The Sun &

Modern Physics

The Sun – A typical Star • The only star in the solar

system

• Diameter: 110 that of Earth

• Mass: 300,000 that of Earth

• Density: 0.3 that of Earth (comparable to the Jovians)

• Rotation period = 24.9 days (equator), 29.8 days (poles)

• Temperature of visible surface = 5800 K (about 10,000º F)

• Composition: Mostly hydrogen, 9% helium, traces of other elements Solar Dynamics Observatory Video

How do we know the Sun’s

composition?

• Take a spectrum of the Sun, i.e. let sunlight fall unto a prism

• Map out the dark (Fraunhofer) lines in the spectrum

• Compare with known lines (“fingerprints”) of the chemical elements

• The more pronounced the lines, the more abundant the element

Sun

• Compare Sun’s

spectrum (above)

to the fingerprints

of the “usual

suspects” (right)

• Hydrogen: B,F

Helium: C

Sodium: D

Thermodynamic Beginnings of

Star Models (c. 1850)

Excitement about newly discovered laws

of Thermodynamics (Mayer, Helmholtz)

– Energy is conserved: ΔU = Q – W (Change in energy content equals heat transferred minus work done)

– Cannot be created, only transformed

Energy Conservation is a balance sheet

Realization that most energy on Earth is

supplied by the Sun and must come from

“something”

The meteorological Star (Lane,

Ritter, Emden) Meteorological Star Model:

Stars are balls of gas: gas pressure against gravity

Modeled after convective equilibrium of Earth's

atmosphere (Kelvin 1850s)

Lane 1870: stars can be stable even though gravity

works to contract them

Ritter 1880: yes, and many different ways of

achieving stability are available

Emden 1907: Gaskugeln – a summative book

What we want from a Star Model (I)

Density in all parts of the star: ρ(r)

Temperature in all parts of the star: T(r)

Pressure in all parts of the star: P(r)

(Usually a spherical star is assumed, so r is

the radial variable (distance to center))

Main Idea: Hydrostatic Equilibrium

Gravity and thermodynamic pressure are

in balance → the star is stable (doesn't

shrink or expand)

Three Mechanisms of Energy

Transfer

In stars: either convection or radiation

Criterion: if temperature gradient is too steep

(superadiabatic) then radiation dominates

Gaskugeln: Stars as Gas Balls

Stars: Self-gravitating gas balls with a general,

polytropic relation (index n) between their

density and pressure: P = Kρ1+1/n

Temperature inversely proportional to radius

Hottest at center

Contracting → heat up

Expanding → cool down

Densest at center

This is all THEORY! What do

we OBSERVE?

Stellar Spectra:

mass produced at Harvard after 1880

Classified by “computers” (Maury, Cannon)

→spectral classes

Distances to stars: parallax, proper motion

Masses from binary stars (Kepler motion)

Brightness plus distance yields Luminosity

Sizes of a few (Michelson)

Stellar Spectra: Dark

Lines in front of a

continuous “rainbow”

Initially classified by strength of H lines: ABCDE...

Hyades star cluster

seen through an

objective prism

Focus on the Sun’s outward

appearance

The outer layers of the sun

• Photosphere

– Most of the light we see comes from the photosphere:

dense blackbody radiation

• Chromosphere

– Above the photosphere, about 4000 km deep

– Pinkish glow

– 10,000 thinner than photosphere

emission spectrum, red Hα line

• Corona

– Outermost layer

– looks like a crown during eclipses

– Very hot, very dilute

Chromosphere

• Above the photosphere• Gas too thin to glow

brightly, but visible during a solar eclipse– Characteristic pinkish color is

due to emmision line of hydrogen

• Solar storms erupt in the chromosphere

Solar Corona

• Thin, hot gas above the chromosphere

• High temperature produces elements that have lost some electrons

– Emission in X-ray portion of spectrum

• Cause of high temperatures in the corona is unknown

Sunspots

• Dark, cooler regions of photosphere first observed by Galileo

• About the size of the Earth

• Usually occur in pairs

Sunspots and Magnetism

• Magnetic field lines are stretched by the Sun’s rotation

• Pairs may be caused by kinks in the magnetic field (Babcock model)

Sunspot

Cycle

• Schwabe (1843): number of sunspots fluctuates

with a maximum about every 11 years: solar

maxima & minima occur

• Magnetic field of the sun reverses every 11 years

22 year cycle

• Formation location varies over the course of the

cycle

Understanding Stars

• “Understanding” in the scientific sense means coming up with a model that describes how they “work”:

– Collecting data (Identify the stars)

– Analyzing data (Classify the stars)

– Building a theory (Explain the classes and their differences)

– Making predictions

– Testing predictions by more observations

A bit of Modern Physics to

understand Stars

• The classical laws of physics are only an

approximation at slow speed and

macroscopic objects!

• Theory of Relativity (1905/1915)

– Need to use when speeds are comparable to

speed of light: c

• Quantum Mechanics (1900/1913/1925)

– Need to use when objects are atomic size, when

observing the object will change the object: h

Consequences (Super-short Version)

• E = mc2, we can transform mass into energy and

vice versa. Mass is not conserved, energy is

Particle accelerators

• The emission/absorption

spectra of gases are explained

by quantum mechanics– Only certain atomic energy levels

are allowed! Jumping from one

to the other, electrons give/gobble

up energy (emission/absorption)

Elements are not Elementary: the

Building Blocks of Nature

• Atoms are made from protons, neutrons,

electrons

• Chemical elements are named by the number A

of protons in their nucleus

• Atoms with same A but different number of

neutrons N are called isotopes or nuclides

Classify Stars – to understand

them!

• What properties can we measure?

– distance

– velocity

– temperature

– size

– luminosity

– chemical composition

– Mass

• Which properties are

useful/significant?

Classification of the Stars:

Temperature

Class Temperature Color Examples

O 30,000 K blue

B 20,000 K bluish Rigel

A 10,000 K bluish-white Vega, Sirius

F 8,000 K white Canopus

G 6,000 K yellow Sun, Centauri

K 4,000 K orange Arcturus

M 3,000 K red Betelgeuse

Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me

Making Sense of Stellar

Properties

Lots of data → How to sort them?

Spectral Type

Temperature

Size

Mass

Luminosity

Hertzsprung and Russell realize around 1910 that a two-

dimensional classification scheme is necessary, since

different versions (giants, dwarfs...) of stars of identical

spectral type exist

The Key Tool to understanding Stars: the

Hertzsprung-Russell diagram

• Hertzsprung-Russell diagram is luminosity vs.

spectral type (or temperature)

• To obtain a HR diagram:

– get the luminosity. This is your y-coordinate.

– Then take the spectral type as your x-coordinate, e.g.

K5 for Aldebaran. First letter is the spectral type: K

(one of OBAFGKM), the arab number (5) is like a

second digit to the spectral type, so K0 is very close to

G, K9 is very close to M.

The Hertzsprung Russell-Diagram (HRD)

• Example: Aldebaran, spectral type K5,

luminosity = 160 times that of the Sun

O B A F G K M Type

… 0123456789 0123456789 012345…

1

10

100

1000

L

Aldebaran

Sun (G2)

160

Hertzsprung-Russell Diagram

The Hertzprung-

Russell Diagram

• A plot of absolute

luminosity (vertical

scale) against

spectral type or

temperature

(horizontal scale)

• Most stars (90%) lie

in a band known as

the Main Sequence

HRD: Executive Summary

Most stars are Main Sequence stars (90%)

They seem “normal”, since they are the majority

and obey Stefan-Boltzmann (L=k R2T4)

Other Groups are counter-intuitive

Red Giants: bright yet cool

White Dwarfs: hot yet dim

Supergiants: superbright

regardless of temperature

Hertzsprung-Russell diagrams

… of the closest stars …of the brightest stars