Polarization and Burst Properties of the Repeating FRB~20240209A in a Quiescent Elliptical Host

We report polarimetric observations of the repeating fast radio burst (FRB) source FRB 20240209A with the Green Bank Telescope at L band and 800 MHz. This source has previously been associated with a quiescent elliptical galaxy with a mass-weighted stellar age of approximately 11 Gyr. We detected three bursts, and the brightest burst resolves into eight components that drift toward lower frequencies. The bursts have mutually consistent rotation measures (RMs), and the small extragalactic RM agrees with the low RM predicted from the small host-galaxy dispersion measure ($\mathrm{DM}_\mathrm{host}$). The linear polarization fraction decreases toward lower frequencies within the brightest burst, consistent with depolarization by an RM scatter of $σ_\mathrm{RM}\simeq3.5$ rad m$^{-2}$. This RM scatter is comparable to those of several repeaters in star-forming galaxies. Therefore, FRBs in both star-forming and old, quiescent hosts can reside in relatively complex magneto-ionic environments, which suggests that FRB sources may form through multiple channels.