Use of an excess power method and a convolutional neural network in an all-sky search for continuous gravitational waves

The signal of continuous gravitational waves has a longer duration than the observation period. Even if the waveform in the source frame is monochromatic, we will observe the waveform with modulated frequencies due to the motion of the detector. If the source location is unknown, a lot of templates having different sky positions are required to demodulate the frequency and the required large computational cost restricts the applicable parameter region of coherent search. In this work, we propose and examine a new method to select candidates, which reduces the cost of coherent search by following-up only the selected candidates. As a first step, we consider a slightly idealized situation in which only a single-detector having 100% duty cycle is available and its detector noise is approximated by the stationary Gaussian noise. We combine several methods: 1) the short-time Fourier transform with the re-sampled data such that the Earth motion for the source is canceled in some reference direction, 2) the excess power search in the Fourier transform of the time series obtained by picking up the amplitude in a particular frequency bin from the short-time Fourier transform data, and 3) the deep learning method to further constrain the source sky position. We compare the computational cost and the minimum amplitude of the detectable signal with the coherent matched filtering analysis. With a reasonable computational cost, we find that our method can detect the signal having only 32% larger amplitude than that of the coherent search with 95% detection efficiency.