Results of Exam 2
Congratulations!!
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
1
What Makes the Sun Shine?
• The Sun puts out 4 x 1026 watts
• That’s a very large amount
• The typical power plant puts out 1000 megawatts


109 watts
10,000 power plants put out 1013 watts
• The Sun has been shining for about 4.5 billion
years
• What is a watt?

A watt is a unit of power
Energy per unit time
 Joule/sec

ISP 205 - Astronomy Gary D. Westfall
Lecture 17
2
Thermal and Gravitational Energy
• If the Sun were made of coal and its energy came
from burning, it could only burn at its present rate
for a few thousand years
• Conservation of energy states that energy cannot
be created or destroyed, only converted from one
kind to another
• 19th century scientists speculated that the Sun’s
energy resulted from meteorites falling into the
Sun

Calculations showed that in 100 years, the mass of
meteors would equal the mass of the Earth and that the
period of the Earth’s orbit would be changed by 2
seconds a year
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
3
Gravitational Contraction
• Around 1850, Helmholtz and Kelvin proposed
that the Sun might produce energy by converting
gravitational energy to heat





A shrinking of 40 m per years would be sufficient
Would keep Sun shining for 100 million years
In the 19th century, that seemed long enough
In the 21st century, we know that the Sun and the
Earth are much older than 100 million years
A new source of energy had to be understood in the
20th century
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
4
Mass, Energy, and Relativity
• Einstein formulated the idea that mass and energy
are interchangeable



Mass can be converted to energy
Energy can be converted to mass
E = mc2

Special case of E2 = (mc2)2 + (pc)2




p is the momentum of the mass
At rest, p=0, and we get E = mc2
Energy is equal to mass times a constant
c is the speed of light, 3 x 108 meters/second
c2 is a very large number
 Converting even a small amount of mass creates a lot of
energy

ISP 205 - Astronomy Gary D. Westfall
Lecture 17
5
Mass to Energy
• The vast power of nuclear reactors and weapons
results from the fact that relatively large amounts
of mass are changed to energy in nuclear reactions
• Often one hears that E=mc2 applies only to
nuclear reactions and nuclear explosions
• However, ordinary chemical burning (wood,
gasoline, etc.) also involves a change of mass to
energy


Very small change in mass
A million times smaller than in nuclear processes
• We know that mass can be converted to energy

But how??
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
6
Elementary Particles
• The fundamental components of matter are called
•
elementary particles
The physical objects around us are made of molecules
and atoms, matter


Molecules are groups of atoms
Atoms are made of neutrons, protons, and electrons


The electron is an elementary particle
Protons and neutrons in turn are made of elementary particles called
quarks and gluons
• Antimatter is composed of antiprotons, antineutrons, and
•
antielectrons (positrons)
When matter comes into contact with antimatter, they
annihilate each other
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
7
The Standard Model
• Within the Standard Model, we think that there are 6
kinds of quarks, 6 kinds of leptons, and 4 types of
exchange particles

Nothing else!
• Quarks

Up, down, strange, charm, bottom, top
• Leptons

Electron, muon, tau, electron neutrino, muon neutrino, tau
neutrino
• Exchange particles


Represent the four fundamental forces
Photon, gluon, W and Z bosons, graviton (not observed)
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
8
The Atomic Nucleus
• Most of the mass of an atom is concentrated in the
nucleus
• The nucleus is made of neutrons and protons
bound together by the attractive strong force

The strong force easily overwhelms the
electromagnetic force of the protons trying to repel
each other in the nucleus
• When neutrons and protons are brought together,
they are held together by the strong force and
binding energy is released


The mass of the bound system is less than the mass of
the constituent neutrons and protons
E = mc2
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
9
Fusion and Fission
• The most well bound nucleus is
56Fe


(iron 56)
26 protons and 30 neutrons
Lighter nuclei and heavier nuclei are
less well bound
• Thus we can bind together lighter
•
nuclei to produce more well bound
nuclei and release energy (fusion)
Alternatively, we can break up
heavier nuclei (like uranium) into
lighter nuclei and release energy
(fission)
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
n
235
141
U
92
Ba
n
n
n
Kr
10
The Fuel Cycle of the Sun
• The main fuel cycle of the Sun involves burning
hydrogen to helium
1
1
2

H H H  e   e
2
3
•
•
H H He  
1
3
3
4
1
1
He He He H H
Fusing 1 kg of hydrogen to helium using this
process produces 6.4 x 1014 J which is more than
10 times the Earths annual consumption of
electricity and fossil fuels
The Sun converts 600 million tons of hydrogen to
helium every second
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
11
The Interior of the Sun
• Fusion in the center of the Sun can only occur if
the temperature is very high
• Our knowledge of the center of the Sun relies on
computer models
• The Sun must change

The Sun is burning hydrogen to helium
Will the Sun get brighter or fainter?
 Will the Sun get larger or smaller?


Ultimately the Sun will burn up all its fuel
• We will use all of our observations of the Sun to
constrain the model and calculate things we
cannot observe directly
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
12
Observations of the Sun
• The Sun is a gas

High temperatures mean high pressures
• The Sun is stable


All the forces in the Sun are balanced
Gravitational forces trying to collapse the Sun are
balanced by the outward pressure of the hot gasses

Hydrostatic equilibrum
• The Sun is not cooling down

The Sun radiates energy but generates enough to
maintain its temperature
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
13
Heat Transfer in a Star
• Heat is transferred three ways in a star

Conduction


Convection


Atoms collide with nearby atoms
Currents of warm material rise
Radiation
Energetic photons move away and are absorbed elsewhere
 The gasses of the Sun are opaque to radiation


Opacity
It takes 1 million years for a photon generated deep in the
Sun to reach the surface
 Neutrinos escape in about 2 seconds

ISP 205 - Astronomy Gary D. Westfall
Lecture 17
14
Model Stars
• To describe the parts of the
•
•
•
•
Sun we cannot observed
directly, a model star is
created
Energy is generated through
fusion in the core of the star
which extends 1/4 of the
way to the surface
The core contains 1/3 of the mass of the star
Temperatures reach 15 million K and the density is 150
times the density of water
The energy is transported toward the surface by radiation
until it reaches 70% of the distance from the center to the
surface where convection takes over
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
15
Solar Pulsations
• Astronomers have observed that the Sun pulsates
• Pulsations are measured by measured the radial velocity of the
•
•
surface
The pulsation cycle is typically about 5 minutes
These pulsation can be related to
solar models

Solar seismology
• Measurements using solar
•
•
seismology have sown that
convection occurs 30 % of the way
to the center
Differential rotation persists down
through the convection zone
Helium concentration in the interior
of the Sun is similar to the surface
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
16
Solar Neutrinos
• Neutrinos are created in the solar fusion process
• Neutrinos escape without much interference
• About 3% of the Sun’s generated energy is carried
away by neutrinos
• 3.5 x 1016 solar neutrinos pass through each
square meter of the Earth every second
• First experiments to measure solar neutrinos
found only 1/3 as many as predicted
• Recent experiments have found about 1/2 as many
as predicted
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
17
Neutrino Oscillations
• One explanation for the solar neutrino problem is that
•
•
•
•
•
•
neutrinos oscillate back and forth between the various
kinds of neutrinos
The sun produces only electron neutrinos
En route to the Earth, the electron neutrinos may
spontaneously turn into muon neutrinos that are not
detected
Another problem is the knowledge of the neutrino mass
Standard model says the neutrino has no mass
If the neutrino has mass, then many possibilities are open
As we speak, experimenters are trying to measure the
mass of the neutrino

Science marches on
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
18
Analyzing Starlight
• Stars are not all the same


Some are bright and some are dim
They have different colors
• Color is a good indication of the temperature of
the star


Red is the coolest
Blue is the warmest
Stars in the constellation Orion
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
19
The Brightness of Star
• Luminosity

The total amount of energy emitted per second
• Stars give off energy in all directions

Very little actually reaches our eyes or telescopes
• The amount of light we see is called the apparent
brightness
• If stars all had the same luminosity, then we could
tell how far away they were by their apparent
brightness

Wrong!
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
20
The Magnitude Scale
• Historically, the brightness of a star was classified using
magnitudes

The larger the magnitude, the fainter the star
• Originally, magnitudes of stars were assigned by eye
• In the 19th century, the system of magnitudes was
quantified and the definition that magnitude 1 stars (the
brightest) were 100 times brighter than magnitude 6 stars
(the dimmest)

Each magnitude is brighter by a factor of 2.512

5
100
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
21
Colors of Stars
• To find the exact color of a star, astronomers filter the light through
three filters



U (ultraviolet), 360 nanometers
B (blue), 420 nanometers
V (visual, for yellow), 540 nanometers
• The difference between the magnitude measured through any two
of the filters is called the color index

For example, B - V
• The total magnitude of the star does not affect its color but its
temperature does
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

By agreement, B - V = 0 corresponds a temperature of 10,000 K
B - V = -0.4 corresponds to a hot blue star
B - V = +2 corresponds to a cool red star
The Sun has B - V = 0.62 corresponding to a temperature of 6000 K
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
22
The Spectra of Stars
• Astronomers can analyze the wavelength of the light emitted by
•
•
stars and determine what elements are present in the stars
However, the main reason that stellar spectra look different for
different stars is the temperature of the stars
Hydrogen is the most abundant element and, depending on the
temperature of the star, can be difficult to see spectroscopically
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

Very cool stars have absorption lines in the UV
Very hot stars have their hydrogen completely ionized and there can be no
absorption lines from hydrogen
Around 10,000 K is optimum for observing hydrogen
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
23
Classification of Stellar Spectra
• Stars are classified by their temperatures into
seven main spectral classes

O, B, A, F, G, K, M
 O is the hottest, M is the coolest

Each class is further subdivided into ten subclasses

A0, A1, A2,…, with A0 being the hottest
• The system
came from
looking at the
spectra of stars
and classifying
them according
to how
complicated
they were
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
24
Abundances of the Elements
• By analyzing the spectra of stars, one can identify
elements in the star
• Laboratory measurements are done for the
elements at different temperatures
• Many factors make the identification difficult


Temperature and pressure may make certain elements
invisible
Motion of the star’s surface and rotation of the star can
blue the absorption lines
• Measurements show that hydrogen makes up 75%
of the mass of most stars and helium makes up
25% with a few percent left for the other elements
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
25
A Stellar Census
• The lifetime of stars is long compared with human
existence
• Studying one star can give some information but
not everything we want to know about stars
• We need to study a large number of stars to learn
their secrets
• Stars are very far away so
we use the unit light year
(LY) to measure distances
to stars
The distance light travels in 1
year
12 km
 9.5 x 10
ISP 205 - Astronomy Gary D. Westfall
Lecture 17

26
Luminosities of Nearby Stars
• Let’s look at the stars in
our “immediate”
neighborhood

Within 12 LY of our Sun
• We can immediately see that the Sun is one of the
brightest stars in our neighborhood
• Only 3 magnitude=1 stars are in this group
• Most magnitude=1 stars are far away

Most are hundreds of LY away
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
27
Top 30 Brightest Stars
• Shown on the left are
the 30 brightest stars
as seen from Earth
• The most luminous is
100,000 time more
luminous than the
Sun
• There are no stars that bright near to us
• Stars with low luminosity (0.01Lsun to 0.0001Lsun)
are very common
• A star with L=0.01Lsun cannot be seen unless it is
closer than 5 LY
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
28
Density of Stars in Space
• What is the typical spacing between stars?
• There are 59 stars with 16 LY of Earth
4 3 4
V  R  16 3  17157 LY3
3
3
59
1
stars 

3
3
17157LY 290LY
3
d  290LY 3  6.5LY
• Stars are very far apart
• Stars are very dense objects with lots of space
between them
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
29
Stellar Masses
• We know that the Sun is relatively luminous
• How does the mass of the Sun compare with other
stars?
• A nice way to measure the masses of stars is by
studying binary star systems

Roughly half of stars exist as binaries
• The first binary star was discovered in 1650

Mizar in the middle of the Big Dipper’s handle
• The star Castor in the constellation Gemini is also
a binary
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
30
Observing Binary Stars
• Visual binaries


Both star cans be seen using an optical telescope
Sometimes the two stars are not actually close to each
other but only appear to be close
• Spectroscopic binaries


Spectroscopic lines change with regular period
Only one star is visible
• Recent measurements showed that Mizar was
actually two sets of binary stars
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
31
Masses from the Orbits of Binary Stars
• We can estimate the masses of binary star systems using


D3 = (M1+M2)P2
M1+M2 is the mass of the binary system in units of the Sun’s mass
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
32
•
•
•
•
Range of Stellar Masses
How large can the mass of a star be?
Most stars are smaller than the Sun
There are a few stars known with 100 Msun
The smallest stars have masses of about 1/12 Msun


Objects with masses of 1/100 to 1/12 Msun may produce energy
for a short time
Brown dwarfs




Similar in size to
Jupiter but 10 to 80
times more massive
Failed stars
Difficult to observe
Hydrogen cannot fuse
to helium
ISP 205 - Astronomy Gary D. Westfall
R 136, a
cluster with
stars as masive
as 100 MSun
Lecture 17
33
Lithium Thermometer
• How can we tell a brown dwarf from a small, cool star
• Lithium (3 protons and 4 neutrons) cannot exist in an active star

Convection will take the lithium down into the hot parts of the star and
destroy it
Brown dwarf Gliese 229B
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
34
Mass Luminosity Relation
• Are the mass and
•
luminosity of stars
related?
Yes


The more massive
the star the more
luminous
About 90% of all
stars obey the
relationship shown to
the right
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
35
Diameters of Stars
• The diameter of the Sun is easy to measure

Measure the angle (0.5), measure the distance, get the diameter (1.39
million km)
• All other stars appear to be a point in a telescope
• The diameter of some stars have been measured by studying the
•
dimming of the star’s light as the Moon passes in front of it
The diameter of some stars have been measured using eclipsing
binaries
ISP 205 - Astronomy Gary D. Westfall
Lecture 17
36