Detectability of \(10^5-10 M_{\odot}\) 2 years EMRI at redshift z=3 with eccentricity e_plunge=0.68 [1.0 yr]
FoM
Science investigation and Observational requirement: SI3.1 OR3.1 from Science requirement document.
Compute sky-polarization-inclination average snr for a fiducial EMRI system with eccentricity 0.25 at plunge adn at redshift=3
- OK 26.75 [10 20 40] : SO3 Detectability of \(10^5-10 M_{\odot}\) 2 years EMRI at redshift z=3 with eccentricity e_plunge=0.68
Assuming detection threshold 20. Detectability is OK if average SNR > 20
Summary
We compute the SNR averaged over sky, polarization and inclination.
Neglecting the cross-talk between harmonics the SNR2 is \(<\rho^2> = 4 (M/d_L)^2 \int \sum \frac{|A_{lmn}|^2}{4\pi \dot{f}_{lmn}}\frac{df}{S^{LISA}(f)}\)
We transform the noise PSD into effective strain PSD \(S^{LISA}(f)\)
eccentricity at plunge is 0.1703972239202481, plunge time: 1.9227046089403836
Detailed results
We assume that the amplitude of harmonics at the negative freqs are the CC of the amplitude at positive freqs.
In SNR we use abs(Amplitude), so we convert all n-ve freqs into positive.
We exclude frequencies below 0.0001
We exclude parts of the signal where f˙≈0 - breaks SPA and needs extension (see: https://arxiv.org/pdf/2102.02713.pdf)
Input parameters
- log : log/SO3a_detectability_emri.c1.log
- config : config.yml
- subconfig :
- duration : 1.0 yr
- duty_cycle : 1
- armlength : 2500000000.0 m
- noise : SciRDv1_redbook/noise_background_1_yr.npy
- show : False
- fast : 0
- tdi2 : 1
- freqs : [2e-05, 1]
- force_duration : 1_yr
- report : SciRDv1_redbook/report_SO3a_detectability_emri.c1.md
- mass_range : [100000.0, 10]
- z : 3
- tobs : 2
- e0 : 0.68
- p0 : 19.4
- snr_thresh : 20
- fom_range : [10, 20, 40]
- fom_title : Detectability of $10^5-10 M_{\odot}$ 2 years EMRI at redshift z=3 with eccentricity e_plunge=0.68
- fom_config : SO3/detectability_emri.c1.yml