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

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3 Figure 1.1: Simple Model of Interferometer for Three Different Telescope Separations. The light from each of two point sources on an astrophysical object passes through two apertures as in Young’s double slit experiment and each forms an interference pattern on the image plane behind them. When the two apertures are close together, the interference patterns are broad and their sum adds constructively. As the two apertures are separated, the interference patterns narrow and the sum begins to add destructively.
4 sources are not coaligned perfectly, they will not (necessarily) add constructively. In this case, the visibility of the net fringe pattern may be somewhat less than unity depending on the separation between the slits. As the slit separation is increased, the visibility falls off from unity sinusoidally. When the separation between the slits reaches a characteristic value, D = λ/2 sin(∆θ) (1.2) the two interference patterns are completely out of phase, the fringes add destructively, and the visibility is zero. This type of experiment could be used to measure the angular separation between the stars in a binary, for instance. An interference pattern could be formed between two telescopes placed close together. Then, the telescopes could be separated until the fringes disappear. The angular separation of the two stars would then be given by Equation 1.2. The telescopes, separated by a distance, D, could be said to have a resolution, ∆Θ interferometer = λ/2D radians which is similar to the resolution of a diffraction limited single aperture telescope having size on the order of the interferometer’s separation as previously claimed. For the case of an arbitrary intensity distribution, the fringes measured using the two-slit interferometer will be the superposition of all the point source contributions. Since the net fringes vary sinusoidally with the angular separation between the point sources, the net fringe can be expressed as an integral over the intensity distribution modulated by a sinusoidal response. Mathematically, this is equivalent to a two-dimensional Fourier Transform. This result is known as the Van Cittert-Zernike Theorem (Born and Wolf (1965) [14]), and it states that the complex visibility, V (x, y), is given by, V (x, y) = 1 F ∫ ∞ ∫ ∞ −∞ −∞ I(θ, φ)e −2πi(θx/λ+φy/λ) dθdφ (1.3) where [x,y] is the vector baseline (separation) between the two telescopes, F is the total flux from the source, and I(θ, φ) is the intensity distribution on the sky as a function of the angles θ and φ (which are assumed to be much less than unity). The measured (real-valued) visibility defined in Equation 1.1 is the magnitude of the complex visibility defined above. To reconstruct an arbitrary intensity distribution from visibility measurements, one would need to measure the visibility (and its phase) on every possible baseline. Then, the image could be reconstructed by inverting Equation 1.3. To accomplish this, one might
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: 2 to achieve resolution characteris
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 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
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58 photosphere. These results suppo
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60 Figure 3.13: Continuum Opacity o
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62 assuming only continuum sources.
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64 Figure 3.16: Normalized Syntheti
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Figure 3.17: Density and Temperatur
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68 Figure 3.19: Apparent Size of H
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70 of Fox and Wood (1985) [31] are
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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
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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
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84 phase observed in the continuum
Page 95 and 96:
86 5.1 General Results of 11 µm Sp
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88 depth are the contours plotted a
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90 Figure 5.3: Best Fitting Calcula
Page 101 and 102:
92 of its three parameters. The con
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94 H 2 O on their measured diameter
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96 5.3 Modelling Spectral Features
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98 Figure 5.7: Stellar Intensity Pr
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Figure 5.9: Observed H 2 O Spectral
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Figure 5.10: Höfner Model Predicte
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104 30 km/s causes the spectrum to
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Figure 5.13: o Cet Spectra in Obser
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108 density prediction matches the
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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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