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

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Figure 3.20: The Temperature, Density, and Ionization Fraction in the Wake of a 30 km/s Shock Propogating into a 3000 K, 10 −11 gm/cm 3 Medium (top). The 11 µm Opacity and Integrated Optical Depth of the Post-Shock Region Calculated from Free-Free Hydrogen Processes (bottom). 71
72 3.5 Explanation of Variations in Measured Diameter with Wavelength The focus of the preceding sections has been the systematic consideration of processes which may have affected the apparent size of AGB stars near 11 µm. The necessary corrections for dust, spectral contamination, and continuum center to limb variations were estimated. The result is a set of upper limits for the error in ISI diameter measurements relative to near-IR “continuum” monochromatic and apparent diameters. The theoretical Rosseland diameter is inaccessable from the simple continuum models considered in Section 3.4.3, however it is thought to be close to near-IR monochromatic diameters since most of the stellar flux is emitted in this region. With a good degree of confidence, for the supergiants, α Ori and α Her, we estimate corrections to the ISI measured diameters relative to near-IR continuum and symmetric model apparent diameters to be about -1%. For lower mass, pulsating Miras, such as o Cet, R Leo, and χ Cyg, the extra atmospheric extension increases those corrections to between -3% and -14% depending on phase with an additional ±3% error if dust forms within 2.5R ∗ . Corrections due to spectral lines within the ISI bandpass are predicted to be less than 1% for all stars measured with the ISI continuum P20 bandpass. Having investigated many of the phenomenon responsible for altering the apparent sizes of AGB stars, it should be possible to re-examine the variety of stellar size measurements from Tables 2.2-2.4 in the context of atmospheric morphology. The visible diameter measurements of α Ori displayed in Table 2.2 span the range of 44-58 mas. A systematic increase in apparent size is observed in the strongest TiO bands, and a decrease due to limb darkening may be evident in weaker bands. In addition, dust is a fairly efficient absorber and scatterer in the visible, and very small variations in surface temperature can produce pronounced changes in emitted intensity. (At 500 nm and 3000 K, a 1% change in temperature will change the intensity by 10%.) As a result, there are many ways that the roughly 30% variations in size can be accounted for. A molecular shell of TiO at 1.3R ∗ having varying transparency with wavelength is not unlikely and is capable of reproducing the varying apparent diameters observed. The near-IR diameters are somewhat less variable. Other than the 3.09 µm Keck diameter which is located in an H 2 O band, they span the range of 40-44 mas. They are roughly a lower bound to the visible sizes. Since the TiO molecular lines are weaker in the near-IR, there appears to be no inconsistency between these sizes
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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
Page 29 and 30: 20 Figure 2.1: ISI Data for o Cet f
Page 31 and 32: 22 Figure 2.3: Uniform Disk, Limb D
Page 33 and 34: 24 2.2 Comparison of ISI Data with
Page 35 and 36: 26 Table 2.3: Diameter Measurements
Page 37 and 38: 28 measurements. χ Cyg and R Leo a
Page 39 and 40: 30 metric flux (from the reference
Page 41 and 42: 32 their surface. Very often, mater
Page 43 and 44: 34 Mira. Finally, variations in tim
Page 45 and 46: 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: 70 of Fox and Wood (1985) [31] are
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 and 98: 88 depth are the contours plotted a
Page 99 and 100: 90 Figure 5.3: Best Fitting Calcula
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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The Size, Structure, and Variability of Late-Type Stars Measured ...

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