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

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Beyond Orbital Averages GW obsvns of ICB, are analogous to the high precision Radio wave obsvns of binary pulsars. Uses accurate relativistic ‘timing formula’ (Damour Deruelle 85, Damour Taylor 92).. Requires soln to rel EOM for CB moving in elliptical orbit GW obsvns demand accurate ‘phasing’, i.e. an accurate mathematical modeling of the continuous time evolution of the gravitational waveform. GW emitted from inspiralling circular orbits, contain only two different time scales: orbital motion and radiation reaction Inspiralling eccentric orbits involve three different time scales: orbital period, periastron precession and radiation-reaction time scales. By using an improved ‘method of variation of constants’, one can combine these three time scales, without making the usual approximation of treating the radiative time scale as an adiabatic process. Relies on techniques from (Damour 83, 85) to implement PN ‘phasing’ for elliptical orbits. BRI-IHP06-I – p.94/??
Beyond Orbital Averages Going beyond the average evolution of the orbit under Grav Radn reaction the method allows one to deal with both a ‘slow’ (radiation-reaction time-scale) secular drift and ‘fast’ (orbital time-scale) periodic oscillations. Method implemented at the 2.5PN (Damour, Iyer, Gopakumar) and 3.5PN ( Königsdörffer, Gopakumar) Results compute new ‘post-adiabatic’ short period contributions to the orbital phasing, or equivalently, new short-period contributions to GW polarizations, h+,×, to be explicitly added to PN expn for h+,×, if one treats radiative effects on the orbital phasing in the usual adiabatic approximation. Should be of importance both for the LIGO/VIRGO/GEO network of ground based interferometric GW detectors and for space-based interferometer LISA. BRI-IHP06-I – p.95/??
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Gravitational Waves from Inspiralli
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Introduction Inspiralling Compact B
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Kozai Mechanism One proposed astrop
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Kozai Mechanism, Globular Clusters
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Kicks, Eccentricity Compact binarie
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Related Earlier Work ∗ Peters and
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Earlier Work ∗ GW from an eccentr
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FF as fn of initial eccentricity e0
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Eccentric Signal Plots of s(t) (up
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The Generation Modules Generation p
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Present Work Represent GW from a bi
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PN order of Multipoles For a given
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Radiative moments - Source moments
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3PN EOM for ICB a i = dvi dt AE = 1
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Instantaneous Terms dE dt inst d
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3PN Instantaneous Terms dE dt 2PN
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Transfn of World lines Having obtai
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Energy Flux - Modified Harmonic Coo
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3PN generalised Quasi-Keplerian rep
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3PN generalised Quasi-Keplerian rep
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3PN GQKR - Mhar n = (−2E) 3/2 +11
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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: PART II Based on Phasing of Gravita
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 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
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Periodic variations ˜ l(l; ¯ca) =
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¯n/ni and ñ/n versus l/(2π) n /
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h+(t) and h×(t) Scaled h + (t) Sca
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¯n/ni and ñ/n ēt and ˜et versus
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¯cl and ˜cl ¯cλ and ˜cλ versu
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Validity of Results Circular orbits
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References 1. P. C. Peters, Phys. R
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