An assignment for Paola
Magnitudes, surface brightness, HI mass and other stuff
1. We usually write the equation that defines the relationship between apparent
and absolute magnitude in terms of the distance in parsecs (pc), but galaxies are at
distances of Megaparsecs (Mpc). What is the form of the equation if the distance
is given in Mpc?
2. The "distance modulus" of the galaxy M101 is 29.0.
What is the "distance modulus" of a galaxy? How far away is M101?
Hint: See chapter 2 of Kutner's book.
3. &nsbp Apparent magnitude and surface brightness
We often find it convenient to talk about a galaxy's surface brightness,
expressed in units of magnitudes per square arc second (arcsec).
Suppose that we can describe a galaxy as a thin disk of area A where
A is πR2 for a face-on galaxy of radius R or π(a × b)/4
for an inclined disk of major-to-minor diameter axial ratio a/b.
Let L/A represent the galaxy luminosity divided by the area. What we observe
is the galaxy's surface brightness μ = -2.5 log (L/A). Show that
the observed surface brightness μ can be related to the apparent magnitude
by
μ = m + -2.5 log (A/d2)
where d is the distance to the galaxy. Furthermore, show that
2.5 log (π/4) = 0.26, so that, for diameters measured in arcsec ("),
the expression becomes
μ = m + -2.5 log (a" x b") + 0.26
4. Suppose a galaxy is observed by ALFALFA to have an HI emission line
flux density of 0.96 Jy-km/s and a heliocentric velocity of 4490 km/s.
How would you go about calculating its HI mass? You don't know all the
information you need to do this; what else do you need to know? Let's
discuss this and figure out how to proceed.
Last modified: Wed Feb 11, 2015 by martha