Production of self-absorbed synchrotron spectra steeper than ν^5/2

Abstract

SELF-ABSORBED synchrotron radiation produced by electrons with a power-law distribution of energies has a unique spectral shape: intensity I_ν ∝ ν^5/2(where ν is frequency), irrespective of the power law index of the electrons¹. This well-known result has been applied recently to the 'far-infrared turnovers' observed in the spectra of many radio-quiet active galactic nuclei (AGNs) ^2–4. It has been asserted that the measurement of a spectral index greater than 5/2 at frequencies below the turnover is incompatible with the physics of self-absorbed synchrotron sources. Several observations suggesting larger indices (steeper slopes) ^5–7 between the far-infrared and millimetre bands have been interpreted as evidence that emission by warm dust, not synchrotron radiation, dominates the far-infrared spectrum. Rees⁸ has, however, pointed out that this assertion is not necessarily true. Here we show that plausible electron energy distributions can lead to self-absorbed synchrotron spectra which are steeper than ν^5/2 over 1–1.5 orders of magnitude in frequency. This indicates that none of the existing observations are in fact incompatible with self-absorbed synchrotron radiation as the source.