Detection rates for a new waveform
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Detection rates for a new waveform. astro-ph/0603441. Bence Kocsis , Merse E. Gáspár (E ö tv ö s University, Hungary) Advisor: Szabolcs M á rka (Columbia). background design adopted from The Persistence of Memory, Salvador Dali, 1931. Advantages of the new kind of waveform.

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Detection rates for a new waveform

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Detection rates for a new waveform

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


Advantages of the new kind of waveform

Advantages of the new kind of waveform

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


Very detailed analysis

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 Detection Rate as a function of characteristic frequency


Total cumulative detection rate as a function of minimum separation

Relativistic PE

Total Cumulative Detection Rateas a function of minimum separation

Non-relativistic PE


Total detection rate as a function of total mass

BH/BH

BH/NS

NS/NS

Total Detection Rate as a function of total mass


Conclusions

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?


Conclusions1

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 detection

Signal to Noise Ratio for Matched Filtering Detection

  • Calculable specifically for PE waveforms and detector noise

Noise spectral density


Simple estimates

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 dynamics

v∞

f0 = v0/b0

b0

b∞

v0

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


How precise is that

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


Improved model

Improved model

  • 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

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


Event rate for a single globular cluster per year

Relativistic

PE

Head-on collisions

Event Rate for a Single Globular Cluster per year

Non-relativistic PE

Comoving Event Rate

for d[ln(f0)] bins [yr—1 ]


Maximum luminosity distance

Cosmological distance

Head-on

collisions

Relativistic PE

Maximum luminosity distance

Non-cosmolocial distance

Non-relativistic PE

mBH = 40 M☼


Total detection rate as a function of mass ratio

BH/NS

BH/BH

Total Detection Rate as a function of mass ratio


What uncertainties remain

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

Initial mass distribution of BHs

Model I

Belczynski,

Sadowski,

Rasio, &

Bulik, 2006

probability

Model II


Time evolution of the bh numbers

Time evolution of the BH numbers

O’Leary,

Rasio,

Fregeau,

Ivanovna, &

O’Shaughnessy, 2006


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