We investigate the baryon fraction in dark matter haloes formed in non-radiative gas-dynamical simulations of the \Lambda CDM cosmogony .
By combining a realisation of the Millennium Simulation ( Springel et al . )
with a simulation of a smaller volume focussing on dwarf haloes , our study spans five decades in halo mass , from 10 ^ { 10 } ~ { } h ^ { -1 } ~ { } M _ { \odot } to 10 ^ { 15 } ~ { } h ^ { -1 } ~ { } M _ { \odot } .
We find that the baryon fraction within the halo virial radius is typically 90 \% of the cosmic mean , with an rms scatter of 6 \% , independently of redshift and of halo mass down to the smallest resolved haloes .
Our results show that , contrary to the proposal of Mo et al .
( 2005 ) , pre-virialisation gravitational heating is unable to prevent the collapse of gas within galactic and proto-galactic haloes , and confirm the need for non-gravitational feedback in order to reduce the efficiency of gas cooling and star formation in dwarf galaxy haloes .
Simulations including a simple photo-heating model ( where a gas temperature floor of T _ { floor } = 2 \times 10 ^ { 4 } ~ { } K is imposed from z = 11 ) confirm earlier suggestions that photoheating can only prevent the collapse of baryons in systems with virial temperatures T _ { 200 } \lesssim 2.2 ~ { } T _ { floor } \approx 4.4 \times 10 ^ { 4 } K ( corresponding to a virial mass of M _ { 200 } \sim 10 ^ { 10 } ~ { } h ^ { -1 } ~ { } M _ { \odot } and a circular velocity of V _ { 200 } \sim 35 ~ { } km s ^ { -1 } ) .
Photoheating may thus help regulate the formation of dwarf spheroidals and other galaxies at the extreme faint-end of the luminosity function , but it can not , on its own , reconcile the abundance of sub- L _ { \star } galaxies with the vast number of dwarf haloes expected in the \Lambda CDM cosmogony .
The lack of evolution or mass dependence seen in the baryon fraction augurs well for X-ray cluster studies that assume a universal and non-evolving baryon fraction to place constraints on cosmological parameters .