Ph 343 Lab 5 The Thickness of the Galactic Hydrogen Disk -- Part II

Due: Thursday, November 14, 2002

Purpose: Measure the angular width of the Galactic hydrogen disk at one galactic longitude.

Analysis:
1. For each of your pointings, calculate the average system temperature at each observed frequency and plot average temperature versus frequency.

2. Estimate the receiver temperature plus spill temperature using the ``baseline'' of points at frequencies far from the line center. What is the uncertainty in your estimate? Do this for each pointing.

3. For each pointing, find the difference between the largest temperature measured and your baseline temperature. Is this difference significantly different from zero?

4. For each maximum temperature difference that is significantly larger than zero in part 3, report the frequency of the bin at which the largest temperature difference occurs. What is the radial velocity of the hydrogen gas emitting at that frequency, as calculated with the Doppler formula? (Remember that the sign of the velocity is significant, approaching gas has negative velocities, receding gas has positive.) Does the velocity of the peak emission show any dependence on galactic latitude, $b$?

5. Discuss how the shape of the observed spectrum (temperature difference above baseline as a function of frequency) varies with $b$. At a minimum, discuss whether the spectra at different $b$'s are or are not the same except for a vertical (multiplicative) scaling.

6. Use your peak temperature differences from part 3 to crudely estimate the galactic latitudes (plus and minus) at which the hydrogen emission has fallen to half the value observed at $b=0$.

7. For each of your pointings, subtract your baseline value from the temperature at every frequency and sum the temperature differences over all of the frequency bins that you judge are significantly different from zero. This produces a number that is proportional to the the total amount of hydrogen emission along that line of sight. Estimate (again, fairly crudely) the galactic latitudes at which the total emission drops to half its value at $b=0$. Is the plane thicker or narrower as measured with the total emission as compared to the peak emission?

8. Calculate the column density, $N_H$, of neutral hydrogen (in atoms per square centimeter) along your $b=0$ line of sight using the formula

$$\begin{eqnarray*} N_H &=& (3.88 \times 10^{17} \ {\rm atoms/cm}^2/{\rm kHz}) \in... ... \times 10^{17} \ {\rm atoms/cm}^2/{\rm kHz})\sum T_b \Delta\nu. \end{eqnarray*}$$

Here $T_b$ is the observed brightness temperature of the hydrogen emission, so the sum is the same one as calculated in part 7, and $\Delta\nu$ is the width of the frequency bins in kilohertz (kHz). This formula assumes that the gas is optically thin to 21-cm radiation, which is reasonable for most lines of sight.