Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 14: Star Formation

Readings: Chapter 20

Key Ideas

Raw material of star formation: Giant Molecular Clouds
Formation Stages:: Cloud Collapse and Fragmentation into clumps; Protostar formation from clumps; Onset of Hydrostatic Equilibrium (Kelvin-Helmholz timescale); Ignition of core Hydrogen burning & onset of Thermal Equilibrium
Minimum & Maximum masses of stars

The Sun is Old and in Equilibrium

If we look at the Sun today, some 4.6 Gyr after it formed, we find

It is in Hydrostatic Equilibrium: its internal Pressure and Gravity are in balance, so it neither expands nor contract.
It is in Thermal Equilibrium: Energy Transport balances Energy Generation, so its energy lost by its Luminosity is made up for by nuclear fusion energy generated in its core.

The big question is, how did it get this way?

Steps to Stardom...

Star birth is basically a 2-stage process:

Establish Hydrostatic Equilibrium. This is the Protostar Formation phase
Establish Thermal Equilibrium. This is the Pre-Main Sequence phase

The first question we have to ask is where stars are Born? We learn this by looking around the Galaxy.

The Interstellar Medium

The space between the stars is filled with Gas and dust (fine particulates).

Most of the volume is filled with hot, diffuse (very thin), atomic Hydrogen gas
Embedded within this are clumpy clouds of cold, dense Molecular Hydrogen (H₂) gas.

Young stars are all found in dense gas-rich regions.

This makes sense, since we expect to find new stars close to the raw materials from which they are born.

Giant Molecular Clouds (GMCs)

Interstellar clouds of molecular hydrogen gas (H₂)

Properties:

Sizes: 10-50 parsecs
Masses: ~10⁵ M_sun
Temperatures: 10-30 K
Densities: 10^5-6 molecules/cc

This is a starting density of ~10²⁰ times smaller than that of a star. This means the collapse from cloud to star has a long ways to go.

Collapse of a GMC

A GMC is held up against its own gravity by its internal pressure. This pressure has 2 sources:

Gas pressure from internal heat
Pressure from embedded magnetic fields

If the Gravity becomes larger than the internal Pressure, the entire cloud will start to collapse.

Possible ways to trigger such a collapse include:

Cloud-Cloud collisions.
Shocks from nearby supernova explosions
Passage through a spiral arm of the Galaxy.

Cloud Fragmentation

GMCs are clumpy:

Clump Sizes ~0.1 parsecs
Clump Masses ~few M_sun

High-density clumps are more unstable than low-density regions:

Densest clumps will collapse first and fastest

Result:

GMC fragments into dense cores

Cores have masses comparable to stars.

Building a Protostar

Cores start out low density and transparent:

Photons can leak out, keeping the interior gas cool
Can't build up pressure, and so keep collapsing

Eventually, the core density rises to the point where the core becomes opaque:

Photons get trapped, so the gas heats up
Pressure begins to build up

Eventually, the pressures builds up until it achieves Hydrostatic Equilibrium

Protostellar core continues to grow as fresh material from the surrounding parent cloud falls onto it.

A Quick Beginning...

The protostar phase is very short-lived: only 10^4-5 years.

During this phase:

The Protostar is in Hydrostatic Equilibrium
It remain deeply embedded within their parent gas & dust cloud
It is not yet in Thermal Equilibrium

The combination of "Short Lived" and "Hard to See" means that very few Protostars are observed.

Protostars have Disks

As matter rains onto the Protostar,

Matter along the poles free-falls in rapidly
Matter along the equator will infall more slowly due to angular momentum conservation.

The result is that the infalling gas pancakes, forming a flattened, rotating disk around the equator of the Protostar.

Clearing out the Disk

After the protostar forms, the disk of material begins to clear away:

Some of the matter drains onto the star
Other bits form into planets

Observations suggest that:

The gas in the disk clears away quickly, in ~6 Million years.
The dust grains and solids (pebbles & rocks) take longer

We see dust and "debris" disks around young low-mass stars.

From Protostar to Star

Protostars shine because they are hotter than their surroundings:

Need an energy source to stay hot, but
Central temperature is too cool for nuclear fusion to ignite

Initial energy source is Gravitational Contraction (aka, the Kelvin-Helmholz Mechanism):

The Protostar shrinks slowly, releasing gravitational energy
50% goes into photons, and is radiated away as starlight
other 50% goes into heating the Protostar interior

How long can does this last?

Kelvin-Helmholz Timescale

To understand how long a Protostar can shine by Gravitational Contraction, we need to compare two numbers

The Energy Source: Gravitational Binding Energy (M²/R)
The Energy Loss Rate: Luminosity (L)

The ratio is the Kelvin-Helmholz Timescale:

The Kelvin-Helmholz timescale is ~30 Myr for a 1 solar mass Protostar.

Consequences:

Shorter K-H time for high-mass protostars
Longer K-H time for low-mass protostars

H-R Diagram of pre-Main Sequence evolution for stars of various masses:

The K-H timescale is the time to cross the diagram and land on the Main Sequence.

High-Mass Protostars

Gravitational Collapse is very fast for high-mass protostars:

A 30 M_sun Protostar will collapse in <10,000 years.

As the collapse proceeds, the core temperature gets hotter until it reaches ~10 Million K:

Ignites first P-P chain, then CNO cycle fusion in its hot core

The star lights up, quickly ionizing and blowing away any remaining gas and junk.

Low-Mass Protostars

Gravitational Collapse is slower for low-mass protostars:

1 M_sun Protostar takes ~30 Myr
0.2 M_sun Protostar takes ~1 Gyr

When core Temperature >10 Million K:

Ignite core P-P chain fusion
Stellar wind blows away the cocoon and remaining disk

Settles slowly onto the Main Sequence

The Zero-Age Main Sequence

As the core heats up, H fusion runs faster:

Core Temperature & Pressure rises
Collapse begins to slow down
Pressure = Gravity and core collapse stops
Energy created by P-P chain fusion = Energy lost by shining (Luminosity)

Star reaches the Zero-Age Main Sequence as a full-fledged star in Hydrostatic and Thermal Equilibrium.

Minimum Mass: ~0.08 M_sun

Below 0.08 M_sun, the core never gets hot enough to ignite H fusion.

Object becomes a Brown Dwarf

Resemble "Super Jupiters" in their properties.
Generate energy by the Kelvin-Helmholz mechanism
Only a few hundred are known (very faint)
Shine mostly in the infrared

These are the T dwarfs.

[Hubble Space Telescope images of the Brown Dwarf Gliese 229B]

Maximum Mass: 100-150 M_sun

Above a mass of 100-150 M_sun, the core gets so hot that

Radiation pressure overcomes gravity,
Star becomes unstable & disrupts itself

The ultimate upper mass limit is not well known.

Such stars should be (and are) extremely rare (a few per galaxy).

[Hubble Space Telescope images of a very luminous star]

What can we see?

As we look out into the Galaxy, we see stars in all phases of their life cycles:

If the phase is long-lived, we see many stars in that phase
If the phase is very short, we see only a few stars in that phase

The Pre-Main Sequence phase is longer for lower-mass stars (because of the longer K-H timescale):

We see a few low-mass Protostars
High-Mass Protostars are very rare

The Main Sequence Phase is very long:

We see more M-S stars than Protostars by far

How long is the M-S phase? That's the subject of the next lecture...

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