Spectrum Synthesis: An Introduction
Spectrum synthesis is a technique where a theoretical spectrum is
generated by computer using the known laws of physics. It is a computer
intensive process which allows for a variety of inputs and allows one to match
the obtained spectrum with the theoretical spectrum. By so doing, one
establishes various stellar parameters such as temperature, surface gravity,
abundances among others. Initially a few basic concepts need to be understood,
for example, the equivalent width. The
width is a measure of the intensity of a spectral line, either absorption or
emission. Often times it is normalized by dividing the value by the wavelength.
The beauty of the EW is that it is instrument-telescope independent.
Decades ago, quantitation of elements in stellar atmospheres was done by
constructing curves of growth (see paper below). This was gradually replaced by
synthetic spectroscopy as computing power has increased. Now, one can compute
and display a spectrum on a regular home PC, vary the parameters and match up
your spectrum with the synthetically derived spectrum to zero in on certain
parameters of the star. This is described in greater detail in the paper below.
I have been using the program SPECTRUM by Dr. Richard Gray of Appalachian State
This software, which is freely available runs in a unix environment. I have
been using Cygwin (http://sources.redhat.com/cygwin/)
which allows you to run a unix emulator on your PC. In order to run the
program you need a stellar atmoshpere model (there are thousands of these) which
gives a run of pressure and temperature in the atmospheres outer layers. These
models are the Kurucz Atlas9 models. The figures below give a basic outline as
to how you carry out the procedure. Once the spectrum is computed, you can use
Excel, for example to display the results.
= acceleration of surface gravity
= micro turbulence velocity, think of this as the upwelling and sinking velocity
of surface cells such as solar granulation.
Spectroscopy: From Qualitative to Quantitative Analysis
Dale E. Mais
Abstract: Spectroscopy is a new field of study for the amateur. This
type of exploration by an amateur is the result of the availability of several
types of off-the-shelf spectrometers, which can be coupled to a CCD camera. For
the most part, amateurs pursuing this area have done so more from a qualitative
standpoint: stellar classification and identification of the more prominent
emission and absorption lines in stars and gas clouds. However, a spectrum
contains much more valuable information about the physics of the region under
survey. My talk will describe my initial efforts in the use of synthetic
spectroscopy and how it can be used to determine a variety of stellar parameters
such as temperature and abundances. The process involves the creation of stellar
atmospheric models where a variety of variables can be altered and the resulting
spectrum fitted to the actual spectrum obtained at the telescope to find the
1. S. Kannappan and D. Fabricant, Getting the most from a CCD Spectrograph, Sky and Telescope, 100(1), 125-132, 2000.
Optical Astronomical Spectroscopy, C.R. Kitchin, Institute of Physics
Publishing Ltd, 1995.
3. Astrophysical Formula, K.R. Lang, Springer-Verlag, 2nd edition, 1980.
continuing advance of technology and instruments which are affordable to the
amateur and small observatory community has now made it possible for amateurs to
work in areas of astronomy, until now, previously the domain of the
professional. This includes spectroscopy. The first break-through occurred with
the introduction of low cost CCD detectors. This paved the way for a
breathtaking increase in what the amateur could now accomplish in photometry and
astrometry. Closely coupled to this has been the increase in low cost computing
power and versatile and user-friendly software. Never before has the amateur had
such an array of technology and tools available to conduct and contribute to
the availability of spectrometers has made it possible for the amateur to do
spectroscopy using moderate resolution. Coupled to sensitive CCD detectors,
these instruments, coupled to even modest sized telescopes, allows the amateur
to do a wide variety of projects such as classification, identification of
atoms, ions and molecules in nebulae, stars and interstellar regions. This only
represents the beginning however. The analysis of a spectrum tells one a great
deal about conditions and processes within astronomical objects. This kind of
information is contained within the spectrum, as intensity of the line, the
shape of the line and the presence, absence and ratios of intensities of lines.
I will describe in this paper some of my initial attempts at using software,
freely available, which calculates the spectrum of a star. Various inputs are
possible and a comparison of the computed spectrum with the actual spectrum
allows for the determination of various physical conditions in the atmospheres
My primary instrument for spectroscopy is a Celestron 14, which has had a Byers retrofitted drive system. The Santa Barbara Instrument Group (SBIG) Self Guiding Spectrometer (SGS) is linked to the telescope with a focal reducer giving a final f6 ratio. The CCD camera attached to the spectrometer is the SBIG ST-7E with 9-mm pixel size. The SGS instrument appeared on the market during the later half of 1999 and was aimed at a sub group of amateurs with special interest in the field of spectroscopy. The light from the telescope reaches the entrance slit, which can be 18 or 72-mm wide. The light passes through the slit and reaches the grating and ultimately the CCD cameras imaging chip. The remaining field of view is observed on the guiding CCD chip of the camera and allows the viewer to select a field star to guide upon once the object of interest is centered on the slit. In this paper only results obtained using the 18-mm slit will be presented. The SGS features a dual grating carousal, which, with the flip of a lever, allows dispersions both in the low-resolution mode (~ 4 Angstroms/pixel, ~ 400 Angstroms/mm) or higher resolution mode (~1 Angstrom/pixel, ~100 Angstroms/mm). In the low-resolution mode, about 3000 Angstrom coverage is obtained whereas in the high-resolution mode, about 750 Angstroms. Wavelength calibration was carried out using emission lines from Hydrogen and/or Mercury gas discharge tubes.
attempts at quantitative analysis focused on planetary nebulae. These objects
give rise to emission line spectra in which a number of well-defined species are
observed and their relative intensities are easily measured. In the study of
gaseous nebulae, there are a number of diagnostic lines whose ratios are
sensitive to varying degrees with temperature and electron densities. Equations
have been derived from theoretical starting points, which relate these ratios to
temperatures and densities within the nebula. Two such equations are seen in
equations 1 and 2. Equation 1 relates the line intensity ratios
+ I5007)/I4363 = [7.15/(1 + 0.00028Ne/T1/2)]1014300/T
+ I6584)/I5755 = [8.50/(1 + 0.00290Ne/T1/2)]1010800/T
for transition occurring at 4959, 5007 and 4363 Angstroms for O+2 while equation 2 relates the lines at 6548, 6584 and 5755 Angstroms for N+. Figure 1 shows the results for NGC 7009, The Saturn Nebula.
The emission spectrum of NGC 7009 (above graph) in low-resolution mode. Several
ionized species are indicated. In high-resolution mode, the Ha line is resolved to show the
presence of flanking N+ lines. The bottom part of the figure shows
the curves generated once the appropriate line intensity ratios are inserted
into equations 1 and 2. The intersection of the 2 curves represents the solution
in Temperature and Electron density for the 2 equations. (Temperature = 11,200
K, literature = 13,000 K; Electron density = 30,000/cm3, literature =
The analysis of stellar spectra involves examination of absorption lines,
their positions as far as wavelength and their relative depth (intensity).
Identification of lines and assignment to particular atomic, ionic or molecular
species represents the first step in the analysis. Further analysis involves the
particular shape of lines wherein is buried details such as abundances, surface
gravity, temperature and other physical attributes. Figure 2 shows the spectrum
of 13-theta Cygnus demonstrating the variety of spectral
The high-resolution spectrum of 13-theta Cygnus in the region from Hb
The upper spectrum identifies a number of neutral atomic species. The bottom
spectrum is identical except that different lines for ionized atoms are
lines that can be identified in the atmosphere of this star and generally any star of interest.
The first 50-60 years of astronomical spectroscopy focused on cataloging stars as to type and spectral features. This included more qualitative analysis of the spectra such as line identification. Indeed, these efforts were responsible for the identification of helium, not yet discovered on earth. During the 1930’s, techniques were established which allowed for the quantitation of species observed in spectra. This technique was called “curve of growth” analysis and its basic features are illustrated in Figure 3. This method was strongly dependent upon work carried out in the physics lab to provide reliable values for (f), the oscillatory strength of a line transition. This value is a measure of the likelihood a particular transition will occur producing a particular line feature. Even to this day, many of these values are not known reliably. This technique allowed for the first time, the quantitation of the elements in the atmospheres of stars and established beyond doubt that hydrogen and helium make up the bulk of material in the stars. Before this, the belief was that the relative proportions of the elements in the stars were similar to that found on the earth. In other words, very little hydrogen and helium. Use of this technique continued into the 1960’s and 1970’s. But as computing power has increased and become available to many astronomers, not just those with supercomputer access, a new technique began to take hold, spectral synthesis. Spectrum synthesis is a computing intensive procedure that calculates what the line spectrum should look like under a variety of conditions. Many different things can influence how a spectrum looks such as
3. The use of curve of growth to determine element abundances.
A theoretical curve for a particular atom, iron for example, is generated
as shown in the upper left panel. It is known that the depth of an absorption
line (W, equivalent width) and its dependence on various factors such as
abundance depends to differing degrees with N, the element abundance. Also
required are what’s called oscillator strengths (f), the likelihood of
particular transitions occurring. If one plots, for various iron lines whose f values are
known, theoretical intensities (W) versus increasing abundance, N, one generates
a “theoretical curve of growth for iron.
Next you examine your real spectrum and measure the W for various iron
lines and plot versus f. Finally,
by superimposing both curves and sliding the theoretical over the measured, one
can read N, the column density, as total oscillators (iron) per square cm.
Repeating this procedure many times with other elements allows construction of
relative abundances present in the atmosphere of a star.
of species, temperature and pressure. What spectral synthesis does is to allow
you to input differing conditions and then calculate what the spectrum for a
particular wavelength interval should look like. The way this is done is as
follows: one creates a stellar atmosphere model, which gives a run of
temperature and pressure with depth. This model is used to compute ionization
ratios of different atoms, populations of different energy levels in atoms and
ions, electron density, Doppler broadening and other things as well. Tens of
thousands of potential lines are computed along with their intensities for 40+
of the more common elements, their first and second ionized state and a number
of simple molecular species commonly observed in stellar atmospheres. The
factors you can input are temperature, surface gravity (log g), metallicity
relative to the sun and micro-turbulent velocity (view this as velocity of
granular cells rising or sinking on stellar surface). An example of a synthetic
spectrum between 4200 and 4400 Angstroms is shown in Figure 4. This segment
required about 3 minutes of time on a 1 G Hz machine. Also shown is an expanded
40 Angstroms wide version centered at 4260 A. This spectrum was calculated for
an F5V type star of solar metallicity and surface gravity and temperature
consistent for this type star. It is at once apparent that the excruciating
detail present in the spectrum is not at all observed with real spectrometers
except those with
Synthetic spectrum of a F5V type star. Note the large number of lines
present. Below is an expanded version covering a 40-Angstrom range. The large,
deep line above at approximately 4340 A represents hydrogen gamma line.
the highest resolution attached to the largest telescopes. Fortunately, one of the options available allows for a Gaussian smoothing to provide a wavelength resolution consistent with your particular spectrometer-telescope combination. Shown in Figure 5 is the result of smoothing the synthetic spectrum to match that of the SGS. It is clear when comparing the synthetic spectrum in Figure 4 with the smoothed synthetic spectrum that a great deal of information is lost in the way of blending of various lines into single lines. This is a fact of spectroscopy.
Fortunately, one does not need to know all the intricate details as to
how the spectrum is obtained through the various applications of physical laws.
The atmosphere models are obtained from the inter-net and astronomers collect
these just like one may collect coins or stamps. My collection runs to several
thousand and covers stars with many permutations of temperature, metallicity,
surface gravity and micro-turbulent velocities (MTV). The software package
called SPECTRUM, which is a Unix based system, is then used to carry out
calculations on a particular model over a particular wavelength range.
these efforts can be carried out with a home PC. What is needed is a Unix
emulator. I use a software package called Cygwin, which allows your PC to act as
Smoothing of synthetic spectrum (red) to match the spectrum in resolution with
SGS in high-resolution mode (blue). The line spectrum obtained with the SGS is
shown above with the graph in blue labeled “actual spectrum”.
machine. Once the spectrum is obtained, you can apply the gaussian filter in order to match your resolution, import it into Excel for graphic presentation. Varying some of these parameters while holding others constant is illustrated below in Figure 6 in which the spectrum at three different temperatures of an atmosphere are plotted while holding other conditions such as metal abundance’s, surface gravity and MTV constant.
Effect of temperature on the spectrum of a K1.5V type star in the
4200-4400 Angstrom region. Surface gravity, MTV and metallicity were held
constant. Note how, in general, the lines for various metals become more intense
as the temperature is lowered. An exception is the Hg
line, which is more intense at the higher temperatures examined.
Figure 7 illustrates the same type star but with a constant temperature
of 5000 K and constant MTV and surface gravity, but varying metallicity
abundances relative to the sun. The metallicity of a star is expressed in a
logarithmic manner such that [M/H]star
/ [M/H]sun =0
that a star has the same metallicity as the sun. A value of –0.5 means that a
star is depleted a half-log or 3.2 times in metal compared to the sun whereas a
value of 0.5 means an enhancement of metals by 3.2 times compared to the sun.
Note, as one would expect, the lines become more intense as one proceeds to
Three different metallicity values and the effect upon the absorption
line spectrum of a K1.5V type star. All free parameters were held constant. As
one would expect the lines become more intense as one proceeds from low
metallicity ([M/H] = -0.5 to a higher metallicity of +0.5.
Similar types of graphs can be made which demonstrate the effect of MTV
and surface gravity (Luminosity class). The idea of spectral synthesis is to
take your spectrum and match as closely as possible the spectrum obtained by
synthetic routes by varying the free parameters. When this is done correctly,
temperature, luminosities, abundances and MTV values can be obtained, all from
just a modest resolution instrument available for the amateur. This represents
cutting edge efforts that the amateur can partake in, only generally available
even to the Professionals not many years ago, mainly because of the availability
of computing power of the desk top PC. Figure 8 shows a close match for a F5V
Matching your spectrum to the spectrum computed synthetically is the goal
in spectrum synthesis. As one varies the free parameters, the spectrum begins to
match up with actual spectrum. When as good of fit as is possible has been
found, abundances, temperature, MTV and surface gravity (luminosity) are
The most striking revelation in using this
software to synthesize spectra are the large number of lines that are actually
present. Under the conditions with which most observatory and amateur
spectrometers will function, the resolution will not distinguish all of these
lines. The result is that a majority of lines are actually blends of two or more
lines. Actual line identification most commonly represent the most prominent
line within the blend. This explains the constant drive behind astronomers need
for both higher resolution spectrometers and the necessary greater sized
telescopes required as you spread the light of a spectrum out more and more. To
this end, SBIG has developed a prototype new grating carousal for the SGS, which
contains a 1200- and 1800-line/mm gratings. The 1800 line grating would
represent a 3-fold improvement in resolution over the current 600-line
high-resolution grating. What might we expect from such an improvement? Figure 9
shows a synthetic spectrum, which should match closely with
The red line (marked 600 line grating) represents an actual spectrum over
an 80 Angstrom region centered at 4240 A. The blue line (marked 1800 line
grating) shows the result of synthetically deriving a spectrum with the
resolution expected for a 3-fold improvement over the 600 line grating. The
actual line spectrum is also shown overlaid on the figure.
Note the increased resolution, where previously blended lines are slit
into multiple lines.
what would be observed realistically with an 1800
line grating. As can be seen, many of the blends and shallow dips are now
further resolved into multiple lines. This kind of improvement in resolution
will greatly aid in efforts to better match synthetic spectra with those
actually obtained at the telescope. This kind of increased resolution will make
matching synthetic spectra with the actual spectra more precise and thus a more
accurate determination of the physical characteristics will be obtainable.
What an amateur can now carry out has certainly
come a long ways in recent years. This has been a function of advances in
detector technology, instrumentation and inexpensive desktop computing power.
Amateurs now possess the capabilities of both obtaining spectra which can rival
that obtained at many observatories but also to synthesize spectra with an input
of various physical conditions. Followed by best-fit analysis, the amateur or
small observatory is at a point where cutting edge work can not only be
accomplished but also published in astronomy’s leading journals.
I have tried to demonstrate in this paper my initial attempts to do
qualitative analysis of spectra obtained in my observatory using a modest
(Celestron-14) telescope and the SBIG SGS instrument. Much more work and
learning on my part remain. The software SPECTRUM has many other capabilities
beyond the few I have shown here. For example, it is capable of carrying out a
best-fit analysis of your spectral data to provide the most likely physical
conditions in a stellar atmosphere. What I have shown here is more of a manual
approach to this analysis. This approach was by choice since it was my wish to
get a feel for what the output of the calculations are and what they are telling
you as you systematically change the input parameters. Eventually, I will allow
the software and computer to do what they do best. This will be a story for a
The author wishes to acknowledge Mr. Kurt Snyder
of Ligand Pharmaceuticals for his help in getting the UNIX emulator Cygwin up
and running for me. Also, most importantly, Dr. Richard Gray of Appalachian
State University for freely making available his spectral synthesis software
SPECTRUM, providing the stellar atmosphere models and endless email discussions
on getting the software to work and correctly interpreting the results.