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

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21 assumption that the star is a uniform disk. We illustrate this point in Figures 2.3 and 2.4. Figure 2.3 shows the same o Cet ISI data from Figure 2.1 along with a best-fit uniform disk, limb darkened 5 disk, and Gaussian visibility profile. It is clear that all three functions adequately model the observed data. Figure 2.4 shows the three very different intensity profiles corresponding to the fits from Figure 2.3. We see that some prior knowledge concerning the structure of the star, (for example, how much limb darkening we may expect), is quite important if we are to translate the data into useful measurements. The size of the best-fitting uniform disk is a convenient “diameter” definition for data interpretation, but it is necessary to relate this measured quantity with theory to extract real information about the star. The theoretical quantity most often associated with the size of a star is the Rosseland diameter. This diameter is defined as twice the radius at which the Rosseland opacity 6 equals unity. The ISI diameter measurements made in the years 1999-2001 are displayed in Table 2.1. All diameters are the result of a fit to a uniform disk model. For consistency, only data with spatial frequency greater than 1.75 × 10 6 rad −1 was used. Each observation has a bandpass centered around the wavelength, λ, with a full width ∼2 nm (or 0.16 cm −1 .) The standard observation wavelength of 11.149 µm was chosen because of the relatively small absorption in Earth’s atmosphere or in the circumstellar material at this wavelength. The other observation wavelengths were chosen in some cases to probe an observed spectral feature on the star. The increased opacity on these molecular lines may cause the star to appear larger at these wavelengths as evidenced in the table. These spectral measurements will be discussed in detail in Section 5.4. It should also be noted that statistically significant changes in the diameters of α Ori and o Cet were observed over the course of several years. The fluctuations in α Ori are relatively small (about 5% in magnitude). By comparison, the size of o Cet was seen to change by more than 18%. These time-like changes will be discussed further in Section 4.2. 5 One parameter power law limb darkening. I(θ) = cos(θ) α where α = 2 in this case and θ is the angle between the line of sight and the line connecting the center of the star to a point on its surface. This limb-darkening parametrization is discussed in Hestroffer (1997) [42] 6 The Rosseland opacity is a wavelength averaged opacity weighted towards spectral regions containing the bulk of the emitted flux.
22 Figure 2.3: Uniform Disk, Limb Darkened Disk, and Gaussian Visibility Profiles Fit to ISI Data from o Cet on 28Nov00 Figure 2.4: Intensity profiles which correspond to the uniform disk, limb darkened disk, and gaussian visibility curves from Figure 2.3
Page 1 and 2: The Size, Structure, and Variabilit
Page 3 and 4: 1 Abstract The Size, Structure, and
Page 5 and 6: iv 5 Spectroscopy and ISI Measureme
Page 7 and 8: vi 3.15 Density, Temperature, and C
Page 9 and 10: viii Acknowledgements Over the cour
Page 11 and 12: 2 to achieve resolution characteris
Page 13 and 14: 4 sources are not coaligned perfect
Page 15 and 16: 6 Intensity Profile Hankel Transfor
Page 17 and 18: 8 Figure 1.3: Possible Effective Ba
Page 19 and 20: 10 6LJQDO'HWHFWRU 6LJQDO'HWHFWRU /D
Page 21 and 22: 1995A&A...304...69P 12 Figure 1.5:
Page 23 and 24: Figure 1.6: Stellar Evolution of a
Page 25 and 26: 16 such as Mira variables, become u
Page 27 and 28: 18 wavelengths, however, its range
Page 29: 20 Figure 2.1: ISI Data for o Cet f
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 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 and 98:
88 depth are the contours plotted a
Page 99 and 100:
90 Figure 5.3: Best Fitting Calcula
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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
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104 30 km/s causes the spectrum to
Page 115 and 116:
Figure 5.13: o Cet Spectra in Obser
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108 density prediction matches the
Page 119 and 120:
110 Dixon. The infrared angular dia
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112 [29] M. U. Feuchtinger, E. A. D
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114 [50] A. P. Jacob, T. R. Bedding
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116 [70] A. A. Michelson and F. G.
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118 [92] Martin Schwarzschild. Over
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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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