Parameters estimation for fiducial systems 4.5 yr
FoM
Science investigation and Observational requirement: OR1.1.b from Science requirement document.
- GREAT 0.004187054546978047 [0.5 0.25 0.01] : \(\Delta D_L/D_L\) median for BH + BH system with frequency 1 mHz.
- OK 0.31752367450065344 [1.0 0.5 0.1] : \(\Delta D_L/D_L\) median for WD + WD system with frequency 3 mHz.
- OK 0.01227913785054488 [0.5 0.25 0.01] : \(\Delta D_L/D_L\) median for NS + NS system with frequency 3 mHz.
- OK 0.057108339105145525 [0.5 0.25 0.01] : \(\Delta D_L/D_L\) median for WD + WD system with frequency 5 mHz.
Summary
We have assumed 4.5 yr years of observation with 0.82 duty cycle
For a set of systems with defined masses and initial frequency, we estimated error by conducting monte-carlo over 2000 trials, randomizing inclination, initial phase and polarization (sky position is fixed to the galactic center) and computing FIM for each source. For each system we compute the median and the 68% interval of the errors in the sample.
Below the table of with the median values.
| freq. | Source | \(m_1\) | \(m_2\) | \(\Delta f/f\) med. | \(\Delta A/A\) med. | \(\Delta D_L/D_L\) med. | \(\Delta \Omega\) med. |
|---|---|---|---|---|---|---|---|
| 1 mHz | WD + WD | 0.4 | 0.3 | 2.2e-05 | 3.5e+00 | 3.9e+02 | 2.0e+04 |
| 1 mHz | NS + NS | 1.35 | 1.3 | 2.4e-06 | 3.7e-01 | 4.7e+00 | 2.3e+02 |
| 1 mHz | BH + BH | 25.0 | 15.0 | 2.8e-08 | 4.1e-03 | 4.2e-03 | 3.2e-02 |
| 3 mHz | WD + WD | 0.4 | 0.3 | 2.5e-07 | 1.1e-01 | 3.2e-01 | 6.9e+00 |
| 3 mHz | NS + NS | 1.35 | 1.3 | 2.7e-08 | 1.2e-02 | 1.2e-02 | 8.1e-02 |
| 3 mHz | BH + BH | 25.0 | 15.0 | 1.1e-09 | 1.4e-04 | 1.4e-04 | 1.3e-05 |
| 5 mHz | WD + WD | 0.4 | 0.3 | 7.7e-08 | 5.4e-02 | 5.7e-02 | 8.4e-01 |
| 5 mHz | NS + NS | 1.35 | 1.3 | 8.0e-09 | 6.0e-03 | 6.0e-03 | 9.0e-03 |
| 5 mHz | BH + BH | 25.0 | 15.0 | 4.2e-10 | 7.0e-05 | 7.0e-05 | 1.2e-06 |
Below the table with the 68% confidency interval.
| freq. | Source | \(m_1\) | \(m_2\) | \(\Delta f/f\) 68% | \(\Delta A/A\) 68% | \(\Delta D_L/D_L\) 68% | \(\Delta \Omega\) 68% |
|---|---|---|---|---|---|---|---|
| 1 mHz | WD + WD | 0.4 | 0.3 | 1.5e-05:3.3e-05 | 2.4e+00:1.1e+01 | 2.7e+02:5.8e+02 | 9.0e+03:4.5e+04 |
| 1 mHz | NS + NS | 1.35 | 1.3 | 1.6e-06:3.5e-06 | 2.5e-01:1.1e+00 | 3.4e+00:6.7e+00 | 1.0e+02:5.1e+02 |
| 1 mHz | BH + BH | 25.0 | 15.0 | 1.9e-08:4.1e-08 | 2.9e-03:1.3e-02 | 3.1e-03:1.3e-02 | 1.4e-02:7.0e-02 |
| 3 mHz | WD + WD | 0.4 | 0.3 | 1.7e-07:3.8e-07 | 7.9e-02:3.5e-01 | 2.6e-01:4.0e-01 | 3.1e+00:1.6e+01 |
| 3 mHz | NS + NS | 1.35 | 1.3 | 1.8e-08:4.0e-08 | 8.4e-03:3.4e-02 | 9.4e-03:3.4e-02 | 3.6e-02:1.8e-01 |
| 3 mHz | BH + BH | 25.0 | 15.0 | 7.3e-10:1.5e-09 | 9.7e-05:4.0e-04 | 9.7e-05:4.0e-04 | 5.7e-06:2.7e-05 |
| 5 mHz | WD + WD | 0.4 | 0.3 | 5.1e-08:1.1e-07 | 3.9e-02:1.6e-01 | 4.7e-02:1.6e-01 | 3.7e-01:1.8e+00 |
| 5 mHz | NS + NS | 1.35 | 1.3 | 5.4e-09:1.2e-08 | 4.2e-03:1.8e-02 | 4.2e-03:1.8e-02 | 4.1e-03:2.0e-02 |
| 5 mHz | BH + BH | 25.0 | 15.0 | 2.8e-10:6.2e-10 | 4.8e-05:2.2e-04 | 4.8e-05:2.2e-04 | 5.3e-07:2.6e-06 |
Below we plot, for each system, the distribution of errors and the dependency on the inclination.
