When a spectrum is obtained this is what it will look like. It has to be processed much like any other
image. In addition, note the slant in the spectral lines, and, although not evident, the horizontal line is
slightly tilted. Both have to be corrected. You also have to subtract the sky
background.
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Preprocessing.
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Much can be done in other image processing software, such as CCDSoft or CCDOps, but
IRIS can do it all and more.
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If the integration time is short enough at least 3 images of the target star should be
taken, at least 3 of the dark frames, and at least three offset frames. This is necessary to
primarily get rid of cosmic rays. Also, it is a good practice to take at least 1 calibration
spectra before and after each target frame.
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Take 3 or more flat fields, and a separate set of dark frames.
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Preprocessing
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Although IRIS can do all and much more I have been using CCDSOFT to do the median combines
and flips, and then finish up with IRIS.
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For the target star first create a master dark, STAR_MD, and master offset, MO, from the
multiple dark and offset images by doing a medium combine. It is my understanding that an
offset is only needed if the imaging camera does not have temperature control.
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Next create a master dark for the flat field images by doing a medium combine. Subtract the
master dark from each flat field image and then do a medium combine, MF, of the corrected flat
field images.
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For each target star spectrum, TS_n where n equals the image number, do the following
subtracts and division
TSC_n = (TS_1 – STAR_MD - MO)/MF
and then do a median combine of TSC_n to create TSC
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Finally, if TSC is not already oriented with the blue to the left and the red to the right do a flip. If
your image processing software does not have this capability, you can do it in IRIS.
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Now finish the processing in IRIS. IRIS is used to correct for tilt of the spectrum, slant of
the spectral lines; to subtract the sky background, and finally to optimize (minimize
noise) of the final spectrum.
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First, to get the two important parameters, tilt of the horizontal spectrum and Slant of
the lines, load the target star spectrum and in console mode enter the command >LORI
Make a note of the Tilt angle of -0.105 degrees. Establish the location of the spectrum in the image by
getting the beginning and end of the spectrum along the vertical axis. In this case it is 520 to 540 pixels.
This will be the same range used to crop the Neon spectrum
Now load the Neon calibration spectrum and crop the image to only include the vertical range of the
target spectrum. For my camera the image is 1530 pixels wide. If you are uncertain what it is for your
camera, start x2 at the high end and work down. You need the full width for cropping.
First tilt the cropped spectrum with the >TILT 765 -0.105 command. Note the 765 pivot point on the x
axis because it will have to be used on the target star. The >mirrorxy command brings the image from
the top to the side. Get the tilt angle for each line with the L_ORI command and take the average of the
two which is -1.363
Now do another >mirrorxy to bring the image back to the top. Next make the emission lines vertical by
entering >SLANT 10 -1.363. 10 is the mid point along the y axis. Note the slant angle because it will
have to be applied to the target spectrum. Now Enter >L_OPT to optimize. If blue is not on the left, flip
the spectrum and then Save it with the >SAVE Neon command. A Neon.fit file is created for calibrating
the target star.
Reload the target star spectrum and correct for Tilt and Slant using the values previously obtained,
making sure the reference points are identical to those used for the Neon spectrum. The L_SKY3
command asks to select four points on each side of the spectrum and after selection it applies a linear
relation to the sky background. L_SKY2 applies a median, L_SKY4 a quadratic. Finally, enter L_OPT. It
asks to draw a rectangle around the spectrum.
The L_OPT command creates a 1D spectrum that is the sum of the values in the columns in the area
selected and give less importance to pixels that have received little starlight. The 1D spectrum is
duplicated 20 times so it can be seen. Now save it with an appropriate name, such as
EA_Preprocessed.fit
FLUX CALIBRATION
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Variations in transmission and quantum efficiency between different instruments and detectors
can result in large variations in relative intensity, confounding interpretation. It, therefore, is
necessary to correct, i.e., calibrate, a spectrum so that results from different instruments and
detectors are comparable.
For example:
This is a transmission curve of the Borofloat glass used as the corrector plate for my 16” telescope.
This is the (smoothed) quantum efficiency curve of the CCD chip in my ST8-XME camera. The differential
wavelength reflectivity of the coated mirror surfaces is another transmission factor but this is not shown
here.
To flux calibrate a spectrum of the target star one must
1. Generate an instrumental response curve.
2. apply the curve to the target star spectrum.
3. Correct for the differential transmission by wavelength and elevation through the Earth’s
atmosphere . This converts the flux to an approximation of what it would be in outer space.
Constructing an Instrumental Response Curve
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In estimating an instrumental response curve we are not interested in individual spectral lines,
but instead the general trend of the instrumental response curve. The ideal would be to use
Vega as the reference star because theoretical intensities are available for this star and as a
result a better calibration can be obtained. However, this is not always possible and so the
general procedure is as follows.
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In my example Epsilon Aurigae will be the target star and Gamma Gemini will be the reference
star. Always choose a reference star of spectral type O,B,A, or F. We do not want a lot of
spectral lines because this makes estimating the response curve difficult and so later spectral
types are not desired.
The idea behind constructing an instrumental response curve is the following. Consider the following
graph where the top two profiles, A and B, are target star profiles, and the bottom two, C and D, are
reference star profiles.
Let
A = flux calibrated spectrum of target star
B = instrumental spectrum of target star
C = theoretical spectrum of reference star
D = instrumental spectrum of reference star
The general procedure is to
1. Divide D by C, and then obtain a smoothened curve of the resulting
profile. This is the instrumental response curve, E.
2. Then divide B by E. This gives A, the flux corrected spectrum of the
target star.
To see mathematically what these two divisions do,
Let A = TT = the flux calibrated spectrum of the target star
B = TI = instrumental spectrum of the target star
C = RT = the theoretical spectrum of the reference star
D = RI = instrumental spectrum of the reference star
Then, at a pixel location i the estimated theoretical intensity on the theoretical continuum of the
target star is
TTi = Ki(TIi), where Ki is a proportionality constant at
pixel location i.
but Ki = RTi/RIi which is the theoretical spectrum of the
reference star divided by its instrumental spectrum.
TTi = (RTi/RIi)(TIi)
= (Tii)/(RIi/RTi)
Thus, the denominator is the first division, and
(Tii)/(RIi/Rti) is the second division.
Now to demonstrate how to do this in VSPEC.
It is assumed in the following presentation that the spectrum of Epsilon Aurigae and Gamma
Gemini have been wavelength calibrated. First load the EA profile and then the GG profile by clicking
File and then ‘Open Profile’.
Next, get the spectral type of the reference star. GG is an AOIV star. Activate the reference star profile if
it is not already activated. Then click on Tools and then Library. Next with the right mouse button drag,
in this example, the a0iv.dat file on to the GG profile.
The smooth greenish line is the theoretical intensity of the AOIV spectral type. Next make the Intensity
series the active series. Then click on Operations and then ‘Divide profile by a profile.’ Highlight a0iv.dat
and press OK.
In the upper left corner of the screen note that the box has the word Division. Click on the ‘Erase
graphic’ button to clear the screen.
Then go into the above mentioned box and select Division even though the word is still displayed. Here
is what you see.
Next click on Radiometry and then ‘Compute Continuum.’ The check mark by the Compute Continuum
line is after the fact and will not be present when you open the menu. Note the line changed from green
to red.
Next eliminate spectral lines that would interfere with getting a good response curve estimation. Select
the lines that need to be eliminated and click on the ‘supress zone’ button.
This is the spectrum after surpressing all lines. It is now all noise, or hopefully it is. Next click on the
Execute button.
This is what you get, the un-smoothened response curve superimposed on the intensity series. The
Spline Filter slide bar comes up automatically with the number 20 in the lower middle box. Enter 20,000
or some other appropriate value, and check the x10 box.
Slide the bar until the desired fit is obtained. Click on X to get rid of the Spline Filter box. The series that
needs to be saved is the one called Fit.Division as seen in the upper left corner. If you do not see this,
click on Erase graphic and then select this series.
Click on Edit and then Replace. The following dialogue box comes up. Clicking on OK makes the
Fit.Division series an Intensity series. This is necessary because only an Intensity series can be saved. This
is the instrumental response curve.
This is the response curve after having clicked on ‘Erase graphic’ and re-selecting the intensity series.
It can be used for other spectra in this wavelength range taken with the same telescope and camera. Do
not save it with ‘Save’ or else it will replace the original Intensity file. Do a ‘Save as’ and give it a name
something like ‘Instrumental_Response.’
Next activate the Epsilon Aurigae window and makes sure the Intensity series is active. Then click on
Operations and then ‘Divide profile by a profile.’ In the Selection drop down dialogue box click on
Intensity series associated with the Instrumental_Response profile and then click OK.
Now we want to make the Division series, the lighter colored line, an Intensity series so we can save it.
Click on Edit and then Replace. Make sure the Division series is stated in the drop down dialogue box
and click OK.
This is the result. Save it with ‘Save as’ and give it a name something like EA_Prefinal.
Now the only thing left to do is correct for atmospheric extinction. If this is not done then equivalent
widths between spectroscopists will not be fully comparable if they did not observe the star in the same
location in the sky and at the same topological elevation. This is not easy to do for a spectrum because
the atmospheric transmission varies with wavelength. Fortunately, VSPEC has a procedure that does all
the messy math.
The first parameter needed is Air Mass. This is obtained through the Heliocentric correction drop down
dialogue box, but first the latitude, longitude, and topological elevation needs to be entered in
Preferences. Click on Options, then Preferences, and then Position in the drop down menu.
Next click on Spectrometry and then ‘Heliocentric Correction.’ In the dialogue box enter the RA and DEC
coordinates of the star, and the day, month, and year. The day value is a fractional value composed of
an integer for UT day and the fractional part of 24 hours. It is not necessary to change the value for
‘angstroms.’ For this example the air mass is 1.099.
Click on Radiometry and then Extinction. In the drop down dialogue box enter the air mass. An air mass
of 1.099 will not produce a noticeable effect and so for demonstration purposes a larger value of 3 will
be used. The extinction corrected series is the orange line.
The final step is to save the extinction corrected series called ‘extinct’ in the upper left box. To save the
final series it needs to be made an Intensity series. To do this click on Edit, then Replace, and then click
on OK. Note the series is now blue in color. Save it with a ‘Save as’ and give it some name such as
EA_Final. Now you are ready to start computing Equivalent Widths.