Abstract:

We analized the first violin modes around 180 Hz and compared the measured data with the model.
The estimated Q-value of  is surprizingly consistent with the thermo-elastic damping at 250 K.

Detail:

The strain spectrum from 166 Hz to 192 Hz are shown in the attached figure.
This data was taken around 2023-05-01 15:00 UTC.
The blue dots, red circles, and green curve represent the measured data, the peak point picked up by the matlab code of findpeaks.

The selection threshold is the minimum peak height of 1e-20 /√Hz, and the minimum peak promience (difference between the peak and the floor) of 1e-20 /√Hz.
The number of the found peaks is 29, while the total number should be 32 (4 TMs * 4 fibers * 2 modes).
Some of them are probably not from the violin mode but from the electrical noise.

Each Q-value of the first violin mode is estimated from the peak width and the resonant frequency.
For conservative estimation, we assume the temperature of all TMs and fibers to be 250 K (actually only ETMX at 80 K) and take the median rather than the average to avoid the effect of the too sharp peaks.
The meadian of the Q-values is 1.7e4, and the standard division is 1.1e4.

The estimation is compared to the theoretical calculation.
At 250 K, the thermo-elastic damping is dominant in the suspension thermal noise.
The theoretical Q-value of the violin mode is 2.3e4, consistent with the estimated one.

More realistic suspension thermal noise will be calculated based on this estimated Q-value.