Astro 3310 Fall 2015
LAB #6:
-----Please copy this document to the REPORT sub-directory from the
expanded LAB6_Data_Package_FA15.tar.gz. Then, edit it to write your
answers in all the "______" areas. When finished, create a tar.gz
archive of the REPORT directory and all of its contents, then scp
the file to datafarm.astro.cornell.edu and place it in:
/data/Courses/A3310/FA15/”your netid”/LAB6/
Remember that you will only get credit for the files that you put in
the REPORT sub-directory and copy to datafarm. Please make sure
that you keep a Matlab workbook with all of the commands you used to
answer the questions in the lab. Feel free to comment and organize
your workbook so that it will be easy for us to follow your
algorithms when we execute the doe. If you generate any functions
for the lab, ensure that they are also in the REPORT sub-directory
and properly called from the workbook file. For you convenience,
there is a template for the workbook file already in the REPORT subdirectory.
YOUR NAME: _______________________________
Your NetID: __________
The data package includes four datacubes of Titan, taken with the
SINFONI instrument on the European Very Large Telescope (VLT):
MOV_Titan2_20140715_NGS_OBS_OBJ.fits
MOV_Titan2_20140715_NGS_OBS_OBJ_1.fits
MOV_Titan2_20140715_NGS_OBS_OBJ_2.fits
MOV_Titan2_20140715_NGS_OBS_OBJ_3.fits
And a telluric standard (star with a smooth spectrum to calibrate
the Earth’s atmosphere):
Telluric_Standard_OBS_STD.fits
Each fits file is a self-contained observation, with small offsets
in the pointing of the telescope. There is some variation in the
performance of the adaptive optics system from one observation to
the next, so the image "Point Spread Function" (PSF) varies somewhat
from one datacube to the next. For the problems below, you may use
one datacube, or all of them. You may also combine the four into a
single datacube for improved signal to noise and bad pixel
rejection.
Each datacube consists of a 2172 wavelengths of a 64 x 64 pixel
image of Titan. The wavelength calibration is described in the FITS
header keywords crpix3, crval3, and cdelt3.
Familiarize yourself with the datacubes. You will need to be able
to extract a spectrum of a given pixel, and extract images at a
given wavelength.
Part 1:
Make an average (full disk) spectrum of Titan from one of the
datacubes. Note that there are some bad pixels and invalid data
(NaN values) that you need to handle in order to extract a valid
spectrum. Your spectrum should look mostly like the spectrum in
http://adsabs.harvard.edu/abs/2009Natur.460..873S
Note that some of the features you see in the spectrum are features
of the Earth’s absorption, not Titan.
Use the ESO Sky transmission calculator:
https://www.eso.org/observing/etc/skycalc/ to calculate an
atmospheric absorption spectrum at a similar spectral (wavelength)
resolution as the datacube and compare it to the Titan spectrum.
Answer: Insert a figure of your raw spectrum annotated to
identify features in the Earth’s atmosphere and Titan’s
atmosphere.
Part 2:
The telluric absorption can be corrected by measuring a star with a
smooth spectrum, and dividing the observed spectrum by the observed
telluric absorption. Hot (O, B and A-type) stars have nearly
featureless spectra that are close to a blackbody.
Construct a telluric spectrum using the datacube
Telluric_Standard_OBS_STD.fits, and compare it to the model Earth’s
absorption spectrum. Note that there are some features that are
present in the stellar spectrum that are not in the Earth’s
absorption spectrum (e.g. the 2.16 μm “Brackett-gamma” feature due
to atomic Hydrogen absorption). For the most careful analysis,
these features should be excised from the calibration spectrum
either by interpolation or using a theoretical model of the
spectrum, but for the purposes of this lab, these features may be
ignored, but they will produce small artifacts in the final
spectrum.
To calibrate out the Earth’s absorption in the Titan spectrum using
this stellar spectrum, the Titan spectrum needs to be divided by the
stellar spectrum. Note that this also divides the spectrum by the
spectrum of the star, which is brighter at shorter wavelengths.
This can be corrected by multiplying the spectrum by a Planck
function with the appropriate temperature for the star,
approximately 10700K for a B9V star. There is a function to
calculate the planck function in the SUBROUTINES directory.
Answer:
Insert a figure of your calibrated spectrum
What is the difference between the bright and dark regions of the
Titan spectrum? Hint: imagine what you would see if you were
looking at a reflected spectrum of the Earth illuminated by the hot
spectral calibrator star observed above.
Part 3:
There are archival observations of Titan going back nearly 20 years
using adaptive optics on large ground based telescopes, including
the VLT and also the Keck 10m telescope in Hawaii. Nearly all The
Keck data becomes publically available after an 18 month proprietary
period. There are many more imaging observations than spectroscopic
observations, and those images are taken in filters that probe
different regions of Titan’s atmosphere.
Use the Keck archive search tool
http://www2.keck.hawaii.edu/koa/public/koa.php to find observations
of Titan with the NIRC2 (adaptive optics imaging) instrument. Sice
Titan is a moving object, note that you need to search on the
TARGNAME, not the Object Name, which is resolved into astronomical
co-ordinates.
These observations are taken in a variety of filters, which are
described at http://www2.keck.hawaii.edu/inst/nirc2/filters.html
Choose 2 filters that have a substantial number of observations in
the archival data, and are within the spectral coverage of the titan
datacube, preferably one filter that covers brighter parts of the
spectrum and one that covers darker.
Download at least 5 different epochs of observation in these
filters, and make a figure that compares the images in the different
filters at different times. Note that most observations from the
archive will be delivered uncalibrated, and without much quality
control. You may find that some of the observations are of low
quality, and have to pick and choose. Occasionally the observer may
not have correctly updated the TARGNAME field, mis-pointed the
telescope, or there could be clouds in the way so some of the
observations will be faulty and you need to exercise a little care.
Typically the calibration data is also available from the archive to
dark/sky subtract and flatfield the images. This processing, and
averaging multiple images will yield superior quality images, but is
not essential for the purposes of this lab.
Answer:
Insert a figure of your archival data
Discuss what you have found, and what changes with wavelength and
time.
Part 4:
In the datacube in part 1, there is a bright feature, a cloud.
Extract and compare the spectra of the bright and dark features in
the datacube.
Answer: Insert a figure comparing the bright and dark spectral
features
Part 5:
Due to absorption in Titan’s atmosphere, the observed radius of
Titan changes as a function of wavelength (see the discussion in
http://adsabs.harvard.edu/abs/2014PNAS..111.9042R ). Using the
datacubes above, determine the radius of Titan as a function of
wavelength.
Answer: Insert a figure showing the radius of Titan as a
function of wavelength.
Explain the algorithm you developed to measure the radius of Titan.
Background Reading:
Radiative transfer in atmospheres:
https://geosci.uchicago.edu/~rtp1/papers/PhysTodayRT2011.pdf
Titan Occultation http://adsabs.harvard.edu/abs/2014PNAS..111.9042R
Adaptive Optics Imaging of Clouds in Titan:
http://adsabs.harvard.edu/abs/2009Natur.460..873S