# The Ring Produced by an Extra-Galactic Superbubble in Flat Cosmology

## TL;DR

This paper models the formation of rings from superbubbles in flat cosmology, comparing them to Einstein's rings, and provides a Taylor approximation for angular diameter distance at high redshifts.

## Contribution

It introduces a model for superbubble rings in flat cosmology and derives a Taylor approximation for angular diameter distance at high redshift.

## Key findings

- Superbubbles can produce observable rings with radii up to 10 kpc.
- The ring structure resembles Einstein's rings but originates from different physical processes.
- A new Taylor approximation improves calculations of angular diameter distance at high redshift.

## Abstract

A superbubble which advances in a symmetric Navarro--Frenk--White density profile or in an auto-gravitating density profile generates a thick shell with a radius that can reach 10 kpc. The application of the symmetric and asymmetric image theory to this thick 3D shell produces a ring in the 2D map of intensity and a characteristic `U' shape in the case of 1D cut of the intensity. A comparison of such a ring originating from a superbubble is made with the Einstein's ring. A Taylor approximation of order 10 for the angular diameter distance is derived in order to deal with high values of the redshift.