The oblique geometry of pulsar wind termination shock ensures that the Doppler beaming has a strong impact on the shock emission. We illustrate this using recent relativistic MHD simulations of the Crab Nebula and also show that the observed size, shape, and distance from the pulsar of the Crab Nebula inner knot are consistent with its interpretation as a Doppler-boosted emission from the termination shock. If the electrons responsible for the synchrotron gamma-rays are accelerated only at the termination shock then their short life-time ensures that these gamma-rays originate close to the shock and are also strongly effected by the Doppler beaming. As the result, bulk of the observed synchrotron gamma-rays of the Crab Nebula around 100 MeV may come from its inner knot. This hypothesis is consistent with the observed optical flux of the inner knot provided its optical-gamma spectral index is the same as the injection spectral index found in the Kennel & Coroniti model of the nebula spectrum. The observed variability of synchrotron gamma-ray emission can be caused by the instability of the termination shock discovered in recent numerical simulations. Given the small size of the knot, it is possible that the September 2010 gamma-ray flare of the Crab Nebula also came from the knot, though the actual mechanism remains unclear. The model predicts correlation of the temporal variability of the synchrotron gamma-ray flux in the Fermi and AGILE windows with the variability of the unpulsed optical flux from within 1 arcsec of the Crab pulsar.
The Crab Nebula has been a source of intriguing discoveries and served as a test bed of astrophysics for decades. This is one of the best studied objects beyond the Solar system. It has been observed at all wavelengths, from radio to very high energy gamma-rays. Its non-thermal emission below E b ph 500 MeV is a synchrotron emission of relativistic electrons in the nebula magnetic field and above E b ph it is the inverse Compton emission of the same electrons. The emitting electrons are accelerated up to PeV energies, indicating that the acceleration mechanism is very efficient. The source of energy is the ultra-relativistic magnetic wind from the pulsar (Rees & Gunn 1974;Kennel & Coroniti 1984a), but the actual mechanism of particle acceleration is still a mystery. The main candidates are the diffusive shock ac-celeration at the wind termination shock, the second-order Fermi acceleration in the turbulent plasma of the nebula, including secondary shocks, and the magnetic reconnection events.
Compared to the highly filamentary thermal emission, the non-thermal emission is relatively featureless. Yet, it was discovered already in 1920 that fine and dynamic “wisps” are somehow produced in the center of the nebula (Lampland 1921;Scargle 1969). Later, the X-ray observations discovered the famous jet-torus structure in the inner nebula (Weisskopf et al. 2000;Hester et al. 2002), and the high resolution optical observations with Hubble Space Telescope revealed fine sub-arcsecond structure of the non-thermal emission, including few optical knots (Hester et al. 1995(Hester et al. , 2002)).
The synchrotron life-time of electrons emitting in optics is comparable to the dynamical time-scale of the nebula, and this makes it difficult to spot the exact locations of the particle acceleration cites. In gamma-rays below E b ph , where the life-time becomes short, the angular resolution of the telescopes is insufficient to see the nebula structure. However, the observations indicated variability of the gamma-ray emission in the 1-150 MeV range (Much et al. 1995;de Jager et al. 1996) on the time scale around one year. de Jager et al. (1996) proposed that this emission could originate from the variable optical features seen with HST in the polar regions of the inner nebula, in particular the so-called “anvil”. Variability on a similar time-scale has been recently discovered in the X-ray emission (Wilson-Hodge et al. 2010).
In September 2010, AGILE collaboration reported a three-fold increase of the gamma-ray flux (>100 MeV) from the direction of the Crab Nebula (Tavani et al. 2011), which was immediately confirmed by Fermi LAT collaboration, who reported a six-fold increase of the flux (Abdo et al. 2011). The flare continued for four days, September 18-22, after which the gamma-ray flux returned to the pre-flare level. Fermi also reported that the pulsed emission of the Crab pulsar remained unchanged during the flare, suggesting that the flare originated in the Nebula. Jodrell Bank radio timing observations of the Crab pulsar showed no glitch during the flare, supporting this conclusion (ATel#: 2889). At the same time, INTEGRAL reported no detection of the flare during Sep 19 in the 20-400 keV window (ATel#: 2856) and Swift/BAT did not see any significant variability during the gamma-ray flare in the 14-150 keV range (ATel#: 2893). Swift also reported no evidence for active AGN near the Crab, suggesting that the Crab itself is responsible for the flare (ATel#: 2868). ARGO-YBJ collaboration reported a significant enhancement of the very high energy emission, around 1 TeV, from the Crab nebula during the AGILE-Fermi flare (ATel#: 2921). However, this has not been confirmed by VERITAS andMAGIC collaborations (ATel#: 2967,2968). This discovery seems to have given credit to another event, detected in February 2009, which lasted for approximately 14 days, during which the gamma-ray flux increased by a factor of three or four (Tavani et al. 2011;Abdo et al. 2011). On the SED plots the flares appear as an extension of the synchrotron component further out towards the higher energies, up to 1 GeV for the September flare and a bit less dramatic for the February flare.
The short duration of these flares suggests that their source is rather compact. Unfortunately, no high angular resolution observations of the nebula were carried out during the flares. The Crab Nebula images from Chandra and HST, obtained after the September flare, have not revealed anything especially unusual (ATel#: 2882, ATel#: 2903). They do show a change in the structure of the nebula wisps compared to previous observations, carried out years earlier. However, the large length scale of these wisps shows that they can hardly be a source of the flares. The Chandra images also show a significant change in the position of one of the jet knots, which apparently had moved about 3 towards the pulsar. This may be more significant as this feature is more compact.
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