Rotational Doppler Cartography of Technosignatures on Unresolved Planets

Abstract

The discovery of many Earth-like planets has renewed interest in whether life and technological civilizations exist elsewhere. The Search for Extraterrestrial Intelligence (SETI) seeks evidence for technological civilizations via technosignatures across the electromagnetic spectrum. Here, focusing on artificial radio emissions with extremely narrowband signals, we model Earth as a distant, unresolved source and simulate its narrowband transmissions as observed with current and forthcoming radio facilities. Planetary rotation induces small but coherent Doppler drifts (maximum fractional shift of order $10^{-6}$) that imprint a characteristic, time-varying pattern on the spectrum. We develop a forward-inverse framework that exploits this modulation: adopting a population-weighted model for terrestrial transmitters, we compute time-resolved spectra and then apply a new inversion method that reconstructs the underlying transmitter distribution from the temporal pattern of fractional frequency offsets. In noise-added tests, the method recovers the low-order spherical-harmonic structure of the map and retrieves major population centers despite the north-south degeneracy of unresolved observations. The recovered distribution is expected to correlate with continents, climate zones, and population density. This approach moves SETI beyond mere detection, enabling quantitative cartography of a civilization's activity and inference of host-planet properties through sustained, time-resolved spectroscopy.

Figures (7)

• Figure 1: Global distribution of cities with populations exceeding 100,000. Point size indicates each city's population, and in our simulation each city's transmitter power is assumed to scale with its population.
• Figure 2: Visibility segments on a rotating Earth with coastlines (three central meridians). Each panel shows a circular Earth with coastlines and a latitude-longitude grid; thick red segments near the limb along each latitude mark where a horizontally beamed transmitter would be visible to a distant observer. Panels (A)-(C) are centered on $0^\circ$, $30^\circ$W, and $60^\circ$W, respectively, illustrating how the visibility segments sweep across the world map as the planet rotates eastward. A transmitter moves eastward (left to right) along its latitude and contributes to the signal only while within a red segment. Higher latitudes have longer visible arcs and thus longer dwell times. For clarity, this schematic uses a vertical beam width of $20^\circ$, whereas the simulations use $2.9^\circ$, which yields proportionally shorter arcs.
• Figure 3: Spectrogram when Earth’s rotation axis is perpendicular to the line of sight. (Color scale is logarithmic.) Each pixel is constructed from the sum of populations of cities that are visible to the observer at that time and fractional frequency offset, divided by $10^6$, and plotted as $\log_{10}$ of that quantity. We assume that the corresponding pre-log value is proportional to received signal strength, but its absolute normalization is arbitrary (hence the “arbitrary units” color bar). At time $t=0$, Earth’s prime meridian faces the observer; transmitters at $90^\circ$ W (central North America) produce a positive frequency offset, whereas those at $90^\circ$ E (India) produce a negative offset. Focusing on the positive-frequency side, a bright signal from the U.S. west coast appears, followed by roughly five hours of minimal emission. Around 08:00, transmissions from Japan, Australia, China, and Southeast Asia brighten the signal again, and the bright cluster near 13:00 corresponds to India. As rotation continues, sources in West Asia, Europe, and Africa come into view. Between $\sim$ 17:00 and 19:00, a gap appears at a fractional frequency offset of about $1.4 \times 10^{-6}$, reflecting low population density in three major deserts (the Sahara, Namib, and Kalahari) around $20^\circ$ latitude. By $\sim$ 20:00, South America (followed by North America) rotates into view after the Atlantic. Thus, despite a north–south ambiguity, the spectrogram captures the planet’s transmitter distribution, which is assumed here to follow population.
• Figure 4: Case with Earth's rotation axis tilted by $30^\circ$. Here Earth's axis is tilted by 30° toward the observer (northward tilt), rather than being perfectly perpendicular. (Left) Map of Earth's latitude/longitude lines and visibility segments as in Fig. \ref{['fig:earth-edge']}. In practice, only transmitters between about $60^\circ$ S and $60^\circ$ N are observable, while visibility segments also appear at higher latitudes in this figure because for visual clarity this schematic adopts a vertical beam width of $20^\circ$. (Right) Corresponding spectrogram analogous to Fig. \ref{['fig:spectrogram']} for this tilted orientation.
• Figure 5: Power spectra, $|\tilde{P(m \Omega, \Delta f)}|^2$. The horizontal axis is fractional frequency offset $\Delta f/f_0$ which corresponds to the latitude of radio sources while the vertical axis is frequency which is conjugate to time and equivalent to $m$-th harmonics of emitting planet’s rotation frequency.