The power spectrum of the circular noise

The circular noise is important in connection to Mach's principle, and also as a possible probe of the Unruh effect. In this letter the power spectrum of the detector following the Trocheries-Takeno motion in the Minkowski vacuum is analytically obtained in the form of an infinite series. A mean distribution function and corresponding energy density are obtained for this particular detected noise. The analogous of a non constant temperature distribution is obtained. And in the end, a brief discussion about the equilibrium configuration is given.