University of Michigan - Department of Astronomy

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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 that 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 located near one another in space that were probably 'born' at the same time). The technique you'll be using is called spectroscopic parallax, and is used to determine the distance to young star clusters in our galaxy but more than 10 pc from Earth.

The first step is to learn how to do a rough classification of stellar spectra.  Although Fraunhofer first observed stellar spectra in the early 19th century, it was the turn of the twentieth century before Angelo Secchi and E.C. Pickering began using their spectra to classify stars.  The classification system we use today is based on the one first proposed by Willamina Flemming (who started out as Pickering’s maid!) and refined by Annie Jump Cannon and Antonia Maury.  Cannon and Maury’s work were published as the first Henry Draper Catalogue.  The technique you will use is very similar to the techniques of these women.  Today of course, astronomers can use computers to analyze the light from stars in a much more quantitative manner, allowing more refinement (and more certainty) than the technique you will use, although the basics are still the same.  The odd order of letters is because Flemming’s system put stars in order by the strength of their hydrogen lines: A had the strongest broadest lines, B weaker and thinner, C somewhat weaker still, etc.  Cannon rearranged and combined groups to reflect temperature: O are the hottest, B a little less hot, etc.  (A question you might want to ponder, why would the medium-hot stars have the strongest Balmer lines?)

The spectral type of a star is just a letter and a number that designates what kind of a star it is. From hottest to coolest, the letter categories are O, B, A. F, G, K, M. 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.

The second step is to find the brightness of this star.  Today, astronomers use a device called a photometer (i.e. a photon counter) to measure the flux received from an individual star.  Data are taken over a period of several hours through several different filters, and are usually combined with data taken over the course of several years.  The European Space Agency’s Hipparcos mission made such “photometric” measurements of more than 120,000 stars during its 3 year mission.  However, we need to fit this into a regular lab period, so again you'll be using a more historical technique: estimating the brightness based on the size of a photographic image.

With the spectral type and brightness, you can make a Hertzsprung-Russel (H-R) diagram.  For stars on the main sequence, there is a relationship between the temperature and luminosity.  Using Cannon's classification system, there is a relationship between the spectral type and the temperature.  So, all main sequence stars of the same type have the same luminosity: you can determine the luminosity by knowing the spectral type.  We use a set of standard stars at known distances (how do we know the distances?) to calibrate our luminosity scale. 

The flux or apparent brightness is the amount of light per unit area received from a star, or the total amount of light the star puts out (luminosity) divided by the total area that light shines though.  Since the light is emitted in all directions, the area will be the surface area of a sphere with a radius equal to the distance to the star.  For a star at distance d:

Thus if we can determine the flux and luminosity of a star, we can determine its distance.

A note on Magnitudes and Distance

Historically, astronomers used magnitudes to talk about the brightness of stars.  The first magnitude system was developed by the Greek astronomer Hipparchus, who divided the stars up into 6 groups, calling the brightest group the first magnitude, the second brightest the second magnitude, etc.  Astronomers have refined the system, and now include negatives and numbers larger than 6.  For example, the Sun has an apparent magnitude (m) of -26, Sirius a -1.42, and Hubble can see down to about 30.  The human eye responds to light on a logarithmic scale (i.e. a light source that actually puts out 10 times more photons than another source only looks about 2.5 brighter), so the magnitude system is also logarithmic.  The apparent magnitude system measures the same thing as the flux, but the numbers are in reverse order and a difference of 2.5 in magnitude corresponds to a factor of 10 in flux.  Similarly, the absolute magnitude (M) corresponds to the luminosity, but again a bigger number is dimmer and a difference of 2.5 is equal to a factor of 10 in luminosity.  By converting flux and luminosity into apparent and absolute magnitude, astronomers are able to derive the distance modulus:

where d is the distance to the star in parsecs.  Since m is fairly straightforward to measure, especially from space, but M is less certain (where are all the possible errors?), astronomers sometimes prefer to use the distance modulus (m-M) rather than calculating the distance.


Part 1: Determining the Spectral Type

In lab, you will be given a binder 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. Notice the sequence of letters is 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 instructor will assign 2 - 4 stars from the Pleiades for you to analyze. Write the numbers in the first column of table 1.

Begin by using the flow chart, which asks you to make choices about labelled absorption lines in the particular spectra you are trying to type. Look at one of your Pleiades spectra and follow the flow chart. Try to answer as accurately as possible, and only choose maybe if you really can't decide between yes or no. At the end, you are given a range of spectral types that your star could be, for example F2-F9. Enter this range into table 1.

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. Record which absorption lines you used to decide the spectral type in the Table 1 below. Particularly, include the lines which helped you make the final determination between the numerical subdivisions (note the absence of a line can be as important as its presence, so if you use the fact that a line is missing, include it in your list.) Also record the spectral types for each star.

Your instructor will put a chart on the board with columns for group number, star number and spectral type. Write the information for your stars on the board. You may want to skip to part 2 while waiting for the other groups to write their information up on the board.

Use the class data on the board to determine the average spectral class of each star and write this in table 2. Based on the spectral types, rank all the stars on a scale of 1 - 5 where 1 is very hot and 5 is fairly cool. Record this as the Temperature Rank in table 2

Step 2: Determining the Flux/Apparent Magnitude

On the back of the flowchart is a negative photograph of these ten stars.  A brighter star makes a bigger 'dot' on this photograph. To actually determine the flux or apparent magnitude we would measure the dots and use a calibration curve to convert the dot size into flux or apparent magnitude. That calibration curve can be found at https://dept.astro.lsa.umich.edu/ugactivities/Labs/pleiades/pl_standards.html if you are interested.

The Pleiades is a young star cluster so all the stars in the photograph are main sequence stars at roughly the same distance. This means the brightness depends primarily on their temperature. Rank the stars in terms of their size, where the largest dots correspond to a 1 and the smallest correspond to a 5. Enter this rank in the Size Rank column of table 2.

Compare the Temperature Rank and Size Rank columns of table 2. Place a check mark in the Agreement column for all stars where the two ranks are the same or 1 rank different.

If any of YOUR stars do NOT have a check in the agreement column, note which star(s) here, and try to determine why the temperature and size don't agree.





Table 1 - Determining the Spectral Type of Your Stars
star no. Type range lines used spectral type
 
     
     
     
     

Table 2 - Temperature - Brightness Agreement
star no. Ave spectral Type Temperature Rank Size rank Agreement
 1
       
2
       
3
       
4
       
5
       
6
       
7
       
8
       
9
       
10
       

Questions

  1. In general, how did people do classifying the stars (how well did the temperature rank match with the dot size)?



  2. What were the primary sources of error in determining the spectral types?





  3. How can you tell just from the photograph that the Pleiades is a young star cluster?





  4. Main sequence stars are fairly close to all having the same radius. Why is it important that all the stars be similar in size in this activity?





  5. In order to determine the distance, you need to know the flux (or apparent magnitude) and luminosity (or absolute magnitude) of the stars. Which one (flux or luminosity) can you figure out from the spectral type? Which one can you figure out from the dot size? Explain your answers.


Last update 1/30/12 SAM

Original by MacConnell

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