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 0.04 [20 5 1] : Ms = 500000.0 ; z = 8: chirp mass

- GREAT 0.01 [20 5 1] : Ms = 500000.0 ; z = 5: chirp mass

- GREAT 0.5 [20 5 1] : Ms = 5000000.0 ; z = 8: chirp mass

- GREAT 0.19 [20 5 1] : Ms = 5000000.0 ; z = 5: chirp mass

- OK 1.03 [20 5 1] : Ms = 10000000.0 ; z = 8: chirp mass

- GREAT 0.08 [0.5 0.25 0.1] : Ms = 50000.0 ; z = 8: lum. distance rel. error

- GREAT 0.06 [0.5 0.25 0.1] : Ms = 50000.0 ; z = 5: lum. distance rel. error

- GREAT 0.03 [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 0.15 [0.5 0.25 0.1] : Ms = 5000000.0 ; z = 8: lum. distance rel. error

- GREAT 0.07 [0.5 0.25 0.1] : Ms = 5000000.0 ; z = 5: lum. distance rel. error

- OK 0.03 [0.25 0.05 0.01] : Ms = 50000.0 ; z = 8: mass ratio rel. error

- OK 0.03 [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 0.0 [0.25 0.05 0.01] : Ms = 5000000.0 ; z = 5: mass ratio rel. error

- OK 0.02 [0.25 0.05 0.01] : Ms = 10000000.0 ; z = 8: mass ratio rel. error

- GREAT 0.04 [0.5 0.1 0.05] : Ms = 50000.0 ; z = 8: spin 2 error

- GREAT 0.03 [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 0.0 [0.5 0.1 0.05] : Ms = 500000.0 ; z = 5: spin 2 error

- GREAT 0.03 [0.5 0.1 0.05] : Ms = 5000000.0 ; z = 8: spin 2 error

- GREAT 0.01 [0.5 0.1 0.05] : Ms = 5000000.0 ; z = 5: spin 2 error

- OK 0.06 [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	122.134928	86067.605570	0.000097	0.029724	0.076067	0.067189	3505.572394	0.058333	0.066337	0.015847	0.012963	0.003643	0.000546	0.014253	0.035511	0.033487
50000.000000	5.000000	153.227063	290013.899256	0.000069	0.028712	0.059697	0.051573	2145.765090	0.042714	0.049881	0.014965	0.012238	0.003205	0.000544	0.012596	0.032061	0.028440
500000.000000	8.000000	665.104280	99843.695982	0.000366	0.002458	0.030396	0.026816	3375.894148	0.024109	0.024478	0.001397	0.001229	0.001262	0.000063	0.003043	0.006373	0.004875
500000.000000	5.000000	920.114240	286194.047686	0.000145	0.001947	0.017665	0.015275	1538.474225	0.012717	0.012969	0.001080	0.000900	0.000689	0.000043	0.001862	0.004281	0.003771
5000000.000000	8.000000	206.573999	23087.464915	0.005010	0.010674	0.151680	0.135153	167161.169063	0.119836	0.122226	0.004058	0.009921	0.006681	0.000469	0.013338	0.028799	0.013892
5000000.000000	5.000000	396.116391	56827.676606	0.001867	0.004578	0.070078	0.060305	48983.123365	0.050939	0.051324	0.001995	0.003687	0.002770	0.000177	0.006043	0.012798	0.006469
10000000.000000	8.000000	141.783496	18031.624238	0.010339	0.021203	0.265552	0.241488	596484.431023	0.212581	0.211872	0.005347	0.022277	0.012331	0.001050	0.021468	0.058160	0.020984

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 3.74868279e-45 3.74868279e-45 1.45384261e-55] [2.10000000e-05 3.51079457e-45 3.51079457e-45 1.76691006e-55] [2.20000000e-05 3.31246021e-45 3.31246021e-45 2.12793518e-55] ... [9.99998000e-01 1.35664204e-36 1.35664204e-36 2.82767611e-36] [9.99999000e-01 1.35666152e-36 1.35666152e-36 2.82788487e-36] [1.00000000e+00 1.35668095e-36 1.35668095e-36 2.82809354e-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_500000.0_z_5

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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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