  An analytical model is developed for the mass function of cold dark matter
subhalos at the time of accretion and for the distribution of their accretion
times. Our model is based on the model of Zhao et al. (2009) for the median
assembly histories of dark matter halos, combined with a simple log-normal
distribution to describe the scatter in the main-branch mass at a given time
for halos of the same final mass. Our model is simple, and can be used to
predict the un-evolved subhalo mass function, the mass function of subhalos
accreted at a given time, the accretion-time distribution of subhalos of a
given initial mass, and the frequency of major mergers as a function of time.
We test our model using high-resolution cosmological $N$-body simulations, and
find that our model predictions match the simulation results remarkably well.
Finally, we discuss the implications of our model for the evolution of subhalos
in their hosts and for the construction of a self-consistent model to link
galaxies and dark matter halos at different cosmic times.
