I. Properties

A. Distance from Earth: 93 million miles

Light takes ~ 8 minutes to travel this distance

B. Diameter: 860,000 miles (~ 100 Earths across);

Volume: ~ one million Earths

C. Composition (by mass): ~ Jovian planets
 

Hydrogen (73.4 %)

Helium (25.0 %)

Other elements (1.6 %)
 

Period at equator ~ 25 days; at poles ~ 34 days

Implications for sunís magnetic field; solar activity

(below)

II. Exterior Structure

A. Photosphere (visible surface): ~ opaque gases;

Temperature ~ 5,800 °K
Granulation -- bubbles of rising gas (like boiling liquid)

Temperature ~ 15,000 °K

Emission-line spectrum

C. Corona (outer atmosphere) -- seen during solar eclipses

Extends outward by several solar radii

Temperature > 10⁶ °K (extremely hot, but rarified)

Shape -- modulated by sunís magnetic cycle; round at maximum; elliptical at minimum

Source of solar wind particles (escape from coronal holes)

III. Interior Structure
A. Core -- where energy is produced by fusion

Temperature ~ 15 million °K

Density ~ 150 g/cm³

B. Radiative Zone -- energy escapes by ërandom walkí process (absorption, re-emission of photons), due to high density)

Takes ~ 10⁵ years to be accomplished!

C. Convective Zone (large, small-scale motions permitted (by lower densities)

Where sunís magnetic field is produced (dynamo model)

Complex motions give rise to surface features; growth, decay of sunís magnetic cycle

Two parts: central umbra, lighter penumbra

Appear darker, because temperature ~ 1,500 °K cooler than surroundings; often come in pairs

Concentrations of magnetic field below surface --

blocks convection (and prevents heat) from rising

11-Year Sunspot Cycle -- period of annual mean sunspot number. Relatively steady for 300 years; with

longer-term modulations superimposed

Prior to 1700 -- appears to have been interrupted

(so-called Maunder Minimum); coincident with

"Little Ice Age" in Europe

Latitude drift of sunspots during 11-year cycle:

1. Spots first appear at mid-solar latitudes (start of new cycle) in both N, S hemispheres

2. Spots appear closer to solar equator by end of cycle, disappear

ëButterfly Diagramí -- plot of spot latitude vs. time

V. Magnetic Field Reversals

Complete cycle is 22 years (two sunspot cycles)!

1. In a given cycle, polarities of leading spots are opposite in N, S hemispheres

2. In the following cycle, polarities of leading spots are reversed in both hemispheres [diagram]

How explain two phenomena?

Sunís differential rotation causes the following:

Magnetic field gradually winds up (first sunspot cycle); causes latitude drift in both hemispheres; relaxes.

Field reverses (second sunspot cycle); gradually winds up (causing renewed latitude drift), and relaxes. Repeats.

* * * * * * * *

B. Prominences

Loops of gas, follow magnetic field lines from leading to following spot of pair (~ horseshoe magnet)

Can extend millions of miles into space (eruptive)

C. Solar Flares: tremendous explosions on surface;

Release X-rays, charged particles; travel to Earth; react with our magnetosphere; produce auroral displays

VI. Maunder Minimum

Period from ~ 1645 to ~ 1715, when sunspots ~ disappeared (interruption of 11-year cycle)

Other evidence in support of claim:

A. Numbers of reported aurorae declined sharply

B. Eclipse observations made no mention of sunís whitish corona (anomalously reduced?)

C. Sunís rotation rate apparently sped up, just before Maunder Minimum (cause or effect?)

D. Carbon-14 record, preserved in tree-rings, shows anomalously high abundance; why?

I. Failure of Earlier Theories

Energy output of Sun ~ 4 x 10²⁶ Watts (Joules/second)

What is the source of this phenomenal energy?

For how long has the Sun been shining this way?

Major unanswered questions of astrophysics, after laws of thermodynamics worked out in 19th century (conservation of energy)

1. If the Sunís energy were produced by chemical combustion, it could not have lasted more than a few thousand years

2. If the Sunís energy were produced by gravitational contraction, it could not be any more than ~ 100 million years old (Kelvinís calculations)

"Energy = mass times the speed of light, squared"

Accounts for the enormous release of energy by nuclear processes (where mass is changed into energy)

Difference in mass, between the initial and final products, multiplied by c2, gives the net energy of the reaction (below)

 
Three stages (occur simultaneously in Sunís core):

1. ¹H + ¹H = ²H + e+ + n

2. ¹H + ²H = ³He + g

3. ³He + ³He = ⁴He + 2 ¹H

where ¹H = proton; ²H = deuterium; ³He = Helium;

⁴He = Helium; e⁺ = positron, n = neutrino; g = gamma

But net reaction: 4H = 1 He + Energy

4 Hydrogens are converted into 1 Helium + Energy

4.03130 mass units = 4.00268 mass units + ? Energy

? = 0.02862 mass units ^. c²

Sun converts ~ 600 million tons of Hydrogen into Helium every second;

Yet, has enough mass to last for billions of years!

Proton-Proton Cycle : chief energy source for all young (main-sequence) stars

* * * * * * * *

Sun -- as a star -- remains stable, because of internal balance between pressure and gravity (hydrostatic equilibrium)

Balance is maintained, until star runs out of fuel in its core

III. Solar Neutrino Problem

Neutrinos (n) -- keys to understanding interior of sun/stars

Why? -- unlike photons, which take ~ 10⁵ years to emerge from core,

Neutrinos travel straight out in ~ 2 seconds (very low interactions w/ ordinary matter)

Efforts to measure the sunís neutrino flux at the Earth -- should provide a confirmation of theories of fusion process

Since 1970, experiment by Raymond Davis, Jr., has detected only ~ one-third expected number of neutrinos

How can this discrepancy be explained?

If neutrinos have mass, then ~ two-thirds of neutrinos produced by sun are changed into other kinds, not detectable by Davisís experiment (neutrino oscillation model)

Implications: If true -- new physics, beyond ëstandard modelí)

(a) Newer detectors being built, to measure flux of other neutrinos

(b) Major experiments planned, to study whether neutrinos oscillate (between emission and detection)

I. Introduction

To understand more about the stars, it will be necessary to compare their properties according to one or more standardized scales.

The steps by which this can be accomplished forms the subject of this unit. Why?

ANALOGY: Suppose we could measure height, weight of all the individuals in this room, and plot them on a graph. How would the results appear?

Our goal with the stars will be to construct similar bodies of data, (involving luminosity, temperature), and to plot them on an important graph.

What makes this more difficult, however, is that we canít just assemble all the stars together , at one place and time (like individuals in this room).

TRUER ANALOGY: take same population of individuals, but

(1) all are randomly scattered over area the size of a football field; and (2) you must try and determine heights, weights of all subjects from some other point on the field. Can you see the problems involved?

Thus, you need to establish where you stand, in relation to each person, before you can make any firm deductions.

This exercise employs the chains of reasoning used by astronomers to determine fundamental properties of stars.

II. Apparent Magnitudes

A numerical scale, for comparing brightnesses of stars, as seen from Earth;

Does not take starís actual distance, or luminosity, into account!

Traceable to ancient Greeks (Hipparchus); unaided eye:
 

Brightest stars -- magnitude = 1 (first-magnitude)

Faintest stars -- magnitude = 6 (sixth magnitude)

But what human eye sees as differences in brightness, actually correspond to brightness ratios, between stars

We define the magnitude system as follows:

Difference of 1 magnitude = brightness ratio of ~ 2.512

Difference of 2 magnitudes = brightness ratio of ~ (2.512)²
 

.

.

.

Difference of 5 magnitudes = brightness ratio of ~ (2.512)⁵
 

= brightness ratio of 100 times

All objects in sky can be assigned an apparent magnitude

(analogous to number line); but lower numbers = brighter objects; higher numbers = fainter objects

III. Stellar Distances

Only one way to measure this quantity directly;

Geometric (Trigonometric) Parallax -- make observations of nearby star from opposite sides of Earthís orbit (6 months apart) [actually gives twice the parallax -- diagram 1]

Measure apparent displacement of starís images, with respect to more distant (background) stars

How define parallax? [diagram 2]

A star has a distance of one parsec (1 pc.) when the angle measured at the star, formed by the Earth-Sun distance

(1 A.U.), is one arc-second (1 ") wide.

Note : 1° = 1/360 circle; 1 ë = 1/60 °; 1 " = 1/60 ë = 1/3600 °;

1 parsec ~ 3.26 light years

Relationship of distance and parallax?

Distance (pc.) =                     1
                                parallax (arc-seconds)

All stellar parallaxes are less than 1 arc-second!

Explains why even Tycho Brahe failed to measure stellar parallax (more than 60 times smaller than naked-eye limit!

Ground-based telescopes -- parallaxes only to ~ .05 ";

Hipparcos satellite -- accuracy of < .01 " (few hundred pc.)

IV. Absolute Magnitudes

Knowing a starís Apparent Magnitude (as seen from Earth),

and its Distance (in pcs.), measured from its parallax, allows

us to calculate the starís Absolute Magnitude; that is, its

brightness if the star were moved to a standard distance away

from Earth.

Absolute Magnitude: the apparent magnitude of a star, if it were moved to a distance of exactly 10 parsecs (32.6 l.y.) from Earth.

Inverse-square law: brightness a              1
                                                                 distance ²

Absolute Magnitude removes the distance factor in our observations; it allows all stars to be compared, according to their true brightnesses. Whatever differences remain -- due to the starsí intrinsic luminosities.

V. Luminosities

Suppose we do same for the Sun; What do we find?

If ëmovedí the Sun to a distance of 10 parsecs, what is its absolute magnitude?

Absolute Magnitude Sun ~ 4.83

Given this, and the definition of the magnitude scale, we can make a final conversion factor, and relate the absolute magnitudes of stars to the sunís own luminosity.

Sunís luminosity = 1.0 (by definition)

Starís luminosity = brightness ratio, compared to Sun

[Appendices D, E, in Zeilik, for nearest, brightest stars]

Luminosities, or Absolute Magnitudes, are the first fundamental property of a star that we can learn (analogous to ëheightí of individuals on football field)

Stars can also be grouped into "Luminosity Classes,"

ranging from I (Supergiants), to III (Giants), to V (Main Sequence Dwarfs)
 
 

I. Binary Stars

Gravitationally-bound pairs of stars; orbit center of gravity

A. Visual Binaries

Pair appears separated in large optical telescopes;

visual or photographic observations are recorded

Measurements are taken over many years of pairís

position angle, separation;

Orbit is fitted to data; masses of stars determined by Newtonís laws!

e.g. Alpha Centauri (80-year period)

B. Spectroscopic Binaries

Appear unresolved in large telescopes; two different spectra superimposed

As pair revolves (stars approach, recede from observer),

spectral lines shift back and forth (Doppler Effect);

Eclipsing Binaries -- stars physically eclipse one another

(orbits seen edge-on)

e.g. Algol (in Perseus)

Binary stars provide only direct way of finding stellar masses; the most important factor in a starís evolution!

II. Variable Stars [rough classification]

A. Intrinsic Variables

Regular, pulsating (expanding/contracting)

1. Short-period (< 1 day) RR Lyrae variables

2. Middle-period (1 day < period < 45 days)

Cepheid variables (e.g., d Cephei)

Period-Luminosity Relation -- worked out by Henrietta S. Leavitt (studies of LMC)

Most important -- serve as distance indicators (ëstandard candlesí) to extra-galactic objects (by inverse-square law)

Most accurate value of Hubble Constant (expansion rate of the universe)

3. Long-period (> 45 days) e.g., Mira = o Ceti

B. Extrinsic Variables

Variation due to external causes

1. Nebular (very young, unstable) e.g., T Tauri

(irregular)

2. Eclipsing Binaries (spectroscopic) e.g., Algol

(regular)

C. Cataclysmic Variables (irregular) -- undergo variations of many magnitudes in short time

1. Dwarf novae; novae (outbursts)

Matter, falling onto surface of white dwarf star,

violently heated; can be repeated

2. Supernovae -- true exploding stars (Type I, II)

I. Spectral Classification

Second fundamental property that we can learn about stars (height, weight analogy);

Can be determined independently of starís distance

Wienís Law: spectrum of hot, luminous solid (~ blackbody)

Color is determined by Temperature --

Hottest objects -- blue-violet light;

Coolest objects -- reddish light

l maximum emission a                 1
                                   Temperature °K

Spectral Classification System -- pioneered by Annie J. Cannon -- is a Temperature classification

Seven principal (letter) classes, from hottest to coolest; each further subdivided from 0 to 9

Spectral Classification System

O Hottest --	v. weak H abs. lines ionized He abs. lines	l Orionis > 30,000°K
B	stronger H. abs. lines  neutral He abs. lines	Spica
A	strongest H abs. lines	Vega
F	weaker H abs. lines	Procyon
G	weakest H. abs. Lines	Sun
K	weak abs. lines (metals)	Arcturus
M Coolest--	strong abs. lines (metals)	Antares 3,000°K

Mnemonic -- "Oh, be a fine girl/guy, kiss me."

How does temperature affect appearance of absorption lines?

Unless atoms are kept above minimum temperature/energy,

they cannot absorb incoming wavelengths

e.g., Hydrogen -- shows optimum absorption in A-type stars

III. Role of Stellar Mass

A. A starís initial mass determines its core temperature, and the starís luminosity;

Mass-Luminosity Relation [diagram]; in turn,

A starís mass determines its initial position on the Main Sequence of the H-R Diagram

B. The greater the mass, the higher its core pressure & temperature, and the faster the star burns its fuel; thus,

A starís initial mass determines its Main Sequence lifetime

1. Stars with greatest mass -- have shortest Main-Sequence lifetimes

2. Stars with least mass -- have longest Main- Sequence lifetimes

Analogy: gas-guzzling, 8-cyl. SUV, vs. tiny, 4- cyl. economy car

Sun (4.6 billion years old): ~ half way through its Main-Sequence lifetime (9-10 billion years)
 
 

I. Interstellar Matter

Stars begin their existence in large interstellar (molecular) clouds; initially cold, dark masses of gas, dust inside Milky Way galaxy.

A. Neutral Hydrogen (H I) -- invisible in optical wavelengths; yet may be collisionally excited;

atom emits 21-cm. photon (following spin-flip),

when returns to ground state

Enabled radio astronomers to map spiral structure of our galaxy, when optically impossible (due to dust blocking visible light)

B. Ionized Hydrogen (H II) -- regions where gas has been ionized by strong UV radiation of nearby stars (Kirchoffís Rule 2)

H II regions -- sites of star formation in galaxies

e.g., Orion Nebula (~ 1,500 l.y.); stellar nursery!

C. Interstellar Molecules: complex organic forms

(detected by radio emissions)

e.g., nebulosity surrounding Pleiades cluster

Concentrated in planes of spiral galaxies; ëdark lanesí

of Milky Way; seen in silhouette in edge-on galaxies

Requires corrections to be applied to observations:
 

1. Absorbs light from distant stars as a function of distance

2. Reddens light (shorter wavelengths more easily scattered)
 

Gravitational collapse of interstellar (molecular) cloud; analogous to Solar Nebula; shrinks, grows hotter, perhaps flattens into disk, . . .

Collapse may be triggered/enhanced by collision with another cloud, or shock wave from supernova explosion

Protostar -- shrouded in dusty ëcocooní; invisible at optical wavelengths; but visible in infrared (when temp. reaches ~ 1,500°K)
 

Glimpsed by HST (against bright backgrounds);  proto-planetary disks

How long does process take?

For a one solar-mass star, < 100 million years
 

A. Bipolar outflows -- jets of matter, escaping along axis of rotation

B. Stellar winds -- clear away remaining gas, dust;

allows star to become visible at optical wavelengths;

rapid brightness fluctuations (T Tauri stars)

After star begins fusion process in core, it becomes stable; ëlandsí on Main Sequence of the H-R Diagram, at a position determined by its mass. "Zero-age" M-S star.
 
 

Fundamental problem -- to explain the properties of the H-R Diagram, especially non-Main Sequence stars

I. Four Forces of Nature (in decreasing strength)

A. Strong nuclear (binds nucleons together; overcomes electrical repulsion of protons)

B. Electromagnetic (governs behavior of electrons;

allows atoms to exist)

C. Weak nuclear (governs radioactive decay)

D. Gravitation (attraction of all masses for one another)

Over distances >> than atomic dimensions, gravitation is the strongest force!

Most important factor governing stellar evolution is the starís initial mass (express in solar-mass units)

II. Three Endproducts (based on starís final mass)

A.  0 < Mass_star < ~ 1.4 Mass_sun                                  White Dwarf

B.  ~ 1.4 Mass_sun < Mass_star < ~ 3.0 Mass_sun Neutron Star  (Pulsar)

C.  ~ 3.0 Mass_sun < Mass_star                              Black Hole

III. Evolution of One Solar-Mass Star (Sun)

A. After gravitational collapse of interstellar cloud:

"Zero-age" Main Sequence star (G2 V) formed

Commences Hydrogen fusion (ëburningí) in core;

Temp. ~ 10⁷ °K; hydrostatic equilibrium (balance of pressure, gravity) achieved

Star remains stable for ~ 10 billion years

B. After that time, star develops a core of Helium;

Hydrogen fusion moves into shell around core

Eventually, shell-burning becomes so intense that outer

layers begin to expand, swelling and cooling the surface.

Star begins to move off the Main Sequence, toward upper right; becomes a Red Giant star (engulfs orbit of Mercury)

C. When Helium core reaches temp. ~ 10⁸ °K,

Helium fusion commences (triple-alpha process);

Helium flash

Net reaction: 3 He => 1 C + energy

D. Over time, star builds a Carbon core, surrounded by Helium-burning shell, Helium, Hydrogen-burning shell, and Hydrogen

E. Over longer time, shell-burning grows so intense that outer layers of star are gently blown off into space;

Planetary Nebula (misnomer!) forms around Carbon-core star -- White Dwarf -- diameter ~ Earth! e.g., companion to Sirius

Star (now at hottest stage) moves toward lower left area of H-R Diagram; very hot, but low- luminosity

(extremely small size)

F. White Dwarf star: has density ~ tons/in³

Insufficient pressure, temp., to fuse Carbon into heavier elements

Cannot be further compressed; supported by repulsion of electrons (degeneracy pressure)

After billions of years, cools off into "black dwarf" cinder

* * * * * *

Mass-limit to White Dwarf stars: max. ~ 1.4 solar masses;

If later over-loaded, White Dwarf star explodes as Type I Supernova; leaves ~ no remnant behind

e.g., Tychoís SN 1572 in Cassiopeia

I. Supernovae

Recall that when Mass_star < ~ 1.4 Mass_sun, endproduct is White Dwarf star; supported by electron repulsion (degeneracy)

Critical mass -- Chandresekhar limit; Carbon is heaviest element fused in core of low-mass stars

Today -- consider evolution of more massive stars;

initial stages: ~ low-mass stars, but pass through more quickly: Hydrogen => Helium => Carbon

The greater the mass, the greater the starís core temp., pressure, & luminosity; the faster its fuel is consumed . . .

Thus, heavier elements are fused inside cores of massive stars, releasing energy:

⁴He + ¹²C => ¹⁶O

¹²C + ¹²C => ²⁰Ne + ⁴He

¹⁶O + ¹⁶O => ²⁸Si + ⁴He
 

.

.

.

Star develops complex layers, like an onion . . .

Fusion reactions proceed, up to creation of Iron; but stops!

Iron has the most tightly bound nucleus; absorbs energy; core gets hotter (~ 2 billion °K);

Without a fuel source, core of star quickly collapses;

Electrons and protons are forced together into neutrons; core compressed into sphere of neutrons, ~ 10 km diam., supported by neutron repulsion (degeneracy)

Outer layers of star -- collapse; strike neutron core, bounce; temp., pressure surge; shock wave -- lifts starís outer layers; tremendous explosion -- Supernova (Type II)

Luminosity: ~ a billion suns; as bright as all stars of galaxy!

Much of energy of SN explosion -- carried away by neutrinos; such a ëpulseí observed -- from SN 1987A

1054 A.D. -- SN witnessed as ëguest starí in Taurus; site of

present-day Crab Nebula

* * * * * *

Heavier elements? -- created by neutrons that collide w/ other nuclei (r-process; not same as fusion)

II. Neutron Stars

Can they be observed?

1967 -- Jocelyn Bell -- detected first "pulsars";

Explanation -- rapidly spinning neutron stars;

(1) core collapse sped up rotation (~ ice skater)

(2) magnetic field -- amplified millions of times;

acts as powerful generator

Lighthouse Model -- as beam of energy sweeps across our

line of sight, we see narrow pulse (radio, light, X-ray);

Pulses: slow down gradually -- from loss of rotational energy

Without them, heavier elements could not be distributed throughout cosmos;

Carbon-based life (as we know it) would not be possible:

Low-mass stars -- expell only H, He into space; carbon cores of White Dwarfs -- only liberated in Type I supernovae

C. Sagan: "We are made of star-stuff"; elements {C, O, Si, Fe, . . . }

created inside massive stars; ërecycledí through SN explosions into other stars, planets, & living organisms, who have begun to figure these things out!

III. Black Holes

Mass limit to neutron stars: ~ 3.0 solar masses

(neutron repulsion)

What happens when Massstar > 3 Masssun?

A. Explodes as (Type II) Supernova

B. Core collapses past limit of neutron repulsion

(strong nuclear force is overcome by gravity);

forms a singularity (~ zero volume; ~ infinite density)

C. Einsteinís General Theory of Relativity -- predicts where

gravitational field is so strong; not even light can escape!

Equivalence of gravitational and inertial mass;

Thought experiment -- two elevators; no experiment can tell difference between the two

Acceleration is equivalent to gravitation;

Gravity is caused by the geometry (curvature) of space-time!

Non-Euclidean geometries --

"Space tells matter how to move; matter tells space how to curve"

Empirical evidence:

A. Advance of Mercuryís perihelion -- unexplained by Newtonian gravitation

B. Prediction of bending of starlight around massive objects (sun)

Verified by Eddington at 1919 solar eclipse

C. Universe cannot be static -- must expand or contract  (no evidence)

Expansion measured by Hubble ca. 1929

Modern concept of black hole (K. Schwarzschild)

Can black holes be detected?

If belong to spectroscopic binary systems, seemingly yes!

1. Find binary star w/ invisible companion

(evidence of spectral lines)

2. Calculate mass of invisible companion

(Newtonís Laws)

3. If > 3 solar masses -- black hole candidate

e.g. Cygnus X-1

Could you survive a trip into a black hole? Why/not?

I. Structure

Galileo -- first observed (w/ telescope) that Milky Way

composed of countless stars . . .

Today -- Milky Way as flattened disk, ~ 120,000 l.y. diameter, with central bulge; contains ~ 100 billion stars (solar masses)

often grouped in open clusters

Sun -- located in a spiral arm (Orion), about halfway from center to edge (~ 30,000 l.y. radius); takes ~ 280 million years to make one revolution

Surrounded by few dozen globular clusters -- swarms of older stars, travel as satellites around galactic center (at all angles to disk)

Halo -- spherical; as large or larger than disk; deduced from orbital motions of stars in disk; composed of older stars and ?

(ëdark matterí)

Center (nucleus) -- super-massive black hole? -- contains few million solar masses

How has this picture of the galaxy been achieved?

Period-Luminosity relation (H. Leavitt) -- variable stars

In 1910s -- Harlow Shapley -- used the 100-inch reflector at Mt. Wilson Observatory;

Identified RR Lyrae variables in globular clusters; from

their apparent brightnesses, he calculated their distances

Conjectured that globulars were clustered around center of our galaxy (toward constellation Sagittarius);

Concluded that Sun is not at center of Milky Way, but lies a significant distance away from center; still the view today!

II. Stellar Populations

A. Population I stars -- chiefly hot, young, bluish main- sequence stars

Continuously formed in spiral arms (disk); main constituents of open clusters

Occur where abundant interstellar matter (gas, dust) is present; are byproducts of large interstellar clouds (H II regions)

B. Population II stars -- mostly cooler, older reddish stars, evolved off the main sequence (toward giant/supergiant stages)
Found in bulge; globular clusters; and halo --

regions where little interstellar matter (gas, dust) exists

III. Ages of Star Clusters

How do H-R Diagrams for Open, Globular Clusters compare?

A. Open Clusters

Suppose you have a newly-formed open cluster; all stars lie on Main Sequence ("zero-age")

Most massive stars evolve first, leave M-S to become giants/supergiants . . .

Over longer times, less-massive stars evolve off the M-S . . .

B. Globular Clusters

Turnoff point is low on M-S, implying advanced age;

Feature called Horizontal Branch -- contains low-mass, post-red giant stars, & variable stars

Oldest globular clusters: ~ 12-13 billion years old!

IV. Spiral Arm Formation

Why do spiral arms persist in Milky Way, other galaxies?

If stars orbit the galaxy according to Keplerís Laws, then

inner stars must revolve faster; outer stars revolve slower

Across age of galaxy (~ 13-15 billion years), arms should have wound up completely (e.g., Sun -- made some 40-50 revs.)

But this is not the case! Spiral galaxies have as few as two, distinct arms!

Spiral arms must be regenerated over time -- how?

Spiral Density Wave theory - not completely understood

(especially its origin)

will evolve, die; to be replaced by newer stars . . .

Other ways to form spiral, complex structures -- galactic collisions/interactions (more ahead)

I. From ëSpiral Nebulaeí to Galaxies

Considerable debate, since 18th century, as to nature of ënebulaeí

1840s -- spiral shape of some ënebulaeí first recognized (Rosse); many displayed regular, round/oval shape (unlike gaseous nebulae)

late 1800s -- (a) photography showed vast numbers of ëspiral nebulaeí exist, to limits of observation; what are they?

(b) spectroscopy showed ëspiral nebulaeí to have faint, continuous spectra (like that of stars); NOT emission-line spectra (found in gaseous, planetary nebulae)

Might have decided the issue, but did not; distances were unknown . . .

Arguments became polarized around two conflicting interpretations:

(a) star/planetary systems forming within Milky Way

(b) ëisland universeí model -- other galaxies at immense distances from ours

1920 -- ëGreat Debateí (Shapley, Curtis)

How was issue finally resolved?

1924 -- Edwin Hubble -- 100-inch telescope -- discovered 1st Cepheid variable star within the Andromeda ëNebulaí;

He calculated its distance -- far beyond limits of Milky Way

(determined by Shapley)

Thus, ëisland universeí model was correct; spiral ënebulaeí

are individual galaxies!

II. Hubbleís Classification

Taxonomy -- attempt to bring conceptual order to immense diversity of types (akin to life sciences)

Still employed today, w/ modifications . . .

Three Major Classes (ëtuning-forkí diagram)

A. Elliptical Galaxies

Range from spherical to lens-shaped (flattened)

Chiefly Population II stars; ~ no interstellar matter today; ~ no star formation occurs

B. Spiral Galaxies

Disk-shaped; abundant interstellar matter; Population I & II stars; H II regions in disk

(1) Normal -- spiral arms extend ~ all way in to bulge

Follow continuum from loosely to tightly wound

(2) Barred -- marked by ~ linear bars, extend on either side of nucleus; seemingly do not follow Keplerian dynamics

Spiral arms only begin at ends of bars

Follow continuum from loosely to tightly wound

C. Irregulars

Lack of regular, definable shape; some smaller than spirals (e.g., LMC, SMC -- satellites of Milky Way)

Others -- result from interactions/collisions between larger galaxies; include ring-shaped galaxies

Caveat -- Hubble never intended this classification to be taken as an evolutionary sequence; yet others have done so

Why these differences?

A. Rotation/mass distribution, including ëdark matterí? (more ahead)

B. Collisions/mergers? -- seemingly verified by computer models (e.g., ëAntennaeí galaxies)

Do ellipticals result from merger of 2 spirals?

III. Rotation Curves; ëDark Matterí Problem

Using Doppler Effect, one measures wavelength shifts, and velocities of stars, as function of radius from center of galaxy (Vera Rubin)

Stars nearer edges of disks -- do not slow down, according to Keplerís Laws, but instead travel progressively faster than theory predicts!

Excess velocity -- only accounted for by increasing distribution of mass, away from center of galaxy

ëDark Matterí halo -- otherwise invisible, except for gravitational effects on stellar motions

What is it? No one knows! Yet, it is ~ 10 times as massive as disk itself;

ëDark Matterí -- may comprise 3 90% of mass of universe!

Candidates range from ordinary, to exotic:
 

A. MACHOs -- larger, planet-to-stellar size objects

(brown dwarfs, black holes, . . . )
 

.

.

.
 

B. WIMPs -- elementary particles (neutrinos, . . . )

One of biggest unsolved mysteries in astronomy!

I. Local Group

~ 30 members: Milky Way, Andromeda Galaxy (M31), M33, Magellanic Clouds, & dwarf galaxies (elliptical, irregular)

size: ~ 3 million l.y. across; ~ bound together by gravity

II. Other Clusters

ërichí clusters -- contain hundreds to thousands of galaxies;

tens of millions of l.y. across; yet only see largest members

e.g., Coma Cluster, Virgo Cluster: giant elliptical galaxies;

may ëswallowí/disrupt smaller galaxies by tidal interactions

internal motions -- allow ~ calculations of cluster masses;

if bound together (gravitationally), majority of mass is invisible (evidence of ëdark matterí)

III. Superclusters & Voids

Understanding -- arisen out of newer technologies; enable astronomers to collect data (on galaxy redshifts) by dozens;

Enormous surveys of galactic distances -- plotted three- dimensional distribution of galaxies in ëwedgesí of space

Clusters of galaxies not just randomly distributed; instead:

A. Superclusters (clusters of clusters) composed of knots/filaments, ~ analogous to cellular structures

e.g., ëGreat Wallí -- hundreds of millions of l.y. long

Largest-scale structures in the universe!

How can we explain the existence of these structures?

Problem -- Big Bang (in earliest stages) believed to have been very uniform/smooth;

Cannot account for these ëlumpsí or non-uniformities

Yet, likely a correlation between them, and measured variations in cosmic background radiation (described ahead);

I. Radio Astronomy (historical sketch)

1930s: radio engineer Karl Jansky (Bell Labs) -- assigned problem of isolating sources of static on long-distance calls;

Constructed rotating antenna, dubbed ëmerry go roundí --

Discovered that center of Milky Way is source of ëcosmic staticí; findings published

~ no impact on astronomical community; ëoptical biasí; no training in electronics; treated discovery as curiosity; ignored

early 1940s: radio amateur G. Reber: followed up on Jansky; constructed first parabolic dish antenna; mapped intensity of Milky Way; published findings in Ap. J.

late 1940s -- professional astronomers got involved;

major technical advancements of wartime (e.g., radar);

large antennas constructed; all-sky surveys conducted

Prominent radio sources identified; chief problem -- low resolution; difficulties of correlation with optical sources;

eventual successes -- most beyond Milky Way

Active Galaxies

Galaxies whose centers emit abnormally large amounts of energy; often rapid fluctuations in intensity: puts limits on sizes of sources

Comprise ~ 10% of all galaxies

AGN = Active Galactic Nuclei

Progression of increasing activity:
 

1. Radio galaxies

2. Seyfert galaxies

3. Quasars

II. Radio Galaxies

Chiefly elliptical galaxies; emissions from core, and from

~ symmetrical lobes on either side of nucleus; can extend millions of light years across!

Can emit millions of times more radio energy than normal galaxies

Emission in lobes: synchrotron radiation -- caused by electrons, moving at close to "c", spiral around magnetic field lines;

Twin jets -- emitted from core; collide with gas; spread out, excite lobes

III. Seyfert Galaxies

Spiral galaxies with abnormally bright nuclei; emit ~ same energy as normal galaxy, but in very compact, central region

Emission-line spectra; moderately large redshifts; rapid internal motions;

Rapid fluctuations in intensity; some -- also radio galaxies

IV. Quasars

Powerful radio sources; name -- from quasi-stellar objects

Initially correlated with point (~ stellar) sources

Broad emission-line spectra; large fluctuations in intensity;

some emit jets of matter/energy (e.g., 3C 273)

Enormous redshifts -- receding from us at significant fraction of speed of light!

Conundrum --

A. If redshifts due to Doppler Effect (Hubbleís Law) -- must be at enormous distances; extreme ages

B. If so, then must be extremely luminous, yet compact, objects

What are quasars?

Quasars -- an evolutionary stage in development of a galactic nucleus

Important fact -- we do not see any quasars nearby to us

(of contemporary age);

Represent an early phase in history of universe; only see them today because of associated ëlook-back timesí

Quasars => Seyfert Gals. => Radio Gals. => Normal Gals.

* * * * * *

What is source of prodigious energy (of AGNs)?

Accretion disks, jets produced around super-massive black holes (~ 100 million solar masses)

When stars stray too close -- torn apart by tidal forces;

infalling matter -- accelerated to high speeds; heated up; emits bursts of energy . . .

Magnetic fields, rotation axes -- believed responsible for jets

Most active in early universe, when holes increasing in mass;

after available matter was consumed, became more sedated

(reflects progression above)

Could the Milky Way have been an AGN in the past?

V. Gravitational Lenses

Another fulfillment of predictions arising from Einsteinís General Theory of Relativity:

Bending of light emitted by distant objects, around massive foreground objects

First seen -- in pair of quasar images, having identical redshifts; but interpreted as twin images of single quasar (distorted by intervening galaxy)

Recently -- HST -- provided multiple images of distant, spiral galaxies, distorted by gravity of cluster of nearby, elliptical galaxies! Also -- "Einstein Cross"

Measurements of the distorted images allow calculations of the mass of the galaxy cluster; again, the total mass is ~ 10x the visible mass; further evidence of ëdark matterí

Demonstrations that gravity (curvature of space) is capable of bending light!

VI. Gamma Ray Burst(er)s

One of most active areas of research in last decade

Detection of gamma ray bursts (from < 1 sec. to ~30 sec.) by

Vela military spacecraft (after 1969);

designed to monitor violations of Nuclear Test Ban Treaty (1963); observations -- remained classified for years!

civilian spacecraft, e.g., Compton Gamma Ray Observatory -- launched to study them; correlation of bursts with known sources -- unsolved until recent years

Distribution of sources on sky: ~ uniform; not confined to galactic plane ( > 2,000 bursts compiled)

Two competing interpretations:

A. Galactic halo model -- lower-energy, relatively nearby;

less extreme physics required

B. Cosmological model -- higher energy (occurring in distant galaxies); more extreme physics required

Optical spectra -- finally revealed large redshifts; objects located in galaxies; thought to be "hypernovae"

I. Doppler Effect

Wave phenomenon; arises whenever a source of waves, & observer, are in relative motion; applicable to sound, light, . . .

A. Stationary source -- emits waves of fixed length (l)

B. Source approaches observer -- waves are compressed;

increase in frequency; decrease in wavelength (l);

appear blue-shifted (in the case of light)

C. Source recedes from observer -- waves are expanded;

decrease in frequency; increase in wavelength (l);

appear red-shifted (in the case of light)

Amount of shift is proportional to relative velocity;

D l = v
   l     c

where D l = wavelength shift; l = ëat-restí wavelength;

v = relative velocity; c = speed of light (where v << c)

II. Velocity-Distance Relationship

1910s -- V. M. Slipher (Lowell Observatory) -- discovered that spectra of "spiral nebulae" [galaxies] exhibited redshifts;

Implied that they were moving away from us; their velocities could be calculated;

However, neither their distances, nor their actual natures,

were known; Slipherís data yielded only half of the needed understanding

* * * * *

1920s -- Edwin Hubble -- used the method of Cepheid variable stars, to calculate distances to galaxies, whose redshifts had been measured; second half of ëpuzzleí at last solved!

1929 -- Hubble presented first evidence of velocity-distance relationship (linear):

ëThe farther away a galaxy is, the larger its redshiftí; or,

ëVelocity of a galaxy is directly proportional to its distanceí
 

velocity = H ^. distance

Known as Hubbleís Law!

Consequences of Hubbleís Law:

Entire universe seems to be expanding away from us, in all directions;

All matter in the universe has been flung outwards, from an original explosion, called (by Fred Hoyle) the Big Bang!

       Rate of expansion = slope of line
 

= D velocity
   D distance

= H or Hubbleís Constant

~ 74 +/- 7 km/sec per megaparsec
 

Age of universe (if ignore effects of slowing by gravity):
 

Age = 1
           H
 

was created out of that event (and its aftermath)

Hubbleís Law is the first piece of evidence supporting the Big Bang origin of the universe

III. Cosmic Microwave Background Radiation

1965 -- physicists A. Penzias, R. Wilson -- found that a low- energy form of radiation is coming from all parts of the sky;

called Cosmic Microwave Background (CMB) Radiation -- corresponds to a temperature ~ 3°K; fulfilled predictions of its existence

Interpreted as the ëafterglowí of the Big Bang fireball; long since cooled (as space has expanded)

Formed ~ 300,000 years after the Big Bang, when matter & energy ëdecoupledí; that is, when protons and electrons first combined to form atoms

Penzias, Wilson awarded Nobel Prize in Physics (1978)

* * * * *

1990s -- COBE satellite: made accurate measurements & map of distribution of the CMB radiation;

revealed very small irregularities that may be analogous to the formation of superclusters of galaxies;

oldest observable remnants of Big Bang itself!

Cosmic Microwave Background radiation is second piece of evidence, supporting the Big Bang origin of the universe

I. Cosmological Principle

Cosmology: study of the origin, development, and fate(s) of the universe

* * * * *

Our observations tell us that all distant galaxies are moving away from us, at speeds proportional to their distances (Hubbleís Law)

Was the Milky Way Galaxy itself at the center of the universe?

All galaxies emerged from the center, following Big Bang, but neither Milky Way, nor any other galaxy, was ëspecialí

~ glorified Copernican perspective; ëdemocracyí of reference frames:

No matter where (or in what galaxy) an observer is located, he/she seems to be ëat the centerí of the expansion

"Cosmological Principle": At any given time, the universe appears the same to all observers, regardless of their location; universe is isotropic

II. Fate(s) of the Universe: Standard Big Bang model

Three possible outcomes (two "open"; one "closed");

depends on the total energy balance of the universe

A. If total kinetic energy > total potential energy,

then universe will expand forever, with net positive speed/energy;

Curvature of space is negative (~ saddle-surface)

Grow cold, dark; suffer a ëheat deathí; reach maximum entropy (disorder) [realized in 19th century]

B. If total kinetic energy = total potential energy,

then universe will expand to infinity, but with zero net speed/energy;

"critical density": balance between "open" and "closed"

Curvature of space is zero ("flat"); suffers a ëheat deathí

C. If total kinetic energy < total potential energy,

then universe reaches a maximum size; stops;

and re-collapses onto itself

Curvature of space is positive (~ spherical surface)

fate -- ëBig Crunchí: a universal black hole/singularity;

But if it is able to re-expand (and re-contract) again,

then "oscillating universe" theory

Can we tell which outcome is correct? Not yet! -- conflicting data!

Critical observations:

A. Exact value of Hubbleís Constant, along with the deceleration parameter (gravity should have been slowing the expansion from beginning)

Observations w/ HST indicate that the universe is open, and will expand forever w/ net positive energy

(based on observable matter)

B. Mean (average) density of matter in the universe; extremely difficult to measure

Strong theoretical and observational grounds ("inflationary" model) that the universe has exactly the critical density, and geometry is "flat"
But unresolved issues of ëdark matterí and ëdark energyí may change the entire outcome!

During earliest phases, universe underwent extremely rapid growth (inflation), at speeds much, much faster than "c" (!) [Not a violation of relativity]

It was space-time, & not matter, that expanded this fast

(quantum fluctuation), containing a powerful repulsive force, permitting inflation; gradual decay of that state led to formation of matter

B. Dark Energy

Analogous to Einsteinís "cosmological constant" -- a (fictitious) term inserted into equations of general relativity, to keep universe from contracting; later removed, after Hubbleís Law announced; will it be revived?

Matter, including dark matter, may comprise one-third of universe; other two-thirds may consist of dark energy

Geometries (negative, flat, positive) associated with fate(s) of standard Big Bang models -- may no longer hold true (!)