# On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy

## 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.

- Authors:

- Institute for Particle Physics, ETH Zurich, 8093 Zurich (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22663773

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 836; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTRONOMY; DETECTION; GAMMA RADIATION; SENSITIVITY; SPECTRA; TELESCOPES; TWO-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL SYSTEMS; UNIVERSE

### Citation Formats

```
Ahnen, Max L., E-mail: m.knoetig@gmail.com.
```*On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA5B97.

```
Ahnen, Max L., E-mail: m.knoetig@gmail.com.
```*On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy*. United States. doi:10.3847/1538-4357/AA5B97.

```
Ahnen, Max L., E-mail: m.knoetig@gmail.com. Mon .
"On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy". United States.
doi:10.3847/1538-4357/AA5B97.
```

```
@article{osti_22663773,
```

title = {On Integral Upper Limits Assuming Power-law Spectra and the Sensitivity in High-energy Astronomy},

author = {Ahnen, Max L., E-mail: m.knoetig@gmail.com},

abstractNote = {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.},

doi = {10.3847/1538-4357/AA5B97},

journal = {Astrophysical Journal},

number = 2,

volume = 836,

place = {United States},

year = {Mon Feb 20 00:00:00 EST 2017},

month = {Mon Feb 20 00:00:00 EST 2017}

}

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