Chapter 11: Our Star 11/18/15 5:14 PM
11.1 A Closer Look At The Sun
• Why does the Sun Shine
o It is powered by Nuclear Energy
▪ Nuclear Potential Energy (Core)/Luminosity = 10
o Weight of upper layer compresses lower layer
o Gravitational equilibrium:
▪ Gravity pulling in balances pressure pushing out.
o Energy balance:
▪ Thermal energy released by fusion in core balances
radiative energy lost from surface.
o Gravitational contraction…
▪ provided energy that heated the core as the Sun was
▪ Contraction stopped when fusion started replacing
the energy radiated into space.
• What is the Sun’s Structure We also discuss several other topics like star gas star cycle
o If you want to learn more check out wcupa
▪ 6.9 ⋅ 108 m
▪ (109 times Earth)
▪ 2 ⋅ 1030 kg
▪ (300,000 Earths)
▪ 3.8 ⋅ 1026 watts
o Composition (by mass):
▪ 70 % Hydrogen
▪ 28 % Helium
▪ 2 % heavier elements
o Solar wind:
▪ A flow of charged particles from the surface of the Sun
▪ Outermost layer of solar atmosphere
▪ ~1 million K
▪ Middle layer of solar atmosphere If you want to learn more check out kathleen mclaughlin uconn
▪ ~ 104–105 K
▪ Visible surface of the Sun
▪ ~ 6000 K
o Convection zone:
▪ Energy transported upward by rising hot gas
o Radiation zone:
▪ Energy transported upward by photons
▪ Energy generated by nuclear fusion If you want to learn more check out ecu marketing
▪ ~ 15 million K
11.2 Nuclear Fusion in the Sun
• How does nuclear fusion occur in the Sun We also discuss several other topics like econ 104 goffe quiz 2
▪ Big nucleus splits into smaller pieces.
▪ (Nuclear power plants)
▪ Small nuclei stick together to make a bigger one.
▪ (Sun, stars)
o High temperatures enable nuclear fusion in the core.
o The Sun releases energy by fusing four hydrogen nuclei into one helium nucleus.
▪ o Proton–proton chain fuses hydrogen into helium in the Sun. Don't forget about the age old question of gvsu sociology
▪ ▪ IN
???? 4 protons
???? 4He nucleus
???? 2 gamma rays
???? 2 positrons
???? 2 neutrinos
▪ Total mass is 0.7% lower.
• Solar Thermostat
o Decline in core temperature causes fusion rate to drop, so core contracts and heats up.
o Rise in core temperature causes fusion rate to rise, so core expands and cools down.
o • How does the energy from fusion get out of the Sun? o Energy gradually (over 100’s of thousands of years) leaks out of the radiation zone in the form of randomly bouncing photons.
o Convection (rising hot gas) takes energy to the surface through the convection zone.
o Bright blobs on photosphere where hot gas reaches the surface
• How do we know what is happening inside the Sun? o We learn about the inside of the Sun by
▪ making mathematical models
▪ observing solar vibrations
▪ observing solar neutrinos
o Patterns of vibration on the surface tell us about what the Sun is like inside.
o This plot shows Doppler shifts at Sun’s surface
o Data on solar vibrations agree with mathematical models of solar interior.
o Neutrinos created during fusion fly directly through the Sun.
o Observations of these solar neutrinos can tell us what’s happening in the core.
o Solar neutrino problem:
▪ Early searches (1960’s) for solar neutrinos by Ray Davis, Jr. didn’t find the number predicted by mathematical models.
▪ More recent (2000’s) observations find the right number of neutrinos, but some have changed form. ???? Ray Davis finally won Nobel Prize in 2002
11.3 The Sun–Earth Connection
• What causes solar activity?
o Solar activity is like “weather” on Earth.
▪ Solar flares
▪ Solar prominences
▪ All of these phenomena are related to magnetic
▪ Are cooler than other parts of the Sun’s surface
▪ Are regions with strong magnetic fields.
o Zeeman Effect
▪ We can measure magnetic fields in sunspots by
observing the splitting of spectral lines.
o Charged particles spiral along magnetic field lines. o This excludes hot plasma from entering sunspots. ▪
o Loops of bright gas called solar prominences often connect sunspot pairs.
o Magnetic activity causes solar flares that send bursts of X rays and charged particles into space.
o The corona appears bright in X-ray photos in places where magnetic fields trap hot gas.
o Coronal mass ejections send bursts of energetic charged particles out through the solar system, potentially toward Earth.
o Charged particles streaming from the Sun can cause geomagnetic storms, cause Northern Lights, disrupt electrical power grids, disrupt radio communications, and disable communications satellites.
• How does solar activity vary with time?
o The number of sunspots rises and falls in 11-year cycles.
▪ o The sunspot cycle is related to the winding and twisting of the Sun’s magnetic field.
▪ o Sunspot cycle and Earth’s climate
▪ Despite solar activity at surface, energy output remains the same to within 0.1%
▪ There have been periods of time where solar activity has virtually ceased (e.g. Maunder minimum from 1645 to 1715 corresponding to the Little Ice Age)
▪ Possible that solar activity can have some affect on Earth’s climate, but not certain
Reading Review Chapter 11 11/18/15 5:14 PM
1. According to modern science, approximately how old is the Sun?
a. 4.5 billion years
2. Which of the following correctly describes how the process of gravitational contraction can make a star hot?
a. When a star contracts in size, gravitational potential energy is converted to thermal energy.
b. Gravitational Contraction is a different energy generation mechanism from nuclear fusion
3. What two physical processes balance each other to create the condition known as gravitational equilibrium in stars? a. gravitational force and outward pressure
b. Surface tension is not important in the gravitational equilibrium of stars
4. The source of energy that keeps the Sun shining today is _________.
a. Nuclear Fusion
5. Energy balance in the Sun refers to a balance between _________.
a. the rate at which fusion generates energy in the Sun's core and the rate at which the Sun's surface radiates energy into space
6. From center outward, which of the following lists the "layers" of the Sun in the correct order?
a. Core, radiation zone, convection zone, photosphere,
7. What are the appropriate units for the Sun's luminosity? a. Watts
8. The overall result of the proton-proton chain is that __________.
a. 4H becomes 1H + energy
9. To estimate the central temperature of the Sun, scientists _________.
a. use computer models to predict interior conditions
10. How is the sunspot cycle directly relevant to us here on Earth?
a. Coronal mass ejections and other activity associated with the sunspot cycle can disrupt radio communications and knock out sensitive electronic equipment.
Chapter 12: Surveying the Stars 11/18/15 5:14 PM
12.1 Properties of Stars
• How do me measure stellar luminosity
o Brightness of a star depends on both distance and luminosity. o Luminosity:
▪ Amount of power a star radiates
▪ (energy per second = watts)
o Apparent brightness:
▪ Amount of starlight that reaches Earth
▪ (energy per second per square meter)
o Luminosity passing through each sphere is the same.
▪ Area of sphere:
???? 4π (radius)2
▪ Divide luminosity by area to get apparent brightness.
o The relationship between apparent brightness and luminosity depends on distance:
▪ Brightness = Luminosity/4π (distance)2
o We can determine a star’s luminosity if we can measure its distance and apparent brightness:
▪ Luminosity = 4π (distance)2 ⋅ (Brightness)
• Parallax is the apparent shift in position of a nearby object against a background of more distant objects.
o Apparent positions of the nearest stars shift by about an arcsecond as Earth orbits the Sun.
o The parallax angle depends on distance.
o Parallax is measured by comparing snapshots taken at different times and measuring the shift in the position of the star, which determines the parallax angle, p.
o Parallax and Distance
p = parallax angle
d (in parsecs) = 1
p (in arcseconds)
d (in light-years) = 3.26 ⋅1
p (in arcseconds)
o Most luminous stars:
o Least luminous stars:
o (LSun is luminosity of the Sun)
• The Magnitude Scale
o Used historically to represent luminosity and apparent brightness on a logarithmic scale
o Absolute magnitude denoted by “M” (related to luminosity) o Apparent magnitude denoted by “m” (related to apparent brightness)
o Smaller magnitudes represent brighter stars
o a difference of 5 magnitudes represents a factor of 100 in brightness or luminosity
o For example, a magnitude 1 star is 100 times brighter than a magnitude 6 star
• How do we measure stellar temperatures?
o o Review: every object emits thermal radiation with a spectrum that depends on its temperature.
o An object of fixed size grows more luminous as its temperature rises.
o In addition, the object’s color becomes more blue as its temperature rises
• Properties of Thermal Radiation
o Hotter objects emit more light per unit area at all frequencies. o Hotter objects emit photons with a higher average energy.
???? Hotter stars are bluer
???? Cooler stats are redder
o Level of ionization also reveals a star’s temperature. ▪
o Absorption lines in a star’s spectrum tell us its ionization level. • Pioneers of Stellar Classification
o Annie Jump Cannon and the “computers” at Harvard laid the foundation of modern stellar classification.
• Lines in a star’s spectrum correspond to a spectral type that reveals its temperature:
o (Hottest) O B A F G K M (Coolest)
o Hottest stars:
▪ 50,000 K
o Coolest stars:
▪ 3000 K
o (Sun’s surface is 5800 K)
• How do we measure stellar masses?
o o Binary Star Systems
▪ Systems of two stars that are gravitationally bound to each other
▪ Orbit of a binary star system depends on the strength of gravity, hence masses
▪ We can only measure the masses of stars directly if they are in binary systems
o Types of Binary Star Systems
▪ Visual binary
???? We can directly observe the orbital motions of
▪ Eclipsing binary
???? We can measure periodic eclipses.
▪ Spectroscopic binary
???? We determine the orbit by measuring Doppler
o About half of all stars are in binary systems.
• Mass of a Star
o We measure mass using gravity.
o Direct mass measurements are possible only for stars in binary star systems.
▪ p = period
▪ a = average separation
o Need two out of three observables to measure mass: ▪ Orbital period (p)
▪ Orbital separation (a or r = radius)
▪ Orbital velocity (v)
o For circular orbits, v = 2πr / p
o Most massive stars:
o Least massive stars:
▪ (MSun is the mass of the Sun.)
12.2 Patterns Among Stars
• What is a Hertzsprung–Russell diagram?
o An H-R diagram plots the luminosities and temperatures of stars.
o Luminosity rises from bottom to top
o Surface Temperature rises from right to left
o Most stars fall somewhere on the main sequence of the H-R diagram.
▪ o Stars with similar T and higher L than main-sequence stars must have larger radii: giants and supergiants
o Stars with similar T and lower L than main-sequence stars must have smaller radii: white dwarfs
o A star’s full classification includes spectral type (related to surface temperature) and luminosity class (related to the size): ▪ I — supergiant
▪ II — bright giant
▪ III — giant
▪ IV — subgiant
▪ V — main sequence
▪ Sun — G2 V
▪ Sirius — A1 V
▪ Proxima Centauri — M5.5 V
▪ Betelgeuse — M2 I
o H-R diagram depicts:
▪ Spectral type
• What is the significance of the main sequence?
o Main-sequence stars are fusing hydrogen into helium in their cores, like the Sun.
▪ Luminous main-sequence stars are hot (blue).
▪ Less luminous ones are cooler (yellow or red).
o Mass measurements of main-sequence stars show that the hot, blue stars are much more massive than the cool, red ones.
o The mass of a normal, hydrogen-fusing star determines its luminosity and spectral type.
o o The core temperature of a higher-mass star needs to be higher in order to balance gravity.
o A higher core temperature boosts the fusion rate, leading to greater luminosity.
• Stellar Properties Review
o Luminosity: from apparent brightness and distance ▪ 10-4LSun– 106LSun
▪ Main Sequence Stars: 0.08MSun - 100MSun
o Temperature: from color and spectral type
▪ 3000 K – 50,000 K
o Mass: from period (p) and average separation (a) of binary star orbit
▪ 0.08MSun – 100MSun
• Mass and Lifetime
o Sun’s life expectancy: 10 billion years
▪ Until core hydrogen (10% of total) is used up
o Life expectancy of a 10MSun star:
▪ 10 times as much fuel, uses it 104 times as fast
▪ 10 billion years × 10/104 ~ 10 million years
o Life expectancy of a 0.3MSun star:
▪ 0.3 times as much fuel, uses it 0.01 times as fast
▪ 10 billion years × 0.3/0.01 ~ 300 billion years
???? High luminosity
???? Large radius
???? Low luminosity
???? Small radius
• What are giants, supergiants, and white dwarfs?
• Off the Main Sequence
o Stellar properties depend on both mass and age: those that have finished fusing H to He in their cores are no longer on the main sequence.
o All stars become larger and redder after exhausting their core hydrogen: giants and supergiants.
o Most stars end up small and white after fusion has ceased: white dwarfs.
▪ Supergiants and Giants: Large radii
▪ White Dwarfs: small radii
• Relative radii
o o Giants and supergiants are far larger than main-sequence stars and white dwarfs.
12.3 Star Clusters
• What are the two types of star clusters?
o Open cluster: A few thousand loosely packed stars, found in the Galactic disc
o Globular cluster: Up to a million or more stars in a dense ball bound together by gravity, found in the Galactic halo ▪
• How do we measure the age of a star cluster?
o o Massive blue stars die first, followed by white, yellow, orange, and red stars.
o Pleiades cluster now has no stars with a life expectancy less than 100 million years.
▪ o The main-sequence turnoff point of a cluster tells us its age.
▪ o To determine accurate ages, we compare models of stellar evolution to the cluster data.
o Detailed modeling of the oldest globular clusters reveals that they are about 13 billion years old.
Reading Review Ch. 12 11/18/15 5:14 PM Reading Review 12a
1. The total amount of power (in watts, for example) that a star radiates into space is called its _________.
2. According to the inverse square law of light, how will the apparent brightness of an object change if its distance to us triples?
a. Its apparent brightness will decrease by a factor of 9.
3. Assuming that we can measure the apparent brightness of a star, what does the inverse square law for light allow us to do? a. Calculate the star's luminosity if we know its distance, or calculate its distance if we know its luminosity.
4. If star A is closer to us than star B, then Star A's parallax angle is _________.
a. larger than that of Star B
5. Thermal radiation is defined as _________.
a. radiation with a spectrum whose shape depends only on the temperature of the emitting object
6. According to the laws of thermal radiation, hotter objects emit photons with ________
a. A shorter average wavelength
7. Suppose you want to know the chemical composition of a distant star. Which piece of information is most useful to you? a. The wavelengths of spectral lines in the star’s composition
Reading Review 12b
1. From hottest to coolest, the order of the spectral types of stars is _________.
2. Astronomers can measure a star's mass in only certain cases. Which one of the following cases might allow astronomers to measure a star's mass?
a. The star is a member of a binary star system.
3. The axes on a Hertzsprung-Russell (H-R) diagram represent _________.
a. luminosity and surface temperature
4. On an H-R diagram, stellar radii _________.
a. increase diagonally from the lower left to the upper right
5. On an H-R diagram, stellar masses _________.
a. can be determined for main sequence stars but not for other types of stars
6. How is the lifetime of a star related to its mass? a. More massive stars live much shorter lives than less massive stars.
7. What is the common trait of all main sequence stars? a. They generate energy through hydrogen fusion in their core.
8. What do we mean by the main-sequence turnoff point of a star cluster, and what does it tell us?
a. It is the spectral type of the hottest main sequence star in a star cluster, and it tells us the cluster's age.
Chapter 13: Star Stuff 11/18/15 5:14 PM
13.1 Star Birth
• How do stars form?
o Star-Forming Clouds
▪ Stars form in cold, dark clouds of dusty gas in
▪ The gas between the stars is called the interstellar
• Gravity Versus Pressure
o Gravity can create stars only if it can overcome the force of thermal pressure in a cloud: need a cold cloud
o Gravity within a contracting gas cloud becomes stronger as the gas becomes denser: need a dense cloud
• Mass of a Star-Forming Cloud
o A typical molecular cloud (T = 30 K, density = 300
particles/cm3) must contain at least a few hundred solar
masses for gravity to overcome pressure
o The cloud can prevent a pressure buildup by converting
thermal energy into infrared and radio photons that escape
• Fragmentation of a Cloud
o This simulation begins with a turbulent cloud 1.2 light
years in diameter containing 50 solar masses of gas.
o The random motions of different sections of the cloud
cause it to become lumpy.
o Each lump of the cloud in which gravity can overcome pressure can go on to become a star.
o A large cloud can make a whole cluster of stars.
• Glowing Dust Grains
o As stars begin to form, dust grains absorb visible light, heat up, and emit infrared light.
???? Main figure: infrared
???? Inset: visible
o Long-wavelength infrared light is brightest from regions where many stars are currently forming.
▪ • Thermal Pressure
o Thermal pressure is the result of particles speeding up when the temperature is raised
o If gas heats up then the pressure increases, causing it to expand
o Solar system formation is a good example of star birth. o Cloud heats up as gravity causes it to contract due to conservation of energy. Contraction can continue if thermal energy is radiated away.
o As gravity forces a cloud to become smaller, it begins to spin faster and faster, due to conservation of angular momentum.
o Gas settles into a flat, spinning disk because of collisions between particles.
• Formation of Jets
o Rotation also causes jets of matter to shoot out along the rotation axis.
o Jets are observed coming from the centers of disks around protostars.
• Protostar to Main Sequence
o A protostar contracts and heats until the core temperature is sufficiently high for hydrogen fusion.
o Contraction ends when energy released by hydrogen fusion balances energy radiated from the surface.
o It takes 30 million years for a star like the Sun (less time for more massive stars).
• Summary of Star Birth
o Gravity causes gas cloud to shrink and fragment. o Core of shrinking cloud heats up.
o When core gets hot enough, fusion begins and stops the shrinking.
o New star achieves long-lasting state of balance.
• How massive are newborn stars?
o Low-mass stars are common.
o Very massive stars are rare.
o A cluster of many stars of various masses can form out of a single cloud.
• Upper Limit on a Star’s Mass
o Photons exert a slight amount of pressure when they strike matter.
o Very massive stars are so luminous that the collective pressure of photons drives their matter into space.
o Models of stars suggest that radiation pressure limits how massive a star can be without blowing itself apart.
o Observations have not found stars more massive than about 300MSun.
• Lower Limit on a Star’s Mass
o Fusion will not begin in a contracting cloud if some sort of force stops contraction before the core temperature rises above 107 K.
o Thermal pressure cannot stop contraction because the star is constantly losing thermal energy from its surface through radiation.
o Is there another form of pressure that can stop
▪ Degeneracy Pressure:
???? Laws of quantum mechanics prohibit two
electrons from occupying the same state.
???? ▪ Thermal Pressure:
???? Depends on temperature
???? The main form of pressure in most stars
▪ Degeneracy Pressure:
???? Particles can’t be in same state
???? Doesn’t depend on temperature
• Brown Dwarfs
o Degeneracy pressure halts the contraction of objects with <0.08MSun before the core temperature becomes hot enough for fusion.
o Starlike objects not massive enough to start fusion are brown dwarfs.
o A brown dwarf emits infrared light because of heat left over from contraction.
o Its luminosity gradually declines with time as it loses thermal energy.
• Brown Dwarfs in Orion
o Infrared observations can reveal recently formed brown dwarfs because they are still relatively warm and luminous. o Stars more massive than 300MSun would blow apart.
o Stars less massive than 0.08MSun can’t sustain fusion. o
13.2 Life as a Low-Mass Star
• What are the life stages of a low-mass (less than 2 solar masses) star?
o A star remains on the main sequence as long as it can fuse hydrogen into helium in its core.
o Its main sequence lifetime depends on its mass
o What happens next?
• Life Track After Main Sequence
o Observations of star clusters show that a star becomes larger, redder, and more luminous after its time burning H into He on the main sequence is over.
o Helium fusion does not begin right away because it requires higher temperatures than hydrogen fusion—larger charge leads to greater repulsion.
o The fusion of two helium nuclei doesn’t work, so helium fusion must combine three He nuclei to make carbon.
o • Broken Thermostat
o As the core contracts, H begins fusing to He in a shell around the core.
o Luminosity increases because the core thermostat is broken—the increasing fusion rate in the shell does not stop the core from contracting.
o Expansion of star to radiate high luminosity
• Helium Flash
o The thermostat is broken in a low-mass red giant because degeneracy pressure supports the core.
o The core temperature rises slowly before helium fusion begins.
o The core temperature rises rapidly when helium fusion begins.
o The helium fusion rate skyrockets until thermal pressure takes over and expands the core again.
o o After helium flash, helium core fusion stabilizes
o Helium core-fusion stars neither shrink nor grow because the core thermostat is temporarily fixed.
• Life Track After Helium Flash
o Models show that a red giant should shrink and become less luminous after helium fusion begins in the core. o Why? Because the core expands and hydrogen shell fusion rate slows
o Observations of star clusters agree with these models. o Helium core-fusion stars are found in a horizontal branch on the H-R diagram.
o • How does a low-mass star die?
• Double Shell Fusion
o After core helium fusion stops, He fuses into carbon in a shell around the carbon core, and H fuses to He in a shell around the helium layer.
o This double shell–fusion stage never reaches equilibrium— the fusion rate periodically spikes upward in a series of thermal pulses.
o • Planetary Nebulae
o Double-shell fusion ends with a pulse that ejects the H and He into space as a planetary nebula.
o The core left behind becomes a white dwarf.
o Double shell–fusion ends with a pulse that ejects the H and He into space as a planetary nebula.
o The core left behind becomes a white dwarf.
• End of Fusion
o Fusion progresses no further in a low-mass star because the core temperature never grows hot enough for fusion of heavier elements (although some He fuses with C to make oxygen).
o Degeneracy pressure supports the white dwarf against gravity.
• Life of a Low-Mass Star
o • Life Track of a Sun-Like Star
• What is the fate of Earth?
o During its red giant phase (5 billion years from now), the Sun’s surface will expand almost to the Earth’s orbit,
raising temperatures to 1000 K
o However, slight increases in the luminosity of the Sun will likely cause a runaway greenhouse effect in 1-4 billion years, evaporating Earth’s oceans
o We will need to find another planet or moon to live on before then, if we are still around
13.3 Life as a High-Mass Star
• What are the life stages of a high-mass (greater than 8 solar masses) star?
o • CNO Cycle
o High-mass main- sequence stars fuse H to He at a higher rate using carbon, nitrogen, and oxygen as catalysts
o A greater core temperature enables H nuclei to overcome greater electrostatic repulsion.
• Life Stages of High-Mass Stars
o Life stages of high-mass stars are similar to those of low mass stars:
▪ Hydrogen core fusion (main sequence)
▪ Hydrogen shell fusion (supergiant)
▪ Helium core fusion* (supergiant)
▪ High mass stars form supergiants when they turn off the main sequence
• How do high-mass stars make the elements necessary for life? o
o ▪ Big Bang made 75% H, 25% He—stars make
o ▪ Helium fusion can make carbon in low-mass stars. • Helium Capture in high-mass stars
o High core temperatures allow helium to fuse with heavier elements.
▪ Helium capture builds C into O, Ne, Mg …
• Advanced Nuclear Burning
▪ Core temperatures in stars with >8MSun allow fusion of elements as heavy as iron.
o ▪ Advanced reactions in stars make elements such as Si, S, Ca, and Fe.
• Multiple Shell Burning
o Advanced nuclear burning proceeds in a series of nested “onion-like” shells.
o o Iron is a dead end for fusion because nuclear reactions involving iron do not release energy.
o (Iron has lowest mass per nuclear particle.)
▪ • Evidence for origin of the elements
o It takes some time for stars to synthesize heavier elements from hydrogen and helium (it is still happening now) o Oldest stars (in globular clusters) have less than 0.1% of their mass composed of elements other than hydrogen and helium
o Young stars (in open clusters) contain 2-3% of their mass in the form of heavy elements
o • How does a high-mass star die?
o Iron builds up in the core until degeneracy pressure can no longer resist gravity.
o The core then suddenly collapses, creating a supernova explosion.
• Supernova Explosion
o Core degeneracy pressure eliminated because electrons combine with protons, making neutrons and neutrinos. o Neutrons collapse to the center, forming a neutron star or a black hole
o ▪ Energy and neutrons released in a supernova
explosion may enable elements heavier than iron to form, including Gold (Au) and Uranium (U)
• Supernova energy
o Comes from gravitational potential energy release during core collapse
o Instantaneously releases more than 100 times the energy the Sun radiates in its entire 10 billion-year lifetime! o A supernova can outshine its entire host galaxy! • Supernova Remnant
o Energy released by the collapse of the core drives outer layers into space.
o The Crab Nebula is the remnant of the supernova seen in A.D. 1054.
• Supernova 1987A
o The closest supernova in the last four centuries was seen in 1987.
• How does a supernova explode?
o We don’t exactly know: one of the biggest questions in astrophysics!
o Idea 1: neutron degeneracy pressure makes the collapsing core “bounce” back creating an outgoing shock wave o Idea 2: outgoing neutrinos interact with dense
surroundings, producing an outgoing shock wave
• Summary: Role of Mass
o A star’s mass determines its entire life story because it determines its core temperature.
o High-mass stars have short lives, eventually becoming hot enough to make iron, and end in supernova explosions. o Low-mass stars have long lives, never become hot enough to fuse carbon nuclei, and end as white dwarfs.
• Summary: Life Stages of Low-Mass Star
o Protostar: cloud of gas collapses under gravity
o Main Sequence: H fuses to He in core
o Red Giant: H fuses to He in shell around He core until He flash
o Helium Core Fusion: He fuses to C in core while H fuses to He in shell
o Double Shell Fusion: H and He both fuse in shells o Planetary Nebula: outer layers expelled
o White dwarf star left behind
o • Summary: Reasons for Life Stages
o Core shrinks and heats until it’s hot enough for fusion.
o Nuclei with larger charge require higher temperature for fusion.
o Core thermostat is broken while core is not hot enough for fusion (shell burning).
o Core fusion can’t happen if degeneracy pressure keeps core from shrinking.
• Summary: Life Stages of High-Mass Star
o Protostar: cloud of gas collapses under gravity
o Main Sequence: H fuses to He in core
o Red Supergiant: H fuses to He in shell around He core o Helium Core Fusion: He fuses to C in core while H fuses to He in shell
o Multiple Shell Fusion: many elements fuse in shells o Supernova explosion after iron core collapses
o Neutron star or black hole left behind
o • What about intermediate-mass stars?
o What about stars with masses between 2 and 8 solar masses?
o Burn hydrogen by CNO cycle
o Produce a white dwarf with more oxygen and neon than low-mass stars, but no iron core
o Never undergo core collapse to neutron star or black hole (no supernova)
13.4 Stars in Close Binaries
• How are the lives of stars with close companions different? o
• Thought Question
o The binary star Algol consists of a 3.7MSun main- sequence star and a 0.8MSun subgiant star.
o What’s strange about this pairing?
o How did it come about?
o o Stars in Algol are close enough that matter can flow from the subgiant onto the main-sequence star.
o The star that is now a subgiant was originally more massive.
o As it reached the end of its life and started to grow, it began to transfer mass to its companion (mass exchange). o Now the companion star is more massive.
Reading Review Ch. 13 11/18/15 5:14 PM Reading Review 13a
1. Most interstellar clouds remain stable in size because the force of gravity is opposed by _______ within the cloud.
a. thermal pressure
2. What kind of gas cloud is most likely to give birth to stars? a. a cold, dense gas cloud
3. When does a protostar become a main-sequence star?
a. when the rate of hydrogen fusion becomes high enough to balance the rate at which the star radiates energy into space
4. Approximately what core temperature is required before hydrogen fusion can begin in a star?
a. 10 million K
5. What is the approximate range of masses that newborn main sequence stars can have?
a. 0.1 to 150 solar masses
6. What can we learn about a star from a life track on an H-R diagram? a. the surface temperature and luminosity the star will have at each stage of its life
7. Which of the following lists the stages of life for a low-mass star in the correct order?
a. protostar, main-sequence star, red giant, planetary nebula, white dwarf
8. The main source of energy for a star as it grows in size to become a red giant is _________.
a. hydrogen fusion in a shell surrounding the central core
1. What happens when a main-sequence star exhausts its core hydrogen fuel supply?
a. The core shrinks while the rest of the star expands.
2. In order to predict whether a star will eventually fuse oxygen into a heavier element, you mainly want to know what fact about the star? a. its mass
3. Why is iron significant to understanding how a supernova occurs? a. Iron cannot release energy either by fission or fusion
Chapter 14: The Bizarre Stellar Graveyard11/18/15 5:14 PM
14.1 White Dwarfs
• What is a white dwarf?
• White Dwarfs
o White dwarfs are the remaining cores of dead stars.
o Electron degeneracy pressure supports them against gravity.
o o White dwarfs cool off and grow dimmer with time.
• Size of a White Dwarf
o o White dwarfs with the same mass as the Sun are about the same size as Earth
o Higher-mass white dwarfs are smaller
o Density of a few tons in a teaspoon
• The White Dwarf Limit
o Quantum mechanics says that electrons must move faster as they are squeezed into a very small space.
o As a white dwarf’s mass approaches 1.4MSun, its electrons must move at nearly the speed of light.
o Because nothing can move faster than light, a white dwarf cannot be more massive than 1.4MSun, the white dwarf limit (also known as the Chandrasekhar limit).
▪ Subrahmanyan Chandrasekhar (1910 – 1995)
▪ Nobel Prize 1983
o • What can happen to a white dwarf in a close binary system? o
• Accretion Disks
o Mass falling toward a white dwarf from its close binary companion has some angular momentum.
o The matter therefore orbits the white dwarf in an accretion disk.
o Friction between orbiting rings of matter in the disk transfers angular momentum outward and causes the disk to heat up and glow.
o The temperature of accreted matter eventually becomes hot enough (~10 million K) for hydrogen fusion.
o Fusion begins suddenly and explosively, causing a nova.
o The nova star system temporarily appears much brighter: 100,000 solar luminosities
o The explosion drives accreted matter out into space. o Can be recurrent
• Two Types of Supernova
o Massive star supernova:
▪ Iron core of massive star reaches white dwarf limit and collapses into a neutron star, causing an explosion.
o White dwarf supernova:
▪ Carbon fusion suddenly begins as white dwarf* in close binary system approaches white dwarf limit, causing a total explosion.
o One way to tell supernova types apart is with a light curve showing how luminosity changes with time.
o • Supernova Types:
• Massive Star or White Dwarf?
o Light curves differ (see previous slide)
o Spectra differ (exploding white dwarfs don’t have hydrogen absorption lines)
• Nova or White Dwarf Supernova?
o White dwarf supernovae are 100 000 times more luminous at peak than novae
o Nova: H to He fusion of a layer of accreted matter; white dwarf left intact
o White dwarf supernova: complete explosion of white dwarf(s)*; nothing left behind
14.2 Neutron Stars
• What is a neutron star?
o A neutron star is the ball of neutrons left behind by a massive star supernova.
o The degeneracy pressure of neutrons supports a neutron star against gravity.
o Electron degeneracy pressure goes away because electrons combine with protons, making neutrons and neutrinos.
o Neutrons collapse to the center, forming a neutron star. o
o A neutron star is about the same size as a small city. o • Neutron stars are extremely dense!
o o Recall that atoms are almost entirely empty space, imagine compressing matter to fill space with nuclei
o Masses ranging from 1.4 MSun to 3 MSun compressed into a 12 or 13-km radius
o A paperclip of this material would fall through Earth like a rock through air
• Neutron stars have extreme surface gravity!
o An object dropped from 1 m above the surface of a neutron star would land with a speed of roughly 2000 km/s or 7 million km/hr
o If a neutron star approached Earth, the Earth would fall onto the neutron star, forming a layer on the surface about as thick as your finger
o Escape velocity is nearly half the speed of light
• How were neutron stars discovered?
o • Brief history of neutron stars
o 1920: Rutherford proposes the neutron theoretically o 1933: Chadwick discovers the neutron experimentally o 1934: Baade and Zwicky propose the existence of neutron stars
o 1967: Bell and Hewish discover a neutron star…
• Discovery of Neutron Stars
o o Using a radio telescope in 1967, Jocelyn Bell noticed very
regular pulses of radio emission coming from a single part of the sky.
o The pulses were coming from a spinning neutron star—a pulsar.
• A little bit of history
o At first, they didn’t see how nature could produce such a source and they labeled it LGM-1 for “Little Green Men”
o Eventually, they discovered more sources and realized they were spinning neutron stars
o Hewish received the Nobel prize in 1974 for the discovery when Bell was 31
o Very controversial that Bell was excluded: sexism and ageism?
o o ▪ Blue: X Rays
▪ Red: Visible Light
o A pulsar is a neutron star that beams radiation along a magnetic axis that is not aligned with the rotation axis. o The radiation beams sweep through space like lighthouse beams as the neutron star rotates.
o Periods of milliseconds to seconds, decreasing with time
• Why Pulsars Must Be Neutron Stars
o Circumference of Neutron Star = 2π (radius) ~ 60 km o Spin Rate of Fast Pulsars ~ 1000 cycles per second o Surface Rotation Velocity ~ 60,000 km/s
▪ 20% speed of light
▪ escape velocity from NS
o Anything larger would be torn to pieces!
o Pulsars spin fast (up to nearly 1000 times per second!) because the spin of the massive star’s core increases as it collapses into a neutron star.
▪ Conservation of angular momentum
• What can happen to a neutron star in a close binary system?
o o Matter falling toward a neutron star forms an accretion disk, just as in a white dwarf binary.
o Due to huge gravitational potential-energy release the disk heats and emits x-rays, becoming an X-ray binary. o Accreting matter adds angular momentum to a neutron star, increasing its spin.
o Episodes of fusion on the surface lead to X-ray bursts.
o • X-Ray Bursts
o Matter accreting onto a neutron star can eventually become hot enough for helium to fuse.
o The sudden onset of fusion produces a burst of X rays and new elements.
• National Superconducting Cyclotron Laboratory (NSCL) o We do a lot of work next door at NSCL to understand
explosive nucleosynthesis in novae, supernovae, and x-ray bursts
o This is done using beams of rare isotopes (radioactive atoms) o MSU has #1 Nuclear Physics PhD program in U.S. (for
comparison, MIT is #3)
• Facility for Rare Isotope Beams (FRIB)
o FRIB will allow us to do this even better by providing more rare isotopes
o $700,000,000 project funded by U.S. Department of Energy and the State of Michigan
o Scheduled for completion by early 2020’s
• Neutron Star Mass Limit
o Neutron degeneracy pressure supports a neutron star against gravitational collapse
o Neutron degeneracy pressure can no longer support a neutron star against gravity if its mass exceeds 2-3MSun
14.3 Black Holes: Gravity’s Ultimate Victory
• What is a black hole?
o A black hole is an object whose gravity is so powerful that not even light can escape it. The escape velocity is greater than the speed of light.
o Some massive star supernovae can make a black hole if enough mass falls onto the core.
o Light would not be able to escape Earth's surface if you could shrink it to <1 cm.
• Surface of a Black Hole
o The “surface” of a black hole is the radius at which the escape velocity equals the speed of light.
o This spherical surface is known as the event horizon. o The radius of the event horizon is known as the Schwarzschild radius.
o o Schwarzschild radius is larger for black holes of larger mass. o Schwarzschild radius = 3.0 x Mblack hole/Msun km
o Eg. Schwarzschild radius for a black hole with three solar masses is 9 km
o Eg. Schwarzschild radius for a black hole with a billion solar masses is 3 billion km
o Event horizon is larger for black holes of larger mass. o Schwarzschild radius = 3.0 x Mblack hole/Msun km
o Eg. Schwarzschild radius for a black hole with three solar masses is 9 km
o The event horizon of a 3MSun black hole is about as big as a small city.
o Schwarzschild radius for a black hole with a billion solar masses is 3 billion km:
▪ orbital radius of Uranus around Sun
• General Relativity
o Invented by Einstein between 1907 and 1915
o Gravity bends space and time
o Rules of geometry are different when space isn’t flat o Mass of Sun curves space and time weakly
o Planets follow straightest path on curved space
▪ o Light is bent or “gravitationally lensed” by curved space and time
o Can test General Relativity using objects behind the Sun o A black hole’s mass strongly warps space and time in the vicinity of the event horizon.
• No Escape
o Nothing can escape from within the event horizon because nothing can go faster than light.
o No escape means there is no more contact with an object that falls in. The object increases the black hole’s mass, changes its spin or charge, but otherwise loses its identity. o
o Beyond the neutron star limit, no known force can resist the crush of gravity
o As far as we know, gravity crushes all the matter into a single point known as a singularity
o Physics of singularities is not understood (general relativity + quantum mechanics)
• What would it be like to visit a black hole?
o If the Sun shrank into a black hole, its gravity would be different only near the event horizon.
o Black holes don’t suck in objects orbiting them!
o Light waves take extra time to climb out of a deep hole in spacetime, leading to a gravitational redshift.
▪ o To an external observer, time appears to pass more slowly near the event horizon than far from it
o Tidal forces near the event horizon of a
o 3MSun black hole would be lethal to humans.
o Tidal forces would be gentler near a supermassive black hole because its radius is much bigger.
• Do black holes really exist?
o Black Hole Verification
o X-ray emission shows the presence of an accreting compact object in a binary system
o Need to measure mass
▪ Use orbital properties of binary system
▪ Measure velocity and distance of orbiting gas
o It should be a black hole if it’s not a star and its mass exceeds the neutron star limit (~3MSun)
o Some X-ray binaries contain compact objects of mass
exceeding 3MSun that are likely to be black holes.
o One famous X-ray binary with a likely black hole is in the constellation Cygnus.
14.4 The Origin of Gamma-Ray Bursts
• What causes gamma-ray bursts?
o • Gamma-Ray Bursts
o Brief bursts of gamma rays coming from space were first detected in the 1960s.
o o Observations in the 1990s showed that many gamma-ray bursts were coming from very distant galaxies.
o They must be among the most powerful explosions in the universe—could be the formation of black holes.
• Supernovae and Gamma-Ray Bursts
o Observations show that at least some gamma-ray bursts are produced by supernova explosions.
o Some others may come from collisions between neutron stars. o
Reading Review Chapter 14 11/18/15 5:14 PM Chapter 14a
1. Algol consists of a 3.7 M Sun main-sequence star and a 0.8 M Sun subgiant. Why does this seem surprising, at least at first?
a. The two stars should be the same age, so we'd expect the subgiant to be more massive than the main-sequence star.
2. A typical white dwarf is _________.
a. as massive as the Sun but only about as large in size as Earth
3. The maximum mass of a white dwarf is _________.
a. about 1.4 times the mass of our Sun
4. According to our modern understanding, what is a nova?
a. an explosion on the surface of a white dwarf in a close binary system
5. Suppose that a white dwarf is gaining mass through accretion in a binary system. What happens if the mass someday reaches the 1.4 solar mass limit?
a. The white dwarf will explode completely as a white dwarf supernova.
1. A typical neutron star is more massive than our Sun and about the size (radius) of _________.
a. a small asteroid (10 km in diameter)
2. Pulsars are thought to be _________.
a. rapidly rotating neutron stars
3. How is an X-ray burst (in an X-ray binary system) similar to a nova? a. Both involve explosions on the surface of stellar corpse.
4. Which of the following statements about electron degeneracy pressure and neutron degeneracy pressure is true?
a. Electron degeneracy pressure is the main source of pressure in white dwarfs, while neutron degeneracy pressure is the main source of pressure in neutron stars.
Reading Review 14c
1. What do we mean by the event horizon of a black hole? a. It is the point beyond which neither light nor anything else can escape.
2. Imagine that our Sun were magically and suddenly replaced by a black hole of the same mass (1 solar mass). What would happen to Earth in its orbit?
a. Nothing - Earth's orbit would remain the same.
3. What makes us think that the star system Cygnus X-1 contains a black hole?
a. It emits X rays characteristic of an accretion disk, but the unseen star in the system is too massive to be a neutron star.
4. The Schwarzschild radius of a black hole depends on ________. a. only the mass of the black hole