1. Current Progress and Future Work  We used a Fast Fourier Transform (FFT) algorithm to model h(f) (memory function in the frequency domain). Then we divided it by LISA’s noise spectrum to get k(f) - the filter function in the frequency domain.  By the end of the program, we are planning to finish modeling k(f) and derive k(t) (filter function in the time domain) with the help of the inverse-FFT algorithm. This function will then be used for calculating the signal-to- noise ratio. Detection of Christodoulou memory from EMRIs by LISA Signal processing Olga Petrova 1, Dr. Daniel Kennefick 2 1 Worcester Polytechnic Institute, Worcester, MA 2 University of Arkansas, Fayetteville, AR Introduction  The Christodoulou memory is generated by a gravitational wave (since gravitational waves carry energy, they also have mass. The flux of this mass generates its own gravitational wave)  LISA (laser interferometer space antenna) is a joint NASA- ESA mission that will detect gravitational waves in space.  While ground-based detectors such as LIGO are unlikely to detect Christodoulou memory, it has been proposed that LISA might be able to do so. I would like to thank Dr. Daniel Kennefick for his assistance and NASA for funding the Arkansas Center for Space and Planetary Sciences REU program. Total LISA noise is shown as a dot dash line. This function represents the total noise energy in the detector at each frequency. The detector is most sensitive at frequencies where this function is smallest (between 1 and 11 milliHertz). Source: L. Barack and C. Cutler. Confusion Noise from LISA Capture Sources. http://arxiv.org/PS_cache/gr- qc/pdf/0409/0409010.pdfhttp://arxiv.org/PS_cache/gr- qc/pdf/0409/0409010.pdf This is a graph of the data representing the memory from two black holes spiraling into each other. Positive time is the time before the coalescence. The memory grows as the black holes get closer, and stays constant after they collide. Source: D. Kennefick. Prospects for detecting Christodoulou memory of gravitational waves from a coalescing compact binary and using it to measure neutron-star radii. Methodology and Calculations  We are using Thorne’s formula to estimate the memory function in the time domain h(t) with the following expression:  The LISA noise spectrum can be approximated as: where h m = 3*10 23, f 1 = 10 -3 Hz and f 2 = 10 -1 Hz.  Knowing the noise spectrum, we can construct a filter that lets through a signal while blocking as much noise as possible. The Weiner Optimal Filter for h(t) is given by:  The signal-to-noise ratio (S/N) is given by:  By looking at the S/N value, we can tell how probable is it that the signal we are looking at is in fact that of the Christodoulou memory, and not some kind of noise. (at these frequences the waves become shorter than the interferometer arm) (due to photon shot noise) (due to residual effects which perturb the spacecraft’s inertial motion) A graph of the filter function for LIGO – a ground-based laser interferometer. While this function was derived for the LIGO noise spectrum, we are expecting to get a similar filter for LISA. This filter lets through only those parts of the noisy signal which occur on the most sensitive timescale right around the time that the memory is changing most quickly. This maximises the chance of distinguishing the signal from the noise. Source: D. Kennefick. Prospects for detecting Christodoulou memory of gravitational waves from a coalescing compact binary and using it to measure neutron-star radii.