<p>You might find these websites for your answers:</p>

<ul>
<li><a href="https://www.cv.nrao.edu/course/astr534/SynchrotronSpectrum.html" rel="nofollow noreferrer">https://www.cv.nrao.edu/course/astr534/SynchrotronSpectrum.html</a></li>
<li><a href="http://astronomy.swin.edu.au/cosmos/S/Synchrotron+Emission" rel="nofollow noreferrer">http://astronomy.swin.edu.au/cosmos/S/Synchrotron+Emission</a></li>
<li><a href="https://ui.adsabs.harvard.edu/abs/2006MNRAS.371.1441S/abstract" rel="nofollow noreferrer">https://ui.adsabs.harvard.edu/abs/2006MNRAS.371.1441S/abstract</a></li>
</ul>

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

CC BY-SA 4.0
2019-12-27T21:54:09.953Z
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.)
HDE 226868
CC BY-SA 4.0
2019-12-27T22:09:37.650Z
Are you working on the TeV halos of PWNe?
Kornpob Bhirombhakdi
CC BY-SA 4.0
2019-12-27T22:19:42.763Z
Yep, that was the project - the Crab Nebula in particular.
HDE 226868
CC BY-SA 4.0
2019-12-28T18:00:08.827Z
I think TeV halo of pwn is quite a new topic, right?
Kornpob Bhirombhakdi
CC BY-SA 4.0
2019-12-30T15:09:39.637Z
Reasonably new, yeah. The first reliable TeV observations were of the Crab in 1989 (https://ui.adsabs.harvard.edu/abs/1989ApJ...342..379W/abstract), and the Crab is an extremely bright gamma-ray target relative to other PWNe.
HDE 226868
CC BY-SA 4.0
2019-12-27T21:30:21.867Z
2019-12-27T21:30:21.867Z
Kornpob Bhirombhakdi
<p>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 <span class="math-container">$\sim$</span>1 TeV, a simple power law suffices, i.e. <span class="math-container">$\phi(E)\propto E^{\alpha}$</span>. Most power law models of the Crab find a spectral index of <span class="math-container">$\alpha\simeq-2.47$</span> (e.g. <a href="http://adsabs.harvard.edu/abs/1998ApJ...503..744H" rel="noreferrer">Hillas 1998</a>, <span class="math-container">$\alpha=-2.49\pm0.06$</span>). Using a normal analysis method on one dataset, I found <span class="math-container">$\alpha=-2.469\pm0.02248$</span>, which matches the literature values quite well.</p>

<p>Using the modified analysis method I was testing, however, I found <span class="math-container">$\alpha=-2.316\pm0.02040$</span>. 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 <span class="math-container">$\alpha=-2.316$</span> is unphysical, or reasonable.</p>

<p>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 <span class="math-container">$\alpha$</span> 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 <span class="math-container">$\alpha$</span>, what value would it need to have for me to reject the result as unphysical?</p>

<spectroscopy><nebula><pulsar><gamma-rays>
What are realistic and unrealistic values for the high energy gamma ray spectral indices of pulsar wind nebulae?
HDE 226868
# What are realistic and unrealistic values for the high energy gamma ray spectral indices of pulsar wind nebulae?

(Asked by: username_0 on 2019-08-20)

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](http://adsabs.harvard.edu/abs/1998ApJ...503..744H), $\alpha=-2.49\pm0.06$). 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?

**Tags:** spectroscopy, nebula, pulsar, gamma-rays

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## 1 answers

### Answer by username_1 on 2019-12-27. Score: 1

You might find these websites for your answers:

* <https://www.cv.nrao.edu/course/astr534/SynchrotronSpectrum.html>
* <http://astronomy.swin.edu.au/cosmos/S/Synchrotron+Emission>
* <https://ui.adsabs.harvard.edu/abs/2006MNRAS.371.1441S/abstract>

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

> **Comments:**
> **username_0**: 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.)  
> **username_1**: Are you working on the TeV halos of PWNe?  
> **username_0**: Yep, that was the project - the Crab Nebula in particular.  
> **username_1**: I think TeV halo of pwn is quite a new topic, right?  
> **username_0**: Reasonably new, yeah. The first reliable TeV observations were of the Crab in 1989 (https://ui.adsabs.harvard.edu/abs/1989ApJ...342..379W/abstract), and the Crab is an extremely bright gamma-ray target relative to other PWNe.  

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