Dark Matter JFactory Map

[katrinstreil]

The calculation of the differential J-Factor is by defintion over the line of sight ds and not over the radius dr. When integrating over dr, the integral is missing the substitution of ds: math:: \frac{d J}{d \Omega} = \int_{LoS} ds \rho(r) = \int_{\r_min}^{\r_max} dr \frac{d s}{d r} \rho(r) = \int_{\r_min}^{\r_max} dr frac{r}{sqrt{r2- d2* sin(\theta)**2}} \rho(r)

since r = sqrt{d2 + s2 -2dl cos(\theta)}, where d is the distance to the GC and \theta the separation angle. I also found the integral limits to be incorrect. Integrating from rmin = separation.rad * self.distance to rmax = self.distance accounts only for the line of sight to the object at distance. But the line of sight continues beyond it.

In my solution I included the derivative \frac{d s}{d r} in the _eval_squared method of the corresponding profile class. Therefore the parameter separation has to be passed to the method integral in the corresponding profile class, since it calls _eval_squared.

If there is any need, I can upload my script.

[github-actions[bot]]

Merci! We will respond to your issue shortly. In the meantime, try import gammapy; gammapy.song()

[Bultako]

@kstre

Thanks for spotting this !

I think that the calculation of J-Factor maps in Gammapy was introduced more as a coding exercise than as a feature to compute accurate values. For this, we know that people from the dark matter community very often uses CLUMPY, which provides precise values with rigorous calculations and multiple fine-tuning parameters.

Having said that, you're right that the definition of the differential J-factor is not correct (at least in the documentation, and this has to be fixed) and that calculation of J-factor maps could be actually done in a more proper way, even if this is not the ultimate goal of Gammapy. Could you please paste a gist link to your script or the piece of code that shows how you fix it, please? So we can continue talking on this and agree on how to proceed.

[katrinstreil]

Hi, sorry for the (very) slow response! I created a gist (https://gist.github.com/katrinstreil/eeee9f2969dbc037888f876d5f4e5b9d) with my solution in it. I modified gammapy.astro.darkmatter.profiles.py and gammapy.astro.darkmatter.utils.py to correct for the integral limits and the substitution part. In addition, there is a notebook, which computes and compares the J-Factor map with the NFW profile computed with the original and the modified code.

I would be very happy to discuss this further! https://gist.github.com/katrinstreil/eeee9f2969dbc037888f876d5f4e5b9d

[registerrier]

What is the status here @katrinstreil ?

[Astro-Kirsty]

I checked through the code and this should be closed by #4191

Therefore, I am closing this now.