Detection rates for Detection rates for a a

new waveformnew waveform

background design adopted from The Persistence of Memory, Salvador Dali, 1931

Bence Kocsis, Merse E. Gáspár(Eötvös University,

Hungary)

Advisor:

Szabolcs Márka (Columbia)

astr

o-p

h/

astr

o-p

h/

0603441

0603441

Advantages of the new kind of waveform•Large amplitude –

detectable from large distances•The waveform is known analytically for a large portion of the parameter space

•The physics of the process is well understood

Two objects with sufficiently large masses that approach sufficiently closely produce gravitational radiation that is detectable

Very detailed analysis

• Mass distribution– Neutron stars– Black holes (different

models)•Mass segregation•Mass dependent virial velocity•Relative velocities•General relativistic correction for dynamics and waveform•General relativity for cosmology

–Cosmological volume element–Redshifting of GW frequency and single GC event rate

Total Detection Rate as a function of characteristic

frequency

Total Cumulative Detection Rate

as a function of minimum separation

Relativistic P

E

Non-relativistic P

E

Total Detection Rate as a function of total mass

NS

/NS BH/NS

BH/BH

Conclusions

• PEs are an important source to consider for GW detection

• What could we learn from PE observations?– measure mass distribution of BHs– Constrain abundance of dense clusters

of BHs– test theories

•Are BHs ejected?

Conclusions

• PEs are an important source to consider for GW detection

• What could we learn from PE observations?– measure mass distribution of BHs– Constrain abundance of dense clusters

of BHs– test theories

•Are BHs ejected?

Signal to Noise Ratio for Matched Filtering

DetectionN

oise

spe

ctra

l den

sity

Calculable specifically for PE waveforms and detector noise

SIMPLE ESTIMATES• Rough estimates using only average

quantities– Typical radius of the system: Rgc=1 pc

– Number of regular stars: Ns=106

– Number of compact objects: N=103

– Typical mass of compact objects: m=10 M☼

– Average velocity in the system: v=vvir

– Newtonian dynamicsv∞

v0

f0 = v0 / b0

~ N2 m4/3 R–3 v–1 f0–2/3 = 6.7 x 10–15 yr–1

b∞b0

How precise is that?

• In reality bigger masses are confined within a smaller radius

• Larger mass objects have a smaller velocity

• Gravitational focusing• Detectable volume

Rm–3 ~ m3/2

v∞–1 ~ m1/2

σfoc ~ m4/3

V ~ A3 ~ m5

Detection Rate ~ m8.33

• Mass distribution– Neutron stars

• Thin Gaussian distribution – Black holes

• mmin = 5M☼, 40M☼, 80M☼

• mmax = 20M☼, 60M☼, 100M☼

• p = 0, 1, 2

• Mass segregation• Mass dependent virial velocity• Relative velocities• General relativistic correction for dynamics and

waveform– Test particle emitting quadrupole radiation (Gair et al.

2005)

• General relativity for cosmology– Cosmological volume element– Redshifting of GW frequency and single GC event rate

Improved model

Rm = (m/<m>)–1/2 Rgc

vm = (m/<m >)–1/2 vvir

mmin, mmax, g(m) ~ m–p

vrel ≡ v12 = [(m1–1 + m2

–1) <m>]1/2 vvir

mns ~ 1.35 M☼

Event Rate for a Single Globular Cluster per

year

Com

ovin

g E

vent

Rat

e

for

d[ln

(f0)

] bi

ns [

yr—

1 ]

Relativistic PE

Non-relativistic PE Head-on

collisions

Maximum luminosity distance

Relativistic P

E

Head-on collisions

Non-relativistic PE

Non-cosmolocial distance

Cosmological distance

mBH = 40 M☼

Total Detection Rate as a function of mass

ratio

BH/NS BH/BH

What uncertainties remain?

• Model parameters– What is the mass distribution?

• Are there BHs with masses 20M☼< m < 60M☼?

– Initial mass function extends to mmax ~ 60 – 100 M☼ (Belczynski et al. 2005)

– Detection rates scale with m8.33

• What is the exact # of BHs ejected/retained?– Depending on models: N ~ 1 – 100 (O’Leary et al 2006)– Detection rates scale with N2

• Major caveats– Core collapse??

• Final core radius is yet uncertain, depends on e.g. initial binary fraction (Heggie, Tenti, & Hut, 2006)– Core radius decreases by an additional factor of 1– 14– Detection rates scale with Rcore

– 4

– GW recoil??– leads to a train of signals after an initil PE

Initial mass distribution of BHs

Belczynski, Sadowski, Rasio, & Bulik, 2006

pro

ba

bili

tyModel I

Model II

Time evolution of the BH numbers

O’Leary, Rasio, Fregeau, Ivanovna, & O’Shaughnessy, 2006