About Lesson 7

If you have ever spent much time looking through a small telescope, chances are that you have seen a star cluster. Some of the most famous clusters—the Pleiades, h & χ Persei, M13, M3, and many others—are famous because they are excellent targets for backyard observers.

Beyond their beauty, star clusters, like binary star systems, give us a chance to really make detailed tests of the theories of stellar evolution. In this lesson, we are going to look at star clusters in some depth. We will see that, by studying star clusters, we will be able to tie together all of the concepts from the previous three lessons. We will also find that, taken as a whole, clusters of stars are very interesting objects that can aid us in understanding the entire Universe.

What will we learn in Lesson 7?

By the end of Lesson 7, you should be able to:

• Identify the different types of star clusters that stars inhabit;
• Compare and contrast the HR diagrams for different types of star clusters;
• Describe the process by which astronomers measure the distance and age of a star cluster.

What is due for Lesson 7?

Lesson 7 will take us one week to complete.

Please refer to the Calendar in Canvas for specific time frames and due dates.

There are a number of required activities in this lesson. The chart below provides an overview of those activities that must be submitted for Lesson 7. For assignment details, refer to the lesson page noted.

Lesson 7 Requirements

Requirement	Submitting your work
Lesson 7 Quiz	Your score on this quiz will count towards your overall quiz average.
Lab 2	You will complete Lab 2 and submit it to a Canvas drop box.

Questions?

If you have any questions, please post them to the General Questions and Discussion forum (not email). I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.

Using the unaided eye, from most sites on Earth, you can observe several hundred stars each night. Although the stars all appear as pinpoints of light from our point of view, we have already discussed how telescopes have revealed that many of these stars are binary stars. That is, they are pairs of stars bound together by their mutual gravity. When we studied star formation, we learned that the types of clouds of gas that form stars fragment as they collapse, and that star forming regions tend to form many stars simultaneously and not one at a time. If you survey the sky with a telescope, you can quickly find some regions of the sky that contain examples of clusters of stars. That is, there are regions of space that contain hundreds, thousands, or even millions of stars.

There is one obvious example of a star cluster that is visible to most observers in the winter from the northern hemisphere, and that is the Pleiades. You have probably seen a picture of the Pleiades before, but here is an excellent one.

Incidentally, the Pleiades is a favorite target of astrophotographers, and there are several other very beautiful pictures of the cluster available from APOD (note that there are even more than this, these are just the ones I think are the nicest):

1. Pleiades image from Tony Hallas
2. Pleiades image from Robert Gendler
3. Pleiades image from Matt Russell

This group of stars is also the logo of the Subaru car company (they used to have a link at the US site that described the star cluster and their logo, but they seem to have deleted it, so I swapped in the Australian link). In Japanese, Subaru means “unite,” and this word is also used by Japanese speakers to identify the cluster that we refer to as the Seven Sisters or the Pleiades. The logo on the front of their cars is a representation of the stars in this cluster.

If you look closely at the image above, you will notice a few things about this group of stars:

1. It is dominated by a handful of very bright stars, but there appear to be many, fainter stars surrounding the brightest members.
2. The grouping of stars does not have a well-defined shape or boundary.
3. The brightest stars appear to be blue and to be surrounded by blue, wispy nebulae.
4. The stars are not very densely packed together.

Here are some other examples of similar star clusters:

• NGC 3293
• M6 The "Butterfly Cluster"
• The "Jewelbox Cluster"
• The "Double Cluster" h and chi Persei

The Pleiades and the other clusters above are examples of a class of objects that astronomers refer to as open clusters or sometimes galactic clusters. There is another type of cluster that is not as familiar to most of us, because there are no objects of this type that are easily visible to the naked eye. The claim is that from the darkest site, with good eyes, you should be able to see one example, M13, with your naked eye – but this is challenging enough that these objects are not as commonly known as open clusters. This second type of star cluster is referred to as a globular cluster. Below is an example, M80.

Here are links to some other examples:

• M3 from NOAO's image gallery
• M13 from NOAO's image gallery
• M14 from NOAO's image gallery

These images of "globular clusters" should reveal several strong differences when compared to the images of "open clusters" presented above:

1. There appear to be many more stars in the globular clusters than are seen in open clusters like the Pleiades.
2. Although there is a range of brightness among the individual stars, there are not a few very bright stars that dominate, like in the Pleiades.
3. The clusters appear to be very circular (and if you consider their 3D structure, they are spherical).
4. Many of the brightest stars appear red.
5. The stars are very densely packed together, and the density increases towards the center.

Open clusters and globular clusters are very different in many ways. In this lesson, we will study each of these classes of objects in some depth.

Additional reading from www.astronomynotes.com

• The Hertzsprung-Russell Diagram
• Stellar Evolution:  Mass dependence

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Before returning to open clusters and globular clusters, we are going to revisit the topic of stellar lifetimes, but this time in some more depth. Recall from Lesson 5 on pages 4 and 5 that we talked about how you might quickly estimate the time a star can remain on the Main Sequence and that O stars live substantially shorter lifetimes than M stars. We can actually derive a relationship for the lifetime of a star using what we know already about stars.

From our study of binary stars, we are able to calculate the mass of the stars in the binary system. If you know the distance and the apparent brightness of a star, you can also calculate its luminosity. So, simply using observational data, we have learned that stars along the Main Sequence are a sequence in mass. O stars are the most massive, then B stars, then A, F, G, K, and M stars are the least massive. Since the Main Sequence is also a sequence in luminosity—that is, O stars are the most luminous, then B, then A, F, G, K, and M stars are the least luminous—there must be a relationship between mass and luminosity. If you plot the masses for stars on the x-axis and their luminosities on the y-axis, you can calculate that the relationship between these two quantities is:

$$L\approx M^{3.5}$$

This is usually referred to as the mass-luminosity relationship for Main Sequence stars. For a sample plot of this relationship see:

1. astronomynotes.com
2. The Australia Telescope Outreach and Education Web site

Given our theory for the structure of stars, you can understand where this relationship comes from. Stars on the Main Sequence must be using the energy generated via nuclear fusion in their cores to create hydrostatic equilibrium. The condition of hydrostatic equilibrium is that the pressure is balancing gravity. Since higher mass means a larger gravitational force, higher mass must also mean that higher pressure is required to maintain equilibrium. If you increase the pressure inside a star, the temperature will also increase. So, the cores of massive stars have significantly higher temperatures than the cores of Sun-like stars. At higher temperatures, the nuclear fusion reactions generate energy much faster, so the hotter the core, the more luminous the star.

If you actually look at the equations that govern stellar structure, you can derive from those equations that:

$$L\approx M^n$$

where the exponent varies a bit for stars of different masses, but, in general, is approximately equal to 3.5, as is seen to be the case with the observed masses and luminosities for stars in binary systems.

Below is a plot that obeys this relationship and gives the theoretical calculations of a star's luminosity given its initial mass on the Main Sequence.

Now, let's revisit the topic of stellar lifetimes. The amount of fuel that a star has available for fusion is directly proportional to its mass. The luminosity measures how quickly the star is using that fuel, so, in general, a rough estimate of the lifetime of a star is:

$$t\approx M/L$$

but, you can substitute in using $L\approx M^{3.5}$ and determine that:

$$t\approx M/M^{3.5}=1/M^{2.5}$$

As we continue our study of star clusters, keep this in mind—the more massive a star, the faster it lives its lifetime, and, given the exponent of this relationship, it isn't a linear relationship. That is, a 10 times more massive star doesn't live a lifetime 10 times shorter than the lower mass star, but approximately a 316 times shorter lifetime than the lower mass star!

Clusters like the Pleiades contain on the order of 1,000 stars. The range of open clusters includes objects with hundreds of stars up to perhaps a few thousand stars. The brightest stars in the Pleiades are B and A Main Sequence stars.

Below is a schematic H-R diagram for the Pleiades. We see that, in this cluster, the Main Sequence includes stars of almost every spectral type, and that only a few stars appear to be evolving or have evolved into Red Giant Stars. In some open clusters, we see that the least massive M-type stars have still not made it onto the Main Sequence. That is, they are still in the process of formation.

In the image of the Pleiades, the nebulosity that surrounds the bright stars is very prominent. Recall that these blue regions are called "reflection nebulae," and they are created by the light from the stars scattering off of dust grains in front of the star cluster. This dust is probably a remnant of the molecular cloud that formed the Pleiades. In some other images of open clusters, the stars in the cluster are surrounded by emission nebulae. Astronomers have found that, in general, open clusters do not contain their own gas, but they are often found in the vicinity of gaseous nebulae. Another interesting fact about the location of open clusters on the sky is that they are found to be aligned closely with the "Milky Way," which appears to us from Earth as a patchy band of light on the sky:

Many stars in a variety of open clusters have also been studied spectroscopically. The absorption lines in their spectra tell us about the chemical composition of the stars in the cluster. In general, the spectra of stars in open clusters are very similar to the spectrum of the Sun—these stars have chemical compositions and abundances of the different elements similar to those measured for the Sun. Since astronomers refer to elements heavier than helium as a "metal," the astronomical jargon we use is that we say stars in open clusters have "solar metallicity" or are "metal-rich."

Globular clusters are very massive objects that contain hundreds of thousands or perhaps a million stars. The HR diagram for a typical globular cluster looks very different than that of an open cluster. There are no Main Sequence stars of types OBAF, but there are many red giants. The brightest stars in a globular cluster are those at the tip of the red giant branch in the HR diagram, which explains the red appearance of the bright stars in color images of the clusters, like the one above. You can also see stars populating the horizontal branch (and also why it is called the horizontal branch), the asymptotic giant branch, and even some stars that have colors and magnitudes of F stars, but far fewer than the G stars just below and to the right of them on the Main Sequence.

Below is a schematic diagram of the HR diagram of a typical globular cluster. I have also included the real HR diagram of M55 for comparison.

The density of stars inside a globular cluster is significantly higher than the density of stars around the Sun. We have measured the distance to the nearest star to the Sun, Proxima Centauri, and it is 4.2 light-years, or about 1.3 parsecs. Thus, if we were able to draw a sphere around the Sun with a radius of 1.3 parsecs, it would only contain 2 stars: the Sun and Proxima Centauri. If you were to draw this same sphere in the center of the globular cluster M13, it would contain approximately 10,000 stars. As part of a research study in 1996 of the globular cluster M15, astronomers using the Hubble Space Telescope observed about 30,000 stars within 6.7 pc of the core of this globular cluster. Thus, if the Sun were inside a globular cluster, we would see many thousands of stars in the sky many times brighter than the brightest stars we see in our night sky.

Globular clusters are not found to contain any gas, nor are they, in general, associated with reflection or emission nebulae, like we see with open clusters. Also, unlike open clusters, we find globular clusters in every direction on the sky. They do not seem to have any particular association with the band of light that we call the Milky Way. There are several globular clusters visible near the Milky Way in the part of the sky you studied using the Starry Night file on the last page; however, there are many more distributed all over the sky.

When we observe the stars in globular clusters spectroscopically, we can also measure the abundance of chemical elements in their atmospheres. Again, this observation reveals another difference between these star clusters and open clusters. On average, the abundance of all elements heavier than helium is only 1-10% of the abundance of these same elements in the Sun and in the stars in open clusters.

Additional reading from www.astronomynotes.com

• Confirmation of Stellar Evolution Models

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Star clusters provide us with a lot of information that is relevant to the study of stars in general. The main reason is that we assume that all stars in a cluster formed almost simultaneously from the same cloud of interstellar gas, which means that the stars in the cluster should be very homogeneous in their properties. This means that the only significant difference between stars in a cluster is their mass, but if we measure the properties of one star (age, distance, composition, etc.), we can assume that the properties of the rest of the stars in the cluster will be very similar.

In reality, some stars in the cluster form earlier than others, but compared to their lifetimes, the spread in their formation times is small and can be ignored. We also assume that the stars in a cluster are all the same distance away from us. Again, there is in fact a spread in distance, but, in most cases, this spread is much smaller than the distance to the cluster, so it can be ignored. For example, the outermost stars in the globular cluster M13 are about 50 parsecs from the center of the cluster, but the cluster is about 7,700 parsecs away from us. Finally, we assume that the chemical composition of all of the stars in a particular cluster should be very similar because the cloud of gas from which they formed is expected to have been well mixed, so the individual cloud fragments that formed individual stars should all have contained the same mix of elements and molecules.

When stars form out of a molecular cloud, very high mass stars (perhaps up to about 100 times the mass of the Sun) all the way down to low mass, brown dwarf objects (about 0.08 solar masses) are formed. Observations of newly formed populations of stars have shown us that very few high mass stars form, while many low mass stars form. The drop-off is very steep as you get to higher masses, as well. If you were to survey the stars near the Sun, you would find that about 90% of all stars in our Solar Neighborhood are less than or equal to the Sun's mass. Most of the rest are less than twice the mass of the Sun, and only about 0.5% of all nearby stars are more massive than 8 times the mass of the Sun. Remarkably, observations of star formation in many different locations in the universe seem to indicate that the relative ratios of stars of different masses that form is a universal law. That is, the same relative proportion of high mass compared to low mass stars always forms regardless of the size of the star forming region, the environment in which the star forming region resides, and how long ago the stars formed. Therefore, if we can determine how one cluster of stars formed, we can generalize our findings to apply to all clusters. This idea of a relationship between the number of stars formed in a star forming region and their mass is referred to as the stellar initial mass function.

Let us follow the evolution of an entire cluster of stars through several stages of its lifetime.

This presentation (with credit to Penn State Astronomy & Astrophysics) allows you to click through slides that step you through the evolution. You will see a series of schematic HR diagrams for the stars in a cluster. In each frame, as the stars age, their luminosities and temperatures evolve, changing the overall appearance of the diagram with age.

The presentation progresses in the following way:

1. At an early time stamp in the star cluster’s formation, what we will call t=0, most of the high mass stars have reached the Main Sequence, while some of the lower mass stars are still in the T Tauri phase.
2. Ten million years (10⁷ years) later, the highest mass O stars have used up all of their hydrogen and begin to evolve off the Main Sequence.
3. After 100 million years (10⁸ years), all of the O stars have gone supernova. The B stars begin to evolve off of the Main Sequence.
4. After 1 billion years (10⁹ years), All of the B stars that are massive enough have gone supernova and the rest have evolved into red giants. The A stars begin to evolve off of the Main Sequence.
5. After 5 billion years (5x10⁹ years), The G stars begin to evolve off of the Main Sequence. The red giant branch is populated with some of the originally more massive stars. Some of the first red giant stars that formed have already become white dwarfs.
6. After 10 billion years (10¹⁰ years), The OBAFG stars are all missing from the Main Sequence, the red giant branch is very well populated, and there are also many white dwarfs. Only K & M stars remain on the Main Sequence.

What we see in the sequence is that as a cluster of stars ages, the top of the Main Sequence disappears first. The analogy you often hear is that it is like the wick of a candle—as the cluster stars burn out, the Main Sequence gets shorter. Therefore, if you can identify exactly what type of star is just now undergoing the transition from Main Sequence to red giant (called the Main Sequence Turn-Off), and if you know how long (theoretically) that it takes stars of that type to use up all of their hydrogen, you can estimate the age of that star. Now, because we assume that all of the stars in the cluster formed simultaneously, we can assume that all stars in the cluster have the same age as the most massive star left on the Main Sequence. Astronomers frequently use this technique of Main Sequence Turn-Off fitting to estimate the age of star clusters. The way this is done in practice is the following:

1. Astronomers use computer models to create a theoretical HR Diagram for a population of stars with a specific age, say 500 million years. Instead of plotting the individual points, they plot a line that goes through the points of all of the stars in the HR diagram. Since this line indicates the positions of stars with a specific age, it is called an isochrone.
2. Astronomers plot the observed colors and luminosities for the stars in a star cluster.
3. You find the best match between a theoretical isochrone and the stars in your cluster, and that tells you the age of the cluster.

If you compare the HR diagrams for stages 1-3, these are very similar to the HR diagrams for open clusters. The HR diagram for stage 6 appears to be very similar to that of a globular cluster. Thus, we can conclude that open clusters are young (usually a few tens of millions or hundreds of millions of years old), while globular clusters are very old (typically about 12-13 billion years old). In the image above, you can see a schematic HR diagram with plots of lines that represent the Main Sequence for a number of open clusters. From the location of the Main Sequence Turn-Off, you can see that NGC 2362 is the youngest, then h & χ Persei, and M67 is the oldest of the clusters.

This realization explains several of the other observations that we made of the differences between these two types of clusters. Since open clusters are young, they have not had a chance to move very far from the location where they were born. Thus, there is likely to be leftover material from the molecular clouds in which they formed nearby (which creates the reflection nebulae seen in the Pleiades). The intense radiation from the bright O & B stars in the open clusters can ionize the nearby gas, creating emission nebulae nearby, as well. The light from an open cluster is dominated by the brightest stars in the cluster, which are O & B Main Sequence stars, since no red giants have formed yet. Thus, open clusters should be quite blue.

Since globular clusters are old, they are not found near the regions in which they formed. There is no gas in their vicinity. Even if there was, the stars in globular clusters do not emit much ultraviolet light capable of creating emission nebulae. Thus, we do not expect to find emission nebulae surrounding globular clusters. There are no blue Main Sequence stars left, so the light from a globular cluster should be dominated by the brightest red giants, leading to their very red appearance.

Lastly, we can also explain the difference in chemical composition between open cluster stars and globular cluster stars. Originally, all of the gas in the universe contained few elements heavier than helium. However, as we learned in our study of stellar evolution, heavier elements are created in massive stars and dispersed when they go supernova. Therefore, as time goes on, later generations of stars should contain higher and higher concentrations of heavy elements. Since globular clusters are 12 billion years old, their atmospheres reflect the makeup of the primordial gas from which they formed. Since open clusters have formed relatively recently, they have 10-100 times more heavy elements in their atmospheres.

One question that we have not yet answered is why the Sun is so apparently isolated. If all stars form out of molecular clouds that form many stars at once, why are there not several hundred stars nearby? The reason has something to do with the density differences between star clusters. Remember, open clusters look “fluffy. " That is, they are not very concentrated. Globular clusters, on the other hand, are very densely packed with stars. In open clusters, the gravitational pull of all the stars taken together is not strong enough to keep the stars bound to the cluster. Over time, the individual stars in open clusters drift away, and the cluster dissolves. The gravitational pull by the cluster on the stars in a globular cluster is much stronger, so these clusters are able to retain most of their stars for billions of years. It is likely that the Sun did form as part of an open cluster, but since the Sun is now about 5 billion years old, it has long ago drifted away from the stars that formed out of the same cloud.

Because cluster stars are so homogeneous in their properties, we can often measure a few stars in the cluster and then generalize the result and apply it to the whole cluster. For example, you can measure the age of the cluster by estimating the age of the Main Sequence Turn-Off, as we just saw. Similarly, you can measure the distance to the cluster if you can find some technique to measure the distance to any single star. Since all measurements that you make have some error associated with them, though, if you measure the distance to one star, your estimate of its distance may be off by as much as 10% (the typical level of precision for many techniques). If you can measure many stars in the cluster and get many estimates of the distance, you can get a more precise estimate of the true distance by taking the average of all of the individual distance measurements. Even if all of the individual estimates are off by 10%, the measurement error associated with any one star becomes less important.

Astronomers often use a method of fitting the HR diagrams of clusters to a standard HR diagram in order to measure the clusters' distances more precisely, since this technique uses all of the stars to get a distance measurement. Here is another place where astronomical jargon can be confusing. Recall that the first successful method for measuring the distance to stars was trigonometric parallax. Because of this, the word parallax became used interchangeably with distance measurement. So, even though the term parallax should only refer to the method for measuring the apparent shift of a star, it is not used in that way only. This method of measuring the colors and brightnesses of many stars and comparing them to the colors and luminosities of a known set of stars is referred to as spectroscopic parallax.

You can create a “standard” HR diagram in a few ways. For example, you can theoretically calculate how bright and how hot the stars should be using mathematical models and plot those in a luminosity/temperature version of the HR diagram (an isochrone, just like we discussed previously). Also, if you can measure the distance to many nearby stars by the method of trigonometric parallax, you can convert the apparent brightness measurements for these stars into luminosities. Either way, you have created an HR diagram that shows luminosity on the y-axis. Now, if you measure the apparent brightness and color for many stars in your star cluster, you can plot these stars on the same diagram as your “standard” stars. Because all of the stars in the cluster are the same distance away from us, all of them will have an equal displacement along the y-axis. That is, the cluster's Main Sequence will just appear to be shifted vertically in the HR diagram from the standard stars, because the luminosity of a star drops off due to the inverse-square law for light. If you measure how much fainter you have to shift the entire set of standard stars so that they overlap the Main Sequence of the cluster, you can estimate how far away the cluster is using the relationship:

F_cluster = L_standard / 4πR²

Click through the presentation below from Penn State Astronomy and Astrophysics to see this demonstrated.

In this presentation, we first see an HR diagram for a cluster plotted with luminosity on the y-axis. A blue region is fitted to the Main Sequence of this cluster, providing a calibrated Main Sequence with a known luminosity for all colors. Next, we see a new HR diagram for a nearby cluster with apparent brightness plotted on the y-axis. The calibrated Main Sequence is too bright, but if we shift it down, we can match it to the Main Sequence of the nearby cluster. This gives us an estimate of how much fainter the cluster is compared to the calibrator, which gives an estimate of distance. Lastly, we see the HR diagram for a more distant cluster. It is fainter yet, since it is more distant. However, by just offsetting the calibrated Main Sequence to fainter magnitudes, it matches the Main Sequence of the distant cluster, too, allowing us to measure its distance.

You could apply this same method just using the measurements for one star (that is, measure F_star and estimate L_star from a standard Main Sequence), but since you are lining up the entire Main Sequence of the cluster with the standard HR diagram, you are using many hundreds or thousands of stars to calculate the distance, and the final result is much more precise.

Additional reading from www.astronomynotes.com

• Period-luminosity relation for variable stars

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During most stages of the life of most types of stars, the star is in a stable equilibrium. What this means is that any changes to the star (e.g., in color or luminosity) are quite slow. So, for example, if you were to observe a particular red giant star tonight and then compare it to a measurement made 50 years ago, the color and luminosity of that star will most likely be exactly the same today as during the earlier observation. However, this is not true for all stars. Some stars are intrinsically variable. That is, their properties change in a periodic fashion with a short enough period for us to measure.

There are certain stages in the lifetimes of stars of particular masses where they are unable to achieve a stable equilibrium. During this stage, the star will, for a short time, be radiating more light than its average luminosity. The star will expand, but it will overshoot the radius where it would achieve stability. Since the star expanded, the internal pressure is reduced. Therefore, gravity will be stronger than the pressure resisting contraction, and so the star will then contract. When the star contracts, it again overshoots its equilibrium radius, thereby trapping more radiation inside the star. Therefore, its internal pressure will increase to the point that it exceeds the gravitational force contracting the star. It then expands, its luminosity increases, and the cycle repeats. It turns out that there is a certain region of the HR diagram where stars having that combination of temperature and luminosity also have the proper conditions for this pulsation to occur. That region is called the instability strip, and is labeled in the schematic HR diagram below.

There are two types of pulsating variable stars that are particularly useful to astronomers. These stars, called Cepheid variables (named after the prototypical Cepheid – delta Cephei) and RR Lyrae variables (named after the prototypical RR Lyrae – RR Lyrae) are remarkable, because their periods (the time it takes for them to go from maximum brightness to minimum brightness and back again) are directly correlated to their average luminosities. That is, if you measure their periods by observing them over the course of a few nights, you can determine their luminosity. This is another effect I would love to demonstrate with Starry Night, but unfortunately this is one place where Starry Night fails. You can see the star delta Cephei vary if you watch it carefully night after night and compare its brightness to nearby stars; however, within Starry Night it is always shown with its average brightness.

When these stars were first discovered, it was apparent that there was a relationship between their period and their apparent brightness. The work to calibrate this relationship was performed by the famous  astronomer Henrietta Leavitt at Harvard College Observatory.

Once the distances were measured to a number of pulsating variables, the period-luminosity relationship was established. This allows astronomers to measure the period of a pulsating variable and immediately infer its luminosity without having to measure its trigonometric parallax. A plot of the period-luminosity relationship for metal-rich (type I) and metal-poor (type II or W Virginis) Cepheids is presented at astronomynotes.com.

Because of this remarkable property that the period of a variable star is proportional to its luminosity, these stars make excellent tools for measuring distances. To do so:

1. Observe the Cepheid variable star for enough nights to estimate its period (that is, the time between maximum brightness) and measure its average apparent brightness.
2. Use the plot of the period-luminosity, or a mathematical equation that represents the fit to the data in the plot, to determine the luminosity of the star.
3. Use the standard flux / luminosity / distance equation to measure the distance to the Cepheid.

We will discuss using these stars as distance indicators more in later lessons.

There are not as many resources related to star clusters and variable stars as there are resources covering topics from previous lessons, but here are a few:

1. At Amazing Space, there is a graphic organizer of the differences between open and globular clusters.
2. If you are looking for research projects for students, the American Association of Variable Star Observers (AAVSO) has been using amateur and student astronomers to study variable stars for many years. They can have you up and running observing a variable star very quickly, and they provide you with a lot of background content information.
3. At YouTube, Phil Plait's Crash Course Astronomy series has an episode on star clusters.

Astronomers regard everything we can observe as potential tools for us to use to learn even more about the Universe. Both star clusters and variable stars are useful to confirm our theoretical models for the evolution of stars. We can do this in the case of star clusters, because we can assume the cluster stars were all born at the same time. Variable stars help confirm our models for the physics of stars, but are most useful as distance indicators that we can use to expand our knowledge of the size scale of the Universe.

Reminder - Complete all of the lesson tasks!

You have finished the reading for Lesson 7. Double-check the list of requirements on the Lesson 7 Overview page to make sure you have completed all of the activities listed there before beginning the next lesson.

Directions

1. Continue reading the rest of the SDSS HR Diagram lab from where you left off in Lab 2, Part 1 (you had just worked on Exercise 2).
   There are pages on parallax, creating HR diagrams for an open cluster (the Pleiades) and a globular cluster (Palomar 5). You are not required to do any of the exercises on these pages. However, they are all useful exercises, so please do try them if you find them interesting.
2. Take data and create a detailed HR diagram for Palomar 5 (Exercise 7).
   The lab gives instructions for getting photometric data (that is, the apparent magnitudes) for many stars in the Palomar 5 cluster using the Radial Search or SQL Search tools. Use one of these tools to collect data on a number of stars in Palomar 5. Follow the instructions given in the Exercise 7 box to create an HR diagram for Palomar 5.
3. Answer Question 12 in the SDSS HR Diagram lab: "Can you see the main sequence on this diagram? Can you see any of the giants and supergiants? If so, identify these groups of stars on your diagram."
4. Also, answer the questions below:
   • How does your diagram resemble the schematic HR diagrams you have seen in the lessons or in a textbook?
   • Is it easy or challenging for you to pick out the familiar features listed in Question 12?
   • What limitations are there in your data?
   • What effect do those limitations have on your ability to study the stellar population in this cluster?
   • Do you think you would be able to measure the distance to Palomar 5 with your data? How would you do this?
5. You should now have successfully created a real HR diagram (well actually, a "color-magnitude diagram") for a real globular cluster using data from the Sloan Digital Sky Survey. Please write a brief summary of your work. In your summary, include the following:
   • All of the HR diagrams you plotted in Lab 2, Parts 1 and 2;
   • Your answers to the questions in the Data Analysis section;
   • A brief (paragraph or so) discussion of the lab and how well you think it illustrates some of the concepts we studied in Lessons 5 through 7.
6. Save your work AS A SINGLE DOCUMENT in either a Microsoft Word or PDF file in the following format:
   
   Lab2_AccessAccountID_LastName.doc (or .pdf)
   
   For example, student Elvis Aaron Presley's file would be named "Lab2 _eap1_presley.doc" - This naming convention is important, as it will help me make sure I match each submission with the right student!

Submit your work

Please submit your work to the Lab 2 dropbox in Canvas by the due date indicated on our course calendar.