nonimaging_mar30 (1)

nonimaging_mar30 (1) - Non-Imaging Data Analysis Greg...

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Unformatted text preview: Non-Imaging Data Analysis Greg Taylor University of New Mexico ASTR 423, Spring 2011 Greg Taylor, Synthesis Imaging 2010 2 Outline Introduction Inspecting visibility data Model fitting Some applications Component motion Gamma-ray bursts Blazars Binary stars Gravitational lenses Greg Taylor, Synthesis Imaging 2010 3 Introduction Reasons for model fitting visibility data Insufficient ( u,v )-plane coverage to make an image Inadequate calibration Quantitative analysis Direct comparison of two data sets Error estimation Usually, visibility measurements are independent gaussian variates Systematic errors are usually localized in the ( u,v ) plane Statistical estimation of source parameters Greg Taylor, Synthesis Imaging 2010 4 Inspecting Visibility Data Fourier imaging Problems with direct inversion Sampling Poor ( u,v ) coverage Missing data e.g., no phases (speckle imaging) Calibration Closure quantities are independent of calibration Non-Fourier imaging e.g., wide-field imaging; time-variable sources (SS433) Noise Noise is uncorrelated in the ( u,v ) plane but correlated in the image Greg Taylor, Synthesis Imaging 2010 5 Useful displays Sampling of the ( u,v ) plane Amplitude and phase vs . radius in the ( u,v ) plane Amplitude and phase vs . time on each baseline Amplitude variation across the ( u,v ) plane Projection onto a particular orientation in the ( u,v ) plane Example: 2021+614 GHz-peaked spectrum radio galaxy at z =0.23 A VLBI dataset with 11 antennas from 1987 VLBA only in 2000 Inspecting Visibility Data Greg Taylor, Synthesis Imaging 2010 6 Sampling of the (u,v) plane Greg Taylor, Synthesis Imaging 2010 7 Visibility versus (u,v) radius Greg Taylor, Synthesis Imaging 2010 8 Visibility versus time Greg Taylor, Synthesis Imaging 2010 9 Projection in the (u,v) plane Greg Taylor, Synthesis Imaging 2010 10 Properties of the Fourier transform See, e.g., R. Bracewell, The Fourier Transform and its Applications (1965). Fourier Transform theorems Linearity Visibilities of components add (complex) Convolution Shift Shifting the source creates a phase gradient across the ( u,v ) plane Similarity Larger sources have more compact transforms Greg Taylor, Synthesis Imaging 2010 11 Fourier Transform theorems Greg Taylor, Synthesis Imaging 2010 12 Greg Taylor, Synthesis Imaging 2010 13 Greg Taylor, Synthesis Imaging 2010 14 Greg Taylor, Synthesis Imaging 2010 15 Simple models Visibility at short baselines contains little information about the profile of the source. Greg Taylor, Synthesis Imaging 2010 16 Trial model By inspection, we can derive a simple model: Two equal components, each 1.25 Jy, separated by about 6.8 Two equal components, each 1....
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This note was uploaded on 12/13/2011 for the course ASTRO 423 taught by Professor Gregtaylor during the Fall '11 term at New Mexico.

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nonimaging_mar30 (1) - Non-Imaging Data Analysis Greg...

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