2. Consider the effects on extinction and reddening of dust coagulating into larger and larger particles. Your answers to all parts of this question should be primarily in words and graphs.
1. Warning: This
problem uses real observations of CO in a molecular cloud
and asks some open-ended questions. Below, you will find two spectra
for the dark cloud core L1228. The spectra were obtained by a
colleague of AG's (identity & reference to be revealed in
Solution Set) with the 14-m radio telescope at the Five College
Radio Astronomy Observatory, near Amherst, MA. Assume that the
efficiency of the telescope at FCRAO is such that TA = 0.5 TB.
The spectra shown below are averaged so that they represent a
"beam" which is 4 x 5 in area.. The velocity axis shows
velocity with respect to the Local Standard of Rest, vLSR. The L1228 cloud is at a distance
of 300 pc.
a.) From these two spectra, present one or more hypotheses about the distribution of molecular gas along the line of sight. Show an illustration (both side and front views) for each of your hypotheses. You might want to consider the following in your hypothesis:
b.) Can you suggest additional observations that would clear up any ambiguities in your hypotheses?
c.) Estimate the column density of 13CO along this line of sight, within the velocity range -9< vLSR <-8 km/s. Please be careful to state all of your assumptions.
d.) Outline how you would translate your answer to c. into a total column density, including any additional (customized) observations that might be required.
e.) Suggest and describe an alternative technique for determining
the total column density through this part of this cloud which
would suffer less uncertainty than the one outlined above.
The three-column ASCII
file containing the spectra shown below, as vLSR, TA
(12CO), TA(13CO), can be found at
ftp://cfa-ftp.harvard.edu/pub/agoodman/ay208data/CO.spectra.
The data can be ftp-d outside of a browser or cut & pasted
out of a browser.
2. Consider the effects on extinction and reddening of
dust coagulating into larger and larger particles. Your answers
to all parts of this question should be primarily in words and
graphs.
a.) Show a graph (or drawing) of extinction vs. 1/wavelength
from ultraviolet to mid-infrared wavelengths, for dust along "typical
low-density" lines of sight through the Milky Way's ISM.
The grain size distribution, N(a), for these "typical"
lines of sight is likely to be close to an "MRN distribution,"
with x=3.5 and a=grain
size (see Mathis,
Rumpl & Nordsieck 1979).
b.) Show, in graphical format, how the grain-size distribution
and the extinction vs. 1/wavelength plot you presented in part
a. will be modified as x decreases due to coagulation of
smaller grains into larger ones. The extinction axis on your graph
need not have an exact scale, but do NOT normalize your graph
(as is done in Mathis
1990) so that all extinction curves cross at some arbitrary
point. Instead, consider what effect decreasing the number of
small grains will have on the absolute level of extinction at
a particular wavelength.
c.) As x decreases, what will happen to the color excess,
EB-V, for a given star
observed through a distribution of dust (N(a)) along the
line of sight?
d.) How would your answers to parts b. and c. be modified if
small grains were just destroyed (e.g. by energetic processes)
instead of being accumulated into larger grains?
e.) If a person trying to calibrate some kind of "standard
candle" by observing examples in our Galaxy (e.g. Cepheids)
at optical (e.g. B, V) wavelengths assumes a particular
"typical" grain size distribution by accepting a value
of RV=3.2, but the actual
R-value along a particular line of sight is actually, say
RV=5, how would that
person estimate the error this causes in calculating the standard
candle's unextinguished apparent magnitude at optical wavelengths?
Hint: think about what the person actually measured to estimate
the extinction at all.
f.) What wavelength ranges are most/least effected by changes
in R? Please keep this in mind in your future careers!
Mathis,
J.S. 1990, ARA&A, 28, 37
Mathis, J.S., Rumpl, W. & Nordsieck, K.H. 1977, ApJ, 217, 425