Drift Rates of Narrowband Signals in Long-term SETI Observations for Exoplanets

The Doppler shift of a radio signal is caused by the relative motion between the transmitter and receiver. The change in frequency of the signal over time is called drift rate. In the studies of radio SETI (Search for Extraterrestrial Intelligence), extraterrestrial narrowband signals are expected to appear "chirped" since both the exoplanet and the Earth are moving. Such planet rotation and orbital revolution around the central star can cause a non-zero drift rate. Other relative motions between the transmitter and receiver, such as the gravitational redshift and galactic potential, are negligible. In this paper, we mainly consider the common cases that the drift rate is contributed by the rotations and orbits of the Earth and exoplanet in celestial mechanics perspective, and briefly discuss other cases different from the Earth-exoplanet one. We can obtain the expected pseudosinusoidal drifting result with long-term observations, shorter orbital periods of exoplanets. Exoplanets with higher orbital eccentricities can cause asymmetric drifting. The expected result should be intermittent pseudosinusoidal curves in long-term observations. The characteristics of pseudo-sinusoidal curves, as another new criterion for extraterrestrial signals, can be applied to long-term SETI reobservations in future research.