Log parabolic power-law models used for blazars.

NOTE: This model is now in the Xspec release and this page is superceded by the Xspec manual

These models from Alberto Segreto, Enrico Massaro and Andrea Tramacere are power-laws with an index which varies as a log parabola in energy. They are commonly used in the analysis of the spectra of blazars.


N(E) = (E/pivotE)**(-alpha-beta*log(E/pivotE))

where pivotE is a scale parameter (always frozen) which for optimum results should be set close to the lower energy range of the spectrum being fit. See for instance Massaro et al., 2004.


N(E) = 10**(-beta*(log(E/Ep))**2)/E**2

where Ep is the peak energy in νFν and the normalization the peak flux in the same units. This model is less stable than logpar, particularly when Ep is far from the energy range of the spectrum. However, it directly provides the SED peak energy and flux, which are useful for physical modeling. See for instance Tramacere et al., 2007 and Tramacere et al., 2009.

To use these models download log-parabolic.tar.gz and load as local models using initpackage and lmod.

Keith Arnaud, Lab. for High Energy Astrophysics, NASA/Goddard Space Flight Center

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Last modified: Tuesday, 14-Feb-2023 16:41:58 EST