Multipole Functions for Image Analysis II: Equal Area Weighting and Application to Supernova Remnant Images

TL;DR

This paper introduces equal-area weighted multipole basis functions for 2D image analysis, applies them to supernova remnant images, and provides open-source Python code for practical use.

Contribution

It develops new equal-area weighted multipole functions for circular boundary images and demonstrates their application to supernova remnants with open-source code.

Findings

X-ray radial powers are larger than radio for orders >0.

Angular powers are smaller than radial powers, indicating more radial structure.

Type CC supernova remnants have larger radial powers than Type Ia, especially in X-ray images.

Abstract

New basis functions for 2 dimensional (2D) image analysis with a circular boundary (referred to as multipole analysis) are derived which are equal-area weighted. We present open access Python code hosted by GitHub, with which users can apply the multipole analysis to images. The new multipole analysis is applied to a set of 28 supernova remnants (SNRs) which are selected to have both radio and X-ray images, and have been identified as Type Ia or Type CC. Each pair of SNR images (radio and X-ray) was convolved to the same spatial resolution prior to analysis. The resulting multipole radial powers and angular powers, from order 0 to 5, for a given SNR are different for different multipoles and for a given multipole are different between X-ray and radio images. The X-ray radial powers (for orders >0) are larger on average than the radio radial powers (more radial structure in X-rays than radio). The angular powers are smaller than the radial powers on average (more radial structure than angular structure). Comparing Type Ia and Type CC populations, the radial powers (for orders >0) are on average larger for Type CC than Type Ia for X-ray and radio images, with larger difference for X-ray images. The angular powers (for orders >0) are similar between Type Ia and Type CC for both radio and X-ray images.