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AST 3003S: Galactic and Extragalactic Astronomy
Tutorial 2:
Due: August 26
Question 1:
In a certain part of the North American Nebula, the amount of interstellar
extinction is the visual band is 1.1 magnitudes. The thickness of the nebula is
estimated to be 20pc and is located 700pc from Earth. Suppose that a B spectral
class main-sequence star is observed in the direction of the nebula, and that the
absolute visual magnitude of the star is known to be Mv = -1.1 from the
spectroscopic data. Neglect any other sources of extinction between the observer
and the nebula.
a) Find the apparent visual magnitude of the star if it is lying just in front of the
nebula.
b) Find the apparent visual magnitude of the star if it is lying just behind the
nebula.
c) Without taking the existence of the nebula into consideration, based on the
apparent magnitude, how far away does the star in (b) appear to be.
Question 2:
The Boltzmann factor, e-ΔE/KT helps determine the relative populations of energy
levels. Using the Boltzmann factor, estimate the temperature required for a
hydrogen atom's electron and proton to go from being anti-aligned to aligned. Are
the temperatures in HI clouds sufficient to produce this low-energy excited state?
Hint: Start with the frequency of the transition and only consider thermal energy.
Question 3:
An HI cloud produces a 21-cm line with optical depth at its center of τH = 0.5 (the
line is optically thin). The temperature of the gas is 100K, the line's full width at
half-maximum is 10 km s-1 and the average atomic number density of the cloud
is estimated to be 10 cm-3. Find the thickness of the cloud.
Question 4:
a) Plot the old thin disk's luminosity density as a function of z for R = 8.0 kpc.
b) Prove that for z >>z0
L(R,z) ~ 4L0 e-R/h e-2z/z0
and so z0 = 2zthin is the effective scale height of the luminosity density function.
Question 5:
a) Beginning with Kepler's third law (Equ. 2.35 in C&O), derive an expression for
V(R), assuming the sun travels in a Keplerian orbit about the center of the
galaxy.
b) From your result in (a), derive analytic expressions for the Oort constants A
and B.
c) Determine numerical values for A and B in the solar neighbourhood, assuming
R0 = 8kpc and V0 = 220 km s-1. Express your answer in units of km s-1 kpc-1.
d) Do your answers in (c) agree with the measured values for the Milky Way?
Why or why not?
Question 6:
An object in the galactic plane at longitude l = 45º has a radial velocity of 30
km/s with respect to the LSR. Determine its distance using Oort's formulae.
Question 7:
a) A cepheid has a radial velocity of 80 km.s-1 and its galactic longitude is 145º.
What is the distance of the cepheid?
b) The period of the cepheid is 3.16d and the apparent visual magnitude is 12.3.
What is the distance of the cepheid using this information?
c) Give some possible reasons for the discrepancy.
Question 8:
The peculiar velocities of stars with respect to the LSR appear to show a velocity
dispersion-metallicity relation (i.e. populations of stars have "velocity ellipsoids").
Explain the origin of this effect and how it tells us more about the intrinsic
structure (i.e. composition) of our own Galaxy.