ASTR 321
Test 2
Stellar Properties:
- What are the ranges for the properties of stars? (What is the
most important property of stars mentioned in class?)
- How do we determine radii, temperatures, and
luminositites of stars? What is the
hardest part of determining the luminosities of stars?
- How could we determine the distance to Sun? What method for the
determination of stellar radii has (historically) been the most useful?
Roughly, how does the method work?
- What is the difference between flux and luminosity? Of flux (energy
flow per unit area and per unit time) and luminosity (total power).
Which determines how bright an object appears to us (an observer on Earth?)
The total emission from an object over all wavelengths is its bolometric
luminosity. How are bolometric luminosities determined?
- What information can be extracted from spectra
(both from continuous and
absorption line spectra)? How
is information extracted from spectra?
- Discuss how atoms
are put together (what are electons, protons, and neutrons?),
How large is an atom? How large is the nucleus of an atom? Where is most
of the mass of an atom contained? What force holds an atom together? What force
holds the nucleus together? What determines the type of element an atom is?
What is an isotope?
- Why does the line
spectrum serve as the fingerprint of an element? How do absorption and emission
lines arise? What are Lyman lines, Balmer lines, Paschen lines, Brackett lines,
and Pfund lines?
- Roughly sketch the energy level
diagram for a hydrogen atom.
On your diagram draw arrows to indicate an absorption
process, an emission process, an ionization process, and a recombination
process. Draw another energy level diagram for hydrogen and then indicate the
Lyman, Balmer, Paschen, Brackett, and Pfund transitions.
- Spectral Classification.
What is the Morgan-Keenan (MK) spectral classification scheme? How are
spectra classified in the MK scheme?
(What criteria are used to classify stellar spectra?)
Why do different stars have different appearing spectra? Explain why the
strength of the hydrogren lines change as you go from O --> M.
- Consider a star with temperature T = 10,000 K. This temperature corresponds
to what energy? Give your answer in electron volts. The first excited state of
hydrogen sits 10.2 eV above the ground state. For a star with temperature
10,000 K, what fraction of its particles have energy large enough to excite
hydrogen atoms? what fraction of its particels have energy large enough to
ionize hydrogen atoms? Use the Boltzmann distribution to find your answer.
- Repeat your answer for a star with temperature 5,000 K and for a star with
temperature 30,000 K.
- What is meant by HI, HII, CaII, Fe XXVI? More to the point what is meant
the Roman Numerals appended to the abbreviations for the elements?
- How can we infer that the Sun (or any star) contains iron or other elements
such as carbon, oxygen, nitrogen, and so on.
- What important stellar property is carried by the spectral class of a star?
List the order of the spectral classes from high to low temperature.
- What are the Luminosity Classses? For what types of star do the symbols I, III, and V stand?
- What is a blackbody? Give an example of a blackbody? What is the most
perfect blackbody known? What characeristic of
a blackbody determines its properties? What are
the Wien Law and Stefan-Boltzmann
Law? Which blackbody law is used (and how may it
be used to determine stellar temperatures)?
Why are blackbodies interesting and useful idealizations for astronomers?
How does the color of a blackbody depend on its temperature?
(Draw a plot to support your answer.)
Which of the following blackbodies produces the most IR radiation, a
10,000 K blackbody or a 3,000 K blackobdy.
Which of the two previous blackbodies
appears the reddest?
Stellar Properties
- Sketch an HR diagram. Mark and describe Main
Sequence Stars, giants (Red Giants), Super-Giants, Asymptotic
Giant Branch (AGB) stars, white dwarfs, planetary nebulas, neutron stars.
- Draw lines of constant radius on your HR diagram.
- What is the Mass-Luminosity relation? Use your mass-luminoity relation
to show the masses of stars on the Main Sequence.
How can the mass-luminosity relation be used to infer a
scaling law for stellar lifetimes? What stars have the longest lifetimes,
massive or low mass stars? What is the argument one uses to infer the
relationship which describes how the lifetime of a star depends on its
mass? What is the Kelvin-Helmholtz time scale? the nuclear time scalae?,
the gravitational time scale?
- What is the luminosity function?
- What is the Initial Mass Function?
Use the IMF to find the fraction of stars which produce Type II SN. Use
the IMF to find the fraction of stars which lead to stellar-size black
holes. Which type of stars are the most
numerous in our Galaxy?
- Why is there a lower limit to the mass of mass sequence stars? Why is
there an upper limit to the mass of main sequence stars?
What are different ways
stars can generate energy? What is the most efficient way stars generate
energy? What mechanism is used by Main Sequence
stars to generate energy?
Nuclear Energy Generation--the
conversion of 4 hydrogen nuclei into a helium nucleus + energy + other
particles. What conservation laws are important for consideration of
nuclear fusion? What are leptons? What are bosons? What are quarks?
What are neutrinos? Why is
nuclear fusion so difficult (that is, what is the major impediment to fusion)?
Using the electrostatic potential, thermal energy, strong force, and the
Boltzmann distribution to explain why, classically, nucelar
fusion is difficult.
What is the proton-proton cycle (pp-cycle)? What is the
carbon-nitrogen-oxygen tricycle (CNO cycle)?
What are the energy transport mechanisms used by stars? Which ones are
the most important for the Sun?
What important role outside of energy transport does convection play in
the observable properties of the Sun?
Main Seqeunce stars are in equilibrium;
both mechanical equilibrium (hydrostatic
equilibrium -- stars are not changing in size very quickly) and thermal
equilibrium (the temperature structures of stars are not changing
very quickly --
the energy losses due to radiation and particles from
stars are roughly balanced by the energy production due to
nuclear fusion reactions). Show that, in the absence of pressure effects,
a star like the Sun would collapse (due to gravity) in less than 1 hour.
Contrast this time for low mass and high mass stars. Use dimensional
arguments to justify your answer.
- Write the equations of stellar structure.
- Why are neutrinos more useful as probes of the interior of the
Sun than are photons (the light we receive from the Sun)? What other
methods are used to probe the interior of the Sun? What was the
Solar Neutrino Problem? How was the Solar Neutrino Problem resolved?
Use dimensional arguments to show how the temperature of star
dominated by radiation pressure scales with the mass and radius of
a star.
Use dimensional arguments to show how the density of a star
varies with mass.
Use dimensional arguments to show how the radius of a star
varies with mass.
Use dimensional arguments to show the rough mass where radiation
pressure and gas pressure play similar roles in the structure of a
star
Use dimensional arguments to show how the luminosity of a Main
Sequence star depends on mass for a star dominated by electron
scattering, or by bound-free or free-free transitions.
Use dimensional arguments to find the timescale on which stars collapse.
On an HR diagram,
sketch evolutionary tracks followed by the Sun, a 5 Solar mass
star, and a massive star. Indicate the stages of evolution,
the energy sources for each phase, the dominant
energy transport mechanism, and whether the
core is degenerate or nondegenerate.
What are the Hayashi and Henyey tracks? What is the Jeans mass? Use the
Virial Theorem to make a rough estimate of the Jeans mass. Explain how the
notion of the Jeans mass can be used to understand fragmentation of a
collapsing Interstellar Medium Cloud. What are protostars, T Tauri stars? How
are they powered?
State the Russell-Vogt Theorem. What are the assumptions that underlie
the Russell-Vogt Theorem? Describe counter-examples to the
Russell-Vogt Theorem.
The orbit of the Earth is increasing slowly in size by 15 cm per year. If
the increase in orbital size arises from a change in the mass of the Sun, find
the rate at which the Solar mass must be changing. Compare this rate to the
rate of mass loss produced by nuclear fusion. Compare this rate to the rate
of mass loss carried off by the Solar Wind. How does the Solar Wind compare to
the winds from massive stars?
Thermal Pulses occur at which phase of the Sun's evolution? Why does the
nuclear generation output of the Sun "pulse"? How does the pulsing combined
with the properties of the envelope of the Sun combine
to produce a planetary nebula? Describe instabilities which can lead to
thermal pulsing.
Use dimensional arguments to find the density above which the electrons in
a pure hydrogen plasma at temperature T become degnerate. The Helium Flash
occurs when the mass density is 100,000 gm per cubic centimeter and the
temperature is aroudn 200,000,000 K. At what temperature is degeeneracy lifted
in the core of the Sun during the flash? Compare the energy generation rate at
the end of the flash to the beginning of the flash. What is the Carbon flash?
In which kinds of stars do we expect a Carbon flash?
Solve the stellar structure equations to find the pressure structure for
a star whose density distribution falls off as the inverse of the radius, that
is, as 1/r. If the pressure in the star is given by the perfect gas law, find
the temperature structure of the star. Find the radius within which 50 % of the
star's luminosity is generated for the proton-proton chain.
In a Type Ia SN, carbon ignites when the density is around 1,000,000,000
gm per cubic centimeter. For a 1.2 Solar mass white dwarf, this corresponds to
a radius of what size for the white dwarf?
Show that the burning of carbon can disrupt the white dwarf.
Suppose the white dwarf is composed of equal parts Mg and Ne. These elements
ignite at a density of 3,000,000,000 gm per cubic centimeter. Show that a Ne-Mg
white dewarf will not produce a Type Ia SN.
Both reactions yield about 0.001 mc2,
where m is the mass involved in the reactions.
Use dimensional arguments to show how the radius of a white
dwarf scales with
its mass. Consider both nonrelativistic and relativistic white dwarfs.
Argue why there is an upper mass limit for white dwarf stars. What is the name
of this limit? Using dimensional arguments, find and evaluate this limit in
c.g.s..
Describe in words, the different stages of white dwarf cooling.
Using dimensional arguments find an expression for the white dwarf cooling
time. Roughly how long does it take a white dwarf to cool to 0.0001 of its
initial luminosity, according to your expression.
At the current time, the Sun generates energy through the proton-proton
chain. The proton-proton chain is around 0.7 % efficient.
If nuclear reactions in the core of the Sun were to shut-down today, estimate
the time it would take for us to observe the event. Use a random walk
argument.
Define the term nuclesosynthesis.
Compare the r-process and
the s-process. The s-process is known to occur in AGB stars. What is the
evidence which supports this?
Stars are categorized as low or high mass stars based on what criterion? Whydoes the Sun's nuclear processing in its core stop after helium burning?
Sketch a typical Type Ia SN light curve.
Describe the energy source for each phase of the evolution of the light
curve. Note
Ni56+e-
---> Co56 + neutrino + 2.72x10-6erg, and
Co56+e-
---> Fe56 + neutrino + 5.76x10-6erg
The half-life for the decays are 6.08 d and 77.1 d, respectively.
SN 1987a is, arguably, the single most important observational result
in stellar evolution over the last 50 years. Argue why this is so and
cite results which support your answer.
Calculate the energy released during the SN 1987a outburst. How long did
the different parts of the outburst last? What were the
significant parts of SN 1987a's energy budget? Support your answer
with rough, but appropriate, observational results.
Estimate the energy liberated in the following stellar events:
- normal nuclear burning lifetime of the Sun
- normal nuclear burning lifetime of a 25 solar mass star
- Type Ia SN event
- Type II SN event