The Size, Structure, and Variability of Late-Type Stars Measured ...

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89 R gas = 1.0R ∗ Spectral Line Depth R gas = 1.2R ∗ R gas = 2.0R ∗ Figure 5.2: Fractional Absorption or Emission for a Thin Shell of Gas of Radius, R gas , as a Function of its Optical Depth, τ gas , and the Intensity Ratio, B ν (T gas )/B ν (T ∗ ), for Three Values of R gas . τ gas
90 Figure 5.3: Best Fitting Calculated Absorption of H 2 O vs. Observed Absorption in R Leo. Each diamond represents a different observed H 2 O line. distribution which is likely very dynamic in nature. The modelling of this time-dependent line formation is somewhat more complicated and we will return to it in Section 5.3. 5.2 Continuum Measurements at 11.149 µm The presence of a gas shell surrounding a star will also affect its intensity distribution at the transition frequency provided that the line opacity is non-negligible. To illustrate the effect that our model shell of gas would have on a diameter measurement, we calculate the model intensity profile and visibility function that would be observed at the wavelength corresponding to the peak of the strong emission and absorption lines, respectively, from o Cet at 897.44 cm −1 assuming the best fit parameters for N H2 O, T gas , and R gas . This spectral line is the stronger of the pair of lines seen on o Cet in Figure 5.1 near 897.4 cm −1 . This particular line has an optical depth of 0.217 in emission and 0.032 in absorption. The
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The Size, Structure, and Variabilit
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1 Abstract The Size, Structure, and
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iv 5 Spectroscopy and ISI Measureme
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vi 3.15 Density, Temperature, and C
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viii Acknowledgements Over the cour
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2 to achieve resolution characteris
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4 sources are not coaligned perfect
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6 Intensity Profile Hankel Transfor
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8 Figure 1.3: Possible Effective Ba
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10 6LJQDO'HWHFWRU 6LJQDO'HWHFWRU /D
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1995A&A...304...69P 12 Figure 1.5:
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Figure 1.6: Stellar Evolution of a
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16 such as Mira variables, become u
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18 wavelengths, however, its range
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20 Figure 2.1: ISI Data for o Cet f
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22 Figure 2.3: Uniform Disk, Limb D
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24 2.2 Comparison of ISI Data with
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26 Table 2.3: Diameter Measurements
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28 measurements. χ Cyg and R Leo a
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30 metric flux (from the reference
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32 their surface. Very often, mater
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34 Mira. Finally, variations in tim
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36
Page 47 and 48: 38 Figure 3.2: Intensity Distributi
Page 49 and 50: 40 Figure 3.4: Ratio of the Best-Fi
Page 51 and 52: Figure 3.5: Synthetic Near-Infrared
Page 53 and 54: 44 Angular Diameter (mas) 60 50 40
Page 55 and 56: 46 wavelengths which would cause th
Page 57 and 58: 48 3.4.1 Static Radiative Transfer
Page 59 and 60: 50 Figure 3.8: Ratio of Photospheri
Page 61 and 62: 52 3.4.2 The Effect of Dynamic Phen
Page 63 and 64: 54 Figure 3.10: “Standard” Bowe
Page 65 and 66: 56 extension is reflected at wavele
Page 67 and 68: 58 photosphere. These results suppo
Page 69 and 70: 60 Figure 3.13: Continuum Opacity o
Page 71 and 72: 62 assuming only continuum sources.
Page 73 and 74: 64 Figure 3.16: Normalized Syntheti
Page 75 and 76: Figure 3.17: Density and Temperatur
Page 77 and 78: 68 Figure 3.19: Apparent Size of H
Page 79 and 80: 70 of Fox and Wood (1985) [31] are
Page 81 and 82: 72 3.5 Explanation of Variations in
Page 83 and 84: 74 Figure 3.21: 2.1 µm Image of 25
Page 85 and 86: 76 at visible wavelengths either by
Page 87 and 88: 78 4.1 Implications of Diameter Mea
Page 89 and 90: 80 11 µm Diameter of o Cet vs. Dat
Page 91 and 92: 82 Figure 4.3: A uniform intensity
Page 93 and 94: 84 phase observed in the continuum
Page 95 and 96: 86 5.1 General Results of 11 µm Sp
Page 97: 88 depth are the contours plotted a
Page 101 and 102: 92 of its three parameters. The con
Page 103 and 104: 94 H 2 O on their measured diameter
Page 105 and 106: 96 5.3 Modelling Spectral Features
Page 107 and 108: 98 Figure 5.7: Stellar Intensity Pr
Page 109 and 110: Figure 5.9: Observed H 2 O Spectral
Page 111 and 112: Figure 5.10: Höfner Model Predicte
Page 113 and 114: 104 30 km/s causes the spectrum to
Page 115 and 116: Figure 5.13: o Cet Spectra in Obser
Page 117 and 118: 108 density prediction matches the
Page 119 and 120: 110 Dixon. The infrared angular dia
Page 121 and 122: 112 [29] M. U. Feuchtinger, E. A. D
Page 123 and 124: 114 [50] A. P. Jacob, T. R. Bedding
Page 125 and 126: 116 [70] A. A. Michelson and F. G.
Page 127 and 128: 118 [92] Martin Schwarzschild. Over
Page 129: 120 [114] P. Woitke, D. Krüger, an
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