Lambda Cold Dark Matter ( \Lambda CDM ) is now the standard theory of structure formation in the Universe .
We present the first results from the new Bolshoi dissipationless cosmological \Lambda CDM simulation that uses cosmological parameters favored by current observations .
The Bolshoi simulation was run in a volume 250 h ^ { -1 } Mpc on a side using \sim 8 billion particles with mass and force resolution adequate to follow subhalos down to the completeness limit of V _ { circ } = 50 km s ^ { -1 } maximum circular velocity .
Using merger trees derived from analysis of 180 stored time-steps we find the circular velocities of satellites before they fall into their host halos .
Using excellent statistics of halos and subhalos ( \sim 10 million at every moment and \sim 50 million over the whole history ) we present accurate approximations for statistics such as the halo mass function , the concentrations for distinct halos and subhalos , abundance of halos as a function of their circular velocity , the abundance and the spatial distribution of subhalos .
We find that at high redshifts the concentration falls to a minimum value of about 4.0 and then rises for higher values of halo mass , a new result .
We present approximations for the velocity and mass functions of distinct halos as a function of redshift .
We find that while the Sheth-Tormen approximation for the mass function of halos found by spherical overdensity is quite accurate at low redshifts , the ST formula over-predicts the abundance of halos by nearly an order of magnitude by z = 10 .
We find that the number of subhalos scales with the circular velocity of the host halo as V _ { host } ^ { 1 / 2 } , and that subhalos have nearly the same radial distribution as dark matter particles at radii 0.3-2 times the host halo virial radius .
The subhalo velocity function N ( > V _ { sub } ) scales as V _ { circ } ^ { -3 } .
Combining the results of Bolshoi and Via Lactea-II simulations , we find that inside the virial radius of halos with \mbox { $V _ { circ } $ } = 200 ~ { } \mbox { km~ { } s$ { } ^ { -1 } $ } the number of satellites is N ( > V _ { sub } ) = ( V _ { sub } / 58 ~ { } \mbox { km~ { } s$ { } ^ { -1 } $ } ) ^ { -3 } for satellite circular velocities in the range 4 ~ { } \mbox { km~ { } s$ { } ^ { -1 } $ } < V _ { sub } < 150 ~ { } \mbox { km~ { } s$ { } ^ { -1 } $ } .