Deep view of Composite SNR CTA1 with LHAASO in $\gamma$-rays up to 300 TeV

The ultra-high-energy (UHE) gamma-ray source 1LHAASO J0007+7303u is positionally associated with the composite SNR CTA1 that is located at high Galactic Latitude $b\approx 10.5^\circ$. This provides a rare opportunity to spatially resolve the component of the pulsar wind nebula (PWN) and supernova remnant (SNR) at UHE. This paper conducted a dedicated data analysis of 1LHAASO J0007+7303u using the data collected from December 2019 to July 2023. This source is well detected with significances of 21$\sigma$ and 17$\sigma$ at 8$-$100 TeV and $>$100 TeV, respectively. The corresponding extensions are determined to be 0.23$^{\circ}\pm$0.03$^{\circ}$ and 0.17$^{\circ}\pm$0.03$^{\circ}$. The emission is proposed to originate from the relativistic electrons and positrons accelerated within the PWN of PSR J0007+7303. The energy spectrum is well described by a power-law with an exponential cutoff function $dN/dE = (42.4\pm4.1)(\frac{E}{20\rm\ TeV})^{-2.31\pm0.11}\exp(-\frac{E}{110\pm25\rm\ TeV})$ $\rm\ TeV^{-1}\ cm^{-2}\ s^{-1}$in the energy range from 8 TeV to 300 TeV, implying a steady-state parent electron spectrum $dN_e/dE_e\propto (\frac{E_e}{100\rm\ TeV})^{-3.13\pm0.16}\exp[(\frac{-E_e}{373\pm70\rm\ TeV})^2]$ at energies above $\approx 50 \rm\ TeV$. The cutoff energy of the electron spectrum is roughly equal to the expected current maximum energy of particles accelerated at the PWN terminal shock. Combining the X-ray and gamma-ray emission, the current space-averaged magnetic field can be limited to $\approx 4.5\rm\ \mu G$. To satisfy the multi-wavelength spectrum and the $\gamma$-ray extensions, the transport of relativistic particles within the PWN is likely dominated by the advection process under the free-expansion phase assumption.