By Sahay, S K

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**Additional info for Studies in Gravitational Wave Data Analysis**

**Example text**

In general, c depends both on t1 and t2 . e. its performance is, statistically speaking, independent of time, then c depends only on τ ≡ t2 − t1 . 1: Analytical fits to noise power spectral densities Sn (f ) of ground based interferometers. 37 assume that c(τ ) = c(−τ ). For data from real detectors the above average can be replaced by a time average under the assumption of ergodicity: c(τ ) = 1 T T /2 −T /2 n(t)n(t − τ )dt. 2) The assumption of stationarity is not strictly valid in the case of real GW detectors; however, if their performance does not vary greatly over time scales much larger than typical observation time scales, stationarity could be used as a working rule.

As with vibrational noise, this is increased by the bouncing of the light between the mirrors. Unlike bars, interferometers measure only at frequencies far from the resonant frequency, where the amplitude of vibration is smaller. Thus, the pendulum suspensions have thermal noise at a few Hz, but measurements will be made above 20 or 30 Hz in the first detectors. Internal vibrations of the mirrors have natural frequencies of several kilohertz. By ensuring that both kinds of oscillations have very high Q, one can confine most of the vibration energy to a small bandwidth around the resonant frequency, so that at the measurement frequencies the vibration amplitudes are small.

The other goes back towards the input laser. Normally one arranges that no light goes to the interference sensor, so that only when a gravitational wave passes does a signal register there. This means that all the light normally returns to the mirror, apart from small losses at the mirrors. Since mirrors are of good quality, only one part in 103 or less of the light is lost during a 1 ms storage time. By placing a power-recycling mirror in front of the laser, one can reflect this wasted light back in, allowing power to build up in the arms until the laser merely resupplies the mirror losses.

### Studies in Gravitational Wave Data Analysis by Sahay, S K

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