Line: 1 to 1  

 
Changed:  
< <  CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries  
> >  cbwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binaries  
Deleted:  
< <  
RMKI Virgo group (Hungary, Budapest)Motivations  
Line: 10 to 9  
Motivations  
Changed:  
< <  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:  
 
Changed:  
< < 
 
> > 
 
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 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.
 
Changed:  
< <  In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/grqc/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 cbwavesdesc.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/grqc/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 cbwavesdesc.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
 
Changed:  
< < 
 
> > 
 
 
Line: 43 to 44  
 
Changed:  
< <  The generated job description files can be submitted to condor clusters by launchin the command:
 
> >  The generated job description files can be submitted to condor clusters by launching the command:
 
 
Line: 52 to 53  
1) CBC pipelines  
Changed:  
< <  We have started by the investigation of nonspinning, 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 nonspinning, 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, nonspinning motions and waveformsWe constructed a nonspinning 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
 
Changed:  
< <  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  
Changed:  
< <  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  
Changed:  
< <  According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity Ã\x{fffd}Âµ=0.40.7.  
> >  According to our investigations circularization happens but a tiny eccentricity is retained by binaries with initial eccentricity ε=0.40.7.  
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 Ã\x{fffd}Âµ=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 
Line: 1 to 1  

 
Line: 16 to 16  
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.  
In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/grqc/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 cbwavesdesc.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:  
< < 
 
> > 
 
Changed:  
< <  
> >  
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 cutoff of the data usual analysis pipelines but its value is at will.  
Added:  
> >  
Download
 
Line: 81 to 82  
Changed:  
< <  According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity ε=0.40.7.  
> >  According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity Ã\x{fffd}Âµ=0.40.7.  
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 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 Ã\x{fffd}Âµ=0.4 is indicated at 40Hz frequency cut. [Here the overlap of our purely circular and eccentric templetes were determined.]  
2) Burst pipelines  
Line: 95 to 96  
Orbital evolution of an eccentric binary and the associated waveform  
Changed:  
< <  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  
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  
Line: 1 to 1  

 
Changed:  
< <  CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binariesRMKI Virgo group (Hungary, Budapest)  
> > 
 
Added:  
> >  RMKI Virgo group (Hungary, Budapest)  
MotivationsThe 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 methodThe 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:  
< < 
 
> > 
 
In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/grqc/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 cbwavesdesc.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
 
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.  
> >  
Changed:  
< <  The generated job description files can be submitted to condor clusters by launchin the command:
 
> >  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 cutoff of the data usual analysis pipelines but its value is at will.  
Download
 
Changed:  
< < 
The simulation
The simulationThe input parameters for the simulations are the
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 cutoff 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  
> > 
 
Changed:  
< <  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.
 
Changed:  
< <  Circular, nonspinning waveformsWe started with the construction of a nonspinning 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: 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:
 
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
 
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 = (rminrmax)/(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:  
> >  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.]  
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.  
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.  
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:
Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.
Template bank generationThe methodWe generate the templates in the following way:
As an example:
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=0.40.7.  
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 pregenerated templates from this bank.  
> >  
Changed:  
< <  Questions, problems
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
 
> > 
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 cutoff 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.'''
ResultsWe 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, nonspinning waveformsWe started with the construction of a nonspinning 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: The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.
Eccentric waveforms, frequency modulationDue 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 = (rminrmax)/(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: 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):
Effect of spin, amplitude modulationIn 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).
The high modulation is clearly visible in both cases.
Generic spinning, eccentric waveformsHaving armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.
 
> >  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:  
> > 
Orbital evolution of an eccentric binary and the associated waveform  
Changed:  
< <  
> >  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.  
> >  
Changed:  
< <  Template bank generationThe method  
> > 
Orbital evolution of an eccentric double spinning binary and the associated waveform  
Changed:  
< <  We generate the templates in the following way:
 
> >  m1=24, m2=8, ε0=0.8, s1=s2=1, δ1=45°, δ2=135° , D=2.5 10^23 m  
Changed:  
< <  As an example:  
> >  
Changed:  
< <  The idea of an offline template bank  
> > 
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 pregenerated templates from this bank.  
> > 
The time dependence of the eccentricity and the satisfaction of the energy conservation  
Changed:  
< <  Questions, problems
 
> > 
Line: 1 to 1  

 
Changed:  
< <  Spinning and eccentric inspiral waveforms  RMKI Virgo group (Hungary, Budapest)  
> >  CBwaves: A C++ code producing physically adequate precise waveforms for spinning and eccentric binariesRMKI Virgo group (Hungary, Budapest)  
Changed:  
< <  The targetOur 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.
 
The method  
Changed:  
< <  We use the results of Kidder http://xxx.lanl.gov/abs/grqc/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.
In determining the motion of the bodies and the waveforms yielded the setup proposed by Kidder http://xxx.lanl.gov/abs/grqc/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 cbwavesdesc.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:
Download
 
Changed:  
< <  For more details see: http://www.kfki.hu/~vasuth/CBwaves.pdf  
> >  The simulation
 
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.  
> >  
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, nonspinning waveforms  
Changed:  
< <  We started with the construction of a nonspinning 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:  
> >  We started with the construction of a nonspinning 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:  
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 = (rminrmax)/(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:  
> >  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 = (rminrmax)/(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:  
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).  
Line: 60 to 79  
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:  
Line: 75 to 94  
 
Changed:  
< <  As an example:  
> >  As an example:  
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 pregenerated 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 pregenerated templates from this bank.
Questions, problems
The simulationThe input parameters for the simulations are the
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 cutoff 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.'''
ResultsWe 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, nonspinning waveformsWe started with the construction of a nonspinning 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: The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.
Eccentric waveforms, frequency modulationDue 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 = (rminrmax)/(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: 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):
Effect of spin, amplitude modulationIn 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).
The high modulation is clearly visible in both cases.
Generic spinning, eccentric waveformsHaving armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.
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:
Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.
Template bank generationThe methodWe generate the templates in the following way:
As an example:
The idea of an offline template bankSince 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 pregenerated templates from this bank.  
Questions, problems

Line: 1 to 1  

Added:  
> > 
Spinning and eccentric inspiral waveforms  RMKI Virgo group (Hungary, Budapest)
The targetOur 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 methodWe use the results of Kidder http://xxx.lanl.gov/abs/grqc/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 simulationThe input parameters for the simulations are the
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 cutoff 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.'''
ResultsWe 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, nonspinning waveformsWe started with the construction of a nonspinning 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:The slow rise in the amplitude and frequency is observable, results of earlier studies are nicely reproduced.
Eccentric waveforms, frequency modulationDue 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 = (rminrmax)/(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: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):
Effect of spin, amplitude modulationIn 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).
The high modulation is clearly visible in both cases.
Generic spinning, eccentric waveformsHaving armed with all the machinery developed so far we are ready to produce some completely general spinning, eccentric templates best describing physical reality.
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:
Ther has remaind quite a non negligible eccentricity even at the very end of the inspiral phase.
Template bank generationThe methodWe generate the templates in the following way:
As an example:
The idea of an offline template bankSince 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 pregenerated templates from this bank.
Questions, problems
