HAP Workshop 2014 on data analysis for indirect dark matter searches

Tutorials - Tuesday

The Toy Model

In the following, we will consider a toy model, namely a sphere (radius 0.2 kpc) of constant dark matter density 150 GeV/cm³ that is located at a distance of 8.5 kpc from Earth.  We fix the annihilation cross section to 3·10^-26 cm³s^-1 and the mass of the DM particles to M=500 GeV.

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Task 1: Calculation of Annihilation Rates and Fluxes 

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1. Calculate the DM annihilation rate (per day) in a volume as big as the Earth assuming a local dark matter density of 0.3 GeV/cm³.
2. What is the annihilation rate (per s) in the volume of the toy model if DM consists of Majorana particles?
3. How does the annihilation rate change when DM consists of Dirac particles?
4. Assume that the branching fraction for annihilation into two photons of energy M is 10^-4. What would be the flux of 500 GeV photons from the toy model (in cm^-2 s^-1) at the location of the Earth if the total annihilation rate would come from a point-like source (and not a sphere of radius 0.2 kpc)? Assume an experimental energy resolution of 20% (i.e. 100 GeV) and compare with the Crab Nebula flux in the range between 400 and 600 GeV.

Hints:

• 1 pc = 1 parsec = 3.08·10¹⁶ m
• Earth's radius is 6371 km
• For so-called Majorana particles, particles and antiparticles are identical. For Dirac particles they are distinct.
• The Crab Nebula is the standard candle of gamma-ray astronomy. Its differential flux at 500 GeV is about 1.74e-10 cm^-2 s^-1 TeV^-1.

Answers: Talk and root script

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Task 2: Work with DarkSUSY

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In the following, it is assumed that you have the virtual machine (with Linux) running and that you work in the directory HAPworkshop_Day2_DarkSUSY

1. Use DarkSUSY to run over 4 MSUGRA benchmark models and to plot the annihilation spectrum
   • Have a look at the file dstest-isasugra-hapws.mod, containing a number of benchmark models.
   • Run the program dstest-isasugra-hapws which reads the file dstest-isasugra.mod and processes the models. Store the output in a log file (./dstest-isasugra-hapws >& bm.log)
   • Inspect the log file and count how many models survived.
   • Run the script parseoutput.pl (./parseoutput.pl bm.log) on the log file to get the photon energy spectrum for any surviving models, which will be stored in an ascii file called              bm.log.model.<i>.dat
   • Use the script plot_spectrum.C to plot the annihilation spectra from this output file. Calculate the number of photons (i) above 1 GeV, (ii) above 10 GeV, and (iii) above 100 GeV. What is the average photon energy above those three threshold energies?
   • Overplot the photon spectrum for the process of dark matter annihilating into up or down (anti-)quarks, given by:
      
     

      

     with    ,  , and the parameters:

      

     a = -1.5

     b = 0.047

     c = -8.7

     d = 9.14

     e = -10.3
     Repeat the calculation of photon counts and of average photon energies. Compare the two spectra. Which spectrum will be easier to detect with a gamma-ray detector?
2. Perform a parameter scan: 
   • Inspect the file dstest-isasugra-hapws-scan.mod containing various msugra models (5 parameters)
   • Run dstest-isasugra-hapws-scan and keep the output (./dstest-isasugra-hapws-scan >& scan.log)
   • Run parseoutput_scan.pl (./parseoutput_scan.pl scan.log) on the log file which produces scan.log.model.dat . The three columns contain <sigmav> (cm³s^-1), tan(beta) and neutralino mass (GeV).
   • Plot <sigmav> vs neutralino mass using plot_scan.C which runs on scan.log.model.dat.
   • A scan with finer binning has been prepared (takes several hours to run), use sigmavmass_finer.dat as the input file for plot_scan.C to plot the results of this scan
   • Generate own set of models using GenMod.C (choose the parameter ranges and binning) - this will overwrite the previous version of dstest-isasugra-hapws-scan.mod, which is saved as dstest-isasugra-hapws-scan.mod_orig for comparison. Repeat the steps above.

Answers: Talk and root script with input file