GSFCJPL

1
Laser Interferometer Space Antenna (LISA)
Time-Delay Interferometry and the LISA
Zero-Signal-Solution (ZSS)
Massimo Tinto Jet Propulsion Laboratory, Californ
ia Institute of Technology
JPL, May 7, 2004
M.Tinto S. Larson Phys. Rev. D., To be
Submitted this weekend!
GSFC?JPL
2
Earth vs. Space-based Interferometers

• Earth-based interferometers have arm lengths
  essentially equal. This is in order to directly
  remove laser frequency fluctuations at the
  photodetector, where the two beams interfere.
• They operate in the long-wavelength limit (Lltlt
  l).
• By contrast, LISA will have arm lengths
  significantly different (DL/L 10-2), with L 5
  x 106 km
• Over much of its sensitivity frequency-band, LISA
  will not operate in the long-wavelength regime.
• Time-of-flight delays in the response to the
  wave, and travel times along the arms must be
  allowed for in order to derive a correct theory
  of the LISA response to the signal and the noises.

TDI!
M. Tinto Phys. Rev. D, 53, 5354 (1996) Phys.
Rev. D, 58, 102001 (1998) M. Tinto, J.W.
Armstrong, Phys. Rev. D, 59, 102003 (1999).
3
The Gravitational Wave Signal
Estabrook, F.B., Wahlquist, H.D.,
Gen.Relativ.Gravit. 6,439 (1975)
Speed of light c 1
2
n0
m cos(q)
q
L
n0
1
f
4
The two-way Doppler Data
2
T2
L
n0
1
T1
F.B. Estabrook, M. Tinto, J.W. Armstrong, Phys.
Rev. D, 62, 042002 (2000)
5
Long-Wavelength Limit
6
Long-Wavelength Limit (Cont.)
The 3 Equal-Arm Michelson Interferometers
2
2
L
1
3
3
1
7
The 3 Equal-Arm Michelson Interferometers (Cont)
2
2
L
1
3
3
1
8
The M1 vs. M1M2M3
Gravitational Wave Shield!!
9
Sensitivities
X Y Z
Unequal-Arm Michelson
10
M1M2 M3 (or z )

• The gravitational wave background will be below
  the anticipated sensitivity curve of z by several
  orders of magnitude.
• This provides a way for estimating the
  instrumental noise sources z greatly attenuates
  the gravitational wave signal, but instrumental
  noise persists.
• This allows us to infer the actual on-orbit LISA
  instrumental noise in the sensitive TDI
  combinations, and in turn to detect the
  stochastic background.
• The z combination can of course be used also as a
  discriminator for sinusoidal signals and bursts.

M. Tinto, J.W. Armstrong, F.B. Estabrook, Phys.
Rev. D, 63, 021101(R) (2001).
11
M1M2 M3 (or z ) (Cont.)

• Below 5 mHz, the spectrum of the instrumental
  noise can
• be estimated using z with a relative error of
  20
• This leads to a negligible loss in SNR ( 2)
  when doing
• matched filtering
• Directly translates into a 20 sensitivity
  loss when
• searching for a stochastic background using
  excess noise
• It seems possible to use z to construct
  estimators of the
• instrumental noise that are good enough for
  the data
• analysis, both for signal detection and for
  signal estimation.

J. Sylvestre, M. Tinto, Phys. Rev. D, 68,
102002 (2003)
12
The ZSS The concept!
M. Tinto, F.B. Estabrook, J.W. Armstrong, Phys.
Rev. D 69, 082001, 2004
13
The Coordinate System
14
The ZSS Simplified Version (equal arms)
Y. Gursel M. Tinto, Phys. Rev. D 40, Vol. 12,
3884, (1989)
15
To be continued!