1 / 32

Keplerian-Type Parametrization: Relevance for Interferometric GW Detectors & SKA

Explore the significance of Keplerian-type parametrization for compact binaries and its relevance in the dynamics of Interferometric GW Detectors and SKA. Understand the post-Newtonian dynamics, efforts from Jena for various detectors, and the theoretical implications for SKA. Discover the parametric solutions and equations involved in accurate dynamics analysis. Learn about the detailed parametric solutions, corrections, and applications for Compact Binaries to enhance GW detection efficiency.

cicely
Télécharger la présentation

Keplerian-Type Parametrization: Relevance for Interferometric GW Detectors & SKA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Keplerian-type parametrization : Its relevance for LISA & SKA Achamveedu Gopakumar TPI, FSU-Jena, GermanyBirmingham: 30/3/06

  2. The point to realize Post-Newtonianaccurate dynamics of compact binaries along with the associated Keplerian-type parametric solution will be required to realize science potential of Interferometric GW Detectors & SKA

  3. Plan • Symbolic introduction to post-Newtonian (PN) dynamics, relevant for compact binaries • Efforts from Jena relevant for VIRGO, A-LIGO, LISA,… • Theoretical efforts useful for SKA

  4. Introduction

  5. Introduction: I • Three stages for the dynamics of compact binaries (NS-NS, NS-BH, BH-BH) Early inspiral Late stages of inspiral & subsequent plunge Ring-down

  6. Introduction: II • Till the early stages of late inspiral, post-Newtonian (PN) approximation holds good • PN approximation gives corrections to Newtonian gravitational theoryin terms of (v/c)2 ~ (G m /c2 r) Compact binaries are treated like point-masses

  7. Introduction : III • The dynamics of compact binaries in PN approximation is recently determined, both in near-zone orbital dynamics and in far-zone flux computations, to third & halfPN order : corrections up to (v/c)7 • L. Blanchet, T. Damour, G. Schäfer(Esposito-Farese, Faye, Jaranowski, Iyer, ..)

  8. Introduction: IV • H ( r, p)3.5PN= H0( r, p)+H1( r, p)+H2( r, p)+H2.5( r, p)+H3( r, p)+H3.5( r, p) [For the near zone orbital dynamics] • Similar expansions for hx(t), h+(t), ω(t) [ farzone measurable quantities] • Crucial to the templates for ICBs in quasi circular orbits

  9. Parametric solution: I • 3PN accurate conservative dynamics allows Keplerian type parametric solution • H ( r, p) PN= H0( r, p)+H1( r, p)+H2( r, p)+H3( r, p)+Hso( r, p,s1,s2) • Such solution exists even when compact objects spin

  10. Keplerian parametrization :I • Dynamics of point masses in Newtonian gravity allows Keplerian parametrization Radial motion • R = a ( 1 - e cos u )Angular motion • φ –φ0 = v = 2 tan-1 [ ( [ 1 + e]/ [ 1 - e ] )(1/2) tan u/2]Kepler Equation • l = n ( t - t0 ) = u - e sin u

  11. Keplerian parametrization :II • u & v have geometrical meaning • 3PN accurate conservative dynamics of point masses also allows Keplerian type parametric solution

  12. Parametric solution: II • Radial motionr = ar ( 1 - er cos u ) • Angular motionφ –φ0 = (1 + k ) v + ( f 4 φ + f6φ) sin 2 v + ( g 4 φ + g 6 φ ) sin 3 v + i 6 φ sin 4 v+ h 6 φ sin 5 v v= 2 tan-1 [ ( [ 1 + eφ]/ [ 1 - e φ] )(1/2) tan u/2]

  13. Parametric solution: III • 3PN accurate Kepler Equationl = n ( t - t0 ) = u - et sin u+ ( g4t + g6t ) (v - u) + ( f4t+ f6t ) sin v + i6t sin 2 v+ h6t sin 3 v • n & k are gauge invariant quantities if expressed in terms of E, J, m 1 & m 2

  14. Parametric solution: IV • Complicated parametric solution with Hso( r, p,s1,s2)Details in papers from Jena in 2004 & 2005 • There are 3 PN accurate (related) eccentricities e r , e t , eφ • Orbital elements & functions are PN accurate expressions in E, J, m 1 & m 2

  15. Parametric solution: V • Our efforts extends seminal works ofDamour, Deruelle, Schäfer & Wex • 1PN accurate Keplerian-type parametric solution is crucial for Damour-Deruelletiming formula

  16. LOTS OF APPLICATIONS Relevant for GW interferometrs & SKA

  17. Publications: I • T. Damour, A.G & B. Iyer Phys. Rev. D 70, 064028 (2004) • R. M. Memmesheimer, A.G & G. Schäfer Phys. Rev. D 70, 104011 (2004) • C. Königsdörffer & A. G Phys. Rev. D 71, 024039 (2005)

  18. Publications: II • A. G & C. Königsdörffer Phys. Rev. D 72 (Rapid Communications), 121501 (2005) • C. Königsdörffer & A. G Phys. Rev. D, 73, 044011 (2006) • C. Königsdörffer & A. G (gr-qc/0603056) • M. Tessmer& A.G, to be published(2006)

  19. Credits • DFG’s SFB/TR7Gravitationswellenastronomie(activities ofSchäfer’s group in Jena) • Collaborations with researchers in France, Germany, UK & USA

  20. Theoretical inputs useful for GW detectors

  21. Ready-to-use templates • Highly accurate & efficient ready-to-use GW templates for compact binaries of arbitrary mass ratio moving in inspiralling eccentric orbits • We adapted an approach of Damour that gave the heavily employed timing formula for relativistic binary pulsarsT. Damour, A.G, C.Königsdörffer, B.R. Iyer,..

  22. Our templates • Plots of h+(t) showing 3 relevant time scales Orbital evolution is NOT adiabatic (fully 3.5PN accurate)

  23. Our templates • Quasi-periodic variations in orbital elements • We can handle arbitrary eccentricities

  24. Applications… LISA will require these templates to hear GWs from • Galactic Stellar mass binaries • Intermediate mass BH binaries • SupermassiveBH binaries

  25. Templates for EMRIs ? • Our hx& h+should be employed to detect early stages of Extreme Mass Ratio Inspirals • Spin effects will be included soon.. • Current kludges are less accurate & inefficient • To benchmark self force computations

  26. hx& h+ for LIGO-VIRGO ? : I • Compact binaries in inspiralling eccentric orbits are plausible sources of GWs even for LIGO & VIRGO Lots of short period highly eccentric IBCs should exist • Scenarios for Short Gamma ray BurstsDavies, Leavan & King (2005), Page et.al (2006) Grindlay, Zwart & McMillan, Nature (2006) • Chaurasia & Bailes scenario (2005)

  27. hx& h+ for LIGO-VIRGO ? : II • Kozail Oscillations associated with hierarchical triplets • Interplay between GW induced dissipation & stellar scattering in the vicinity of an IMBHHopman & Alexander (2005) • Realistic dense star clusters simulations Talk by R. Spurzem

  28. SKA related investigations

  29. CreatingLISA-SKAlink: I • LISA & SKA(Square Kilometre Array)may become operational by2015+ • LISA & SKA can be used to answerWAS EINSTEIN 100 % RIGHT ?

  30. CreatingLISA-SKAlink: II • LISA & SKA will see simultaneously BinaryPulsars (What can we learn ?) • GWs from such binary pulsars will not display the effect of radiation reaction • They may be in eccentric orbits(We are working with S.Bose, M. Kramer,..)

  31. Riddle for LISA-SKA • The terminal recoilassociated with BH merger may leave signatures that may be observed with LISA & SKA Terminal recoil estimatesDamour & A.G (2006)

  32. Summary • PN accurate dynamics of spinning compact binaries of arbitrary mass ratio moving in inspiralling eccentric orbits will be required by GW & SKA communities • There are more avenues to explore

More Related