Temporal truncation#
Mission lifetime constraints#
In the detector projection computation for space- and Moon-based detectors, a truncation is applied at low frequencies: specifically, if the coalescence happens at time \(t_c\), the waveform is set to zero for all times \(t\) such that
where \(t_m\) is the mission lifetime. This is an optimistic choice, since it amounts to assuming that the system at hand will merge precisely at the end of the mission’s lifetime.
This correction is not required for Earth-based detectors, since they are necessarily constrained to \(f \gtrsim 1 \text{Hz}\), and even the lightest compact objects will not take more than a few days to merge from those frequencies, which is much shorter than any sensible mission duration.
Non-CBC sources do not respect these considerations, but at the moment GWFish
does not offer strong support for them.
max_frequency_cutoff details#
This parameter allows one to truncate the waveform at a specific upper frequency. It is integrated with the mission lifetime constraint, i.e. the “coalescence time” is adapted to be the time for which the given frequency is reached.
The redefine_tf_vectors parameter#
Certain GWFish functions (see here) offer the boolean parameter redefine_tf_vectors.
In the default configuration this is False, which means that in the computation of all relevant
integrals the frequency grid is fixed to be the one from the detector definition (for examples see the list of included detectors).
For the typical CBC sources seen by ground-based detectors, this is a good approximation, since they span a wide range of frequencies.
Some low-frequency sources, on the other hand, evolve very slowly in frequency, meaning that performing the integrals on a fixed grid with bounds corresponding to the mission lifetime would result in few or even no grid points in the integration region.
If this can happen, one should activate redefine_tf_vectors: this option will compute the frequency
region in which the given signal evolves, and define custom time and frequency vectors to specifically
cover that region. This slows down evaluation, but it is necessary in some cases.