Download Stars - Mike Brotherton

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Material from Chapters 8
and 9 in Horizons by Seeds
Everything you always wanted to
know about stars…
The Spectra of Stars
Inner, dense layers of a
star produce a continuous
(black body) spectrum.
Cooler surface layers absorb light at specific frequencies.
Spectra of stars are absorption spectra.
Spectrum provides temperature, chemical composition
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The Balmer Thermometer
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Balmer line strength is sensitive to temperature:
Most hydrogen atoms are ionized =>
weak Balmer lines
Almost all hydrogen atoms in the
ground state (electrons in the n = 1
orbit) => few transitions from n = 2
=> weak Balmer lines
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Measuring the Temperatures of Stars
Comparing line strengths, we can
measure a star’s surface temperature!
Spectral Classification of Stars (I)
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Temperature
Different types of stars show different
characteristic sets of absorption lines.
Spectral Classification of Stars (II)
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Mnemonics to remember the
spectral sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
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Stellar spectra
A
F
G
K
M
Surface temperature
O
B
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We have learned how to determine a star’s
• surface temperature
• chemical composition
Now we can determine its
• distance
• luminosity
• radius
• mass
and how all the different types of stars
make up the big family of stars.
Distances to Stars
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d in parsec (pc)
p in arc seconds
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1
d= p
Trigonometric Parallax:
Star appears slightly shifted from different
positions of Earth on its orbit
The farther away the star is (larger d),
the smaller the parallax angle p.
1 pc = 3.26 LY
The Trigonometric Parallax
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Example:
Nearest star,  Centauri, has a parallax of p = 0.76 arc seconds
d = 1/p = 1.3 pc = 4.3 LY
With ground-based telescopes, we can measure
parallaxes p ≥ 0.02 arc sec
=> d ≤ 50 pc
This method does not work for stars
farther away than about 50 pc
(nearly 200 light-years).
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Intrinsic Brightness
The more distant a
light source is, the
fainter it appears.
The same amount of light
falls onto a smaller area at
distance 1 than at distance 2
=> smaller apparent
brightness.
Area increases as square of distance => apparent
brightness decreases as inverse of distance squared
Intrinsic Brightness /
Flux and Luminosity
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The flux received from the light is proportional to its
intrinsic brightness or luminosity (L) and inversely
proportional to the square of the distance (d):
L
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F~ 2
d
Star A
Star B
Earth
Both stars may appear equally bright, although
star A is intrinsically much brighter than star B.
The Size (Radius) of a Star
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We already know: flux increases with surface
temperature (~ T4); hotter stars are brighter.
But brightness also increases with size:
A
Star B will be
brighter than
star A.
B
Absolute brightness is proportional to radius squared, L ~ R2.
Quantitatively:
L = 4  R2  T4
Surface area of the star
Surface flux due to a
blackbody spectrum
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Example:
Polaris has just about the same spectral type
(and thus surface temperature) as our sun, but
it is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 = 10,000
times more than our sun’s.
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Organizing the Family of Stars:
The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures,
different luminosities, and different sizes.
Absolute mag.
or
Luminosity
To bring some order into that zoo of different
types of stars: organize them in a diagram of
Luminosity versus Temperature (or spectral type)
Hertzsprung-Russell Diagram
Spectral type: O
Temperature
B
A
F
G
K
M
The Hertzsprung Russell Diagram
Most stars are
found along the
main sequence
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The Hertzsprung-Russell Diagram (II)
Same
temperature,
but much
brighter than
MS stars
 Must be
much larger
 Giant
Stars
Radii of Stars in the
Hertzsprung-Russell Diagram
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Rigel
Betelgeuse
Polaris
Sun
100 times smaller than the sun
Luminosity
Classes
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Ia Bright Supergiants
Ia
Ib
II
Ib Supergiants
II Bright Giants
III
III Giants
IV
IV Subgiants
V
V Main-Sequence
Stars
Luminosity effects on the width of
spectral lines
Same spectral type,
but different
luminosity
Lower gravity near the surfaces of giants
 smaller pressure
 smaller effect of pressure broadening
 narrower lines
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Examples:
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• Our Sun: G2 star on the main sequence:
G2V
• Polaris: G2 star with supergiant luminosity:
G2Ib
Binary Stars
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More than 50% of all
stars in our Milky Way
are not single stars, but
belong to binaries:
Pairs or multiple
systems of stars which
orbit their common
center of mass.
If we can measure and
understand their orbital
motion, we can
estimate the stellar
masses.
The Center of Mass
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center of mass =
balance point of the
system.
Both masses equal
=> center of mass is
in the middle, rA = rB.
The more unequal the
masses are, the more
it shifts toward the
more massive star.
“Placeholder” on Masses
• We can get masses of stars by measuring
how they move in binary systems
according to Newton’s Law of Gravitation.
• I’ll save some of the details for exo-solar
planets session. Plenty of other things to
cover right now…
Masses of Stars
in the
HertzsprungRussell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~ M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
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Masses in units
of solar masses
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The Mass-Luminosity Relation
More massive
stars are more
luminous.
L ~ M3.5
Surveys of Stars
Ideal situation:
Determine properties
of all stars within a
certain volume.
Problem:
Fainter stars are
hard to observe; we
might be biased
towards the more
luminous stars.
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A Census of the Stars
Faint, red dwarfs
(low mass) are
the most
common stars.
Bright, hot, blue
main-sequence
stars (highmass) are very
rare.
Giants and
supergiants
are extremely
rare.
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The Interstellar Medium (ISM)
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The space between the stars is not
completely empty, but filled with very
dilute gas and dust, producing some of
the most beautiful objects in the sky.
We are interested in the
interstellar medium because
a) dense interstellar clouds are
the birth place of stars
b) dark clouds alter and absorb
the light from stars behind them
The Various Appearances of the ISM
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Three kinds of nebulae
1) Emission Nebulae (HII Regions)
Hot star illuminates
a gas cloud;
excites and/or
ionizes the gas
(electrons kicked
into higher energy
states);
electrons
recombining, falling
back to ground
state produce
The Fox Fur Nebula
emission lines.
NGC
2246
The
Trifid
Nebula
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2) Reflection Nebulae
Star illuminates gas and
dust cloud;
star light is reflected by
the dust;
reflection nebula appears
blue because blue light is
scattered by larger angles
than red light;
Same phenomenon makes
the day sky appear blue (if
it’s not cloudy).
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Emission and Reflection Nebulae
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3) Dark Nebulae
Dense clouds
of gas and
dust absorb
the light from
the stars
behind;
appear dark
in front of the
brighter
background;
Barnard 86
Horsehead Nebula
Interstellar Reddening
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Blue light is strongly scattered and
absorbed by interstellar clouds
Red light can more easily
penetrate the cloud, but is
still absorbed to some extent
Infrared
radiation is
hardly absorbed
at all
Barnard 68
Visible
Interstellar
clouds make
background
stars appear
Infrared
redder
Interstellar Absorption Lines
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The interstellar medium produces
absorption lines in the spectra of stars.
These can be
distinguished from stellar
absorption lines through:
a) Absorption from wrong
ionization states
b) Small line width (too
low temperature; too low
density)
c) Multiple components
(several clouds of ISM
with different radial
velocities)
Narrow absorption lines from Ca II: Too low
ionization state and too narrow for the O
star in the background; multiple components
Structure of the ISM
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The ISM occurs in two main types of clouds:
• HI clouds:
Cold (T ~ 100 K) clouds of neutral hydrogen (HI);
moderate density (n ~ 10 – a few hundred atoms/cm3);
size: ~ 100 pc
• Hot intercloud medium:
Hot (T ~ a few 1000 K), ionized hydrogen (HII);
low density (n ~ 0.1 atom/cm3);
gas can remain ionized because of very low density.
The Various Components of
the Interstellar Medium
Infrared observations reveal the
presence of cool, dusty gas.
X-ray observations reveal the
presence of hot gas.
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Shocks Triggering
Star Formation
Henize 206
(infrared)
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The Contraction of a Protostar
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From Protostars
to Stars
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Star emerges
from the
enshrouding
dust cocoon
Ignition of H
 He fusion
processes
Evidence of Star Formation
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Nebula around
S Monocerotis:
Contains many massive,
very young stars,
including T Tauri Stars:
strongly variable; bright
in the infrared.
Protostellar Disks and Jets –
Herbig-Haro Objects
Disks of matter accreted onto the protostar (“accretion
disks”) often lead to the formation of jets (directed
outflows; bipolar outflows): Herbig-Haro objects
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Protostellar Disks and Jets –
Herbig-Haro Objects (II)
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Herbig-Haro Object HH34
Herbig-Haro 34 in Orion
• Jet along the
axis visible as
red
• Lobes at each
end where jets
run into
surrounding gas
clouds
Motion of Herbig-Haro 34 in Orion
Hubble Space Telescope Image
• Can actually see the knots in the jet move with time
• In time jets, UV photons, supernova, will disrupt
the stellar nursery
Globules
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Evaporating gaseous globules
(“EGGs”): Newly forming stars
exposed by the ionizing radiation
from nearby massive stars
The Source of Stellar Energy
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Stars produce energy by nuclear fusion of
hydrogen into helium.
In the sun, this
happens
primarily
through the
proton-proton
(PP) chain
The CNO Cycle
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In stars slightly
more massive
than the sun, a
more powerful
energy generation
mechanism than
the PP chain
takes over:
the CNO
cycle.
Fusion into Heavier Elements
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Fusion into heavier elements than C, O:
requires very high
temperatures; occurs
only in very massive
stars (more than 8
solar masses).
Hydrostatic Equilibrium
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Imagine a star’s
interior composed of
individual shells
Within each shell, two
forces have to be in
equilibrium with each other:
Outward pressure
from the interior
Gravity, i.e. the
weight from all
layers above
Hydrostatic
Equilibrium (II)
Outward pressure force
must exactly balance the
weight of all layers
above everywhere in the
star.
This condition uniquely
determines the interior
structure of the star.
This is why we find stable
stars on such a narrow strip
(main sequence) in the
Hertzsprung-Russell diagram.
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Stellar Models
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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.
The Life of Main-Sequence Stars
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Stars gradually
exhaust their
hydrogen fuel.
In this process of
aging, they are
gradually
becoming brighter,
evolving off the
zero-age main
sequence.
Lifetime on Main Sequence
• L  M3.5
T  fuel / L = M/M3.5 = M-2.5
Example: M=2 MSun
L = 11.3 LSun T =1/5.7 TSun
Spectral
Type
O5
B0
A0
F0
G0
K0
M0
Mass
(Sun = 1)
40
15
3.5
1.7
1.1
0.8
0.5
Luminosity
(Sun = 1)
Years on Main
Sequence
405,000
1  106
13,000
11  106
80
440  106
6.1
3  109
1.4
8  109
0.46 17  109
0.08 56  109
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Material from Seeds chapters 10-11
The Deaths and End States
of Stars
The End of a Star’s Life
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When all the nuclear fuel in a star is used up,
gravity will win over pressure and the star will die.
High-mass stars will die first, in a gigantic
explosion, called a supernova.
Less massive stars will
die in less dramatic
events.
Evolution off the Main Sequence:
Expansion into a Red Giant
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Hydrogen in the core
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
Expansion onto the Giant Branch
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Expansion and
surface cooling during
the phase of an
inactive He core and
a H-burning shell
Sun will expand beyond Earth’s orbit!
Degenerate Matter
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Matter in the He core has no
energy source left.
 Not enough thermal
Electron energy
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.
Red Giant Evolution
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H-burning shell keeps
dumping He onto the core.
He core gets denser and
hotter until the next stage
of nuclear burning can
begin in the core:
He fusion through the
“triple-alpha process”:
4He
+ 4He  8Be + 
+ 4He  12C + 
The onset of this process
is termed the
8Be
helium flash
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Evidence for Stellar Evolution:
Star Clusters
Stars in a star cluster all have
approximately the same age!
More massive stars evolve more
quickly than less massive ones.
If you put all the stars of a star cluster
on a HR diagram, the most massive
stars (upper left) will be missing!
HR Diagram of a Star Cluster
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High-mass stars
evolved onto the
giant branch
Turn-off point
Low-mass stars
still on the main
sequence
Estimating
the Age of
a Cluster
The lower on
the MS the
turn-off point,
the older the
cluster.
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Red Dwarfs
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Recall:
Stars with less
than ~ 0.4
solar masses
are completely
convective.
 Hydrogen and helium remain well mixed
throughout the entire star.
 No phase of shell “burning” with expansion to giant.
Star not hot enough to ignite He burning.
Sunlike Stars
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Sunlike stars
(~ 0.4 – 4
solar masses)
develop a
helium core.
 Expansion to red giant during H burning shell
phase
 Ignition of He burning in the He core
 Formation of a degenerate C,O core
White Dwarfs
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Degenerate stellar remnant (C,O core)
Extremely dense:
1 teaspoon of white dwarf material: mass ≈ 16 tons!!!
Chunk of white dwarf material the size of a beach
ball would outweigh an ocean liner!
white dwarfs:
Mass ~ Msun
Temp. ~ 25,000 K
Luminosity ~ 0.01 Lsun
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Low luminosity; high temperature => White dwarfs are found in
the lower center/left of the H-R diagram.
The Chandrasekhar Limit
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!
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The Final Breaths of Sun-Like Stars:
Planetary Nebulae
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Remnants of stars with ~ 1 – a few Msun
Radii: R ~ 0.2 - 3 light years
Expanding at ~10 – 20 km/s ( Doppler shifts)
Less than 10,000 years old
Have nothing to do with planets!
The Helix Nebula
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The Formation of Planetary Nebulae
Two-stage process:
The Ring Nebula in Lyra
Slow wind from a red giant blows
away cool, outer layers of the star
Fast wind from hot, inner
layers of the star overtakes
the slow wind and excites it
=> planetary nebula
Planetary Nebulae
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Often asymmetric, possibly due to
• Stellar rotation
• Magnetic fields
• Dust disks around the stars
The Butterfly Nebula
A Gallery of P-N from Hubble
Mass Transfer in Binary Stars
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In a binary system, each star controls a finite region of space,
bounded by the Roche lobes (or Roche surfaces).
Lagrangian points = points of
stability, where matter can
remain without being pulled
toward one of the stars.
Matter can flow over from one star to another
through the inner lagrange point L1.
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Recycled Stellar
Evolution
Mass transfer in a binary
system can significantly
alter the stars’ masses and
affect their stellar evolution.
White Dwarfs in Binary Systems
Binary consisting of white dwarf +
main-sequence or red giant star
=> WD accretes matter from the
companion
Angular momentum
conservation => accreted
matter forms a disk, called
accretion disk.
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X ray
emission
T ~ 106 K
Matter in the
accretion disk heats
up to ~ 1 million K
=> X ray emission
=> “X ray binary”.
Nova Explosions
Nova Cygni 1975
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Hydrogen accreted
through the accretion
disk accumulates on the
surface of the white
dwarf
 Very hot, dense layer
of non-fusing hydrogen
on the white dwarf
surface
 Explosive onset of H
fusion
 Nova explosion
T Pyxidis
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Recurrent
Novae
In many
cases, the
mass transfer
cycle
resumes after
a nova
explosion.
 Cycle of
repeating
explosions
every few
years –
decades.
The Fate of our Sun
and the End of Earth
• Sun will expand to a red
giant in ~ 5 billion years
• Expands to ~ Earth’s orbit
• Earth will then be
incinerated!
• Sun may form a planetary
nebula (but uncertain)
• Sun’s C,O core will
become a white dwarf
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The Deaths of Massive Stars: Supernovae
Final stages of fusion
in high-mass stars (>
8 Msun), leading to the
formation of an iron
core, happen
extremely rapidly: Si
burning lasts only for
~ 1 day.
Iron core ultimately collapses,
triggering an explosion that
destroys the star:
Supernova
The Crab Nebula–Supernova from 1050 AD
• Can see expansion between 1973 and 2001
–
Kitt Peak National Observatory Images
Supernova Remnants
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X rays
The Crab Nebula:
Remnant of a
supernova observed
in a.d. 1054
Optical
The Cygnus Loop
The VeilANebula
Cassiopeia
The Famous Supernova of 1987:
Supernova 1987A
Before
At maximum
Unusual type II supernova in the Large
Magellanic Cloud in Feb. 1987
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Observations of Supernovae
Supernovae can easily be seen in distant galaxies.
• Supernova 1994D in NGC 4526
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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
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Neutron Stars
A supernova
explosion of an
M > 8 Msun star
blows away its
outer layers.
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The central core Pressure becomes so high
will collapse into that electrons and protons
combine to form stable
a compact object
neutrons throughout the
of ~ a few Msun.
object.
Typical size: R ~ 10 km
Mass: M ~ 1.4 – 3 Msun
Density:  ~ 1014 g/cm3
 Piece of neutron
star matter of the
size of a sugar cube
has a mass of ~ 100
million tons!!!
Discovery of Pulsars
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Angular momentum conservation
=> Collapsing stellar core spins up
to periods of ~ a few milliseconds.
Magnetic fields are amplified
up to B ~ 109 – 1015 G.
(up to 1012 times the average
magnetic field of the sun)
=> Rapidly pulsed (optical and radio) emission from some
objects interpreted as spin period of neutron stars
The Crab Pulsar
Pulsar wind + jets
Remnant of a supernova observed in A.D. 1054
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The Crab Pulsar
Visual image
X-ray image
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Light curves of the Crab Pulsar
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The Lighthouse Model of Pulsars
A pulsar’s
magnetic field
has a dipole
structure, just
like Earth.
Radiation
is emitted
mostly
along the
magnetic
poles.
Images of Pulsars and
other Neutron Stars
The Vela pulsar moving
through interstellar space
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The Crab
Nebula and
pulsar
Neutron Stars in Binary Systems:
X-ray binaries
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Example: Her X-1
2 Msun (F-type) star
Neutron star
Orbital period =
1.7 days
Accretion disk material heats to several million K
=> X-ray emission
Star eclipses neutron
star and accretion
disk periodically
Pulsar Planets
Some pulsars have
planets orbiting
around them.
Just like in binary pulsars,
this can be discovered
through variations of the
pulsar period.
As the planets orbit
around the pulsar, they
cause it to wobble
around, resulting in slight
changes of the observed
pulsar period.
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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.
If you could compress
Earth to a smaller radius
=> higher escape velocity
from the surface.
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vesc
vesc
vesc
The Schwarzschild Radius
=> There is a limiting radius
where the escape velocity
reaches the speed of light, c:
2GM
Rs = ____
c2
G = gravitational constant
M = mass
Rs is called the
Schwarzschild radius.
Vesc = c
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Schwarzschild Radius
and Event Horizon
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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”
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“Black Holes Have No Hair”
Matter forming a black hole is losing
almost all of its properties.
black holes are completely
determined by 3 quantities:
mass
angular momentum
(electric charge)
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Gravitational
Potential
The Gravitational Field
of a Black Hole
Distance from
central mass
The gravitational potential
(and gravitational attraction
force) at the Schwarzschild
radius of a black hole
becomes infinite.
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General Relativity Effects
Near Black Holes
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An astronaut descending down
towards the event horizon of
the black hole will be stretched
vertically (tidal effects) and
squeezed laterally.
General Relativity Effects
Near Black Holes (II)
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Time dilation
Clocks starting at
12:00 at each point.
After 3 hours (for an
observer far away
from the black hole):
Clocks closer to the black
hole run more slowly.
Time dilation
becomes infinite at
the event horizon.
Event horizon
General Relativity Effects
Near Black Holes (III)
gravitational redshift
All wavelengths of emissions
from near the event horizon
are stretched (redshifted).
 Frequencies are lowered.
Event horizon
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Observing Black Holes
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No light can escape a black hole
=> Black holes can not be observed directly.
If an invisible compact
object is part of a binary,
we can estimate its
mass from the orbital
period and radial
velocity.
Mass > 3 Msun
=> Black hole!
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Compact object with
> 3 Msun must be a
black hole!
Gamma-Ray Bursts (GRBs)
Short (~ a few s), bright bursts of gamma-rays
GRB of May 10, 1999:
1 day after the GRB
2 days after the GRB
Later discovered with X-ray and optical
afterglows lasting several hours – a few days
Many have now been associated with host
galaxies at large (cosmological) distances.
Probably related to the deaths of very
massive (> 25 Msun) stars.
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