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Additional features

We here list the features added after the publication of arXiv:2207.06910.

Developed by Francesco Iacovelli and Michele Mancarella.

Extension of TaylorF2 down to the Kerr ISCO of the remnant BH

The TaylorF2_RestrictedPN waveform can be extended up to the Kerr ISCO of the remnant BH (rather than assuming it to be a Schwarzschild BH), computed as in arXiv:2108.05861 (see Appendix C in particular), with the fits from arXiv:1605.01938. This can be done thanks to the which_ISCO flag as follows:

mywf = waveforms.TaylorF2_RestrictedPN(which_ISCO='Kerr')

Implementation of a function to compute the waveform overlap

We added a function to compute the overlap between two waveforms on two sets of event parameters. This is defined as

$${\rm overlap}(h_1, h_2) = \frac{(h_1|h_2)}{\sqrt{(h_1|h_1)(h_2|h_2)}} \quad {\rm with}\quad (h_1|h_2) = 4 {\rm Re}\int_{f_{\rm min}}^{f_{\rm max}} \frac{\tilde{h}_1(f) \tilde{h}_2(f)}{S_n(f)} {\rm d}f$$

with $h_i$ being the signal as a function of the parameters, the tilde indicates the Fourier transform, $(h_1|h_2)$ denoting the standard scalar product, and $S_n(f)$ being the detector power spectral density (PSD).

This can be computed both from a GWSignal object or a DetNet object as

overlap = myNet.WFOverlap(WF1, WF2, Params1, Params2)

with WF1 and WF2 being two waveform objects and Params1 and Params2 being tow dictionaries containing the parameters of the events (as the standard inputs of the SNR or FisherMatr functions). This will return an array with the overlaps of the two waveforms on the two sets of parameters, with the overlap being 1 in case of perfect match.

Addition of the spin-induced quadrupole coefficient due to tidal effects to TaylorF2

The TaylorF2_RestrictedPN waveform can include the spin-induced quadrupole coefficient as a function the dimensionless tidal deformability, computed as in Eq. (15) of arXiv:1608.02582 with coeffs from third row of Table I. This can be done thanks to the use_QuadMonTid flag as follows:

mywf = waveforms.TaylorF2_RestrictedPN(is_tidal=True, use_QuadMonTid=True)

Notice the is_tidal flag has to be set to True for this to work (the spin-induced quadrupole coefficient for a BH is 1).

Implementation of a TEOBResumSPA waveform model wrapper

We added a wrapper to use the TEOBResumSPA waveform model of the TEOBResumS family, available on Bitbucket here, see arXiv:2104.07533, arXiv:2012.00027, arXiv:2001.09082, arXiv:1904.09550, arXiv:1806.01772, arXiv:1506.08457, arXiv:1406.6913. This is a frequency-domain waveform model which can be used both for BBH, BNS and NSBH binaries, including contribution of higher-order modes and tidal effects. It can be used simply as

mywf = waveforms.TEOBResumSPA_WF()

The flag is_tidal=True can be used if willing to include tidal effects, and the argument modes can be used to specify which modes to include in the analysis. It has to be a list of 2-elements lists containig the l and m of the desired modes (in this order), as e.g.

mywf = waveforms.TEOBResumSPA_WF(modes=[[2,1], [2,2]])

In this case the waveform includes the dominant quadrupole (l=2, m=2) mode plus the sub-dominant (l=2, m=1) mode. The default is to include all the modes up to l=4, i.e. modes=[[2,1], [2,2], [3,1], [3,2], [3,3], [4,1], [4,2], [4,3], [4,4]]

The implementation matches the one used in the examples available here.

When using this waveform model, derivatives are computed using numerical differentiation (finite differences).

To use this model in the calculate_forecasts_from_catalog.py script, set --wf_model='TEOBResumSPA' for the BBH version, or --wf_model='TEOBResumSPA_tidal' to include tidal effects.

Implementation of functions to compute the relative orientation and distance between detectors

We added a function to compute the relative orientation of two detectors with respect to the great circle that joins them. This can be used as

angle = utils.ang_btw_dets_GC(det_1, det_2)

with det_1 and det_2 being two dictionaries containing the latitude ('lat'), longitude ('long') and orientation (xax) of the two detectors (in degrees), as the ones given in the detectors dictionary present in the gwfastGlobals.py module.

To compute their great circle distance we added the function

dist_GC = utils.dist_btw_dets_GC(det_1, det_2)

whose output is given in kilometers.

We further added a function to compute the great circle chord length between two detectors

dist_GC = utils.dist_btw_dets_Chord(det_1, det_2)

whose output is again given in kilometers.