ISP 205 - Astronomy Gary D. Westfall1Lecture 17 Results of Exam 2 Congratulations!!

1ISP 205 - Astronomy Gary D. Westfall Lecture 17

Results of Exam 2Results of Exam 2

Congratulations!!


What Makes the Sun Shine?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


Thermal and Gravitational EnergyThermal 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


Gravitational ContractionGravitational 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


Mass, Energy, and RelativityMass, 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


Mass to EnergyMass 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??


Elementary ParticlesElementary 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


The Standard ModelThe 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)


The Atomic NucleusThe 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


Fusion and FissionFusion 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)

nU235Ba141Kr92nnn


The Fuel Cycle of the SunThe Fuel Cycle of the Sun• The main fuel cycle of the Sun involves burning

hydrogen to helium

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1H+1H→2H+e++νe2H+1H→ 3He+γ3He+3He→ 4He+1H+1H

• 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


The Interior of the SunThe 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


Observations of the SunObservations 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


Heat Transfer in a StarHeat 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


Model StarsModel 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


Solar PulsationsSolar 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


Solar NeutrinosSolar 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


Neutrino OscillationsNeutrino 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


Analyzing StarlightAnalyzing 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


The Brightness of StarThe 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!


The Magnitude ScaleThe 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

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1005


Colors of StarsColors 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


The Spectra of StarsThe 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


Classification of Stellar SpectraClassification 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


Abundances of the ElementsAbundances 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


A Stellar CensusA 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


Luminosities of Nearby StarsLuminosities 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


Top 30 Brightest StarsTop 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


Density of Stars in SpaceDensity of Stars in Space• What is the typical spacing between stars?• There are 59 stars with 16 LY of Earth

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V =43

πR3 =43

π163 =17157 LY3

ρstars=59

17157LY 3 =1

290LY 3

d = 290LY 33 =6.5LY

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

between them


Stellar MassesStellar 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


Observing Binary StarsObserving 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


Masses from the Orbits of Binary StarsMasses 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


Range of Stellar MassesRange 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


Lithium ThermometerLithium 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


Mass Luminosity RelationMass 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


Diameters of StarsDiameters 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. Westfall1Lecture 17 Results of Exam 2 Congratulations!!

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