Obs

The obs.py module is a collection of observables, which are suitable to detect anisotropies in the arrival directions of cosmic rays.

Cosmic ray observables

obs.energy_energy_correlation(vec, energy, vec_roi, alpha_max=0.25, nbins=10, **kwargs)

Calculates the Energy-Energy-Correlation (EEC) of a given dataset for a given ROI.

Parameters

• vec – arrival directions of CR events shape=(3, n)

• energy – energies of CR events in [EeV]

• vec_roi – position of ROI center shape=(3,)

• alpha_max – radial extend of ROI in radians

• nbins – number of angular bins in ROI

• kwargs –

  additional named arguments

  • bin_type: indicates if binning is linear in alpha (‘lin’)

    or with equal area covered per bin (‘area’)

  • e_ref: indicates if the ‘mean’ or the ‘median’ is taken for the average energy

  • ref_mode: indicates if ‘e_ref’ is taken within ‘bin’ or the whole ‘roi’

  • verbose: if False, dont print warnings

Returns

omega_mean: mean values of EEC (size: nbins)

Returns

alpha_bins: angular binning (size: nbins)

Returns

ncr_bin: average number of CR in each angular bin (size: nbins)

obs.thrust(p, weights=None, minimize_distances=None, ntry=1000)

Thrust observable for an array (n x 3) of 3-momenta. Returns 3 values (thrust, thrust major, thrust minor) and the corresponding axes.

Parameters

• p – 3-momenta, (3 x n) matrix with the columns holding px, py, pz

• weights – (optional) weights for each event, e.g. 1/exposure (1 x n)

• minimize_distances – Instead of maximizing the distances to n3, this will miniminze the distances to n2 axis

• ntry – number of samples for the brute force computation of thrust major

Returns

tuple consisting of the following values

• thrust, thrust major, thrust minor (shape: (3))

• thrust axis, thrust major axis, thrust minor axis (shape: (3, 3))

obs.two_pt_auto(v, bins=180, **kwargs)

Angular two-point auto correlation for a set of directions v. WARNING: Due to the vectorized calculation this function does not work for large numbers of events.

Parameters

• v – directions, (3 x n) matrix with the rows holding x,y,z

• bins – number of angular bins or np.ndarray with bin in radians

• kwargs –

  additional named arguments

  • weights : weights for each event (optional)

  • cumulative : make cumulative (default=True)

  • normalized : normalize to 1 (default=False)

Returns

bincount of size bins (or len(bins))

obs.two_pt_cross(v1, v2, bins=180, **kwargs)

Angular two-point cross correlation for two sets of directions v1, v2. WARNING: Due to the vectorized calculation this function does not work for large numbers of events.

Parameters

• v1 – directions, (3 x n1) matrix with the rows holding x,y,z

• v2 – directions, (3 x n2) matrix with the rows holding x,y,z

• bins – number of angular bins or np.ndarray with bin in radians

• kwargs –

  additional named arguments

  • weights1, weights2: weights for each event (optional)

  • cumulative: make cumulative (default=True)

  • normalized: normalize to 1 (default=False)

Returns

bincount of size bins (or len(bins))