Lecture 15Lecture 15

main sequence evolution

Recall: Initial cloud collapseRecall: Initial cloud collapse

A collapsing molecular cloud starts off simply: In free-fall, assuming the pressure gradients are too small to have much

effect The gas is approximately isothermal, if gas is optically thin so energy can be

efficiently radiated away.

1

3

8 02

00

r

rrG

dt

dr

The time it takes for the shell containing mass Mr to collapse to r=0 is the free-fall time scale:

2/1

0

1

32

3

G

t ff

FragmentationFragmentation

•Clouds don’t collapse to form one giant star. Stars tend to form in groups or clusters

2/12/3

4

35

HJ mG

kTM

•As isothermal collapse progresses, the increase in density means the Jeans mass must decrease.

•Thus if the cloud has some density inhomogeneities, smaller clumps within the cloud may collapse later on.

Adiabatic cloud collapseAdiabatic cloud collapse

We have assumed an isothermal collapse, which is approximately true if energy can be radiated away efficiently. As the density increases, however, the gas becomes optically thick.

At the other extreme, no energy is transported out of the cloud, and the collapse is adiabatic. In this case, the temperature rises as the cloud collapses.

Thus the Jeans mass increases during collapse. The point where fragmentation stops depends on the point when the collapse becomes adiabatic.

2/1JM

Minimum Jeans massMinimum Jeans mass

Make a crude estimate of the lower mass limit of fragmentation.

SunJ Me

TM 25.0014.0

4/1

29min,

Other effectsOther effects

Our estimate is crude, but gives an idea of the basic principles involved. We have neglected:

In using the Jeans criterion, we were assuming a static cloud, and not accounting for the energy of collapse

The details of radiative transport, vaporization of dust grains, dissociation of molecules, ionization of atoms.

Rotation: this will lead to the formation of a disk Departure from spherical symmetry Magnetic fields

•A fully numerical calculation (first done by Richard Larson, 1969) can improve the precision by including these and other physical effects.

Evolution of a solar mass protostarEvolution of a solar mass protostar

1. Isothermal collapse begins2. Collapse becomes

adiabatic, and cloud heats up.

Evolution of a solar mass protostarEvolution of a solar mass protostar

1. Isothermal collapse begins2. Collapse becomes

adiabatic, and cloud heats up.

3. A quasi-stable protostar forms, radiating gravitational potential energy

4. Collapsing material continues to accrete onto a disk

5. Core collapse continues when dust vapourizes and H2 dissociates.

Evolution of a solar mass protostarEvolution of a solar mass protostar

1. Isothermal collapse begins2. Collapse becomes

adiabatic, and cloud heats up.

3. A quasi-stable protostar forms, radiating gravitational potential energy

4. Collapsing material continues to accrete onto a disk

5. Core collapse continues when dust vapourizes and H2 dissociates.

6. Nuclear fusion begins, and an energetic jet expels material and angular momentum from the system

Herbig-Haro objectsHerbig-Haro objects

Jets associated with star formation interact with the surrounding ISM, exciting the gas and forming bright, emission line objects. These are HH objects.

Here we can actually see the stellar disk, illuminated by the central, obscured, star

A movie of a HH jet

Stellar disksStellar disks

Young main sequence stars often still have disks, even after the molecular cloud has been dispersed.

Infrared-emitting dust disk around -Pic. The central star has been subtracted.

The dust disk around Vega. At least one large planet is known to exist within this disk.

Quasi-stable collapseQuasi-stable collapse

•The quasi-static evolution of a protostar depends on the timescale for liberating gravitational potential energy, compared with the free-fall timescale.

Recall the Kelvin-Helmholtz timescale: years 1010

3 72

SunSun

SungravKH RL

GM

L

Et

•If the collapsing protostar is heated to ~3000 degrees, where do you expect it to lie on the HR diagram, relative to its future main sequence position?

The Hayashi trackThe Hayashi track

•The Hayashi track represents a boundary set by convection.

Cooler stars are unstable because the energy cannot be transported rapidly enough.

Zero age main sequenceZero age main sequence

The point where stars first reach the main sequence and begin equilibrium hydrogen burning is the Zero Age Main Sequence (ZAMS). The time taken to reach the ZAMS is inversely related to mass

Mass (MSun) Time to reach ZAMS (106 years)

15.0 0.0617

9.0 0.1505

5.0 0.5759

3.0 2.514

2.25 5.855

1.5 18.21

1.25 29.45

1.0 50.16

0.5 155.0

BreakBreak

Recall: main sequence structureRecall: main sequence structure• The three divisions in a stellar interior are the nuclear burning core,

convective zone and radiative zone. • Energy, in the form of gamma-rays, is generated solely in the nuclear

burning core. • Energy is transferred towards the surface either in a radiative manner or

convection depending on which is more efficient at the temperatures, densities and opacities.

The end of the MS: Solar mass starsThe end of the MS: Solar mass stars

•The main sequence phase ends with the depletion of hydrogen in the core.

Isothermal He core hydrogen burning continues in a shell around

the He core.

Solar mass starsSolar mass stars

•The H-shell burning phase produces even more energy than the core-burning phase

R and L increase, but T decreases This is the subgiant branch

When the isothermal core gets massive enough, it cannot support the envelope and collapses (on the Kelvin-Helmholtz timescale)

Degenerate coresDegenerate cores

•When the density of a gas gets sufficiently high, the Pauli exclusion principle applies: no two fermions (e.g. electrons) can occupy the same quantum state.

Pressure becomes due to the nonthermal motions of electrons, and is independent of temperature

3/5P

• A solar mass star’s core will collapse when it reaches ~13% of the total stellar mass.

• Lower mass stars have more degenerate cores: thus the cores may never collapse before the next stage of nuclear burning begins.

Stellar evolutionStellar evolution

Stars on the main sequence have a finite lifetime

•Red giants, red supergiants, and white dwarfs are all examples of stars that have evolved off the main sequence.

•The luminosity and effective temperature are the main observable predictions of stellar models.

00006.0~Universe

star

t

t

900~Universe

star

t

t

Stellar evolution: overviewStellar evolution: overview

•As the core loses pressure, it collapses and heats up(~2 million years)

•New energy sources cause envelope to expand and luminosity to increase, producing red giants (~20 million years)

Stellar evolution: overviewStellar evolution: overview

•Red giants lose most of their envelopes in an expanding shell of low density gas (planetary nebula , ~10,000 years)

Stellar evolution: overviewStellar evolution: overview

•The remnant core cools and fades to become a white dwarf (which lives for billions of years).