Module to set the pointers to the required energy and flux functions. Normally, a user is not required to call this function to generate a waveform.
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Module to set the pointers to the required energy and flux functions. Normally, a user is not required to call this function to generate a waveform.
- Author
- Sathyaprakash, B. S.
Prototypes
LALInspiralChooseModel()
-
f:
Output containing the pointers to the appropriate energy, flux, frequency, timing and phasing functions.
-
ak:
Output containing the PN expnasion coefficients.
-
params:
Input containing binary chirp parameters.
Description
This module gives the post-Newtonian expansions and/or P-approximants to the energy, its derivative and gravitational-wave flux functions. More specifically, the static REAL8
functions below give Taylor expansions of dE/dv, and {\cal F}(v), P-approximants of e(v), dE/dv (derived from e(v)) and {\cal F}(v).
LALInspiralChooseModel
is used to set pointers to the required energy and flux functions E^{\prime}_T(v), \mathcal{F}_T(v), E^{\prime}_P(v) and \mathcal{F}_P(v), in expnFunc,
as also the GW phasing and frequency fucntions used in the various approximants to generate the waveform. More specifically pointers are set to the following functions in the structure expnFunc:
-
EnergyFunction *dEnergy
-
FluxFunction *flux
-
InspiralTiming2 *timing2
-
InspiralPhasing2 *phasing2
-
InspiralPhasing3 *phasing3
-
InspiralFrequency3 *frequency3
LALInspiralChooseModel
also outputs in ak
the last stable orbit (LSO) velocity v_\textrm{LSO} (as ak->vn
) defined by the equation E'(v_\textrm{LSO})=0, the values of the GW frequency f_\textrm{LSO}=v_\textrm{LSO}^3/(\pi m) (as ak->fn
) and time (as ak->tn
) elapsed from params->fLower
to smaller of fCutOff
and ak->fn
by evaluating the integral
\begin{equation}
t_n = t_{0} - m \int^{v_n}_{v_0} \frac{E^{\prime}(v)}{\mathcal{F}(v)} \, dv\,,
\end{equation}
where t_{0} (usually equal to zero) is the user specified starting time for the waveform when the wave frequency reaches params->fLower
and v_{0}= (\pi m f)^{1/3} (with f=<tt>params->fLower</tt>) is the velocity at time t_{0}. Note that E'(v) and {\cal F}(v) are defined in f->dEnergy
and f->flux.
Algorithm
Numerical integration is used to compute ak->tn.
Uses
LALInspiralTofV
Notes
-
See Damour, Iyer and Sathyaprakash, PRD 57, 885, 1998 for further details. Damour, Iyer and Sathyaprakash, PRD 63, 044023, 2001 is a resource paper that summarizes how to generate waveforms in different approximations to the dynamics of a compact binary under radiation reaction.
-
The Pade Approximant for the 1PN expansion is undefined as also EOB at orders less than 2PN. BCV is independent of the PN order. Spinning waveforms are only defined at the highest PN order.
Definition in file LALInspiralChooseModel.c.