Exercise 1: Emission Lines and Central Star Temperature

Planetary nebulae are hot glowing gas clouds ejected by dying low- to intermediate-mass stars. The nebulae glow because they are heated by energetic ultraviolet photons from the exposed stellar core. According to Kirchhoff's laws, the light produced by a planetary nebula should be an emission spectrum, with spikes of emission at specific wavelengths corresponding to the elements in the gas. A spectrum can be displayed as a picture showing stripes of color at the wavelength of each emission line, or as a graph, plotting the amount of light at each wavelength.

In this exercise, you will learn how to

Ionization in a Planetary Nebula

The central star in a planetary nebula is the exposed core of the original star. The temperature of the central star in a planetary nebula can be quite high, sometimes exceeding 200,000 K. (Eventually, all central stars will cool and become white dwarfs, and the planetary nebulae will expand and fade from view.) Typically, central star temperatures range from about 30,000 K to 100,000 K. At these high temperatures, a star will emit a great deal of radiation energetic enough to ionize the atoms in the nebula; the amount of radiation at each wavelength depends on the temperature, according to the Planck Law, otherwise known as "blackbody radiation."

Of particular interest is the amount of ultraviolet radiation emitted; some ultraviolet photons have so much energy that they can ionize the atoms in the nebula, stripping off one or more electrons. The amount of energy required to produce the next higher level of ionization in an atom is called its ionization potential, usually expressed in electron volts (eV). In general, heavier atoms are more easily ionized for the first time than lighter atoms are. If an atom is already ionized, the remaining electrons are held more tightly, and it becomes even harder to remove the next electron to ionize the atom more highly. The overall degree of ionization of atoms in a planetary nebula depends on the temperature of the central star. For two stars with the same radius, a hotter star emits more photons at all energies than a cooler star does, and a greater proportion of those photons will be emitted at higher energies. Therefore a hotter star is capable of ionizing more atoms to higher ionization states than a cooler star is. So, by examining the spectrum of a planetary nebula to see what ionization states of the various elements are present, you can get an idea of the temperature of the central star.

Plotting a Spectrum

All spectra in the database are listed on the Browse page. Clicking on the name of any planetary nebula takes you to the "Spectrum Display" page for that nebula. To expand any region of the graphed spectrum, hold the left mouse button down at one corner of the region you wish to enlarge, drag the mouse to the opposite corner of that region, and then release the mouse button. You can do this repeatedly to keep enlarging. To get back to the full plot, click on the "Zoom Out" radio button under the graph display. The horizontal axis of these graphs is the wavelength in Angstroms, and the vertical axis is the flux (in ergs cm-2 s-1Angstrom-1).

Identifying Emission Lines

The Templates page contains a set of spectra labelled with the wavelengths of emission lines seen in planetary nebulae and identifying the ion producing each emission line. The name of the element is given using the standard chemical symbol from the periodic table (e.g., H=hydrogen, N=nitrogen, Ne=neon, etc.). The ionization state of the element is indicated by a Roman numeral suffix in the following way: neutral=I, singly ionized=II, doubly ionized=III (i.e. ionization state = Roman numeral -1). For example, O III means doubly ionized oxygen, O+2. Certain electron transitions involve energy levels that are said to be metastable; the resulting emission lines are called forbidden lines, which really only means that they are less likely to occur than emission lines from the ordinary kind of transitions. Conditions in planetary nebulae, as it turns out, are extremely conducive to the production of this kind of emission line, and in fact, most of the emission lines you will see in these spectra are forbidden lines, which are denoted by brackets around the ion designation (i.e. a forbidden line produced by doubly ionized oxygen would be written as [O III].

The Exercise

You may find it helpful to print out this page of instructions.

Listed below are three planetary nebulae whose central stars have very different temperatures. You will examine the spectra of each nebula and by noticing the presence or absence of certain emission lines, be able to rank them in order of the temperature of the central star.

  1. Print out the data table for this exercise. Notice that there is an identical table for each planetary nebula, containing a selection of forbidden lines produced by highly ionized atoms in the nebular gas. The first column gives the wavelength of the emission line, and the second identifies the element and the ionization stage. The third column lists the ionization potential of the preceding ionization stage. For example, for [K IV] (which means K+3) the relevant ionization potential is that of K+2, since we are interested in the energy required to ionize K+2 one step further to K+3.
  2. Click on the name of one of the planetary nebulae above; this will take you to its spectrum display. Expand the spectrum around each of the wavelengths listed in the data table, and look for that particular emission line. Note its absence or presence and fill in the appropriate table. Because of the relative motion between the Earth and each nebula, the wavelengths may be Doppler-shifted slightly from their nominal values. If you are not sure whether the line is really there, write "?" in the table.
  3. Repeat for the other two nebulae.
  4. Examine each table. Of the elements producing emission lines that you detected, note which has the highest ionization potential, meaning which element requires the most energy to reach its observed ionization state. The higher the maximum ionization potential, the hotter the central star must be.
  5. You can now rank these three planetary nebulae on that basis. Fill in the "results" portion of the data table in descending order of stellar temperature.
  6. You might want to search the literature for determinations of the stellar temperatures for these planetary nebulae to see if your relative ranking is correct. And you also might like to try this for some of the other nebulae on the Browse page.
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