Difference: CBwavesPresentation (1 vs. 6)

Revision 62011-06-23 - IstvanRacz

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META TOPICPARENT name="CBwaves"


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CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries
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cbwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries
 
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RMKI Virgo group (Hungary, Budapest)


Motivations

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Motivations

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The cbwaves software calculates the gravitational waves emitted by generic configuration compact binary systems but it is also capable to follow the time evolution of open systems. Our principal aim was to construct highly accurate templates describing waveforms generated by inspiral spinning and eccentric binaries within the PN ramework. We have already carried out some preliminary investigations measuring the effectivity of the template banks, applied currently by the CBC working groups, in recognizing them.
>
>
The cbwaves software is to determine the gravitational waves emitted by generic configuration compact binary systems but it is also capable to follow the time evolution of open binary systems. Our principal aim was to construct highly accurate templates describing waveforms generated by inspiral spinning and eccentric binaries within the PN framework. We have already carried out some preliminary investigations testing the effectivity of the template banks, applied currently by the CBC working groups, in recognizing spinning and eccentric injections.

In short terms our aims are to:

 
  • provide an effective tool for the parameter estimation group
  • if possible increase the sensitivity of the CBC searching pipelines
Changed:
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<
  • apply it in modelling some of the burst type events
>
>
  • apply it in modelling some of the burst type events.
 

The method

Changed:
<
<
The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary value of the eccentricity --- by direct integration of the equation of motion of the bodies.
  • The waveforms are calculated in time domain (BUT)
  • The waveforms can also be determined in frequency domain by using implemented FFT.
  • The spin weighted (s=-2) spherical harmonics of the waveforms are also be provided.
>
>
The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary value of the eccentricity --- by direct integration of the equation of motion of the bodies. The radiation field is determined simultaneously in the time domain by evaluating the analytic waveforms relevant for the yielded motion of the sources.
  • Hence the waveforms are calculated in time domain (BUT)
  • the waveforms can also be determined in frequency domain by using implemented FFT
  • the spin weighted (s=-2) spherical harmonics of the waveforms are also be provided.
 
Changed:
<
<
In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 --- which is known to be accurate upto 2.5 PN order had been applied. A short summary of the implemented methods and expressions and the specifications of the parameters can be found in the cbwaves-desc.pdf file located in the doc directory coming together with the software. The equations of motion are integrated numerically. The applied method is known to be 4th order accurate. The radiation field is determined in the time domain by evaluating the analitic waveforms relevant for the yielded motion of the sources.
>
>
In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 --- which is known to be accurate upto 2.5 PN order had been applied. A short summary of the implemented methods and expressions and the specifications of the parameters can be found in the cbwaves-desc.pdf file located in the doc directory coming together with the software. The equations of motion are integrated numerically. The applied method is known to be 4th order accurate.
 

The most important input parameters

  • r --------- the initial (minimal) separation of the two bodies [m]
  • m1,m2 ---- the mass of the two bodies [m]
  • ε --------- the initial eccentricity
Changed:
<
<
  • S1,S2 ----- the spin of the objects is s_A, where A = 1,2 and s_A = sqrt(s_Ax^2+s_Ay^2+s_Az^2). [For a black hole 0. < s_A/mA^2 < 1, for most neutron star models 0 < s_A/mA^2 < 0.7]
>
>
  • s1,s2 ----- the spin of the objects is sA, where A = 1,2 and sA^2 = sAx^2+sAy^2+sAz^2. [For a black hole 0. < sA < 1, for most neutron star models 0 < sA < 0.7. The spin vectors are given as: SA=sA?mA^2.]
 
  • θ1,θ2 --- the orientation of the spin vectors SA with respect to the orbital angular momentum L

Line: 43 to 44
 
  • The examples/cbwgen.pl perl executable is an example script which demonstrates how to generate .ini files
  • The .des files for submission to condor clusters.
Changed:
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<
The generated job description files can be submitted to condor clusters by launchin the command:
  • condor_submit <name of .des file>
    To contact the maintainers or send patches please us the following email address:
    <cbwaves@rmki.kfki.hu> :::::: Please feel free to use it but do not forget to refer to "cbwaves" :-).
>
>
The generated job description files can be submitted to condor clusters by launching the command:
  • condor_submit <name of .des file>
    To contact the maintainers or send patches please us the following email address:
    <cbwaves@rmki.kfki.hu> :::::: Please feel free to use it but do not forget to refer to "cbwaves" :-).
 


Some of the characteristic results

Line: 52 to 53
 

1) CBC pipelines

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We have started by the investigation of non-spinning, circular templates and examined, in a modest step by step approach, the effect on the yielded waveforms by turning on eccentricity and the inclusion of spins for more generic configurations.
>
>
We have started with the investigation of non-spinning, circular binaries and examined latter the changes of the motion and the yielded waveforms while eccentricity and spins were turned on in a step by step approach.
 

Circular, non-spinning motions and waveforms

We constructed a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. Samples for a circular non spinning orbit and for the emitted waveform with slow rise in the amplitude and frequency:

Line: 65 to 66
 Due to the effect of radiation the motion tends to circularize, however not as fast as generally believed. The temporary value of the eccentricity can always be determined by the relation
  • ε = (rmin-rmax)/(rmin+rmax),
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<
<
where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points.
>
>
where rmin and rmax denote the minimum and maximum distances between the two masses, i.e. the distances at the turning points.
  Due to non negligible eccentricity the waveforms suffer a frequency modulation. [On the figures below only a short section of the evolution is indicated.]

Effect of spin, amplitude modulation

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In a case of the inclusion of spins the emitted gravitational wave acquires a considerable large amplitude modulation. On the left panel only one of the bodie possesses spin (s1=0.7) which is aligned with the orbital angular momentum. On the right panel the both of the bodies possess spins (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3). The modulation is clearly visible in both cases.
>
>
In a case of the inclusion of spins the emitted gravitational wave acquires a considerable large amplitude modulation. On the left panel only one of the bodies possesses spin (s1=0.7) which is aligned with the orbital angular momentum. On the right panel the both of the bodies possess spins (s1=0.7, θ1=0; s2=0.4, θ2=π/3). The modulation is clearly visible in both cases.
 
Line: 82 to 83
 
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According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity \x{fffd}µ=0.4-0.7.
>
>
According to our investigations circularization happens but a tiny eccentricity is retained by binaries with initial eccentricity ε=0.4-0.7.
 
Changed:
<
<
For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity \x{fffd}µ=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]
>
>
For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity ε=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templates were determined.]
 

2) Burst pipelines

Revision 52011-06-23 - IstvanRacz

Line: 1 to 1
 
META TOPICPARENT name="CBwaves"


Line: 57 to 57
  We constructed a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. Samples for a circular non spinning orbit and for the emitted waveform with slow rise in the amplitude and frequency:
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circ-orbit.png circ-wave.png
>
>
 


Eccentric motions and waveforms ---> frequency modulation

Line: 69 to 69
  Due to non negligible eccentricity the waveforms suffer a frequency modulation. [On the figures below only a short section of the evolution is indicated.]
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<
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ecc-orbit.png ecc-wave.png
>
>
 

Effect of spin, amplitude modulation

In a case of the inclusion of spins the emitted gravitational wave acquires a considerable large amplitude modulation. On the left panel only one of the bodie possesses spin (s1=0.7) which is aligned with the orbital angular momentum. On the right panel the both of the bodies possess spins (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3). The modulation is clearly visible in both cases.

Changed:
<
<
strong-spin.png strong-double-spin.png
>
>
 

Generic waveforms for spinning and eccentric binaries

As indicated above the cbwaves software is capable to determine the evolutions and the yielded waveforms of completely general spinning, eccentric binaries. The simultaneous effect of amplitude and frequency modulation is transparent! Fitting analytic formulas to all the possible waveforms seems not to be feasible.

Changed:
<
<
spin-ecc-wave1.png spin-ecc-wave2.png
>
>
  According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity \x{fffd}µ=0.4-0.7.
Changed:
<
<
spinecceffect.jpg ecc-evolution-massranges.jpg
>
>
  For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity \x{fffd}µ=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]
Changed:
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<
ecc-snrdropp.jpg
>
>
 

2) Burst pipelines

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An indication that one can use our cbwaves software to investigate burst type events generated by an open binary.
>
>
An indication that one can use our cbwaves software to modell single burst type events emitted by an open binary.
 
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h_plus_orbit.JPG h_plus.JPG
>
>
 

Orbital evolution of an eccentric binary and the associated waveform

m1=24, m2=8, ε=0.8, D=2.5 10^23 m

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nospin-ecc-early-orbit.jpg nospin-ecc-early-h.jpg
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>
 
Changed:
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nospin-ecc-late-orbit.jpg nospin-ecc-late-h.jpg
>
>
 

Orbital evolution of an eccentric double spinning binary and the associated waveform

m1=24, m2=8, ε=0.8, s1=s2=1, θ1=45, θ2=135 , D=2.5 10^23 m

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doublespin-ecc-early-orbit.jpg doublespin-ecc-early-h.jpg
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>
 
Changed:
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doublespin-ecc-late-orbit.jpg doublespin-ecc-late-h.jpg
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The Foruier spectrum of the early part of the evolution of an eccentric binary

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nospin-ecc-early-h-fft.jpg
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The time dependence of the eccentricity and the satisfaction of the energy conservation

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ecc-evolution-frequency.jpg
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>

Revision 42011-06-23 - MatyasVasuth

Line: 1 to 1
 
META TOPICPARENT name="CBwaves"


Line: 16 to 16
 
  • apply it in modelling some of the burst type events

The method

Changed:
<
<
The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary of value the eccentricity --- by direct integration of the equation of motion of the bodies.
>
>
The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary value of the eccentricity --- by direct integration of the equation of motion of the bodies.
 
  • The waveforms are calculated in time domain (BUT)
  • The waveforms can also be determined in frequency domain by using implemented FFT.
  • The spin weighted (s=-2) spherical harmonics of the waveforms are also be provided.

In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 --- which is known to be accurate upto 2.5 PN order had been applied. A short summary of the implemented methods and expressions and the specifications of the parameters can be found in the cbwaves-desc.pdf file located in the doc directory coming together with the software. The equations of motion are integrated numerically. The applied method is known to be 4th order accurate. The radiation field is determined in the time domain by evaluating the analitic waveforms relevant for the yielded motion of the sources.

The most important input parameters

Changed:
<
<
  • r ------- # the initial (minimal) separation of the two bodies [m]
  • m1,m2 ------- # the mass of the two bodies [m]
  • ε ------- # the initial eccentricity
  • s1,s2 ------- # the spin of the objects is s_A, where A = 1,2 and s_A = sqrt(s_Ax^2+s_Ay^2+s_Az^2). [For a black hole 0. < s_A < 1, for most neutron star models 0 < s_A < 0.7]
  • δ1,δ2 ------- # the orientation of the spin vectors SA with respect to the orbital angular momentum L
>
>
  • r --------- the initial (minimal) separation of the two bodies [m]
  • m1,m2 ---- the mass of the two bodies [m]
  • ε --------- the initial eccentricity
  • S1,S2 ----- the spin of the objects is s_A, where A = 1,2 and s_A = sqrt(s_Ax^2+s_Ay^2+s_Az^2). [For a black hole 0. < s_A/mA^2 < 1, for most neutron star models 0 < s_A/mA^2 < 0.7]
  • θ1,θ2 --- the orientation of the spin vectors SA with respect to the orbital angular momentum L
 
Changed:
<
<
SourceFrame.JPG
>
>
  The simulation starts at the turning point of the radial motion determined by the minimal distance of the bodies. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data usual analysis pipelines but its value is at will.
Added:
>
>
 

Download

tgz cbwaves-1.0.0-4.tgz
rpm (src) cbwaves-1.0.0-4.src.rpm
Line: 81 to 82
  spin-ecc-wave1.png spin-ecc-wave2.png
Changed:
<
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According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity ε=0.4-0.7.
>
>
According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity \x{fffd}µ=0.4-0.7.
  spinecceffect.jpg ecc-evolution-massranges.jpg
Changed:
<
<
For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity ε=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]
>
>
For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity \x{fffd}µ=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]
  ecc-snrdropp.jpg

2) Burst pipelines

Line: 95 to 96
 h_plus_orbit.JPG h_plus.JPG

Orbital evolution of an eccentric binary and the associated waveform

Changed:
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<
m1=24, m2=8, ε0=0.8, D=2.5 10^23 m
>
>
m1=24, m2=8, ε=0.8, D=2.5 10^23 m
  nospin-ecc-early-orbit.jpg nospin-ecc-early-h.jpg

nospin-ecc-late-orbit.jpg nospin-ecc-late-h.jpg

Orbital evolution of an eccentric double spinning binary and the associated waveform

Changed:
<
<
m1=24, m2=8, ε0=0.8, s1=s2=1, δ1=45, δ2=135 , D=2.5 10^23 m
>
>
m1=24, m2=8, ε=0.8, s1=s2=1, θ1=45, θ2=135 , D=2.5 10^23 m
  doublespin-ecc-early-orbit.jpg doublespin-ecc-early-h.jpg

Revision 32011-06-23 - IstvanRacz

Line: 1 to 1
 
META TOPICPARENT name="CBwaves"
Changed:
<
<

CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries

RMKI Virgo group (Hungary, Budapest)

>
>


CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries

 
Added:
>
>

RMKI Virgo group (Hungary, Budapest)


 

Motivations

The cbwaves software calculates the gravitational waves emitted by generic configuration compact binary systems but it is also capable to follow the time evolution of open systems. Our principal aim was to construct highly accurate templates describing waveforms generated by inspiral spinning and eccentric binaries within the PN ramework. We have already carried out some preliminary investigations measuring the effectivity of the template banks, applied currently by the CBC working groups, in recognizing them.

Line: 12 to 17
 

The method

The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary of value the eccentricity --- by direct integration of the equation of motion of the bodies.

Changed:
<
<
  • The waveforms are calculated in time domain
  • They also can be determined in frequency domain by using the implemented FFT.
  • The spin weighted (s=-2) spherical harmonics expansion of the radiative field is also given.
>
>
  • The waveforms are calculated in time domain (BUT)
  • The waveforms can also be determined in frequency domain by using implemented FFT.
  • The spin weighted (s=-2) spherical harmonics of the waveforms are also be provided.
  In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 --- which is known to be accurate upto 2.5 PN order had been applied. A short summary of the implemented methods and expressions and the specifications of the parameters can be found in the cbwaves-desc.pdf file located in the doc directory coming together with the software. The equations of motion are integrated numerically. The applied method is known to be 4th order accurate. The radiation field is determined in the time domain by evaluating the analitic waveforms relevant for the yielded motion of the sources.
Added:
>
>

The most important input parameters

  • r ------- # the initial (minimal) separation of the two bodies [m]
  • m1,m2 ------- # the mass of the two bodies [m]
  • ε ------- # the initial eccentricity
  • s1,s2 ------- # the spin of the objects is s_A, where A = 1,2 and s_A = sqrt(s_Ax^2+s_Ay^2+s_Az^2). [For a black hole 0. < s_A < 1, for most neutron star models 0 < s_A < 0.7]
  • δ1,δ2 ------- # the orientation of the spin vectors SA with respect to the orbital angular momentum L
 
Changed:
<
<
The examples/cbwgen.pl perl executable is an example script which demonstrates how to generate .ini files and .des files for submission to condor clusters.
>
>
SourceFrame.JPG
 
Changed:
<
<
The generated job description files can be submitted to condor clusters by launchin the command:
  • condor_submit <name of .des file>
>
>
The simulation starts at the turning point of the radial motion determined by the minimal distance of the bodies. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data usual analysis pipelines but its value is at will.
 

Download

tgz cbwaves-1.0.0-4.tgz
rpm (src) cbwaves-1.0.0-4.src.rpm
rpm (x86_64) cbwaves-1.0.0-4.x86_64.rpm
Changed:
<
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rpm (i386) cbwaves-1.0.0-4.i386.rpm

The simulation

nospin-ecc-early-h.jpg nospin-ecc-early-h-fft.jpg

ecc-evolution-frequency.jpg ecc-evolution-frequency-validity.jpg

The simulation

The input parameters for the simulations are the

  1. the relative distance of the two mass
  2. the relative velocity
  3. m1, m2
  4. s1, s2
  5. phi1, phi2, the angle of the spins respect to the orbital angular momentum

The initial relative speed is determined as if the two mass were orbiting on a Keplerian orbit around each other, having epsilon eccentricity.The simulation starts in one of the turning point of the radial motion. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data analysis pipelines.

'''Due to the direct integration of motion, the simulation of any spin, angle and eccentricity configuration is possible with this methd.'''

Results

>
>
rpm (i386)

cbwaves-1.0.0-4.i386.rpm

 
Changed:
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We have started the investigation step by step from basic non spinning, circular templates and examined the effect of various configurations on the produced waveform.
>
>
A sample .ini file can be found in the etc directory of the package.
  • The examples/cbwgen.pl perl executable is an example script which demonstrates how to generate .ini files
  • The .des files for submission to condor clusters.
 
Changed:
<
<

Circular, non-spinning waveforms

We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png

The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.

>
>
The generated job description files can be submitted to condor clusters by launchin the command:
  • condor_submit <name of .des file>
    To contact the maintainers or send patches please us the following email address:
    <cbwaves@rmki.kfki.hu> :::::: Please feel free to use it but do not forget to refer to "cbwaves" :-).


Some of the characteristic results

1) CBC pipelines

We have started by the investigation of non-spinning, circular templates and examined, in a modest step by step approach, the effect on the yielded waveforms by turning on eccentricity and the inclusion of spins for more generic configurations.

Circular, non-spinning motions and waveforms

We constructed a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. Samples for a circular non spinning orbit and for the emitted waveform with slow rise in the amplitude and frequency:

circ-orbit.png circ-wave.png


Eccentric motions and waveforms ---> frequency modulation

 
Changed:
<
<

Eccentric waveforms, frequency modulation

>
>
Due to the effect of radiation the motion tends to circularize, however not as fast as generally believed. The temporary value of the eccentricity can always be determined by the relation
  • ε = (rmin-rmax)/(rmin+rmax),
 
Changed:
<
<
Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png
>
>
where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points.
 
Changed:
<
<
Due to non negligible eccentricity the waveforms suffer a frequency modulation, demonstrated in the figure below. The orbit of an eccentric binaries and their produced waveform (extract only, not showing the full evolution):
>
>
Due to non negligible eccentricity the waveforms suffer a frequency modulation. [On the figures below only a short section of the evolution is indicated.]
  ecc-orbit.png ecc-wave.png
Deleted:
<
<
 

Effect of spin, amplitude modulation

Changed:
<
<
In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).
>
>
In a case of the inclusion of spins the emitted gravitational wave acquires a considerable large amplitude modulation. On the left panel only one of the bodie possesses spin (s1=0.7) which is aligned with the orbital angular momentum. On the right panel the both of the bodies possess spins (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3). The modulation is clearly visible in both cases.
  strong-spin.png strong-double-spin.png
Changed:
<
<
The high modulation is clearly visible in both cases.

Generic spinning, eccentric waveforms

>
>

Generic waveforms for spinning and eccentric binaries

 
Changed:
<
<
Having armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.
>
>
As indicated above the cbwaves software is capable to determine the evolutions and the yielded waveforms of completely general spinning, eccentric binaries. The simultaneous effect of amplitude and frequency modulation is transparent! Fitting analytic formulas to all the possible waveforms seems not to be feasible.
  spin-ecc-wave1.png spin-ecc-wave2.png
Changed:
<
<
The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:

spin-ecc-ecc-develop.png

Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.

Template bank generation

The method

We generate the templates in the following way:

  1. Generate the template and downsampling it to 4096 Hz
  2. Since the longest template is only around 14 sec, we allocate a 65536 long memory area.
  3. The template is then copied into this memory area shifting it to to end, so state as Swarzschild ISCO is always at the very end of the memory area. The rest of the area is filled with zero.
  4. Using the usual overlap function the overlap is calculated between two neighbouring template. (No scan on tc or phic)

As an example: spacing.jpg overlap.jpg

The idea of an offline template bank

>
>
According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity ε=0.4-0.7.
 
Changed:
<
<
Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.
>
>
spinecceffect.jpg ecc-evolution-massranges.jpg
 
Changed:
<
<

Questions, problems

  1. Since it is not possible to describe these templates with closed analytical formula, it is difficult to determine the optimal placing and the number of templates necessary for a given minimal match. The only method is a brute-force trial-and-error. Does anybody have a better idea ?
  2. The generation of the templates takes quite a lot of time. What about pre-generating a template bank with high enough tmeplate density, so it can just be downloadad and downsampled according to the actual PSD of the data if necessary. It would safe quite a lot of time !
  3. When calculating the overlap how we should deal with tc and phic ? Does it have a meaning in this case ? (I guess not).
  4. Is there any widely accepted method how to deal with seven parameter (m1,m2, ecc, s1,s2, phi1, phi2) template bank ? Or how to reduce the number of dimension in parameter space ?
  5. Should we try to figure out the optimal spacing or simple equal steps in parameter space in enough ?

The simulation

>
>
For those who are interested in the effect of this tiny eccentricity on the SNR it might be informative to look at the figure below indicating the loss of SNR where on the horizontal axis the value of the retained part of the initial eccentricity ε=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]
 
Changed:
<
<
The input parameters for the simulations are the
  1. the relative distance of the two mass
  2. the relative velocity
  3. m1, m2
  4. s1, s2
  5. phi1, phi2, the angle of the spins respect to the orbital angular momentum
>
>
ecc-snrdropp.jpg

2) Burst pipelines

 
Changed:
<
<
The initial relative speed is determined as if the two mass were orbiting on a Keplerian orbit around each other, having epsilon eccentricity.The simulation starts in one of the turning point of the radial motion. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data analysis pipelines.

'''Due to the direct integration of motion, the simulation of any spin, angle and eccentricity configuration is possible with this methd.'''

Results

We have started the investigation step by step from basic non spinning, circular templates and examined the effect of various configurations on the produced waveform.

Circular, non-spinning waveforms

We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png

The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.

Eccentric waveforms, frequency modulation

Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png

Due to non negligible eccentricity the waveforms suffer a frequency modulation, demonstrated in the figure below. The orbit of an eccentric binaries and their produced waveform (extract only, not showing the full evolution):

ecc-orbit.png ecc-wave.png

Effect of spin, amplitude modulation

In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).

strong-spin.png strong-double-spin.png

The high modulation is clearly visible in both cases.

Generic spinning, eccentric waveforms

Having armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.

spin-ecc-wave1.png spin-ecc-wave2.png

>
>
An indication that one can use our cbwaves software to investigate burst type events generated by an open binary.
 
Changed:
<
<
The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:
>
>
h_plus_orbit.JPG h_plus.JPG

Orbital evolution of an eccentric binary and the associated waveform

 
Changed:
<
<
spin-ecc-ecc-develop.png
>
>
m1=24, m2=8, ε0=0.8, D=2.5 10^23 m
 
Changed:
<
<
Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.
>
>
nospin-ecc-early-orbit.jpg nospin-ecc-early-h.jpg
 
Changed:
<
<

Template bank generation

The method

>
>
nospin-ecc-late-orbit.jpg nospin-ecc-late-h.jpg

Orbital evolution of an eccentric double spinning binary and the associated waveform

 
Changed:
<
<
We generate the templates in the following way:
  1. Generate the template and downsampling it to 4096 Hz
  2. Since the longest template is only around 14 sec, we allocate a 65536 long memory area.
  3. The template is then copied into this memory area shifting it to to end, so state as Swarzschild ISCO is always at the very end of the memory area. The rest of the area is filled with zero.
  4. Using the usual overlap function the overlap is calculated between two neighbouring template. (No scan on tc or phic)
>
>
m1=24, m2=8, ε0=0.8, s1=s2=1, δ1=45, δ2=135 , D=2.5 10^23 m
 
Changed:
<
<
As an example: spacing.jpg overlap.jpg
>
>
doublespin-ecc-early-orbit.jpg doublespin-ecc-early-h.jpg
 
Changed:
<
<

The idea of an offline template bank

>
>
doublespin-ecc-late-orbit.jpg doublespin-ecc-late-h.jpg

The Foruier spectrum of the early part of the evolution of an eccentric binary

 
Changed:
<
<
Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.
>
>
nospin-ecc-early-h-fft.jpg

The time dependence of the eccentricity and the satisfaction of the energy conservation

 
Changed:
<
<

Questions, problems

  1. Since it is not possible to describe these templates with closed analytical formula, it is difficult to determine the optimal placing and the number of templates necessary for a given minimal match. The only method is a brute-force trial-and-error. Does anybody have a better idea ?
  2. The generation of the templates takes quite a lot of time. What about pre-generating a template bank with high enough tmeplate density, so it can just be downloadad and downsampled according to the actual PSD of the data if necessary. It would safe quite a lot of time !
  3. When calculating the overlap how we should deal with tc and phic ? Does it have a meaning in this case ? (I guess not).
  4. Is there any widely accepted method how to deal with seven parameter (m1,m2, ecc, s1,s2, phi1, phi2) template bank ? Or how to reduce the number of dimension in parameter space ?
  5. Should we try to figure out the optimal spacing or simple equal steps in parameter space in enough ?
>
>
ecc-evolution-frequency.jpg

Revision 22011-06-22 - IstvanRacz

Line: 1 to 1
 
META TOPICPARENT name="CBwaves"
Changed:
<
<

Spinning and eccentric inspiral waveforms - RMKI Virgo group (Hungary, Budapest)

>
>

CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries

RMKI Virgo group (Hungary, Budapest)

 
Changed:
<
<

The target

Our aim is to construct inspiral templates for spinning and eccentric binaries within the PN approximation and compare the performance of this template bank with existing ones.
>
>

Motivations

 
Added:
>
>
The cbwaves software calculates the gravitational waves emitted by generic configuration compact binary systems but it is also capable to follow the time evolution of open systems. Our principal aim was to construct highly accurate templates describing waveforms generated by inspiral spinning and eccentric binaries within the PN ramework. We have already carried out some preliminary investigations measuring the effectivity of the template banks, applied currently by the CBC working groups, in recognizing them.
  • provide an effective tool for the parameter estimation group
  • if possible increase the sensitivity of the CBC searching pipelines
  • apply it in modelling some of the burst type events
 

The method

Changed:
<
<
We use the results of Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 to describe the relative acceleration of the binary and the radiation field far from the source. His expressions are valid to 2.5 PN order (radiation reaction involved, higher order effects can be added later).
>
>
The cbwaves software calculates the gravitational waves emitted by generic binary neutron stars (BNSs) or binary black holes (BBHs) --- with arbitrary orientation of the spins and with arbitrary of value the eccentricity --- by direct integration of the equation of motion of the bodies.
  • The waveforms are calculated in time domain
  • They also can be determined in frequency domain by using the implemented FFT.
  • The spin weighted (s=-2) spherical harmonics expansion of the radiative field is also given.

In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 --- which is known to be accurate upto 2.5 PN order had been applied. A short summary of the implemented methods and expressions and the specifications of the parameters can be found in the cbwaves-desc.pdf file located in the doc directory coming together with the software. The equations of motion are integrated numerically. The applied method is known to be 4th order accurate. The radiation field is determined in the time domain by evaluating the analitic waveforms relevant for the yielded motion of the sources.

The examples/cbwgen.pl perl executable is an example script which demonstrates how to generate .ini files and .des files for submission to condor clusters.

The generated job description files can be submitted to condor clusters by launchin the command:

  • condor_submit <name of .des file>

Download

tgz cbwaves-1.0.0-4.tgz
rpm (src) cbwaves-1.0.0-4.src.rpm
rpm (x86_64) cbwaves-1.0.0-4.x86_64.rpm
rpm (i386) cbwaves-1.0.0-4.i386.rpm
 
Changed:
<
<
For more details see: http://www.kfki.hu/~vasuth/CBwaves.pdf
>
>

The simulation

nospin-ecc-early-h.jpg nospin-ecc-early-h-fft.jpg

 
Changed:
<
<
The equations of motion are integrated numerically with the 4th order Runge–Kutta method, and then inserted into the general expression of the radiation field. As a result we generate time domain inspiral waveforms and stop the calculations at the Schwarzschild ISCO, 6M.
>
>
ecc-evolution-frequency.jpg ecc-evolution-frequency-validity.jpg
 

The simulation

Line: 30 to 52
 We have started the investigation step by step from basic non spinning, circular templates and examined the effect of various configurations on the produced waveform.

Circular, non-spinning waveforms

Changed:
<
<
We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png
>
>
We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png
  The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.

Eccentric waveforms, frequency modulation

Changed:
<
<
Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png
>
>
Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png
  Due to non negligible eccentricity the waveforms suffer a frequency modulation, demonstrated in the figure below. The orbit of an eccentric binaries and their produced waveform (extract only, not showing the full evolution):
Line: 47 to 67
 

Effect of spin, amplitude modulation

Changed:
<
<
In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).
>
>
In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).
  strong-spin.png strong-double-spin.png
Line: 60 to 79
  spin-ecc-wave1.png spin-ecc-wave2.png
Changed:
<
<
The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:
>
>
The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:
  spin-ecc-ecc-develop.png
Line: 75 to 94
 
  1. The template is then copied into this memory area shifting it to to end, so state as Swarzschild ISCO is always at the very end of the memory area. The rest of the area is filled with zero.
  2. Using the usual overlap function the overlap is calculated between two neighbouring template. (No scan on tc or phic)
Changed:
<
<
As an example: spacing.jpg overlap.jpg
>
>
As an example: spacing.jpg overlap.jpg
 

The idea of an offline template bank

Changed:
<
<
Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.
>
>
Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.

Questions, problems

  1. Since it is not possible to describe these templates with closed analytical formula, it is difficult to determine the optimal placing and the number of templates necessary for a given minimal match. The only method is a brute-force trial-and-error. Does anybody have a better idea ?
  2. The generation of the templates takes quite a lot of time. What about pre-generating a template bank with high enough tmeplate density, so it can just be downloadad and downsampled according to the actual PSD of the data if necessary. It would safe quite a lot of time !
  3. When calculating the overlap how we should deal with tc and phic ? Does it have a meaning in this case ? (I guess not).
  4. Is there any widely accepted method how to deal with seven parameter (m1,m2, ecc, s1,s2, phi1, phi2) template bank ? Or how to reduce the number of dimension in parameter space ?
  5. Should we try to figure out the optimal spacing or simple equal steps in parameter space in enough ?

The simulation

The input parameters for the simulations are the

  1. the relative distance of the two mass
  2. the relative velocity
  3. m1, m2
  4. s1, s2
  5. phi1, phi2, the angle of the spins respect to the orbital angular momentum

The initial relative speed is determined as if the two mass were orbiting on a Keplerian orbit around each other, having epsilon eccentricity.The simulation starts in one of the turning point of the radial motion. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data analysis pipelines.

'''Due to the direct integration of motion, the simulation of any spin, angle and eccentricity configuration is possible with this methd.'''

Results

We have started the investigation step by step from basic non spinning, circular templates and examined the effect of various configurations on the produced waveform.

Circular, non-spinning waveforms

We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png

The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.

Eccentric waveforms, frequency modulation

Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png

Due to non negligible eccentricity the waveforms suffer a frequency modulation, demonstrated in the figure below. The orbit of an eccentric binaries and their produced waveform (extract only, not showing the full evolution):

ecc-orbit.png ecc-wave.png

Effect of spin, amplitude modulation

In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).

strong-spin.png strong-double-spin.png

The high modulation is clearly visible in both cases.

Generic spinning, eccentric waveforms

Having armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.

spin-ecc-wave1.png spin-ecc-wave2.png

The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:

spin-ecc-ecc-develop.png

Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.

Template bank generation

The method

We generate the templates in the following way:

  1. Generate the template and downsampling it to 4096 Hz
  2. Since the longest template is only around 14 sec, we allocate a 65536 long memory area.
  3. The template is then copied into this memory area shifting it to to end, so state as Swarzschild ISCO is always at the very end of the memory area. The rest of the area is filled with zero.
  4. Using the usual overlap function the overlap is calculated between two neighbouring template. (No scan on tc or phic)

As an example: spacing.jpg overlap.jpg

The idea of an offline template bank

Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.

 

Questions, problems

  1. Since it is not possible to describe these templates with closed analytical formula, it is difficult to determine the optimal placing and the number of templates necessary for a given minimal match. The only method is a brute-force trial-and-error. Does anybody have a better idea ?

Revision 12011-06-20 - IstvanRacz

Line: 1 to 1
Added:
>
>
META TOPICPARENT name="CBwaves"

Spinning and eccentric inspiral waveforms - RMKI Virgo group (Hungary, Budapest)

The target

Our aim is to construct inspiral templates for spinning and eccentric binaries within the PN approximation and compare the performance of this template bank with existing ones.

The method

We use the results of Kidder http://xxx.lanl.gov/abs/gr-qc/9506022 to describe the relative acceleration of the binary and the radiation field far from the source. His expressions are valid to 2.5 PN order (radiation reaction involved, higher order effects can be added later).

For more details see: http://www.kfki.hu/~vasuth/CBwaves.pdf

The equations of motion are integrated numerically with the 4th order Runge–Kutta method, and then inserted into the general expression of the radiation field. As a result we generate time domain inspiral waveforms and stop the calculations at the Schwarzschild ISCO, 6M.

The simulation

The input parameters for the simulations are the

  1. the relative distance of the two mass
  2. the relative velocity
  3. m1, m2
  4. s1, s2
  5. phi1, phi2, the angle of the spins respect to the orbital angular momentum

The initial relative speed is determined as if the two mass were orbiting on a Keplerian orbit around each other, having epsilon eccentricity.The simulation starts in one of the turning point of the radial motion. The initial orbital frequency is set to 19 Hz (as such, the emitted gravitational wave frequency is 38 Hz) due to the 40 Hz low frequency cut-off of the data analysis pipelines.

'''Due to the direct integration of motion, the simulation of any spin, angle and eccentricity configuration is possible with this methd.'''

Results

We have started the investigation step by step from basic non spinning, circular templates and examined the effect of various configurations on the produced waveform.

Circular, non-spinning waveforms

We started with the construction of a non-spinning circular waveform template bank to serve as a reference for the forthcoming studies. An examples is shown for a circular non spinning orbit and for the emitted waveform: circ-orbit.png circ-wave.png

The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.

Eccentric waveforms, frequency modulation

Due to the effect of radiation the motion tends to circularize, however no in all circumstances. The actual eccentricity of the system can always be calculated from the following equation epsi = (rmin-rmax)/(rmin+rmax). Where rmin and rmax is the minimum and maximum distance between the two mass, i.e. the distance in the turning points. This can easily be determined during simulation, and we obtain the eccentricity and its evolution during the inspiral. An example of this is shown in the picture below: ecc-during-inspiral.png

Due to non negligible eccentricity the waveforms suffer a frequency modulation, demonstrated in the figure below. The orbit of an eccentric binaries and their produced waveform (extract only, not showing the full evolution):

ecc-orbit.png ecc-wave.png

Effect of spin, amplitude modulation

In a case of spin the emitted gravitational wave suffers an amplitude modulation. This is demonstrated in the pictures. On the left picture only one of the star has spin of 0.7 and is aligned with the orbital angular momentum. On the right picture the both having spin (s1=0.7, phi1=0 ; s2=0.4, phi2=pi/3).

strong-spin.png strong-double-spin.png

The high modulation is clearly visible in both cases.

Generic spinning, eccentric waveforms

Having armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.

spin-ecc-wave1.png spin-ecc-wave2.png

The nice simultaneous effect of amplitude and frequency is very well visible! The fitting of an analytic formula to this waveform is really difficult. It is interesting to see, how the eccentricity is changing during such an inspiral:

spin-ecc-ecc-develop.png

Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.

Template bank generation

The method

We generate the templates in the following way:
  1. Generate the template and downsampling it to 4096 Hz
  2. Since the longest template is only around 14 sec, we allocate a 65536 long memory area.
  3. The template is then copied into this memory area shifting it to to end, so state as Swarzschild ISCO is always at the very end of the memory area. The rest of the area is filled with zero.
  4. Using the usual overlap function the overlap is calculated between two neighbouring template. (No scan on tc or phic)

As an example: spacing.jpg overlap.jpg

The idea of an offline template bank

Since the computation of the templates is a quite time consuming process, we plan to setup an offline template bank. The corressponding fcuntion in lalapps_inspiral would just download the pre-generated templates from this bank.

Questions, problems

  1. Since it is not possible to describe these templates with closed analytical formula, it is difficult to determine the optimal placing and the number of templates necessary for a given minimal match. The only method is a brute-force trial-and-error. Does anybody have a better idea ?
  2. The generation of the templates takes quite a lot of time. What about pre-generating a template bank with high enough tmeplate density, so it can just be downloadad and downsampled according to the actual PSD of the data if necessary. It would safe quite a lot of time !
  3. When calculating the overlap how we should deal with tc and phic ? Does it have a meaning in this case ? (I guess not).
  4. Is there any widely accepted method how to deal with seven parameter (m1,m2, ecc, s1,s2, phi1, phi2) template bank ? Or how to reduce the number of dimension in parameter space ?
  5. Should we try to figure out the optimal spacing or simple equal steps in parameter space in enough ?
 
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