[Paper Review] Cross Calibration of Imaging Air Cherenkov Telescopes with Fermi

M. Meyer, D. Horns+1 more|arXiv (Cornell University)|Dec 18, 2009

Astrophysics and Cosmic Phenomena21 references4 citations

TL;DR

This paper presents a cross-calibration method between Fermi/LAT and ground-based Imaging Air Cherenkov Telescopes (IACTs) using an updated model of the Crab nebula's spectral energy distribution (SED), which includes synchrotron and inverse Compton emission from a two-component electron population. By fitting the model to Fermi's high-precision γ-ray measurements, the authors derive energy scaling factors that reduce systematic uncertainties in IACT energy measurements from ~15% to below 1%, enabling consistent combination of Fermi and ground-based data for improved astrophysical measurements.

ABSTRACT

An updated model for the synchrotron and inverse Compton emission from a population of high energy electrons of the Crab Nebula is used to reproduce the measured spectral energy distribution from radio to high energy gamma-rays. By comparing the predicted inverse Compton component with recent Fermi measurements of the nebula's emission, it is possible to determine the average magnetic field in the nebula and to derive the underlying electron energy distribution. The model calculation can then be used to cross calibrate the Fermi observations with ground based air shower measurements. The resulting energy calibration factors are derived and can be used for combining broad energy measurements taken with Fermi in conjunction with ground based measurements.

Motivation & Objective

• To reduce systematic energy scale uncertainties in ground-based IACTs, which currently stand at ~15%, by cross-calibrating with Fermi/LAT data.
• To develop a physically consistent model of the Crab nebula's broadband SED, incorporating synchrotron and inverse Compton emission from relativistic electrons.
• To derive energy scaling factors for IACTs (H.E.S.S., MAGIC, HEGRA) that align their energy measurements with the Fermi/LAT energy scale.
• To apply the cross-calibration to improve constraints on the diffuse γ-ray background and assess the significance of excesses in cosmic-ray electron spectra.
• To establish the Crab nebula as a reliable standard candle for high-energy γ-ray astronomy across multiple energy bands.

Proposed method

• An updated model of the Crab nebula's SED is constructed using a two-population electron energy distribution and a constant magnetic field, with spatial distributions modeled as Gaussians.
• Synchrotron and inverse Compton (IC) emission are calculated using standard particle physics formulas: the single-particle emissivity for synchrotron (Eq. 2) and IC (Eq. 3) emission, including kinematic variables (Eq. 5) and the IC distribution function (Eq. 6).
• The seed photon fields—cosmic microwave background, synchrotron radiation, dust emission, and optical lines—are convolved with the electron density to compute the effective IC photon density.
• The model is fitted to Fermi/LAT data in the 100 MeV–300 GeV range to determine the average magnetic field and electron spectrum, which then serves as a reference for cross-calibration.
• Energy scaling factors are derived by comparing the model-predicted IC flux with IACT measurements; these factors correct for systematic energy scale offsets in IACT data.
• The cross-calibration is applied to the H.E.S.S. and Fermi electron+positron spectra to derive conservative upper limits on the diffuse γ-ray background, accounting for systematic uncertainties in energy scale.

Experimental results

Research questions

• RQ1 What is the average magnetic field strength in the Crab nebula, as constrained by Fermi/LAT measurements of the inverse Compton component?
• RQ2 How can the energy scale uncertainty of ground-based IACTs be reduced from ~15% to below 1% using a physically consistent model of the Crab nebula?
• RQ3 To what extent does the cross-calibration affect the interpretation of excesses in cosmic-ray electron spectra, such as the ATIC peak?
• RQ4 Can the cross-calibrated IACT and Fermi data be used to derive more robust upper limits on the diffuse γ-ray background at TeV energies?
• RQ5 How does the inclusion of multiple seed photon fields (CMB, synchrotron, dust, optical lines) improve the accuracy of the SED model?

Key findings

• The average magnetic field in the Crab nebula is determined to be consistent with the model that best fits Fermi/LAT data, enabling accurate IC flux prediction.
• The derived energy scaling factors for IACTs are: H.E.S.S. at 0.961 ± 0.004, MAGIC at 1.03 ± 0.01, HEGRA at 1.042 ± 0.005, and Fermi/LAT at 1.00 (reference), reducing systematic uncertainties in energy scale.
• After applying the cross-calibration, the peak in the ATIC electron+positron spectrum becomes less likely, indicating it may be an artifact of energy scale uncertainty.
• The cross-calibration enables a more reliable comparison of H.E.S.S. and Fermi data, leading to conservative upper limits on the diffuse γ-ray background with reduced systematic uncertainty.
• The model successfully reproduces the broadband SED of the Crab nebula from radio to TeV γ-rays, validating its use as a calibration standard.
• The cross-calibration method provides a robust framework for future standardization of γ-ray measurements across different instruments and energy bands.