1. BREAKDOWN OF PN TEMPLATES FOR MASSIVE INSPIRALING BINARIES OBSERVED BY LIGO-I: The Necessity to Expand the Template Family Kip S. Thorne CaRT, California Institute of Technology LSC Meeting Baton Rouge, LA - 15 March 2001 LIGO-G010150-00-R

2. 2 Overview The most likely sources for detection are the inspiral of BH/BH and BH/NS binaries, with large total masses, M  10Msun »Because of event rate estimates [Kalogera] »Also, more massive systems give larger signals For these systems, a large fraction of the signal to noise comes from the late inspiral stage (“IBBH regime”), where Post- Newtonian templates may have substantial errors. To deal with this in matched-filter searches, we must expand the template family to cover a function space that is large enough to include (or come close to) the real, unknown waveforms This may be possible because the number of cycles in the IBBH regime is fairly small. The later the inspiral stage, the worse the errors but the smaller the number of cycles. These most frequent sources may well have substantial spins [cf. Kalogera’s estimates]; we must include spin-induced modulations in the templates. This talk: Some rough numerical estimates

3. 3 Frequency Band For LIGO-I noise curve, Newtonian, quadrupole approximation 6% of (S/N) 2 comes from f<f L = 60 Hz and 6% from f<f U = 300 Hz 88% of (S/N) 2 [94% of S/N] is from f L < f < f U fLfL fUfU

4. 4 Number of GW Cycles and Modulation Cycles Newtonian, quadrupole approximation Number of GW cycles ~ M/  »plot for equal mass binaries, M/  = 4 »2.5 times larger for M1=10 M2 Upper limit on number of modulation cycles 1 10 100 M/Msun 6 20 15 10 30 Number of GW cycles at f L < f < f U Number of GW cycles lost at f> f U Limit on Number of Modulation Cycles

5. 5 Frequency of Waves at Onset of PN Failure Onset of failure: » in extreme-mass-ratio [“Teukolsky formalism”] case, adding terms higher than 2PN causes phasing to change by > 1/2 cycle »see Brady, Creighton, Thorne, IBBH paper For total binary mass above 15Msun, the entire frequency band f L < f < f U is in the failure regime!! 5 10 100 Frequency, Hz 60 200 150 100 300 Onset of PN Failure 50 20 3 Mass/Msun.060.30.50.80.94(S/N) 2 before failure

6. 6 Number of GW Cycles and Modulation Cycles in Failure Regime Number of GW cycles ~ M/  »plot for equal mass binaries, M/  = 4 »2.5 times larger for M1=10 M2 A few tens of cycles for equal mass case; up to 200 for 10:1 mass ratio Modulation cycles could be comparable to GW cycles 1 10 100 M/Msun 6 20 15 10 30 Number of GW cycles at f L < f < f U Limit on Number of Modulation Cycles

7. 7 Conclusion In view of the low expected event rates for LIGO-I, and the likelihood that spinning, massive binaries are the dominant sources, it is essential to include the precession-induced modulations and widen the template space to compensate for PN failure. Failing to do so could quite possibly reduce the observed event rate in LIGO-I from several to zero. Widening the template space may be feasible because: »The number of cycles in the PN Failure Regime is fairly small: a few tens to several hundred. »The later the inspiral stage, the worse the errors,but the smaller the number of cycles.