The redshift dependence ofthe structure ofm assive C D M halos

A B ST R A C T W e use two very large cosm ologicalsim ulationsto study how the density prolesof relaxedCDM dark halos depend on redshift and on halo m ass.W e conrm that these prolesdeviate slightly butsystem atically from the NFW form and are better approxim atedbytheem piricalform ula, dlog�=dlogr / r � ,�rstused byEinastotot starcountsin theM ilky W ay.Thebest-�tvalueoftheadditionalshapeparam eter, �, increasesgradually with m ass,from � � 0:16 forpresent-day galaxy halosto � � 0:3 for the rarest and m ost m assive clusters.Halo concentrations depend only weakly on m ass at z = 0,and this dependence weakens further at earlier tim es.At z � 3 the average concentration ofrelaxed halos does not vary appreciably overthe m ass rangeaccessibletooursim ulations(M �3�10 11 h 1 M � ).Furtherm ore,in ourbiggest sim ulation,theaverageconcentration ofthe m ostm assive,relaxed halosisconstantat hc200i� 3:5to4for0 � z � 3.Theseresultsagreewellwith thoseofZhaoetal(2003b) and supporttheidea thathalo densitiesreectthedensity oftheuniverseatthetim e they form ed,as proposed by Navarro,Frenk & W hite (1997).W ith their original param eters,the NFW prescription overpredictshalo concentrationsathigh redshift. Thisshortcom ing can bereduced by m odifying thedenition ofhalo form ation tim e, although the evolution ofthe concentrations ofM ilky W ay m ass halos is stillnot reproduced well.In contrast,the m uch-used revisions ofthe NFW prescription by Bullock et al.(2001) and Eke,Navarro & Steinm etz (2001) predict a steeper drop in concentration atthe highestm assesand strongerevolution with redshiftthan are com patible with ournum ericaldata.M odifying the param etersofthese m odels can reducethediscrepancyathigh m asses,buttheoverlyrapid redshiftevolution rem ains. These results have im portant im plications for currently planned surveys ofdistant clusters. K ey w ords: m ethods:N-body sim ulations { m ethods:num erical{dark m atter { galaxies:haloes{ galaxies:structure