Theoretical Investigations on the Dark Matter and Gas Content of Large Spheroidal Systems

Abstract

I present new approaches to probe the interplay between the dark matter (DM) and gas content of early-type galaxies, groups and clusters of galaxies, developed over the course of three distinct projects.

In the first project, I utilize the redshift distribution of galaxy lenses in known gravitational lens systems to discriminate amongst cosmological models and to constrain galaxy evolution parameters. I propose a new nested Monte Carlo method to quantify the effects of incomplete data. I apply the lens-redshift test to an improved sample of seventy lens systems derived from recent observations, primarily from the SDSS, SLACS and the CLASS surveys. I find that the limiting factor in applying the lens-redshift test derives from poor statistics, including incomplete information samples and biased sampling. Many lenses that uniformly sample the underlying true image separation distribution will be needed to use this test as a complementary method to measure the value of the cosmological constant or the properties of evolving galaxies.

In the second project, I present an analytic formulation for the equilibrium gas density profile of early-type galaxies that explicitly includes the contribution of stars in the gravitational potential. I build a realistic model for an isolated elliptical galaxy and explore the equilibrium gas configurations as a function of multiple parameters. For an assumed central gas temperature, k_BT₀ = 0.6 keV, I find that neglecting the gravitational effects of stars, which can contribute substantially in the innermost regions, leads to an underestimate of the enclosed baryonic gas mass by up to ∼65 per cent at the effective radius and by up to ∼15 per cent at the Navarro-Frenk-White (NFW) scale radius, r _s, depending on the stellar baryon fraction. This formula is therefore important for estimating the baryon fraction in an unbiased fashion. Moreover, the new formulation is relevant when interpreting X-ray data. I compare my composite isothermal model to the standard β-model used to fit X-ray observations of early-type galaxies, to determine the value of r _s. Assuming a 10 per cent stellar baryon fraction, I find that the exclusion of stars from the gravitational potential leads to (i) an underestimate of r_s by ∼80 per cent and (ii) an overestimate of the enclosed DM at r_s by a factor of ∼2, compared to the equivalent β-model fit results when stars are not taken into account. For higher stellar mass fractions, a β-model is unable to accurately reproduce my solution, indicating that when the observed surface brightness profile of an isolated elliptical galaxy is found to be well fitted by a β-model, the stellar mass fraction cannot be much greater than ∼10 per cent.

In the third project, I constrain gas and DM parameters of galaxy groups and clusters, by comparing X-ray scaling relations to theoretical expectations, obtained assuming that the gas is in hydrostatic equilibrium with the DM and follows a polytropic relation. I vary four parameters: the gas polytropic index Γ, its temperature at large radii T_ξ , the DM logarithmic slope at large radii ζ and its concentration c_vir. When comparing the model to the observed mass-temperature (M–T) relation of local clusters, my results are independent of both T_ξ and c_vir. I thus obtain constraints on Γ, by fixing the DM profile, and on ζ, by fixing the gas profile. For an NFW DM profile, I find that 6/5 < Γ < 13/10, which is consistent with numerical simulations and observations of individual clusters. Taking 6/5 < Γ < 13/10 allows the DM profile to be slightly steeper than the NFW profile at large radii. Upon including local groups, I constrain the mass-dependence of Γ and the value of T_ξ. Interestingly, with Γ = 6/5 and ζ = –3, I reproduce the observed steepening/breaking of the M–T relation at low mass, if 10⁶ < T _ξ < 10⁷ K, consistent with simulations and observations of the warm-hot intergalactic medium. When extrapolated to high redshift z, the model with a constant Γ reproduces the expected self-similar behaviour. I also account for the observed, non-self-similar relations provided by some high-z clusters, as they provide constraints on the evolution of Γ. Comparing my model to the observed luminosity-temperature relation, I discriminate between different M–c _vir relations: a weak dependence of c_vir on mass is currently preferred by data. This simple theoretical model accounts for much of the complexity of recent, improved X-ray scaling relations, provided that I allow for a mild dependence of Γ on mass or for T _ξ consistent with intercluster values.