Measurement of Cosmic-Ray Density in the Spiral Arms toward Galactic Anticenter

Using nearly 17 years of Fermi-LAT data, we analyzed the diffuse gamma-ray emission associated with different spiral arms of the Milky Way in the ranges $l = 105^\circ$ to $145^\circ$ and $b = -5^\circ$ to $5^\circ$. The gamma-ray emissions from these spiral arms all exhibited clear pion-bump features, which can be well explained by a power-law spectrum of cosmic-ray protons. The spectral indices corresponding to the three distinct spiral arms -- the Local Arm, the Perseus Arm, and the Outer Arm -- are found to be approximately $-2.75$, $-2.55$, and $-2.80$, respectively. The energy densities of the cosmic rays above 10 GeV are estimated to be all around 0.2$\rm~eV~cm^{-3}$. We further compared our results with previous studies, which have established various propagation models predicting that cosmic ray density decreases and spectra soften with increasing Galactocentric radius. We found higher densities and harder spectral indices than predicted in the outer Galaxy, suggesting possible contributions from a larger halo, slower magnetic field decay, or a combination of these and other effects. In particular, the spectral hardening observed in the Perseus Arm may be attributed to locally enhanced cosmic-ray acceleration.