, 1.59 and 2.15 microns, through intermediate band pass filters in looking for the luminosity effe cts of the H“ opacity which the models p red ict. As his photometry covers the spectral regions in which most of the stellar radiation falls, Johnson (1964, 1966) has proposed a revision, based on his measurements, of the effective temperature scale originally set up by Kuiper (1938). After calibrating his photometry and approximating the stellar energy distribution in the unobserved and unobservable spectral regions, he integrates the observed energy distribution to obtain a total lrrad lance. By applying this technique to stars whose angular diameters are at least approximately known, he derives effective temperatures and bolometric corrections for these stars. He then finds a color index which varies smoothly with temperature for his "fundamental11 stars, and assigns a temperature to any star which has a measured color index. Originally, Johnson (196*0 used the (R + I)* (J + K) index, but has since (Johnson, 1966) found that the (I - L) index is a more sensitive temperature indicator for H stars. The revised temperature scale assigns higher temper­ ature to the late K and M stars. Johnson's calculations are sensitive to the absolute calibration of the photom­ etry and particularly to the fluxes assigned to the unobserved stellar spectral regions. Johnson (1966) approximates the 1.64 micron flux excess and the depres­ sions due to stellar water vapor by considering the balloon observations on 7 K and M stars obtained by Woolf, Schwarzschi1d, and Rose (1964). Walker (1966), who included 1.6 micron measurements, obtained temperatures about 100-1 7 5 °K higher for K5 to M3 stars than did Johnson. Thus, there is some uncertainty in whether or not Johnson's calculations adequately account for all of the stellar flux. The re la tio n between a given color index and temper­ ature appears not to be unique for all stars. In the case of carbon stars, Yamashlta (1967) found two distinct 4 sequences when he plotted the spectroscopic temperature classes against the color temperatures derived by Mendoza and Johnson (1965) from their (R + l)-(J + K) index. Mendoza (1967) found that this d uality is not removed if the (I - L) index is used. I t is notable that there is a trend for the sequence of lower temperature to be clas­ s ifie d as being more abundant in C 2 . in fa c t, Solomon and Stein (1966) attribute the depression noted by Johnson, Mendoza, and Wisniewski (1965) in the J band (1.25 microns) of some carbon stars to strong electronic transitions of C 2 and CN. Molecular absorption in stars has long been known to occur. Keenan (1963) uses band strengths of TiO and VO to determine spectral classes for the M stars and the Swan C2 bands for the carbon stars. Furthermore, molecules which have infrared transitions can have the most profound influence on the physical structure of a cool star and its emergent flux, but only rather recently has it been possible to study these infrared absorptions. Kuiper (1962, 1963), Sinton (1962), Boyce and SInton (1965)» Moroz (1966), Slnton (1968), and Woolf, SchwarzschtId, and Rose (1964) have detected the presence of water vapor and CO In low resolution infrared spectra of stars. Slnton (1968) measured p artia l equivalent widths of the CO first overtone in stars cooler than K4 and studied the variation of it and the 1.9 micron HjO 5 band in the variable stars R Leo and \ Cyg over a cycle. The balloon spectrometry of Woolf, Schwarzschi1d and Rose (196*t), above essentially ail of the atmospheric water vapor (~80000 ft), enabled them to measure total equivalent widths of the 1.4 and 1.9 micron H^O bands in R Leo and Mira.