University of Michigan - Department of Astronomy

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Version: Magnitude

updated: 04/19/2000


Spectral Classification and the Pleiades

I have looked farther into space than ever [a] human being did before me.
  --William Herschel, c. 1780

Objectives

Introduction

There are several different concepts which work together in this lab to finally give us the answer we are looking for, the distance to the Pleiades. (The Pleiades is a star cluster, i.e., a group of stars which are located near one another in space and were probably 'born' at the same time). The first step is to learn how to do a rough classification of stellar spectra. This lets you determine the spectral type of a star from its spectrum. The second step is to find the apparent magnitude of this star. Armed with these two facts, spectral type and apparent magnitude, of a group of stars, you can construct a Hertzsprung-Russel (H-R) diagram also known as a color-magnitude diagram. From here, it is a few short steps to finding the distance modulus (the difference between the apparent and absolute magnitudes), which tells you the distance to this group of stars. As you read through the steps, try to understand how each part of this lab fits together to give us the final distance answer -- each different, though quite important individually.


Step One: Determining the Spectral Type

The spectral type of a star is just a letter and a number that designates what kind of a star it is. O stars are the hottest, and M stars are the coolest stars. The differences between spectral types show up in the absorption lines of the spectra of stars. Some astronomers spend their whole careers determining detailed spectral types, but in this lab, you're just going to make a rough estimate for ten stars in the Pleiades star cluster.

In lab, you will be given a large envelope by your instructor which should contain:

WARNING --

Lay out the standard star spectra sheets in front of you, so that you can see the whole sequence of stars from O to M. These are your reference spectra. These standard stars tell you what an A0 (or any other) star spectra should look like. Notice the sequence of letters subdivided by numbers, which go from 0-9 for each letter. The wavelength scales on the standard spectra are all consistent with each other, so you can follow absorption lines up and down the page between spectral types. The Pleiades spectra are also consistent with themselves (notice how the few labelled lines follow in the same place from spectrum to spectrum), however they are not on the same scale as the standard spectra. The absorption lines in the Pleiades spectra are more widely separated than the standard star spectra. Although this makes life a little more difficult, you'll find it doesn't pose a major problem for classification.

Your job in this part is to determine the letter and number of the ten stars in the Pleiades for which we have spectra. In other words, you have to determine if a star is a type A8, G9, or F0. But don't feel overwhelmed -- your instructor will explain in class how to do this. You don't just have to look at the standard spectra and psychically pick out which one you think matches. This would indeed be very hard to do. Instead, look at the flow chart in your envelope of materials.

The flow chart asks you to make choices about labelled absorption lines in the particular spectra you are trying to type (is the G-band stronger than the Ca I line? yes/no/maybe). So, you look at one Pleiades spectrum at a time and make these decisions. I would suggest that you avoid choosing "maybe" as an answer and just choose "yes" or "no" because answering maybe is too easy and tends to lead you down the wrong path. After answering a couple of questions like these, you are given a range of spectral types that your star could be, for example F2-F9.

Don't stop at this point, though, because you need a more specific answer. So now go to the standard star spectra sheets and look at this range of spectral types (F2-F9 in our example). Look at how particular spectral lines (like the Hydrogen lines or Calcium lines) change their relative intensities through this range of spectral types. Now you must pick some of these lines and decide where your Pleiades spectrum fits in amongst the standard star spectra. You must use the relative intensities of two different lines (in the standard and the Pleiades) to decide this, and not the intensity of a single Pleiades line versus a single standard line because the brightness of the Pleiades spectra is not the same as the brightness of the standards.

Write which absorption lines you used to decide the spectral type in the Table 1. Particularly, include the lines which helped you make the final determination between the numerical subdivisions. Also record the spectral types for each star. You're done with the spectral typing now (and also most of the work in the lab); congratulations!


Step 2: Determining the Apparent Magnitude

The apparent magnitude of a star is a measure of its brightness as we see it here on Earth. We have a negative photograph of these ten stars in the Pleiades. Now, a brighter star makes a bigger 'dot' on this photograph, so if we knew how to turn the dot-size into a magnitude, we could just measure the sizes of the star-images on the photograph to find out their apparent magnitudes. Luckily, we do know how to turn dot-size into magnitudes. There is a graph/table in this lab which gives you a calibration curve between star-image diameter (dot-size) and apparent blue magnitude. Great. All you have to do is measure the diameter of each of the ten stars (numbered on the photograph) to the nearest 0.1 mm. Then look at the graph/table and find your measurement on the 'diameter' axis, follow this line up to the curve, and then over to find the apparent blue magnitude. Record these results in your data table. You are now done with everything that must be done in lab, but you may wish to stay and plot up your results with the rest of your lab group (I'd advise doing this to check for mistakes!).


Step 3: Making an H-R Diagram

You have the information you need to make an H-R diagram for these ten Pleiades stars. You know the apparent blue magnitude and the spectral type. Plot these quantities in Graph 1: H-R Diagram that is provided. You should find that the stars fall fairly close to a main sequence shape. Now plot all the stars listed in the standard star main sequence table in this lab, using a different symbol than the one you used to plot the Pleiades stars. These stars are all main sequence stars that have known spectral types and apparent and absolute magnitudes (how do they know the absolute magnitude? -think about it). These stars should fall on a very well-defined main sequence that is displaced vertically from your data points.

Draw a 'best-fit' line through these points from the table. A best-fit line is a curve that goes through, or near, as many points as possible. It is NOT a jagged line that goes from point-to-point (don't just connect the dots). Draw a smooth line that follows the overall shape your eye sees. This shows you what a main sequence line should look like. Now draw a best-fit line through the points from the Pleiades data that you gathered. Hopefully they're somewhat similar. (If not, consider where you think your errors probably are the spectral classification). Now you're ready for the final step.


Step 4: Determining the distance

The stars in the Pleiades are just normal stars, just like the stars that you plotted from the table, assuming that both are main sequence stars and that the laws of physics in the Pleiades is the same as for these known stars. Therefore, the same type of star should have the same intrinsic brightness whether it is in the Pleiades or not. Having the same intrinsic brightness is the same thing as having the same absolute magnitude. So, the stars in the Pleiades have the same absolute magnitudes as the known stars that you plotted, and you can now find the difference between the absolute and apparent magnitude of the stars in the Pleiades. This is just the vertical difference between the two main sequence lines that you drew!

You need to measure this vertical offset between the two curves. Choose several places (e.g., A0, B0, F0, K0) along the curve and find the difference (m-M) at these points; this is the distance modulous. Consider again where your errors probably are when you choose where to measure, and mark clearly on the graph where you measured and what value you got. Then take the average of all of the differences you measured to find an average (m-M) to use. Rembering that (m-M) is just the distance modulus, you can now calculate the distance to the Pleiades cluster in parsecs using the following formulae:

Equation 1: Distance Modulous Equation

Equation 2: Distance Modulous Equation reworked

You can convert this result (in parsecs) to light-years by multiplying by 3.26 light years per parsec. Write your final distance measurement in the space provided. This distance result is actually an average distance to the Pleiades stars that we used in this exercise. However, the result isn't too far off the distance to any particular star, because we have assumed that the distance separations within the star cluster are small compared with the distance between Earth and the star cluster. It should also be noted that we will tend to overestimate the actual distance to the Pleiades in this exercise, because we have neglected to take into account the dimming of starlight as it travels through interstellar dust on its way to Earth.

Measuring distances is a very difficult task in astronomy, yet it yields many rewards. Once you know the distance to say, a star in our galaxy, it can lead to a lot of other information. You can calculate how much light the star is giving off (its luminosity) to learn about theoretical aspects of stellar interiors like energy production or hydrodynamics. In the case of visual binary star systems, you can use the distance information to calculate the masses of the stars with Kepler's Third Law. In all cases, you can learn about the structure of the galaxy by seeing which stars populate which places.

As we try to extend our grasp further into the universe, we find we need new methods for measuring distances. Relatively close to Earth, within about 10 parsecs, we can use the parallax method to measure the distance to stars, like you did in the parallax lab. However, there are many more interesting things further away from the Earth than 10 parsecs. So we need some new methods, one of which you have just used, spectroscopic parallax.

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