1. Amplitude and time calibration of the gw detector AURIGA
Jean-Pierre Zendri
for the AURIGA collaboration
WP1 meeting, Frascati March 2006

2. The model-based calibration
General Realativity +
Motion equation
Lumped Model for the bar+transducer system
WP1 meeting, Frascati March Jean-Pierre Zendri

3. Risk of systematic errors
The lumped model is not fully sotisfactory for broad band detectors (we have to consider much more modes)
Effective field
Edge effects
The effective mass of the transducer is not well known
Not all the in-situ value of the circuit parameters is well know
Mode form factor (not well known)
Parasitic capacitance (not well known)
WP1 meeting, Frascati March Jean-Pierre Zendri

4. The Auriga calibration method :
First assumption: LINEARITY
Can be measured !
WP1 meeting, Frascati March Jean-Pierre Zendri

5. Detector diagnostic:thermal noise
Assuming only linearity !!
WP1 meeting, Frascati March Jean-Pierre Zendri

6. Thermal noise in presence of cold-damping
The AURIGA detector is cold damped
Qm-True: the true Q-value of the m-mode
Qm-Meas: the measured Q-value of the m-mode in the presence of cold damping
Fluctuation dissipation theorem in presence of cold damping
In order to predict the thermal noise PSD in the presence of CD the true value of the quality fator of the mode is required
WP1 meeting, Frascati March Jean-Pierre Zendri

7. ‘True’ Q-factor Measurement
Experimental set-up for the measurement of Q-True
Ring down example (mode 2)
Proportional to the square of the
Transformer mutual inductane
WP1 meeting, Frascati March Jean-Pierre Zendri

8. Thermal noise example Detector equivalent temperature
Fit of the SQUID output PSD
WP1 meeting, Frascati March Jean-Pierre Zendri

9. The energy absolute Calibration
SQUID Input PSD
sp: spourius
m: main
hv: high voltage plate
hv2
hv1
hv3
sp2 m1
sp1 m2 m3
WG1 meeting, Frascati March Jean-Pierre Zendri

10. The force amplitude calibration
If the bar is excited by a force with FT F(w)
SQUID Input Current
Amplitude Calibration const.
Canonical transfer function
In particular for an impulsive force F(t)=Bd(t) (i.e. F(w)=B)
In order to get the amplitude calibratin two additional ASSUMPTIONS are required: 1)The bar effective mass is half of its physical mass (Ass. II)
2) The functional form of force transfer function (Ass. III)
WP1 meeting, Frascati March Jean-Pierre Zendri

11. The gw amplitude calibration
ASSUMPTION IV (general relativity+unidimensional elastic bodie )
H(w):Fourier transform of the gw signal
Iin(w): measured SQUID input current
WP1 meeting, Frascati March Jean-Pierre Zendri

12. Measure of the bar effective mass (Exp. Test of Assunction II)
Room temperature test (before cooling down the detector)
Meq-bar=1240 ± 90 kg
Meq-bar-AssII=1170 kg (test OK <10%)
WG1 meeting, Frascati March Jean-Pierre Zendri

13. Experimental transfer function Test of Assunction III
Canonical three mode transfer function
Experimental set-up
Experimental results
The experimental transfer function is slightly different from the three mode TF usually assumed as true
WP1 meeting, Frascati March Jean-Pierre Zendri

14. The relevance of the force transfer function
Blue: three mode theoretical transfer function
Red: 8 mode exerimental transfer function
For Impulsive events (IGEC) the Montecarlo simulation gives a difference of the amplitude estimation of less then 3%
But
WP1 meeting, Frascati March Jean-Pierre Zendri

15. Ansys simulation (in progress)
Simplifications
No electrical resonator
No Calibrator plate
No transducer edge effetcs
Bar in free fall (no suspensions)
No LC resonator and SQUID case, no wires holders
WP1 meeting, Frascati March Jean-Pierre Zendri

16. Transducer+Bar Calibrator+Bar
WG1 meeting, Frascati March Jean-Pierre Zendri

17. Ansys simulation of a gravitational wave
General relativity prediction
Force field acting on the bar
WP1 meeting, Frascati March Jean-Pierre Zendri

18. Ansys results (preliminay)
The FEM calculated force transfer function is similar to the experimental one (Assumption III) . But the two spourious modes (sp1,sp2) are missing.
The calibrator TF has the same frequency shape as the measured one
In our frequency range the gravitational wave transfer function is only slightly different of the Calibrator TF (in progress)
The bar effective mass is as Assumption II
GW transfer function m2
High Voltage plate (HV1,2,3) m1
Missing !
These results are preliminary, still we have to include in the model the electrical resonator and the teflon spacer in the transducer.
WP1 meeting, Frascati March Jean-Pierre Zendri

19. Conclusions for the amplitude calibration
The Auriga calibration method use a minimal set of assumptions reducing the systematic error contribution
1. Assuming only linearity the detctor energy calibration is obtained with an accuracy better than 10% (Q uncertainty)
2. The force amplitude calibration is obtained assuming the effective mass of the bar equal to half of the bar physical mass and a force transfer function. The achieved precision is 5% (neglecting the systematic error)
3.The gravitational wave amplitude is obtained with the same precison as 2. assuming that the tidal force formula is true.
• The proper shape of the force-gw transfer function is under investigation. However the impulsive amplitude estimation is affected by the used TF only a factor 3%
WP1 meeting, Frascati March Jean-Pierre Zendri

20. Arrival time estimation
Motivation
Decrease as much as possible the coincidence window for a network of detectors (i.e. decrease the false alarm rate)
Determine the source location in the sky
Arrival time error (for impulsive signals)
WK filter output
WP1 meeting, Frascati March Jean-Pierre Zendri

21. Time resolution for high SNR
Exitation voltage
Raw data
Filtered output
|TimeInjection-Timeestimated| < 1ms
WP1 meeting, Frascati March Jean-Pierre Zendri

22. Time resolution for low SNR
Phase noise
Experimental arrival time distrib. SNR15
Hardware Injection
For impulsive signals
WG1 meeting, Frascati March Jean-Pierre Zendri

23. Time resolution for low SNR
Peak number error
Measured arrival time distribution
Arrival time error vrs SNR
WP1 meeting, Frascati March Jean-Pierre Zendri