Bright bursts with sub-millisecond structures of FRB 20230607A in a highly magnetized environment

We report the observations of a repeating FRB 20230607A for 15.6 hours spanning 16 months using the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) with the detection of 565 bursts. We present three bright bursts with detailed temporal/spectral structures. We also report that one burst carries a narrow component with a width of only 0.3 ms, which is surrounded by broader components. This suggests that repeaters can make both narrow and broad components in one burst. With the narrow spike, we precisely measure the dispersion measure (DM) of $362.85 \pm 0.15 \;{\rm pc\,cm^{-3}}$ and the Faraday rotation measures (RMs) of and $-12249.0\pm 1.5 \; {\rm rad\,m^{-2}}$. We also analyze the statistical distribution of the burst parameters, including waiting times, temporal widths, central frequencies and frequency widths, fluences and energies, all showing typical distributions of known active repeaters. In particular, most bursts show narrow spectra with $\Delta\nu/\nu_0 = 0.125\pm 0.001$. This fact, together with the narrow 0.3 ms spike, strongly suggests a magnetospheric origin of the FRB emission. Based on a predicted correlation between RM and the luminosity of a persistent radio source (PRS) by Yang et al., we predict that PRS should have a specific luminosity of the order of $10^{29} \ {\rm erg \ s^{-1} \ Hz^{-1}}$ and encourage a search for such a PRS.