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 0.06 [20 5 1] : Ms = 500000.0 ; z = 8: chirp mass

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

- GREAT 0.86 [20 5 1] : Ms = 5000000.0 ; z = 8: chirp mass

- GREAT 0.33 [20 5 1] : Ms = 5000000.0 ; z = 5: chirp mass

- OK 1.78 [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

- OK 0.02 [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 0.04 [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

- OK 0.02 [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	85.778400	66040.565910	0.000134	0.041150	0.107141	0.095249	4865.175700	0.082926	0.092768	0.022061	0.018132	0.005047	0.000766	0.019627	0.049428	0.047152
50000.000000	5.000000	107.730730	209362.138348	0.000093	0.040016	0.082602	0.071367	2925.938133	0.059568	0.068664	0.020599	0.017015	0.004339	0.000751	0.017224	0.043568	0.039905
500000.000000	8.000000	466.134243	55570.261568	0.000621	0.003483	0.042703	0.037610	5084.987271	0.033926	0.033793	0.001962	0.001813	0.001778	0.000095	0.004293	0.009066	0.006962
500000.000000	5.000000	645.748044	158819.182367	0.000237	0.002777	0.024808	0.021596	2221.758897	0.018362	0.018524	0.001528	0.001294	0.000945	0.000062	0.002642	0.006011	0.005381
5000000.000000	8.000000	167.953320	13290.460292	0.008553	0.017154	0.205072	0.184728	238577.105633	0.163053	0.162425	0.005141	0.016940	0.009801	0.000758	0.017918	0.044006	0.017706
5000000.000000	5.000000	343.719964	27545.324050	0.003272	0.006823	0.087044	0.075243	67671.203421	0.064037	0.063717	0.002401	0.006358	0.004063	0.000295	0.007934	0.017369	0.008063
10000000.000000	8.000000	101.287775	10108.338463	0.017798	0.036767	0.439501	0.433552	917523.945554	0.355688	0.348633	0.007855	0.035047	0.019671	0.001652	0.033496	0.094632	0.029920

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 7.71748532e-41 7.71748532e-41 8.45230844e-54] [2.10000000e-05 5.48584269e-41 5.48584269e-41 7.52449171e-54] [2.20000000e-05 3.96262828e-41 3.96262828e-41 6.82098233e-54] ... [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

Full data set growth1_m_50000.0_z_5

PE data growth1_m_500000.0_z_8

Full data set growth1_m_500000.0_z_8

PE data growth1_m_500000.0_z_5

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PE data growth1_m_5000000.0_z_8

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PE data growth1_m_5000000.0_z_5

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PE data growth1_m_10000000.0_z_8

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