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Gravitational Wave Data Analysis and Parameter Estimation


Gravitational waves (GWs) are ripples in spacetime created by compact binary coalescence (CBC) events, wherein compact objects (black holes, neutron stars, and white dwarfs) coalesce. The resulting object creates a wave that, upon reaching our interferometers here on Earth, causes a phase shift in the detector arms. The detectors measure this phase shift as a differential strain. That is the change in the detector arm's length, delta L(t), divided by the detector arm's baseline length (4km), L_0.  The detector measures this change as differential strain (h(t)). From this strain, the detector produces time-series data that, when analyzed, can reveal information about the objects that formed them. Information such as the mass and spin of a black hole, and therefore information about the parent stars from which they originate. With this information, we can create tests for Einstein's theory of general relativity, which was originally published in November of 1915.
There are 2 LIGO detectors in the United States, with one located in Hanford, Washington, and the other in Livingston, Alabama. The detectors function the same way as a Michelson interferometer. 

In order for the detectors to produce unbiased data, they need to be properly calibrated. Firstly, light passes through the primary reflective mirror (PRM) and encounters a beamsplitter. This splits the beam into 2 beams perpendicular with respect to the adjacent faces from which they originally entered the 4km arms. Each arm has a Fabry-Perot cavity, also sometimes called a "power recycling mirror". The first mirror (the closest to the beam splitter) has a 99% reflective coating; this allows only 1% of the incident light to enter the cavity. This causes the laser to reflect back and forth, increasing its intensity, due to the 100%-reflective test mass at the cavity's other end. Instead of making a bright spot via constructive interference where there is an integer (m) phase shift of 2(m)pi , after the split beams recombine, the light reflected inside of our cavity creates a dark spot via destructive interference where the light waves are out of phase by some odd multiple of Pi/2 (pi/2, 3pi/2, 5pi/2...). This means that the LIGO detectors use a dark spot as the default baseline that will be measured. 

As a GW passes through the detector, a strain delta(L)/L is applied to the arm, which causes an extremely small differential arm length (DARM) to change by 10^(-20) meters. This causes a phase shift where, hopefully, a bright spot is created and then exits the beamsplitter towards our readout sensor.

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