Spectroscopy

The work described here was done as part of my HET 606 "Tools of Modern Astronomy" project as part of Swinburne Astronomy Online's Masters of Science in Astronomy program.  As part of that project I built a simple spectrograph and used it to obtain the spectra of three bright stars and determine their spectral class.  The text below was modified from my project report.  My new comments will be visible in red.

While I have generally enjoyed all of my Swinburne projects, this was particular enjoyable and satisfying since I had to build the spectrograph myself and I could barely contain myself when I obtained my first slice of the spectrum of Betelguese.

This is a comparison of that slice and a high resolution spectrum of Betelgeuse from the Santa Barbara Instrument Group website for their Self Guiding Spectrograph.  SBIG is a major manufacturer of CCD cameras for the amateur market (including my two cameras) as well as making amateur spectrographs.

The upper spectrum is mine and the lower is from the SBIG website.  Band A is the hydrogen beta band at 4861.3 Angstroms and the two bands marked B are a Magnesium doublet at 5167.3 and 5172.7 Angstroms. 

While my spectrum is not as well resolved as the one made with the commercial SBIG spectrograph, the simple fact that I was able to see bands and align them with the SBIG spectrum was thrilling to me.

I have included 5 sections from my report--

Function of a spectrograph

A spectrograph’s purpose is to disperse the different wavelengths present in a star’s light onto a detector.  It does that by the interplay of the following components:

The objective (o in the right panel or the source in the left panel of Figure 2) in this case is the telescope and serves to gather sufficient light that will be collimated, dispersed and then focused by the other elements before being detected by the recorder.

Figure 2. Two schematics for spectrographs using either mirrors (left) or lenses (right) as the collimating and focusing elements and a diffraction grating (left) or a prism (right) as the dispersing element. (From Spectroschematicweb (left) and Thackery (right))

The slit is positioned at the focal point of the telescope (not shown in the left panel and s in the right panel of Figure 2) and serves to control the resolution of the spectrograph, especially when the object being imaged is extended like a galaxy or planetary nebula, by allowing only a thin slice of light into the spectrograph.  The spectrograph develops an image of the slit on the detector; therefore, the narrower the slit the higher the resolution of the spectrograph.  However, it does this at the expense of light entering the system (Mcdonaldweb).  The slit can be dispensed with if one is imaging stars as they are essentially point sources.  This is because, in this slitless case, the spectrum will be a series of images of the star whose size is dependent on the resolution of the telescope.  This is illustrated if one takes a spectrum of an extended object using a slitless spectrograph.  Figure 3 shows an image of M57, the Ring Nebula (left) and an M57 spectrum (right) taken with my spectrograph.  The slit also prevents the entry of spurious light into the spectrograph.

The collimating element (the upper mirror in the left panel and c in the right panel of Figure 2) serves to convert the diverging rays from the object (they are diverging after they pass the focal point) and make them parallel before they strike the dispersing element.  If this element is a lens, then because no lens is perfectly achromatic the light exiting this element will not be perfectly parallel but will diverge or converge slightly depending on its wavelength (Thackery). 

Figure 3.  Images of the Ring Nebula taken at 0^th order dispersion (left) and 1^st order dispersion (right).  Notice that the spectrum (right) shows multiple images of the object positioned at their appropriate wavelength (from right to left Hβ at 4861 Å, and two [OIII] transitions at 4959 Å and 5007 Å respectively (Planetaryweb).

The dispersive element is the heart of the spectrograph and has the function of separating the light into its component wavelengths.  There are three types of dispersive elements—the prism, the diffraction grating and the grism.  The prism, often with a 60 degree angle, was the first and oldest of these elements.  It uses the differences in the speed of light of different wavelength in the prism material to separate the wavelengths of light (Dispersionwiki).  It has the disadvantage that the dispersed light must pass through it.  This requires that the prism be of high quality and homogeneity.  Glass, which is the material that is usually used, also absorbs ultraviolet radiation, which makes observations in this region impossible without using a more expensive material like quartz in the prism.  The diffraction grating has a series of parallel lines, either etched on glass or on a metal reflective surface, depending on whether it is a transmission or reflection grating.  These lines are very closely spaced (thousands of lines/mm is not uncommon) and act like many very closely spaced slits which disperse the wavelengths of light that interact with them.  Reflection diffraction gratings do not suffer from the limitation of absorbing ultraviolet and can be used to examine features found there (Diffractiongratingweb, Thackery). 

Figure 4.  A magnified image of the surface of a diffraction grating.  One disadvantage of diffraction gratings is their formation of multiple spectra.  Each of these spectral orders is seen at a different angle (β₁ and β_-1 are two of these angles).  Blazing, making the grooves longer on one side than on the other, causes most of the light to be concentrated in one of the multiple orders of spectra that the diffraction grating produces.  From Birney et. al.

The grism is a special combination of a transmission diffraction grating and a prism (the name is made up from the two words).  It is designed to disperse the wavelengths around a fixed wavelength that is not dispersed.  This causes the spectrum to appear around an image of the object at the non-dispersed wavelength.  It is predominantly used for multi-object spectroscopy (Grismweb).

The focusing element (the lower mirror in the left panel and c’ in the right panel of Figure 2) focuses the now dispersed light onto the detector.

The detector is used to detect and quantify the amount of light in the dispersed spectrum.  Originally, the eye was used to visually observe the dispersed light (when the eye is used, the dispersing instrument is called a spectroscope, not a spectrograph), but this was replaced with film and more recently by charge coupled devices (CCD).

Design and construction of a spectrograph

Some initial design considerations were

I was able to find two extremely helpful websites dealing with spectrograph design to help me with the design considerations for my spectrograph (Classicalspectrographweb and Designspectrographweb).  They described the construction of diffraction grating spectrographs that used camera lenses as the collimating and focusing lenses.  Their collimating lens was a free standing 135mm F2.8 lens and their focusing lens was a 50mm lens attached directly to their CCD detector.  I have a number of camera lenses and I decided to use an 85mm F/1.8 Nikkor lens as my collimator and a 50mm Canon lens attached to my Santa Barbara Instrument Group (SBIG) ST-8XE CCD camera.  I obtained the appropriate adapter from SBIG to couple the lens to the CCD camera (if you get one of these for a Canon lens, be sure to confirm that they are sending you the shorter threaded connector between the CCD camera and the lens adapting piece.  The longer connector won't work).  The telescope that I used for this project was a Takahashi Mewlon 250, which has a native focal length of 3000mm and an objective of 250mm giving it a focal ratio of F/12.  Using the focal reducer, the focal length is reduced to 2300mm and F/9.2. 

Following the calculation in the Designspectrographweb, I determined that there would be no vignetting due to the collimator since its focal length is less than the focal length of the telescope (F/1.8 < F/9.2).  I also calculated that the diameter of the collimated beam would be 9.2mm.  Because I was using a much longer focal length telescope than they were in their discussion, when I calculated the resolution, R, using their example of a 600 lines/mm diffraction grating and an angle of 38 degrees for the total angle (γ) between the incident and diffracted ray, I got a value of only 615.  Since I wanted to achieve a better resolution than this, I decided to use a diffraction grating with 1200 lines/mm.  I also decided to use the total angle suggested by the Classicalspectrographweb site of 28.5 degrees. 

Using these parameters, I found that the angle of incidence (α) would be 34.2 degrees and the angle of diffraction (β) would be 5.6 degrees.  I also found that the resolution, R, which is defined as the wavelength of light observed divided by the resolution at that wavelength (λ/Δλ), would be 1256 at a wavelength of 5500Å, which should be near the center of my spectra.  Spectrographs with R values of greater than 1000 are considered medium resolution.  The degree of dispersion (ρ), which is defined as the number of Angstroms of spectrum per pixel, would be 1.49 Å/pixel.  Because of the smaller collimated beam, I decided to get a 25mm 1200 lines/mm ruled diffraction grating from Edmund Scientific (part number NT43-005) along with a kinematic square optical mount to hold it.  The last calculation was to determine the diameter of the dispersed beam using the above values.  Unfortunately, this is where I made an error by placing the front of the lens too far from the grating.  This allowed me to place the weight of the camera closer to the telescope, which helped with the balancing situation, but this made the beam so dispersed by the time it reached the detector, that I had vignetting.  This only meant that I couldn’t use the full width of the CCD chip but the performance of the center was as expected, as we shall see.  

This shows the arrangement of the collimating lens (at the bottom), the diffraction grating in its kinematic mount and the CCD camera with its focusing lens attached on the spectrograph.  This image was taken before the excess wood was removed as shown below.

I had to decide how I would attach the spectrograph to the back of my telescope.  The Mewlon has a removable back plate, which is normally used to allow air to circulate around the mirror to aid in temperature equilibration.  There is space between the back of the mirror and the metal isthmuses in Figure 7 left panel.  Because I needed to ensure stability in both the attachment of the spectrograph and prevent any possible flexure of the optical path of the spectrograph, I decided to use a piece of ¾ inch plywood attached to the back of the telescope and as the support of the spectrograph itself.  I realized that this would make the entire spectrograph heavier, but I knew that my Takahashi NJP mount could easily support the added weight.  A central hole was cut in the plywood just large enough to go over the central projection seen in Figure 7.  Holding the plywood to the back of the telescope was done by passing U-bolts covered in rubber tubing between the mirror and the back piece of metal at the three sites indicated in Figure 7 left panel (the metal isthmuses at 1:30, 6 and 10:30), then through a ¼ inch sheet of cork between the plywood and the metal back to protect the finish and to act as a shock absorber and then finally through the plywood back as shown in Figure 7 middle panel.

To ensure that the CCD camera was at the right height to match the light path, I placed the CCD camera on the back of the telescope, and then placed the spectrograph bottom plywood piece against the camera just as it will be when attached and marked where the bottom plywood and the back plywood met.  This allowed me to correctly position the metal brackets seen in the middle panel of Figure 7.  I made a holder for the collimator lens (with the help of my friend Max Cleveland.  Thanks, Max).  I made a paper template with the proper angle (28.5 degrees) measured on it.  The distance to the focal point (the metal back distance) for the focal reducer was marked; the position of the collimation lens holder was marked based on positioning the front of the lens 85mm from the focal point.  I also marked a position for the diffraction grating and for attaching the CCD camera.  Appropriate sized holes were drilled at each point, the three pieces were added and their alignments checked.  They were temporarily removed and as much excess plywood as possible was removed to decrease the weight.  Then the components were reattached.  The spectrograph was attached to the back of the telescope (Figure 7 right panel) and was then ready to use. 

Figure 7.  The back of my Mewlon 250 telescope without and with the plywood back (left and middle panels respectively).  The spectrograph attached to the telescope (right panel)

Using the spectrograph to obtain stellar spectra

With the telescope set up and the spectrograph in place, it was time to obtain spectra.  First, the telescope was properly polar aligned using its polar alignment scope.  This ensures that the star will not drift during spectra acquisition.  Then the CCDSoft software in the computer was connected to the CCD camera and the camera was cooled to between -10 and -15 degrees below zero Celsius.  To achieve rough focus, the telescope was turned on the Moon and a card was placed at the focal point.  An out-of-focus image of the Moon was observed on the card.  The focuser was then adjusted to bring this lunar image to focus.  To achieve better focus, the diffraction grating was positioned for simple reflection on the CCD camera chip.  Images of the first star, Vega, were taken and the focuser was adjusted to give best focus (in a manner analogous to Figure 3 left panel).

The diffraction grating was then returned to the appropriate angle for the 1^st order spectrum (34.2 degrees) and when an image was taken a bright streak was seen on the CCD detector.  No obvious dark lines were seen, but I soon realized that I could see the absorption bands if I moved the detector in Right Ascension (RA) during the image acquisition.  This caused the spectrum to be spread over a greater number of pixels and lowered the intensity to the point where the absorption bands were easily visible.  I took 5 images for Vega spectrum for 5 seconds each while moving the telescope back and forth in RA.  I then used the kinematic holder for the diffraction grating to move it up and down the spectrum generating 10 overlapping spectrum fragments.  Once I had completed the Vega spectrum, I moved on to the second and third targets—Capella and Betelgeuse and did the same (on Betelgeuse, I moved the telescope for 10 seconds per image acquisition).  I did not do dark subtraction or flat fielding since the images were taken for such short times that they were quite clean.

I then used Registax (Registaxweb) to combine the 5 subimages to make a complete spectrum fragment.  I brought the spectrum fragments into Adobe Photoshop CS.  I noticed that the spectral lines were not always equally sharp across the image.  As the resolution is limited by the seeing in the absence of a slit, presumably the regions of reduced sharpness represent times when the stellar image was blurred by the seeing.  In order to remove the influence of these blurred images, I selected slices along the spectrum fragment that were 1 pixel in height in a region where the bands were sharp.  These images were about 40 CCD pixels high and took about 5 seconds to make so this one pixel represents about 1/8^th of a second of seeing.  I then copied the slice and expanded it back to 40 pixels in height.  If the image was particularly noisy, I used the Despeckle feature of Photoshop to smooth it before slice selection.  

These spectrum fragments were then combined in Adobe Photoshop to generate complete spectra for each of these stars (Figure 8).  

This figure shows the ten slices for Betelgeuse and the final combined spectrum.

Figure 8.  Comparison of my spectra for Betelgeuse, Vega and Capella and stars with similar characteristics.  Each set consists of a published spectra (upper in each case) and my spectra (lower in each case).  I have marked the Balmer series lines through the H8 band and placed a wavelength scale at the bottom.  My Betelgeuse spectrum is compared with a published Betelgeuse spectrum from SBIGweb and my Vega and Capella spectra are compared to A1V and G4V stellar spectra respectively from Poggeweb (used with permission from Richard Pogge).  The image is a link to a high resolution image which can take substantial magnification, but is fairly large (around 3 Mb) so it make take a while to load.  I have added Mirfak (alpha Persei) to this group of star spectra.  It is compared to a F5v spectrum from Poggeweb.  It is a F5Ib supergiant.

At the time of design, I had considered that using the more dispersed 2^nd order spectrum might make it possible to get higher resolution spectra.  To test this, I set the diffraction grating’s angle of incidence to 57 degrees which should have been in the middle of the 2^nd order spectrum.  When I tried to find features in the spectrum of Vega that should have been in this vicinity, I was unable to do so.  I kept finding features from the infrared portion of the 1^st order spectrum instead.  It was at this point that I realized that the overlap of the infrared portion of the 1^st order was strong enough to make seeing the 2^nd order spectrum impossible.  I then thought to try using an infrared filter that I use for planetary imaging to suppress the 1^st order spectrum.  This necessitated my removal of the focal reducer which changes the focal length from 2300mm to 3000mm.  When I did this I was able to find the 2^nd order spectrum.  Figure 9 is an example that shows the higher dispersion in the spectrum of Capella.  

Figure 9.  Comparison of the 1st and 2nd order spectra of Capella

I found a paper dealing with the spectrum of Capella (K. O. Wright, The Spectrum of Capella, Publications of the Dominion Astrophysical Observatory, 1954, Vol. 10, No. 1, pages 1-45.) that showed regions of the spectrum in detail.  One of these regions is from about 4030 Angstroms to 4080 Angstroms.  This is found in my second order spectrum shown above just above the "2nd" in "2nd order".  I scaled this part of my image to match the scale of the spectral region from the paper.  I also used the "Slice" function from the Iris astronomical software by Christian Buil (Irisweb) to make a graph of this region and compared it with the graph of this region of the spectrum from the paper.  The results of this comparison can be seen below.  The upper panel of each set of two is from the paper and the lower panel is from my data.

Another factor that enters into this comparison is the fact that Capella is a binary star system with a period of 104.023 days.  Using the date for the data acquisition in the paper and the date that I acquired my data, I figured out that when I acquired my data the star was on day 43.5 of its orbit.  The three spectra in the top panel above shows spectra acquired at three different points in the orbit.  One with primary to the red phase, one with the primary to the violet phase and one in between.  The phase at the time when I did my spectrum is closest to the 53 day phase and shows good agreement with both my spectrum compared to the paper's spectrum for that phase and the graph of my spectrum compared to either of the graphs shown.  When I removed the focal reducer and then used the 2nd order spectrum, it increased my resolution, R, from about 1200 to about 3000.  This accounts for the improvement in the resolving power of the spectrograph.

Determining the spectral classification of these stars

With this information it is possible for us to determine the spectral classification of these stars.  The MK classification system that is in use today consists of two major parts—a classification (the OBAFGKM system) whose divisions are based on the differences between the chemical make up of the stars and a classification (the I through V system for supergiants through main sequence stars) whose divisions are based on the differences in the luminosity of the stars.

The first thing that needs to be done is to roughly assign these three stars to a spectral class by comparing their total spectra with the distribution of neutral and ionized metals and hydrogen present in their spectra.

Figure 10. A plot of the distribution of Hydrogen and neutral and ionized metals versus spectral class.   From Classificationweb.  

The simplest of the three is probably Vega.  It has the simplest spectra that is dominated by a relatively few lines.  These lines correspond to hydrogen which means that according to Figure 10 it is probably towards the end of the B class, within the A class or near the beginning of the F class.  Figure 10 also tells us that if it is within the B class we ought to see neutral helium lines and if it is within the F class we ought to see ionized metals.  Capella is next easiest.  The hydrogen lines are still visible, although they are much weaker than in Vega.  Consulting the plot in Figure 10, this suggests that it is either within the G class or at the beginning of the K class or it is within the B class.  If it is the latter, we ought to see neutral helium lines.  If it is the former, we ought to see neutral metals.  Betelgeuse is last and probably the most difficult initially.  It has the most bands including some areas with strong absorbances over broad areas.  This is the hallmark of absorbance due to molecules rather than elemental absorbances.  This would place it in the K or M class, which are the only stars in this group cool enough to contain molecules.  Assignment could be achieved by examining the spectrum for ionized metals which might be present in a K class star, but might not be present in an M class star. 

Figure 11 shows a detailed comparison of part of the spectrum of Vega with known spectra of the A spectral class.  The position of a neutral helium line that is known to be present in the B spectral class is noted at position 2 (Yamashita et. al.).  Clearly, the smoothness of the spectra and the weakness of the Ca II line indicates that Vega belong high in the A spectral class or even in the B spectral class.  Even the A1 spectral class shows a small number of spectral lines other than hydrogen.  Examination of spectral class B9 shows a weak band for helium at 4026 Å, which seems to correspond to the band seen in my spectra.  Comparing my Vega spectra with those of A class stars of different luminosity classes, the width of the hydrogen lines indicates that it is not a member of the Ia or Ib supergiant class and probably not a member of the III giant class.  I propose that Vega is either a A0 or B9 class and that it is either a IV subgiant or a V main sequence star.  Vega is known to be a A0V star.

Figure 11. A comparison of A class spectra with that of Vega. 

Figure 12. A comparison of G class spectra with that of Capella. 

Figure 12 shows a detailed comparison of Capella with members of the G spectral class.  An examination of the lines identified in the figure shows a mixture of ionized and neutral metals and does not show any helium lines.  This would be consistent with it being a member of the G spectral class.  The only line that I could identify that is diagnostic within the G spectral class is the CN band at 4216 Å, which decreases in intensity compared to the Ca I band at 4277 Å as one goes from G9 to G0.  My spectra shows the intensity being near the middle of the range (compare 4 and 6 in the upper panel).  Comparison of my spectra with stars in the G5 spectral class but with different luminosity classes shows a similar result (compare bands 5 and 7 in the lower panel).  I would place Capella in the middle of the G class and in the III giant luminosity class.  Capella is a binary star system with two G stars—a G0III and a G5III.

Figure 13 shows a detailed comparison of the spectra of Betelgeuse with M class spectra.  The identified bands are all for neutral metals, which is one of the hallmarks of the cool stars of the M class as are the molecular absorption bands for titanium dioxide (TiO₂).  The strength of the molecular absorption band places Betelgeuse in the M spectral class.  The strength of the titanium dioxide bands would put it above the middle of the group, possibly above a M4 or M3 class.  The weakness of the Ca I 4227 Å band would place Betelgeuse near the top of the luminosity class.  I would put Betelgeuse near the top of the M class, between an M0 and an M4 and would put it in either the I or II luminosity class.  Betelgeuse is known to be a M2Ib star.

Figure 13.  A comparison of M class spectra with that of Betelgeuse. 

For each of Figures 11, 12 and 13, the central spectra is mine.  The detailed spectra came from Yamashita et. al.  The upper spectra show variation in the compositional spectral class, while the lower spectra show how that the spectra vary with luminosity class.

References

Spectroscopywiki  http://en.wikipedia.org/wiki/Spectroscopy

J. B. Hearnshaw, “The Analysis of Starlight—One hundred and fifty years of astronomical spectroscopy”, Cambridge University Press, 1986.

Morgan, Keenan and Kellman, An Atlas of Stellar Spectra with an outline of spectral classification, Astrophysical monographs, University of Chicago press, 1943.  http://nedwww.ipac.caltech.edu/level5/ASS_Atlas/frames.html

Spectroschematicweb http://en.wikipedia.org/wiki/Image:Spectrometer_schematic.gif

A. D. Thackery, “Astronomical Spectroscopy”, Macmillan Company, New York , 1961.

Mcdonaldweb http://mcdonaldobservatory.org/research/instruments/instrument.php?i_id=8

Planetaryweb http://www.astrosurf.com/buil/us/spe6/planet.htm

Dispersionwiki http://en.wikipedia.org/wiki/Dispersion_%28optics%29

Diffractiongratingweb http://www.britannica.com/eb/article-9030420/diffraction-grating

Grismweb http://nicmosis.as.arizona.edu:8000/GRISM.html

Spectroscopyweb http://www.astro.sunysb.edu/fwalter/AST443/spectroscopy.html

Coudeweb http://www.daviddarling.info/encyclopedia/C/coude_focus.html

CurvedDGweb http://cord.org/cm/leot/course06_mod09/mod06_09.htm

Echellegratingwiki http://en.wikipedia.org/wiki/Echelle_grating

Echellespectraweb http://zuserver2.star.ucl.ac.uk/~sk/osl/projects/as/spect.html

Objectiveprismweb http://everything2.com/index.pl?node_id=1509605

Longslitweb http://isc.astro.cornell.edu/~sloan/research/longslit.html

Dan F. Lester, Gary J. Hill, Greg Doppmann, and C.S. Froning, Coolspec: A Near-Infrared Long-Slit Spectrometer for McDonald Observatory, Publications of the Astronomical Society of the Pacific, 2000,  Vol. 112, 384-396. http://www.journals.uchicago.edu/PASP/journal/issues/v112n769/200067/200067.web.pdf

SDSSweb http://www.sdss.org/background/telescope.html

Classicalspectrographweb http://www.dlr.de/jupex/spectograph/internet/hresol0.htm

Designspectrographweb http://astrosurf.com/buil/us/stage/calcul/design_us.htm

Registaxweb  http://www.astronomie.be/registax/

SBIGweb http://www.sbig.com/sbwhtmls/spectrometer2.htm

Poggeweb http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit1/SpTypes/index.html

Irisweb http://www.astrosurf.com/buil/us/iris/iris.htm

Classificationweb http://zuserver2.star.ucl.ac.uk/~pac/spectral_classification.html

Yasumasa Yamashita, Kyoji Nariai and Yuji Norimoto, “An Atlas of Representative Stellar Spectra”, University of Tokyo press, 1978.