2.1 Basic Processess and the Algorithm

Based on the merging trees of DM haloes computed as discusses in Ch. 1, we proceed to compute in detail the history of the DM substructures corresponding to galaxies. We start at the bottom of the DM merging tree computed in Ch. 1; when two DM haloes coalesce into a larger one,  they survive as substructures in the newly formed DM halo until

1) they loose their orbital angular momentum due to dynamical friction and their orbits eventually decay until they reachthe centre of the new DM halo thus becomeing part of the central dominant galaxy

2) they merge with the other substructures present in the halo.

Thus, as time proceeds (going upward along the hierarchical level of the DM trees computed in Ch. 1), the subclumps accumulate in the host haloes, as shown in fig. 2.1

Fig. 2.1. The evolution of subclumps in the DM merging trees. The lighyt circles and the dashed lines correspond to the DM halo masses and to their links, as they result from the Monte Carlo computation  explained in Ch. 1. The dark spots represent the subclumps surving as overdens DM clumps (galactic DM haloes) with mass m inside the host haloes with mass M. Their evolution is explained in the text. The initial condition (at the bottom of the tree) is set assuming m=M.

We shall refer to the subclumps as galactic clumps. Their mass is m. The mass of the host haloes where they reside is M.

1. The orbital decay

This is computed (like in Somerville & Primack 1999) by following the evolution of the radial distance r_g from the halo centre after the equation (Eq. 2.1)

where m and M are the masses of the galactic DM subclump and M a,d Vc are the mass and the circular velocity of the host DM halo, while f(ε) ≈ 0.78 is a function depending on the orbital angular momentum  ε=J/J_c (J_c being the value corresponding to a circular orbit with the same energy). The initial conditions and the iterative computation of the orbital decay decsribed by eq. 1 depend on the merging history of the host DM halo, according to the following scheme.

In newly formed DM haloes, or in haloes at the bottom of the tree:
	rg= αrad R (R is the virial radius of the host DM halo, αrad=1) is set as initial condition for eq. 1
	m=M
	ε           is extracted from a uniform distribution  between 0.02 and 1
	Memb      (the number of galactic subclumps in the considered halo) is set to 1
If the considered galaxy belongs to a DM halo with mass M which is included into a larger one (with mass M2) in the considered time step and  M<M2-M (i.e., M is not the main progenitor of M2)
	The radial distance rg is reset to new initial conditions rg=αentr R (where 0.5 < αentr < 1 see, e.g., Cole et al. 2002)
	ε it is extracted from a uniform distribution between 0.02 and 1
In the remaining cases
	rg decays following the above equation
	The more massive galaxy in the halo is assigned to be the central dominant galaxy with rg =0

The galactic radii are taken to be the tidal radii r_td (see here for details on their computation). When a galaxy radial distance r_g becomes smaller than the radius t_td of the central dominant galaxy, it coalesce with the cD. Its mass is added to that of the cD.

2. The binary aggregations bewteen satellite galaxies

They occurr at a rate t_agg^-1=n Σ V_rel, where n is the number density of the satellite galaxies in the common DM halo, S is the cross sectionfor merging, and V_rel≈√2 V_c is the galaxy average relative velocity. We adopt the cross section given in Menci et al. 2002.

where m’ and m are the masses of the two merging partner. For any given mass m, a mass m’ is randomly selected among  the galactic sub-clumps in the same host halo of mass M. The average aggregation timescale t_agg is compared with the time Δt hat the two galaxies spent in the same DM halo. If t_agg ≤ Δt the two galactic subclumps merge. The merger is assigned a mass m₂=m+m’ and a circular velocity computed assuming the virial equilibrium; the radius of the new galaxy is taken to be the tidal radius.

Proceed to the Next Section

Back to the Galaxy Merging History page

Back to the Main Page