PURPOSE: to discuss the interstellar medium and how it affects astronomical observing

MATERIALS: calculator, dice, penny, Opacity Worksheet (1 sheet), graph paper (1)

INSTRUCTIONS: complete your prelab, print out these pages, and complete the activities

2.1. (1 pt) Which of the following are methods of detecting the ISM?

 a)   21 cm radiation, absorption, electron scattering
 b)   rotational emission, scattering, thermal emission
 c)   21 cm radiation, rotational emission, thermal emission
 d)   rotational emission, thermal emission, spectral line broadening

2.2. (6 pts) Match each component of the ISM with its corresponding temperature. (Note: You may use a
temperature range for more than one ISM component).

a) cold molecular H₂    __________

2.4. (2 pts) Now click on image number 34e - the Rosette nebula (NGC 2237). Indicate which type of
nebula (emission, dark, or reflection) this is and give a reason.

2.5. (2 pts) Now click on image number 20b - the Horsehead nebula (NGC 2023). Indicate which type of
nebula (emission, dark, or reflection) this is and give a reason.

2.6. (1 pt) Finally, open image number 65b - the Lagoon nebula (M8) and examine it. What do you think
the many different colors (red, yellow, green, blue, etc.) likely represent?

Actually, it turns out that the red regions correspond to excited hydrogen (and maybe nitrogen) gas while
the blue regions are graphite and CO dust grains. The green region is likely to be oxygen molecules and
the large yellow region is thought to be a complex combination of CO, NH₃, oxygen complexes, TiO,
CH₃OH, and some iron-based molecules like FeSiO₄. When studying the ISM, image colors (if they are
not false colored during image reduction) are a very important piece of observational information.

2.7. (3 pts) If a nebula or GMC had an average temperature of T = 10 K, a density of ρ = 1 x 10^-15 kg/m³, and is about L = 1 x 10¹⁵ m in size, how much molecular hydrogen gas M_H is present?

2.8. (3 pts) If the local interstellar medium is representative of the ISM in the Universe as a whole, then use Figure 4 in lab text section 2.1 to calculate how much more hydrogen gas is in a typical ISM cloud than silicate (Si) dust grains?

3.1. (1 pt) What is the obscuration of light?

3.2. (1 pt) Optical depth is

 a)   the farthest distance our telescopes on Earth can see
 b)   the number of times a photon of light interacts with another photon, atom, or molecule
 c)   a measure how much light is obscured by an ISM cloud
 d)   the depth of an ISM cloud

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**EXPERIMENT**
Here we will illustrate the "random walk" phenomenon of light photons in outerspace.

Obtain the Opacity Worksheet page, a penny, and a six-sided die. Now, before giving the instructions,
you will have to use your imagination a little. Suppose that there is a star behind a nebula or giant molecular
cloud ready for its "random walk". Your 'Opacity Worksheet’ is a two-dimensional representation of this
cloud of gas molecules and dust grains. Light from the star enters the cloud from the upper left and strikes
the atom labeled #1. There are only six directions it can now go. To simulate random re-radiation of the
photon, roll a die and multiply the number you roll by 2. The result is the clock face direction 2, 4, 6, 8, 10,
or 12 o’clock as shown in the figure at the bottom left corner of your worksheet. Use a penny to represent
the photon and move it along with each roll of the die. Continue this process until the photon ‘leaves’ the
cloud. We assume that any photon leaving the cloud in the 4 o’clock direction will reach our telescope on
Earth. It should be counted as a success. Any photon which leaves the cloud in any other direction will
never reach our telescope and is therefore considered a failure.

3.3. (2 pts) Complete this exercise 5 times, keeping track of the number of successes and failures.

3.4. (1 pt) Find your success ratio (i.e., # of successes divided by total number of tries) for line radiation.

To simulate a continuum scenario, each time the photon encounters an atom we must decide whether it
will get scattered or move through the cloud undisturbed. Roll the die as we did before. This time,
however, if you roll a 6, assume the photon is scattered. If you roll any other number, multiply it by 2
and move the photon as you did in the first activity. If a photon is scattered, determine the direction of
scatter by rolling the die and moving the penny as you did in the first trials.

3.5. (2 pts) Complete the continuum photon exercise 5 times, keeping track of the number of successes and failures:

3.6. (1 pt) Find your success ratio (i.e., # of successes divided by total number of tries) for continuum.

3.7. (2 pts) Use the success ratio from #3.4 to determine the approx. optical depth for line radiation
photons in an ISM cloud. Is the cloud in this case optically thick or thin?

3.8. (2 pts) Use the success ratio from #3.6 to determine the approx. optical depth for continuum
photons in a cloud. Is this cloud in this case optically thick or thin?

3.9. (2 pts) A star has (B-V)_OBSERVED = 1.8 and (B-V)_INTRINSIC = 0.6. What is the color excess of this star?

3.10. (2 pts) What is the total reddening (A) for the star in #3.9?

3.11. (3 pts) The same star has a magnitude of m = 13.0 and an absolute magnitude of M = 5. Given its
total reddening from question #3.10, what is this object’s distance (d)?

3.12. (3 pts) Based on the values you have already calculated for A and d, what is the extinction coefficient (k) for this system?

3.13. (1 pt) The average size of some particles in the observed ISM region is σ = 3 x 10^-6 cm³. Are these particles more likely to be gas atoms or dust grains?

3.14.   If we manipulate the equations in the text, we find the relation that : n = k / (1.086 σ).

a) (2 pts) Use the average particle size given in #3.13 and k from #3.12 to find the density, n, of the ISM region.







b) (1 pt) What phase of hydrogen gas is likely dominating this region?


c) (2 pts) Use an optical depth of τ = 0.087 to find the size of the cloud (in parsecs).

3.15.   The table here gives data for dust extinction as a function of wavelength.

a) (5 pts) Use the provided graph paper to plot this data, making the standard interstellar extinction curve
for our 5 … tick marks of 0.02 for A < 0.1 and ticks of 0.2 for A > 0.2). Connect all the data points and label.


b) (2 pts) In general, does the amount of extinction in our Galaxy increase or decrease as you move towards longer wavelengths? Give one possible reason for this.





c) (1 pt) The main components of ISM dust in order of size are carbon, water, and silicon. Knowing
there is a relation between particle size and wavelength absorbed, use the periodic table (see 'Nature
of Light' lab) to label each of the three peaks on your plot with the appropriate material. Be sure to
turn in your graph with the rest of your lab activities.

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**EXPERIMENT**
Let's make some different interstellar extinction curves using the "Dust in the Interstellar Medium" applet, © Shodor Education Foundation, Inc.

First, open this webpage. Notice that the main frame has two options. Click on the applet entitled
'Multiple Material Model' and familiarize yourself with it. Also notice on the main webpage there is
a link to 'Instructions' in the yellow column frame on the left ... please click on this link and read the
information before beginning. Here are some helpful hints for the multiple material model:

- Color Coding:

3.16. (1 pt) Experiment with creating extinction curves for different types of dust. Try changing both the
sizes and densities for a particular type. How is extinction generally affected by increasing grain size/density?
(HINT: larger optical depth means more extinction of light).

3.17. (1 pt) Reset the applet so only the average interstellar extinction curve (blue) is visible. Create
the two following curves for silicate grains: i) σ = 0.001, n = 1.44e17 for small grains and ii) σ = 0.1,
n = 8.59e9 for larger grains. Describe the characteristics of both curves as compared to the blue curve.
(HINT: you may sketch them if this is easier).

3.18. (1 pt) Reset the applet again. Create two graphite grain curves: i) σ = 0.001, n = 2.25e15 and
ii) σ = 0.1, n =
8.59e9. Again describe both curves, sketching them if you like.

3.19. (1 pt) Based on your results in #3.17 and #3.18, how do the two major types of ISM dust grains
- silicate and graphite - contribute differently to the obscuration of light?

3.20. (3 pts) Change both the sizes and densities of all three types of dust grains to try and match the
shape of the average interstellar extinction curve (blue). This may take alot of experimenting and a little
time. When you feel you have the best match possible, record the variables below:

DUST TYPE	Grain Size (μm)	Density (cm-2)
amorphous carbon
graphite
silicate

SECTION 4 ACTIVITIES :

4.1. (3 pts) An interstellar cloud has a radius of R = 1.54 x 10¹⁵ m across. It has a density of
ρ = 1 x 10^-15 kg/m³, a mass of M = 1 x 10³³ kg, and an area of A = 7.45 x 10³⁰ m². What is
the force of gravity on this cloud?

4.2. (3 pts) The cloud exhibits a pressure of P = 2.3 x 10^-9 kg / m · s². Use this to find the force of pressure on this cloud.

4.3. (2 pts) Based on your results to #4.1 and #4.2 above, is this interstellar cloud in hydrostatic equilibrium? Is the cloud collapsing or is it already in its stable protostar stage?

4.4. (3 pts) Based on the given density and size of the cloud, what is its approximate temperature?

4.5. (3 pts) Calculate the total infall time (in yrs) for the cloud to collapse into a star.

4.6. (3 pts) Calculate the luminosity L (in watts) of the star which can be formed from this interstellar cloud.

4.7. (3 pts) The Sun’s luminosity is 3.9 x 10²⁶ watts. How many times greater is this star’s luminosity than the Sun's?

4.8. (2 pts) Look at this image of the Eagle Nebula, a well-known star forming region. Describe the
nebula and comment on how star formation may take place in this region of interstellar space.

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