everything you always wanted to know about stars… material from chapters 8 and 9 in horizons by...
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Everything you always wanted to know about stars…
Material from Chapters 8 and 9 in Horizons by
Seeds
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The Spectra of StarsInner, 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 ThermometerBalmer line strength is sensitive to temperature:
Almost all hydrogen atoms in the ground state (electrons in the n = 1 orbit) => few transitions from n =
2 => weak Balmer lines
Most hydrogen atoms are ionized => weak Balmer lines
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Measuring the Temperatures of Stars
Comparing line strengths, we can measure a star’s surface temperature!
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Spectral Classification of Stars (I)
Tem
pera
ture
Different types of stars show different characteristic sets of absorption lines.
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Spectral Classification of Stars (II)0
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Oh Oh Only
Be Boy, Bad
A An Astronomers
Fine F Forget
Girl/Guy Grade Generally
Kiss Kills Known
Me Me Mnemonics
Mnemonics to remember the spectral sequence:
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Stellar spectra
OB
A
F
G
KM
Surface tem
perature
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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.
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Distances to Stars
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.
d = __ p 1
d in parsec (pc) p in arc seconds
1 pc = 3.26 LY
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The Trigonometric ParallaxExample:
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
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Intrinsic Brightness / Flux and Luminosity
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):
F ~ L__d2
Star AStar B Earth
Both stars may appear equally bright, although star A is intrinsically much brighter than star B.
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The Size (Radius) of a StarWe already know: flux increases with surface temperature (~ T4); hotter stars are brighter.
But brightness also increases with size:
A BStar B will be brighter than
star A.
Absolute brightness is proportional to radius squared, L ~ R2.
Quantitatively: L = 4 R2 T4
Surface area of the starSurface 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.
To bring some order into that zoo of different types of stars: organize them in a diagram of
Luminosity versus Temperature (or spectral type)
Lum
inos
ity
Temperature
Spectral type: O B A F G K M
Hertzsprung-Russell Diagram
orA
bsol
ute
mag
.
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The Hertzsprung Russell Diagram
Most stars are found along the main sequence
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The Hertzsprung-Russell Diagram (II)
Stars spend most of their active
life time on the Main Sequence.
Same temperature,
but much brighter than
MS stars
Must be much larger
Giant Stars
Same temp., but
fainter → Dwarfs
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Radii of Stars in the Hertzsprung-Russell Diagram
10,000 times the
sun’s radius
100 times the
sun’s radius
As large as the sun
100 times smaller than the sun
Rigel Betelgeuse
Sun
Polaris
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Luminosity Classes
Ia Bright Supergiants
Ib Supergiants
II Bright Giants
III Giants
IV Subgiants
V Main-Sequence Stars
IaIb
II
III
IV
V
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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:
• Our Sun: G2 star on the main sequence:
G2V
• Polaris: G2 star with supergiant luminosity:
G2Ib
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Binary StarsMore 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.
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The Center of Masscenter 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.
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“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…
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Masses of Stars in the
Hertzsprung-Russell Diagram
Masses in units of solar masses
Low m
asses
High masses
Mass
The higher a star’s mass, the more luminous
(brighter) it is:
High-mass stars have much shorter lives than
low-mass stars:
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
L ~ M3.5
tlife ~ M-2.5
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The Mass-Luminosity Relation
More massive stars are more
luminous.
L ~ M3.5
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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.
Giants and supergiants
are extremely rare.
Bright, hot, blue main-sequence
stars (high-mass) are very
rare.
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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 Interstellar Medium (ISM)0
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The Various Appearances of the ISM 0
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Three kinds of nebulae1) 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 emission lines. The Fox Fur Nebula NGC 2246The 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 Nebulae0
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3) Dark Nebulae
Barnard 86
Dense clouds of gas and
dust absorb the light from
the stars behind;
appear dark in front of the
brighter background;
Horsehead Nebula
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Interstellar Reddening
Visible Infrared
Barnard 68
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
Interstellar clouds make background stars appear
redder
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Interstellar Absorption LinesThe 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
Narrow absorption lines from Ca II: Too low ionization state and too narrow for the O
star in the background; multiple componentsb) Small line width (too low temperature; too low
density)
c) Multiple components (several clouds of ISM
with different radial velocities)
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Structure of the ISM
• HI clouds:
• Hot intercloud medium:
The ISM occurs in two main types of clouds:
Cold (T ~ 100 K) clouds of neutral hydrogen (HI);
moderate density (n ~ 10 – a few hundred atoms/cm3);
size: ~ 100 pc
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.
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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
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Henize 206 (infrared)
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The Contraction of a Protostar 0
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From Protostars to Stars
Ignition of H He fusion processes
Star emerges from the
enshrouding dust cocoon
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Evidence of Star FormationNebula around S Monocerotis:
Contains many massive, very young stars,
including T Tauri Stars: strongly variable; bright
in the infrared.
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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)
Herbig-Haro Object HH34
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Herbig-Haro 34 in Orion
• Jet along the axis visible as red
• Lobes at each end where jets run into surrounding gas clouds
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Motion of Herbig-Haro 34 in Orion
• Can actually see the knots in the jet move with time
• In time jets, UV photons, supernova, will disrupt the stellar nursery
Hubble Space Telescope Image
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GlobulesEvaporating gaseous globules (“EGGs”): Newly forming stars
exposed by the ionizing radiation from nearby massive stars
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The Source of Stellar EnergyStars produce energy by nuclear fusion of
hydrogen into helium.
In the sun, this happens primarily
through the proton-proton
(PP) chain
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The CNO Cycle
In stars slightly more massive than the sun, a more powerful
energy generation mechanism than
the PP chain takes over:
the CNO cycle.
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Fusion into Heavier Elements
Fusion into heavier elements than C, O:
requires very high temperatures; occurs only in very massive stars (more than 8
solar masses).
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Hydrostatic EquilibriumImagine 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
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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 ModelsThe 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.
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The Life of Main-Sequence Stars
Stars gradually exhaust their
hydrogen fuel.
In this process of aging, they are
gradually becoming brighter,
evolving off the zero-age main
sequence.
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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
SpectralType
Mass(Sun = 1)
Luminosity(Sun = 1)
Years on Main Sequence
O5 40 405,000 1 106
B0 15 13,000 11 106
A0 3.5 80 440 106
F0 1.7 6.1 3 109
G0 1.1 1.4 8 109
K0 0.8 0.46 17 109
M0 0.5 0.08 56 109
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The Deaths and End States The Deaths and End States of Starsof Stars
Material from Seeds chapters 10-11
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The End of a Star’s LifeWhen 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.
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Evolution off the Main Sequence: Expansion into a Red Giant
Hydrogen in the core completely converted into He:
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
“Hydrogen burning” (i.e. fusion of H into He)
ceases in the core.
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Expansion onto the Giant Branch
Expansion and surface cooling during
the phase of an inactive He core and
a H-burning shell
Sun will expand beyond Earth’s orbit!
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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.
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Ele
ctro
n e
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Red Giant Evolution
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 +
8Be + 4He 12C +
H-burning shell keeps dumping He onto the core.
The onset of this process is termed the
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!
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High-mass stars evolved onto the
giant branch
Low-mass stars still on the main
sequence
Turn-off point
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Estimating the Age of a Cluster
The lower on the MS the
turn-off point, the older the
cluster.
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Red DwarfsRecall:
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.
Mass
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Sunlike Stars
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
Mass
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White DwarfsDegenerate stellar remnant (C,O core)
Extremely dense:
1 teaspoon of white dwarf material: mass ≈ 16 tons!!!
white dwarfs:
Mass ~ Msun
Temp. ~ 25,000 K
Luminosity ~ 0.01 Lsun
Chunk of white dwarf material the size of a beach ball would outweigh an ocean liner!
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Low luminosity; high temperature => White dwarfs are found in
the lower center/left of the H-R diagram.
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The Chandrasekhar LimitThe 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
The Helix Nebula
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!
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The Ring Nebula in Lyra
The Formation of Planetary NebulaeTwo-stage process:
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
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Planetary NebulaeOften asymmetric, possibly due to
• Stellar rotation
• Magnetic fields
• Dust disks around the stars
The Butterfly Nebula
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A Gallery of P-N from Hubble
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Mass Transfer in Binary StarsIn 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.
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White Dwarfs in Binary SystemsBinary 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.
Matter in the accretion disk heats up to ~ 1 million K => X ray emission => “X ray binary”.
T ~ 106 K
X ray emission
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Nova Explosions
Nova Cygni 1975
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
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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.
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The Fate of our Sunand 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
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The Crab Nebula–Supernova from 1050 AD
• Can see expansion between 1973 and 2001– Kitt Peak National Observatory Images
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Supernova Remnants
The Cygnus Loop
The Veil Nebula
The Crab Nebula:
Remnant of a supernova observed
in a.d. 1054
Cassiopeia AOptical
X rays
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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.
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• Supernova 1994D in NGC 4526
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Type I and II SupernovaeCore 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
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!!!
A supernova explosion of an M > 8 Msun star blows away its outer layers.
The central core will collapse into a compact object of ~ a few Msun.
Pressure becomes so high that electrons and protons
combine to form stable neutrons throughout the
object.
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Discovery of Pulsars
=> Collapsing stellar core spins up to periods of ~ a few milliseconds.
Angular momentum conservation
=> Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars
Magnetic fields are amplified up to B ~ 109 – 1015 G.
(up to 1012 times the average magnetic field of the sun)
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The Crab Pulsar
Remnant of a supernova observed in A.D. 1054
Pulsar wind + jets
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The Crab Pulsar
Visual image X-ray image
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Light curves of the Crab Pulsar0
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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.
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Images of Pulsars and other Neutron Stars
The Vela pulsar moving through interstellar space
The Crab Nebula and
pulsar
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Neutron Stars in Binary Systems: X-ray binaries
Example: Her X-1
2 Msun (F-type) star
Neutron star
Accretion disk material heats to several million K => X-ray emission
Star eclipses neutron star and accretion disk periodically
Orbital period = 1.7 days
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Pulsar PlanetsSome 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 HolesJust 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!
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Escape VelocityVelocity needed to
escape Earth’s gravity from the surface: vesc
≈ 11.6 km/s.
vesc
Now, gravitational force decreases with distance (~ 1/d2) => Starting out high
above the surface => lower escape velocity.
vesc
vescIf you could compress
Earth to a smaller radius => higher escape velocity
from the surface.
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The Schwarzschild Radius
=> There is a limiting radius where the escape velocity
reaches the speed of light, c:
Vesc = cRs = 2GM ____ c2
Rs is called the Schwarzschild radius.
G = gravitational constant
M = mass
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Schwarzschild Radius and Event Horizon
No object can travel faster than the speed of light
We have no way of finding out what’s
happening inside the Schwarzschild radius.
=> nothing (not even light) can escape from 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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The Gravitational Field of a Black Hole
Distance from central mass
Gra
vita
tion
al
Po
ten
tial
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
An astronaut descending down towards the event horizon of
the black hole will be stretched vertically (tidal effects) and
squeezed laterally.
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General Relativity Effects Near Black Holes (II)
Time dilation
Event horizon
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.
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General Relativity Effects Near Black Holes (III)
gravitational redshift
Event horizon
All wavelengths of emissions from near the event horizon are stretched (redshifted).
Frequencies are lowered.
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Observing Black HolesNo 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!
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Gamma-Ray Bursts (GRBs)Short (~ a few s), bright bursts of gamma-rays
Later discovered with X-ray and optical afterglows lasting several hours – a few days
GRB of May 10, 1999: 1 day after the GRB 2 days after the GRB
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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