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

▪ Introduction– SLGT

– Binary black holes

▪ Detector and sources– Power spectral density

– Signal to noise ratio

▪ Detection Rate

▪ Summary

KKN & Pilot study for SLGT

▪ KKN (KASI-KISTI-NIMS) collaboration

▪ 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

▪ SLGT (Superconducting Low-frequency Gravitational-wave Telescope)– SOGRO (Superconducting Omin-directional Gravitational Radiation

Observatory)

Introduction to SLGT

▪ Superconducting test masses are magnetically levitated.

▪ Tensor GW detector by combining six test masses

ℎ𝑖𝑖 𝑡 =2

𝐿𝑥+𝑖𝑖 𝑡 − 𝑥−𝑖𝑖 𝑡

ℎ𝑖𝑗 𝑡 =1

𝐿𝑥+𝑖𝑗 𝑡 − 𝑥−𝑖𝑗 𝑡 − 𝑥−𝑗𝑖 𝑡 − 𝑥+𝑗𝑖 𝑡 , 𝑖 ≠ 𝑗

▪ Source direction and wave polarization can be determined by a single detector.

▪ 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

▪ GRB/Supernova, Spinning Neutron star, Cosmological Sources, …

▪ Compact Binary Coalescence (CBC)– Strongest source

– Predictable wave forms

– Detectable frequency & Strength for ground-based detectors

Formation of Binary Black Hole (BBH)

▪ Environment

– Field or disk ▪ Stellar binary evolution

▪ Mass transfer, common envelope, …

– Globular cluster or galactic center▪ Dynamics of cluster – core collapse, mass segregation

▪ Three-body process

▪ Capture driven by gravitational radiation (GR capture)

▪ Intermediate mass black hole

Main target of SLGT

▪ Frequency range of SLGT• Lower than aLIGO: 0.1-10 Hz

▪ Highest inspiral frequency of BBH

• Innermost Stable Circular Orbit (ISCO) 𝑟𝐼𝑆𝐶𝑂 =6𝐺𝑀

𝑐2

• 𝑓𝐼𝑆𝐶𝑂,𝐺𝑊 =1

𝜋

1

6

3/2 𝑐3

𝐺(𝑚1+𝑚2)~

4396

𝑀

𝑀⊙

Hz

▪ Intermediate Mass Black Hole (IMBH) binary

▪ Intermediate Mass Ratio Inspiral (IMRI)

ASD & SNR of BBH

▪ ASD (Amplitude spectral density)𝑆ℎ(𝑓) = 2𝑓1/2 ෨ℎ(𝑓)

▪ SNR (Signal to noise ratio)

𝜌 = 4න0

𝑓𝐼𝑆𝐶𝑂 ෨ℎ(𝑓)2

𝑆𝑛(𝑓)𝑑𝑓

▪ For the inspiral phase,

෨ℎ(𝑓) =2

𝐷

5

96𝜋−2/3

1 + 𝑧 𝐺𝑀𝑐

𝑐3

5/6

𝑐𝑓−7/6

wℎ𝑒𝑟𝑒 𝐷 𝑧 = (1 + 𝑧)𝑐

𝐻0න0

𝑧 𝑑𝑧′

Ω𝑚(1 + 𝑧′)3+Ω𝑘(1 + 𝑧′)2+ΩΛ

(Dalal et al. 2006, Abadie et al. 2010, Moore et al. 2015)

Inspiral + Merger + Ringdown

▪ For the non-precessing spins (Ajith et al. 2011)

▪ ෨ℎ 𝑓 = 𝐴 𝑓 𝑒−𝑖Ψ 𝑓

𝐴 𝑓 = 𝐶𝑓1−7/6

𝑓′−76 1 +

𝑖=2

3

𝛼𝑖𝑣𝑖 𝑖𝑓 𝑓 < 𝑓1

𝜔𝑚𝑓′−23 1 +

𝑖=1

2

𝜀𝑖𝑣𝑖 𝑖𝑓 𝑓1 ≤ 𝑓 < 𝑓2

𝜔𝑟ℒ 𝑓, 𝑓2, 𝜎 𝑖𝑓 𝑓2 ≤ 𝑓 < 𝑓3

𝑤ℎ𝑒𝑟𝑒 𝑓′ ≡ Τ𝑓 𝑓1 , 𝑣 ≡ 𝜋𝑀𝑓 Τ1 3, 𝜀1 = 1.4547𝜒 − 1.8897, 𝜀2 = −1.8153𝜒 + 1.6557,

𝛼2 = − Τ323 224 + Τ451𝜂 168 , 𝛼3 = Τ27 8 − Τ11𝜂 6 𝜒, 𝜂 ≡𝑚1𝑚2

𝑚1+𝑚22 , χ ≡

𝑚1𝜒1+𝑚2𝜒2

𝑚1+𝑚2,

ℒ: 𝐿𝑜𝑟𝑒𝑛𝑡𝑧𝑖𝑎𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛

𝜇𝑘 ≡ 𝑓1, 𝑓2, 𝜎, 𝑓3 , 𝜋𝑀𝜇𝑘 = 𝜇𝑘0 +

𝑖=1

3

𝑗=0

𝑁

𝑦𝑘𝑖𝑗𝜂𝑖𝜒𝑗 , 𝑁 ≡ min(3 − 𝑖, 2)

Horizon distance

Binary: face on Equal mass Τ𝑚1 𝑚2 = 1,SNR 𝜌 = 5

IMBH formation (Giersz et al. 2016)

▪ Existence of IMBH?– Extrapolating the relation between the BH mass and the velocity dispersion

of host galaxy to the globular cluster (Gultekin et al. 2009)

– Observational evidences ?(Patruno et al. 2006, Maccarone et al. 2007, Oka et al. 2016, Kiziltan et al. 2017)

▪ 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)

▪ Fregeau et al. (2006), Amaro-Seoane & Santamaria (2010)

where 𝑑2𝑀𝑆𝐹/𝑑𝑉𝑐𝑑𝑡𝑒 : star formation rate (SFR) per unit comoving volume and unit local time

(Madau & Pozzetti 2000, Steidel et al. 1999, Blain et al. 1999)

𝑔𝑐𝑙: fraction of star forming mass that goes into star clusters

𝑔: fraction of clusters that have IMBHBs

𝑓(𝑀𝑐𝑙): distribution function of cluster masses (Zhang & Fall 1999, 𝑓 𝑀𝑐𝑙 ∝ 𝑀𝑐𝑙−2, 103.5 − 107M⊙)

▪ Mass fraction of IMBHB in the cluster is assumed to be 𝑓𝐺𝐶 = 2 × 10−3.

SFR model

▪ SF1 (Madau & Pozzetti 2000)𝑑2𝑀𝑆𝐹1

𝑑𝑉𝑐𝑑𝑡𝑒= 0.3ℎ65𝐹 𝑧

exp 3.4𝑧

exp 3.8𝑧 +45M⊙ yr

-1 Mpc-3

▪ SF2 (Steidel et al. 1999)

𝑑2𝑀𝑆𝐹2

𝑑𝑉𝑐𝑑𝑡𝑒= 0.15ℎ65𝐹 𝑧

exp 3.4𝑧

exp 3.4𝑧 +22M⊙ yr

-1 Mpc-3

▪ SF3 (Blain et al. 1999)

𝑑2𝑀𝑆𝐹3

𝑑𝑉𝑐𝑑𝑡𝑒= 0.2ℎ65𝐹 𝑧

exp 3.05𝑧−0.4

exp 2.93𝑧 +15M⊙ yr

-1 Mpc-3

where ℎ65 = ℎ/0.65

and 𝐹 𝑧 = Ω𝑀 1 + 𝑧 3 + Ω𝑘 1 + 𝑧 2 + ΩΛ/(1 + 𝑧)3/2

▪ Double cluster channel (collision of two clusters)

▪ 𝑅𝑑𝑜𝑢𝑏𝑙𝑒 = 𝑃𝑚𝑒𝑟𝑔𝑅𝑠𝑖𝑛𝑔𝑙𝑒 (𝑃𝑚𝑒𝑟𝑔 ∈ [0.1,1])

▪ Should be considered more– Tensor detector– IMBHB mass fraction– More BH mergers in a cluster– Higher modes of GWs– IMRI rates– Orbital hang-up (BH spin effect)

Detection Rate of IMBH binary (IMBHB)

Estimation Conservative Reference Optimistic

Assumptions

SNR 𝜌 = 5, 𝜂 = 0.25, 𝜒 = 0, 𝑡𝑜𝑏𝑠 = 1 year, 𝑓𝐺𝐶 = 2 × 10−3

Averaged over binary orientation

𝑀𝐵𝐵𝐻,𝑚𝑎𝑥 = 2 × 104 M⊙,

𝑔𝑐𝑙 = 0.0025,𝑔 = 0.1,Τ𝑅𝑑𝑜𝑢𝑏𝑙𝑒 𝑅𝑠𝑖𝑛𝑔𝑙𝑒 = 0.1

𝑀𝐵𝐵𝐻,𝑚𝑎𝑥 = 2 × 104 M⊙,

𝑔𝑐𝑙 = 0.1,𝑔 = 0.1,Τ𝑅𝑑𝑜𝑢𝑏𝑙𝑒 𝑅𝑠𝑖𝑛𝑔𝑙𝑒 = 0.5

𝑀𝐵𝐵𝐻,𝑚𝑎𝑥 = 105 M⊙,

𝑔𝑐𝑙 = 0.1,𝑔 = 0.5,Τ𝑅𝑑𝑜𝑢𝑏𝑙𝑒 𝑅𝑠𝑖𝑛𝑔𝑙𝑒 = 1

Detection Rate [yr-1] 0.013 0.72 7.5

Summary

▪ BBH sources for SLGT (0.1-10 Hz) are studied.

▪ aSOGRO (50m) is expected to detect BBH coalescences.– IMBHBs up to ~105 M⊙.

– IMRIs with ~104 M⊙.

– GW150914-like BBH inspirals ?

▪ Detection rate of IMBHBs are expected (0.013-7.5) yr-1 with aSOGRO (50m).– But highly dependent on the detector sensitivity and astrophysical

models.