Results of Exam 2

1
Results of Exam 2
Congratulations!!
2
What Makes the Sun Shine?

• The Sun puts out 4 x 1026 watts
• Thats 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

3
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 Suns
  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 Earths orbit would be
  changed by 2 seconds a year

4
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

5
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, p0, 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

6
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 Emc2 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??

7
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

8
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)

9
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

10
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)

11
The Fuel Cycle of the Sun

• The main fuel cycle of the Sun involves burning
  hydrogen to helium

• 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

12
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

13
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

14
Heat Transfer in a Star

• Heat is transferred three ways in a star
• Conduction
• Atoms collide with nearby atoms
• Convection
• 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

15
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

16
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

17
Solar Neutrinos

• Neutrinos are created in the solar fusion process
• Neutrinos escape without much interference
• About 3 of the Suns 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

18
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

19
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
20
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!

21
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

22
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
• 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

23
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
• 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

24
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

25
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 stars 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

26
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
• 9.5 x 1012 km

27
Luminosities of Nearby Stars

• Lets 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 magnitude1 stars are in this group
• Most magnitude1 stars are far away
• Most are hundreds of LY away

28
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 L0.01Lsun cannot be seen unless it
  is closer than 5 LY

29
Density of Stars in Space

• What is the typical spacing between stars?
• There are 59 stars with 16 LY of Earth

• Stars are very far apart
• Stars are very dense objects with lots of space
  between them

30
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 Dippers handle
• The star Castor in the constellation Gemini is
  also a binary

31
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

32
Masses from the Orbits of Binary Stars

• We can estimate the masses of binary star systems
  using
• D3 (M1M2)P2
• M1M2 is the mass of the binary system in units
  of the Suns mass

33
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

R 136, a cluster with stars as masive as 100 MSun
34
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
35
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

36
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 stars light as the
  Moon passes in front of it
• The diameter of some stars have been measured
  using eclipsing binaries