We introduce Copernicus Complexio ( coco ) , a high-resolution cosmological N-body simulation of structure formation in the \Lambda { CDM } { } model . coco follows an approximately spherical region of radius \sim 17.4 h ^ { -1 } { Mpc } embedded in a much larger periodic cube that is followed at lower resolution .
The high resolution volume has a particle mass of 1.135 \times 10 ^ { 5 } h ^ { -1 } { M } _ { \odot } ( 60 times higher than the Millennium-II simulation ) . coco gives the dark matter halo mass function over eight orders of magnitude in halo mass ; it forms \sim 60 haloes of galactic size , each resolved with about 10 million particles .
We confirm the power-law character of the subhalo mass function , \overline { N } ( > \mu ) \propto \mu ^ { - s } , down to a reduced subhalo mass M _ { sub } / M _ { 200 } \equiv \mu = 10 ^ { -6 } , with a best-fit power-law index , s = 0.94 , for hosts of mass \langle M _ { 200 } \rangle = 10 ^ { 12 } h ^ { -1 } { M } _ { \odot } .
The concentration-mass relation of coco haloes deviates from a single power law for masses M _ { 200 } < \textrm { a few } \times 10 ^ { 8 } h ^ { -1 } { M } _ { \odot } , where it flattens , in agreement with results by Sanchez-Conde et al .
The host mass invariance of the reduced maximum circular velocity function of subhaloes , \nu \equiv V _ { max } / V _ { 200 } , hinted at in previous simulations , is clearly demonstrated over five orders of magnitude in host mass .
Similarly , we find that the average , normalised radial distribution of subhaloes is approximately universal ( i.e .
independent of subhalo mass ) , as previously suggested by the Aquarius simulations of individual haloes .
Finally , we find that at fixed physical subhalo size , subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts .