1

Lecture 2: Gas Cooling and Star

Formation

How to make a galaxy

Create Hydrogen, Helium and dark matter in a Big BangAllow quantum fluctuations to cause some regions to be denser than others

Ensure a large amount of dark matter, so there is enough mass to ensure the dense regions collapse due to gravity

Add Dark Energy so the Universe expands at correct rate

THESE ARE THE BASIC INGREDIENTS OF COSMOLOGY

THE PILLARS ARE:Abundances of Light ElementsThe Cosmic Microwave BackgroundThe Large Scale Structure in the Distribution of GalaxiesThe Expanding Universe

How to make a galaxy

Create Hydrogen, Helium and dark matter in a Big BangAllow quantum fluctuations to cause some regions to be denser than others

Ensure a large amount of dark matter, so there is enough mass to ensure the dense regions collapse due to gravity

Gas cools to central regions of dark matter halos Dens gas then forms stars

Add Dark Energy so the Universe expands at correct rate

Dark matter particles are collisionless and only detectable in bulk by their gravitational influence Baryons radiate - a sure sign that dissipative processes are at work. Dissipative means baryonic matter can loose energy by radiative processes, resulting in a loss of thermal energy from the system. So the baryonic component shrinks within the dark matter halos.

Once the gas is stabilised by thermal pressure, loss of energy by radiation is an effective way of decreasing internal pressure, allowing region to contract and re-establish pressure equilibrium.

Gas cools, settles into a disk, surrounded by a dark matter halo

Dissipation

Important Cooling Processes

Type Reaction NameFree-Free e– + X+ → γ + e– + X+ Bremsstrahlung

Free-Bound e– + X+ → X + γ Recombination

Bound-Free e– + X → 2e– + X+ Collisional Ionization

Bound-Bound e– + X → e– + X Collisional Excitation

Electron-Photon γ + e–→ γ + e– Inverse Compton Scattering

Inverse Compton Scattering

When relativistic electron collides with a low energy photon, e.g. the CMB. Imparts energy to the photon. The gas therefore cools.

Inverse of Compton scattering where photon imparts energy to a slow electron.

Important when Telectrons >> Tphotons

Important at: High redshifts

CMB: T ~ 2.73(1+z)K

γ + e–→ γ + e–

As the Universe expands, cooling times become long, so unimportant at low redshifts.X-rays from inverse Compton Scattering are also commonly seen in supernovae and active galactic nuclei (AGNs).

Bremsstrahlung

Happens in very hot gasses where the atoms already ionised.

A charged particle is accelerated around the nucleus of an ionised atom.

The strong electromagnetic attraction alters the course of the charged particle.

Important at Temperatures:

Primordial* Gas > 106KEnriched** Gas > 107K

*primorial gas: hydrogen + helium**enriched gas: additional metals from stars/supernovae

e– + X+ → γ + e– + X+

1. Collisional ExcitationAtoms are excited by collisions with electrons, then radiatively decay to the ground state

At lower Temperatures (but still > 104 K) several processes occur. Each is Temperature dependentas well as metallicity dependent e– + X → e– + X

2. Collisional Ionization

Atoms ionized by collisions with electrons: kinetic energy equal to ionisation threshold is removed form the gas. Gas therefore cools.

e– + X → 2e– + X+

3. Recombination

Atoms ionized by collisions with electrons: kinetic energy equal to onisation threshold is removed form the gas. Gas therefore cools.

e– + X+ → X + γ

Fine StructureIf gas is enriched, collisions with neutral hydrogen and the few free electrons excite fine structure levels of low ions such as OI, CII.

At low Temperatures (< 104 K) cooling rates drop as most electrons have recombined.

Neutral Hydrogen

If gas is primordial, cooling only proceeds (slowly) via formation of H2 which proceeds via gas phase reactions such as:

e– + H0 → γ + H− followed by

H− + H0 → H2 + e– and/or

H+ + H0 → H2+ + γ then H2

++ H0→ H2+ H+

Cooling rates can be calculated: Primordial Gas

Cooling rates can be calculated: Enriched Gas

Cooling rates can be calculated: More detailed determination

Assumes collisional ionization equilibriumAssumes photo-ionization equilibrium

Mass of Collapsed Halos

Using Press-Schechter or simulations, we know the mass of halos that have collapsed at various redshifts. We know the virial temperatures (see table).

So we can use our knowledge of cooling times to determine whether gas will cool to the centre of the halos.

To collapse we require that the cooling time is less than the free fall, or

dynamical time, tcool < tdyn

In this case energy can be removed sufficiently quickly to allow rapid gravitational collapse to take place.

Cooling Time

Dynamical Time

For a sphere:

~ 6.5 × 109 f ½ n ⅓ yr where f is the gas fraction of the cloud and n is the density.

This uses crude approximations to the cooling rates from the various processes

Λ is the cooling rate

Cooling Time versus Dynamical Time

Thus setting tcool = tdyn we get:

T63/2 ~ f -1/2 n -1/2 ≈ 2.5

Using the Virial theorem to relate Temperature & density to the Mass of the dark matter halos, we find that:

M = 1.2 ×1013 T63/2

f 3/2 n -1/2 (units of solar masses)

Thus, according to our cooling rates, dissipational collapse will occur when M ≤ 3 ×1013 f 2

For small f this gives us approximately Galaxy Masses

Virial Temperature and Pressure Support

Gas experiencing a strong virial shock has its kinetic infall energy thermalized and is heated to the virial temperature

Pressure supports the gas against gravitational collapse.

But radiative cooling processes allow gas to dissipate energy

Conservation of Angular Momentum results in gas forming a disk

Angular Momentum in Dark Matter Halos

We can Calculate the distribution of angular momentum of dark matter halosBullock et al 2001

Angular Momentum in Disks

Successes of simple model!

Model disk formation using or simple assumptions of cooling of gas that was shock heated to the virial temperature

Simple assumption: the disk scale-lengths are related to the radial size and angular momentum of the dark matter halos :

rdisk λ rvirial

e.g.

Successfully reproduce a population of galaxies that match the observed Tully-Fisher relation

Relates the rotational velocity of galaxies (Vc) to their Magnitude (M)

Cold FlowsHow good are our assumptions?Does gas really shock at the virial radius??

How good are our assumptions?Does gas really shock at the virial radius??Certainly, structure formation is not spherical in CDM

Gas in simulations does not shockCools along the filamants ``Cold Mode” Accretion

Cold Flows

Cold Flows

Brooks et al. 2009Cold gas can stream allthe way into the disk region without ever shock heating

Cold Mode accretion dominates for galaxies with mass < 2.5×1011 M*

See Keres et al 2005

~

Cold Mode Accretion

Stars form in centre of Dark Matter Halos

Star Formation

Gas Fragments into Giant Molecular Clouds (GMCs)where star formation occurs

Collapse of GMCsA cloud, becomes unstable and begins to collapse when it lacks sufficient gaseous pressure support to balance gravity (Jeans Crtieria) and when shear forces in the disc are not too large (Toomre Criteria).

The Jeans MassA cloud, becomes unstable and begins to collapse when it lacks sufficient gaseous pressure support to balance gravity.

When the sound-crossing time is less than the free-fall time, pressure forces win and the system bounces back to equilibrium.

However, when the fee-fall time is less than the sound crossing time, gravity wins and the region collapses.

The Jeans MassAssume GMCs are self gravitating, homogeneous, isothermal sphere:

Free-fall tiime

Sound crossing time

For

The Jeans Mass

Then the Jeans Mass is

RJ is ½ the Jeans length

The Toomre Criteria

Large regions will be torn apart by the shear faster than they tend too collapse, namely faster than the gravitational free-fall time.

These regions within disks are able to collapse if:

Q = csκπGΣ

< 1

Where κ is the epicycle frequency

κ = √2( Vc2

R2

Vc

RdVc

dR )+½

and Σ is the surface density of the gas

Star FormationSince gas is required for star formation, it is logical to look at the relation between the Star Formation rate (SFR) and the surface density of gas

Star formation in spiral galaxies have shown the Schmidt law to be a surprisingly good description

Star Formation

Star Formation

Star Formation

Star Formation

The Initial Mass Function (IMF)

N(M) ∝ M-αdM (e.g. Kroupa 2001)

N(M) ∝ M-2.35 dM for M>Msun (Salpeter 1953)

Bulk

of m

ass in

tegra

lConsider an ensemble of stars born in a molecular cloud (single stellar population)

The distribution of their masses can be described piecewise by power-laws