Sparke & Gallagher problem 2.5 - the part on page 67 that we did not already do in class.

Sparke & Gallagher problem 2.13
You may omit the "advanced" part in the final parenthesis.

Sparke & Gallagher problem 2.17

Use the Dias Open Cluster Catalog and the Harris Globular Cluster Catalog to answer this question.

Do not kill yourself on this if the data format is inconvenient. I provide these links in the hopes that they'd be easy to plot. If that isn't true, plot some subset. The point is to see how things are arranged, not to plot every last datum. On the other hand, grocking large data sets will be an essential skill for the Astronomer of Tomorrow.

A. Plot the RA & Dec of the open clusters.

i. What does this tell you about the structure of the Milky Way?

ii. What does this tell you about the orientation of the solar system within the Milky Way?

iii. What quantitative measure about the orientation can you extract from this plot?

B. Add the globular clusters to your plot.

i. What qualitatively new information does this add?

ii. What does the distribution of open and globular clusters suggest about the location of star formation in the Milky Way at different epochs?

iii. Estimate the RA & Dec of the center of the Milky Way.

Include a copy of your plot with your answers.

A. How many arcseconds are in one radian?

B. If Σ_B is the B-band surface brightness is solar luminosities per square parsec, show that the surface brightness μ_B in magnitudes per square arcsecond is

μ_B = 27.05 - 2.5 log(Σ_B). [Hint: what would the surface brightness of the Milky Way be if the sun were the only star in a square 1pc on a side? How does the angle subtended by an object relate to its physical area? What is the sloar absolute magnitude in the B-band? And log(20626.5)?]

C. Spiral and irregular galaxies have an azimuthally averaged radial light profile that is well approximated in many cases by the "exponential disk": Σ(r) = Σ₀ e^-r/r_d, where Σ₀ is the central surface brightness (in solar luminosities per square parsec) and r_d is the scale length (in kpc) of a galaxy fit by this description.

i) Show that in units of magnitudes per square arcsecond the exponential disk becomes μ(θ) = μ₀+1.086 θ/α, where θ is the observed radius in arcseconds.
[Hint: how does the observed angular radius relate to the physical radius? How must α relate to r_d?]

ii) Integrate Σ(r) from φ = 0 to 2π and r = 0 to x scale lengths (r = xr_d) to obtain an expression for the luminosity enclosed by x scale lengths.
[Hint: the differential area of a circle is dA = r dr dφ.]

• Is the total luminosity finite as x ⇒ ∞ infinity? If so, what is it?
• How many scale lengths contain half the total light? (This is known as the half-light radius, r_e.)
• Plot the cumulative enclosed luminosity L(< x).