Interferometric observations of pre-main sequence disks - Caltech ...

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26 Introduction to interferometry 2.2 Basic principle of astronomical interferometry A fundamental property of interferometers is the angular resolution. Classical diffraction theory has established the Reyleigh Criterion for defining the (diffraction-limited) resolution∆θ of a filled circular aperture of diameter D, at the observational wavelength λ: ∆θ=1.22 λ D rad. (2.3) Considering a binary star system, this criterion corresponds to the angular separation on the sky where one stellar component is centered on the first null of the diffraction pattern of the other; the binary is then said resolved. A similar criterion can be defined for an interferometer: the same binary system is resolved by an interferometer if the fringe contrast goes to zero at the longest baseline. As shown in Fig. 2.1, this correspond to the angular separation∆θ=λ/2B. The fringe contrast is historically called visibility and, for the simple two-slit interferometer considered here, can be written as |V|= Imax− Imin Imax+ Imin = Fringe amplitude , (2.4) Average Intensity where Imin and Imax denote the minimum and maximum intensity of the fringes. From this definition, it follows that the left and the right fringe patterns of Fig. 2.1 have visibility of 1 and 0, corresponding respectively to non resolved and resolved sources. Moreover, if the source is shifted with respect to the optical axis of the system (see the right panel of Fig. 2.1), the corresponding fringe patter is also shifted by the same an- gleφ, called phase. Visibility and phase are usually expressed together as the complex visibility V=|V|e iφ , which completely defines a pattern of interference fringes. The importance of measuring complex visibilities derives from the van Cittert– Zernike theorem (see Thompson et al., 2001 for a complete discussion) which relates the fringe contrast to the Fourier components of the impinging brightness distribution. In particular, the theorem states that for spatially incoherent sources in the far field, the value of the visibility V, measured with a baseline B, is equal to the normalized
2.2 Basic principle of astronomical interferometry 27 Figure 2.2: Schematic representation of an interferometer composed by the telescopes or anten- nas. If the source brightness distribution has a small angular extension, it can be approximated with a function I(l,m) in a plane tangential to the celestial sphere. The corresponding spatial frequency are measured in the uv plane as described in the text. Fourier transform of the sky brightness distribution corresponding to the fringe spatial frequency u=B/λ rad −1 ; the phase of the fringe pattern is also equal to the Fourier phase of the same spatial frequency component. In the real case of a bi-dimensional astronomical source whose radiation comes from a small portion of the sky, it is possible to define a system of Cartesian coordinates (l, m) on the tangent plane to the celestial sphere at the point where the object is located, and express the surface brightness as a function I(l, m). In this case, the van Cittert–Zernike
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Page 28 and 29: 20 Scientific overview We propose a
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Page 57 and 58: 3.2 Model description 49 the pressu
Page 59 and 60: 3.3 Results 51 Photospherical heigh
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Page 65 and 66: 3.4 Discussion 57 the value ofǫ, t
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76 Large dust grains in the inner r
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Face-on disk image Baseline (m) V 2
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V 2 1 0.8 0.6 0.4 0.2 0 0 50 100 15
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CHAPTER 5 More on the “puffed-up
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5.1 Fuzzy and sharp rims 97 opacity
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5.2 New shapes for the rim 99 grain
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5.3 New observational results 101 (
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5.3 New observational results 103 w
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CHAPTER 6 Constraining the wind lau
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6.1 Introduction 109 λ Fλ (erg cm
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6.2 Observations and data reduction
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6.3 Results and discussions 113 V V
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6.4 Conclusions 115 note however th
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Part IV The structure of the outer
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120 The keplerian disk of HD 163296
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Part V Conclusions and future prosp
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152 Summary and Conclusions ∼1 an
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154 Summary and Conclusions disk in
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CHAPTER 9 Future developments As my
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9.1 Gas in the inner disk of Herbig
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9.2 Probing planet formation throug
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Published papers • Isella, A.; Te
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172 BIBLIOGRAPHY [2000] Bodenheimer
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174 BIBLIOGRAPHY [2004] Gail H.-P.,
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176 BIBLIOGRAPHY Arizona Press, Tuc
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178 BIBLIOGRAPHY [2001] Thompson A.
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