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

FoM

Science investigation and Observational requirement: SI 3.2.2b 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 \(z = 2\) with SNR\(>10\)

- GREAT 0.01 [0.1 0.03 0.01] : Relative error on the source frame component mass 1.

System of mass 1e7 at z=2.

- GREAT 0.01 [0.1 0.03 0.01] : Relative error on the source frame component mass 2.

System of mass 1e7 at z=2.

- GREAT 0.002 [0.1 0.006 0.002] : Absolute error on spin 1.

System of mass 1e7 at z=2.

- OK 0.004 [0.1 0.006 0.002] : Absolute error on spin 2.

System of mass 1e7 at z=2.

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
500000.000000	2.000000	1611.390486	1830673.656479	0.000028	0.001369	0.007213	0.005877	547.413514	0.004040	0.004146	0.000748	0.000611	0.000252	0.000025	0.000968	0.002373	0.002189
1000000.000000	2.000000	2754.799379	1231586.925766	0.000048	0.000650	0.005901	0.004882	513.181147	0.003316	0.003348	0.000360	0.000302	0.000231	0.000014	0.000621	0.001425	0.001260
5000000.000000	2.000000	1847.845924	373384.721997	0.000261	0.000768	0.013964	0.011494	4221.171753	0.007792	0.007886	0.000380	0.000517	0.000493	0.000027	0.001210	0.002956	0.001121
10000000.000000	2.000000	1185.962720	209996.044584	0.000623	0.001529	0.023554	0.018899	16308.697267	0.012968	0.013109	0.000677	0.001244	0.000940	0.000059	0.002031	0.004326	0.002124

MBHB with waveform IMRPhenomHM of

• mass = [500000.0, 1000000.0, 5000000.0, 10000000.0] solar mass
• mass ratio in [1, 10] (log uniform),
• redshift = [2]
• 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=500000.0, z=2

Ms=1000000.0, z=2

Ms=5000000.0, z=2

Ms=10000000.0, z=2

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.growth2.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.growth2.md
- snr_thresh : 10
- fom_range : []
- fom_parameter : []
- fom_title : Reconstructing the cosmic history (spin measurements)
- fom_or : ['SI 3.2.2b']
- fom_objective : Detectability/PE for MBHB
- fom_config : SO2/parameter_estimation.growth2.yml
- output : SciRDv1_redbook/data_SO2a_parameter_estimation.growth2.pkl
- mass_range : [500000.0, 1000000.0, 5000000.0, 10000000.0]
- z_range : [2]
- 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 $z = 2$ with SNR$>10$
- foms : [{'system': 3, 'value': 'dm1s/m1s', 'good': 0.03, 'bad': 0.1, 'extra': 0.01, 'title': 'Relative error on the source frame component mass 1.', 'descr': 'System of mass 1e7 at z=2. '}, {'system': 3, 'value': 'dm2s/m2s', 'good': 0.03, 'bad': 0.1, 'extra': 0.01, 'title': 'Relative error on the source frame component mass 2.', 'descr': 'System of mass 1e7 at z=2. '}, {'system': 3, 'value': 'dchi1', 'good': 0.006, 'bad': 0.1, 'extra': 0.002, 'title': 'Absolute error on spin 1.', 'descr': 'System of mass 1e7 at z=2. ', 'round': 3}, {'system': 3, 'value': 'dchi2', 'good': 0.006, 'bad': 0.1, 'extra': 0.002, 'title': 'Absolute error on spin 2.', 'descr': 'System of mass 1e7 at z=2. ', 'round': 3}]

Download

PE data growth2_m_500000.0_z_2

Full data set growth2_m_500000.0_z_2

PE data growth2_m_1000000.0_z_2

Full data set growth2_m_1000000.0_z_2

PE data growth2_m_5000000.0_z_2

Full data set growth2_m_5000000.0_z_2

PE data growth2_m_10000000.0_z_2

Full data set growth2_m_10000000.0_z_2