Capabilities of advanced resonant spheres

1. Capabilities of advanced resonant spheres Michele Maggiore Dépt. de Physique Théorique Université de Genève

2. Can resonant detectors be useful in the era of advanced ITFs ? • Sensitivity • Complementarity of the informations • “Practical aspects” (duty cycle, costs, …)

3. Sensitivity • a resonant sphere, with R= 1m, M=33 ton at the SQL, can reach (see talk of E. Coccia) Sh (f)≈ 3 * 10-23 Hz-1/2 over a bandwidth Δf ≈ 200 Hz centered around f ≈ 1 kHz in this bandwidth , this is comparable to 2nd generation ITFs

5. based on “straightforward” extensions of existing technologies • read-out at 20 ħ already achieved • cooling of large resonant-masses to T=0.1 K already demonstrated (→ 2nd generation ) • further improvement in principle possible • read-out: dual, QND techniques • larger masses: e.g. hollow sphere, R=2m, M=200 ton, at the SQL: Sh (f)≈ 5 * 10-24 Hz-1/2 at f ≈ 400 Hz (→ 3nd generation )

6. Complementarity • resonant bars, ITFs: only one output → h+F+(θ,φ)+ h× F×(θ,φ) • sphere: 5 outputs, the 5 degenerate quadrupolar modes → the two polarizations h+ and h× → the propagation directionn (mod n → − n ) →one veto

7. Angular sensitivity define ΔΩ =π [(Δθ)2 + sin2θ (Δφ)2] → for a sphere ΔΩ =2π /SNR(Zhou-Michelson 1995) • better than a 3-ITF correlation! a unique telescope: 4π coverage + good angular resolution • in a 5-mode system, it is enough to have an average SNR=2 per mode to get a total SNR=10 • the duty cycle of a single sphere could be much larger than the common time of a 3 –ITF correlation

8. The veto: hij ni nj = Σm 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 )

9. Multi-frequency capability • Resonant bars: σn ≈ 1/n2, (n odd) → the first harmonic (n=3) has f3 =3 f1 , σ3 = (1/9)σ1 • for a sphere , f n=2,l=2 ≈ 2 f n=1,l=2 σn=2,l=2 ≈ 0.4 σn=1,l=2 • for hollow spheres, one can even have σn=2,l=2 ≈ σn=1,l=2 (Monitored with two TIGAs) Coccia, Fafone, Frossati, Lobo and Ortega (1998)

10. 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 n=1 monopole mode • measure h+ and h× at f2 (spectral informations) Unprecedented level of background rejection !

11. Coalescing binaries h+ = (2/r)Mc5/3 (π f )2/3 (1+cos2ί ) cos Φ h× = (4/r)Mc5/3 (π f )2/3 cos ί sin Φ df/dt =[ (95/5)π8/3 ] 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 ί • h+or h× now give r (luminosity distance) Furthermore: • the sphere also gives the direction

12. Stochastic backgrounds • sphere-sphere correlation: γmm’~ δmm’ • 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 m=0, ±1 vanish (→ chopping) the correlators with m=±2 are equal

13. Can resonant detectors be useful in the era of advanced ITFs ? • Sensitivity competitive, in a smaller bandwidth • Complementarity of the informations • sourcedirection , h+ and h×separately • 4 πcoverage • 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