Detection rates for a new waveform background design adopted from The Persistence of Memory, Salvador Dali, 1931 Bence Kocsis, Merse E. Gáspár (Eötvös University, Hungary) Advisor: Szabolcs Márka (Columbia) astro- ph/

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 PE Non-relativistic PE

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 Detection Noise spectral density  Calculable specifically for PE waveforms and detector noise

SIMPLE ESTIMATES Rough estimates using only average quantities –Typical radius of the system: R gc =1 pc –Number of regular stars: N s =10 6 –Number of compact objects: N=10 3 –Typical mass of compact objects: m=10 M ☼ –Average velocity in the system: v=v vir –Newtonian dynamics v∞v∞ v0v0 f 0 = v 0 / b 0 ~ N 2 m 4/3 R –3 v –1 f 0 –2/3 = 6.7 x 10 –15 yr –1 b∞b∞ b0b0

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 R m –3 ~ m 3/2 v ∞ –1 ~ m 1/2 σ foc ~ m 4/3 V ~ A 3 ~ m 5 Detection Rate ~ m 8.33

Mass distribution –Neutron stars Thin Gaussian distribution –Black holes m min = 5M ☼, 40M ☼, 80M ☼ m max = 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 R m = (m/ ) –1/2 R gc v m = (m/ ) –1/2 v vir m min, m max, g(m) ~ m –p v rel ≡ v 12 = [(m 1 –1 + m 2 –1 ) ] 1/2 v vir m ns ~ 1.35 M ☼

Event Rate for a Single Globular Cluster per year Comoving Event Rate for d[ln(f 0 )] bins [yr —1 ] Relativistic PE Non-relativistic PE Head-on collisions

Maximum luminosity distance Relativistic PE Head-on collisions Non-relativistic PE Non-cosmolocial distance Cosmological distance m BH = 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 m max ~ 60 – 100 M ☼ (Belczynski et al. 2005) –Detection rates scale with m 8.33 What is the exact # of BHs ejected/retained? –Depending on models: N ~ 1 – 100 (O’Leary et al 2006) –Detection rates scale with N 2 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 R core – 4 –GW recoil?? –leads to a train of signals after an initil PE

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

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