INTERFEROMETER. Albert Abraham Michelson Michelson Interferometer (1852-1931)
Possibility of detecting CHRISTODOULOU MEMORY of GRAVITATIONAL WAVES by using LISA (Laser...
1
Possibility of detecting CHRISTODOULOU MEMORY of GRAVITATIONAL WAVES by using LISA (Laser Interferometer Space Antenna) •Thus, the final form of the memory is •One advantage that LISA will have over ground-based observatories like LIGO is no low- frequency seismic noise disturbances. •LISA’s frequency band and long arm length will allow it to achieve much greater signal-to-noise ratio than LIGO. •Using A FORTRAN 77 programming simulation, our code will be used to compare against an earlier code written by Olga Petrova and analytic work by Gary Stange. Acknowledgement I would like to show my gratitude to Dr. Dan Kennefick and Arkansas Center for Space and Planetary Sciences for allowing me the opportunity to work on this project. Special thanks to NASA and REU for funding. Photos and information from: LISA -- Probing the Universe with Gravitational Waves, Version 1.0, January 19, 2007 and http://lisa.nasa.gov/index.html LISA’s quest includes: 1. observation of binary systems of black holes, neutron stars, and white dwarves in our Milky Way galaxy. 2. observation of binary systems involving super-massive black holes (SMBH) in distant galaxies 3. the search for gravitational wave emission from the Big Bang period. 4. testing Einstein's relativity theories. COMPUTER MODELLING • The time taken for a binary system to coalesce from an orbital radius “a” to a common center is where is the reduced mass of the binary system, and M is its total mass. • The mathematical form of the Christodoulou Memory is then given by where r is the effective distance between Earth and the binary system, and is the angle of orientation of the system as seen by the observer. • In the calculation, M is considered to be 10 6 solar mass and to be 1 solar mass. is given a value of 90 degrees. Key Features of LISA •First dedicated space-based gravitational wave observatory consisting of three spacecrafts 5 million km apart from each other • Will use advanced laser interferometry to directly measure gravitational waves • Can detect variations in its own spatial dimensions of 5 X 10 -14 m, only 5 times the diameter of a nucleus!! • Able to detect very low-frequency band waves; from 0.1 mHZ to 100 mHz PHYSICS in action • Einstein’s Theory of General Relativity predicts that masses in motion generate waves that travel through space-time at the speed of light • The flux of such waves from a system itself generates a change in the gravitational field which propagates like a wave • This “wave of a gravitational wave” is referred to as the Christodoulou Memory. We will investigate whether LISA will be able to detect this interesting second- ι ι t r c M μ = h(t) 2 2 4 11 2 3 5 sin 18 sin 1 4 1 5G 32 3 2 3 4 5 256 5 μM G a c = t 18 17 4 1 5G 32 3 4 11 2 3 5 t r c M M = h(t) c 5 a 4 The signal shown here is the sum of the gravitational waveform and simulated LISA noise disturbances. The waveform stands up well above the noise indicating a high signal-to- noise ratio. This graph of h(t) against t uses FORTRAN 77 to show what may happen at the final stage of coalescence of the binary system. The model is yet to be fully completed.
Transcript of Possibility of detecting CHRISTODOULOU MEMORY of GRAVITATIONAL WAVES by using LISA (Laser...
Possibility of detecting CHRISTODOULOU MEMORY of GRAVITATIONAL WAVES by using
LISA (Laser Interferometer Space Antenna)
•Thus, the final form of the memory is
•One advantage that LISA will have over ground-based observatories like LIGO is no low- frequency seismic noise disturbances. •LISA’s frequency band and long arm length will allow it to achieve much greater signal-to-noise ratio than LIGO.
•Using A FORTRAN 77 programming simulation, our code will be used to compare against an earlier code written by Olga Petrova and analytic work by Gary Stange.
AcknowledgementI would like to show my gratitude to Dr. Dan Kennefick and Arkansas Center for Space and Planetary Sciences for allowing me the opportunity to work on this project. Special
thanks to NASA and REU for funding. Photos and information from: LISA -- Probing the Universe with
Gravitational Waves, Version 1.0, January 19, 2007 and http://lisa.nasa.gov/index.html
LISA’s quest includes:1. observation of binary systems of black holes, neutron stars, and white dwarves in our Milky Way galaxy. 2. observation of binary systems involving super-massive black holes (SMBH) in distant galaxies3. the search for gravitational wave emission from the Big Bang period.4. testing Einstein's relativity theories.
COMPUTER MODELLING• The time taken for a binary system to coalesce from an orbital radius “a” to a common center is
where is the reduced mass of the binary system, and M is its total mass. • The mathematical form of the Christodoulou Memory is then given by
where r is the effective distance between Earth and the binary system, and is the angle of orientation of the system as seen by the observer.
• In the calculation,M is considered to be106 solar mass and to be 1 solar mass. is given a value of 90 degrees.
Key Features of LISA•First dedicated space-based gravitational wave observatory consisting of three spacecrafts 5 million km apart from each other• Will use advanced laser interferometry to directly measure gravitational waves• Can detect variations in its own spatial dimensions of 5 X 10-14 m, only 5 times the diameter of a nucleus!! • Able to detect very low-frequency band waves; from 0.1 mHZ to 100 mHz
PHYSICS in action• Einstein’s Theory of General Relativity predicts that masses in motion generate waves that travel through space-time at the speed of light• The flux of such waves from a system itself generates a change in the gravitational field which propagates like a wave• This “wave of a gravitational wave” is referred to as the Christodoulou Memory. We will investigate whether LISA will be able to detect this interesting second-order wave.
ιι
trc
Mμ=h(t) 2
2
411
235sin
18
sin1
4
1
5G
32
3
23
45
256
5
μMG
ac=t
18
174
1
5G
32
3411
235
trc
MM=h(t)
c5a4
The signal shown here is the sum of the gravitational waveform and simulated LISA noise disturbances. The waveform stands up well above the noise indicating a high signal-to-noise ratio.
This graph of h(t) against t uses FORTRAN 77 to show what may happen at the final stage of coalescence of the binary system. The model is yet to be fully completed.
