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Laser Interferometer Space Antenna (LISA). Time-Delay Interferometry with Moving Spacecraft Arrays. Massimo Tinto Jet Propulsion Laboratory, California Institute of Technology. 8 th GWDAW, Dec. 17-20, 2003, Milwaukee, Wisconsin. GSFC JPL. - PowerPoint PPT Presentation
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GSFCJPL
Laser Interferometer Space Antenna (LISA)Time-Delay Interferometry with
Moving Spacecraft Arrays
Massimo Tinto
Jet Propulsion Laboratory,California Institute of Technology
8th GWDAW, Dec. 17-20, 2003, Milwaukee, Wisconsin
W.M. Folkner et al., C.Q.G., 14, 1543, (1997)
Unequal-arm Interferometers
P.D
Laser
P.D
L2
L3
, p(t)
2(t)
3(t))()()2()()(
)()()2()()(
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tntpLtptht
tntpLtptht
M. Tinto, & J.W. Armstrong, Phys. Rev. D, 59, 102003 (1999).
)()(:
)()(][)()(
)()(][)()(
33333
22222
iiLttDwhere
tntpIDDtht
tntpIDDtht
)()])(())([()]()(][[)]()(][[
)(][)(][)(
33222233
33222233
322233
tpIDDIDDIDDIDDtnthIDDtnthIDD
tIDDtIDDtX
S.V. Dhurandhar, K.R. Nayak, and J-Y. Vinet, Phys. Rev. D, 65, 102002 (2002).
itwo-way phase measurements
Time-delay Interferometry
• It is best to think of LISA as a closed array of six one-way delay lines between the test masses.
• This approach allows us to reconstruct the unequal-arm Michelson interferometer, as well as new interferometric combinations, which offer advantages in hardware design, in robustness to failures of single links, and in redundancy of data.
M. Tinto: Phys. Rev. D, 53, 5354 (1996); Phys. Rev. D, 58, 102001 (1998) J.W. Armstrong, F.B. Estabrook, and M. Tinto: Ap. J., 527, 814 (1999)F.B. Estabrook, M. Tinto, & J.W. Armstrong, Phys. Rev. D, 62, 042002 (2000)M. Tinto, D.A. Shaddock, J. Sylvestre, & J.W. Armstrong: Phys. Rev. D 67, 122003 (2003)
1
3*
2
L2
L1
L3
2n
1n
3n
o
1*
3
2*
• One can actually regard X as given by the interference of two beams that propagate within the two arms of LISA, each experiencing a delay equal to (2L2 + 2L3) .
• X is actually a zero-area Sagnac Interferometer, synthesized by properly combining measurements from each arm.
L3L2
1
2
3
)]()([)]()([)(32222333tDDttDDttX
Unequal-arm Interferometers (Cont.)
D.A. Shaddock, M. Tinto, F.B. Estabrook & J.W. Armstrong, Phys. Rev. D, 68, 061303 (R) (2003).
Six-Pulse Data Combinations
)()(13,133,322112,122,2331
)()()(
)()(
1,123,11,123,1
1,213,233,132,122,321,31
noisesSecondaryGWpppp
..
.L1
L2
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3
2
1
--
? ?
D.A. Shaddock, M. Tinto, F.B. Estabrook & J.W. Armstrong, Phys. Rev. D, 68, 061303 (R) (2003).
Eight-Pulse Data Combinations
..
.L2
L3
3
2
1.
..L1
L2
L3
3
2
1
..
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L2
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(X, Y, Z)
(P, Q, R)
(U, V, W)(E, F, G)
Monitor Relay
Beacon
Unequal-arm Michelson
Moving spacecraft Arrays and Clocks Synchronization
• The analysis above assumed the clocks onboard the LISA S/Cs to be synchronized to each other in the frame attached to the LISA array.
• In a rotating reference frame, the Sagnac effect prevents the implementation of the Einstein’s Synchronization Procedure, i.e. synchronization by transmission of electromagnetic signals (GPS is a good example of this problem!)
• To account for the Sagnac effect, one introduces an hypothetical inertial reference frame, and time in this frame is the one adopted by the spacecraft clocks!
• In other words, the onboard receivers have to convert time information received from Earth to time in this inertial reference frame (SSB).
M. Tinto, F.B. Estabrook, & J.W. Armstrong, gr-qc/0310017, October 6, 2003N. Asbby, “The Sagnac effect in the GPS System”, http://digilander.libero.it/solciclos/
Moving spacecraft Arrays and Clocks Synchronization (Cont.)
• In the SSB frame, the differences between back-forth delay times are very much larger than has been previously recognized.
• The reason is in the aberration due to motion and changes of orientation in the SSB frame.
• With a velocity V=30 km/s, the light-transit times of light signals in opposing directions (Li, and L’i) will differ by as much as 2VL (a few thousands km)
• They will also change in time due to rotation (0.1 m/s); this however is significantly smaller than the spacecraft relative velocity (10 m/s).
TDI with Moving spacecraft Arrays• The “first-generation” TDI expressions do not
account for:– The Sagnac Effect– Time-dependence (velocity) of the arm lengths in the
TDI expressions (the “Flex-effect”) • Both effects prevent the perfect cancellation of the
laser frequency fluctuations in the “first-generation” TDI combinations.
• With a laser frequency stability of 30 Hz/Hz1/2
the remaining laser frequency fluctuations could be as much as 30 times larger than the secondary noise sources.
D.A. Shaddock, Phys. Rev. D: to appear; gr-qc/0306125
Cornish & Hellings, Class. Quantum Grav. 20 No 22 (21 November 2003) 4851-4860 D.A. Shaddock, M. Tinto, F.B. Estabrook & J.W. Armstrong, Phys. Rev. D, 68, 061303 (R) (2003).
The Sagnac Effect and the Sagnac Combinations
• In presence of rotation, the amount of time spent by a beam to propagate clockwise is different by the time it spends to propagate counterclockwise along the same arm => (L1, L2, L3, L’1, L’2, L’3).
• The Sagnac effect prevents the perfect cancellation of the laser frequency fluctuations in the existing expressions of the Sagnac combinations ().
• @ 10-3 Hz the laser frequency fluctuations remaining in () would be about 30 times larger than the secondary noise sources.
kmLLLLLL 14||4|)()(| 3'
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L3
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L3
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“Flexy”
32
1
D.A. Shaddock, M. Tinto, F.B. Estabrook & J.W. Armstrong, Phys. Rev. D, 68, 061303 (R) (2003).
Systematic Approach
• Is there a general procedure for deriving the “2nd generation” TDI combinations?
• YES!
M. Tinto, F.B. Estabrook, & J.W. Armstrong, gr-qc/0310017, October 6, 2003
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Systematic Approach (Cont.))(),(),(),(
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How Does the LISA Sensitivity Change?
• Once the laser frequency fluctuations are removed, the corrections to the signal and the secondary noises (optical path, proof-mass, etc.), introduced by the extra delays due to the Sagnac (14 km) and flexy (~ 300 m) effects, are many orders of magnitude below the signals and secondary noises determined by the “1st generation” TDI expressions:
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1
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LLtXtXtX