report SO2a localization.c1.md

Multimessenger astronomy, enabling pre-localization, fig.7 [4.5 yr]

FoM

Science investigation and Observational requirement: SI 3.2.3a from Science requirement document.

For a MBHBs with source-frame mass of \(3.10^5, 3.10^6 and 1.10^7\) M\(_\odot\) at \(z = 1\).

- OK 40.02 [20 40 60] : Cumulative SNR 3 days before merger.

System with \(M = 3.10^6 M_\odot\), z=1.

- OK 0.04 [0.25 0.06 0.02] : Error on time of coalescence (in days) 3 days before merger.

System with \(M = 3.10^6 M_\odot\), z=1.

- OK 189.36 [300 200 150] : Error on advanced sky localization (in square degree) 4 hours before merger.

System with \(M = 3.10^6 M_\odot\), z=1.

Summary

MBHB with waveform IMRPhenomHM of

mass in 3.000000e+05-1.000000e+07 solar mass (log uniform)
mass ratio in [1, 10] (log uniform),
redshift in [1.0] (uniform in comoving volume)
chi in [0 - 0.99] (uniform))

Conducting monte-carlo over 2000 trials, randomizing spins, sky position and orientation

Ms_3.0e+05_t_all

PEoft c1-Ms_3.0e+05_t_all

SNR

time	0.5	0.05	0.95
7.0 d	214.01609834577297	104.79211397964032	455.20009918820864
3.0 d	311.3295310283719	149.1233019845553	676.6326029979693
1.0 d	502.51385133676314	238.35555564896094	1097.3829635092545
10.0 h	786.3219094215256	370.4398135450109	1730.2080605457195
4.0 h	1428.3390310134541	653.2181045566023	3160.002553225246
1.0 h	2856.4381455981966	1260.6863018436302	6434.891357961001
0.0 h	4305.026181119427	1817.336862625613	9736.316399714891

Sky errors

time	0.5	0.05	0.95
7.0 d	3.9338268903202547	0.4646044944547214	14.264646145296464
3.0 d	2.781270015411082	0.24047664891083223	10.99267286702147
1.0 d	2.1169180339806544	0.1035647955726441	8.894765136824414
10.0 h	1.7071276420979353	0.04884107136017092	7.888845353426529
4.0 h	1.3427772421371837	0.01875816807198871	7.25270653999802
1.0 h	0.955340641010453	0.00591715930139281	6.535699881148412
0.0 h	0.1526807178319445	0.0015091831896176576	1.0141082040436409

Tc errors

time	0.5	0.05	0.95
7.0 d	0.0012562083005627483	0.0007320799102793637	0.002231621607282509
3.0 d	0.00042569988889627243	0.0002361323809562341	0.0007803261525313298
1.0 d	0.0001249908455336675	7.041254496586211e-05	0.00023824484013402117
10.0 h	5.597566388876716e-05	2.9842140387261362e-05	0.00010603626572909911
4.0 h	3.066236605463253e-05	1.3664682861708834e-05	7.062936916563861e-05
1.0 h	1.932587290143799e-05	4.904326041369241e-06	6.249682597779471e-05
0.0 h	7.39243819509051e-06	9.01663108993699e-07	2.2426395536348383e-05

Ms_3.0e+06_t_all

PEoft c1-Ms_3.0e+06_t_all

SNR

time	0.5	0.05	0.95
7.0 d	17.79211790553152	7.569101884415375	39.97192081215843
3.0 d	40.02195985906117	17.769816132117064	87.6316749482472
1.0 d	94.8053573012439	42.776825901767836	206.54041691030895
10.0 h	171.65883480625448	78.5409351067152	374.68178427853695
4.0 h	291.8922627886727	130.13721455646393	640.1055651519065
1.0 h	578.943147232194	250.0325770944397	1339.5856653928117
0.0 h	6316.592996799178	2269.3697721675303	15913.472586092148

Sky errors

time	0.5	0.05	0.95
7.0 d	3688.7109233460997	105.72991177149818	53011.972100139596
3.0 d	1395.312489356243	25.029921972747083	19490.48705248544
1.0 d	565.8983800674396	5.656543521469765	8387.490166652908
10.0 h	324.10654008532254	2.175528476150497	5478.676565867137
4.0 h	189.35521361557784	0.7912015102735457	3974.584569843334
1.0 h	58.9375502789799	0.1634864045420174	2546.3131004836528
0.0 h	0.23802137495397732	0.0007197246714301591	37.069104577869425

Tc errors

time	0.5	0.05	0.95
7.0 d	0.18541269591387724	0.06570632288744487	0.5017311163536456
3.0 d	0.039833797989185765	0.015672880164103373	0.1013291358788605
1.0 d	0.007270392921761742	0.0031123578398033554	0.017124506082611825
10.0 h	0.002318801984459614	0.0011343461229578983	0.005293051593184803
4.0 h	0.0009346494092761389	0.00042706188068857655	0.0024331361661378737
1.0 h	0.0002858614495027047	7.881205254643761e-05	0.0012073198865437636
0.0 h	1.1793778040680833e-05	1.2907088380463048e-06	0.0001531307833627266

Ms_1.0e+07_t_all

PEoft c1-Ms_1.0e+07_t_all

SNR

time	0.5	0.05	0.95
7.0 d	2.495620289238083	0.7695326978399522	9.275267422001356
3.0 d	10.200715731240825	3.516423495492074	30.06784283599567
1.0 d	42.97745069048864	17.669473217677375	103.34596441937214
10.0 h	98.98013906403227	42.630831966007335	231.24099322885934
4.0 h	214.27105435214713	89.86318689977679	512.3397398140982
1.0 h	691.3397581537686	257.24127405483483	1766.4067531906887
0.0 h	3104.7063995294284	1102.1273735554523	7428.977383758756

Sky errors

time	0.5	0.05	0.95
7.0 d	253354.22043549374	4598.322073338011	10135501.120320953
3.0 d	40822.8595511226	617.2852188142066	1594025.5900551637
1.0 d	7017.482152934672	59.211141281856136	267276.09493974666
10.0 h	2163.1140646329113	11.459186903901118	98703.73340914077
4.0 h	631.8687221757243	2.062224802928504	45613.58756685296
1.0 h	75.3631226105062	0.1312404958579057	13327.52298172297
0.0 h	0.9424516500595006	0.003613845212246121	481.8818945313042

Tc errors

time	0.5	0.05	0.95
7.0 d	4.16937343929096	0.7468126991690117	17.55794491335507
3.0 d	0.53003110996679	0.12894967452286085	1.9016818381057712
1.0 d	0.05723783333502449	0.017793459785356878	0.16615284043493017
10.0 h	0.012971439816677338	0.005204507645973326	0.03363578451161246
4.0 h	0.0029213759001081637	0.0009770717409372887	0.008135161692508924
1.0 h	0.00045751698204566884	0.00016074466702621735	0.0026847962839527503
0.0 h	2.9020457942604806e-05	6.846066959150491e-06	0.0004897713706046405

Detailed results

at merger

waveform parameters

'''

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]]
t0 : 0.7
DeltatL_cut : -18299.558214969933
modes : [(2, 2), (2, 1), (3, 3), (4, 4)] '''

Input parameters


- log : log/SO2_localization.c1.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_localization.c1.md
- sky_thr_fom : [100.0]
- coal_thr_fom : [4]
- fom_range : [15, 20, 25]
- time_fom_sky : [4]
- time_fom_coal : [48]
- fom_title : Multimessenger astronomy, enabling pre-localization, fig.7
- fom_config : SO2/localization.c1.yml
- fom_or : SI 3.2.3a
- fom_objective : Detectability/PE for MBHB
- output : SciRDv1_redbook/data_SO2a_localization.c1.pkl
- mass_range : [300000.0, 3000000.0, 10000000.0]
- z_range : [1.0]
- time_range : [<Quantity 7. d>, <Quantity 3. d>, <Quantity 1. d>, <Quantity 10. h>, <Quantity 4. h>, <Quantity 1. h>, <Quantity 0. h>]
- fom_obj : For a MBHBs with source-frame mass of $3.10^5, 3.10^6 and 1.10^7$ M$_\odot$ at $z = 1$.
- mass_ratio_range : [1, 10]
- foms : [{'mass': 3000000.0, 'time': <Quantity 3. d>, 'value': 'snr', 'good': 40, 'bad': 20, 'extra': 60, 'title': 'Cumulative SNR 3 days before merger.', 'descr': 'System with $M = 3.10^6 M_\\odot$, z=1.'}, {'mass': 3000000.0, 'time': <Quantity 3. d>, 'value': 'tc', 'good': 0.06, 'bad': 0.25, 'extra': 0.02, 'title': 'Error on time of coalescence (in days) 3 days before merger.', 'descr': 'System with $M = 3.10^6 M_\\odot$, z=1.'}, {'mass': 3000000.0, 'time': <Quantity 4. h>, 'value': 'sky', 'good': 200, 'bad': 300, 'extra': 150, 'title': 'Error on advanced sky localization (in square degree) 4 hours before merger.', 'descr': 'System with $M = 3.10^6 M_\\odot$, z=1.'}]