Stas' notes

Neil's Comments on Stas' notes

Curt's analytic kludge EMRI spec (Note: one fig missing and refs need work.)

Here are results of a small Monte-Carlo simulation. I start with distribution of parameters for generation of EMRI waveforms. There are two different type of data with EMRI: the data strem with loud EMRI (coherent SNR~100) and quite EMRI (coherent SNR~40).

For loud EMRI we use the following parameter distribution: the distance is fixed to 1Gpc (to be confirmed), mu is uniform [5,15]solar mass, M uniform [5,20]x10^5 solarmass, spin uniform [0.2, 0.8]M^2, tilde_gamma_0, Phi0, phi_S, phi_K, alpha uniform [0, 2pi], cos of thetaS, thetaK, lambda uniform [-1,1], estimated t_end uniform [2,3]years, estimated e_plunge uniform [0.15, 0.25]. Some values are estimated because using estimated e-plunge, we integrate simplified equations backwards (time t_end) to estimate initial orbital frequency and eccentricity, which is fead into the waveform generating routine. t_end is usually underestimated. The actual distribution of parameters are presented in the following two figures (Monte-Carlo with 100 signals) , . EMRI signal is supposed to be embedded in 3 years of data.

For quite EMRI we use the fixed distance 3Gpc (to be confirmed) all parameter range are the same except masses: mu is uniform [9.7,10.3] and M is uniform [0.97, 1.3]10^6 solarmass. Here is the figures from monte-carlo simulation (100 signals) which show distribution of parameters: ,

Additional feature in the latest waveform generation code is that one can specify duration of the data stream in years, then the signal wil l last between half duration and full duration of the data. In case of the duration of data different from 3 years, the distance should be adjusted so that the signal give SNR ~ 100 for “loud” EMRI and SNR ~ 40 for “quiet” EMRI.

Following the scheme outlined in Barack & Cutler we have estimated SNR for random EMRI of duration between 1 and 2 years placed at the luminocity distance 1Gpc. Other parameters are distributed as prescribed above. In this two figure one can see: Fig1. spectra (strain per root square), red is noise PSD, and blue is signal’s spectrum , Fig2. accumulation of SNR, (red is instanteneous snr on a given freq, blue is accumulative snr) for EMRI which last ~1.4 years, nu_end = 0.001 Hz, e_end = 0.203, total SNR ~ 83. Next we have estimated SNR for a single ifo (hI in Cutler’98) for 200 randomly chosen signals, and the results are presented in this figure: . Upper two figures should help in choosing the distance for “loud” and |”quiet” EMRIs, as it gives SNR vs masses. Going from 2 years to 4 years should increase SNR by sqrt(2) and approximately the same factor comes from including hII (second effecive ifo). However the SNR dispersion looks quite large: sigma ~0.3 x meanSNR, which suggest that we might want to decrease distance to say 0.7-0.8 Gpc for 2 years of data, and 1.0 - 1.15 Gpc for 4 years (????)