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