Statistical properties of substructures around Milky Way-sized haloes
  and their implications for the formation of stellar streams
  Stellar streams originating in disrupted dwarf galaxies and star clusters are
observed around the Milky Way and nearby galaxies. Such substructures are the
important tracers that record how the host haloes have accreted progenitor
galaxies. Based on the cosmological context, we investigate the relationship
between structural properties of substructures such as length and thinness at
$z=0$, and orbits of their progenitors. We model stellar components of a large
sample of substructures around Milky Way-sized haloes by combining
semi-analytic models with a high-resolution cosmological $N$-body simulation.
Using the Particle Tagging method, we embed stellar components in progenitor
haloes and trace phase-space distributions of the substructures down to $z=0$.
We find that the length and thinness of substructures vary smoothly as the
redshift when the host haloes accrete their progenitors. For substructures
observed like streams at $z=0$, a large part of the progenitors is accreted by
their host haloes at redshift $0.5\lesssim z\lesssim 2.5$. Substructures with
progenitors out of this accretion redshift range are entirely or less disrupted
by $z=0$ and cannot be observed as streams. We also find that the distributions
of length and thinness of substructures vary smoothly as pericenter and
apocenter of the progenitors. Substructures observed like streams tend to have
the specific range of $10\ {\rm kpc} \lesssim r_{\rm peri}\lesssim100\ {\rm
kpc}$ and $50\ {\rm kpc} \lesssim r_{\rm apo}\lesssim300\ {\rm kpc}$.
