# What are realistic and unrealistic values for the high energy gamma ray spectral indices of pulsar wind nebulae?

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?

• 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.) Dec 27, 2019 at 21:54