Do Ultrahigh Energy Cosmic Rays Come from Active Galactic Nuclei and Fermi $\gamma$-ray Sources?

We study possible correlations between ultrahigh energy cosmic rays (UHECRs), observed by Auger, AGASA and Yakutsk, and nearby active galactic nuclei (AGNs) and $Fermi$ sources. We consider the deflection effects by a Galactic magnetic field (GMF) model constrained by the most updated measurements. We found that the average deflection angles of UHECRs by the Galactic magnetic fields are less than $4^\circ$. A correlation between the Auger cosmic-ray events and nearby AGNs with a significance level of $\sim 4\sigma$ was found for the Auger UHECR data sets with or without deflection correction. No correlation was found between the AGASA/Yakutsk events with nearby AGNs. Marginal correlations between the Auger events and the $Fermi$ sources, and between AGASA events and $Fermi$ AGNs were found when the deflections calculated by the GMF model were considered. However, no correlation was found between the Yakutsk data and $Fermi$ sources. Some $Fermi$ sources are close to the arrival directions of UHECR events detected by Auger, AGASA, and Yakutsk, most of which are probably chance coincidence rather than objects producing UHECRs in the nearby Universe. Four $Fermi$ sources, NGC 4945, ESO 323-G77, NGC 6951, and Cen A, within 100~Mpc have UHECR events within $3.1^{\circ}$ from their positions, which could potentially be cosmic ray accelerators. However, the association can only be confirmed if more UHECRs are preferably detected in these directions.