# Bow shocks, bow waves, and dust waves. III. Diagnostics

## TL;DR

This paper introduces the tau-eta diagnostic diagram to analyze stellar bow structures, distinguishing between different types and estimating stellar wind mass-loss rates, with implications for revising previous measurements.

## Contribution

It proposes a novel tau-eta diagram method for analyzing bow shocks, bow waves, and dust waves, improving classification and mass-loss rate estimation.

## Key findings

- Identified at least 4 candidates for radiation-supported bow waves.
- Suggested a potential twofold revision of previous stellar wind mass-loss rates.
- Compared new diagnostic with previous methods, highlighting improvements.

## Abstract

Stellar bow shocks, bow waves, and dust waves all result from the action of a star's wind and radiation pressure on a stream of dusty plasma that flows past it. The dust in these bows emits prominently at mid-infrared wavelengths in the range 8 to 60 micron. We propose a novel diagnostic method, the tau-eta diagram, for analyzing these bows, which is based on comparing the fractions of stellar radiative energy and stellar radiative momentum that is trapped by the bow shell. This diagram allows the discrimination of wind-supported bow shocks, radiation-supported bow waves, and dust waves in which grains decouple from the gas. For the wind-supported bow shocks, it allows the stellar wind mass-loss rate to be determined. We critically compare our method with a previous method that has been proposed for determining wind mass-loss rates from bow shock observations. This comparison points to ways in which both methods can be improved and suggests a downward revision by a factor of two with respect to previously reported mass-loss rates. From a sample of 23 mid-infrared bow-shaped sources, we identify at least 4 strong candidates for radiation-supported bow waves, which need to be confirmed by more detailed studies, but no strong candidates for dust waves.