Download Lecture15

Lecture 15
main sequence evolution
Recall: 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.
 8G 0 r02  r0 
dr
 
  1
dt
3
r


The time it takes for
the shell containing
mass Mr to collapse
to r=0 is the freefall time scale:
1/ 2
 3 1 

t ff  
 32 G 0 
Fragmentation
• Clouds don’t collapse to form one giant star. Stars
tend to form in groups or clusters
 5kT
M J  
 GmH



3/ 2
1/ 2
 3 


 4 
• 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 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.
M J   1/ 2
Thus the Jeans mass increases during collapse. The point where
fragmentation stops depends on the point when the collapse
becomes adiabatic.
Minimum Jeans mass
Make a crude estimate of the lower mass limit of
fragmentation.
1/ 4
 T 
M J ,min  0.014 9 2 
 e 
 0.25M Sun
Other 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 protostar
1. Isothermal collapse begins
2. Collapse becomes adiabatic,
and cloud heats up.
Evolution of a solar mass protostar
1. Isothermal collapse begins
2. 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 protostar
1. Isothermal collapse begins
2. 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 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 disks
Young main sequence stars often still have disks, even
after the molecular cloud has been dispersed.
Infrared-emitting dust disk
around b-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 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:
• 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?
t KH
2
3 GM Sun


 107 years
L
10 LSun RSun
Egrav
The 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 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
Break
Recall: 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 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 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 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
P   5/ 3
• 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 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.
t star
tUniverse
~ 0.00006
t star
tUniverse
~ 900
Stellar 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: overview
• Red giants lose most of their envelopes in an expanding shell of low
density gas (planetary nebula , ~10,000 years)
Stellar evolution: overview
• The remnant core
cools and fades to
become a white dwarf
(which lives for
billions of years).