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gravitational_waves

Module which holds all functions which are related to the properties of the gravitational wave.

GW 

GW(universe_i, PTA)

For a population of M black holes, calculate the per-pulsar redshift timeseries a^{(n)}(t).

Parameters:

  • `universe_i` –

    the realisation of the universe, i.e. the BH-BH population

  • `PTA` –

    The PTA configuration used to observe the GWs from the BH-BH population

compute_a 

compute_a()

Compute the a(t) timeseries.

pairwise_angular_separation 

pairwise_angular_separation(ra_rad, dec_rad)

Compute the pairwise angular separations for a set of celestial coordinates in radians.

This function takes arrays of right ascension (RA) and declination (Dec), both in radians, and returns an NxN matrix of angular separations, where N is the length of the input arrays. Each entry (i, j) in the output is the angular separation between the coordinate pair (ra_rad[i], dec_rad[i]) and (ra_rad[j], dec_rad[j]).

Parameters

ra_rad : numpy.ndarray 1D array of right ascensions in radians, of length N. dec_rad : numpy.ndarray 1D array of declinations in radians, of length N.

Returns

sep_rad : numpy.ndarray NxN matrix (2D array) of pairwise angular separations in radians.

Notes

The spherical distance formula used is:

cos(theta) = sin(dec1) * sin(dec2)
            + cos(dec1) * cos(dec2) * cos(ra1 - ra2)

where (ra1, dec1) and (ra2, dec2) are coordinate pairs in radians.

hellings_downs 

hellings_downs(θ)

Compute the Hellings–Downs function for an angle θ (in radians).

Parameters

θ : np.ndarray or float Angular separation between pulsars in radians

Returns

np.ndarray or float Hellings-Downs correlation values