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ASTR 3130, Majewski [SPRING 2015]. Lecture Notes

ASTR 3130 (Majewski) Lecture Notes



  • Chapters 12-13 of Birney et al.

  • Chapters 4, 15 and 19 of Roy & Clarke.

  • Chapter 6 of Howell.


  • Spectroscopy is the study of spectra. Very much like the study of photometry - same kinds of info but better. Photometry = very coarse spectroscopy.
  • By the way, in case it isn't obvious, we can look at spectra either in 2-D form (as it lands on the focal plane of the spectrrograph), but, more typically and usefully, graphically, as a plot of flux versus wavelength:
  • From .

  • 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 must 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 λ0 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.

      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.

  • 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, we have different orbitals, or angular momentum quantum numbers, 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 1896 in the Sun by Dutch physicist Zeeman.
    • 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 corona 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 corona) -- 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 Halpha (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.
    • 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.

    • 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 = δE δt, the amount of time δt an atom spends in an energy level and the mean range of energy δE 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.
      • 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.
  • 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 Wλ with same area as line

    • Wλ for an element X is function of stellar T, g, [X/H]
    • In practice, the continuum level Ic can be hard to determine if there are many lines in the spectrum
  • 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 (see Seyfert 2 spectrum below).

    • 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.

    • 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.

      The Balmer continuum creates a sudden drop in the ultraviolet flux of hot stars near 3700-3800 Angstroms. This is often referred to as the "Balmer Jump".


      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.

  • "Forbidden Lines"

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

    • Normally, atoms can be excited by collisions or by absorption of photons. After excitation, 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 the probability for emission is so low that the low emission rate is not seen in the laboratory.

        In high density environments typically seen on Earth and in stellar atmospheres, collisional de-excitation will happen well before the de-excitation by photon emission can occur.
      • But in a nebula around a hot star, there are (1) many electrons free to excite atoms/ions at the right energy, and so many ionized atoms, but (2) the gas overall is at such low density that the excited atoms/ions are "left alone" long enough that they are free to de-excite by photon emission before they suffer collisional de-excitation; thus you can get lots of emission and the creation of strong emission in these otherwise "forbidden" lines. Famous ones:
        • [O II] -- 3727 Å
        • [O III] -- 4959, 5007 Å
        • [N II] -- 6584, 6548 Å
        • [Ne III] -- 3867, 3968 Å
      • We indicate a forbidden line transition by putting square braces around the name, as above.
    • Until 1927, these lines were unidentified because they are not seen under normal Earth conditions gas densities are just too high (we cannot even make a vacuum as low as the conditions in nebulae!).

      Thus, because these lines were first seen in the spectra of nebulae, it was thought that a new atomic element prominent only in nebulae had been discovered (this supposedly new element was called "Nebulium").

      Of course, this was just a misinterpretation of the situation, which is driven by the hot, but low density conditions seen in emission nebulae.


  • Emission Nebula (Orion)
  • Active Galactic Nuclei
  • There are various classes of "Active Galactic Nuclei". The major AGN classes are distinguished by their spectral character, but this character is thought to be primarily due to how we view the objects, and that there is a basic structure of these objects that is shared.

    The so-called "unified model" of AGN envisions a basic physical structure of gas and dust around a central, supermassive black hole in the center of these galaxies.

    The gas includes ionized gas that is both rapidly moving (creating Doppler broadened lines in a "broad-line region (BLR)") and some that is less rapidly moving at larger radius (creating a "narrow line region (NLR)").

    Depending on the viewing angle to the object, you can see the NLR, or both the NLR and BLR, or even the NLR + BLR + the collimated jet coming out along the poles of the system.

    (Left) From
    (Right) From .

    Here is how this system will look based on viewing angle, creating the spectroscopically differentiated AGN classes:

    • Seyfert 2: narrow lines only; LINER: "Low-Ionization Nuclear Emission Region"
    • Seyfert 1: two sets of lines superimposed
      1. Narrow lines (~100 km/s)

        Permitted & forbidden transitions

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

        Permitted lines only

        High density gas (forbidden lines collisionally suppressed)

    • Quasar (QSO) - almost no emission from host galaxy; extremely bright


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 in the Sun's spectrum identified by Fraunhofer:

  • Fraunhofer worked from red to ultraviolet, so his system of naming lines goes in that direction.

  • Pictures below show lines from from ultraviolet to red.

An image showing the Fraunhofer lines. From

This simpler plot excerpts the most commonly known lines that you should memorize. Knowing these lines in the spectrum of the Sun, which is a middle of the road spectral type, is a helpful starting point in any discussion of spectral lines for most other spectral types (which typically will express these same lines to lesser or greater degree).

As astronomical spectroscopy evolved, some of the Fraunhofer names were retained in common parlance, some have been mostly forgotten, and some were retained, but in a slightly altered form:

Fraunhofer name wavelength (Angstroms) source of the line most common way the line is referred to now
A 7594 Molecular oxygen in earth's atmosphere "telluric A band" or "atmospheric A band"
B 6867 Molecular oxygen in earth's atmosphere "telluric B band" or "atmospheric B band"
C 6563 Hα (H alpha line of hydrogen) "H alpha"
*D1 5896 Sodium "Sodium D doublet" (D1 and D2 together)
*D2 5890 Sodium "Sodium D doublet" (D1 and D2 together)
E1 5270 Iron
**Eb 5183-5168 Magnesium "Magnesium b" (written "Mgb" -- but NOT a molecule!)
F 4861 Hβ (H beta line of hydrogen) "H beta"
*G 4308 Blend of band of methane and iron "G band"
*H 3968 Once-ionized calcium "Calcium H & K lines" (written "Ca II H+K")
*K 3933 Once-ionized calcium "Calcium H & K lines" (written "Ca II H+K")

*Still commonly used name (e.g., "sodium D lines (NaD)", "G band" and "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.

The spectrum of the daytime sky is, of course, dominated by the solar spectrum. This shows a plot of the daytime sky with Fraunhofer and other features identified. From Wikipedia.
Classification of stellar spectra:

  • In late 1800s, originally classed into groups of like spectra (A, B, C, D ....), primarily based on appearance of Fraunhofer lines.

  • In 1888, Harvard astronomer Antonia Maury reordered into a sequence based on progressions of appearing and disappearing lines (see below).

    She also combines/removes redundant/spurious classes to get OBAFGKM sequence.

  • Later improved and subdivided into subclasses from 0 to 9 by Harvard colleague Annie Jump Cannon.

  • In early 1900s, became clear that differences in spectral types along sequence are based primarily on a temperature sequence (e.g., work by 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, making the Balmer series exgremely prominent.


    The following plot shows the relative expression of different spectral lines as a function of spectral class (temperature). Recall that "metal" means any atom heavier than helium.


    The following plot is similar to the above plot, but identifying specific lines.

Principal Spectral Class Sequence

The following spectra, shown from 7000 to 4000 Å, illustrate how specific lines come and go as a function of temperature.

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. Can you find the Balmer lines?

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 artificially flat for ease of comparison based on lines.

Actual stellar spectra, including the variation of flux by wavelength due to blackbody temperature, look something like this (note, this is showing the ACTUAL stellar spectral energy distributions, not those affected by the instrument and telescope sensitivity/throughput by wavelength).

HINT FOR SPECTROSCOPY LAB: 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 26-inch refractor and spectrograph optics, chromospheric aberration effects of the refractor, and quantum efficiency variations in the CCD camera.

ASTR 3130 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 for comparison.
  • For example, could compare strength of Balmer lines to CaII H+K as one discriminator.
  • How to identify lines?
    • Use comparison source lamps; identify Hg, Ne lines from atlas published in lab manual:
    • Here is a better looking version of a calibration lamp that gives a better sense of the relative intensity of lines (but unfortunately including Ar gas, which we do not have)
      (Left) A composite of the wavelength calibration spectra. The left spectrum corresponds to the Neon calibration lamp, while the right shows the Mercury/Argon calibration spectrum (Argon lines are the broad, dark lines above 7000 Angstroms). The middle strip contains the combination both lamps. These spectra were taken using the low resolution 240g/mm grating. (Right) The simple version of Hg and Ne emission from the top of this webpage. This is not as useful as the left hand image.

      The Hg/Ne lines appear on either side of the spectrum of the star (if done properly!).

    • Use Fraunhofer lines from sky spectrum you collect in Part 1 of the Lab as a guide to wavelengths and as a guide to what a solar spectrum looks like with your equipment.
    • THOUGHT PROBLEM: What is the "spectral type" of the sky spectrum and why?

Luminosity Effects in Stellar Spectra

Secondary effects on the strengths of lines come about due to the pressure of the gas producing the lines because this determines the rate at which electrons may be captured by ions, and so 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.
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., giant) stars and, 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 the usually subtle luminosity differences in stars of same spectral type.

Three A stars of different luminosity class. From

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.

But these subtle differences are important for gauging differences correctly with spectroscopic parallax (gauging the absolute magnitude of a star based on its spectrum), and 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.



An other 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, for a give temperature, are less luminous than their more metal-rich counterparts.

(Actually, 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 F4 star is in the color plot shown above -- compare to the normal metallicity F5 star above it in that same figure.

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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 © 2002,2006,2008,2012,2015 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 313 and Astronomy 3130 at the University of Virginia.