The effect of dark matter-dark radiation interactions on halo abundance
  -- a Press-Schechter approach
  We study halo mass functions with the Press-Schechter formalism for
interacting dark matter models, where matter power spectra are damped due to
dark acoustic oscillations in the early universe. After adopting a smooth
window function, we calibrate the analytical model with numerical simulations
from the "effective theory of structure formation" (ETHOS) project and fix the
model parameters in the high mass regime, $M_{\rm h}\gtrsim3\times10^{10}\;{\rm
M}_{\odot}$. We also perform high-resolution cosmological simulations with halo
masses down to $M_{\rm h}\sim10^8\;{\rm M}_{\odot}$ to cover a wide mass range
for comparison. Although the model is calibrated with ETHOS1 and CDM
simulations for high halo masses at redshift $z=0$, it successfully reproduces
simulations for two other ETHOS models in the low mass regime at low and high
redshifts. As an application, we compare the cumulative number density of
haloes to that of observed galaxies at $z=6$, and find the interacting dark
matter models with a kinetic decoupling temperature below $0.5\ \rm{keV}$ is
disfavored. We also perform the abundance-matching analysis and derive the
stellar-halo mass relation for these models at $z=4$. Suppression in halo
abundance leads to less massive haloes that host observed galaxies in the
stellar mass range $M_*\simeq 10^5-10^7\ {\rm M}_{\odot}$.
