Matching of the continuous gravitational wave in an all sky search

We investigate the matching of the continuous gravitational wave in an all sky search in reference to the Earth based laser interferometric detectors. We consider the source location as the parameters of the signal manifold and templates corresponding to different source locations. For fixed source frequency fo, under the transformation θT → π − θT ; 0 ≤ θT ≤ π, we found that the matching of the signals is almost same for arbitrary observation time Tobs and φ (celestial longitude), where θT are the templates in θ (celestial colatitude) space. Though insignificant, we observed variation in the matching of signals for different θ, detector positions and orientations. However, this insignificant mismatch scales with fo. Consequently, matching of the signals fall with fo. In φ space, under the transformations φT → π − φT ; 0 ≤ φT ≤ π and φT → 3π − φT ; π ≤ φT ≤ 2π, we found that the matching of the signals fall with Tobs, fo, θ and φ, where φT are the templates in φ space.