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Dependence on primary cosmic ray flux





In [1]:



    


import matplotlib.pyplot as plt
import numpy as np

#import solver related modules
from MCEq.core import MCEqRun
import mceq_config as config
#import primary model choices
import crflux.models as pm

Create an instance of an MCEqRun class. Most options are defined in the mceq_config module, and do not require change. Look into mceq_config.py or use the documentation.

If the initialization succeeds it will print out some information according to the debug level.





In [2]:



    


mceq_run = MCEqRun(
#provide the string of the interaction model
interaction_model='SIBYLL2.3c',
#primary cosmic ray flux model
#support a tuple (primary model class (not instance!), arguments)
primary_model=(pm.HillasGaisser2012, "H3a"),
# Zenith angle in degrees. 0=vertical, 90=horizontal
theta_deg=0.0
)



    


















    






MCEqRun::set_interaction_model(): SIBYLL23C
ParticleManager::_init_default_tracking(): Initializing default tracking categories (pi, K, mu)
MCEqRun::set_density_model(): Setting density profile to CORSIKA ('BK_USStd', None)
MCEqRun::set_primary_model(): HillasGaisser2012 H3a

Solve and store results

This code below computes fluxes of neutrinos, averaged over all directions, for different primary models.





In [4]:



    


# Bump up the debug level to see what the calculation is doing
config.debug_level = 2



    











In [5]:



    


#Define equidistant grid in cos(theta)
angles = np.arccos(np.linspace(1,0,11))*180./np.pi

#Power of energy to scale the flux
mag = 3

#obtain energy grid (nver changes) of the solution for the x-axis of the plots
e_grid = mceq_run.e_grid

p_spectrum_flux = []

#Initialize empty grid
for  pmcount, pmodel in enumerate([(pm.HillasGaisser2012,'H3a'),
                                   (pm.HillasGaisser2012,'H4a'),
                                   (pm.GaisserStanevTilav,'3-gen'),
                                   (pm.GaisserStanevTilav,'4-gen')]):
    
    mceq_run.set_primary_model(*pmodel)
    
    flux = {}
    for frac in ['mu_conv','mu_pr','mu_total',
                 'numu_conv','numu_pr','numu_total',
                 'nue_conv','nue_pr','nue_total','nutau_pr']:
        flux[frac] = np.zeros_like(e_grid)
        

    #Sum fluxes, calculated for different angles
    for theta in angles:
        mceq_run.set_theta_deg(theta)
        mceq_run.solve()
        #_conv means conventional (mostly pions and kaons)
        flux['mu_conv'] += (mceq_run.get_solution('conv_mu+', mag)
                           + mceq_run.get_solution('conv_mu-', mag))

        # _pr means prompt (the mother of the muon had a critical energy
        # higher than a D meson. Includes all charm and direct resonance
        # contribution)
        flux['mu_pr'] += (mceq_run.get_solution('pr_mu+', mag)
                         + mceq_run.get_solution('pr_mu-', mag))

        # total means conventional + prompt
        flux['mu_total'] += (mceq_run.get_solution('total_mu+', mag)
                            + mceq_run.get_solution('total_mu-', mag))

        # same meaning of prefixes for muon neutrinos as for muons
        flux['numu_conv'] += (mceq_run.get_solution('conv_numu', mag)
                             + mceq_run.get_solution('conv_antinumu', mag))

        flux['numu_pr'] += (mceq_run.get_solution('pr_numu', mag)
                           + mceq_run.get_solution('pr_antinumu', mag))

        flux['numu_total'] += (mceq_run.get_solution('total_numu', mag)
                              + mceq_run.get_solution('total_antinumu', mag))

        # same meaning of prefixes for electron neutrinos as for muons
        flux['nue_conv'] += (mceq_run.get_solution('conv_nue', mag)
                            + mceq_run.get_solution('conv_antinue', mag))

        flux['nue_pr'] += (mceq_run.get_solution('pr_nue', mag)
                          + mceq_run.get_solution('pr_antinue', mag))

        flux['nue_total'] += (mceq_run.get_solution('total_nue', mag)
                             + mceq_run.get_solution('total_antinue', mag))


        # since there are no conventional tau neutrinos, prompt=total
        flux['nutau_pr'] += (mceq_run.get_solution('total_nutau', mag)
                            + mceq_run.get_solution('total_antinutau', mag))

    #average the results
    for frac in ['mu_conv','mu_pr','mu_total',
                 'numu_conv','numu_pr','numu_total',
                 'nue_conv','nue_pr','nue_total','nutau_pr']:
        flux[frac] = flux[frac]/float(len(angles))
        
    p_spectrum_flux.append((flux,mceq_run.pmodel.sname,mceq_run.pmodel.name))



    


















    






MCEqRun::set_primary_model(): HillasGaisser2012 H3a
MCEqRun::set_theta_deg(): Zenith angle   0.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1033.81g/cm2
MCEqRun::solve(): for 588 integration steps.
solv_MKL_sparse(): Performance:   2.77ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.64sec
MCEqRun::set_theta_deg(): Zenith angle  25.84
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1148.37g/cm2
MCEqRun::solve(): for 652 integration steps.
solv_MKL_sparse(): Performance:   2.74ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.79sec
MCEqRun::set_theta_deg(): Zenith angle  36.87
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1291.43g/cm2
MCEqRun::solve(): for 730 integration steps.
solv_MKL_sparse(): Performance:   2.64ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.94sec
MCEqRun::set_theta_deg(): Zenith angle  45.57
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1475.12g/cm2
MCEqRun::solve(): for 830 integration steps.
solv_MKL_sparse(): Performance:   2.78ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.31sec
MCEqRun::set_theta_deg(): Zenith angle  53.13
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1719.54g/cm2
MCEqRun::solve(): for 962 integration steps.
solv_MKL_sparse(): Performance:   3.02ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.91sec
MCEqRun::set_theta_deg(): Zenith angle  60.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2060.60g/cm2
MCEqRun::solve(): for 1142 integration steps.
solv_MKL_sparse(): Performance:   3.41ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.91sec
MCEqRun::set_theta_deg(): Zenith angle  66.42
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2569.28g/cm2
MCEqRun::solve(): for 1402 integration steps.
solv_MKL_sparse(): Performance:   2.83ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.97sec
MCEqRun::set_theta_deg(): Zenith angle  72.54
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 3407.46g/cm2
MCEqRun::solve(): for 1806 integration steps.
solv_MKL_sparse(): Performance:   2.73ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.94sec
MCEqRun::set_theta_deg(): Zenith angle  78.46
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 5037.05g/cm2
MCEqRun::solve(): for 2496 integration steps.
solv_MKL_sparse(): Performance:   2.77ms/iteration
MCEqRun::solve(): time elapsed during integration:  6.91sec
MCEqRun::set_theta_deg(): Zenith angle  84.26
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 9422.43g/cm2
MCEqRun::solve(): for 3837 integration steps.
solv_MKL_sparse(): Performance:   2.84ms/iteration
MCEqRun::solve(): time elapsed during integration: 10.91sec
MCEqRun::set_theta_deg(): Zenith angle  90.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 36583.25g/cm2
MCEqRun::solve(): for 7445 integration steps.
solv_MKL_sparse(): Performance:   5.36ms/iteration
MCEqRun::solve(): time elapsed during integration: 39.90sec
MCEqRun::set_primary_model(): HillasGaisser2012 H4a
MCEqRun::set_theta_deg(): Zenith angle   0.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1033.81g/cm2
MCEqRun::solve(): for 588 integration steps.
solv_MKL_sparse(): Performance:   3.34ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.97sec
MCEqRun::set_theta_deg(): Zenith angle  25.84
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1148.37g/cm2
MCEqRun::solve(): for 652 integration steps.
solv_MKL_sparse(): Performance:   3.06ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.01sec
MCEqRun::set_theta_deg(): Zenith angle  36.87
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1291.43g/cm2
MCEqRun::solve(): for 730 integration steps.
solv_MKL_sparse(): Performance:   3.05ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.24sec
MCEqRun::set_theta_deg(): Zenith angle  45.57
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1475.12g/cm2
MCEqRun::solve(): for 830 integration steps.
solv_MKL_sparse(): Performance:   3.02ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.51sec
MCEqRun::set_theta_deg(): Zenith angle  53.13
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1719.54g/cm2
MCEqRun::solve(): for 962 integration steps.
solv_MKL_sparse(): Performance:   4.42ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.26sec
MCEqRun::set_theta_deg(): Zenith angle  60.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2060.60g/cm2
MCEqRun::solve(): for 1142 integration steps.
solv_MKL_sparse(): Performance:   3.95ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.53sec
MCEqRun::set_theta_deg(): Zenith angle  66.42
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2569.28g/cm2
MCEqRun::solve(): for 1402 integration steps.
solv_MKL_sparse(): Performance:   3.61ms/iteration
MCEqRun::solve(): time elapsed during integration:  5.06sec
MCEqRun::set_theta_deg(): Zenith angle  72.54
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 3407.46g/cm2
MCEqRun::solve(): for 1806 integration steps.
solv_MKL_sparse(): Performance:   3.01ms/iteration
MCEqRun::solve(): time elapsed during integration:  5.45sec
MCEqRun::set_theta_deg(): Zenith angle  78.46
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 5037.05g/cm2
MCEqRun::solve(): for 2496 integration steps.
solv_MKL_sparse(): Performance:   3.19ms/iteration
MCEqRun::solve(): time elapsed during integration:  7.97sec
MCEqRun::set_theta_deg(): Zenith angle  84.26
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 9422.43g/cm2
MCEqRun::solve(): for 3837 integration steps.
solv_MKL_sparse(): Performance:   3.00ms/iteration
MCEqRun::solve(): time elapsed during integration: 11.52sec
MCEqRun::set_theta_deg(): Zenith angle  90.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 36583.25g/cm2
MCEqRun::solve(): for 7445 integration steps.
solv_MKL_sparse(): Performance:   5.83ms/iteration
MCEqRun::solve(): time elapsed during integration: 43.44sec
MCEqRun::set_primary_model(): GaisserStanevTilav 3-gen
MCEqRun::set_theta_deg(): Zenith angle   0.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1033.81g/cm2
MCEqRun::solve(): for 588 integration steps.
solv_MKL_sparse(): Performance:   2.93ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.73sec
MCEqRun::set_theta_deg(): Zenith angle  25.84
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1148.37g/cm2
MCEqRun::solve(): for 652 integration steps.
solv_MKL_sparse(): Performance:   3.61ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.37sec
MCEqRun::set_theta_deg(): Zenith angle  36.87
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1291.43g/cm2
MCEqRun::solve(): for 730 integration steps.
solv_MKL_sparse(): Performance:   3.29ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.41sec
MCEqRun::set_theta_deg(): Zenith angle  45.57
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1475.12g/cm2
MCEqRun::solve(): for 830 integration steps.
solv_MKL_sparse(): Performance:   4.35ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.63sec
MCEqRun::set_theta_deg(): Zenith angle  53.13
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1719.54g/cm2
MCEqRun::solve(): for 962 integration steps.
solv_MKL_sparse(): Performance:   3.48ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.36sec
MCEqRun::set_theta_deg(): Zenith angle  60.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2060.60g/cm2
MCEqRun::solve(): for 1142 integration steps.
solv_MKL_sparse(): Performance:   3.62ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.14sec
MCEqRun::set_theta_deg(): Zenith angle  66.42
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2569.28g/cm2
MCEqRun::solve(): for 1402 integration steps.
solv_MKL_sparse(): Performance:   3.40ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.77sec
MCEqRun::set_theta_deg(): Zenith angle  72.54
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 3407.46g/cm2
MCEqRun::solve(): for 1806 integration steps.
solv_MKL_sparse(): Performance:   3.18ms/iteration
MCEqRun::solve(): time elapsed during integration:  5.74sec
MCEqRun::set_theta_deg(): Zenith angle  78.46
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 5037.05g/cm2
MCEqRun::solve(): for 2496 integration steps.
solv_MKL_sparse(): Performance:   3.80ms/iteration
MCEqRun::solve(): time elapsed during integration:  9.50sec
MCEqRun::set_theta_deg(): Zenith angle  84.26
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 9422.43g/cm2
MCEqRun::solve(): for 3837 integration steps.
solv_MKL_sparse(): Performance:   4.20ms/iteration
MCEqRun::solve(): time elapsed during integration: 16.14sec
MCEqRun::set_theta_deg(): Zenith angle  90.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 36583.25g/cm2
MCEqRun::solve(): for 7445 integration steps.
solv_MKL_sparse(): Performance:   6.14ms/iteration
MCEqRun::solve(): time elapsed during integration: 45.69sec
MCEqRun::set_primary_model(): GaisserStanevTilav 4-gen
MCEqRun::set_theta_deg(): Zenith angle   0.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1033.81g/cm2
MCEqRun::solve(): for 588 integration steps.
solv_MKL_sparse(): Performance:   3.29ms/iteration
MCEqRun::solve(): time elapsed during integration:  1.94sec
MCEqRun::set_theta_deg(): Zenith angle  25.84
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1148.37g/cm2
MCEqRun::solve(): for 652 integration steps.
solv_MKL_sparse(): Performance:   3.37ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.21sec
MCEqRun::set_theta_deg(): Zenith angle  36.87
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1291.43g/cm2
MCEqRun::solve(): for 730 integration steps.
solv_MKL_sparse(): Performance:   3.76ms/iteration
MCEqRun::solve(): time elapsed during integration:  2.76sec
MCEqRun::set_theta_deg(): Zenith angle  45.57
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1475.12g/cm2
MCEqRun::solve(): for 830 integration steps.
solv_MKL_sparse(): Performance:   3.71ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.09sec
MCEqRun::set_theta_deg(): Zenith angle  53.13
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 1719.54g/cm2
MCEqRun::solve(): for 962 integration steps.
solv_MKL_sparse(): Performance:   3.16ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.05sec
MCEqRun::set_theta_deg(): Zenith angle  60.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2060.60g/cm2
MCEqRun::solve(): for 1142 integration steps.
solv_MKL_sparse(): Performance:   3.25ms/iteration
MCEqRun::solve(): time elapsed during integration:  3.72sec
MCEqRun::set_theta_deg(): Zenith angle  66.42
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 2569.28g/cm2
MCEqRun::solve(): for 1402 integration steps.
solv_MKL_sparse(): Performance:   3.38ms/iteration
MCEqRun::solve(): time elapsed during integration:  4.75sec
MCEqRun::set_theta_deg(): Zenith angle  72.54
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 3407.46g/cm2
MCEqRun::solve(): for 1806 integration steps.
solv_MKL_sparse(): Performance:   5.08ms/iteration
MCEqRun::solve(): time elapsed during integration:  9.19sec
MCEqRun::set_theta_deg(): Zenith angle  78.46
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 5037.05g/cm2
MCEqRun::solve(): for 2496 integration steps.
solv_MKL_sparse(): Performance:   4.47ms/iteration
MCEqRun::solve(): time elapsed during integration: 11.16sec
MCEqRun::set_theta_deg(): Zenith angle  84.26
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 9422.43g/cm2
MCEqRun::solve(): for 3837 integration steps.
solv_MKL_sparse(): Performance:   4.50ms/iteration
MCEqRun::solve(): time elapsed during integration: 17.30sec
MCEqRun::set_theta_deg(): Zenith angle  90.00
MCEqRun::solve(): Launching euler solver
MCEqRun::_calculate_integration_path(): X_surface = 36583.25g/cm2
MCEqRun::solve(): for 7445 integration steps.
solv_MKL_sparse(): Performance:   8.72ms/iteration
MCEqRun::solve(): time elapsed during integration: 64.94sec

Plot with matplotlib





In [6]:



    


#get path of the home directory + Desktop
desktop = os.path.join(os.path.expanduser("~"),'Desktop')



    











In [8]:



    


for pref, lab in [('numu_',r'\nu_\mu'), 
                  ('mu_',r'\mu'), 
                  ('nue_',r'\nu_e')
                 ]:
    plt.figure(figsize=(4.5, 3.5))
    for (flux, p_sname, p_name), col in zip(p_spectrum_flux,['k','r','g','b','c']):
        
        plt.loglog(e_grid, flux[pref + 'total'], color=col, ls='-', lw=2.5,
                  label=p_sname, alpha=0.4)
        plt.loglog(e_grid, flux[pref + 'conv'], color=col, ls='--', lw=1,
                   label='_nolabel_')
        plt.loglog(e_grid, flux[pref + 'pr'], color=col,ls='-', lw=1, 
                   label='_nolabel_')
    plt.xlim(50,1e9)
    plt.ylim(1e-5,1)
    plt.xlabel(r"$E_{{{0}}}$ [GeV]".format(lab))
    plt.ylabel(r"$\Phi_{" + lab + "}$ (E/GeV)$^{" + str(mag) +" }$" + 
               "(cm$^{2}$ s sr GeV)$^{-1}$")
    plt.legend(loc='upper right')
    plt.tight_layout()

    # Uncoment if you want to save the plot
    # plt.savefig(os.path.join(desktop,pref + 'flux.pdf'))

Save as in ASCII file for other types of processing





In [12]:



    


for (flux, p_sname, p_name) in p_spectrum_flux:
    np.savetxt(open(os.path.join(desktop, 'numu_flux_' + p_sname + '.txt'),'w'),
    zip(e_grid, 
        flux['mu_conv'],flux['mu_pr'],flux['mu_total'],
        flux['numu_conv'],flux['numu_pr'],flux['numu_total'],
        flux['nue_conv'],flux['nue_pr'],flux['nue_total'],
        flux['nutau_pr']),
    fmt='%6.5E',
    header=('lepton flux scaled with E**{0}. Order (E, mu_conv, mu_pr, mu_total, ' +
            'numu_conv, numu_pr, numu_total, nue_conv, nue_pr, nue_total, ' +
            'nutau_pr').format(mag)
    )

Content source: afedynitch/MCEq

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