Difference: CBwavesPresentation (3 vs. 4)

Revision 42011-06-23 - MatyasVasuth

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META TOPICPARENT name="CBwaves"

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  • apply it in modelling some of the burst type events

The method

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<		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.
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>		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

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  • 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
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>
  • 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
 
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<		SourceFrame.JPG
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  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.
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Download

tgz cbwaves-1.0.0-4.tgz
rpm (src) cbwaves-1.0.0-4.src.rpm
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  spin-ecc-wave1.png spin-ecc-wave2.png
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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.
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>		According to our investigations circularisation happens but a tiny eccentricity is retained by binaries with initial eccentricity Ã\x{fffd}µ=0.4-0.7.
  spinecceffect.jpg ecc-evolution-massranges.jpg
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<		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.]
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>		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}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

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 h_plus_orbit.JPG h_plus.JPG

Orbital evolution of an eccentric binary and the associated waveform

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<		m1=24, m2=8, ε0=0.8, D=2.5 10^23 m
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>		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

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<		m1=24, m2=8, ε0=0.8, s1=s2=1, δ1=45°, δ2=135° , D=2.5 10^23 m
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>		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
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