Letters to the Editor

Hadronic beam models for quasars and microquasars

¹ ICREA & Institut de Ciències de l’Espai (IEEC-CSIC), Campus UAB, Facultat de Ciències, Torre C5-parell, 2a planta, 08193 Barcelona, Spain
e-mail: dtorres@ieec.uab.es
² Institut für Theoretische Physik, and Institut für Astro- und Teilchenphysik, Leopold-Franzens-Universität Innsbruck, Technikerstr. 25, 6020 Innsbruck, Austria

Received: 10 January 2011
Accepted: 2 February 2011

Abstract

Context. Most of the hadronic jet models for quasars (QSOs) and microquasars (MQs) found in the literature represent beams of particles (e.g. protons). These particles interact with the matter in the stellar wind of the companion star in the system or with crossing clouds, generating γ-rays via proton-proton processes.

Aims. Our aim is to derive the particle distribution in the jet as seen by the observer, so that the γ-ray and neutrino yields can be properly computed.

Methods. We use relativistic invariants to obtain the transformed expressions in the cases of both a power law and power law with a cutoff particle distribution in the beam. We compare them with previous expressions used earlier in the literature.

Results. We show that formerly used expressions for the particle distributions in the beam as seen by the observer are in error, with the differences being strongly dependent on the viewing angle. For example, for Γ = 10 (Γis the Lorentz factor of the blob) and angles larger than  ~20°, the calculation used earlier entails an overprediction (order of magnitude or more) of the proton spectra for E > Γmc², whereas it always overpredicts (two orders of magnitude) the proton spectrum at lower energies, for all the viewing angles.

Conclusions. All the results for photon and neutrino fluxes in hadronic models are affected in beams that have made use of the earlier calculation. Given that correct γ-ray fluxes will in almost any case be significantly diminished in comparison with published results and that the time of observations in Cherenkov facilities grows with the square of the flux-reduction factor in a statistically limited result, the possibility of observing hadronic beams is undermined.