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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| static REAL8 | dEt0 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEt2 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEt4 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEt6 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft0 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft2 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft3 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft4 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft5 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft6 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Ft7 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | ep2 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | ep4 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | ep6 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEp2 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEp4 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | dEp6 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp3 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp4 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp5 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp6 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp7 (REAL8 v, expnCoeffs *ak) |
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| static REAL8 | Fp8PP (REAL8 v, expnCoeffs *ak) |
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| void | LALInspiralChooseModel (LALStatus *status, expnFunc *f, expnCoeffs *ak, InspiralTemplate *params) |
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| int | XLALInspiralChooseModel (expnFunc *f, expnCoeffs *ak, InspiralTemplate *params) |
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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()
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f: Output containing the pointers to the appropriate energy, flux, frequency, timing and phasing functions.
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ak: Output containing the PN expnasion coefficients.
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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:
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EnergyFunction *dEnergy
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FluxFunction *flux
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InspiralTiming2 *timing2
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InspiralPhasing2 *phasing2
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InspiralPhasing3 *phasing3
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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
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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.
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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.
1.9.4