Principal component analysis of spectral line data: Analytic formulation
Monthly Notices of the Royal Astronomical Society
Oxford University Press
This is the final version of the article. Available from OUP via the DOI in this record.
Principal component analysis is a powerful statistical system to investigate the structure and dynamics of the molecular interstellar medium, with particular emphasis on the study of turbulence, as revealed by spectroscopic imaging of molecular line emission. To date, the method to retrieve the power-law index of the velocity structure function or power spectrum has relied on an empirical calibration and testing with model turbulent velocity fields, while lacking a firm theoretical basis. In this paper, we present an analytic formulation that reveals the detailed mechanics of the method and confirms previous empirical calibrations of its recovery of the scale dependence of turbulent velocity fluctuations. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.
CB is funded in part by the UK Science and Technology Facilities Council grant ST/J001627/1 (‘From Molecular Clouds to Exoplanets’) and the ERC grant ERC-2011-StG_20101014 (‘LOCALSTAR’), both held at the University of Exeter.
Monthly Notices of the Royal Astronomical Society, 2013, Vol. 433, pp. 117 - 126