Exercise 2: Detecting Interstellar Reddening

In this exercise, you will learn how interstellar reddening affects the spectrum of a planetary nebula. Comparing the spectra of several nebulae, you will be able to determine which are more or less affected by interstellar reddening. Combining these results with the galactic latitudes of these planetary nebulae, you will be able to conclude something about the distribution of interstellar dust in our Milky Way Galaxy.

The Balmer Decrement

In the Bohr model of the hydrogen atom there are many distinct energy levels, between which electrons can transfer if they emit or absorb the proper amount of energy. Upward moves require absorption of energy, while downward ones release energy. Downward electron transitions that end on the second energy level are called the Balmer series, and are important in optical astronomy, since these are the only transitions that involve visible light. The first three of these are called Hα, Hβ, and Hγ, for the transitions from 3-2, 4-2, and 5-2, respectively. When many ionized hydrogen atoms are recombining, as in a planetary nebula where atoms are being ionized and recombining all the time, the captured electrons cascade down through the energy levels, emitting photons of the appropriate wavelengths as they fall. The likelihood of any particular downward jump is dictated by atomic constants, and thus the ratios of all possible transitions can be calculated. This leads to the "Balmer decrement," the well known ratios among the intensities of the Balmer lines, where Hα is the strongest line, Hβ is weaker, Hγ is weaker still, and so on. Under typical conditions in planetary nebulae these ratios are (from Osterbrock, Astrophysics of Planetary Nebulae and Active Galactic Nuclei, University Science Books, 1989):

Hα/Hβ = 2.86 and Hγ/Hβ = 0.47

The Phenomenon of Interstellar Reddening

Thus, the Balmer decrement, the intensity ratios of Balmer lines in all planetary nebulae, should be roughly the same. However, this is not what is observed. Interstellar reddening produced by micron-sized dust particles selectively dims shorter-wavelength, bluer light more than it does longer-wavelength, redder light, leading to Balmer line ratios that differ systematically from the theoretical predictions. A planetary nebula lying behind a cloud of interstellar dust will be observed to have the intensity ratios Hα/Hβ more than 2.86, and Hγ/Hβ less than 0.47. The more dust, the greater the disparity between the observed and theoretical Balmer decrements. Turning this concept around, from the size of the discrepancy between observed and theoretical Balmer decrements, astronomers can infer the amount of interstellar reddening, and therefore, dust, between us and a given planetary nebula.

The Milky Way Galaxy and Galactic Coordinates

Our solar system and all of the planetary nebulae in this database reside in the Milky Way Galaxy. The Milky Way is a flattened spiral of stars, gas, and dust, surrounded by a more spheroidal, extended, and much more diffuse region, called the galactic halo. Locations in the Milky Way are conveniently specified by galactic coordinates, similar to latitude and longitude as seen by someone viewing from the center of the Earth. The origin of the galactic coordinate system, though, is not at the center of the Milky Way, but rather, is located at the sun's position, because that's where we are as we view the heavens.

The Browse page of this website lists galactic coordinates for each planetary nebula as "lll.l (sign)bb.b," where lll.l is the galactic longitude in degrees, and bb.b is the galactic latitude in degrees. The plus or minus sign before the galactic latitude indicates whether the object is above or below the galactic plane, respectively.

The Exercise

Listed below are eight planetary nebulae. For each of them, you will estimate the relative intensities of the Hα and Hβ lines and compare them with the theoretical prediction of 2.86 and with each other. Finally, you will be able to come to some conclusions about the distribution of dust in the Milky Way.

Data Collection

  1. Print out a copy of the data table for this exercise. You may also find it helpful to print out this page as well.
  2. The wavelength of Hα is 6563 Angstroms, and for Hβ it is 4861 Angstroms. Take a moment to look at the relevant templates for wavelength identifications to familiarize yourself with the appearance of the spectrum in the vicinity of these Balmer lines. You will find it helpful to print out a copy of the templates containing them.
  3. Review the Help page to make sure you know how to view and expand a spectrum.
  4. Click on one of the nebulae listed above. This will get you to the "View Spectrum" page where you will see the full spectrum of the nebula.
  5. Locate the Hα line and expand the spectrum to zoom in on this wavelength region. Repeat if necessary to give a good view of the line. (It is usually bracketed on either side by two lines that come from nitrogen.) Now zoom in on the upper part of the line so that you can get a good estimate of the maximum intensity (height) at the center. Write this maximum height down in the data table, remembering to include the scale exponent, given at the top left of the graph window (e.g., x10-12).
  6. Zoom back out to the full spectrum by pressing on the "zoom out" button under the spectrum display. Now zoom in on the bottom of the Hα line. Read the level of the continuum, or base level of the spectrum near the Hα line, and record it on the data sheet.
  7. Subtract the continuum level from the maximum height and record the Hα net height in the data table. Zoom back out to the full spectrum.
  8. Repeat steps 5-7 for the Hβ line.
  9. Now calculate the observed ratio of Hα/Hγ using the net heights and write the result in the last column of the data table.
  10. Repeat steps 5-9 for all remaining nebulae.

Data Analysis

  1. Fill in Table 2 of the data table, listing the nebulae in order from highest Hα/Hβ to lowest.
  2. Fill in the last column with each nebula's galactic latitude, without the plus or minus sign (i.e., use the absolute value of the galactic latitude).
  3. What trend do you notice between the galactic latitude and the value of the Hα/Hβ ratio?
  4. Remember that the amount of reddening depends how much dust you are looking through along the line of sight to any nebula. This in turn depends on the thickness of the dust and the distance to the nebula. If all of these nebulae were at the same distance from us (which they are not, although most of the objects in this sample are at similar distances), what does your conclusion from step 3 imply about the distribution of dust in the Milky Way? Can you find images or other material from your textbooks or reliable websites to support your conclusion?