Estimation of the upper limit on the level of an undetected noise. Application to the study of millisecond pulsars

Assuming a power law noise model of the power spectral density, the time stability of oscillators may be characterized by several noise levels. In the case of levels of the same order of magnitude, the multivariance method yields a measurement of the levels and an assessment of the measurement precision. On the other hand, in the case of a noise swamped by another noise, it may be impossible to get such measurements. However, it is of importance to set an upper limit on the level of this noise. For example, this problem occurs in the millisecond pulsar study since the low frequency noise due to the stochastic background of gravitational waves is far lower than the white observational noise. The authors developed a method based upon a bayesian approach. It consists in calculating the conditional probability distribution for the real noise level knowing the measurements. From this calculation, they deduce a confidence limit for the real noise. The details of this method are described. With this method, the authors place a limit on the low frequency noise level due to the stochastic background of gravitational waves on the millisecond pulsar PSR 1855+09. From this limit, they deduce a possible very long term behaviour of a pulsar time based on the observations of PSR 1855+09