# Relation between positional & strength asymmetries of double radio sources associated with active galaxies

## TL;DR

This paper demonstrates the equivalence between two different parameterizations of asymmetries in double radio sources associated with active galaxies, linking positional and strength asymmetries through a unified mathematical expression.

## Contribution

It introduces a unified parameter that combines positional and strength asymmetries, revealing their fundamental identity in double radio sources.

## Key findings

- The combined parameter is mathematically equivalent to a form involving arm and strength ratios.
- The relation applies to sources with different hotspot brightness configurations.
- Provides a new perspective for analyzing asymmetries in radio galaxy structures.

## Abstract

We bring out the identity between two ways of defining a single parameter to combine positional & strength asymmetries of extended extragalactic double radio sources associated with active galaxies. Thus, (r.s - 1)/[(1 + r).(1 + s)], combining arm ratio r (defined to be <= 1, i.e., shorter to longer arm) & strength ratio s (in the sense closer to farther, so that it may be <, > or = 1), is identical to -(1/2)[(1 - fr)/(1 + fr) - t], where fr is strength ratio defined >= 1 (i.e., stronger to weaker), & t = +/- (Q - 1)/(Q + 1), +/- signs applying respectively to doubles with closer hotspot fainter & those with closer hotspot brighter, while Q is arm ratio defined >= 1. Keywords: active galaxies - double radio sources - bilateral symmetry - arm ratio - flux ratio

---
Source: https://tomesphere.com/paper/0909.4284