The location of the Crab pulsar emission region: restrictions on synchrotron emission models

Abstract

Recent observations of the Crab pulsar show no evidence of a spectral break in the infrared regime. It is argued that the observations are consistent with a power-law spectrum in the whole observable infrared-optical range. This is taken as the starting point for evaluating of how self-consistent incoherent synchrotron models fare in a comparison with observations. Inclusion of synchrotron self-absorption proves important as does the restriction on the observed size of the emission region imposed by the relativistic beaming thought to define the pulse profile. It is shown that the observations can be used to derive two independent constraints on the distance from the neutron star to the emission region; in addition to a direct lower limit, an indirect measure is obtained from an upper limit to the magnetic field strength. Both of these limits indicate that the emission region is located at a distance considerably greater than the light cylinder radius. The implications of this result are discussed, and it is emphasized that, for standard incoherent synchrotron models to fit inside the light cylinder, rather special physical conditions need to be invoked.

The optical and NIR spectrum of the Crab pulsar with X-shooter

“…The theoretical discussion in Björnsson et al (2010) highlighted that the main question regarding α ν is whether or not it is consistent with a value of 1/3. This is the highest possible value for optically thin incoherent synchrotron radiation as the emission mechanism.…”

“…This was followed by several investigations that provided data with medium-sized (2 − 4 m) telescopes more than 15 years ago (e.g., Sollerman et al 2000;Carramiñana et al 2000;Beskin & Neustroev 2001;Romani et al 2001;Fordham et al 2002). These observations were also followed by a series of theoretical papers aiming to interpret the optical emission (e.g., Björnsson et al 2010;Massaro et al 2006;O'Connor et al 2005;Crusius-Wätzel et al 2001). Yet, while important from a theoretical perspective, the exact shape of the non-thermal optical-near-infrared (NIR) spectralenergy-distribution (SED) of this isolated neutron star has remained elusive.…”

“…The actual value of the spectral index α ν (we define the spectral index to be given as the power-law F ν ∝ ν +α ν ) of the pulsar in this region is also of importance for understanding the emission mechanism of pulsars. Björnsson et al (2010) showed for example how the value of the spectral index in the optical-NIR regime translates to limits on the location of the emission zone within the pulsar magnetosphere.…”