Estimating the statistical uncertainty due to spatially correlated noise in interferometric images

Abstract

Interferometers (e.g. ALMA and NOEMA) allow us to obtain the detailed brightness distribution of astronomical sources in 3 dimensions (R.A., Dec., frequency). However, the spatial correlation of the noise makes it difficult to evaluate the statistical uncertainty of the measured quantities and the statistical significance of the results obtained. The noise correlation properties in the interferometric image are fully characterized and easily measured by the noise autocorrelation function (ACF). We present the method for (1) estimating the statistical uncertainty due to the correlated noise in the spatially integrated flux and spectra directly, (2) simulating the correlated noise to perform a Monte Carlo simulation in image analyses, and (3) constructing the covariance matrix and chi-square ${\chi }^2$ distribution to be used when fitting a model to an image with spatially correlated noise, based on the measured noise ACF. We demonstrate example applications to scientific data showing that ignoring noise correlation can lead to significant underestimation of statistical uncertainty of the results and false detections/interpretations.

Published in JATIS with the updated title, 42 pages, 14 figures; Python codes are available at https://github.com/takafumi291/ESSENCE; We are grateful to the anonymous reviewers for giving insightful comments, which improved the manuscript significantly. Comments are warmly welcomed. arXiv admin note: substantial text overlap with arXiv:2207.12588

References in corpus (8)

• CASA, the Common Astronomy Software Applications for Radio Astronomy
• Kinematic modelling of disk galaxies I. A new method to fit tilted rings to data cubes
• The SAMI Galaxy Survey: Cubism and covariance, putting round pegs into square holes
• A black-hole mass measurement from molecular gas kinematics in NGC4526
• Spiral morphology in an intensely star-forming disk galaxy more than 12 billion years ago
• WISDOM Project - II: Molecular gas measurement of the supermassive black hole mass in NGC4697
• ALMA Observations of a Candidate Molecular Outflow in an Obscured Quasar
• Estimating the statistical uncertainty due to spatially correlated noise in interferometric images

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