A Cepheid is a star that breathes: it expands and contracts with a period of a few days, and its brightness changes along with its size. Astronomers have long used this relationship to measure distances in the universe, but typically they need two types of observations: photometry (how brightness changes) and spectroscopy (how the star's surface moves). Spectrographs are expensive and time-consuming, so for distant Cepheids in other galaxies, often only brightness data are available.

Photometry yields a light curve — a graph showing how the star brightens and dims. Spectroscopy yields a radial velocity (RV) curve — a graph showing how fast the star's surface approaches or recedes from us. Both curves reflect the same pulsational motion, but they are related in a complex way. The authors found that the shapes of these curves are linked through simple relations that depend on the pulsation period. They analyzed 81 short-period Cepheids (periods up to 8 days) with high-quality data and discovered that the ratios of Fourier harmonic amplitudes, such as R21(RV)/R21(LC), correlate tightly with period.

Using these correlations, one can reconstruct the radial velocity curve from the light curve with an accuracy of about 0.60 km/s. For individual stars, the integral of the reconstructed curve (i.e., the radius change over a cycle) matches the real one to better than 1% with a scatter of 4.16%. This paves the way for a purely photometric method of distance determination: if both velocity and period are known from brightness, one can compute the star's radius and luminosity, and hence its distance. This is especially valuable for future sky surveys, such as the Vera Rubin Observatory's Legacy Survey of Space and Time, which will obtain light curves for millions of Cepheids in other galaxies.

This approach is reminiscent of estimating a car's speed by the sound of its engine: without seeing the speedometer, you can gauge how fast it's going and how far away it is from the tone and volume. Astronomers can now estimate distances to Cepheids in distant galaxies using only their flicker — without expensive spectrographs.