6.11. J-factors to fluxes

Note

This section treats the conversion to fluxes/intensities of 1D runs. See Section 7.7 for similarly converting 2D J-factor maps to flux per pixel/intensity maps.

The flux from a single source or from the Galactic halo within a solid angle \(\Delta\Omega\) can be computed in two manners:

  1. Computing the differential energy spectrum for a fixed J-factor or solid angle \(\Delta\Omega\):

    This is done by CLUMPY’s -z module (see Section Section 7):

    $ clumpy -z -D; clumpy -z -i clumpy_params_z.txt
    

    This first generates a default parameter file, and then the \(\gamma\)-ray flux energy spectrum for a source at redshift \(z=0\) and J-factor \(J = 10^{20}\,{\rm GeV}^2{\rm ~cm}^{-5}\). If ROOT is installed, the following plot is shown:

    _images/zD-1.png

    Fig. 6.27 CLUMPY’s -z module to compute flux energy spectra for a given J-factor.

  2. Computing a flux (differential or integrated in energy) as a function of a varying J-factor or solid angle \(\Delta\Omega\):

    This is done by CLUMPY’s -g2 or -h2 modules (see Section 7), depending of considering Galactic DM or a (list of) user-defined halo(s). Here, the user may choose to plot the differential flux or the integrated flux,

    \[\Phi_{\gamma,\nu}(E_{\rm min},E_{\rm max};\,\psi,\theta,\Delta\Omega) = \int\limits_{E_{\rm min}}^{E_{\rm max}}\frac{{\rm d} \Phi_{\gamma,\nu}}{{\rm d} E}(E,\psi,\theta,\Delta\Omega)\, {\rm d}E\,.\]

    Note

    The option gSIM_IS_WRITE_FLUXMAPS = True must be enabled here.

    For the example of the flux from Galactic DM within a solid angle of \(\Delta\Omega\) of an instrument pointed toward the Galactic anti-center \((\psi_0, \theta_0) = (\pi, 0)\):

    $ clumpy -g2 -D; clumpy -g2 -i clumpy_params_g2.txt
    

If ROOT is installed, the following plot of the output data is shown:

_images/g2D-2.png

Fig. 6.28 CLUMPY’s -g2 with default parameters to compute the flux (here: integrated in energy) from Galactic DM as a function of the integration radius \(\alpha_{\rm int}\) of the search cone \(\Delta\Omega\).

Using

$ clumpy -h2 -D; clumpy -h2 -i clumpy_params_h2.txt

produces analogous plots for the remote haloes defined in the $CLUMPY/data/list_generic.txt example file (see Section 7 and the Quick start tutorial):

_images/h2D-flux.png

Fig. 6.29 CLUMPY’s -h2 module with default parameters to compute the flux (here: integrated in energy) from user-defined haloes as a function of the integration radius \(\alpha_{\rm int}\).

In addition to these two possibilies, the -g3/-g4 or -h3 modules can be used analogous to -g2 or -h2 to compute the intensities from Galactic DM or individual halo objects. For example,

$ clumpy -h3 -D; clumpy -h3 -i clumpy_params_h3.txt

compares the intensity profiles of the Abell Cluster and a mock dSphG halo:

_images/h3D-intensities.png

Fig. 6.30 CLUMPY’s -h3 module with default parameters to compute \({\rm d}\Phi/{\rm d}\Omega\) (here: integrated in energy) as a function of the distance \(\theta\) from the halo centre.