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Parameter Estimation for Inspiraling Compact Binaries with LISA

Parameter Estimation for Inspiraling Compact Binaries with LISA. Aaron Rogan and Sukanta Bose Washington State University, Pullman. GWDAW-2004, Annecy, France. NASA-NAG5-12837. History and current affairs. Limits on sky-position accuracy

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Parameter Estimation for Inspiraling Compact Binaries with LISA

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  1. Parameter Estimation for Inspiraling Compact Binaries with LISA Aaron Rogan and Sukanta Bose Washington State University, Pullman GWDAW-2004, Annecy, France NASA-NAG5-12837 Bose / GWDAW-2004

  2. History and current affairs • Limits on sky-position accuracy • Cutler ’98: Michelson var., no Doppler f-modulation, monochromatic sources (galactic binaries & SMBH mergers) • Plus • Takahashi & Seto ’01: Michelson var., no Doppler f-modulation, but • Validity of the long-wavelength approximation • Cornish & Rubbo ’03. • Vecchio & Wikham ’04: good for • This work: Estimates • Use 2nd generation Time-Delay-Interferometry (TDI) variables • Account for Doppler f-modulation, • Study the variation of estimates as a function of all sky positions (10mHz @1yr) Bose / GWDAW-2004

  3. LISA TDI Sensitivity as a function of frequency First generation TDI Second generation TDI Bose / GWDAW-2004

  4. LISA’s directional sensitivityvarying with orbital position [Rogan, SB, CQG 21, ’04.] Bose / GWDAW-2004

  5. Parameter estimates as functions of sky position(without frequency evolution or redshifting) Normalized for SNR=1 Bose / GWDAW-2004

  6. Estimating sky position (No frequency evolution or redshifting) >= 0.06 steradians (for SNR =1) >= 2500 square-degrees Bose / GWDAW-2004

  7. Estimating the chirp The frequency evolution, the source frequency, and the signal amplitude yield the distance to source. [Schutz, Nature 323, ’86] (no redshifting yet) Bose / GWDAW-2004

  8. Chirping versus red-shifting No. of bins 6.0 4.5 3.0 1.5 f (Hz) 0.3 Bose / GWDAW-2004

  9. Parameter estimates comparisonDoppler Shifting vs. no Doppler shifting:The solid angle Bose / GWDAW-2004

  10. Parameter Estimates as a Function of Frequency:Resultswith 2nd gen. TDI (but no redshifting) Bose / GWDAW-2004

  11. Summary • Accurate parameter estimation required for demographics, galaxy formation & structure (galactic binaries) and cosmology (SMBHs); but the former is also crucial for modeling the confusion noise • We also find that: • Compared to Michelson var., the TDI variables, by themselves, do not affect the parameter accuracies; but they do show less sensitivity at f ~ c/L. • important for galactic binaries for f > a few mHz • Doppler f-modulation, : Account for it even for f > 1 mHz Improves targeting, esp. at the ecliptic poles. • Also, LISA’s relatively large sensitivity at 60 and 120 degs helps it target the disk binaries particularly well. • For T =1 year, the spread in frequency due to Doppler modulation is comparable to that caused by chirping (in a 6 BBH) at ~10mHz. Bose / GWDAW-2004

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