Capabilities of advanced Capabilities of advanced resonant spheresresonant spheres

Michele MaggioreMichele MaggioreDépt. de Physique ThéoriqueDépt. de Physique ThéoriqueUniversité de GenèveUniversité de Genève

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

ITFs ?ITFs ?

SensitivitySensitivity Complementarity of the informationsComplementarity of the informations

““Practical aspects” Practical aspects” (duty cycle, costs, …) (duty cycle, costs, …)

SensitivitySensitivity a resonant sphere, with R= 1m, M=33 tona resonant sphere, with R= 1m, M=33 ton at the SQL, can reach at the SQL, can reach (see talk of E. Coccia)(see talk of E. Coccia) SShh (f)≈ 3 * 10 (f)≈ 3 * 10-23-23 Hz Hz-1/2-1/2

over a bandwidth over a bandwidth ΔΔf ≈ 200 Hzf ≈ 200 Hzcentered around centered around f ≈ 1 kHz f ≈ 1 kHz

in this bandwidth , this is comparable to 2in this bandwidth , this is comparable to 2ndnd generation ITFsgeneration ITFs

based on “straightforward” extensions of based on “straightforward” extensions of existing technologies existing technologies read-out at 20 ħ already achievedread-out at 20 ħ already achieved cooling of large resonant-masses tocooling of large resonant-masses to T=0.1 K already demonstratedT=0.1 K already demonstrated

((→ → 22ndnd generation generation )) further improvement in principle possiblefurther improvement in principle possible

read-out: dual, QND techniquesread-out: dual, QND techniques larger masses: e.g. hollow sphere, R=2m, larger masses: e.g. hollow sphere, R=2m,

M=200 ton, at the SQL:M=200 ton, at the SQL: SShh (f)≈ 5 * 10 (f)≈ 5 * 10-24-24 Hz Hz-1/2 -1/2 at at f ≈ 400 Hzf ≈ 400 Hz

((→ → 33ndnd generation generation ))

ComplementarityComplementarity resonant bars, ITFs: only one outputresonant bars, ITFs: only one output → → hh++FF++((θθ,,φφ ))+ + hh×× F F××((θθ,,φφ )) sphere: 5 outputs, the 5 degenerate sphere: 5 outputs, the 5 degenerate

quadrupolar modes quadrupolar modes → → the two polarizationsthe two polarizations h h+ + and hand h××

→ → the propagation directionthe propagation direction n n (mod (mod n n → − → − n )n ) →→ one vetoone veto

Angular sensitivityAngular sensitivity define define ΔΩΔΩ = =ππ [( [(ΔθΔθ))22 + sin + sin22θθ ( (ΔφΔφ))22]]

→ → for a sphere for a sphere ΔΩΔΩ =2 =2ππ /SNR /SNR (Zhou-Michelson 1995)(Zhou-Michelson 1995)

better than a 3-ITF correlation!better than a 3-ITF correlation! a unique telescope: 4a unique telescope: 4ππ coverage + good angular resolution coverage + good angular resolution

in a 5-mode system, it is enough to havein a 5-mode system, it is enough to have an average SNR=2 per mode to get a total SNR=10an average SNR=2 per mode to get a total SNR=10 the duty cycle of a single sphere could be much the duty cycle of a single sphere could be much larger than the common time of a 3 –ITF correlationlarger than the common time of a 3 –ITF correlation

The veto:The veto: hhij ij nni i nnj j = = ΣΣmm h hm m YY2m 2m m=-2,…,2m=-2,…,2

the sphere measures the 5 quantities the sphere measures the 5 quantities hhmm

→ → reconstruct the matrix reconstruct the matrix hhijij

→ → check that is has a check that is has a zero eigenvaluezero eigenvalue (within a precision O(1/SNR) )(within a precision O(1/SNR) )

we are checking the we are checking the transverse nature of transverse nature of GWsGWs ! !

Powerful way to discriminates GWs from noisePowerful way to discriminates GWs from noise (easily implemented as an on-line trigger )(easily implemented as an on-line trigger )

Multi-frequency capabilityMulti-frequency capability Resonant bars: Resonant bars: σσnn ≈ 1/n ≈ 1/n22, , (n odd)(n odd)→ → the first harmonic (n=3) has the first harmonic (n=3) has

ff33 =3 f =3 f11 , , σσ3 3 = = (1/9)(1/9) σσ11 for a sphere , for a sphere , f f n=2,l=2 n=2,l=2 ≈ 2 f ≈ 2 f n=1,l=2n=1,l=2 σσn=2,l=2 n=2,l=2 ≈ 0.4 ≈ 0.4 σσn=1,l=2 n=1,l=2 for hollow spheres, one can for hollow spheres, one can even have even have σσn=2,l=2 n=2,l=2 ≈ ≈ σσn=1,l=2n=1,l=2 (Monitored with two TIGAs)(Monitored with two TIGAs)

Coccia, Fafone, Frossati, Lobo and Ortega (1998)

Examples of applications of this Examples of applications of this multi-mode, 2-window systemmulti-mode, 2-window system

Bursts with power both at fBursts with power both at f11 and f and f22 : : at fat f1 1 ::

pass one vetopass one veto (transversality) (transversality) determine the direction determine the direction measure measure hh+ + and and hh×× at f at f11

at fat f2 2 :: pass one more vetopass one more veto (transversality) (transversality) a second independent determination of the direction !a second independent determination of the direction ! (optical counterpart ?)(optical counterpart ?) one more veto from the n=1 monopole modeone more veto from the n=1 monopole mode measure measure hh+ + and and hh×× at f at f2 2 (spectral informations)(spectral informations)

Unprecedented level of background rejection !Unprecedented level of background rejection !

Coalescing binariesCoalescing binaries hh+ + = (2/r)= (2/r) MMcc

5/3 5/3 ( (ππ f ) f )2/3 2/3 (1+cos(1+cos22 ίί ) cos ) cos ΦΦ hh×× = (4/r) = (4/r) MMcc

5/3 5/3 ( (ππ f ) f )2/3 2/3 cos cos ίί sin sin ΦΦ df/dt =[ df/dt =[ (95/5)(95/5) ππ8/38/3 ] M ] Mcc

5/3 5/3 f f11/311/3

If the sphere is very massive so that the second window is still in the If the sphere is very massive so that the second window is still in the coalescing phase: coalescing phase:

from the time needed to sweep between the two from the time needed to sweep between the two windows → windows → MMcc (Coccia and Fafone, (Coccia and Fafone, 96)96)

Then we can repeat the standard argumentThen we can repeat the standard argumentthat coalescing binaries are standard candles that coalescing binaries are standard candles (Schutz, (Schutz,

86)86) hh++//hh×× gives gives cos cos ίί hh++ or or hh× × now give now give r (luminosity distance)r (luminosity distance)Furthermore:Furthermore: the sphere also gives the directionthe sphere also gives the direction

Stochastic backgroundsStochastic backgrounds sphere-sphere correlation: sphere-sphere correlation: γγmm’mm’ ~ ~ δδmm’mm’

20 vanishing off-diagonal correlators20 vanishing off-diagonal correlators

→→ signal choppingsignal chopping 5 identical diagonal correlators;5 identical diagonal correlators; effective integration time effective integration time TT→ → 5 T5 T

sphere-ITF correlationsphere-ITF correlation

5 correlators ITF with the mode (m=-2,…,2) 5 correlators ITF with the mode (m=-2,…,2) the correlators with m=0, the correlators with m=0, ±1 vanish ±1 vanish (→ (→

chopping)chopping) the correlators with m=the correlators with m=±2 are equal±2 are equal

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

SensitivitySensitivity competitive, in a smaller bandwidthcompetitive, in a smaller bandwidth Complementarity of the informationsComplementarity of the informations

sourcesource direction , hdirection , h+ + and hand h×× separatelyseparately 4 4 ππ coveragecoverage high background rejectionhigh background rejection

““Practical aspects” Practical aspects” (duty cycle, costs, …) (duty cycle, costs, …) much higher than the common time of 3 ITFmuch higher than the common time of 3 ITF costs of order 2costs of order 2% of an advanced ITF% of an advanced ITF