Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH
Periodic variations ˜ l(l; ¯ca) = ˜λ(l; ¯ca) = ñ(l) n dl + ˜cl(l) , ñ n + ¯ k ñ n + ˜ k dl + ˜cλ(l) , ˜k ≡ (∂k/∂n)ñ + (∂k/∂et)˜et denotes the oscillatory piece in k. Finally, to complete our study of the oscillatory contributions associated with the reactive dynamics, we compute the integrals and add them to the previous results for ˜cl(l) and ˜cλ(l), respectively. BRI-IHP06-I – p.144/??
Periodic variations ˜ l(l; ¯ca) = ξ 5/3 η 15(1 − e 2 t )3 (602 + 673e 2 t )χ + (314 − 203e 2 t − 111e 4 t ) ln χ − (602 + 673e 2 t ) + −98 + 124e2 t + 46e4 t − 72e6 t χ + + + ξ 5/3 η 5(1 − e 2 t )7/2 ξ 7/3 η 4200(1 − e 2 t )4 ξ 7/3 η 280(1 − e 2 t )9/2 96 + 292e 2 t + 37e 4 t − 105(1 − e2 t )3 χ 2 2 tan −1 [827796 − 601720η · · · · · · βt sin u 1 − βt cos u + et sin u χ 20368 − 14784η · · · · · · 2 tan −1 βt sin u + et 1 − βt cos u BRI-IHP06-I – p.145/??
- 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: 3PN accurate conservative dynamics
- Page 123 and 124: 3PN accurate conservative dynamics
- Page 125 and 126: 3PN accurate conservative dynamics
- Page 127 and 128: 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: Periodic variations Above results m
- 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
Periodic variations<br />
˜ l(l; ¯ca) =<br />
ξ 5/3 η<br />
15(1 − e 2 t )3<br />
<br />
(602 + 673e 2 t )χ + (314 − 203e 2 t − 111e 4 t ) ln χ − (602 + 673e 2 t )<br />
+ −98 + 124e2 t + 46e4 t − 72e6 t<br />
χ<br />
+<br />
+<br />
+<br />
ξ 5/3 η<br />
5(1 − e 2 t )7/2<br />
ξ 7/3 η<br />
4200(1 − e 2 t )4<br />
ξ 7/3 η<br />
280(1 − e 2 t )9/2<br />
<br />
96 + 292e 2 t + 37e 4 t<br />
<br />
− 105(1 − e2 t )3<br />
χ 2<br />
<br />
<br />
2 tan −1<br />
[827796 − 601720η · · · · · ·<br />
<br />
βt s<strong>in</strong> u<br />
1 − βt cos u<br />
<br />
<br />
+ et s<strong>in</strong> u χ<br />
<br />
<br />
20368 − 14784η · · · · · ·<br />
<br />
2 tan −1<br />
<br />
βt s<strong>in</strong> u<br />
+ et<br />
1 − βt cos u<br />
BRI-IHP06-I – p.145/??
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