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Astron. Astrophys. 361, 1073-1078 (2000)

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1. Introduction

Stereoscopic systems of imaging atmospheric Cherenkov telescopes (IACTs) such as the HEGRA IACT system (Daum et al. 1997) allow to reconstruct the directions and energies of TeV gamma-rays with high precision. The analysis techniques, the control of systematics, and the understanding of the angular resolution function of the instrument (Pühlhofer et al. 1997, Aharonian et al. 1999b, Hofmann et al. 1999) has progressed to a level that one can start to study the characteristics of extended sources on a scale of a few arcminutes. These scales start to become interesting in disentangling the emission mechanisms for Galactic TeV gamma-ray sources such as the Crab Nebula or the pulsar PSR B1706-44. In this paper, we present, as a case study, an investigation of the size of the emission region of the Crab Nebula at TeV energies.

The Crab Nebula is one of the best-studied objects in the sky, in all wavelength regimes. It has been established as a TeV gamma-ray source by the Whipple group, using the imaging atmospheric Cherenkov technique (Weekes et al. 1989, Vacanti et al. 1991), and has been studied with many other Cherenkov telescopes. The precise spectral shape of gamma-ray emission from the Crab Nebula has been the subject of a number of recent publications (Hillas et al. 1998, Tanimori et al. 1998, Konopelko 1999a). The spectrum is consistent with a power-law extending from a few 100 GeV out to energies of 50 TeV and beyond. Contrary to observations in the X-ray and GeV gamma-ray regimes, the TeV gamma-ray emission does not show a pulsed component attributable to a direct contribution from the Crab Pulsar; pulsed emission is below 3% of the DC flux (Aharonian et al. 1999c, Burdett et al. 1999). The commonly accepted model for VHE gamma-ray production in the Crab Nebula assumes electron acceleration in the termination shock of the pulsar wind at a distance of about 0.1 pc (0.2´) from the pulsar (see, e.g., Kennel & Coroniti (1984), De Jager & Harding (1992), Atoyan & Aharonian (1996), Aharonian & Atoyan (1998)). The electrons diffuse out into the Nebula and produce a characteristic two-component electromagnetic spectrum: synchrotron emission dominates at most energies up to about 0.1 GeV, whereas the inverse Compton process generates higher-energy gamma-rays with energies from the GeV range up to 100 TeV and beyond. From the relative strength of the two components, values for the average magnetic field of 15-30 nT have been derived (Hillas et al. 1998, De Jager & Harding 1992, Atoyan & Aharonian 1996).

The Crab Nebula represents an extended source of electromagnetic radiation. Since the electrons loose energy as they expand out into the Nebula, primarily due to synchrotron losses, the effective source size is predicted to shrink with increasing energy of the radiation, with radio emission extending up to and beyond the filaments visible in the optical, whereas hard X-rays and multi-TeV gamma-rays should be produced primarily in the direct vicinity of the shock (see, e.g., Kennel & Coroniti (1984), De Jager & Harding (1992), Atoyan & Aharonian (1996), Amato et al. (1999)). At TeV energies, a second production mechanism for gamma-rays could be the hadronic production by protons accelerated in the shock (Atoyan & Aharonian 1996) or resulting from decays of secondary neutrons produced in the pulsar magnetosphere (Bednarek & Protheroe 1997); gamma rays are produced in interactions with the surrounding material, e.g. in the filaments (Atoyan & Aharonian 1996). This contribution might be enhanced due to a trapping of protons in local magnetic fields associated with the filaments, increasing the interaction probability. Given that the size of the Crab Nebula - with its about 4´ by 3´ extension in the optical - is comparable to the angular resolution achieved for TeV gamma rays by the HEGRA system of imaging atmospheric Cherenkov telescopes (IACTs), a study of the size of the TeV emission region of the Crab Nebula is now possible with meaningful sensitivity. This paper reports such an analysis, based on data collected over the last years with the HEGRA IACT system.

For comparison and later reference, we will briefly summarize the existing information on the size of the Crab Nebula, as a function of the energy of the radiation. An obvious problem in such a compilation is that there is no unique definition of `size'. For comparison with the TeV results given later, the most relevant quantity is an rms size, gained by approximating the intensity distribution by a two-dimensional Gaussian, or by directly calculating the rms width by projecting or slicing the intensity distribution along an axis, and averaging over directions. Rms width values based on 5 GHz radio data (Wilson 1972), optical data from Woltjer (1957) as displayed in Wilson (1972), and 0.1-4.5 keV X-ray data (Harnden & Seward 1984) are compiled in Hillas et al. (1998). Additional rms values were obtained for the 327 MHz radio data of Bietenholz et al. (1997), and for the 22-64 keV X-ray data of Makishima et al. (1981). These data are shown in Fig. 1 as full circles. The bulk of the size values quoted in the literature refer to a different measure, the full width at half maximum (FWHM), which unfortunately in case of a structured intensity distribution depends also on the resolution of the instrument. In some cases, data are only available along a specific direction, and do not allow to average over the long and short axis of the Nebula. In particular in earlier X-ray data, the contributions of the pulsar and of the surrounding nebula are not separated. Fig. 1 includes (as open circles) FWHM size data, averaged over the long and short axis, at radio wavelengths (Wilson 1972) and in the optical, NUV, FUV, and X-ray, as given in Hennessy et al. (1992). Also shown are X-ray data compiled in Ku et al. (1976), which refer to the width along the [FORMULA] direction (open squares). A clear trend for decreasing source size with increasing energy is evident, considering either the rms size values, the averaged FWHM size values, and the fixed-direction X-ray widths. Included as dashed line is the frequency dependence of the synchrotron emission region as sketched in Kennel & Coroniti (1984). The size of the emission region for inverse-Compton TeV gamma rays can be predicted using the average magnetic field to relate synchrotron photon energies to electron energies and to inverse-Compton gamma rays; from such arguments, one concludes that the size for TeV gamma-rays should correspond to the X-ray size. The rms size predicted for the TeV gamma-ray emission region by the detailed calculations of Atoyan & Aharonian (1996) is included in Fig. 1. Basically, inverse-Compton TeV gamma-rays should emerge from the toroidal X-ray emission region clearly visible in the ROSAT data (Hester et al. 1995) and in the recent Chandra image (Weisskopf et al., 2000), as already speculated earlier by Aschenbach & Brinkmann (1975). The projected semi-major and semi-minor axes of the emission torus are 38" and 18", respectively. Due to the nonuniform strength of X-ray emission along the torus, the resulting emission profile is roughly elliptical, and its center is shifted N relative to the pulsar location by about 0.3´. Hadronic production mechanisms are expected to generate larger source sizes, of the scale of the size of the nebula (shaded region in Fig. 1).

[FIGURE] Fig. 1. Angular size of the Crab nebula at different frequencies. Full circles: rms size, averaged over directions. Open circles: half width at half maximum (HWHM, defined as FWHM/2), averaged over the long and short axis. Open squares: HWHM along the [FORMULA] direction. See text for references. The dashed line indicates the frequency dependence of the size of the (synchrotron-radiation) emission region as given by Kennel & Coroniti (1984), and the full square shows the rms size predicted for inverse-Compton gamma-rays at TeV energy (Atoyan & Aharonian 1996). The dashed region indicates the rms size range of the filaments, the likely scale for hadronic production mechanisms. The triangles show the upper limits on the rms source size at TeV energies derived in this work.

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© European Southern Observatory (ESO) 2000

Online publication: October 10, 2000