# On Integral Upper Limits Assuming Power Law Spectra and the Sensitivity in High-Energy Astronomy

## TL;DR

This paper presents a method to translate integral upper limits into spectrum parameters for power law spectra, clarifying the sensitivity of high-energy telescopes in non-thermal astrophysics.

## Contribution

It introduces a simple, direct relation between integral upper limits and power law spectrum parameters, aiding interpretation of observational constraints.

## Key findings

- Unified framework for upper limit translation
- Enhanced understanding of telescope sensitivity
- Application to high-energy astrophysics data

## Abstract

The high-energy non-thermal universe is dominated by power law-like spectra. Therefore results in high-energy astronomy are often reported as parameters of power law fits, or, in the case of a non-detection, as an upper limit assuming the underlying unseen spectrum behaves as a power law. In this paper I demonstrate a simple and powerful one-to-one relation of the integral upper limit in the two dimensional power law parameter space into the spectrum parameter space and use this method to unravel the so far convoluted question of the sensitivity of astroparticle telescopes.