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From Sterl Phinney
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1. Describe at least 4 methods that have been used to measure
the masses of "black holes" in galactic nuclei, and discuss
their pros, cons, and error budgets.

2. It is commonly believed that 70% of the mass-energy in the
universe is in the form of "dark energy" or a cosmological constant.
Explain the observational and theoretical basis for this belief.
You may be asked to derive some relevant cosmological equations
to justify your assertions.

3. Describe the major processes which are believed to have made the
present-day power spectrum of density fluctuations differ, on scales
from
1kpc to 1Gpc, from the primordial (post-inflation) "Zeldovich" n=1
powerlaw.

4. Explain why core collapse occurs in globular clusters.
What stops it?  Why have galaxies not undergone core collapse?

5. Explain why accretion disks accrete, why they radiate,
and why they have finite thickness.  What is the "alpha parameter,"
and why is it used?

6. Draw a Hertzsprung-Russell diagram, with labelled Luminosity and
Temperature axes, and on this draw a main sequence (with some
stellar masses labelled), describe the main features of
the post-main sequence evolution of stars of different masses,
and their final states 10^{10} years after birth.

7. What is the temperature of the cosmic microwave background, and
what is the photon-to-baryon ratio?
Is the temperature of the cosmic neutrino background expected
to be the same or different?  Explain why as quantitatively as you can.

8. Derive the Eddington luminosity, and discuss at least three
different astronomical circumstances where it is important.

9. The outer crusts of neutron stars, and the cores of old white
dwarfs may be crystallized.  Explain how one would estimate the
crystallization temperature. Describe some observational consequences
of crystallization in white dwarfs and neutron stars.

10. A pulsar has P=3s, Pdot=3x10^{-12} s/s.  How many such pulsars
might one expect in the Milky Way?  Assuming it is a vacuum dipole,
estimate the polar cap radius, and the voltage difference across
the polar cap.  Explain why you would or would not expect it to be 
surrounded by enough charges to deviate the fields substantially from 
the electromagnetic vacuum configuration.

11. Derive Jeans Theorem for stellar dynamics, and give an
example of its application in astronomy.

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From Judy Cohen (2004)
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1.  Describe the nature and history of the Solar neutrino problem,
the experiments used to study this issue, and its current status.


2.  How does one construct a model for the chemical evolution
of a galaxy ?  What are the input assumptions/physics of such
a model ?


3.  How and where are the elements heavier than Fe formed ?  



4.  A star is found in the halo of of our Galaxy with
[Fe/H] = -4.0 dex.  Calculate approximately how many
supernovae contributed to its metals and indicate the
assumptions that must be made to do this calculation.


5.  A main sequence star of 0.6 Msun in a metal poor globular cluster
once had a 3 Msun companion, now a white dwarf.
What amount of mass must have been transferred across this
binary system to double the C/Fe ratio in the 0.6 Msun star ?
Indicate the
assumptions that must be made to do this calculation.


6.  What is the Schechter luminosity function for galaxies ?
Given a count N(mag) that extends very faint, how can one
derive the LF for galaxies at redshifts 1 to 3 ?


7.  How does one find objects that are in the Solar system
beyond the Kuiper belt and what do we know about what is
out there ?

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From Sari: (2003)
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1) A sphere of gas of radius R has a temperature $T$. What is
its bolometric luminosity, if its optical depth for photons
of energy $kT$ is $\tau$. What would be its spectrum if the main 
source of opacity at all wavelengths is small dust grains.

2) Describe and compare the sensitivities of astrometry and 
radial velocity techniques for finding extrasolar planets.

3) A powerlaw spectrum of relativistic electrons is embedded 
in a uniform magnetic field. Give an example of a possible
resulting spectrum.

4) The semimajor axis of Venus around the sun is 0.72AU. 
About how often does it get close to earth (opposition)? What is 
the eccentricity that its gets due to interaction with earth 
every such period.

5) How long does it take for a black hole of mass M to evaporate?
What black hole masses could survive through the age of the universe?

6) How many photons per second are received by Keck from a 20th magnitude
object in the R band filter? Given the solar luminosity, how long of 
exposure HST needs to take at a Kuiper Belt object of 100km to detect 
a hundred photons?

7) Explain what is dynamical friction. Give an expression for its
magnitude for a body moving within a uniform stationary background of 
mass density $\rho$.

8) What is the relaxation timescale of a globular cluster?

9) What are the nuclear processes in the Sun? What is the Sun's 
luminosity and mass? Based only on these, how long will it shine?

10) What are the Lagrange points? what is the Roch lobe, and what
is its significance? Derive its size for the case of a very large
mass ratio.


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lynne's example questions: (2003)
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Describe the various ways of estimating distances to stars in the Galaxy,
starting with the most accurate and proceeding to less reliable methods.

A pulsar is observed (via the period of the arrival pulses) to rotate
at a rate of 500 Hz.  Show using numerical arguments that this object 
must be a neutron star and not a giant, main sequence dwarf, or white dwarf.

What is the Schwarzschild radius of an object with mass of the sun?

Why is the Galaxy opaque at wavelengths shorter than 912 A?

In normal main sequence stars, what forces balance the star against 
gravitational collapse?   As a star like the sun evolves, will these
forces be adequate?  What support mechanism takes over and on what physical
variables does this mechanism depend?

Desribe various sources of opacity in stellar atmospheres.  What are the
dominant sources in main sequence O stars?  M stars?

Estimate the time interval between physical collisions of stars
in a globular cluster (include the effects of gravitational interactions).
What measurements would you have to make in order to derive a numerical
answer?

Sketch the interstellar extinction curve labelling the axes and 
describing its salient features.  How could you use extinction 
as a function of wavelength to estimate the size a typical dust grain 
in interstellar space?

Under what conditions is the Sobolev approximation valid?

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From Nick Scoville: (2003)
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sample back-of envelope questions from nzs


1) What is meant by the initial mass function ?
   Suppose you have 1000 M_sun in a star cluster, 
   Estimate the number of OB stars.
   Estimate the total cluster luminosity.
   
2) The infrared emission from galaxies is produced by 
   what processes. What is the energy density of the 
   diffuse starlight at a typical location in the 
   disk of the Milky Way. What would be the 
   temperature of dust in this radiation field ?
   What wavelength should this emission peak ?
   
These questions would be prefaced with reference to 
one of the research seminars from the last year.

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From Richard Ellis (2003)
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1. Recently, Wendy Freedman and Ned Wright have attempted to measure the
so-called "extragalactic background light", the residual signal from
unresolved faint sources. Why is this signal important to detect both at
optical and near-infrared wavelengths? Consider how you would remove the
contribution of resolved sources whose surface density as a function of
apparent magnitude goes as $N(m)dm \propto 10^{\gamma\,m}\,dm$?

2. Sketch the Schechter function which has become the standard template
for representing the galaxy luminosity function. Why do all luminosity
functions (stars, galaxies, quasars) have this characteristic form? What
are the significant parameters of the Schechter function and how are they
measured in a redshift survey? Why has there been so much difficulty
establishing a precise value for the faint end slope? Why is it important
to know this slope?

3. Explain how supernovae of Type Ia have been used by Saul Perlmutter,
Adam Riess and their colleagues to determine that the universe is now
accelerating. One of the most important goals of recent HST supernovae
campaigns is to look back to the era when the Universe was not
accelerating. Explain why determining the rate of expansion at various
epochs is key to understanding the nature of dark energy.

4. For many years it was thought elliptical galaxies were spheroids
flattened by rotation. What TWO dynamical measurements were necessary to
prove that this is in fact not the case. How do you explain the fact that
low luminosity ellipticals rotate relatively rapidly compared to their
more massive counterparts? What does this tell us about how ellipticals
might have formed?

5. There is a lot of current interest in estimating "photometric
redshifts" for faint galaxies. Given we have large telescopes and
efficient spectrographs why is this so popular? How does the technique
work in practice and what are the possible pitfalls?

6.  Describe the observational evidence that leads to the supposition that
galaxies are embedded in halos of dark matter. How convincing is it? How
might the mean density profile of the dark matter halo around normal
spiral galaxies be measured?

7. Explain with a sketch how it is thought that spiral structure can be
sustained in a differential rotating disk galaxy.

8. What use is gravitational lensing other than a beautiful vindication of
the effects of General Relativity? Present some observations which
illustrate the astrophysical usefulness of this phenomenon.

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From SRK (2003)
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[1] We heard a fair bit about Type I and Type II quasars? 
    Explain the observational characteristics of type I and type II quasars?
    What is the column density for type II quasars?
    [You should be able to write an order of magnitude expression
    for the Compton cross section.]

[2] The Chandrashekar mass limit is fundamental to astronomy.
     Derive the Chandrashekhar mass limit

[3] TeV astronomy is becoming very fashionable these days. A number of
    Galactic and extra-galactic TeV sources have now been detected.
    Estimate the optical depth for a 100 TeV photon streaming through the
    intergalactic medium at z=0.
   
    Related question: what would we obtain by inferring the optical
    depth of GeV sources that GLAST may find.

[4] Type Ia supernovae have been in the news recently. What is their
    peak luminosity (optical band; V band magnitude will do). What
    powers these supernovae?  (Expect to know 1 FOE and 0.5 solar mass
    of iron or know the mass defect of Ni-F).

[5] What are the the main phases of ISM? Describe the principal cooling 
    processes for the phases. 

[6] Consider an ordinary supernova taking place in a circumstellar medium
    of uniform density.  Describe the three phases (coasting, non-radiative
    and radiative). For each case, write down radius as a function of
    time.

[7] The same as above except the explansion is high relativistic.

[8] Superluminal motion is seen in quasars and micro-quasars.
    Explain the physics.

[9] On the main sequence (at least for stars similar to the Sun
    and lower mass stars), $R \propto M$. Can you explain this 
    intriguing result?

[10] Plot on a radius-mass diagram the following classes of objects:
     gas giants, brown dwarfs, white dwarfs, neutron stars, main sequence stars.
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SRK 2004:
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I will also use questions that were asked during the final exam
for Ay 125 (2004)
   http://www.astro.caltech.edu/~srk/Option/ay125-final04.pdf
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Marc Kamionkowsk:
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For Radiative Processes
    http://www.astro.caltech.edu/~srk/Option/radiative_problems.pdf