Pulsars are rapidly rotating neutron stars that emit radiation across the electromagnetic spectrum, from radio to $\gamma$-rays. We use the rapid binary population synthesis suite COMPAS to model the Galactic population of canonical pulsars. We account for both radio and $\gamma$-ray selection effects, as well as the motion of pulsars in the Galactic potential due to natal kicks. We compare our models to the catalogues of pulsars detected in the radio, and those detected in $\gamma$-rays by Fermi, and find broad agreement with both populations. We reproduce the observed ratio of radio-loud to radio-quiet $\gamma$-ray pulsars. We further examine the possibility of low spin-down luminosity ($\dot{E}$) pulsars emitting weak, unpulsed $\gamma$-ray emission and attempt to match this with results from a recent $\gamma$-ray stacking survey of these pulsars. We confirm the correlation between the latitude of a pulsar and its $\dot{E}$ arises due to natal kicks imparted to pulsars at birth, assuming that all pulsars are born in the Galactic disk.

The discovery that blazars dominate the extra-galactic $\gamma$-ray sky is a triumph in the Fermi era. However, the exact location of $\gamma$-ray emission region still remains in debate. Low-synchrotron-peaked blazars (LSPs) are estimated to produce high-energy radiation through the external Compton process, thus their emission regions are closely related to the external photon fields. We employed the seed factor approach proposed by Georganopoulos et al. It directly matches the observed seed factor of each LSP with the characteristic seed factors of external photon fields to locate the $\gamma$-ray emission region. A sample of 1 138 LSPs with peak frequencies and peak luminosities was adopted to plot a histogram distribution of observed seed factors. We also collected some spectral energy distributions (SEDs) of historical flare states to investigate the variation of $\gamma$-ray emission region. Those SEDs were fitted by both quadratic and cubic functions using the Markov-chain Monte Carlo method. Furthermore, we derived some physical parameters of blazars and compared them with the constraint of internal $\gamma\gamma$-absorption. We find that dusty torus dominates the soft photon fields of LSPs and most $\gamma$-ray emission regions of LSPs are located at 1–10 pc. The soft photon fields could also transition from dusty torus to broad line region and cosmic microwave background in different flare states. Our results suggest that the cubic function is better than the quadratic function to fit the SEDs.

The discovery of γ-ray emission from 5 radio-loud narrow-line Seyfert 1 galaxies revealed the presence of a possible emerging third class of AGNs with relativistic jets, in addition to blazars and radio galaxies. The existence of relativistic jets also in this subclass of Seyfert galaxies opened an unexplored research space for our knowledge of the radio-loud AGNs. Here, we discuss the radio-to-γ-rays properties of the γ-ray emitting narrow-line Seyfert 1 galaxies, also in comparison with the blazar scenario.