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Detection rates for a new waveform

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Detection rates for a new waveform

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Detection rates for a new waveform

astro-ph/0603441

BenceKocsis,

Merse E. Gáspár

(Eötvös University, Hungary)

Advisor:

Szabolcs Márka (Columbia)

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

Two objects

with sufficiently large masses

that approach sufficiently closely

produce gravitational radiation

that is detectable

- 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

- 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

Relativistic PE

Non-relativistic PE

BH/BH

BH/NS

NS/NS

- 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?

- 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?

- Calculable specifically for PE waveforms and detector noise

Noise spectral density

- 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 dynamics

v∞

f0 = v0/b0

b0

b∞

v0

~ N2m4/3 R–3 v–1 f0–2/3= 6.7 x 10–15 yr–1

- 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

- Neutron stars
- 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

mns~ 1.35 M☼

mmin, mmax, g(m)~ m–p

Rm = (m/<m>)–1/2 Rgc

vm = (m/<m >)–1/2 vvir

vrel ≡ v12 = [(m1–1 + m2–1) <m>]1/2 vvir

Relativistic

PE

Head-on collisions

Non-relativistic PE

Comoving Event Rate

for d[ln(f0)] bins [yr—1 ]

Cosmological distance

Head-on

collisions

Relativistic PE

Non-cosmolocial distance

Non-relativistic PE

mBH = 40 M☼

BH/NS

BH/BH

- 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

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

- What is the mass distribution?
- 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

- Final core radius is yet uncertain, depends on e.g. initial binary fraction (Heggie, Tenti, & Hut, 2006)
- GW recoil??
- leads to a train of signals after an initil PE

- Core collapse??

Model I

Belczynski,

Sadowski,

Rasio, &

Bulik, 2006

probability

Model II

O’Leary,

Rasio,

Fregeau,

Ivanovna, &

O’Shaughnessy, 2006