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Astron. Astrophys. 347, 370-374 (1999)

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1. Introduction

The EGRET detection aboard the Compton Gamma Ray Observatory of at least two supernova remnants (Esposito et al. 1996) and more than fifty active galactic nuclei (Thomson et al. 1995) has given strong evidence of particle acceleration in these objects. This evidence is strengthened even more by the detection of SN 1006 (Tanimori et al. 1998) and the BL Lac objects Mkn 421 (Punch et al. 1992) and Mkn 501 (Quinn et al. 1996) by ground based Cherenkov detectors at TeV energies.

A particularly attractive mechanism for producing the required radiating high energy particles is the diffusive shock acceleration scheme, which has already been put forward to predict TeV radiation from supernova remnants (Drury et al. 1994, Mastichiadis 1996) or explain the observed flaring behaviour in X-rays and TeV [FORMULA]-rays from active galactic nuclei (Kirk et al. 1998). This scheme was originally proposed as the mechanism responsible for producing the nuclear cosmic ray component in shock waves associated with supernova remnants (Krymsky 1977, Axford 1981). Based on this picture many authors (Bogdan & Völk 1983, Moraal & Axford 1983, Lagage & Cesarsky 1983, Schlickeiser 1984, Völk & Biermann 1988, Ball & Kirk 1992, Protheroe & Stanev 1998) have used, under various guises, a simplified but physically intuitive treatment of shock acceleration, sometimes referred to as a "box" model.

In this paper we examine the underlying assumptions of the "box" model (Sect. 2) and we present an alternative more physical version of it (Sect. 3). We then include synchrotron and inverse Compton losses as a means of spectal modification and we determine the conditions under which "pile-ups" can occur in shock accelerated spectra (Sect. 4). The "box" model can also be extended to include the nonlinear effect of the particle pressure on the background flow (Sect. 5).

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© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999