Small-scale Substructure in Dark Matter Haloes: Where Does Galaxy Formation Come to an End?

Models of structure formation based on cold dark matter predict that most of the small dark matter haloes that first formed at high redshift would have merged into larger systems by the present epoch. Substructure in present-day haloes preserves the remains of these ancient systems, providing the only direct information we may ever have about the low-mass end of the power spectrum. I describe some recent attempts to model halo substructure down to very small masses, using a semi-analytic model of halo formation. I make a preliminary comparison between the model predictions, observations of substructure in lensed systems, and the properties of local satellite galaxies.