A. Light and Atoms

B. Observing Stars

C. Structure of Stars

D. Evolution of Stars

A. LIGHT and ATOMS

1. Light

How do we see?

An object must give off light, and our eye must receive the light, in order to see the object.

That light can be emitted by the object (e.g., a lightbulb or the Sun)

Or, light from another source can be reflected off the object (a pen reflecting a lightbulb or the Moon reflecting sunlight)

If there is no light, can't see an object

Light is an Electromagnetic Wave.

changing electric and magnetic force.

wavelength (lambda) = distance between waves;

period (P) = time between waves;

frequency (f) = number of waves per unit time

Demo: weighted rope

Analogy: Buses

[BE: 1747 (wave)]

Mechanical Universe, Program 40: chapt 4 - light waves; 10 - Newton; 11 - Huygens; 12-15 - waves; 17 - lines of force; 19 - oscillating charge; 40 - telescope

Light is a Stream of Photons

Higher Energy Photons = Shorter Wavelength Light

e_photon = hf = hc/lambda

Spectrum of Light

   x-rays      (< 20 nm)         (high energy, short wavelength)
   ultraviolet (20 nm - 0.4 microm)
                  blue      \
                  green     |
   visible        yellow    }    lambda = 0.4-0.7 micrometers
                  orange    |
                  red       /
   infrared    (1 microm - 1 mm)
   microwave   (1 mm - 1 cm)
   radio       (> 1 cm)           (low energy, long wavelength)

[Examples: AST disk: radio 470, MW 471, visible 473, UV 474, XR 475]
      

2. Telescopes and Detectors

Most astronomical information comes from light we analyze.

a. Telescope

Like lens of eye

Functions

i. Collect Photons (primary) L = F x Area

ii. Resolve close objects Theta_min = lambda/diameter

iii. Magnify objects

[Light gathering: AST disk 539]

Location: mountain tops - air absorption, seeing, lights

[BE: 1745 (atmos. transmission)]

Demo: spot aimed at board; rays and mirrors on black board; laser beam in smoke box.

[Historical: AST disk: Gallileo 7028; Herschel 7043,44; Ross 7046]

[Schematic: AST disk: examples 563-576; refractor 568-570; reflector 571-576; prime 7061; cassegrain 616, 7310 ...]

[Photographs of telescopes: AST disk: 581-84, 546, 618]

[AST disk:

Lick: 7310 (construction diag), 11 (telescope), 16-22

Mauna Kea: 7775-83 (diagram and details)

Palomar: 8663-69, telescope 8693, prime 8700-06, coude 8707-10

Mt. Wilson: 7805-11, construction 7861-7903, mule rd 7849

VLA: 8489,96 control, 8480 size, 8503 see through]

Keck video

b. Detectors

Functions

i. collect photons over a long time (integrate)

ii. convert data to permanent medium

iii. Wider range of wavelength sensitivity

i. Photograph

(about 2% efficient, small dynamic range 10², non-linear-so hard to calibrate)

ii. Electronic detectors (light meter, CCD)

more efficient 80%, linear, large dynamic range 10⁵,

[AST disk: phot exposure 540-544, Photometer, 600, 603, CCD 622-23]

[AST disk: 577-607, 608-618, 619-625]

c. Spectrograph

Separates light by energy (wavelength, color)

[AST disk: spectrograph diag 608, stellar spectra plate 618, H spectrum 6700, solar spectrum 6739]

3. Atoms

Matter is made of atoms.

Atom - Different atom for each element.

Nucleus orbited by Electrons.

Nucleus - Composed of protons (+ charge) and neutrons (0 charge).

Contains most of atoms mass.

Electrons (- charge) - Orbit nucleus, attracted by electric force.

Electric Force -

Produced by charge,

Opposite charges attract, like charges repel.

Decreases with distance

Element determined by number of protons in nucleus

(H has 1 proton, He has 2 protons, C has 6 protons).

[BE: 1764 (He atom)]

Crude Model - atom = solar system

If person = proton or neutron, electron = cotton candy orbiting 100 km (60 mi) away (Flint).

If nucleus = raisin, electron=400 m away, next atom 2.5-25 mi away.

If sun = 3 ft diam ball, Earth=raising 100 m away, nearest star=distance to Sun

Electrons can only orbit nucleus at certain allowed distances.

Electrons in smaller orbits have lower energy than electrons in larger orbits. (Takes energy to move electron from small to large orbit against pull of electric force.)

Neutral Atoms - number of electrons = number of protons.

Usual state at low temperature.

Ions - some or all of electrons have been knocked out of atom.

Usual state at high temperature.

[BE: 1765 (He ion)]

States of Matter

Gas - atoms move around freely. Interact (exert electric force on each other) only during collisions.

Liquid - atoms move around, but not freely. Always exerting electric force on each other.

Solid - atoms held in place by electric force. Can only vibrate about fixed position.

Temperature measures motion of atoms (and molecules, nuclei, electrons).

hotter = move faster

kT = 1/2 mv²

4. Emission and Absorption of Light

Photons are emitted and absorbed when electrons are accelerated and change their energy.

i. Thermal (Blackbody) Radiation

Hotter -> Bluer (higher energy photons)

move faster, more violent collisions

e_photon = kT, lambda_peak = 3x10^-3 m/T(K)

Hotter -> Brighter (more photons)

move faster, more collisions

F = sigma T⁴

Bigger -> Brighter (more photons)

more atoms, electrons

Luminosity = Flux x Area

Demo: bulb, reostat (slides)

Planck spectrum, AST disk 498-499]

Planck spectrum, BE: 1766-1768]

ii. Emission and Absorption by gas atoms

A photon (electromagnetic radiation) is emitted or absorbed when an electron changes its energy. [An electron can also change energy in a collision.]

An electron orbiting the nucleus of an atom is continually accelerated, so should radiate, but doesn't.

Origin of quantum mechanics

Only certain orbits (energy levels) are allowed an electron in an atom.

Energy levels of atoms (elevator analogy).

Electron energy decreases (jumps to smaller, lower energy, orbit) -> emit a photon

Absorb a photon -> electron energy increases (jumps to larger, higher energy, orbit)

Photon Energy = Change in Electron's energy

To be absorbed, photon must have just the right amount of energy to make the electron jump to a higher energy, larger orbit.

Demo: salts in flame, discharge tubes

[AST disk: 500]

[Atomic levels & transitions: Ring of Truth, Atoms: 4507-5020]

[Mech. Univ. prog. 49: Atoms, chapt 20, orbiting e^- radiates, spirals in; 22-Planck; 24-Bohr model, emission & absorption; 26-sizes of orbits & energy; 27-frequencies of emission and absorption]

AST disk: Hg, Na vapor lamps graph of intensity 559-576]

Continuous, Emission and Absorption spectra

B. Observations - Measuring Stars

We can observe two important pieces of information about a star

1. Luminosity (L)

Observe (measure) Apparent Brightness (B)
[Example: print from photographic plate]

Observe (measure) Distance - parallax

            
distance   = halfway across Earth's orbit /angle of parallactic shift
            
d [parsec] = 1 / p [seconds of arc]

[BE: 1739-40] or Fig 5-24

[Shut one eye, then the other: further a pen away from eyes, the further it seems to move against the background.]

European satellite Hipparcos measured parallax for 120,000 stars.

      
Luminosity = rate of energy loss = energy radiated per second
          (how big a light bulb)
      
Luminosity = Brightness x Area the energy is spread over

      
Luminosity = Brightness x Area of a sphere of radius the distance
                                                  from the star to us

           L     =     B      x 4 x pi x d2 
           B     =     L      / 4pi d2 

This is the Inverse Square Law

[BE: inverse square law 1746] or Fig. 15-3 in book

Demo: lamps through squares

Demo: two balloons, one twice the radius of the other

2. Surface Temperature

Two methods: measure color or look at spectrum

Color

lambda_peak[A] = 3x10⁺⁷[KxA]/ T[K]

Angstrom [A]= 10^-10 m

Fig. 13-8

Hydrogen Balmer Spectrum -> temperature

Balmer lines formed when electron in 2nd energy level absorbs a photon, or when an electron in a higher energy level jumps down to the 2nd level and emits a photon.

[See Fig. 13-19]

Only gas at an intermediate temperature (=10⁴ K) has a large fraction of atoms excited with electrons in the 2nd energy level.

[See Figure 13-8]

Colder gas: electrons in ground state,

Hotter gas: electrons knocked out of atom (ionized).

[AST disk: 506-511] [Figure 14-2]

[BE: H energy levels 1763; spectrum + plot 1829; solar spectrum 1828; spectral types 1867 (all), 1825 (A0-F0), 1826 (G0-K5); vega+arcturus 1837]

[BE: types of spectra 1757-58, spectral glass plate 1824]

Video: Ring of Truth, Doubt: 3620-4157; Cecelia Payne: interpreting spectra

Hertzsprung-Russell (HR) Diagram

Whenever have data - look for correlations

Usually a scatterplot, e.g. Apparent magnitude and spectral type [Fig. 15-4]

Plot Luminosity vs. Surface Temperature

The HRD for the closest stars doesn't look the same as for the brightest stars [Fig. 15-7]

In our neighborhood of the Galaxy:

90% of stars Main Sequence

10% of stars White Dwarfs

1% of stars Red Giants and Supergiants

Two stars with same surface temperature -> same energy flow per square inch. Star with larger luminosity has larger radius, bigger size.

L = 4 pi R² sigma T⁴_surface

[BE: HR diag with star sizes 1769]

3. Mass & Relative Size using Binary Stars

The spectrum of binary stars is doubled and shifts due to Doppler Effect

[BE: binary star spectrum 1853]

Measure orbital period and velocity (Doppler Shift) of eclipsing binaries.

Delta lambda / lambda = v/c

Demo: doppler ball, video of a ripple tank

[BE: doppler effect 1748-1751; 1752-1755]

Use Kepler's third law to determine mass

M₁ + M₂ = D³[AU]/P²[yr] = V³ P/(4 pi G)

Eclipsing Binaries periodically change luminosity

[BE: binary stars eclipse diagram 1909-1918]

Get relative sizes

Mass - Luminosity Relation

Luminosity vs. Mass

Large mass stars have high luminosity

90% of stars follow mass-luminosity relation, must be main sequence stars. Hence mass determines location of star on main sequence.

C. Stellar Structure

The Sun

What can we learn? Questions.

a. See Light, heats the Earth -> Sun emits energy. What is the source of the energy?

b. Spectrum, Color -> surface temperature =6000 K. What makes sun hot?

c. Kepler's third law -> mass of sun = 2x10³⁰ kg

M(sun) + M(planet =0) = (4 pi²/G) D³/P²

d. Size of sun (R = 7x10⁸ m)

e. Average mass density = mass/volume = 1.4 x density of water

f. Spectrum -> composition:

number of atoms 90% H, 8% He; by mass 75% H, 23% He, 2% everything else

g. Sun hasn't changed. Is very stable. What keeps sun stable?

h. Atmosphere of Sun is dynamic. What causes changes?

1. Forces: Gravity and Pressure

a. Gravity pulls in (keeps sun from dispersing into space, holds star together)

b. Pressure pushes out (keeps sun from collapsing)

Pressure is force exerted by colliding particles (atoms, ions, electrons, nuclei)

Higher Density -> particles closer -> more collisions -> higher pressure

Higher Temperature -> particles move faster -> more and harder collisions -> higher pressure

Perfect Gas Law: P=nkT, (n=N/volume = number density of particles)

[movies: computer simulation of pressure; video: Mechanical Universe, ]

c. Equilibrium: Pressure balances Gravity

Pressure balances weight of overlying material:

Pressure = weight of material above.

Pressure increases toward center

PxA = P R² = F_gravity =G M²_Sun/R²

2. Energy: Generation and Loss

a. Energy Generation

Source of Energy - Thermonuclear Fusion Reactions

4 ¹H -> ⁴He + energy

Nuclei are fused together by the Nuclear force

Must do work to pull nuclei apart against pull of nuclear force

-> nucleons (protons and neutrons) have more energy when apart,

less when fused together -> release nuclear potential energy when fuse.

Nuclear force has a very short range, = size of nucleus.

To react, nuclei must collide

To Collide, nuclei must move fast enough to overcome their repulsive electric force (due to positively charged protons in each nucleus)

Thus nuclear fusion can only occur when nuclei move very fast, at high temperatures

Higher Temperature -> more nuclei collide -> higher rate of nuclear fusion energy generation

b. Energy Loss

Heat is produced in core, but lost (radiated away to space) from surface.

Heat is transported from hot core to cool surface by

i. Radiation - random walk of photons

activity: balloons

ii. Convection - circulation: gas is heated, hot gas rises, cools, cool gas sinks

Rate of energy loss (Luminosity) depends on how good an insulator the star is.

The easier photons can travel through the gas, the poorer the insulation -> the greater the luminosity.

c. Equilibrium: Rate of energy generation = rate of energy loss

3. Structure of Stars is determined by two balance conditions:

a. Balance between pressure and gravity

[BE: balance 1922]

b. Balance between energy generation and energy loss

Feedback interaction between temperature, pressure, energy generation, expansion, contraction and gravity keeps stars stable-thermostat.

[BE: sun structure diag 1921]

4. Tests

a. solar neutrino experiment

b. helio-seismology

demo: driven spring resonances

fig: dc²/c²

c. mass-luminosity relation

D. Stellar Evolution

Evolution of Stars is driven by two processes:

i. Loss of Energy to space

ii. Fusion of nuclei in core reduces number of particles

How star evolves is determined by upsetting two balance conditions.

1. Birth

Stars

Compression of interstellar cloud of H and He gas and dust by shocks

Makes gravity stronger than pressure.

Cloud contracts, gets denser and hotter.

Eventually core gets hot enough for nuclear fusion reactions to occur.

[BE: interstellar grain diag 2540]

[BE: Eagle 2388; horsehead 2372-73; Bok globules 2476, 78; Orion 2274, 2287,2289, Pleiades 1934-1937]

Planetary Systems

Form at the same time as star

Disk of material left over from star's formation

[Activity: Percent of proto-planetary systems on HST picture]

2. Maturity: H Fusion in Core - Main Sequence

4 ¹H -> ⁴He + energy

More massive stars have higher luminosity (Mass - Luminosity Relation).

More mass -> more gravity,

need higher pressure, requires higher temperature

-> makes nuclear fusion reactions go faster

-> more photons to get to surface

-> makes star expand -> reduces insulation

-> larger luminosity.

More massive stars use up H faster, have shorter lives

Main stage of a stars nuclear fusing life (80% for the Sun)->stable

3. Old Age: All stars become Red Giants

a. The beginning and ends of stars is a recent understanding

The Hertzsprung-Russell Diagram was known in 1913 to be the key to stellar evolution

But how do stars move on the HRD as they evolve?

First idea was that red giants-> blue giants->white dwarfs-> red dwarfs

Current idea is that a massive blue dwarf-> blue giant-> red giant-> neutron star or black hole or complete disruption

a less massive dwarf (like Sun)-> red giant-> white dwarf

b. H exhaustion in core

He core contracts -> gets hotter -> heats surrounding shell

-> H shell fusion -> envelope expands, cools,

->luminosity increases.

Example: Betelgeuse

c. He core fusion

In stars of mass greater than about 0.4M_Sun the contracting core eventually gets hot enough to fuse He nuclei:

3 ⁴He -> ¹²C + energy,

4 ⁴He -> ¹⁶O + energy.

[He fusion requires higher temperature than H fusion because He nuclei have 2 protons.

Greater charge produces a stronger electric repulsion, so nuclei must move faster to overcome the repulsion and collide.]

d. Nucleosynthesis of heavier nuclei

More massive stars have a larger gravity -> higher maximum possible central temperature.

Hence can fuse more massive nuclei with more protons.

Most massive nucleus that can be fused with release of energy is iron.

To make more massive nuclei requires input of energy. Occurs only in supernova explosions.

Life history of a star is Loss of Energy to space and Gravitational Contraction of core. Contraction is temporarily halted by stages of nuclear fusion energy generation in core.

Tests

HR diagram of star clusters

activity: cluster HR diags

[BE: open clusters: 1955, 1960, Hyades 1956]

[BE: globular clusters: 1963, 1968, 1969]

4. Death of Stars

When all possible nuclear fuels are used up, the core of a star contracts. All stars end their lives as either dense, compact objects, or are completely disrupted.

a. Small Mass Stars -> White Dwarfs

Supported by pressure of degenerate electrons:

Contracts until electrons are squeezed sufficiently (wavelength decreases) for their energy to increase -> move faster -> collide harder -> produce high enough pressure to halt contraction.

         Delta(x) Delta(mv) = h   Uncertainty Principle
         lambda = h/mv            Particle Wavelength
                  

Larger mass

-> larger gravity, need higher pressure

-> electrons must move faster

-> must be squeezed more

-> smaller size white dwarf.

Maximum Mass of White Dwarf = 1.4 M_Sun.

Stars of mass 1-8 M_Sun expel enough mass as wind and planetary nebula during Red Giant stage to end up below the mass limit.

[BE: ring nebula 1991, 1996-7; other 2012]

HST image of NGC 6543, formerly a star of same mass of Sun

Note the white dwarf revealed in the center.

White Dwarfs cool off slowly at fixed size = size of Earth.

[Model: an insulated coffee cup]

This HST picture of the Globular Cluster M4 shows the many hot but extremely dim white dwarfs.

b. Large Mass Stars (>8 M_Sun) explode as Supernova

Triggered by Carbon detonation or Iron core collapse.

Energy comes from gravitational potential energy.

E = PE_gravity = GM(star)²/R(neutron star) = 10⁴⁶ Joules

(For comparison L_Sun x age = 4x10²⁶ J/s x 5x10⁹ yr x 3x10⁷ s/yr = 6x10⁴³ J)

E = NkT = (M(star)/m_H)kT, so T = 10¹² K

SN: 1006, 1054 (Crab), 1572 (Tycho), 1604 (Kepler)

[BE: Crab 2091, 95-6; Tycho 2145; Kepler 2134; CasA 2067-69, other galaxy 2162]

HST Image of the Cygnus Loop, remnant of a Supernova which blew over 15,000 years ago.

SN 1987A: comparison of theory and observation

neutrino burst -> core collapse (extremely hot);

burst lasted several seconds -> diffused out;

energy = 10⁸ L_galaxy;

mass of collapsed core = 1.4 M_Sun

progenitor star blue (not red) supergiant -> smaller, shock reached surface faster (2 hours between neutrino burst and optical light)

[BE: 1987A 2042-3, 2045, 2052-53, 2055, rings 2056]

[BE: evol seq blue, RG, SN, 1900-03]

This HST picture of SN1987A shows the shocked shells from the former red giant before it became a blue giant and supernovaed. No remnant at all is evident.

This supernova in the distant Whirlpool Galaxy looks as bright as a Globular Cluster

i. Neutron Stars (small remnant)

Supported by pressure of degenerate neutrons.

About size of Lansing.

Single star 8-22 M_Sun (?)

Gas from binary companion falling onto neutron star gets very hot and emits x-rays.

kT = G M_NS m_H/R_NS = 10¹² K

Rotating neutron stars beam radio waves (sometimes even visible light and x-rays) like an airport beacon or lighthouse - Pulsars

Maximum mass = 3 M_Sun

[BE: Crab 2098, accretion 1884, 1889,1903]

ii. Black Holes (large remnant)

Single star >22 M_Sun (?)

Matter contracts to singularity. Gravity so strong, not even light can escape.

Star appears to get dimmer and redder.

Event Horizon

surface where escape velocity = speed of light.

Outside Event Horizon can escape, inside can not.

V(escape) = c = (2GM/R)^1/2

R = 2GM/c²

Black Hole only effects surroundings by long range forces - gravity and electric.

Hence, can only determine mass, charge and rotation of a black hole.

Black hole has no hair.

Gravitational radiation

accelerating mass -> waves in gravitational force (shape of space-time)

-> Black Holes settle down to stationary state

Photons escaping from vicinity of a black hole lose energy, are redshifted.

To distant observer, time appears to slow down near Event Horizon

Gas falling into a black hole gets very hot and emits x-rays, similar to neutron star.

[BE: accretion disks: 2195, 2199-2205, 2206-2211, 2212-2226]

Can only distinguish black hole from neutron star by its mass.

If mass > neutron star mass limit, must be a black hole.

Mini black holes can evaporate.

Tidal forces pull apart particle-antiparticle pairs created by quantum fluctuations outside event horizon.

Pull one into black hole, other can escape.

iii. Complete Disruption

It's possible that the supernovae explosion destroys the star altogether.

Not clear when this happens, but it might be a more common end for massive binary star systems.

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The following are examples of midterm questions we might ask about topics under D.4 Stellar Evolution: Death of Stars, since this topic is not included in your homework.

1. Following the exhaustion of hydrogen in their cores, all stars become
(a) white dwarfs.
(b) red giants.
(c) supernovas.
(d) neutron stars.
(e) black holes.

2. The event horizon of a black hole is the surface where
(a) no events occur.
(b) if you are inside you can't escape.
(c) the force of gravity becomes infinite.
(d) the density becomes infinite.
(e) everything is sucked in.

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Links to other Stellar Structure and Evolution Resources

George Mason University Astronomy Course

Iowa State University Index of Astronomy Resources

The Sun: a Pictorial Introduction

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This page will be updated continually throughout the course. Updated: 1997.04.07 (Monday) 17:15:36 EDT
This page has been accessed times.

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Visions of the Universe

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Beth Hufnagel's home page, email: bhufnage4@pilot.msu.edu

Bob Stein's home page, email: steinr@pilot.msu.edu