Could the TeV emission of starburst galaxies originate from pulsar wind nebulae?

While the GeV γ-ray emission of starburst galaxies (SBGs) is commonly thought to arise from hadronic interactions between accelerated cosmic rays and interstellar gas, the origin of the TeV γ-ray emission is more uncertain. One possibility is that a population of pulsar wind nebulae (PWNe) in these galaxies could be responsible for the TeV γ-ray emission. In this work, we first synthesize a PWNe population in the Milky Way and assess their contribution to the γ-ray emission of the Galaxy, using a time-dependent model to calculate the evolution of the PWN population. Such a synthetic PWN population can reproduce the flux distribution of PWNe identified in the Milky Way given a distribution of the initial state of the pulsar population. We then apply it to starburst galaxies and quantitatively calculate the spectral energy distribution of all PWNe in the SBGs NGC 253 and M82. We propose that TeV γ-ray emission in starburst galaxies can be dominated by PWNe for a wide range of parameter space. The energetic argument requires that η_e × v_SN > 0.01 yr^-1, where η_e is the fraction of spin-down energy going to electrons and v_SN is the supernova rate. By requiring the synchrotron emission flux of all PWNe in the galaxy not to exceed the hard X-ray measurement of NGC 253, we constrain the initial magnetic field strength of PWNe to be $\lesssim 400\,\mu{\rm G}$. Future observations at higher energies with the Large High Altitude Air Shower Observatory (LHAASO) or the next-generation neutrino observatory IceCube-Gen2 will help us to understand the origin of the TeV γ-ray emission in SBGs better.