Abstract
The ratio of baryonic to dark matter densities is assumed to have remained constant throughout the formation of structure. With this, simulations show that the fraction f gas ( z ) of baryonic mass to total mass in galaxy clusters should be nearly constant with redshift z . However, the measurement of these quantities depends on the angular distance to the source, which evolves with z according to the assumed background cosmology. An accurate determination of f gas ( z ) for a large sample of hot ( kT e >5 keV), dynamically relaxed clusters could therefore be used as a probe of the cosmological expansion up to z <2. The fraction f gas ( z ) would remain constant only when the correct cosmology is used to fit the data. In this paper, we compare the predicted gas mass fractions for both Λ cold dark matter ( Λ CDM) and the R h = ct Universe and test them against the three largest cluster samples (LaRoque et al. 2006 Astrophys. J. 652, 917–936 ( doi:10.1086/508139 ); Allen et al. 2008 Mon. Not. R. Astron. Soc. 383, 879–896 ( doi:10.1111/j.1365-2966.2007.12610.x ); Ettori et al. 2009 Astron. Astrophys. 501, 61–73 ( doi:10.1051/0004-6361/200810878 )). We show that R h = ct is consistent with a constant f gas in the redshift range z ≲ 2 , as was previously shown for the reference Λ CDM model (with parameter values H 0 =70 km s −1 Mpc −1 , Ω m =0.3 and w Λ =−1). Unlike Λ CDM, however, the R h = ct Universe has no free parameters to optimize in fitting the data. Model selection tools, such as the Akaike information criterion and the Bayes information criterion (BIC), therefore tend to favour R h = ct over Λ CDM. For example, the BIC favours R h = ct with a likelihood of approximately 95% versus approximately 5% for Λ CDM.
Highlights
The idea that clusters might provide an independent probe of cosmological expansion took root following a series of non-radiative hydrodynamical simulations showing that the gas mass fraction, fgas = Mgas/Mtot, in the largest dynamically relaxed clusters remains approximately constant with redshift [1,2]
Under the assumption that the ratio of baryonic to dark matter densities, ρb/ρd, is independent of redshift at least out to z 2, the geometry of the Universe can be constrained in this way because the measured baryonic mass fraction depends on the assumed angular diameter distance to the source, which is used along with the inferred density to obtain Mgas. (This assumption may have to be modified if, and when, new physics beyond the standard model implies that baryons and/or dark matter may be created or annihilated with time since the big bang.) The baryonic matter content of galaxy clusters is dominated by the X-ray-emitting intracluster gas, whose mass exceeds that of optically luminous material by a factor of approximately 6 [10,11]
To facilitate a quick visual comparison between the various models, we show in figures 1–6 the data obtained for the reference Λ cold dark matter (ΛCDM) cosmology, paired with the same set of data re-calibrated for the Rh = ct Universe
Summary
For if the behaviour of fgas with redshift were different for different expansion rates, we could not be certain that fgas should remain constant In their high-resolution simulations, Kravtsov et al [12] incorporated the effects of radiative cooling and galaxy formation on the baryon fraction, including the impact on star formation, metal enrichment and stellar feedback. Simulations with even greater sophistication than these were carried out by Ettori et al [13], this time including the effects of feedback through galactic winds and conduction They found that the baryon fraction within a fixed overdensity increases slightly with redshift, though the impact at large cluster-centric distances (i.e. r > r500) is nearly independent of the physics included in the calculations.
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