Formation times, mass growth histories and concentrations of dark matter
  haloes
  We develop a simple model for estimating the mass growth histories of dark
matter halos. The model is based on a fit to the formation time distribution,
where formation is defined as the earliest time that the main branch of the
merger tree contains a fraction f of the final mass M . Our analysis exploits
the fact that the median formation time as a function of f is the same as the
median of the main progenitor mass distribution as a function of time. When
coupled with previous work showing that the concentration c of the final halo
is related to the formation time tf associated with f \sim 0.04, our approach
provides a simple algorithm for estimating how the distribution of halo
concentrations may be expected to depend on mass, redshift and the expansion
history of the background cosmology. We also show that one can predict log10 c
with a precision of about 0.13 and 0.09 dex if only its mass, or both mass and
tf are known. And, conversely, one can predict log10 tf from mass or c with a
precision of 0.12 and 0.09 dex, approximately independent of f. Adding the mass
to the c-based estimate does not result in further improvement. These latter
results may be useful for studies which seek to compare the age of the stars in
the central galaxy in a halo with the time the core was first assembled.
