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This summer, I was working on a project fitting very high energy gamma ray spectra of the Crab Nebula, a pulsar wind nebula. At energies about $\sim$1 TeV, a simple power law suffices, i.e. $\phi(E)\propto E^{\alpha}$. Most power law models of the Crab find a spectral index of $\alpha\simeq-2.47$ (e.g. Hillas 1998, $\alpha=-2.49\pm0.06$). Using a normal analysis method on one dataset, I found $\alpha=-2.469\pm0.02248$, which matches the literature values quite well.

Using the modified analysis method I was testing, however, I found $\alpha=-2.316\pm0.02040$. We believe that method is a poor choice because I showed the calculated flux values were incompatible with previous observations. The spectral index also cast doubts on its viability. However, I was wondering if, for a random pulsar wind nebula, a slightly harder spectral index like $\alpha=-2.316$ is unphysical, or reasonable.

Therefore, I'm wondering: What is the distribution of spectral indices for power-law models of very high energy spectra of pulsar wind nebulae? Do we have a large enough population of pulsar wind nebulae that we can determine what a typical value for $\alpha$ is, and what range we would expect a spectral index to fall into? In other words, could if I had obtained a certain value for $\alpha$, what value would it need to have for me to reject the result as unphysical?

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You might find these websites for your answers:

We have a large amount of high energy emission these days, and the third reference shows the distribution from 394 GRBs.

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  • $\begingroup$ These seem like they might be a start, although I'm don't know to what extent the x-ray results can be extrapolated to higher energies. It seems like the spectral indices are obtained from around the 2-10 keV range, and it's not clear to me how good of a proxy that is for spectra at $E\sim$ 1 TeV. (That uncertainty's largely just because of me - I have no experience with PWN spectra from x-rays on downwards.) $\endgroup$ – HDE 226868 Dec 27 '19 at 21:54
  • $\begingroup$ Are you working on the TeV halos of PWNe? $\endgroup$ – Kornpob Bhirombhakdi Dec 27 '19 at 22:09
  • $\begingroup$ Yep, that was the project - the Crab Nebula in particular. $\endgroup$ – HDE 226868 Dec 27 '19 at 22:19
  • $\begingroup$ I think TeV halo of pwn is quite a new topic, right? $\endgroup$ – Kornpob Bhirombhakdi Dec 28 '19 at 18:00
  • $\begingroup$ Reasonably new, yeah. The first reliable TeV observations were of the Crab in 1989 (ui.adsabs.harvard.edu/abs/1989ApJ...342..379W/abstract), and the Crab is an extremely bright gamma-ray target relative to other PWNe. $\endgroup$ – HDE 226868 Dec 30 '19 at 15:09

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