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Introduction to SLGT:Binary Black Hole Coalescence and Gravitational wave detection in 0.1-10 Hz
Yeong-Bok Bae (KASI)Sang-Hyeon Ahn (KASI), Gungwon Kang (KISTI), ChungleeKim (KASI), Whansun Kim (NIMS), John J. Oh (NIMS), Sang Hoon Oh (NIMS), Chan Park (KISTI), Edwin J. Son (NIMS), Yong Ho Lee (KRISS)
Outline
βͺ Introductionβ SLGT
β Binary black holes
βͺ Detector and sourcesβ Power spectral density
β Signal to noise ratio
βͺ Detection Rate
βͺ Summary
KKN & Pilot study for SLGT
βͺ KKN (KASI-KISTI-NIMS) collaboration
βͺ Pilot study for SLGT is funded by NST (2017.03.01.~2017.12.31.)
KASI (Korea Astronomy & Space Science Institute
KISTI(Korea Institute of Science and Technology Information)
NIMS (National Institute for Mathematical Science)
Introduction to SLGT
βͺ SLGT (Superconducting Low-frequency Gravitational-wave Telescope)β SOGRO (Superconducting Omin-directional Gravitational Radiation
Observatory)
Introduction to SLGT
βͺ Superconducting test masses are magnetically levitated.
βͺ Tensor GW detector by combining six test masses
βππ π‘ =2
πΏπ₯+ππ π‘ β π₯βππ π‘
βππ π‘ =1
πΏπ₯+ππ π‘ β π₯βππ π‘ β π₯βππ π‘ β π₯+ππ π‘ , π β π
βͺ Source direction and wave polarization can be determined by a single detector.
βͺ Enlargement of SGG (Superconducting Gravity Gradiometer)
Paik et al. 2016
Introduction to SLGT
http://rhcole.com/apps/GWplotter/
eLISA
aLIGO
SLGT
Gravitational Wave(GW) sources
βͺ GRB/Supernova, Spinning Neutron star, Cosmological Sources, β¦
βͺ Compact Binary Coalescence (CBC)β Strongest source
β Predictable wave forms
β Detectable frequency & Strength for ground-based detectors
Formation of Binary Black Hole (BBH)
βͺ Environment
β Field or disk βͺ Stellar binary evolution
βͺ Mass transfer, common envelope, β¦
β Globular cluster or galactic centerβͺ Dynamics of cluster β core collapse, mass segregation
βͺ Three-body process
βͺ Capture driven by gravitational radiation (GR capture)
βͺ Intermediate mass black hole
Main target of SLGT
βͺ Frequency range of SLGTβ’ Lower than aLIGO: 0.1-10 Hz
βͺ Highest inspiral frequency of BBH
β’ Innermost Stable Circular Orbit (ISCO) ππΌππΆπ =6πΊπ
π2
β’ ππΌππΆπ,πΊπ =1
π
1
6
3/2 π3
πΊ(π1+π2)~
4396
π
πβ
Hz
βͺ Intermediate Mass Black Hole (IMBH) binary
βͺ Intermediate Mass Ratio Inspiral (IMRI)
ASD & SNR of BBH
βͺ ASD (Amplitude spectral density)πβ(π) = 2π1/2 ΰ·¨β(π)
βͺ SNR (Signal to noise ratio)
π = 4ΰΆ±0
ππΌππΆπ ΰ·¨β(π)2
ππ(π)ππ
βͺ For the inspiral phase,
ΰ·¨β(π) =2
π·
5
96πβ2/3
1 + π§ πΊππ
π3
5/6
ππβ7/6
wβπππ π· π§ = (1 + π§)π
π»0ΰΆ±0
π§ ππ§β²
Ξ©π(1 + π§β²)3+Ξ©π(1 + π§β²)2+Ξ©Ξ
(Dalal et al. 2006, Abadie et al. 2010, Moore et al. 2015)
Inspiral + Merger + Ringdown
βͺ For the non-precessing spins (Ajith et al. 2011)
βͺ ΰ·¨β π = π΄ π πβπΞ¨ π
π΄ π = πΆπ1β7/6
πβ²β76 1 +
π=2
3
πΌππ£π ππ π < π1
πππβ²β23 1 +
π=1
2
πππ£π ππ π1 β€ π < π2
ππβ π, π2, π ππ π2 β€ π < π3
π€βπππ πβ² β‘ Ξ€π π1 , π£ β‘ πππ Ξ€1 3, π1 = 1.4547π β 1.8897, π2 = β1.8153π + 1.6557,
πΌ2 = β Ξ€323 224 + Ξ€451π 168 , πΌ3 = Ξ€27 8 β Ξ€11π 6 π, π β‘π1π2
π1+π22 , Ο β‘
π1π1+π2π2
π1+π2,
β: πΏπππππ‘π§πππ ππ’πππ‘πππ
ππ β‘ π1, π2, π, π3 , ππππ = ππ0 +
π=1
3
π=0
π
π¦πππππππ , π β‘ min(3 β π, 2)
Horizon distance
Binary: face on Equal mass Ξ€π1 π2 = 1,SNR π = 5
IMBH formation (Giersz et al. 2016)
βͺ Existence of IMBH?β Extrapolating the relation between the BH mass and the velocity dispersion
of host galaxy to the globular cluster (Gultekin et al. 2009)
β Observational evidences ?(Patruno et al. 2006, Maccarone et al. 2007, Oka et al. 2016, Kiziltan et al. 2017)
βͺ Formation mechanisms1. Direct collapse of PopIII stars (Madau & Rees 2001)
2. Runaway merging of massive main sequence stars in dense young star clusters (Portegies Zwart et al. 2004)
3. Accretion of gas on the stellar mass BHs (Leigh et al. 2013)
4. Buildup of BH mass through the mergers in dynamical interactions and mass transfers in binaries (Giersz et al. 2015)
Detection Rate of IMBH binary (IMBHB)
βͺ Fregeau et al. (2006), Amaro-Seoane & Santamaria (2010)
where π2πππΉ/πππππ‘π : star formation rate (SFR) per unit comoving volume and unit local time
(Madau & Pozzetti 2000, Steidel et al. 1999, Blain et al. 1999)
πππ: fraction of star forming mass that goes into star clusters
π: fraction of clusters that have IMBHBs
π(πππ): distribution function of cluster masses (Zhang & Fall 1999, π πππ β πππβ2, 103.5 β 107Mβ)
βͺ Mass fraction of IMBHB in the cluster is assumed to be ππΊπΆ = 2 Γ 10β3.
SFR model
βͺ SF1 (Madau & Pozzetti 2000)π2πππΉ1
πππππ‘π= 0.3β65πΉ π§
exp 3.4π§
exp 3.8π§ +45Mβ yr
-1 Mpc-3
βͺ SF2 (Steidel et al. 1999)
π2πππΉ2
πππππ‘π= 0.15β65πΉ π§
exp 3.4π§
exp 3.4π§ +22Mβ yr
-1 Mpc-3
βͺ SF3 (Blain et al. 1999)
π2πππΉ3
πππππ‘π= 0.2β65πΉ π§
exp 3.05π§β0.4
exp 2.93π§ +15Mβ yr
-1 Mpc-3
where β65 = β/0.65
and πΉ π§ = Ξ©π 1 + π§ 3 + Ξ©π 1 + π§ 2 + Ξ©Ξ/(1 + π§)3/2
βͺ Double cluster channel (collision of two clusters)
βͺ π πππ’πππ = ππππππ π πππππ (πππππ β [0.1,1])
βͺ Should be considered moreβ Tensor detectorβ IMBHB mass fractionβ More BH mergers in a clusterβ Higher modes of GWsβ IMRI ratesβ Orbital hang-up (BH spin effect)
Detection Rate of IMBH binary (IMBHB)
Estimation Conservative Reference Optimistic
Assumptions
SNR π = 5, π = 0.25, π = 0, π‘πππ = 1 year, ππΊπΆ = 2 Γ 10β3
Averaged over binary orientation
ππ΅π΅π»,πππ₯ = 2 Γ 104 Mβ,
πππ = 0.0025,π = 0.1,Ξ€π πππ’πππ π π πππππ = 0.1
ππ΅π΅π»,πππ₯ = 2 Γ 104 Mβ,
πππ = 0.1,π = 0.1,Ξ€π πππ’πππ π π πππππ = 0.5
ππ΅π΅π»,πππ₯ = 105 Mβ,
πππ = 0.1,π = 0.5,Ξ€π πππ’πππ π π πππππ = 1
Detection Rate [yr-1] 0.013 0.72 7.5
Summary
βͺ BBH sources for SLGT (0.1-10 Hz) are studied.
βͺ aSOGRO (50m) is expected to detect BBH coalescences.β IMBHBs up to ~105 Mβ.
β IMRIs with ~104 Mβ.
β GW150914-like BBH inspirals ?
βͺ Detection rate of IMBHBs are expected (0.013-7.5) yr-1 with aSOGRO (50m).β But highly dependent on the detector sensitivity and astrophysical
models.