A Technique for Removing Large-scale Variations in Regularly and Irregularly Spaced Data

Abstract

In many astrophysical systems, smooth large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that have small-scale fluctuations by turbulence. In redshifted 21 cm observations, we also have two types of signals—the Galactic foreground emissions that change smoothly and the redshifted 21 cm signals that fluctuate fast in frequency space. In many cases, the large-scale variations make it difficult to extract information on small-scale fluctuations. We propose a simple technique to remove smooth large-scale variations. Our technique relies on multi-point structure functions and can obtain the magnitudes of small-scale fluctuations. It can also be used to design filters that can remove large-scale variations and retrieve small-scale data. We discuss how to apply our technique to irregularly spaced data, such as rotation measure observations toward extragalactic radio point sources.