Name(s) ______

______

Distances to the Stars in Leo

Objective - To determine the distances to seven of the brightest stars in the constellation Leo using the method of spectroscopic parallax; to compare the results to the more accurate distances derived from measured parallaxes.

Introduction - If the distance to the star is known via its measured parallax, it is a trivial matter for astronomers, or anyone else for that matter, to determine the absolute magnitude of the star using the magnitude equation. The Hipparcos Satellite has cataloged more than 2.5 million stars and measured parallaxes as small as 0.001 of an arc second. This small angle belongs to stars 1000 parsecs away. Our galaxy is approximately 30,000 pc in diameter, which means that most stars are too far away to have a measurable parallax. In these cases, the distance to the star must be determined by some other method.

We can use our knowledge of the H-R Diagram and our analysis of a star's spectrum to determine stellar distances. From the strength of the lines in a star's spectrum, we can give it a spectral type and luminosity class. We can use the luminosity to find its absolute magnitude and thus its distance. Finding the distances to stars based upon their spectral type and luminosity is known as the method of "spectroscopic parallax" (even though it has no parallax measurement involved). This method is not easy nor is it exact; however, it has proved to be one of the best ways to learn about the more distant stars.

The first part of this method involves determining the star's spectral type and luminosity class. Astronomers can determine a star's spectral type based on the absorption lines in the spectrum of the star. The hottest stars, spectral types O anb B show weakened hydrogen lines (too hot--hydrogen atoms are ionized) with some helium lines. Spectral type A stars have extremely strong hydrogen lines (temperatures just right). As stars get cooler, more lines will appear as heavier elements [for example, calcium (Ca), and iron (Fe)] recapture their electrons. The singly ionized calcium atoms (Ca II) are especially strong in spectral type G stars. Spectral type K stars have very weak hydrogen lines (too cold) but strong iron lines and similar heavy elements. The width of a line can be used to determine an approximate luminosity for a star. For a given element, supergiant stars will have narrow lines and dwarf stars will have broad lines. Here is an example of the luminosity effect for spectral type A0 stars, from A0 Ia to A0 V, and a white dwarf. Note that the lines of the white dwarf are so broad that they are smeared out.

Thought question: after looking at this effect, how accurate do you think astronomers are in determining the luminosity of a star this way?

Important note: the spectra shown in this lab are negatives: absorption lines appear bright while the background continuum appears dark.
Spectra are from An Atlas of Representative Stellar Spectra, 1978, (Halsted Press, all rights reserved)
  1. Figures 1 and 2 (online) show a series of standard spectra used to classify stars and the 7 stars in Leo that have already been classified as well as those 7 that you need to classify. You may either classify the stars working with the on-line frames, or print each frame and work with the hard copies.

o  First, take a look at the 7 stars in Leo that have already been classified, and compare each to the corresponding standard spectrum.

o  Use the examples shown in Fig. 1 to guide you in classifying the remaining 7 stars, shown in Fig. 2.

Note: because of the need to keep the image sizes small, some image quality had to be sacrificed. Note, too, that there may be a shift in some of the spectra, and with respect to the "line key" at the top of the page. By resizing the browser window (wider or narrower), you can eliminate some of the misalignment. Let the line patterns and strengths guide you in your classification. Also, the standard spectra are for luminosity class "V" only. Do not worry about being extremely accurate -- this is not an exact science!
  1. List your best guesses as to the spectral types in Column 3 of Table 1. The luminosity classes are already given for you (these would be way too difficult for us to figure out).
  2. After you have given your best effort at classifying the stars, check your guesses against the correct spectral types (no cheating Tommy and Dennis!). Fill in the correct spectral types in Column 4, and use these values for the rest of the exercise.
  3. Assign each star an absolute magnitude based on its spectral type and luminosity class. You must use the H-R Diagram to do this. Fill in Table 1.
  4. Solving for the distance in the magnitude formula, M = m - 5*log(d) + 5, we get:
Solve for the exponent of 10 first, then either punch the "inv log" keys or the 10x key on your calculator. Calculate the distance to each of the 7 stars based upon the absolute magnitude from spectroscopic parallax.
  1. For the 7 unclassified stars, fill in Table 1 for the distances determined from the measured parallax values, where d = 1/parallax (d is in parsecs for parallax measured in seconds of arc).

Questions. Answer the following questions.

  1. Pretend you need to tell your non-scientist roommate how distances are determined using spectroscopic parallax (in other words, summarize what you just did). Do so in terms that he or she will understand.
  1. In your own words, summarize why the spectroscopic parallax method is an important tool for astronomers.
  1. The major disadvantage of the spectroscopic parallax method is that it is not very accurate. Why is this? Consider specifically the errors or uncertainties you might expect at each step in the process.
  1. Reconsider the measured parallax method. For stars within a measurable range, what primary factor contributes to the errors or uncertainties with this method?
  1. As an astronomer, you are asked to choose between the spectroscopic parallax and measured parallax methods. Which one would you choose and why?

Identification of the Stars in Leo

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Table 1: Distances to Stars in Leo

Star ID / Star Name / "Your Best Guess"
Spectral
Type / Actual
Spectral
Type / Luminsity
Class / Apparent
Magnitude
(m) / Absolute
Magnitude
(M) from
Spectrscpic
Parallax / Distance
from
Spectrscpic
Parallax / Measured
Parallax
(arc sec) / Distance
from
Measured
Parallax
r Leo / (none) / N/A / B1 / I / 3.85 / ~ -6 / 900 / N/A / **
h Leo / 30 Leonis / N/A / A0 / I / 3.48 / ~ -5 / 500 / N/A / **
s Leo / (none) / N/A / B9 / V / 4.05 / ~ 2 / 25 / 0.017 / 59
b Leo / Denebola / N/A / A3 / V / 2.14 / ~ 2 / 10 / 0.076 / 13
d Leo / Zosma / N/A / A5 / V / 2.55 / ~ 1 / 20 / 0.040 / 25
z Leo / Aldhafera / N/A / F0 / III / 3.44 / ~ 1 / 32 / 0.025 / 40
m Leo / Ras Elased Borealis / N/A / K2 / III / 3.88 / ~ 2 / 25 / 0.025 / 40
a Leo / Regulus / V / 1.36 / 0.038
g1 Leo / Al Geiba A* / III / 2.14 / 0.036
e Leo / Ras Elased Australis / II / 2.98 / 0.009
q Leo / Chort / V / 3.34 / 0.036
g2 Leo / Al Geiba B* / III / 3.39 / 0.036
o Leo / Subra / V / 3.52 / 0.034
R Leo*** / (none) / III / 7.5 (ave) / N/A / **
* Visual Binary ** Distance is too far for a measurable parallax ***Variable Star
Luminosity class symbols: V = dwarf, IV = subgiant, III = giant, II = luminous giant, I = supergiant.

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