#
Hierarchical Structure Formation

Under models for hierarchical structure formation,
little
things collapse first and big things collapse later. This is the
natural
outcome of Cold Dark Matter, and has made it **the
leading cosmological model of structure formation.**

## So what really does collapse first?

In order to collapse, remember, a parcel of gas must
be
Jeans
unstable. So let's calculate the Jeans mass immediately after
recombination,
when structure can first collapse.

**Temperature:** ~ 3000
K

**Baryonic Density:**
we can get this from the present day baryonic density.
if we insert rough numbers, we get
So putting these numbers in, we find that just after
recombination,
the Jeans mass is

**M**_{J} ~ 2x10^{6}
M_{sun}

which is just about the mass of a dwarf galaxy. Anything smaller than that could not
collapse. Anything
larger than that could, but more massive objects are characteristically
less dense, and will take longer to collapse.

As larger structure develops, it collapses
gravitationally
and the formal Jeans equation does not really apply. Rather than
massive
clouds collapsing as one (**monolithic collapse**),
we instead have ensembles of smaller objects (ie protogalaxies or
galaxies)
falling together to form larger structures.

## Building structure hierarchically

This is a "**merger tree**",
describing the evolution of structure in a hierarchical universe (from
Lacey and Cole MNRAS 262 627 1993)

*So when did this object
form?*

Can we watch this kind of structure form? *Numerical
simulations of cosmology! *Here is the collapse of a portion of
the universe which becomes a galaxy cluster. It is shown in **comoving
coordinates**, where the expansion of the Universe is scaled
out
of the picture.

Courtesy
Paul Bode, UPenn

This hierarchical collapse continues on smaller scales to form galaxy
clusters.