Reconstructing the cosmic history (mass measurements) [4.5 yr]

FoM

Science investigation and Observational requirement: SI 3.2.2a from Science requirement document.

Detection of MBHB with source-frame mass in the range \(10^4-10^7\) M\(_\odot\) and formation redshift in the range \(z = 5-8\) with SNR\(>10\)

Measuring ['chirp mass'] with a given relative precision in \%.

- GREAT 0.01 [20 5 1] : Ms = 50000.0 ; z = 8: chirp mass

- GREAT 0.01 [20 5 1] : Ms = 50000.0 ; z = 5: chirp mass

- GREAT 0.05 [20 5 1] : Ms = 500000.0 ; z = 8: chirp mass

- GREAT 0.02 [20 5 1] : Ms = 500000.0 ; z = 5: chirp mass

- GREAT 0.66 [20 5 1] : Ms = 5000000.0 ; z = 8: chirp mass

- GREAT 0.24 [20 5 1] : Ms = 5000000.0 ; z = 5: chirp mass

- OK 1.45 [20 5 1] : Ms = 10000000.0 ; z = 8: chirp mass

- OK 0.11 [0.5 0.25 0.1] : Ms = 50000.0 ; z = 8: lum. distance rel. error

- GREAT 0.08 [0.5 0.25 0.1] : Ms = 50000.0 ; z = 5: lum. distance rel. error

- GREAT 0.04 [0.5 0.25 0.1] : Ms = 500000.0 ; z = 8: lum. distance rel. error

- GREAT 0.02 [0.5 0.25 0.1] : Ms = 500000.0 ; z = 5: lum. distance rel. error

- OK 0.21 [0.5 0.25 0.1] : Ms = 5000000.0 ; z = 8: lum. distance rel. error

- GREAT 0.09 [0.5 0.25 0.1] : Ms = 5000000.0 ; z = 5: lum. distance rel. error

- OK 0.04 [0.25 0.05 0.01] : Ms = 50000.0 ; z = 8: mass ratio rel. error

- OK 0.04 [0.25 0.05 0.01] : Ms = 50000.0 ; z = 5: mass ratio rel. error

- GREAT 0.0 [0.25 0.05 0.01] : Ms = 500000.0 ; z = 8: mass ratio rel. error

- GREAT 0.0 [0.25 0.05 0.01] : Ms = 500000.0 ; z = 5: mass ratio rel. error

- GREAT 0.01 [0.25 0.05 0.01] : Ms = 5000000.0 ; z = 8: mass ratio rel. error

- GREAT 0.01 [0.25 0.05 0.01] : Ms = 5000000.0 ; z = 5: mass ratio rel. error

- OK 0.03 [0.25 0.05 0.01] : Ms = 10000000.0 ; z = 8: mass ratio rel. error

- GREAT 0.05 [0.5 0.1 0.05] : Ms = 50000.0 ; z = 8: spin 2 error

- GREAT 0.04 [0.5 0.1 0.05] : Ms = 50000.0 ; z = 5: spin 2 error

- GREAT 0.01 [0.5 0.1 0.05] : Ms = 500000.0 ; z = 8: spin 2 error

- GREAT 0.01 [0.5 0.1 0.05] : Ms = 500000.0 ; z = 5: spin 2 error

- GREAT 0.04 [0.5 0.1 0.05] : Ms = 5000000.0 ; z = 8: spin 2 error

- GREAT 0.02 [0.5 0.1 0.05] : Ms = 5000000.0 ; z = 5: spin 2 error

- OK 0.09 [0.5 0.1 0.05] : Ms = 10000000.0 ; z = 8: spin 2 error

- GREAT 0.0 [0.2 0.05 0.01] : Ms = 50000.0 ; z = 8: chirp mass

- GREAT 0.0 [0.2 0.05 0.01] : Ms = 50000.0 ; z = 5: chirp mass

- GREAT 0.0 [0.2 0.05 0.01] : Ms = 500000.0 ; z = 8: chirp mass

- GREAT 0.0 [0.2 0.05 0.01] : Ms = 500000.0 ; z = 5: chirp mass

- GREAT 0.01 [0.2 0.05 0.01] : Ms = 5000000.0 ; z = 8: chirp mass

- GREAT 0.0 [0.2 0.05 0.01] : Ms = 5000000.0 ; z = 5: chirp mass

- GREAT 0.01 [0.2 0.05 0.01] : Ms = 10000000.0 ; z = 8: chirp mass

Summary

Ms	z	snr	tdet_s	dMc/Mc	dq/q	dDL/DL	dz/z	dM	dm1s/m1s	dm2s/m2s	dm1/m1	dm2/m2	dchieff	dMf/Mf	dchi1	dchi2	diota
50000.000000	8.000000	85.778403	66040.565910	0.000134	0.041144	0.107053	0.094744	4861.105680	0.082830	0.093058	0.022083	0.018127	0.005087	0.000767	0.019573	0.049406	0.047150
50000.000000	5.000000	107.730734	209362.138348	0.000093	0.040016	0.082761	0.071078	2925.879344	0.059321	0.068522	0.020605	0.017027	0.004347	0.000755	0.017226	0.044275	0.039904
500000.000000	8.000000	466.134828	56129.989723	0.000542	0.003474	0.042617	0.037513	4778.415472	0.033563	0.033612	0.001957	0.001762	0.001685	0.000089	0.004203	0.009055	0.006955
500000.000000	5.000000	645.748778	159318.166168	0.000215	0.002771	0.024787	0.021415	2195.040279	0.017954	0.018339	0.001531	0.001288	0.000918	0.000061	0.002576	0.006010	0.005375
5000000.000000	8.000000	168.002077	14484.003068	0.006577	0.013817	0.208622	0.186800	216242.262814	0.161614	0.164278	0.005092	0.012871	0.008955	0.000621	0.017610	0.039293	0.016337
5000000.000000	5.000000	343.781026	32184.176735	0.002449	0.005753	0.085732	0.073707	59392.487388	0.061998	0.062366	0.002350	0.004683	0.003547	0.000229	0.007597	0.015956	0.007376
10000000.000000	8.000000	101.411613	12002.008510	0.014515	0.029801	0.394814	0.388290	847312.643513	0.325213	0.328419	0.007818	0.032456	0.018780	0.001496	0.033357	0.086933	0.028247

MBHB with waveform IMRPhenomHM of

• mass = [50000.0, 500000.0, 5000000.0] solar mass
• mass ratio in [1, 10] (log uniform),
• redshift = [8, 5]
• t0 in [0.10 - 0.95] (uniform)
• chi in [0.00 - 1.00] (uniform))

Conducting monte-carlo over 1000 trials, randomizing spins, sky position and orientation

Assuming SNR threshold for detection: 10.0

For derived parameters (dz/z, dMf/Mf), random samples are drawn from the inverse Fisher, derived quantities are computed and we extract their standard deviation and mean.

For the following waveform parameters (dMc/Mc, dDL/DL, dq/q), we use a log10 parameterization.

We report observer frame errors.

Detailed results

Ms=50000.0, z=8

Ms=50000.0, z=5

Ms=500000.0, z=8

Ms=500000.0, z=5

Ms=5000000.0, z=8

Ms=5000000.0, z=5

Ms=10000000.0, z=8

waveform_params

'''

• minf : 2e-05
• maxf : 1
• fend : None
• tmin : 0.0
• tmax : None
• phiref : 0.0
• fref_for_phiref : 0.0
• toffset : 0.0
• TDI : TDI2AET
• acc : 0.0001
• order_fresnel_stencil : 0
• approximant : IMRPhenomHM
• responseapprox : full
• frozenLISA : False
• TDIrescaled : False
• LISAconst : {'OrbitOmega': 1.9909865927683783e-07, 'OrbitPhi0': 0.0, 'Orbitt0': 0.0, 'OrbitR': 149597870700.0, 'OrbitL': 2500000000.0}
• LISAnoise : [[2.00000000e-05 4.71195758e-45 4.71195758e-45 6.70580303e-55] [2.10000000e-05 4.71334803e-45 4.71334803e-45 8.15094275e-55] [2.20000000e-05 4.71480631e-45 4.71480631e-45 9.81798275e-55] ... [9.99998000e-01 2.73617388e-36 2.73617388e-36 5.73895037e-36] [9.99999000e-01 2.73619429e-36 2.73619429e-36 5.73933494e-36] [1.00000000e+00 2.73621460e-36 2.73621460e-36 5.73971931e-36]]
• timetomerger_max : 4.5
• modes : [(2, 2), (2, 1), (3, 3), (4, 4)] '''

Input parameters

- log : log/SO2_parameter_estimation.growth1.log
- config : config.yml
- subconfig : 
- duration : 4.5 yr
- duty_cycle : 0.82
- armlength : 2500000000.0 m
- noise : SciRDv1
- show : False
- fast : 0
- tdi2 : 1
- freqs : [2e-05, 1]
- force_duration : 4.5_yr
- report : SciRDv1_redbook/report_SO2a_parameter_estimation.growth1.md
- snr_thresh : 10
- fom_range : [20, 5, 1]
- fom_parameter : ['dMc/Mc']
- fom_title : Reconstructing the cosmic history (mass measurements)
- fom_or : ['SI 3.2.2a']
- fom_objective : Detectability/PE for MBHB
- fom_config : SO2/parameter_estimation.growth1.yml
- output : SciRDv1_redbook/data_SO2a_parameter_estimation.growth1.pkl
- mass_range : [50000.0, 500000.0, 5000000.0]
- z_range : [8, 5]
- mass_z_points : [[10000000.0, 8]]
- spin_range : [0, 1]
- mass_ratio_range : [1, 10]
- fom_obj : Detection of MBHB with source-frame mass in the range $10^4-10^7$ M$_\odot$ and formation redshift in the range $z = 5-8$ with SNR$>10$
- foms : [{'system': 0, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 50000.0 ; z = 8: lum. distance rel. error', 'descr': None}, {'system': 1, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 50000.0 ; z = 5: lum. distance rel. error', 'descr': None}, {'system': 2, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 500000.0 ; z = 8: lum. distance rel. error', 'descr': None}, {'system': 3, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 500000.0 ; z = 5: lum. distance rel. error', 'descr': None}, {'system': 4, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 5000000.0 ; z = 8: lum. distance rel. error', 'descr': None}, {'system': 5, 'value': 'dDL/DL', 'extra': 0.1, 'good': 0.25, 'bad': 0.5, 'title': 'Ms = 5000000.0 ; z = 5: lum. distance rel. error', 'descr': None}, {'system': 0, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 50000.0 ; z = 8: mass ratio rel. error', 'descr': None}, {'system': 1, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 50000.0 ; z = 5: mass ratio rel. error', 'descr': None}, {'system': 2, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 500000.0 ; z = 8: mass ratio rel. error', 'descr': None}, {'system': 3, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 500000.0 ; z = 5: mass ratio rel. error', 'descr': None}, {'system': 4, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 5000000.0 ; z = 8: mass ratio rel. error', 'descr': None}, {'system': 5, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 5000000.0 ; z = 5: mass ratio rel. error', 'descr': None}, {'system': 6, 'value': 'dq/q', 'extra': 0.01, 'good': 0.05, 'bad': 0.25, 'title': 'Ms = 10000000.0 ; z = 8: mass ratio rel. error', 'descr': None}, {'system': 0, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 50000.0 ; z = 8: spin 2 error', 'descr': None}, {'system': 1, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 50000.0 ; z = 5: spin 2 error', 'descr': None}, {'system': 2, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 500000.0 ; z = 8: spin 2 error', 'descr': None}, {'system': 3, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 500000.0 ; z = 5: spin 2 error', 'descr': None}, {'system': 4, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 5000000.0 ; z = 8: spin 2 error', 'descr': None}, {'system': 5, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 5000000.0 ; z = 5: spin 2 error', 'descr': None}, {'system': 6, 'value': 'dchi2', 'extra': 0.05, 'good': 0.1, 'bad': 0.5, 'title': 'Ms = 10000000.0 ; z = 8: spin 2 error', 'descr': None}, {'system': 0, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 50000.0 ; z = 8: chirp mass', 'descr': None}, {'system': 1, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 50000.0 ; z = 5: chirp mass', 'descr': None}, {'system': 2, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 500000.0 ; z = 8: chirp mass', 'descr': None}, {'system': 3, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 500000.0 ; z = 5: chirp mass', 'descr': None}, {'system': 4, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 5000000.0 ; z = 8: chirp mass', 'descr': None}, {'system': 5, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 5000000.0 ; z = 5: chirp mass', 'descr': None}, {'system': 6, 'value': 'dMc/Mc', 'extra': 0.01, 'good': 0.05, 'bad': 0.2, 'title': 'Ms = 10000000.0 ; z = 8: chirp mass', 'descr': None}]

Download

PE data growth1_m_50000.0_z_8

Full data set growth1_m_50000.0_z_8

PE data growth1_m_50000.0_z_5

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PE data growth1_m_500000.0_z_8

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PE data growth1_m_5000000.0_z_8

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PE data growth1_m_10000000.0_z_8

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