Gravitational Clustering

Hierarchical clustering

Theoretical and observational data on galaxy clustering suggest that there is a hierarchy in structure formation that starts with early, low massive objects and finishes with late, massive ones, these latter arising from the gravitational clustering of the former.

It is generally believed that the first objects, as well as their subsequent clusterings, have their origin in small amplitude density inhomogeneities which have grown by gravitational instability as the universe expanded. The evolution of density inhomogeneities passes through two distinct stages:

  • linear regime: the perturbation expands while its small amplitud increases. Owing to the independence of the Fourier modes the set of equations governing the amplitud evolution can be solved analytically.
  • non-linear regime: for high amplitudes the perturbation begins to collapse and finally virializes giving rise to a newborn object. In this regime the Fourier modes are coupled together and the only accurate way to follow the evolution of pertubations is by means of numerical simulations.
Alternatively, theoretical models can also be used to deal with the non-linear regime. Press & Schechter (1974; PS) proposed an innovative method, founded on features of the linear density field, capable of giving the mass distribution of collapsed objects. The fact that the predicted mass function fits those from N-body simulations suggests the capability of the PS formalism to describe the real clustering process. This formalism has been extended (Lacey & Cole 1993) to allow the calculation of some interesting quantities related to the growth history of collapsed objects, such as the merger and accretion rates and the survival and formation times, which complete the gravitational clustering view.

Structrure of dark matter halos

Cosmological N-body simulations show that the structure of relaxed dark-matter halos can be described by a universal density profile, characterized by a scale radius and a characteristic density. Once the halo mass is fixed this profile has only one free parameter, say the scale radius r_s or, equivalently, the halo concentration c defined as the ratio between the virial radius R and r_s. The concentration shows a clear dependence on the halo mass, with massive halos having lower concentrations. This is the so-called mass-concentration relation.

This correlation, as well as other two recently found relating the concentration to the halo formation epoch and the mass inside the scale radius, can be explained through a model of evolution for r_s taking into account that halos grow inside-out (keeping their inner structure unaltered) between major mergers. Here we provide a FORTRAN code that computes the typical r_s value for relaxed halos in CDM cosmologies according to our evolutive model.

Convergence studies in cosmological N-body simulations suggest that the inner slope of the halo density profile does not tend to a power-law for vanishing radii, but becomes increasingly shallower. Thus, NFW-like laws do not fit well the density profile in the halo inner region. A law with a decreasing inner slope (as the Sersic law) do a better job in wide range fittings. We have developed a FORTRAN code that computes time-independent relations involving scale parameters of the NFW and Sersic laws. These time-independent relations arise from the inside-out growth of halos and allows the determination of the profile parameters for halos of mass M at any time.

Global properties and structure of the hot gas within dark halos

The baryonic gas trapped in dark matter halos reaches a hydrostatic equilibrium state within the gravitational potential dominated by the dark matter. In massive halos the gas temperature is high enough to cause the emission of X-rays. Under the assumption that gravity is the only process driving the evolution of the dark and baryonic components in galaxy systems, some relations, known as scaling laws, arise between the X-ray emitting properties and the mass of the systems. The fact that real systems show deviations from these relations means that some non-gravitational mechanisms are also at play.

We have build an analytic model for a preheated, polytropic hot gas in hydrostatic equilibrium within an NFW dark halo potential taking into account the inside-out growth of the halo between major mergers. We have applied the model to study the observed X-ray properties of galaxy groups and clusters at z=0.

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