Capabilities of advanced resonant spheres

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Capabilities of advanced resonant spheres

• Michele Maggiore
• Dépt. de Physique Théorique
• Université de Genève

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Can resonant detectors be useful in the era of
advanced ITFs ?

• Sensitivity
• Complementarity of the informations
• Practical aspects (duty cycle, costs, )

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Sensitivity

• a resonant sphere, with R 1m, M33 ton
• at the SQL, can reach (see talk of E.
  Coccia)
• Sh (f) 3 10-23 Hz-1/2
• over a bandwidth ?f 200 Hz
• centered around f 1 kHz
• in this bandwidth , this is comparable to 2nd
  generation ITFs

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• based on straightforward extensions of existing
  technologies
• read-out at 20 h already achieved
• cooling of large resonant-masses to
• T0.1 K already demonstrated
• (? 2nd generation )
• further improvement in principle possible
• read-out dual, QND techniques
• larger masses e.g. hollow sphere, R2m, M200
  ton, at the SQL
• Sh (f) 5 10-24 Hz-1/2 at f 400 Hz
• (? 3nd generation )

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Complementarity

• resonant bars, ITFs only one output
• ? hF(?,f ) h F(?,f )
• sphere 5 outputs, the 5 degenerate quadrupolar
  modes
• ? the two polarizations h and h
• ? the propagation direction n (mod n ? - n )
• ? one veto

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Angular sensitivity

• define ?O p (??)2 sin2? (?f)2
• ? for a sphere ?O 2p /SNR
  (Zhou-Michelson 1995)
• better than a 3-ITF correlation!
• a unique telescope 4p coverage good
  angular resolution
• in a 5-mode system, it is enough to have
• an average SNR2 per mode to get a total
  SNR10
• the duty cycle of a single sphere could be much
• larger than the common time of a 3 ITF
  correlation

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The veto

• hij ni nj Sm hm Y2m m-2,,2
• the sphere measures the 5 quantities hm
• ? reconstruct the matrix hij
• ? check that is has a zero eigenvalue
• (within a precision O(1/SNR) )
• we are checking the transverse nature of GWs !
• Powerful way to discriminates GWs from noise
• (easily implemented as an on-line
  trigger )

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Multi-frequency capability

• Resonant bars
• sn 1/n2, (n odd)
• ? the first harmonic (n3) has
• f3 3 f1 , s3 (1/9) s1
• for a sphere ,
• f n2,l2 2 f n1,l2
• sn2,l2 0.4 sn1,l2
• for hollow spheres, one can
• even have sn2,l2 sn1,l2
• (Monitored with two TIGAs)

Coccia, Fafone, Frossati, Lobo and Ortega (1998)
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Examples of applications of this multi-mode,
2-window system

• Bursts with power both at f1 and f2
• at f1
• pass one veto (transversality)
• determine the direction
• measure h and h at f1
• at f2
• pass one more veto (transversality)
• a second independent determination of the
  direction !
• (optical counterpart ?)
• one more veto from the n1 monopole mode
• measure h and h at f2 (spectral
  informations)
• Unprecedented level of background rejection !

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• Coalescing binaries
• h (2/r) Mc5/3 (p f )2/3 (1cos2 ? )
  cos F
• h (4/r) Mc5/3 (p f )2/3 cos ? sin
  F
• df/dt (95/5) p8/3 Mc5/3 f11/3
• If the sphere is very massive so that the second
  window is still in the coalescing phase
• from the time needed to sweep between the two
  windows ? Mc
  (Coccia and Fafone, 96)
• Then we can repeat the standard argument
• that coalescing binaries are standard candles
  (Schutz, 86)
• h/h gives cos ?
• h or h now give r (luminosity distance)
• Furthermore
• the sphere also gives the direction

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• Stochastic backgrounds
• sphere-sphere correlation ?mm dmm
• 20 vanishing off-diagonal correlators
• ? signal chopping
• 5 identical diagonal correlators
• effective integration time T? 5 T
• sphere-ITF correlation
• 5 correlators ITF with the mode (m-2,,2)
• the correlators with m0, 1 vanish (?
  chopping)
• the correlators with m2 are equal

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Can resonant detectors be useful in the era of
advanced ITFs ?

• Sensitivity
• competitive, in a smaller bandwidth
• Complementarity of the informations
• source direction , h and h separately
• 4 p coverage
• high background rejection
• Practical aspects (duty cycle, costs, )
• much higher than the common time of 3 ITF
• costs of order 2 of an advanced ITF