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

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…

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

The Various Appearances of the ISM 0

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

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)

The Contraction of a Protostar 0

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

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

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

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

ne

rgy

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

HR Diagram of a Star Cluster 0

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

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.

T Pyxidis0

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

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

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

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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