MBHB as standard sirens [1.0 yr]

FoM

Science investigation and Observational requirement: SI6.2 OR6.2 from Science requirement document.

Compute detectable MBHBs (\(SNR>10\)) using representative masses and distance from three astro models (popIII, heavy-delyaed, heavy-no-delay) and assess probability of their localization better than \(10 m{deg}^2\)

- OK 110 [100 110 111] : SO6 Probability of advanced localization

Localization is OK if probability > 50% to get the error in the sky better than 10 deg^2.

color code
red ---
yellow 1--
green -1-
blue --1
Population combined FoM values
heavy-nodelay 100 [74.16992188 40.77148438 14.69726562]
heavy-delay 110 [76.46484375 60.00976562 23.14453125]
popIII 0 [40.18554688 2.05078125 0. ]

Summary

MBHB with waveform IMRPhenomHM of

  • mass in [140000.0, 47000.0, 14000.0] solar mass
  • mass ratio = 0.99,
  • redshift in [2.7, 4.5, 6.6]
  • chi in [0 - 0.99] (uniform))

Conducting monte-carlo over 2048 trials, randomizing spins, sky position and orientation

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-nodelay - 140000.0 2.7

  • For mass 140000.0 and redshift 2.7: probability of sky error <= 10 deg^2 is 74.17% and SNR >= 10 is 100.0% and for both conditions is 74.17%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-nodelay - 47000.0 4.5

  • For mass 47000.0 and redshift 4.5: probability of sky error <= 10 deg^2 is 40.77% and SNR >= 10 is 100.0% and for both conditions is 40.77%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-nodelay - 14000.0 6.6

  • For mass 14000.0 and redshift 6.6: probability of sky error <= 10 deg^2 is 14.7% and SNR >= 10 is 99.95% and for both conditions is 14.7%

Sky localization distribution for 14000.0 6.6

MBHB with waveform IMRPhenomHM of

  • mass in [300000.0, 130000.0, 22000.0] solar mass
  • mass ratio = 0.99,
  • redshift in [2.8, 4.9, 7.0]
  • chi in [0 - 0.99] (uniform))

Conducting monte-carlo over 2048 trials, randomizing spins, sky position and orientation

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-delay - 300000.0 2.8

  • For mass 300000.0 and redshift 2.8: probability of sky error <= 10 deg^2 is 76.46% and SNR >= 10 is 100.0% and for both conditions is 76.46%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-delay - 130000.0 4.9

  • For mass 130000.0 and redshift 4.9: probability of sky error <= 10 deg^2 is 60.01% and SNR >= 10 is 100.0% and for both conditions is 60.01%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR heavy-delay - 22000.0 7.0

  • For mass 22000.0 and redshift 7.0: probability of sky error <= 10 deg^2 is 23.14% and SNR >= 10 is 100.0% and for both conditions is 23.14%

Sky localization distribution for 22000.0 7.0

MBHB with waveform IMRPhenomHM of

  • mass in [32000.0, 6000.0, 2500.0] solar mass
  • mass ratio = 0.99,
  • redshift in [2.5, 4.3, 5.8]
  • chi in [0 - 0.99] (uniform))

Conducting monte-carlo over 2048 trials, randomizing spins, sky position and orientation

Remove 0 (over 2048) failed sources

Detection probability localization/SNR popIII - 32000.0 2.5

  • For mass 32000.0 and redshift 2.5: probability of sky error <= 10 deg^2 is 40.19% and SNR >= 10 is 100.0% and for both conditions is 40.19%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR popIII - 6000.0 4.3

  • For mass 6000.0 and redshift 4.3: probability of sky error <= 10 deg^2 is 2.05% and SNR >= 10 is 99.9% and for both conditions is 2.05%

Remove 0 (over 2048) failed sources

Detection probability localization/SNR popIII - 2500.0 5.8

  • For mass 2500.0 and redshift 5.8: probability of sky error <= 10 deg^2 is 0.0% and SNR >= 10 is 97.8% and for both conditions is 0.0%

Sky localization distribution for 2500.0 5.8

Sky localization precision versus SNR for 2500.0 5.8

Detailed results

waveform paramters

'''

  • minf : 2e-05
  • maxf : 1
  • fend : None
  • tmin : None
  • tmax : 1.0
  • 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 3.26116899e-45 3.26116899e-45 -2.35000529e-51] [ 2.10000000e-05 3.04638010e-45 3.04638010e-45 -2.59086519e-51] [ 2.20000000e-05 2.86794944e-45 2.86794944e-45 -2.84347125e-51] ... [ 9.99998000e-01 1.12081104e-36 1.12081104e-36 2.92351422e-36] [ 9.99999000e-01 1.12081125e-36 1.12081125e-36 2.92372017e-36] [ 1.00000000e+00 1.12081141e-36 1.12081141e-36 2.92392603e-36]]
  • t0 : 0.0
  • modes : [(2, 2), (2, 1), (3, 3), (4, 4)] '''

waveform paramters

'''

  • minf : 2e-05
  • maxf : 1
  • fend : None
  • tmin : None
  • tmax : 1.0
  • 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 3.26116899e-45 3.26116899e-45 -2.35000529e-51] [ 2.10000000e-05 3.04638010e-45 3.04638010e-45 -2.59086519e-51] [ 2.20000000e-05 2.86794944e-45 2.86794944e-45 -2.84347125e-51] ... [ 9.99998000e-01 1.12081104e-36 1.12081104e-36 2.92351422e-36] [ 9.99999000e-01 1.12081125e-36 1.12081125e-36 2.92372017e-36] [ 1.00000000e+00 1.12081141e-36 1.12081141e-36 2.92392603e-36]]
  • t0 : 0.0
  • modes : [(2, 2), (2, 1), (3, 3), (4, 4)] '''

waveform paramters

'''

  • minf : 2e-05
  • maxf : 1
  • fend : None
  • tmin : None
  • tmax : 1.0
  • 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 3.26116899e-45 3.26116899e-45 -2.35000529e-51] [ 2.10000000e-05 3.04638010e-45 3.04638010e-45 -2.59086519e-51] [ 2.20000000e-05 2.86794944e-45 2.86794944e-45 -2.84347125e-51] ... [ 9.99998000e-01 1.12081104e-36 1.12081104e-36 2.92351422e-36] [ 9.99999000e-01 1.12081125e-36 1.12081125e-36 2.92372017e-36] [ 1.00000000e+00 1.12081141e-36 1.12081141e-36 2.92392603e-36]]
  • t0 : 0.0
  • modes : [(2, 2)] '''

Input parameters


- log : log/SO6a_localization_mbhb.log
- config : config.yml
- subconfig : 
- duration : 1.0 yr
- duty_cycle : 0.75
- armlength : 2500000000.0 m
- noise : CBE_1yr_6yr_tdi2/noise_background_1_yr.npy
- show : False
- fast : 0
- tdi2 : 1
- freqs : [2e-05, 1]
- force_duration : 1_yr
- report : CBE_1yr_6yr_tdi2/report_SO6a_localization_mbhb.md
- fom_data : ['CBE_1yr_6yr_tdi2/SO6a-fom-data-mbhb.heavy-nodelay.npy', 'CBE_1yr_6yr_tdi2/SO6a-fom-data-mbhb.heavy-delay.npy', 'CBE_1yr_6yr_tdi2/SO6a-fom-data-mbhb.popIII.npy']
- fom_title : MBHB as standard sirens
- fom_config : ['SO6/localization_mbhb.heavy-nodelay.yml', 'SO6/localization_mbhb.heavy-delay.yml', 'SO6/localization_mbhb.popIII.yml']
- inc_trick : False

Download

Full simulation results heavy-nodelay

Full simulation results heavy-delay

Full simulation results popIII