Unit 4
Chapter 15
The Sun
Properties
 Radius: 700,000 km
 Mass: 2.0 × 1030 kg
 Density: 1400 kg/m3 or 1.4 xH2O
 Rotation: Differential
 Period: about a month
 Surface temperature: 5800 K
 The apparent surface of the Sun is the Photosphere
Luminosity
 total energy radiated by the Sun – can be calculated from the fraction of that energy that
reaches Earth.
 This diagram illustrates how one can extrapolate from the radiation hitting Earth to the entire
output of the Sun.
Mathematical models,
 consistent with observation and physical principles, provide information about the Sun’s
interior.
 In equilibrium, inward gravitational force must be balanced by outward pressure
 Although the average density of the Sun is only slightly more dense than water the density at
the core is extremely high. The temperature is relatively low at the surface but is near 15 million
K in the core.
The Solar interior
 has been understood theoretically for years.
 In recent years we have been able to investigate it by observation.
 Doppler shifts of solar spectral lines indicate a complex pattern of vibrations that can be used
much like seismic waves on the Earth to determine the interior construction of the Sun.
Energy transport
 in gases is limited to convection and radiation.
 In the radiation zone the particles are so tightly packed that the energy can only pass by
radiation. The radiation zone is relatively transparent; the cooler convection zone is opaque.
The Heart of the Sun
 Before we can discuss how the heat of the Sun is generated we have to consider the following:
Four Forces of Nature
Force
Strength
Strong Nuclear (pull)
1040
Electro-Magnetic
1028
Weak Nuclear (push)
1026
Gravitational
1

Einstein’s famous equation for the equivalence of matter and energy
Proton –Proton Chain
 This is the first step in the three-step fusion process that powers most stars.
 The ultimate result of the process is


The helium stays in the core;
The energy is in the form of gamma rays, which gradually share their energy with the body of
the Sun as they travel out from the core, emerging in all of the wavelengths of the
electromagnetic spectrum;
 The neutrinos escape without interacting
The Solar Atmosphere
 The cooler chromosphere, is the pink layer above the photosphere. It is hard to see directly as
the sun is too bright, unless Moon completely covers the photosphere.
 The much less dense corona can also be seen during a total eclipse. Temperatures here range
from 1 to 4 million K.
 Solar corona changes along with sunspot cycle; it is much larger and more irregular at sunspot
peak
Features of the the Sun’s Surface
 The visible top layer of the Sun, the Photo-sphere, is the top convection zone and is granulated.
The areas of upwelling hot gas are bright, surrounded by areas of sinking cooler gas.
 Sunspots are the most fascinating of all the solar features. Galileo saw them in 1610 and they
have been studied actively ever since. They appear dark because they are slightly cooler than
the surroundings. The dark central part is the umbra and lighter surrounding part is the
penumbra
 The Sun reverses magnetic polarity every 11 years. Sun spots cycle through a maximum every
polarity cycle . It takes two 11 year half-cycles to make one full 22 year cycle
 Schematic Formation of Sunspots : Notice the interaction between magnetic field lines and the
differential rotation. Magnetic lines trapped in the plasma stretch and break to form Sun Spots
They are like the ends of bar magnets with lines of force looping between them.
 At the beginning of a half cycle most of the Sun spots are near 30 degrees north and south. By
the end most are nearer the equator
 The number of Sunspots go through a maximum each half cycle. Some half cycles show more
activity than others.
 Over the years efforts have been made, with few successes, to correlate sun spot activity with
events on the Earth. The coincidence of the Maunder minimum with the mini-ice-age in Europe
is often designated as a cause-and-effect.
 A Solar flare is a large explosion on Sun’s surface, driving matter into space in seconds or
minutes. This matter adds to the Solar Wind.
 Hot matter escapes Sun often through coronal holes in Coronal Mass Ejections, which can be
seen in X-ray images as bright white spots
Neutrinos
 are emitted directly from the core of the Sun, and escape, interacting with virtually nothing.
 Being able to observe these neutrinos would give us a direct picture of what is happening in the
core. Unfortunately, they are no more likely to interact with Earth-based detectors than they are


with the Sun; the only way to spot them is to have a huge detector volume and to be able to
observe single interaction events.
This is a large solar neutrino detector. Interactions (dim flashes) take place in the liquid, which
reaches the top of the dome when full, Detection is by the glass photomultiplier tubes.
Detection of solar neutrinos has been going on for more than 30 years now; despite very
different detection methods and energy sensitivities, all experiments agree that they are seeing
about 30–50% of the expected number of neutrinos. Could be:
•
Problem with solar model
•
Problem with our understanding and detection of neutrinos
• The second option seems more likely today.
Chapter 16
The Nature of Stars
Stellar Distance Scales
• Light Year = the distance that light travels in one year
• Parsec = the distance to a point where 1 AU subtends one second of arc
• Remember that nearby stellar distances can be measured using parallax
Nearest star to the Sun is
• Proxima Centauri which is a member of a 3-star system: Alpha Centauri complex
• Model of distances:
o Sun is a marble, Earth is a grain of sand orbiting 1 m away
o Nearest star is another marble 270 km away
o Solar system extends about 50 m from Sun; rest of distance to nearest star is basically
empty
Brightest stars
• were known to, and named by, the ancients (Procyon)
• In 1604, stars within a constellation were ranked in order of brightness, and labeled with
Greek letters (Alpha Centauri)
• In the early 18th century, stars were numbered from west to east in a constellation (61
Cygni)
• As more and more stars were discovered, different naming schemes were developed (G5115, Lacaille 8760, S 2398)
• Now, new objects are simply labeled by their celestial coordinates
Brightness Scales
 Apparent magnitude
o Hippachus
o 1st to 6th
o Spica (1st Mag), Vega (0 Mag)
 Brightness (Luminocity)
o measured by light meter
Absolute Magnitude
 An Apparent Magnitude difference of 5 represents a Brightness ratio of 100/1
 The Absolute Magnitude (M) of stars is defined as the apparent magnitude that the star
would have if were at 10 parsecs distance. Then the following ratio holds:
M
m
 2
2
10
d
Note: This is not exact – there are constants left out
Luminosity, or absolute brightness,
o is a measure of the total power radiated by a star.
 Apparent brightness is how bright a star appears when viewed from Earth; it depends on
the absolute brightness but also on the distance of the star Two stars that appear equally
bright might be a dimmer, nearer star and a brighter, farther star
Temperature
 The color of a star is indicative of its temperature. Red stars are relatively cool, while blue ones
are hotter.
 Spectral classes make up a Temperature Sequence
O, B, A, F, G, K, M
o Hottest
o M coolest
o Oh Be A Fine Girl Kiss Me
Size
 For the vast majority of stars that cannot be imaged directly, size must be calculated knowing
the luminosity and temperature:


 Supergiant stars are more than 100 solar radii
 Giant stars are between 10 and 100 solar radii
 Upper main sequence stars are 8 to 100 solar radii
 Average stars are .5 to 8 solar radii
 Dwarf stars are ,1 to .5 solar radii
Ejnar Hertzsprung (8 Oct, 1873 - 21 Oct, 1967) was a Danish chemist and astronomer. Henry Norris
Russell (Oct 25, 1877 – Feb 18, 1957) was an American Astronomer.
 Together they invented one of most useful graphs in Astronomy
 The Hertzsprung– Russell Diagram
o The H–R diagram plots stellar luminosity against surface temperature. This is an H–R
diagram of a few prominent stars
o Once many stars are plotted on an H–R diagram, a pattern begins to form. These are the
80 closest stars to us; note the dashed lines of constant radius.The darkened band is
called the main sequence, as this is where most stars are.
o An H–R diagram of the 100 brightest stars looks quite different, These stars are all more
luminous than the Sun. Two new categories appear here – the red giants and the blue
giants.
o Clearly, the brightest stars in the sky appear bright because of their enormous
luminosities, not their proximity.
 Major Sections of the H-R Diagram.
o They start with the Main Sequence
o then the two Giant Stages
o then finally the White Dwarf Stage
 About 90% of stars lie on the main sequence; 9% are giants and 1% are white dwarfs.
Spectroscopic parallax:
 has nothing to do with parallax,
 but does use spectroscopy to extend our ability to determine the distance to a star
1. Measure the star’s apparent magnitude (brightness) and spectral class (temperature)
2. Use temperature to estimate luminosity
3. Apply inverse-square law to find distance
 Spectroscopic parallax can extend the cosmic distance scale to several thousand parsecs.
 The spectroscopic parallax calculation can be misleading if the star is not on the main sequence.
The width of spectral lines can be used to define luminosity classes
Determination of Stellar Masses
 Many stars are in binary pairs; measurement of their orbital motion allows determination of the
masses of the stars.
 Visual binaries can be measured directly; this is Kruger 60:
 Study of spectral lines reveals the motion of spectroscopic binaries and hence their spacing.
From that the masses are calculated.
 The mass of a star is also correlated with its radius, and very strongly correlated with its
luminosity.
 Mass is also related to stellar lifetime

Using the mass–luminosity relationship

The most massive stars have the shortest lifetimes – they have a lot of fuel but burn it at a very
rapid pace.
On the other hand, small red dwarfs burn their fuel extremely slowly, and can have lifetimes of a
trillion years or more.

Chapter 17
Formation of Stars
Star formation
 is an ongoing process in the Universe. Star-forming regions are seen in our galaxy as well as
others
 Star formation happens when part of a dust cloud begins to contract under its own gravitational
force; as it collapses, the center becomes hotter and hotter until nuclear fusion begins in the
core.
 When looking at just a few atoms, the gravitational force is nowhere near strong enough to
overcome the random thermal motion. Even a massive cloud of gas and dust will remain just a
cloud until some shock wave or pressure wave arrives to initiate its gravitational collapse
 The collapse process from nebula to star is similar for all stars and can be followed by observing
the temperature produced by the compression
Stages of Star Formation
 Stage 1: An interstellar cloud starts to contract, probably triggered by a shock or pressure wave.
As it contracts, the cloud fragments into smaller, irregular size pieces.
 Stage 2:
o





Individual cloud fragments begin to collapse. Once the density is high enough, there is
no further fragmentation.
Stage 3:
o The interior of the fragment has begun heating, and is about 10,000 K.
Stage 4:
o The core of the cloud is now a protostar, and the surface temperature is high enough to
make its first appearance on the H–R diagram
Stage 5
o Planetary formation around the star has likely begun, but the protostar itself is still not
in equilibrium – all heating that effects the system comes from the gravitational
collapse.
The last stages can be followed on the H–R diagram.
The protostar’s luminosity decreases even as its temperature rises because it is becoming
more compact.
Stage 6
o the core reaches 10 million K, and nuclear fusion begins.
o The protostar has become a star but it not yet on the main sequence.
o This stage is often called the T Tauri stage and it is a period of adjustment. T Tauri stars
are mostly between 105 and 108 years in age, are of low mass (0.5 to 3.0 M¤),
surrounded by hot, dense envelopes; and are losing mass via stellar winds with typical
v¥= ~100 km/s.
Stage 7
o
o
The star continues to contract and increase in temperature, until it is in equilibrium.
The star has reached the main sequence and will remain there as long as it has hydrogen
to fuse.
The Main Sequence
 The main sequence is a band, rather than a line, because stars of the same mass can have
different compositions.
 Most important: Stars do not move along the main sequence! Once they reach it, they are in
equilibrium, and do not move until their fuel begins to run out.
Chapter 18
Evolution from the Main Sequence
During its stay on the main sequence, any fluctuations in a star’s condition are quickly restored; the star
is in equilibrium
Again to follow the post-main-sequence evolution of a star we will resort to the stage method. Not
every star adheres to this sequence but it serves to describe the steps that many stars take’
Even while on the main sequence, Stage 7, the composition of a star’s core is changing.
 Eventually, as hydrogen in the core is consumed, the Star leaves the main sequence,
 Stage 8.
o Its evolution from then on depends very much on the mass of the star:
o


Low-mass stars go quietly. Medium-mass stars struggle. High-mass stars go out with a
bang!
o When the fuel in the core is used up the fusion ceases. The result is a contraction of the
Star and the formation of a new fusion furnace in a shell around the helium core.
Stage 9: The Red-Giant Branch.
o The now much larger surface of the furnace causes outer layers of the star to expand
and cool. It is now a red giant, extending out beyond the orbit of Mercury. Despite its
cooler surface temperature, its luminosity increases enormously due to its large size.
Stage 10: Helium fusion.
o Once the core temperature has risen to 100,000,000 K, the helium in the core can fuse,
through a three-alpha process:
o
The 8Be nucleus is highly unstable, and will decay in about 10–12 sec unless an alpha
particle fuses with it first. This is why high temperatures and densities are necessary.
o The helium flash: The pressure within the helium core is almost totally due to “electron
degeneracy” – two electrons cannot be in the same quantum state, so the core cannot
contract beyond a certain point. This pressure is almost independent of temperature so
when the helium starts fusing, the pressure cannot adjust and the core explodes
completely disrupting the surrounding shell furnace.
o Helium begins to fuse extremely rapidly; within hours to days the enormous energy
output is over, but the star is now on its way to White Dwarf
Stage 13
o Disruption of the hydrogen furnace throws the star out of equilibrium and it starts to
shrink, but it has much heat to dissipate from the Helium Flash. The result is the surface
gets smaller as the surface temperature gets higher, causing movement across the
graph toward the blue while maintaining nearly the same brightness.
Stages 11 and 12 depend very much on the mass of the star.
o From .5 to 1.4 solar masses the transition from the horizontal branch White Dwarf
goes smoothly.
o From 1.4 to about 5.5 solar masses they must shed the extras mass to get down to the
Chandrasakar limit of 1.4 solar masses, then they can transition to White Dwarf.
The Instability Strip, still Stage 10
 As the dying star moves along the horizontal branch it encounters a region, discovered by
Hertsprung, called the Instability Strip. The star becomes a variable star changing brightness
slightly in a very few days.
 Henrietta Levitt discovered a direct relationship of Period to Luminosity of the Cephied
Variables and the RR Lyra Variables
Some stars with more than about 5.5 solar masses have a different problem.
 The Helium flash becomes a permanent nuclear furnace.
 The Helium core fuses helium to carbon and the shield furnace continues to fuse Hydrogen to
Helium and the star is now in a some what stable state. Many stars go into a new Red Giant
condition for a period. This is the Asymptotic Giant Branch, Stage 11
Chapter 19
Death of Stars
Low Mass Stars on the lower Main Sequence of the H_R Diagram have extremely long lifetimes. Their
entire original mass of Hydrogen is available as fuel. When all the hydrogen of the star is used (fused to
Helium) it collapses quietly to a Helium White Dwarf
Stars with masses of about ½ M to about 8 M follow roughly the evolution of a 1 M star.
Mass Loss Among Red Giants
 Stars just larger than 1.4 M lose their extra mass through accelerated stellar wind
 Stars with masses up to 8 or 9 M often have their outer layers go unstable and explode. The
result is a Nova
o A Nova is seen from Earth as a sudden brightening of an existing star. The explosion is
very bright for a few days to weeks as the gas expands. Then it fades as the gas expands
and cools.
o This process can be repeated every 3 or 4 hundred years until the star reaches the mass
limit then it can go White Dwarf.
More than half the stars in the sky are double stars and are close enough to share matter when one
goes Giant. The larger star goes giant 1st and dumps its extra mass to the smaller Main Sequence star
until it is under the mass limit then it quietly goes to White Dwarf. When the now bloated 2nd star goes
giant it feeds back to the White Dwarf where it is ejected by explosion and we see it as a Nova.




A large star has a great number of shell fusion furnaces.
The ‘ashes’ from one furnace serves as fuel for the next.
The inner most ash layer is Iron.
A high-mass star can continue to fuse elements in its core right up to iron (after which the fusion
reaction is energetically un-favored).
As heavier elements are fused, the reactions go faster and the stage is over more quickly.
 A 20-solar-mass star will fuse carbon for about 10,000 years, but its iron core lasts less than a
year.
 On the left, nuclei gain mass through fusion; on the right they loose it through fission.
 Iron is the crossing point; when the core has fused to iron, no more fusion can take place.
 Many elements are formed during normal stellar fusion.
 Some are made during the supernova explosion.
A supernova is a one-time event – once it happens, there is little or nothing left of the progenitor star.
 There are two different types of supernovae, both equally common:
o Supernova I, which is a supernova explosion around a core which implodes
o Supernova II, which is an explosion of the core resulting in the complete destruction of
the star
A super nova has not occurred in our part of the Milky Way since the invention of the telescope so we
have not had the opportunity to study one up close. We have seen many in other galaxies as well as
remnants in our galaxy.
Supernovae I arise in two ways.
 The first kind, a single star SNI, comes from an explosion in the Silicon layer around the Iron
core of a large star.
 The second kind, comes from interaction of large binary stars.
 The iron is very reluctant to fuse. Sometimes the Oxygen and Silicon layers around the core
become unstable and explode, imploding the Iron to a Neutron Star
 Normally a large star would die as a Supernova. In a binary situation, however, it dumps its
excess mass over to its smaller companion and becomes a White Dwarf.
 The now very large companion finishes its life and goes giant dumping its excess matter on
the white dwarf.
 The multi-layered star around the white dwarf is very unstable and explodes in a Supernova
imploding the White Dwarf to a Neutron Star.
 The classic results of a Supernova I are the expanding debris of the explosion, a neutron star
and a Pulsar
The Crab Nebula
 is the result of a Supernova in 1054. It was observed and location recorded by the Chinese. We
see the expanding debris of the explosion today at that location.
Often as a large star ages much of the fuel is used up and deposited as ‘ash’ in the iron core. The inward
pressure on the iron core is enormous, due to the high mass of the star. As the core continues to
become more and more dense, the protons react with one another to become neutrons + a flood of
neutrinos + much energy.
These local hot spots initiate fusion of the iron which triggers formation of all of the elements more
massive than iron + more neutrinos and much more energy. The energy builds up in a cascade effect
producing a gigantic explosion and the complete destruction of the star, known as a Supernova II
 The classic results of a Supernova II are:
o Collapse of the iron core
o Flood of neutrinos
o Super explosion debris cloud
o Complete disassembly of the star
While doing a theoretical study of Supernovae Zwysic and Baade in the 1930’s predicted the existence of
Neutron Stars but they had never been seen even with the 200 inch Hale telescope on Mount Palomar.
The first one found, much later, was associated with a Pulsar in the Crab nebula.
Neutron Stars
 1–3 solar masses, are so dense that they are very small.
 about 10 km in diameter, compared to Manhattan.
 As the parent star collapses, the neutron core spins very rapidly, conserving angular
momentum. Typical periods are fractions of a second.
 Again as a result of the collapse, the neutron star’s magnetic field becomes enormously strong.
 In 1967 Jocelyn Bell led a group of graduate students at the University of Cambridge in England
in a search for Radio Sources in the sky. They discovered a source that emitted extraordinarily
regular pulses. After some initial confusion, it was realized that this was rardiation from a
neutron star, spinning very rapidly.
Why do neutron Stars pulse?
 Strong jets of matter and beams of light are emitted at the magnetic poles, as that is where they
can escape. If the rotation axis is not the same as the magnetic axis,
 the two beams will sweep out circular paths. If the Earth lies in one of those paths, we will see
the star blinking on and off.
 The velocities of the material in the Crab nebula can be extrapolated back, using Doppler shifts,
to the original explosion point.
Review of Death of Stars