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

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Implication of Eccentricity for GWDA Martel Poisson Investigated reduction in SNR if eccentric signals are recd but searched for in data by circular templates - nonoptimal signal processing Found that for a binary system of given total mass, the loss increases with increasing eccentricity For a given eccentricity, loss decreases as total mass is increased Fitting factor (FF) (Apostolatos) to measure degree of optimality of a given set of templates. FF is the ratio of the actual signal-to-noise ratio, obtained when searching for eccentric signals using circular templates, to the SNR that would be obtained if eccentric templates were used. FF close to unity indicates that the circular templates are quite effective at capturing an eccentric signal. FF much smaller than unity indicates that the circular templates do poorly, and a set of eccentric templates would be required for a successful search. The loss in event rate caused by using nonoptimal templates is given by 1 − FF 3 . BRI-IHP06-I – p.13/??
FF as fn of initial eccentricity e0 e0 1.0 + 1.0 1.4 + 1.4 1.4 + 2.5 1.4 + 5.0 1.4 + 10 3.0 + 6.0 6.0 + 6.0 8 .00 0.998 0.997 0.999 0.998 0.998 0.998 0.998 .05 0.960 0.976 0.985 0.992 0.992 0.998 0.996 .10 0.898 0.931 0.947 0.965 0.976 0.984 0.993 .15 0.836 0.879 0.902 0.930 0.946 0.961 0.975 .20 0.762 0.822 0.854 0.893 0.913 0.934 0.955 .25 0.695 0.761 0.802 0.852 0.885 0.903 0.930 .30 0.630 0.637 0.749 0.805 0.850 0.868 0.900 .35 0.569 0.581 0.693 0.753 0.811 0.829 0.867 .40 0.513 0.520 0.635 0.698 0.765 0.783 0.827 .45 0.454 0.460 0.574 0.637 0.714 0.732 0.781 .50 0.397 0.402 0.513 0.576 0.656 0.675 0.728 .55 0.348 0.350 0.452 0.513 0.595 0.614 – .60 0.297 0.303 0.396 0.452 0.534 – – .65 0.257 0.231 0.344 – – – – BRI-IHP06-I – p.14/??
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 and 10: Kicks, Eccentricity Compact binarie
Page 11 and 12: Related Earlier Work ∗ Peters and
Page 13: Earlier Work ∗ GW from an eccentr
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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