According to the standard model of
cosmology (known as the
ΛCDM model), the formation of satellite galaxies is intricately connected to the observed
large-scale structure of the Universe. Specifically, the ΛCDM model is based on the premise that the observed large-scale structure is the result of a bottom-up hierarchical process that began after the
recombination epoch in which
electrically neutral hydrogen atoms were formed as a result of
free electrons and
protons binding together. As the ratio of neutral hydrogen to free protons and electrons grew, so did fluctuations in the baryonic matter density. These fluctuations rapidly grew to the point that they became comparable to
dark matter density fluctuations. Moreover, the smaller mass fluctuations grew to
nonlinearity, became
virialized (i.e. reached gravitational equilibrium), and were then hierarchically clustered within successively larger bound systems. The gas within these bound systems condensed and rapidly cooled into
cold dark matter halos that steadily increased in size by coalescing together and accumulating additional gas via a process known as
accretion. The largest bound objects formed from this process are known as
superclusters, such as the
Virgo Supercluster, that contain smaller
clusters of galaxies that are themselves surrounded by even smaller
dwarf galaxies. Furthermore, in this model dwarfs galaxies are considered to be the fundamental building blocks that give rise to more massive galaxies, and the satellites that are observed around these galaxies are the dwarfs that have yet to be consumed by their host.
Accumulation of mass in dark matter halos A crude yet useful method to determine how dark matter halos progressively gain mass through mergers of less massive halos can be explained using the excursion set formalism, also known as the extended
Press-Schechter formalism (EPS). Among other things, the EPS formalism can be used to infer the fraction of mass M_2 that originated from collapsed objects of a specific mass at an earlier time t_1 by applying the
statistics of
Markovian random walks to the trajectories of mass elements in (S,\delta)-space, where S = \sigma^2(M) and \delta = {\rho(x) - \bar{\rho} \over \bar{\rho} } represent the mass
variance and overdensity, respectively. In particular the EPS formalism is founded on the
ansatz that states "the fraction of trajectories with a first upcrossing of the barrier \delta_S = \delta_{critical}(t) at S > S_1 = \sigma^2(M_1) is equal to the mass fraction at time t that is incorporated in halos with masses M". Consequently, this ansatz ensures that each trajectory will upcross the barrier \delta_S = \delta_{critical}(t) given some arbitrarily large S, and as a result it guarantees that each mass element will ultimately become part of a halo. Nevertheless, the utility of the EPS formalism is that it provides a
computationally friendly approach for determining properties of dark matter halos.
Halo merger rate Another utility of the EPS formalism is that it can be used to determine the rate at which a halo of initial mass M merges with a halo with mass between M and M+ΔM. This rate is given by \mathcal{P}(\Delta M | M,t)\operatorname{d}\ln\Delta M \operatorname{d} \ln t = \frac{1}{\sqrt{2\pi}}\Bigg[\frac{S_{1}}{(S_1 - S_2)}\Bigg]^{3/2} \exp \Bigg[- \frac{\delta_c^2(S_1 - S_2)}{2S_1 S_2}\Bigg]\Bigg|\frac{\operatorname{d} \ln \delta_c}{\operatorname{d} \ln t}\Bigg| \Bigg|\frac{\operatorname{d} \ln S_2}{\operatorname{d} \ln \Delta M}\Bigg| \frac{\delta_c}{\sqrt{S_2}} \mathrm{d} \ln t \, \mathrm{d} \ln \Delta M where S_1 = \sigma^2(M), S_2 = \sigma^2(M + \Delta M). In general the change in mass, \Delta M, is the sum of a multitude of minor mergers. Nevertheless, given an infinitesimally small time interval \operatorname{dt} it is reasonable to consider the change in mass to be due to a single merger events in which M_1 transitions to M_2. == Galactic cannibalism (minor mergers) ==