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Dynamical Tides in Exotic Stellar Binaries

Dynamical Tides in Exotic Stellar Binaries. Dong Lai Cornell & KITP. 2/4/2010 KITP. Three Problems: Neutron Star Binaries (NS/NS or NS/BH) White Dwarf Binaries (WD/WD, WD/NS, etc) An eccentric pulsar/massive MS Binary. Coalescing NS Binaries: The last three minutes.

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Dynamical Tides in Exotic Stellar Binaries

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  1. Dynamical Tides in Exotic Stellar Binaries Dong Lai Cornell & KITP 2/4/2010 KITP

  2. Three Problems: • Neutron Star Binaries (NS/NS or NS/BH) • White Dwarf Binaries (WD/WD, WD/NS, etc) • An eccentric pulsar/massive MS Binary

  3. Coalescing NS Binaries: The last three minutes • Most promising sources of GWs • for LIGO/VIRGO • To detect GWs, need accurate wave • forms (orbital phase evolution).

  4. Equilibrum Tide M, R M’ k2=Apsidal motion const (Love number) ==> Equilibrium tide important only at small separation (just prior to merger) (understood in 1990s: Bildsten & Cutler, Kochenek, DL, Rasio & Shaipro , etc) • Numerical GR Quasi-equilibrium NS binary sequence • (Baumgarte, Shapiro, Teukolsky, Shibata, Meudon group, etc. 1990s--200x) • Recent (semi-analytic) GR calculation of tidal effect • (Hinderer, Flanagan, Poisson, Damour etc 2008-…)

  5. Dynamical Tides: Resonant Excitation of NS Modes

  6. Results: • For R=10 km, slow-spin NSs, the number of missing cycles < 0.1, • not measurable • Number of missing cycles • Important for larger (e.g. 15 km) NS • For rapidly spinning NSs (> a few 100 Hz), many resonant channels lead to • large GW phase error Summary: Resonant Excitations of NS Modes During Binary Inspiral Non-rotating NS: G-mode (Reisenegger & Goldreich 1994; DL 1994) Rotating NS: G-mode, F-mode, R-mode (Ho & DL 1999) Inertial modes (DL & Wu 2006) R-mode (excited by gravitomagnetic force; Racine & Flanagan 2006)

  7. Compact White Dwarf Binaries (WD/WD, WD/NS, WD/BH) Ongoing work with Jim Fuller (Cornell) • Possible SN Ia progenitors • Sources for LISA (EM counterparts…)

  8. Resonant tidal excitation of g-modes in WD (assuming non-rotating WD for now…) Orbital equations that include 1. Back-reaction of excited modes on orbit 2. Gravitational radiation reaction

  9. Semi-analytic result: ===> Resonant mode amplitude up to ~8% Resonant mode energy up to

  10. Bad News: Displacement ~ R in envelope ==> Linear calculation is problematic Nonlinear damping important

  11. Tentative Summary: Dynamical Tides in Compact WD Binaries • Long before merger, may transfer a lot of energy to • internal modes/waves (nonlinear), making WD bright. • More works to be done… • Main venue for angular momentum transfer (synchronization) • Relevant to GW detection by LISA, SN Ia progenitors

  12. Dynamical Tides in an Eccentric Pulsar/MS Binary DL96,97; cf. Kumar & Quataert 97,98 Relevant facts: PSR J0045-7319 B star companion: Orbit: (spinning, S & L misaligned) Key observation: orbital decay

  13. Mechanism of Orbital Decay (Equilibrium tide does not work, regardless of tidal Q…) Dynamic tide: At each periastron passage, energy (and J) is transferred to internal modes (g-modes), which is (partially) damped ==> orbital decay Dominant modes are those with

  14. Energy in modes Steady state: typically Secular orbital evolution: Orbital energy

  15. Energy in modes Steady state: typically Secular orbital evolution: Orbital energy Mean motion resonance: when

  16. Spin Effects • Retrograde rotation increases • energy transfer to modes • ==> faster orbital decay • Pseudo-synchronization J transfer (for e=0.8) Energy transfer By contrast, equilibrium tidal eqn gives • All these will be complicated by • differential rotation

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