Homework #2E

Stars & Spectroscopy
Due Monday, February 27th, 2012
54 Points possible
You may complete this homework alone or in groups of TWO (no more).  If you work in a pair, ONLY TURN IN ONE ASSIGNMENT (listing both CID numbers at the top).    All work should be IN YOUR OWN WORDS,  TYPED, and STAPLED with each part clearly labeled (points will be deducted if this is not the case!)   
As always, don't hesitate to ask me and/or your TAs for help.  Also remember that group discussions may prove fruitful -- just make sure you (or your pair) write up your own answers in your own words.

Introduction:
In class we've discussed how astronomers are able to use spectroscopy to determine the physical characteristics of distant objects.  We've also started (or are about to start) discussing stars including how we classify them as well as their formation and evolution.  In this homework you'll be using a combination of real observational data, theoretical evolutionary models based on observations, and some educational simulations to answer a series of questions covering all of these topics You will also have a chance to test those handy critical thinking skills as you draw your own conclusions about the star formation and evolution process!



Part 1: Spectral Classification of Stars (4 pts each)

Below you will find a set of spectra of stars that fall in one of the standard classifications for "Main Sequence Stars" - stars which are fusing hydrogen into helium in their cores.  Note that each spectrum in each figure is for a different star with a unique spectral classification (listed above and to the right of the spectrum).  Classifications range from O5 V - M4 V where the V implies a main sequence star. (You'll notice a few stars with III or IV instead of V - those are giants!) Examine these figures closely and then answer the questions below.  *Note that you may find it helpful to right click the graphs and view them individually and/or print them out.*


QUESTIONS (4 points each):

The Balmer Series of Hydrogen has its strongest lines at 6563 Angstroms (H-alpha) , 4861 Angstroms (H-beta), and 4341 Angstroms (H-gamma).  Examine the H-beta line in the following 6 stars: O5 V, B6 V, A7 IV, G2 IV,  K5 V, M2 V

1. What type of spectral *lines* are these?  (choose only 1 of Kirchoff's 3 laws)  How do you know?


2. Place the 6 stars specified above in an order based on the strength of their H-beta lines, from STRONGEST to WEAKEST (Stronger lines are bigger.) What do you think this implies about the amount of atomic hydrogen in the outer layers of these stars?  (Hint: remember that in any given moment, a single atom can only absorb or emit a single photon!)  


3. Compare the general shape of the spectra of all six stars and think about where the peak might be for each.  Note that some stars will require you to *extrapolate* off of the graph by following the slope of the spectrum.   Use this information combined with your knowledge of the relationship between peak wavelength and temperature (i.e. Wien's law!) place all 6 stars in order of Temperature, explaining how you came to the order you did.

4. Are your sequences for #2 and #3 the same?  Knowing that the original stellar classification system began with the letter A, what might you conclude the original scheme was based upon?    

5.
Which has more atomic hydrogen in it's atmosphere: an O star or an A star? Which has a hotter surface temperature: an O star or an A star? Why might this be?  (hint: Think about your answers from #2-4 and speculate!)

Part 2: Observations of stars & the H-R Diagram (4 pts each)

INTRO:

Guess what?  The sequence you derived above in #3 is in fact the current classification scheme we use to classify stars both on and off of the main sequence (see p.230-231 in your book.) Remember that main sequence stars are fusing Hydrogen into Helium to support themselves against gravity. When a star is on the main sequence there are well defined relationships between the four fundamental stellar properties: Luminosity (L),  Surface Temperature (T, Teff, or Tsurf, or equivalently Spectral Type), Radius (R), and Mass (M). These relationships stay fairly constant the entire time the star is on the main sequence.

 (Note: When stars are forming *AND* when stars are evolving off of the main sequence R, L, and T change significantly.  This is the subject of part 3 of this homework)

While we can't see inside the stars as they evolve (nor can we really follow a single star through millions and billions of years of evolution) we *can* use something called The H-R Diagram to check out temperatures and luminosities of stars different evolutionary states to investigate how T and L change, telling us what's going on inside of the star! (READ THIS for a nice introduction and historical explanation of the use of an H-R Diagram.)
The term main sequence actually refers to a well-defined region of the the H-R Diagram, termed Luminosity Class V (roman numeral five).
Other regions include the subgiant and giant branches (Luminoisty classes IV and III), the Supergiants (Luminosity classes I and II)  as well as the white dwarf region, defined as such because they are groupings of similar luminosities.

So for parts 2 and 3 of this homework you will be answering questions that ask you to combine your knowledge of spectral types, information learned from H-R Diagrams, as well as some cool animations.  Begin by taking a look at the HR Diagram below (which includes data for actual stars shown to scale!)

   


You may also enjoy playing with the following HR Diagram Explorer.

The following questions can be answered by using either the diagram above, the simulator, or both.


6. 
Consider the following stars in the diagram above: Proxima Centauri, the Sun, Sirius, and Bellatrix.  Examine the stars in order of MASS from the least massive to the most massive.  Also take a look at their temperatures, luminosities, and radii.  Do you notice a trend in the stellar properties of these main sequence stars?  If yes, please describe the trend.

7. List the 7 main spectral classes in order of MASS from least massive to most massive.

8. Is it ever possible to have an M star with a higher Luminosity than an A or a B star?  Explain your answer.

9. Check out this simulator which shows the age (on the lower left)  at which stars turn off of the main sequence.  Called the main sequence turn-off (!) , this age is basically the end of the main sequence lifetime of a given star.  Find the main sequence turn-off for the 4 stars (who were in fact) named in question 6.

10. What can you conclude about the dependence of main sequence lifetime on mass?  What do you think is happening inside a star at the main sequence turn-off?

11. Below are images and  H-R diagrams of 2 clusters: The Pleiades (an open cluster) and 47 Tucanae (a globular cluster).
Using the simulator in question #9 to help you, figure out the age of each cluster and explain how you got your answers.
(Hint: Remember B-V is another way to measure surface Temperature - look at the H-R Diagram Explorer if you need help converting to Temperature)
(Hint #2: When looking at star clusters, it is assumed that all stars were born at the same time!)

The Pleiades (image from Hubble, data from Kharchenko et al. (2004))


47 Tucanae: (Image from ESO, diagram contains 2368 stars, taken from several studies consolidated in the database of Philip et al. (1976))




Part 3: Stellar Evolution & the H-R Diagram (2 pts each)

Take a look at this animation of how L and T change during the formation and evolution of a LOW MASS STAR (Mass < 3 solar masses or so)
Now watch this video of what's going on inside a low mass star during the later stages of evolution (note: PN stands for Planetary Nebula)
Finally watch this video of the evolution of a HIGH MASS star (M > 3 solar masses)

12.  When a protostar is approaching the main sequence, what is happening to its Temperature?  What about its Luminosity?  

13.  What is going on inside of a red giant star?  How does the surface temperature of a red giant compare to when it was on the main sequence?

14.  What are the oldest objects on the HR Diagram shown in Part 2?

15.  What will happen to Bellatrix when she "dies?"  

16. Will this happen before or after the Sun becomes a red giant?  How do you know?



This page was created by Joanna Levine and is maintained by her.
Last updated on October 13, 2011