This paper studies how the Milky Way’s rotation changes the low‑frequency gravitational‑wave background that the space detector LISA will observe. Waves from millions of unresolved binary stars in our Galaxy form a diffuse “stochastic background.” Because stars move around the Galaxy, their motion Doppler‑shifts the waves in a way that depends on direction. The authors show that this direction‑dependent Doppler effect is measurable and that ignoring it would bias the recovered properties of the background.

To reach this conclusion the authors built a realistic model of the Galaxy. They combined a bulge‑plus‑disk map of where stars sit with a smooth fit to the observed Galactic rotation curve to describe star speeds. They then derived the correct Doppler boost for gravitational waves coming from each line of sight and integrated the contribution of all unresolved sources to get a sky‑dependent power spectrum. Finally, they used two statistical tools — a Fisher‑matrix forecast and Markov‑chain‑Monte‑Carlo sampling — to predict how well LISA could tell apart models that do or do not include the rotation effect.

The forecasts show the rotation effect should be detectable. The authors compute a signal‑to‑noise ratio for the difference between the full rotating model and a rotation‑free model of about 4.7 for two years of observation and about 5.3 for five years. They also find that fitting data with the wrong (non‑rotating) model produces biases comparable to the statistical errors. For example, in one two‑parameter test the bias in the spectrum amplitude is about 0.9 times its statistical uncertainty, and the bias in the characteristic “knee” frequency is about 1.4 times its uncertainty. The paper gives numerical bias and error estimates for these parameters and confirms the Fisher forecasts by sampling the likelihood directly.