Evidence of gradients of density and magnetic field in the remnant of Tycho's supernova

By using surface brightness maps of Tycho's supernova remnant (SNR) in radio and X-rays, along with the properties of thermal and synchrotron emission, we have derived the post-shock density and magnetic field strength distributions over the projection of this remnant. Our analysis reveals a density gradient oriented towards the north-west, while the magnetic field strength gradient aligns with the Galactic plane, pointing eastward. Additionally, utilizing this magnetic field map, we have derived the spatial distributions of the cut-off frequency and maximum energy of electrons in Tycho's SNR. We further comment on the implications of these findings for interpreting the gamma-ray emission from Tycho's SNR.