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 huge 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 an 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. Also, we assume that the signal has no spin-down, that the polarization angle, the inclination angle, and the initial phase are fixed to be psi = 0, cos iota = 1, and phi(0) = 0, and that they are treated as known parameters. We combine several methods: (1) the short-time Fourier transform with the resampled 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. The computational cost and the detection probability are estimated. The injection test is carried out to check the validity of the detection probability. We find that our method is worthy of further study for analyzing O(10(7)) sec strain data.