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Detection rates for a new waveform

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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  1. 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

  2. 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

  3. 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

  4. Total Detection Rate as a function of characteristic frequency

  5. Relativistic PE Total Cumulative Detection Rateas a function of minimum separation Non-relativistic PE

  6. BH/BH BH/NS NS/NS Total Detection Rate as a function of total mass

  7. 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?

  8. 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?

  9. Signal to Noise Ratio for Matched Filtering Detection • Calculable specifically for PE waveforms and detector noise Noise spectral density

  10. 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

  11. 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

  12. 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

  13. 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 ]

  14. Cosmological distance Head-on collisions Relativistic PE Maximum luminosity distance Non-cosmolocial distance Non-relativistic PE mBH = 40 M☼

  15. BH/NS BH/BH Total Detection Rate as a function of mass ratio

  16. 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

  17. Initial mass distribution of BHs Model I Belczynski, Sadowski, Rasio, & Bulik, 2006 probability Model II

  18. Time evolution of the BH numbers O’Leary, Rasio, Fregeau, Ivanovna, & O’Shaughnessy, 2006

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