1. Suppose a distant quasar has the following spectrum
a) What is the redshift z of this object?
b) What is its recessional velocity?
c) Now, suppose detailed observations have revealed that the quasar in question has a true space velocity
which is sufficiently large so that relativistic effects may not be discounted. Under these restrictions, what
is its recessional velocity? Were the observations correct?
2. Consider a proton which is traveling in a cloud of hot gas (HII) near the center of an active galactic
nucleus. This cloud is 1pc from the AGN and is at the highest temperature possible for spherical dust to
exist without vaporizing.
a) Given that dust cannot exist above 2000K, find the luminosity of the AGN (Hint: Set the flux absorbed by the dust at the given distance equal to the emitted luminosity of the dust given its radius and
temperature and solve for L).
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b) Suppose that the particle is traveling at an “average” speed (you may select your favorite average speed
for gases). Compute this average speed.
c) Assume that the particle enters an orbit of the AGN with an initial tangential speed equal to that found
in part (b). If the mass of the AGN is 108 M , compute how quickly the particle is traveling (tangential
speed) once it reaches the Schwarzschild radius of the central black hole.
d) Now find the (constant) centripetal acceleration experienced by the proton during its fall into the black
hole, and use this value to find the time taken for the particle to fall in from its original distance of 1pc.
e) What average luminosity was given off by this proton during its trip, and how many protons would need
to make such a journey to power the AGN? What is the mass of this number of protons? Is this a reasonable
number?
3. Compare and contrast type Ia and type II supernovae. Be sure to include information on their spectra
and uses as standard candles
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4. Consider the following light curve, which graphs apparent magnitude v. time. We will assume the stars
lie on the main sequence.
a) Find the flux in W/m2 , as observed from earth, of i) the system, ii) the brighter star (“star 1”), and iii)
the dimmer star (“star 2”).
b) We can observe (from Doppler shifts) that the velocities of the stars are v1 = 70km/s and v2 = 50km/s.
Using this information in conjunction with the light curve, deduce the radii of the two stars.
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c) The spectrum of star 1 is given by the blue curve in the following diagram
Find the luminosity and absolute magnitude of star 1 and the distance to the system.
d) Find the separation of the stars in au.
5. Describe the spectrum one would expect to see from an HII region. What sort of objects inhabit HII
regions?
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6. Consider the following light curve:
a) This star’s spectrum peaks at 29µm. Find its radius.
b) Now suppose that the flux from this star as observed on earth is .1W/m2 . Find the distance to the star.
7. Say we have a binary system (observed edge-on) with components A and B. We can spectroscopically
resolve these two stars. This information gives vA = 60km/s and vb = 80km/s. Also, the period of the
system is 303 days.
a) Find the masses of the two objects.
b) Calculate the distance along the line joining stars A and B which one would need to transverse in order
to encounter the edge of the Roche lobe of star A.
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c) The spectrum of star B, a main sequence star, follows:
Using this information, find the luminosity of star B given that its outer edge extends to the intersection of
Roche lobes found in (b).
d) Suppose that, in fact, star B is more luminous than the value found in (c). What type of variable system
is this, and what is its eventual fate?
e) Now suppose that we are observing the system at an inclination i = 50◦ between the plane of the orbit
and our line of sight. Redo part (a) with this new assumption.
8. a) Explain why the value of Hubble’s constant H0 may be used to estimate the age of the universe.
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b) Consider the following diagram:
Assuming Ωm = 5 and Ωv = 0, is the estimate for the age of the universe made in (a) too large or too small?
Explain. What will happen to H0 in this universe as time increases?
c) Describe one piece of evidence for the big bang which is separate from Hubble’s Law or Hubble’s Constant
9. Describe the evolution of galaxies and galaxy clusters. Be sure to address (a) the chemical composition of
the galaxies over time, including star populations, (b) the objects comprising the galaxies and their relative
abundances at different times, and (c) the morphology of the galaxies.
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10. Consider the following spectrum which we will assume comes from a spiral galaxy (despite the fact that
it may not in fact bear any resemblance to the spectrum of a spiral galaxy):
a) Using the Pr3 6195.61 line, find the rotational velocity of this spiral.
b) Assuming that the galaxy’s size is roughly equivalent to that of the MWG, estimate the mass of the
galaxy
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c) The rotation curve is of the form “A” in the following diagram:
What do you conclude about the accuracy of the mass estimate? What would be concluded if the rotation
curve were similar to “B”?
d) Given that this galaxy’s apparent magnitude is m = 25.2 as well as the reference information that
LM W G = 2.6 × 1010 L and vrot M W G = 250km/s, find the distance to the galaxy in question.
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