Transcript Stellar Models

Stellar Models
The structure and evolution of a star is determined
by the laws of
• Hydrostatic equilibrium
• Energy transport
• Conservation of mass
• Conservation of energy
A star’s mass (and chemical
composition) completely
determines its properties.
That’s why stars initially all line up along the main sequence.
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
At masses below 0.08
Msun, stellar
progenitors do not get
hot enough to ignite
thermonuclear fusion.
 Brown
Dwarfs
Evolution off the Main Sequence: Expansion into a
Red Giant
When the hydrogen in the
core is completely
converted into He:
“Hydrogen burning” (i.e.
fusion of H into He) ceases
in the core.
H burning continues in a
shell around the core.
He Core + H-burning shell
produce more energy than
needed for pressure
support
Expansion and cooling of
the outer layers of the star
 Red
Giant
Summary of Post Main-Sequence Evolution of
Stars
Supernova
Fusion
proceeds;
formation
of Fe core.
M > 8 Msun
Evolution of 4
- 8 Msun stars
is still
uncertain.
Mass loss in
stellar winds
may reduce
them all to <
4 Msun stars.
Fusion stops
at formation
of C,O core.
M < 4 Msun
M < 0.4 Msun
Red dwarfs:
He burning
never ignites
Estimating the Age of a Cluster
The
lower on
the MS
the turnoff point,
the older
the
cluster.
Cepheid Variables:
The Period-Luminosity Relation
The variability period of a
Cepheid variable is
correlated with its
luminosity.
The more luminous it
is, the more slowly it
pulsates.
=> Measuring a Cepheid’s
period, we can determine
its absolute magnitude!
Degenerate Matter
Matter in the He core has
no energy source left.
 Not enough thermal
pressure to resist and
balance gravity
 Matter assumes a
new state, called
degenerate
matter:
Pressure in degenerate core
is due to the fact that
electrons can not be packed
arbitrarily close together
and have small energies.
The Remnants of Sun-Like Stars: White
Dwarfs
Sun-like stars build up
a Carbon-Oxygen (C,O)
core, which does not
ignite Carbon fusion.
He-burning shell keeps
dumping C and O onto
the core. C,O core
collapses (because no
further nuclear fusion)
and the matter
becomes degenerate.
 Formation of
a White
Dwarf
White Dwarfs (3)
The more massive a white dwarf,
the smaller it is!
 Pressure becomes larger, until electron degeneracy
pressure can no longer hold up against gravity.
WDs with more than ~ 1.4 solar masses can not exist!
Chandrasekhar Limit = 1.4 Msun
Recycled Stellar
Evolution
Mass transfer in a
binary system can
significantly alter the
stars’ masses and
affect their stellar
evolution.
Type I and II Supernovae
Core collapse of a massive star:
Type II Supernova
If an accreting White Dwarf exceeds the
Chandrasekhar mass limit, it collapses,
triggering a Type Ia Supernova.
Type I: No hydrogen lines in the spectrum
Type II: Hydrogen lines in the spectrum
White Dwarfs & Neutron Stars
The more massive a white dwarf,
the smaller it is!
electron
degeneracy
pressure
neutron
degeneracy
pressure
 Pressure becomes larger, until electron degeneracy
pressure can no longer hold up against gravity.
WDs with more than ~ 1.4 solar masses can not exist!
Chandrasekhar Limit = 1.4 Msun
Formation of Neutron Stars (2)
Lighthouse Model of Pulsars
A Pulsar’s
magnetic field
has a dipole
structure, just
like Earth.
Radiation
is emitted
mostly
along the
magnetic
poles.
Jocelyn Bell
1943 “Little Green Man”
Gravitational Radiation:
General Relativity: Any rapid
change in gravitational field should
spread outward gravitational
radiation at the speed of light.
The orbital period of the binary
pulsar is slowly growing shorter as
the neutron stars gradually spiral
toward each other – they are
radiating away gravitational energy.
First indirect evidence of
gravitational radiation.
Arecibo Observatory
Black Holes
Just like white dwarfs (Chandrasekhar limit: 1.4 Msun),
there is a mass limit for neutron stars:
Neutron stars can not exist with
masses > 3 Msun
We know of no mechanism to halt the collapse of a
compact object with > 3 Msun.
It will collapse into a single point – a singularity:
=> A Black Hole!
Escape Velocity
Velocity needed to
escape Earth’s
gravity from the
surface: vesc ≈ 11.6
km/s.
Now, gravitational
force decreases with
distance (~ 1/d2) =>
Starting out high
above the surface =>
lower escape velocity.
vesc
vesc
vesc
If you could compress Earth to a smaller radius =>
higher escape velocity from the surface
The Schwarzschild Radius
=> There is a limiting radius where
the escape velocity reaches the
speed of light, c:
2GM
Rs = ____
c2
G = Universal const. of gravity
M = Mass
Rs is called the Schwarzschild
Radius.
Vesc = c
Schwarzschild Radius and Event Horizon
No object can travel
faster than the
speed of light
=> nothing (not even
light) can escape from
inside the
Schwarzschild radius
• We have no way of
finding out what’s
happening inside the
Schwarzschild radius.
 “Event horizon”
The Mass of the Milky Way
If all mass were concentrated in the center,
the rotation curve would follow a modified
version of Kepler’s 3rd law
rotation curve = orbital velocity
as function of radius
The Mass of the Milky Way (2)
Total mass in the disk of
the Milky Way:
Approx. 200 billion solar
masses
Additional mass in an
extended halo:
Total: Approx. 1 trillion
solar masses
Most of the mass is not
emitting any radiation:
Dark Matter!
Stellar Populations
Population I: Young stars: metal
rich; located in spiral arms and
disk
Population II: Old stars: metal
poor; located in the halo
(globular clusters) and nuclear
bulge
A Black Hole at the Center of Our Galaxy
By following the orbits of individual stars near the center of
the Milky Way, the mass of the central black hole could be
determined to ~ 2.6 million solar masses
Rotation Curves of Galaxies
From blue / red shift of spectral
lines across the galaxy
 infer rotational velocity
Observe frequency of
spectral lines across a galaxy.
Plot of rotational velocity vs.
distance from the center of
the galaxy: Rotation Curve
Galaxy Classification
Ellipticals:
Spirals:
Sa
E0, …, E7
E0 = Spherical
Large nucleus;
tightly wound
arms
E1
Sb
Sc
E7 = Highly
elliptical
E6
Small nucleus;
loosely wound
arms
Interacting Galaxies
Cartwheel Galaxy
Particularly in rich
clusters, galaxies can
collide and interact.
Galaxy collisions can
produce
ring galaxies and
NGC 4038/4039
tidal tails.
Often triggering active
star formation:
starburst galaxies
Starburst Galaxies
Starburst galaxies: Galaxies in which stars are
currently being born at a very high rate.
Starburst galaxies contain many young stars and
recent supernovae, and are often very rich in gas
and dust; bright in infrared:
ultraluminous infrared galaxies
Cepheid Distance Measurement
Repeated
brightness
measurements of
a Cepheid allow
the
determination of
the period and
thus the absolute
magnitude.
 Distance
Model for Seyfert Galaxies
Seyfert I:
Strong, broad emission lines from rapidly
moving gas clouds near the BH
Gas clouds
Emission lines
UV, X-rays
Accretion disk
Dense dust torus
Seyfert II:
Supermassive black
hole
Weaker,
narrow
emission
lines from
more slowly
moving gas
clouds far
from the BH
Quasar Red Shifts
z=0
z = 0.178
z = 0.240
Quasars have
been detected at
the highest red
shifts, beyond
z~6
z = 0.302
z = 0.389
z = Dl/l0
This indicates distances of several Gigaparsec
Hubble’s Law
Recession Velocity (km/s)
Distant galaxies are flying
away (= receding) from us
with a speed proportional
to distance
Distance (Mpc)
The Necessity of a Big Bang
If galaxies are moving away from each other with a
speed proportional to distance, there must have
been a beginning, when everything was
concentrated in one single point:
The Big Bang!
?
The Cosmic Background Radiation (2)
After recombination, photons can travel
freely through space.
Their wavelength is only stretched (red
shifted) by cosmic expansion.
Recombination:
z = 1000; T = 3000 K
This is what we can observe today as the cosmic
background radiation!
Apparent Magnitude of Type
Ia Supernovae
The Accelerating Universe
Red Shift z
In fact, SN Ia measurements showed that the
universe is accelerating!
The Cosmological Constant
• Cosmic acceleration can be explained with the
“Cosmological Constant”, L (upper-case lambda)
• L is a free parameter in Einstein’s fundamental
equation of general relativity; previously believed to
be 0.
• Energy corresponding to L can account for the
missing mass/energy (E = m*c2) needed to produce
a flat space-time.
“Dark Energy”

The Contents of the Universe
Dark Energy: 70 %
Dark Matter: 26 %
"Visible" Matter: 4 %
• We only “see” about 4 % of all the mass and
energy in the Universe!
• The nature of about 96 % of our
Universe is yet mysterious and
unknown!