Header LALSimInspiralPrecess.h

Detailed Description

Functions to take an arbitrary waveform time series and impose the effects of causing the viewing angle to precess about a cone of L around J. The cone currently has a constant opening angle.

Author

Chris Pankow

Prototypes
int	XLALSimInspiralPrecessionRotateModes (SphHarmTimeSeries *h_lm, REAL8TimeSeries *alpha, REAL8TimeSeries *beta, REAL8TimeSeries *gam)
	Takes in the h_lm spherical harmonic decomposed modes and rotates the modes by Euler angles alpha, beta, and gamma using the Wigner D matrices. More...
int	XLALSimInspiralConstantPrecessionConeWaveformModes (SphHarmTimeSeries **h_lm_tmp, double precess_freq, double a, double phi_precess, double alpha_0, double beta_0)
	Takes in the l=2, abs(m)=2 decomposed modes as a strain time series and imposes the effect of a constant cone of precession. More...
int	XLALSimInspiralConstantPrecessionConeWaveform (REAL8TimeSeries **hp, REAL8TimeSeries **hx, SphHarmTimeSeries *h_lm, double precess_freq, double a, double phi_precess, double alpha_0, double beta_0)
	Takes in the spherical harmonic decomposed modes as a strain time series and imposes the effect of a constant cone of precession. More...
int	XLALSimInspiralOrientationMatrixForL2 (REAL8 mtx[3][3], COMPLEX16 h22, COMPLEX16 h2m2, COMPLEX16 h21, COMPLEX16 h2m1, COMPLEX16 h20)
	Determine the `‘preferred direction’' matrix for the l=2 subspace from the relevant mode decomposed h. More...
int	XLALSimInspiralOrientationMatrixDirection (REAL8 vec[3], REAL8 mtx[3][3])
	Determine a direction vector from the orientation matrix. More...
int	XLALSimInspiralPrecessionRotateModesOut (SphHarmTimeSeries **hlm_out, SphHarmTimeSeries *hlm_in, const REAL8TimeSeries *alpha, const REAL8TimeSeries *beta, const REAL8TimeSeries *gam)
	Takes in the h_lm spherical harmonic decomposed modes and rotates the modes by Euler angles alpha, beta, and gamma using the Wigner D matrices, analog to int XLALSimInspiralPrecessionRotateModes but with 2 crucial differences: More...

Function Documentation

XLALSimInspiralPrecessionRotateModes()

int XLALSimInspiralPrecessionRotateModes	(	SphHarmTimeSeries *	h_lm,
		REAL8TimeSeries *	alpha,
		REAL8TimeSeries *	beta,
		REAL8TimeSeries *	gam
	)

Takes in the h_lm spherical harmonic decomposed modes and rotates the modes by Euler angles alpha, beta, and gamma using the Wigner D matrices.

e.g.

\(\tilde{h}_{l,m}(t) = D^l_{m',m} h_{l,m'}(t)\)

Parameters

h_lm	spherical harmonic decomposed modes, modified in place
alpha	alpha Euler angle time series
beta	beta Euler angle time series
gam	gamma Euler angle time series

Definition at line 36 of file LALSimInspiralPrecess.c.

XLALSimInspiralConstantPrecessionConeWaveformModes()

int XLALSimInspiralConstantPrecessionConeWaveformModes	(	SphHarmTimeSeries **	h_lm_tmp,
		double	precess_freq,
		double	a,
		double	phi_precess,
		double	alpha_0,
		double	beta_0
	)

Takes in the l=2, abs(m)=2 decomposed modes as a strain time series and imposes the effect of a constant cone of precession.

This is accomplished by taking the axis of the binary rotational plane and rotating the Y_lm such that it appears to "precess" around a fixed J direction. Note that h_2_2 and h_22 are modified in place.

Future revisions will change the first two pointers to this: COMPLEX16TimeSeries** h_lm

and add unsigned int l

Thus the input h_lm will be considered a list of pointers to the h_lm for a given l and the appropriate action will be taken for all of the submodes.

Parameters

h_lm_tmp	(l,m) modes, modified in place
precess_freq	Precession frequency in Hz
a	Opening angle of precession cone in rads
phi_precess	initial phase in cone of L around J
alpha_0	azimuth btwn center of cone and line of sight
beta_0	zenith btwn center of cone and line of sight

Definition at line 95 of file LALSimInspiralPrecess.c.

XLALSimInspiralConstantPrecessionConeWaveform()

int XLALSimInspiralConstantPrecessionConeWaveform	(	REAL8TimeSeries **	hp,
		REAL8TimeSeries **	hx,
		SphHarmTimeSeries *	h_lm,
		double	precess_freq,
		double	a,
		double	phi_precess,
		double	alpha_0,
		double	beta_0
	)

Takes in the spherical harmonic decomposed modes as a strain time series and imposes the effect of a constant cone of precession.

The result is returned in the physical waveforms hp, hx, after they have been resummed from the modified h_lm waveforms.

NOTE: the h_lm modes will be modified in place

Parameters

hp	Output precessing plus polarization
hx	Output precessing cross polarization
h_lm	Input non-precessing (l,m) modes
precess_freq	Precession frequency in Hz
a	Opening angle of precession cone in rads
phi_precess	initial phase in cone of L around J
alpha_0	azimuth btwn center of cone and line of sight
beta_0	zenith btwn center of cone and line of sight

Definition at line 216 of file LALSimInspiralPrecess.c.

XLALSimInspiralOrientationMatrixForL2()

int XLALSimInspiralOrientationMatrixForL2	(	REAL8	mtx[3][3],
		COMPLEX16	h22,
		COMPLEX16	h2m2,
		COMPLEX16	h21,
		COMPLEX16	h2m1,
		COMPLEX16	h20
	)

Determine the `‘preferred direction’' matrix for the l=2 subspace from the relevant mode decomposed h.

Modifies mtx in place.

Parameters

mtx	3x3 orientation matrix, modified in place
h22	l=2, m=2 h sample
h2m2	l=2, m=-2 h sample
h21	l=2, m=1 h sample
h2m1	l=2, m=-1 h sample
h20	l=2, m=0 h sample

Definition at line 246 of file LALSimInspiralPrecess.c.

XLALSimInspiralOrientationMatrixDirection()

int XLALSimInspiralOrientationMatrixDirection	(	REAL8	vec[3],
		REAL8	mtx[3][3]
	)

Determine a direction vector from the orientation matrix.

NOTE: vec should be initialized to be a unit vector – its value is used, then replaced

Parameters

vec	3 dim unit vector, modified in place
mtx	3x3 orientation matrix

Definition at line 301 of file LALSimInspiralPrecess.c.

XLALSimInspiralPrecessionRotateModesOut()

int XLALSimInspiralPrecessionRotateModesOut	(	SphHarmTimeSeries **	hlm_out,
		SphHarmTimeSeries *	hlm_in,
		const REAL8TimeSeries *	alpha,
		const REAL8TimeSeries *	beta,
		const REAL8TimeSeries *	gam
	)

Takes in the h_lm spherical harmonic decomposed modes and rotates the modes by Euler angles alpha, beta, and gamma using the Wigner D matrices, analog to int XLALSimInspiralPrecessionRotateModes but with 2 crucial differences:

• leaves unaltered the input SphericalHarmonicTimeSeries
• The Wigner DMatrix rotation function XLALWignerDMatrix() is called with arguments (alpha, -beta, gamma), instead of (alpha, beta, gamma), to ensure that (h+ + i hx)(alpha,beta,gamma)=Sum_{lmm'} Y_lm(0,0) D_mm'(alpha,beta,gamma) h_lm'(0,0,0)

Parameters

hlm_out	spherical harmonic decomposed modes, output
hlm_in	spherical harmonic decomposed modes, input
alpha	alpha Euler angle time series
beta	beta Euler angle time series
gam	gamma Euler angle time series

Definition at line 353 of file LALSimInspiralPrecess.c.