Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

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Compact star clusters Yet another scenario that can create inspiralling eccentric binaries with short periods involves compact star clusters. It was noted that the interplay between GW-induced dissipation and stellar scattering in the presence of an intermediate-mass black hole can create short-period highly eccentric binaries C. Hopman and T. Alexander (2005) A very recent attempt to model realistically compact clusters that are likely to be present in galactic centers indicates that compact binaries usually merge with eccentricities G. Kupi, P. Amaro-Seoane, and R. Spurzem (2006), BRI-IHP06-I – p.9/??
Related Earlier Work ∗ Peters and Mathews (1963,64), Seminal work ∗ Wahlquist (1987), Spacecraft Doppler detection of GW from CB, Newtonian GW polarization ∗ Lincoln Will (1990), Osculating orbital elements, Numerical integration, effects of eccentricity and dominant radiation damping on GW polarisations ∗ Wagoner Will (1976), Blanchet Schäfer(1989,1993), Junker Schäfer (1992), Rieth-Schäfer (1997) 1PN and 1.5PN FZ fluxes, GW polarizations for CB in eccentric orbits ∗ Moreno-Garrido, Buitrago and Mediavilla, (1994, 95) effect on GW polarizations of introducing by hand some secular effects either in the longitude of the periastron or in the semi-major axis and eccentricity. BRI-IHP06-I – p.10/??
Page 1 and 2: Gravitational Waves from Inspiralli
Page 3 and 4: Introduction Inspiralling Compact B
Page 5 and 6: Kozai Mechanism One proposed astrop
Page 7 and 8: Kozai Mechanism, Globular Clusters
Page 9: Kicks, Eccentricity Compact binarie
Page 13 and 14: Earlier Work ∗ GW from an eccentr
Page 15 and 16: FF as fn of initial eccentricity e0
Page 17 and 18: Eccentric Signal Plots of s(t) (up
Page 19 and 20: The Generation Modules Generation p
Page 21 and 22: Present Work Represent GW from a bi
Page 23 and 24: PN order of Multipoles For a given
Page 25 and 26: Radiative moments - Source moments
Page 27 and 28: 3PN EOM for ICB a i = dvi dt AE = 1
Page 29 and 30: Instantaneous Terms dE dt inst d
Page 31 and 32: 3PN Instantaneous Terms dE dt 2PN
Page 33 and 34: Transfn of World lines Having obtai
Page 35 and 36: Energy Flux - Modified Harmonic Coo
Page 37 and 38: 3PN generalised Quasi-Keplerian rep
Page 39 and 40: 3PN generalised Quasi-Keplerian rep
Page 41 and 42: 3PN GQKR - Mhar n = (−2E) 3/2 +11
Page 43 and 44: 3PN GQKR - Mhar + Φ = 2 π 70 16
Page 45 and 46: Orbital average - Energy flux -MHar
Page 47 and 48: Orbit Averaged Energy Flux - MHar <
Page 49 and 50: Comments Note: No term at 2.5PN. 2.
Page 51 and 52: Comments Useful internal consistenc
Page 53 and 54: Gauge Invariant Variables < ˙ E >
Page 55 and 56: Gauge Invariant Variables < ˙ E3PN
Page 57 and 58: Hereditary Contributions F 3PN tail
Page 59 and 60: Log terms in total energy flux Summ
Page 61 and 62:
Log terms in total energy flux FZ t
Page 63 and 64:
Complete 3PN energy flux - Mhar <
Page 65 and 66:
Complete 3PN energy flux - Mhar <
Page 67 and 68:
Present Work Extends the circular o
Page 69 and 70:
Angular Momentum Flux Hereditary co
Page 71 and 72:
Far Zone Angular Momentum Flux dJi
Page 73 and 74:
Far Zone Angular Momentum Flux dJi
Page 75 and 76:
3PN AMFlux - Shar dJi dt dJi dt
Page 77 and 78:
Orbital Averaged AMF - ADM Using th
Page 79 and 80:
Orbital Averaged AMF - ADM 〈 dJ d
Page 81 and 82:
Orbital Averaged AMF - ADM 〈 dJ d
Page 83 and 84:
Evoln of orbital elements under GRR
Page 85 and 86:
Evoln of orbital element n under GR
Page 87 and 88:
Evoln of orbital element n under GR
Page 89 and 90:
Evoln of orbital element et under G
Page 91 and 92:
Evoln of orbital element ar under G
Page 93 and 94:
Evoln of orbital element ar under G
Page 95 and 96:
PART II Based on Phasing of Gravita
Page 97 and 98:
Beyond Orbital Averages Going beyon
Page 99 and 100:
Phasing of GWF TT radn field is giv
Page 101 and 102:
Phasing of GWF Orbital phase = φ,
Page 103 and 104:
Method of variation of constants A
Page 105 and 106:
Method of variation of constants c1
Page 107 and 108:
Method of variation of constants At
Page 109 and 110:
Method of variation of constants An
Page 111 and 112:
Method of variation of constants Al
Page 113 and 114:
Method of variation of constants Fo
Page 115 and 116:
Method of variation of constants Du
Page 117 and 118:
Implementation Compute 3PN accurate
Page 119 and 120:
3PN accurate conservative dynamics
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
3.5PN accurate reactive dynamics A
Page 131 and 132:
3.5PN accurate reactive dynamics Fi
Page 133 and 134:
3.5PN accurate reactive dynamics dc
Page 135 and 136:
3.5PN accurate reactive dynamics 4
Page 137 and 138:
Secular variations d¯n dt dēt dt
Page 139 and 140:
Periodic variations To complete thi
Page 141 and 142:
Periodic variations One can analyti
Page 143 and 144:
Periodic variations ˜cl = − 2ξ5
Page 145 and 146:
Periodic variations Above results m
Page 147 and 148:
Periodic variations ˜ l(l; ¯ca) =
Page 149 and 150:
¯n/ni and ñ/n versus l/(2π) n /
Page 151 and 152:
h+(t) and h×(t) Scaled h + (t) Sca
Page 153 and 154:
¯n/ni and ñ/n ēt and ˜et versus
Page 155 and 156:
¯cl and ˜cl ¯cλ and ˜cλ versu
Page 157 and 158:
Validity of Results Circular orbits
Page 159:
References 1. P. C. Peters, Phys. R
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Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

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