Parameter Estimation for Inspiraling Compact Binaries with LISA

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Parameter Estimation for Inspiraling Compact
Binaries with LISA

• Aaron Rogan and Sukanta Bose
• Washington State University, Pullman

GWDAW-2004, Annecy, France
NASA-NAG5-12837
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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 _at_1yr)

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LISA TDI Sensitivity as a function of frequency
First generation TDI
Second generation TDI
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LISAs directional sensitivityvarying with
orbital position
Rogan, SB, CQG 21, 04.
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Parameter estimates as functions of sky
position(without frequency evolution or
redshifting)
Normalized for SNR1
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Estimating sky position (No frequency evolution
or redshifting)
gt 0.06 steradians (for SNR 1) gt 2500
square-degrees
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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)
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Chirping versus red-shifting
No. of bins
6.0
4.5
3.0
1.5
f (Hz)
0.3
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Parameter estimates comparisonDoppler Shifting
vs. no Doppler shiftingThe solid angle
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Parameter Estimates as a Function of
FrequencyResults with 2nd gen. TDI (but no
redshifting)
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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 gt a
  few mHz
• Doppler f-modulation, Account for it even
  for f gt 1 mHz Improves targeting, esp. at the
  ecliptic poles.
• Also, LISAs 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.