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ASTR 5110, Majewski [FALL 2017]. Lecture Notes

ASTR 5110 (Majewski) Lecture Notes



  • Chapter 6 of Howell, CCD Astronomy

  • Schroeder, Astronomical Optics, Chapter X.

  • Kitchin, Astrophysical Techniques, Chapter 4.

  • Chapters 11-13 of Birney.

Pejzaz Spektrum Barw (Landscape of the Color Spectrum) by Wieslaw Sadurski, 150 x 120 cm (from

  • Spectroscopy is the study of the distribution of light from a source at a higher resolution than in the case of photometry - same kinds of info but better. Photometry = very coarse spectroscopy.
  • Recall:

    • Blackbody -- a perfect radiator -- hypothetical body that absorbs all incident EM radiation. Has reached equilibrium temperature, then re-radiates in a characteristic pattern dependent only on T.
    • Wien's Law:

    • Stefan-Boltzmann Law: Total energy emitted per second per cm 2 by a blackbody:
  • The presence of gases in the atmospheres of stars or surrounding/near any blackbody perturbs the continuous blackbody spectrum with the introduction of lines corresponding to electron transitions.
  • Absorption Emission

  • Excitation -- When an electron is in an energy level above the lowest possible one -- excited state
  • Rydberg formula:
  • Depending on the relative positions of the gas and the blackbody (continuous) source, we get either a continuous spectrum, an emission line (bright line) spectrum, or an absorption line (dark line) spectrum:

  • Ionization -- When electron absorbs enough energy to escape from the atom (atom becomes an ion) -- ionized

Information derived from Spectra

  • Chemical composition of the gas

    Of course, each chemical element (and ion, isotope and molecule) has a characteristic "fingerprint" pattern of emission/absorption lines corresponding to specific energy levels possible for electrons in that species.

    From gasemit/gasemit.html.

    The presence of an element can often be determined by seeing its characteristic lines in a spectrum.

    All other things equal (e.g., pressure and temperature), the stronger a line, the more of the element that is present.
  • Physical state of the gas

    Note, when discussing the physical state of the gas, we mean in the atmosphere of the star.

    For example, for temperatures of stars, we distinguish between the observed temperature corresponding to the outer layers of the star (the so-called surface temperature) which are typically in the thousands of Kelvin, and the central temperatures, which are much hotter -- typically millions of Kelvin and hot enough for nuclear fusion to occur.

    • Degree of excitation or ionization

      Number of excited or ionized atoms is reflected in the strengths of lines corresponding to these transitions or ionized species.

    • Temperature of the gas
    • We have learned to measure the temperatures of stars using their electromagnetic spectra, following experiments first done by the physicist Kirchhoff in the 19th century.

      Bad Philosophy Footnote: Click here for a related description of one of the worst, but not one of the last, faulty prognostications about science by a philosopher.

      • Obviously, Wien's Law at most basic level.

        But can do better than this by looking at line patterns...

      • Hotter gas -- greater degree of ionization, molecular dissociation, and excitation
    • Density/pressure of the gas
      • Higher density/pressure -- greater degree of excitation
    • Therefore, the strength of an absorption line depends not only on total abundance of species but in the fraction of those atoms in the correct state of ionization and excitation to produce the line.
  • Relative velocity of source
  • REFERENCE: See Chapter 13 of Birney for information pertinent to Doppler and rotational velocities.

    The Doppler effect causes the observed wavelength of lines to be shifted from their emitted rest wavelength.

    where 0 is rest wavelength

    Doppler velocity:

    The relative velocity of the source to the observer is given by the redshift or blueshift of its lines.



    For example, imaging a source that is orbiting an object at large distance. We can see the orbit reflected in the shifting of the spectral lines.

    From star_velocity.html.
    Observing the redshifts of galaxies has been critical to understanding the expansion of the universe.


    Five galaxies and their spectra:

    This is a famous picture showing the spectra of five galaxies at different distances (estimated from their relative sizes as shown on the left) and the correlation of these distances with their redshift. The Ca II H and K line doublet shown in the spectra can be seen to shift to higher redshift as compared to the comparison spectrum (the series of emission lines at the top and bottom of each frame) as the galaxies get farther away. From

  • Rotation of a source

    • Seen as differential Doppler shift of spectral lines
    • Example: galaxy rotation curve

      Image of a disk galaxy. The observer places a slit along the galaxy that admits light to the spectrograph only from those parts of the image within the slit.

      This is an image of the above-illuminated slit after passing through a spectrograph. From bottom to top is shown multiple images of the slit at each wavelength -- but, since only two wavelengths of light are illuminating the slit from the galaxy in this part of the spectrum, only two images of the slit, one from each wavelength, is shown. Moreover, the image of the slit is "split" and shifted from left to right because one side of the galaxy is approaching and the other receding relative to the center of the galaxy. This shows the rotation of the galaxy.

      On the left, a spiral galaxy image, with spiral arms delineated by H II regions. On the right, the light a narrow strip running along the major axis of the galaxy has been spread into a spectrum, between about 6500 and 6800 Å. The rotation of the galaxy is seen in the emission lines from Hα at 6563 Å (the brightest line), as well as other fainter lines in this region due to [N II]. H II regions appear reddish in this image because of the prominence of the Hα line in the red region of the spectrum. From

      The rotation curve of the galaxy, its rate of rotation as a function of distance from the center of the galaxy, can be derived from the spectrum.

    • Example: Planet rotation

      From m/mais/Planets.htm.

      In the above examples we can resolve the changing velocity from side to side of the source. But if the source is unresolved -- e.g., the typical star is smaller than the seeing size -- then the spectrum from one side of the source is jumbled (or smeared) with the other (by the seeing). In this case, we can see that the lines in the spectrum are broadened, and to amount depending on the amount of differential rotation (rotation speed) across the source.

  • Expansion of a source
    • The expansion of a source, as in the case of rotation above, means that different parts of the source will have different relative velocities than other parts.

    • Common situations where we see an expanding source is in the case of a nova (the release of the outer layers of a dying moderate mass star), a supernova (an explosive, more complete destruction of a more massive star), or in certain types of pulsational variable stars, like Cepheids or RR Lyrae (which both show expansion and contraction).

    • If the source is unresolved, then again we will have a smearing of the different velocities of the gases that are either absorbing or emitting lines of radiation, and consequently we will see a broadening of the lines, similar to the unresolved rotating source case.

    • However, a very special case sometimes occurs when we have an unresolved source that includes both absorption and emission line regions. In this case we can see P Cygni profiles in the spectral lines, which include an absorption part blueshifted with respect to a companion emission part.

      The geometry of the source that produces a P Cygni profile is shown in the figure below.

    • As part of your spectroscopy lab, you will measure the velocity of the expansion of the shell in the nova star P Cygni, the prototype object for which this phenomenon is named.

    • To get an idea of how the shell velocity affects the appearance of the line, click here.

  • Strength of magnetic field
    • Recall that each electron in an atom must have a different quantum state (Pauli Exclusion Principle).

      For a given energy level n, have different orbitals, or angular momentum quantum number, L (e.g., L=0 is "s", L=1 is "p", L=2 is "d", L=3 is "f", etc.).

      Each of these orbitals L have 2L+1 sublevels, possible, and these are expressed in the presence of a magnetic field, which causes the electrons to precess.

      From light/zeeman-split.html.
    • In the presence of a magnetic field, lines corresponding to certain orbitals will undergo Zeeman splitting , slightly shifting the energies of the sublevels of the orbitals. Discovered in Sun 1896 by Dutch physicist.
    • Only certain spectral lines have this, those corresponding to levels that are NOT "s", since for "s" we have L=0 and therefore only 2L+1=1 states.

    Zeeman splitting from the intense magnetic fields near a sunspot. From ASTR1020/sun.html.
  • The stronger the external magnetic field, the wider is the split line separation.


  • One dimensional spectra:
  • We usually take a spectrum with a detector that yields a two-dimensional image. One dimension shows wavelength and the other is the distance along the slit.

    Recall that the wavelength dimension is really an infinite set of pictures of the slit of a spectrograph at each wavelength.

    If this concept is confusing to you, here is a picture of the chromosphere of the Sun after passing through a spectrograph without using a slit (slitless spectroscopy).

    The image of the Sun during an eclipse passed through a prism shows that the outer parts of the Sun (the chromosphere) -- where flares and prominences are made -- emits light in certain emission lines. Each image here corresponds to a picture of the Sun in one wavelength. The most prominent image here is the Hα (6563 Å) emission line. From

    To analyze a spectrum with modern methods, we normally look at one-dimensional cross-sections showing the relative intensity as a function of wavelength:

    From Abell's Exploration of the Universe, Fourth Edition.

  • Line profile:
  • When we look at the shaped of lines in one-dimensional spectra...

    • Shape of the line has a core and wings.
    • At any point we have a characterizing line depth, l, and, at the location of the center of the line, a core line depth, lc .
  • Equivalent width:
    • A way of describing the strength of a line.
    • where S is the line profile area in (counts)x(mm); Ic is the intensity of the continuum (counts); and d is the dispersion (mm/Å)

      W = Area of rectangle of height Ic and width W with same area as line

    • As you might guess from its definition, the EWs for absorption lines are positive, those for emission lines are negative.

      How EW works for an emission line. Image from
    • W for an element X is function of stellar Teff, g, [X/H]
    • In practice, the continuum level Ic can be hard to determine if there are many lines in the spectrum.
    A summary of these line feature descriptions is given by Lena:

    From Lena, Observational Astrophysics.

  • Line Strength and Curve of Growth:
  • Let W be the equivalent width of a line and N be the number of absorbing atoms for that line.

    • When a line grows in strength, it first gets deeper at a rate that is proportional to the number of atoms that can produce the line (see lines 1-4 in the figure below).

    • From Abell's Exploration of the Universe, Fourth Edition.

      Thus, when there are few absorbers, the strength of the line is linearly related to the number of atoms (optically thin regime):

      W ∝ N

    • For a great enough abundance of atoms, the line saturates (completely removes all of the light at the center of the line -- see line 5 in the figure above).

    • With the addition of more atoms the strength of the line increases only moderately, and only by growing the wings (see lines 6-11 in the figure above).

      Growing the wings means broadening the lines, but this can only happen if the corresponding energies of the slightly shifted wavelengths can cause the transition. There are several ways that can happen:

      • natural broadening -- Energy levels are not perfectly sharp and there is a small range of energies allowed for a transition to occur (a result of the Heisenberg Uncertainty Principle, h=Et, the amount of time t an atom spends in an energy level and the mean range of energy E in an energy level are related).
      • Doppler broadening -- Because atoms are moving rapidly, they "see" wavelengths of photons they encounter at different wavelengths than we do on Earth. Also called thermal broadening, since the velocity distribution of atoms is related to the temperature of the gas.
      • collisional broadening -- Perturbing the energy levels slightly so that the transitions can occur through the absorption of photons of slightly different energy from normal. The perturbing occurs when one atom/ion passes near or collides with another one (recall our discussion of bands in solids). This is perhaps the most important source of broadening in strong lines.
      • Zeeman effect -- Another source of perturbation that allows photons of different energy to be absorbed.
    • Thus, as the line is becoming optically thick and saturates, the equivalent width no longer grows as fast as linear with N, and can only grow by expanding the wings through the above processes. At first, Doppler broadening dominates the increase in line strength and to a fair approximation:

      W ∝ (ln N )1/2

    • However, eventually, as the density of atoms increases even more, collisional broadening takes over the growth of the wings and then:

      W ∝ (N )1/2

    • These three regimes give rise to the complicated curve of growth of a spectral line:

      The optically thin, optically thick (saturated) and very optically thick (very saturated) regimes are visible here in this curve of growth. From Carroll and Ostlie, "An Introduction to Modern Astrophysics" (Addison-Wesley 1996).
      In the figure, f is the oscillator strength of the atomic transition in question, which is a measure of the likelihood that the transition will occur, and N is the column density of of atoms in the proper state to absorb the photon of interest.

      By measuring the W of a line, the curve of growth allows you to determine the true abundance of an element in the proper state if you know the oscillator strength. (In fact, you measure only the atoms in the "proper state" and get the total number of atoms for the element by using the Boltzmann and Saha equations to determine the fraction of atoms in this state.)

      For a nice, detailed description of this, see here.

  • Terms for closely spaced lines:
  • In some case you have one transition that has several possible, slightly different energies possible.

    For example, 3p level in sodium has two possible total angular momentum levels, j=1/2 and j=3/2, induced by the magnetic energy of the electron spin in the presence of the internal magnetic field caused by the orbital motion (spin-orbit effect).

    Famous NaD doublet at 5890 and 5896 Å. From hbase/quantum/sodzee.html.

    This results in a line doublet corresponding to the transition.

    Note that this is not the same as the Zeeman effect, which is additional splitting induced by outside magnetic field.

    From hbase/quantum/sodzee.html.

    Thus, we often see very closely placed lines in a spectrum

    • doublets, triplets, etc. are as described above splitting in same energy transition in same element, e.g., NaD doublet (5890, 5896 A) and Mgb triplet (5167, 5173, 5184 A).

      Highly magnified view of Mg triplet region shown in the spectrum of an F star. The triplet is marked. Other lines shown are unrelated. From

      Highly magnified view of Na doublet region shown in the spectrum of an F star. The doublet is marked D1 and D2. Other lines shown are unrelated. From

    • blends are chance near coincidences of lines from different transitions/different atoms. Undesirable usually. A famous set is the N II lines at 6548, 6583 Å which always make measuring the H Balmer line at 6563 Å difficult:

      The Hα + N II lines are visible in the center here. In low resolution studies (of galaxies, nebulae) these lines often blend together and must be measured as one. From
    • bands are large numbers of lines near one another from molecular vibrational, rotational modes (as discussed in an earlier lecture). A famous example is the MgH band starting at 5211 Å.

      Bands usually have a maximum intensity near one edge, called a bandhead, and a gradually decreasing intensity on the other side.
      Spectrum of a K giant and a K dwarf of about the same temperature and chemical abundance. Note that the surface gravity of the dwarf is stronger resulting in stronger lines from neutral sodium and neutral Mg and the MgH molecule. The Mg features are clustered together near the bandhead at 5100 Å.

    • a continuum of lines is created at wavelengths corresponding to many successive electron transitions with nearly similar energies, which occurs between low numbered energy levels (n1=1,2,...) and high energy levels (n2 approaching infinity).

      As can be seen from Rydberg formula, when n2 gets large, the change in 1/n2 is small, and the corresponding energy absorbed approaches a limit (corresponding to the ionization energy of the atom from the n1 level). Thus, the lines get ever closer together, until they pile up at nearly the same wavelength and we have a dramatic drop in the flux level of a star at that point. Photons more energetic than the continuum wavelength ionize the atom.

      Example: Note the increased bunching of lines and the Balmer continuum or Balmer jump (n1=2 transitions) near 4000 Å in the spectrum of this A type star (spectrum is shown from 3500 to 5000 Å).

      The Lyman continuum (n1=1 transitions) occurs at 912 Å.

      NOTE: Astronomers uses the simple expression "continuum" to mean two things -- don't confuse the "continuum" of lines with the "continuum" of the spectrum, which means the level of flux from the blackbody emission part of the spectrum of the star.

  • Line naming convention for ions in astronomy
  • For an element X:

    • Line from a neutral element X I

      e.g. H I, Fe I, Na I
    • Line from a once-ionized species X II

      e.g. Ca II H+K lines, N II
    • Line from a twice-ionized species X III

      e.g. Si III
    Note that the ionized forms of an atom have different locations for the energy level transitions in the outermost remaining electron.

  • Isotopes

    The isotopes of atoms have slightly different line locations

      For example, the spectrum of neutral deuterium (D I) lines is nearly the same as, but shifted by 0.027% with respect to, neutral hydrogen (H I) lines.

    A small portion of the FUSE spectrum of the white dwarf star WD 1634-573. Each panel shows the spectral region near a hydrogen absorption line. The blue regions indicate the spectral fingerprint of deuterium (marked "D I"). The depth and shape of these fingerprints compared to others such as oxygen and regular hydrogen, tells astronomers the relative abundance of deuterium in the gas being sampled on the sight line to the star. Note that the x-axis has been converted from wavelength into a velocity scale. (Graphic courtesy of JHU FUSE project.)
  • "Forbidden Lines"

    These are line transitions seen in emission in certain hot nebulae that are not seen on Earth -- thus "forbidden".

    "Forbidden" is a misleading term -- a better one would be "extremely unlikely".

    • Normally, atoms can be excited by collisions or by absorption of photons. De-excitation / emission occurs rapidly ~ 10-8 - 10-7 seconds
    • However, some ionized atoms have metastable levels that they can remain in for several seconds to hours.
      • Normally probability for emission is so low that low emission rate is not seen in laboratory.
      • Need very low densities for this to occur, otherwise the rate of collisional excitation will exceed the rate of spontaneous emission and the line is not seen.

      • In a nebula around a hot star -- many ionized atoms that remain collisionally undisturbed long enough to emit photon, get lots of emission -- strong lines. Famous ones:
        • [Ne III] -- 3869, 3968 Å
        • [O II] -- 3727 Å
        • [O III] -- 4959, 5007 Å
        • [N II] -- 6548, 6583 Å
      • We indicate a forbidden line transition by putting square braces around the name, as above.
      • There are "semi-forbidden" transitions too, such as:

        • C III] -- 1909 Å
        • C II] -- 2326 Å
    • Until 1927, forbidden lines were unidentified because not seen under normal Earth conditions (gas density) -- "Nebulium" -- "new element found in nebulae" only. (Also, often seen redshifted in extragalactic objects, further confusing matters.)


  • Emission Nebula (Orion)
  • This is the classical spectrum of hot, low density gas:

  • Seyfert 2: Galaxies (mostly spiral) with extremely bright small nuclei that show broad emission lines in their spectra, but generally of order a few hundred km/s.

  • LINER: "Low-Ionization Nuclear Emission Region" is a Galactic nucleus that shows an emission line spectrum dominated by low-ionization states of neutral or weakly ionized elements (e.g., O II, N II, S II) and only weak emission lines from higher-ionization states (e.g., O III, N III). Spectroscopically, they resemble Seyfert 2 galaxies, except that the low-ionization lines, e.g., [O I] 6300 A and [N II] 6548 A, 6583 A, are relatively strong" (quote from

    The observed linewidths in LIBERS are similar to those observed in Seyfert galaxies and indicate rapid motion.

    Such a spectrum indicates Seyfert-like activity probably not related to stars but due either to the massive central object in the nucleus or to shock waves generated by supernovae.

    LINERs are more abundant in early (S0, Sa, Sb) disk galaxies than in other types. LINERS are much more common than Seyfert galaxies (about 1/3 of all nearby, largish galaxies are LINERS).
  • Seyfert 1: Galaxies with bright nuclei with spectra having two sets of lines superimposed:
    1. Narrow lines (~100 km/s) as in Seyfert II

      Permitted & forbidden transitions

      Low density ionized gas
    2. Broad lines/wings (104 km/s)

      Permitted lines only

      High density gas (forbidden lines collisionally suppressed)

  • Quasar (QSO) - almost no emission from host galaxy; extremely bright nucleus, resembling a Seyfert I.


REFERENCE: Birney's Chapter 12.

Spectrum of the Sun: Fraunhofer lines

  • Set of absorption lines in the continuous (blackbody) spectrum of the Sun.

  • Discovered in 1802 by William Hyde Wollaston.
  • Named after Fraunhofer (1787-1826), who invented and used a diffraction grating and determined the relative positions of hundreds of lines. Did not know their origin.

  • Interpreted by Bunsen (1811-1899) and Kirchhoff (1824-1887).

From sci122/Programs/p27/p27.html.

Names of the most prominent lines identified by Fraunhofer:

  • Fraunhofer worked from red to ultraviolet, names go that direction.

  • Picture below shows lines from from ultraviolet to red.

*A 7594 Molecular oxygen band in earth's atmosphere
*B 6867 Molecular oxygen band in earth's atmosphere
C 6563
*D1 5896 Sodium
*D2 5890 Sodium
E1 5270 Iron
**Eb 5183-5168 Magnesium triplet
F 4861
*G 4308 Blend of band of methane and iron
*H 3968 Ionized calcium
*K 3933 Ionized calcium

* Still commonly used names, for example:
  • "atmospheric A band"

  • "atmospheric B band"

  • as we saw in the discussion of chromatic aberration and refractive optics, the terms "c" and "f" lines are still used in optical studies where a hydrogen emission lamp is used as a source.

  • "sodium D lines (NaD)"

  • "G band"

  • "calcium H and K lines (Ca II H+K)"

** In this case the name has morphed from "Eb" into "Mgb" to indicate that magnesium is the source of the line.

Here is a better dispersed image of the solar spectrum. See if you can identify the Fraunhofer lines in this spectrum:

From Astronomy Picture of the Day,
Note also how the number of metal lines increases dramatically towards the blue.

Classification of stellar spectra:

  • Originally in groups of like spectra by Father Secchi in the 1860s and 1870s.

  • Expanded into groups A, B, C, D, .... Q by Williamina Fleming (in Pickering's Lab at Harvard) in the 1890s.

  • Later reordered into a sequence based on progressions of appearing and disappearing lines by Antonia Maury and Annie Jump Cannon (also "Pickering's Women") by early 1900s.

  • Cannon also dropped all letters except OBAFGKM, with P=planetary nebula and Q="peculiar".

  • In 1920s, differences in spectral types along sequence recognized to be primarily a temperature sequence, also by one of "Pickering's Women", Cecilia Payne(-Gaposchkin).

  • Note, based on outdated theories on how stars evolve, bluer spectral types are called "Early types" and redder spectral types are called "later types".

      (Note that before the correct theory of stellar evolution was developed, scientists thought that all stars started out hot and blue, and then faded to cool and red. In fact, stellar evolution is NOT like this, and is, in fact much more complicated. Indeed, most stars spend most of their life pretty much at one color and temperature.)

  • Our ability to distinguish spectral types in classifying stars is based on dominant spectral lines seem as a function of stellar atmospheric temperature.
  • Different stellar atmosphere temperatures mean presence of different energy photons as well as how often and how intense are collisions between molecules, atoms and ions. This affects, in turn:

    • the molecular equilibrium -- the possibility of association or dissociation of atoms into molecules.
      • One sees the most numerous molecular bands in cool stars, whereas hotter stars generally dissociate molecules into atoms.
      • The strength of molecular bonds determines in how hot an atmosphere one can see different lines.

        • Strongly bonded molecules like CH and CN are seen in stars as warm as the Sun (later than G type).
        • Slightly cooler (KM types) stars will still show several kinds of hydrides, like MgH, CaH, CaOH.
        • Only the coolest stars (M types) are strongly dominated by molecular bands, with their spectra featuring strong bands from TiO, VO.
    • the ionization equilibrium -- different levels of complete electron liberation from atoms and different levels of ionization in atoms.
      • The coolest stars (KM) will have only neutral atoms.

      • As the temperature increase to G types, start seeing easily ionized atoms like Na II, Ca II.
      • For hot stars like A,F types, see Mg II, Si II, Fe II.

      • In the hottest stars (O type), even see ionized helium and multiply ionized atoms like N III, S IV, etc.
    • the excitation equilibrium -- the expression of different energy level (spectral line) transitions.
      • For example, in coolest stars can't even excite hydrogen atoms to n=2 level, and no Balmer lines (transitions from n=2 to higher levels) can be produced.
      • At spectral type A, the temperature is hot enough (10,000 K) that the n=2 level is maximally occupied by hydrogen atoms, and one sees the strongest Balmer lines.



Principal Spectral Class Sequence

Shown from 7000 to 4000 Å.

Spectral subclasses: Originally, for more precision each spectral type was divided into ten transitional forms, from 0 to 9 (e.g., B0, B1, B2, ... B9), but through time some of these subclasses were combined or discarded, others added, until we have the currently accepted set of spectral classes:

Actual spectral classification sequence from 4000-7000 Å (in color!).

Actual spectral classification sequence from 4000-7000 Å. At the bottom are three special cases, an F4 type star that is very metal poor, a late type star (M4.5e) with emission lines from coronal activity, and an early type star (B1) with emission lines. NOAO/AURA/NSF image adapted from html/im0649.html.

These spectra were created by Mike Briley, University of Maryland in the late 1980's. They are computer synthesized models of star spectra. The spectra have been "flattened" to remove the very strong variation in the overall flux balance for stars of different temperatures (Wien's law), so that one can easily see the changing darkness of the different lines with temperature. Hot, "early-type" stellar spectra are at the top of the figure, and the late type, cool, stellar spectra at the bottom. In real life, the hot stars have most of their flux in the blue part of the spectrum, while the cool ones are very red. Enjoy the view and watch how some different dark absorption lines and molecular bands vary in strength with stellar effective temperature.
Corresponding one dimensional spectra shown in a part of the spectrum traditionally used to classify stars, from 3500 to 5000 Å. Note that again the spectra have been made wth artificially flat continua for ease of comparison based on lines.

Actual stellar spectra, including the variation of flux by wavelength due to blackbody temperature, looks something like this.

Note that when you undertake spectral classification for your laboratory assignment, you should not depend on the slopes of the spectra to get the spectral type correct, because a number of wavelength sensitive systematics affect what you will actually record, including the transmissivity of the 40-inch telescope and spectrograph optics, vignetting effects, and quantum efficiency variations in the CCD camera.

ASTR 5110 Laboratory: Spectral Classification

  • In the Spectroscopy Lab you will be able to see and identify the various ion strengths, and compare the relative strengths to get spectral class. (You should be able to do to at least a half spectral type or better.)
  • Again, heed warning above not to trust overall continuum levels as a guide to spectral type.

  • Use Jaschek, Birney, Turnshek et al. atlas, Morgan et al. atlas, Washington Atlas, Jacoby et al. (1984, ApJS, 56, 257) for comparison.
  • Other useful sites on line:

    Harvard Atlas

    Oregon summary on ESO pages

  • For example, could compare strength of Balmer lines to Na D lines.
  • How to identify lines?
    • Use comparison source lamps; identify XeNeAr lines from atlas and calibrate spectra to true wavelength scale.
    • Use Fraunhofer lines from daytime sky spectrum you collect in Part 1 of the Lab. Since this is a solar spectrum, it sets a spectral type reference for you.
    • Ignore any auroral emission from the night sky.

Luminosity Effects in Stellar Spectra

Secondary effects on the strengths and shapes of lines come about due to the pressure of the gas producing the lines.

  • Atmospheric pressure relates to the weight of the atmosphere and this relates to the surface gravity at the photosphere of the star.

  • For the same mass and temperature star, the surface gravity decreases as the star's radius increases.
Thus the pressure decreases for larger (e.g., subgiant, giant, supergiant) stars. This has several effects that might be observable:

  • Ionization Balance

    Because the pressure determines the rate at which electrons may be captured by ions, this effects the ionization equilibrium.

    • By Boyle's law, at the same temperature the density of a gas is proportional the pressure.
    • So, at high pressure the density is higher and there are less ions of a species around because electrons are more accessible to recapture.
    Since the pressure decreases for larger stars, for the same mass, there are more ions than in a smaller star.

    • Thus, in general, the spectrum of a larger star (say, a giant) resembles that of a smaller star of hotter temperature.

    • But this is a simplification, because pressure and temperature act together to affect the ionization equilibrium.

    • In general, it takes a trained eye to see these usually subtle luminosity differences in stars of same spectral type.

  • Line Width

    Another effect on the lines due to differences in surface gravity/pressure is that the pressure broadening of the lines will be different:

    (Top) Comparison of spectral line widths for A3 I and A3 V class stars. The broader lines for the V luminosity class star arises due to the denser outer layers in the atmosphere of the main sequence star. (Bottom) One dimensional versions of the same. From

    Three A stars of different luminosity class. From

  • Molecular Balance

    In a higher pressure, higher density environment, the atoms are pushed closer together and there is more opportunity for molecules to form.

    Thus, late type dwarfs will have stronger molecular bands than giants of same spectral type.

    Spectrum of a K giant and a K dwarf of about the same temperature and chemical abundance. Note that the surface gravity of the dwarf is stronger resulting in stronger lines from neutral sodium and neutral Mg and the MgH molecule. The Mg features are clustered together near 5100 Å, and with a special filter, DDO51, one can actually measure the amount of absorption in that part of the spectrum to aid in distinguishing giant and dwarf stars with simple photometry.

Luminosity Classes

These subtle luminosity/gravity induced differences in stellar spectra are important for gauging distances correctly with spectroscopic parallax (gauging the absolute magnitude of a star based on its spectrum), and are also the origin of spectroscopic luminosity classes.

Luminosity classes represent a second dimension in the classification of a star (the first dimension is spectral class, related to temperature).

We have the following recognized luminosity classes:

  • Ia,Ib = supergiants

  • II = bright giants

  • III = giants

  • IV = subgiant

  • V = dwarf

  • VI = subdwarf

The luminosity class is written after the spectral class, so that, e.g., the Sun is a G2 V star and
Betelgeuse is an M2 I.



Another luminosity class nomenclature often seen, and written as prefixes, includes:

  • d = dwarf type, e.g., dK7 star

  • g = giant type, e.g., gK7 star

  • sd = subdwarf type, e.g., sdK7 star

  • D = white dwarf star, e.g., DA star is a white dwarf with A spectrum.

Abundance Effects in Stellar Spectra

Obviously, low abundance of a particular species in the atmosphere of a star also results in weak expression of lines from that species.

The source of the "subdwarf" class above (luminosity class VI) is from weak-lined stars which have a main sequence lower than that of the metal-rich sequence in the HR diagram.

(In actuality, as we saw from how line blanketing works, if we take metals out of a star it actually gets bluer -- so the subdwarf branch is really a result of the dwarf branch moving to higher temperatures in the color-magnitude diagram than from it moving to lower luminosities.)

An example of a weak-lined star compare to the normal metallicity star of the same effective temperature.

Metallicity differences seen between a very metal poor giant (top) and a very metal rich giant (bottom), seen in early spectra from APOGEE. Note that almost every feature you see in the upper spectrum is from TELLURIC absorption by (on the left) water vapor, (the four sets of bands in the middle) C02 and methane (spike on the right). Vertical spikes to zero mark detector boundaries in APOGEE.

We will have a lot more to say about subdwarfs next semester in ASTR 551.

Extraction and Wavelength Calibration of FOBOS Data

Here is a prescription for a minimalist reduction of the FOBOS data for purposes of undertaking the lab. Notes:

  • In the lab handout I mention using the FOBOS reduction routines written by Jeff Crane. You are free to do so, but the following prescription is more direct and simple and sufficient for our purposes.

  • This procedure is NOT necessarily what would be done if one were to attempt, for example, careful RV reductions, etc. It is just a means to our end here.

  • One major difference with a FOBOS reduction is that we are not subtracting the sky spectra.

    This would normally be required, but our spectra are generally so bright compared to the sky background we can get away with ignoring the sky subtraction.

  • BUT, you should remain cognizant of the locations of the night sky lines using a night sky spectrum for reference.

After the standard overscan and bias correction of each image, there are three main steps:

  1. Extraction of the 1-D spectrum from the 2-D image, and subtraction of the background.

  2. Wavelength calibration.

  3. Global continuum normalization.

0. Preliminaries
  • Overscan-correct every image.

  • Combine biases according to the usual method, and subtract the combined bias for each night from that night's data.

  • Combine the overscan and bias-corrected quartz lamps (use the combine parameters you would normally use with domeflats).

1. Extraction and Background Subtraction

Assuming you have already overscan and bias-corrected all of the images: Enter IRAF and its appropriate spectroscopic packages:

unix> cl -ecl
ecl> twodspec
      apextract.   longslit.  
twodspec> apextract
      apall        apedit       apflatten    apnormalize  apscatter    
      apdefault@   apfind       apmask       aprecenter   apsum        
      apdemos.     apfit        apnoise      apresize     aptrace   

apextract> onedspec
      aidpars@       disptrans      ndprep         sbands         sfit           splot
      autoidentify   dopcor         odcombine      scombine       sflip          standard
      bplot          fitprofs       refspectra     scoords        sinterp        telluric
      calibrate      identify       reidentify     scopy          skytweak       wspectext
      continuum      lcalib         rspectext      sensfunc       slist          
      deredden       mkspec         sapertures     setairmass     specplot       
      dispcor        names          sarith         setjd          specshift    

You should read about the apall task and what it is doing. You should have become familiar with it during the observations. I have found the following parameters of the task to be most helpful for the FOBOS data we collected (note, one difference from the mountain is that this time we will subtract a fit to the background on either side of the main extracted region:

                             Image Reduction and Analysis Facility
PACKAGE = apextract
   TASK = apall
input   =                       List of input images
(output =                     ) List of output spectra
(apertur=                     ) Apertures
(format =            multispec) Extracted spectra format
(referen=                     ) List of aperture reference images
(profile=                     ) List of aperture profile images

(interac=                  yes) Run task interactively?
(find   =                  yes) Find apertures?
(recente=                  yes) Recenter apertures?
(resize =                  yes) Resize apertures?
(edit   =                  yes) Edit apertures?
(trace  =                  yes) Trace apertures?
(fittrac=                  yes) Fit the traced points interactively?
(extract=                  yes) Extract spectra?
(extras =                  yes) Extract sky, sigma, etc.?
(review =                  yes) Review extractions?

(line   =                INDEF) Dispersion line
(nsum   =                   10) Number of dispersion lines to sum or median

                                # DEFAULT APERTURE PARAMETERS

(lower  =                  -5.) Lower aperture limit relative to center
(upper  =                   5.) Upper aperture limit relative to center
(apidtab=                     ) Aperture ID table (optional)

                                # DEFAULT BACKGROUND PARAMETERS

(b_funct=            chebyshev) Background function
(b_order=                    1) Background function order
(b_sampl=          -10:-6,6:10) Background sample regions
(b_naver=                   -3) Background average or median
(b_niter=                   10) Background rejection iterations
(b_low_r=                   3.) Background lower rejection sigma
(b_high_=                   3.) Background upper rejection sigma
(b_grow =                   0.) Background rejection growing radius

                                # APERTURE CENTERING PARAMETERS

(width  =                   5.) Profile centering width
(radius =                  10.) Profile centering radius
(thresho=                   0.) Detection threshold for profile centering

                                # AUTOMATIC FINDING AND ORDERING PARAMETERS

nfind   =                    1  Number of apertures to be found automatically
(minsep =                   5.) Minimum separation between spectra
(maxsep =                1000.) Maximum separation between spectra
(order  =           increasing) Order of apertures

                                # RECENTERING PARAMETERS
(aprecen=                     ) Apertures for recentering calculation
(npeaks =                INDEF) Select brightest peaks
(shift  =                  yes) Use average shift instead of recentering?

                                # RESIZING PARAMETERS

(llimit =                INDEF) Lower aperture limit relative to center
(ulimit =                INDEF) Upper aperture limit relative to center
(ylevel =                  0.1) Fraction of peak or intensity for automatic width
(peak   =                  yes) Is ylevel a fraction of the peak?
(bkg    =                  yes) Subtract background in automatic width?
(r_grow =                   0.) Grow limits by this factor
(avglimi=                   no) Average limits over all apertures?

                                # TRACING PARAMETERS

(t_nsum =                   10) Number of dispersion lines to sum
(t_step =                   10) Tracing step
(t_nlost=                    3) Number of consecutive times profile is lost before quitting
(t_funct=             legendre) Trace fitting function
(t_order=                    4) Trace fitting function order
(t_sampl=                    *) Trace sample regions
(t_naver=                    1) Trace average or median
(t_niter=                   10) Trace rejection iterations
(t_low_r=                   3.) Trace lower rejection sigma
(t_high_=                   3.) Trace upper rejection sigma
(t_grow =                   0.) Trace rejection growing radius

                                # EXTRACTION PARAMETERS

(backgro=                  fit) Background to subtract
(skybox =                    1) Box car smoothing length for sky
(weights=                 none) Extraction weights (none|variance)
(pfit   =                fit1d) Profile fitting type (fit1d|fit2d)
(clean  =                   no) Detect and replace bad pixels?
(saturat=               65000.) Saturation level
(readnoi=                   0.) Read out noise sigma (photons)
(gain   =                   1.) Photon gain (photons/data number)
(lsigma =                   4.) Lower rejection threshold
(usigma =                   4.) Upper rejection threshold
(nsubaps=                    1) Number of subapertures per aperture
(mode   =                   ql)

Then, run the apall task on your star spectra. For example:

onedspec> apall ccd020
Recenter apertures for ccd020?  (yes): 
Resize apertures for ccd020?  (yes): 
Edit apertures for ccd020?  (yes): 

At this point, you should see a plot like this:

This is a slice across the spectrum of the star (in this case averaging over columns 1029-1038), used to identify the spectrum you want. In this case there is only one spectrum there, and it has identified it by the "H" at the peak top of the plot.

  • The width of the upper H shows the range of rows that will be summed together during the extraction (in this case, a total of five rows are extracted around the peak flux in each column of the CCD image).

  • The lower "H-symbols" denote the range of rows that will be used to determine the background level (in this case, four rows to either side of the star spectrum are used to fit a "baseline" background level to subtract, in this case at a level of about 34000 ADU).

If you are satisfied with the selection, type "q".

Note, if you apply apall to an image with multiple spectra in it, you will see multiple peaks, and you have to pick the one you want. The program by default picks the highest peak, as shown below:

If the program should automatically pick the wrong peak (as it did above, if we want the middle one), type a "d" to delete it, move the cursor over the peak you want, and type an "n" to select it. Then type "q".

You will then be asked a series of questions. Unless you have made a mistake at this point and want to stop, say "yes" (or accept the default with a ) to all or else say "no" to all to stop:

Trace apertures for ccd020?  (yes):
Fit traced positions for ccd020 interactively?  (yes): 
Fit curve to aperture 1 of ccd020 interactively?  (yes):
Then you should see a plot, which represents the row containing the peak flux (for the spectrum you have selected) in each column of the CCD image:

If you have set the parameters to apall as above, you should have the plot being fit with a 4th order polynomial with a 10-iteration outlier rejection. (If you have not set this up, you can do so now, or change the order of the fit, by doing a ":niter 10" and a ":order 4".)

Once you are happy with the fit, type "q".

Again, you will be asked questions, and, unless you have made a mistake at this point and want to stop, say "yes" (or accept the default with a ) to all or else say "no" to all to stop:

Write apertures for ccd020 to database?  (yes):
Extract aperture spectra for ccd020?  (yes):
Review extracted spectra from ccd020?  (yes):
Review extracted spectrum for aperture 1 from ccd020?  (yes):
At this point a 1-D image of the extracted spectrum should appear. If the background subtraction has been turned on, the baseline of the plot should be 0 ADU.

At this point, for looking at the spectrum, it is better to use the splot task (see below). Make sure you ask for the extracted, 1-D version of the spectrum you have created with apall, which is has a ".ms" suffix:

onedspec> splot

2. Wavelength Calibration

Next, extract a spectrum of the XeNeAr calibration lamp. The following instructions must be followed anew each time the grating angle in the spectrograph has been changed.

IMPORTANT: If you intend to wavelength calibrate a particular one of the five possible spectra in an image, you must wavelength calibrate by extracting the corresponding XeNeAr spectrum in the same position!

Edit the parameters of identify to look like this:

PACKAGE = onedspec
   TASK = identify

images  =    Images containing features to be identified
(section=          middle line) Section to apply to two dimensional images
(databas=             database) Database in which to record feature data
(coordli= linelists$nearxe_ggss.dat) User coordinate list
(units  =                     ) Coordinate units
(nsum   =                   10) Number of lines/columns/bands to sum in 2D images
(match  =                  -3.) Coordinate list matching limit
(maxfeat=                  100) Maximum number of features for automatic identification
(zwidth =                 100.) Zoom graph width in user units
(ftype  =             emission) Feature type
(fwidth =                   4.) Feature width in pixels
(cradius=                   5.) Centering radius in pixels
(thresho=                   0.) Feature threshold for centering
(minsep =                   2.) Minimum pixel separation
(functio=              spline3) Coordinate function
(order  =                    1) Order of coordinate function
(sample =                    *) Coordinate sample regions
(niterat=                   10) Rejection iterations
(low_rej=                  2.5) Lower rejection sigma
(high_re=                  2.5) Upper rejection sigma
(grow   =                   0.) Rejection growing radius
(autowri=                   no) Automatically write to database
(graphic=             stdgraph) Graphics output device
(cursor =                     ) Graphics cursor input
crval   =                       Approximate coordinate (at reference pixel)
cdelt   =                       Approximate dispersion
(aidpars=                     ) Automatic identification algorithm parameters
(mode   =                   ql)
You should end up with a plot like this:

Now, with reference to the XeNeAr atlas in the FOBOS manual, begin to identify lines in the XeNeAr spectrum:

  • Zoom into specific regions of the plot, using the "X" (zoom in x), `"Y" (zoom in y), and "Z" (zoom in both x and y dimensions).

    You can always zoom out to the original plot using the "r" key.

  • When you have matched the appearance of the lines to the atlas in a given part of the spectrum, begin identifying and marking the lines:

    • Put the cursor on the line and type "m".

    • Type into the graphics window the EXACT wavelength of the line as given in the atlas:

    • Keep marking lines evenly spread across the spectrum.

      You don't have to mark every line, but mark them at regular intervals and over the widest wavelength range as possible.

    • When you have marked at least a dozen, preferably two dozen or more, your plot should look like this after an "r" key.

      (Note, in the following plot, the atlas has run out of lines on the left side, so they haven't been marked.)

Now hit the "l" key, and the program will identify the rest of the lines in the spectrum that happen to be in the XeNeAr linelist.

  • You should see a plot like the following appear:

  • Each of the lines in the linelist will be identified.

  • Note at this point the abscissa of the plot has been put onto a wavelength axis from blue to red.

  • Check the identifications at various points along the spectrum by placing the cursor on lines and typing the "c" key. Make sure that the line identifications match the atlas.

  • If all is ok, type an "f" key, and you can begin the fitting process.

The program now attempts to determine a polynomial fit between the column number in the extracted 1-D spectrum to Å.

A plot like this will appear:

  • If you have set up identify as above, a good fit, with a low RMS (several 0.1 of an Angstrom) should automatically be found, with outlier points (bad line identifications or lines with poor S/N) eliminated.

  • Of course, you can change the order of the fit. A low order should be sufficient (I used 1st order here for this demo, but you might try 2nd order or even 3rd, but don't try to fit EVERY point in the plot).

  • When you are happy with the fit, type "q" and answer yes to the question:

    identify - Ap 1
    Write feature data to the database (yes)? 
    This will create a directory, "database", that contain information on the wavelength fit.

Next we need to couple each stellar spectrum with its corresponding, calibrated XeNeAr spectrum (one for each grating angle position).

Set your refspec parameters as follows:

PACKAGE = onedspec
   TASK = refspectra

input   =                       List of input spectra
(referen=               ccd013) List of reference spectra
(apertur=                     ) Input aperture selection list
(refaps =                     ) Reference aperture selection list
(ignorea=                  yes) Ignore input and reference apertures?
(select =                match) Selection method for reference spectra
(sort   =                     ) Sort key
(group  =                     ) Group key
(time   =                   no) Is sort key a time?
(timewra=                  17.) Time wrap point for time sorting
(overrid=                  yes) Override previous assignments?
(confirm=                  yes) Confirm reference spectrum assignments?
(assign =                  yes) Assign the reference spectra to the input spectrum?
(logfile=       STDOUT,logfile) List of logfiles
(verbose=                   no) Verbose log output?
answer  =                       Accept assignment?
(mode   =                   ql)
Let's say your reference XeNeAr comparison spectrum is ccd013 and your 1-D star spectrum is ccd020. Then type:

onedspec> refspec reference=ccd013.fits select=match
onedspec> hedit REFSPEC1 add+ value="" 
(Note, the hedit step should not have to be required, but for some reason I could not get this to work without doing that.) Then, apply the dispersion correction to the stellar spectrum.

Set the parameters of the task dispcor as:

PACKAGE = onedspec
   TASK = dispcor

input   =                       List of input spectra
output  =                       List of output spectra
(lineari=                  yes) Linearize (interpolate) spectra?
(databas=             database) Dispersion solution database
(table  =                     ) Wavelength table for apertures
(w1     =                INDEF) Starting wavelength
(w2     =                INDEF) Ending wavelength
(dw     =                INDEF) Wavelength interval per pixel
(nw     =                INDEF) Number of output pixels
(log    =                  yes) Logarithmic wavelength scale?
(flux   =                  yes) Conserve flux?
(blank  =                   0.) Output value of points not in input
(samedis=                   no) Same dispersion in all apertures?
(global =                   no) Apply global defaults?
(ignorea=                   no) Ignore apertures?
(confirm=                   no) Confirm dispersion coordinates?
(listonl=                   no) List the dispersion coordinates only?
(verbose=                  yes) Print linear dispersion assignments?
(logfile=                     ) Log file
(mode   =                   ql)

Then apply the dispersion correction for stellar image and create a new wavelength calibrated version,

onedspec> dispcor REFSPEC1 = ' 1.' ap = 1, w1 = 5032.654561154716, w2 = 6778.930914001614, dw = 0.8448361648993223, nw = 2068
  Change wavelength coordinate assignments? (yes|no|NO) (no): ap = 1, w1 = 5032.655, w2 = 6778.931, dw = 0.844836, nw = 2068, log = yes

At this point, the image is wavelength calibrated, as would be seen if you ran

onedspec> splot

Note some useful keystroke commands for adjusting the display in splot for present purposes:

  • "X" to expand X-dimension around the cursor.

  • "Y" to expand Y-dimension around the cursor.

  • "Z" to expand both X and Y dimensions around cursor.

  • "w" allows you to window the display by putting the cursor at the minimum flux to display (type "w" and then "b") and the top flux to display (type "w" and then "t").

  • Alternatively, you can imagine the "box" you want to display and mark the lower left of the box with "E" and upper right with a second "E".

3. Continuum Normalization

At this point, you have wavelength calibrated spectra where the ADU levels reflect not only the relative flux of the star, but (more dominantly) the response function of the FOBOS instrument.

  • As the above image demonstrates, the response function of the instrument is peaked in the center of the image and all stellar spectra will have the same general shape as above.

  • Because it makes it necessary to show a large ADU range, this global shape can make it difficult to see subtle line features across the spectrum.

Thus, it can be useful to remove the general shape of the response function to highlight the lines.

  • Ideally, we would like the continuum level of the spectrum to be level and the lines hang down in proportion to their strength.

  • We could do this by attempting to fit the continuum in the stellar spectrum itself, but this can be fraught with difficulties, particularly for late type stars where large molecular bands can be mistaken for variations in continuum level.

  • It is better to attempt to map the response function using the quartz lamp exposures, which are meant to create "flat", blackbody exposures with wavelength.

  • The following procedure shows how to do this for our data.

  • Note, it may not be possible to "flatten" the spectra exactly, and there is a bit of artistry to this. But the procedure below seems to work reasonably well.

  • Note that it is in principle possible (and slightly simpler) to do this step before wavelength calibration, but the order is not important (it is a question of doing the quartz fitting in wavelength or pixel dimensions).

First apall and wavelength correct your (overscan and bias corrected) averaged quartz exposures appropriate to your stellar spectrum. Don't forget:

onedspec> refspec reference=ccd013.fits select=match
onedspec> hedit REFSPEC1 add+ value=""
add,REFSPEC1 = updated
onedspec> dispcor REFSPEC1 = ' 1.' ap = 1, w1 = 5032.654561154716, w2 = 6778.930914001614, dw = 0.8448361648993223, nw = 2068
  Change wavelength coordinate assignments? (yes|no|NO) (no): ap = 1, w1 = 5032.655, w2 = 6778.931, dw = 0.844836, nw = 2068, log = yes
Next, set-up the continuum task as follows:

PACKAGE = onedspec
   TASK = continuum

input   =    Input images
output  =  Output images
(lines  =                    *) Image lines to be fit
(bands  =                    1) Image bands to be fit
(type   =                  fit) Type of output
(replace=                   no) Replace rejected points by fit?
(wavesca=                  yes) Scale the X axis with wavelength?
(logscal=                   no) Take the log (base 10) of both axes?
(overrid=                   no) Override previously fit lines?
(listonl=                   no) List fit but don't modify any images?
(logfile=              logfile) List of log files
(interac=                  yes) Set fitting parameters interactively?
(sample =                    *) Sample points to use in fit
(naverag=                    1) Number of points in sample averaging
(functio=              spline3) Fitting function
(order  =                   25) Order of fitting function
(low_rej=                   2.) Low rejection in sigma of fit
(high_re=                   0.) High rejection in sigma of fit
(niterat=                   10) Number of rejection iterations
(grow   =                   1.) Rejection growing radius in pixels
(markrej=                  yes) Mark rejected points?
(graphic=             stdgraph) Graphics output device
(cursor =                     ) Graphics cursor input
ask     =                  yes                                       
(mode   =                   ql)

The run the continuum command (here I am running this on just one quartz for demonstration). Note, since the quartz should not have lines in it, a high order fit (here I am using 25th order spline3 fit) is ok to get at the fine details of the shape:

on> continuum
Fit [1,1] of w/ graph  (yes|no|skip|YES|NO|SKIP) (yes): 

Note, the task should remove outliers, but this can make it hard to see what is going on (as in above figure). You can temporarily set :niter 0 to look at the general fit, and then put back to :niter 10 for the final fit. Then quit out with a "q" when you are happy.

Then look at the fit, which should appear relatively smooth:
on> splot
Image band to plot (1:) (1): 

To make you feel good, it may help to normalize this quartz to have a mean level about 1. Guessing the middle value to be about 37500 ADU:

on> e
imar / 37500. 
Check with a splot command that you have the frame normalized as you wish.

Now divide the smoothly fit quartz into the stellar spectra as follows.

NOTE: This seems only to work properly on the version of the stellar spectrum before wavelength calibration:

on> imar /  
on> splot
Image band to plot (1:) (1): 

You'll note that the spectrum is still not flat, but we will fix this later.

By running dispcor again, we can not only put the spectrum back in Angstrom units, but cut off those parts of the spectrum we want to discard:

dispcor REFSPEC1 = ' 1.' ap = 1, w1 = 5032.654561154716, w2 = 6778.930914001614, dw = 0.8448361648993223, nw = 2068
  Change wavelength coordinate assignments? (yes|no|NO) (no): ap = 1, w1 = 5032.655, w2 = 6778.931, dw = 0.844836, nw = 2068, log = yes

on> splot
Image band to plot (1:) (1): 

Now the image is in wavelength units. Note the slope has changed because of the change in the flux per abscissa unit, where the mapping from pixels to Å is not necessarily linear:

Note, after you do this for one spectrum, you can make a decision about which part of the spectrum is good and which parts might be discarded (you can use "c" in splot).

  • In principle you can use dispcor to trim away the garbage.

  • For example, one might decide that only the range from 5080 to 6660 Å are useful parts of the spectrum (this evaluation will change for every time the grating angle in the spectrograph has been changed).

  • Then one could have done the following in dispcor to limit the output to a good part of the spectrum:

on> dispcor REFSPEC1 = ' 1.' ap = 1, w1 = 5032.654561154716, w2 = 6778.930914001614, dw = 0.8448361648993223, nw = 2068
  Change wavelength coordinate assignments? (yes|no|NO) (no): yes
  Starting wavelength (5032.6545611547): 5080.
  Ending wavelength (6778.9309140016): 6660.
  Wavelength interval per pixel (0.84483616489932): 
  Number of output pixels (2068): ap = 1, w1 = 5080., w2 = 6659.843628361729, dw = 0.84483616489932, nw = 1871
  Change wavelength coordinate assignments? (yes|no|NO) (yes): no ap = 1, w1 =    5080., w2 = 6659.844, dw = 0.844836, nw = 1871, log = yes

on> splot
Image band to plot (1:) (1): 

You'll note that the spectrum is still not flat:

  • The residual sloping is presumably mostly related to the spectral energy distribution of the star compared to the quartz lamp, in this case hotter.

  • At this point, however, one can take out this residual slope within the stellar spectrum by using splot and a very low order fit to the continuum.

  • Do this by typing "t", setting :order 1 and then "/".

  • You will see a plot like this:

  • If you "q" out of the splot fitting, the replot will look like this:

    Note that the continuum is not perfectly flat (the region between 6200 and 6500 Å could be done better, and might have been done better with a second order fit above -- but be careful not to remove real molecular band structures in cooler stars!).

  • If you like what you see, you can save it by using the splot "i" key and writing the result to a new file.

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Wien's law figure from Spectra image from Absorption/emission animation from Hydrogen atom transitions image from All other material copyright © 2002, 2005, 2007, 2009, 2011, 2013, 2017 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 511 and Astronomy 5110 at the University of Virginia.