Astrobiology in the Classroom

NASA – CERES Project –http://btc.montana.edu/ceres

Montana State University

Preliminary Edition

“The Rare Earth —

Just how rare is Earth-like complex life?”

How special are the circumstances that have allowed complex life like animals and mammals to develop on Earth? In this activity students systematically investigate the time frame for complex life to develop on Earth. They apply this information to graphs representing stellar mass, luminosity, main-sequence lifetime, and stellar abundance in order to approximate how many other planets there may be harboring Earth-like complex life in our galaxy. By examining the conditions on Earth that have made complex life possible students set limits on how old, bright or massive a neighboring star can be and still support complex Earth-like life.

The Rare Earth — Just how rare is Earth-like complex life?

The Rare Earth hypothesis suggests that Earth-like planets containing complex (animal) life as we know it are likely quite rare in the Universe. This lesson will explore several parameters that have led the scientists Peter Ward and Donald Brownlee to put forth this hypothesis in their book, Rare Earth: Why Complex Life is Uncommon in the Universe. You may wish to refer to this book for a more detailed description of the Rare Earth hypothesis.

Scientists generally agree that the Earth formed about 4.5 billion years ago yet complex life has existed on the Earth for about the last 500 million years. It is still unclear exactly what chain of events lead up to the emergence of complex life on this planet. One of the factors that scientists believe to be necessary is a long period of relatively stable climate resulting from a stable planetary orbit at just the right distance from an appropriate type of star.

Let's begin our search for an appropriate star by looking at the characteristics that make the Sun so appropriate for complex life to flourish on Earth. The Sun is a G-type star in the main-sequence phase of its life, which means that it is engaged in the stable burning hydrogen by nuclear fusion to produce helium in its core, and radiating energy mostly in the form of visible light. The measure of a star’s radiation energy is called luminosity. Although it has been brighter in the past, the Sun has been shining this way for about 5 billion years, making it about half-way through its main sequence lifetime of about 10 billion years. Let’s explore the types of stars that are sufficiently Sun-like to allow complex life to evolve on their planets. Specifically, our first task is to determine what range of stellar masses meet the criteria for complex life, and to calculate the fraction of stars in the Universe that fall within that particular stellar mass range. In other words we want to know: What fraction of the stars in the sky are right for complex life?

Part I: How old, how bright, and how massive should the star be to support complex life?

Graph 1 shows how the main sequence lifetime of a star is related to the star’s mass (dotted line). The graph also shows how the star’s luminosity is related to its mass (solid line). Refer to Graph 1 to answer the following questions:

A. Does stellar mass increase to the right or to the left?

2. Does main sequence lifetime increase upward or downward?

3. Does stellar luminosity increase upward or downward?

4. Which feature on the graph shows how main sequence lifetime is related to stellar mass?

5. Which feature on the graph shows how stellar luminosity is related to stellar mass?

6. How does main sequence lifetime change as stellar mass increases? Does it increase or decrease? Does it change by the same amount for small values of M as it does for large values of M?

7. How does stellar luminosity change as stellar mass increases? Does it increase or decrease? Does it change by the same amount for small values of M as it does for large values of M?

8. Mark the position on the stellar mass axis where the Sun lies. Mark the position on the main sequence lifetime axis where the Sun lies. Mark the position on the stellar luminosity axis where the Sun lies. Place a mark within the graph where these values intersect.

9. What star is represented by the intersection of the two curves?

10. Do stars live longer or shorter, and are they brighter or dimmer, when they have a stellar mass that is less than the Sun’s?

11. Do stars live longer or shorter, and are they brighter or dimmer, when they have a stellar mass that is greater than the Sun’s?

12. How long did it take before complex life developed on Earth? What fraction of the Sun’s main sequence lifetime is this?

13. Based on your answer to question L, estimate the minimum amount of time that a main sequence star can exist and still have a planet that has time to develop Earth-like complex life. Explain your reasoning.

14. Mark on the main sequence lifetime axis the minimum lifetime you estimated in question M. Label this point T_min. Find the stellar mass that corresponds to T_min. Label it on the stellar mass axis as either M_min or M_max. How did you decide which should it be?

15. Find the stellar luminosity that corresponds to the stellar mass that you labeled in question N. Label it on the stellar luminosity axis as either L_min1 or L_max1. How did you decide which should it be?

16. Place a mark on the stellar luminosity axis for a star that is brighter than the star you marked in question O. Find the position on the main sequence lifetime axis that corresponds to this star. Is it possible for complex life to exist on a planet around this star? Why or why not?

17. Place a mark on the stellar luminosity axis for a star that is dimmer than the star you marked in question O. Find the position on the main sequence lifetime axis that corresponds to this star. Is it possible for complex life to exist on a planet around this star? Why or why not?

18. Based on your answers to questions P and Q, was the mark you labeled L_min1 or L_max1 in question O the correct limit? (If you wrote L_min1, does it represent the minimum stellar luminosity for complex life? If you wrote L_max1, does it represent the maximum stellar luminosity for complex life?) Explain your reasoning.

Part II: How bright is too bright for life?

The brighter a star is, the more radiation it gives off, and most of the radiation tends to be at higher frequencies. The Sun emits most of its radiation in the visible frequency range. In general, the higher the frequency of the emitted radiation, the more damaging it is to complex life. For Earth-like life forms, ultraviolet radiation is highly damaging to cells and to DNA. In Graph 2, stellar radiation frequency is plotted on the vertical axis, and stellar luminosity is plotted on the horizontal axis. Use this information to answer the following questions.

A. Find the location of visible radiation on the stellar radiation frequency axis of Graph 2. Find the stellar luminosity that corresponds with this frequency. How does this value compare to the luminosity of the Sun?

2. Place a mark on the stellar luminosity axis that represents your estimate for the limit on how bright a star can be before the frequency of most of its radiation is too damaging for Earth-like complex life to develop easily. Label this mark as either L_min2 or L_max2. How did you decide which should it be?

3. In part I you made an estimate for L_max1 and marked it on Graph 1. In the previous question (B), you made an estimate for L_max2 and marked it on Graph 2. Do your estimated values of L_max1 and L_max2 both predict the same result for the existence of complex life?

4. Explain why L_max1 is a limit on how bright a star can be and still have complex life on a nearby planet.

5. Explain why L_max2 is a limit on how bright a star can be and still have complex life on a nearby planet.

6. Predict whether or not complex life could exist on a planet near a star that: (1) has a main sequence lifetime equal to the time it took for complex life to develop on Earth, and (2) gives off radiation that is mostly in the UV range? Explain your reasoning.

7. Predict whether or not complex life could exist on a planet near a star that: (1) has a main sequence lifetime much shorter than the time it took for complex life to develop on Earth, and (2) gives off radiation that is mostly in the visible range? Explain your reasoning.

8. Imagine that L_max1 is greater than L_max2 for a star_, which value sets the limit for how bright a star can be and still have complex life on a nearby planet? Explain your reasoning

Part III How many stars is that?

Complex life requires a minimum amount of energy to develop. For instance, we might establish that stars with a luminosity less than 0.3L_ are unable to provide enough energy to support complex life on a nearby planet.

A. Place a mark (L_min) on Graph 1 that represents the lower limit on stellar luminosity for complex life.

B. Find the stellar mass that corresponds to L_min and label it as either M_min or M_max. How did you decide which should it be?

C. Can stars with a stellar mass less than this have planets with complex life? Explain your reasoning.

D. Write down the possible range of stellar masses (in units of M_) for stars that can support complex life.

E. Predict whether you think there are more stars, fewer stars or the same amount of stars in our galaxy that lie in the range between M_min and M_ or between M_ and M_max.

F. If you knew how many stars exist for each value of stellar mass, could you better answer the previous question? Provide a detailed description of how you would use this information to answer this question more accurately.

Consider the information shown in Graph 3. The horizontal axis represents the range of stellar masses for main sequence stars. This type of graph, in which information is sorted into bins, is called a histogram. In this case, each bin represents a range of 0.1M_ stellar masses. The total range of stellar masses is from 0 to 10M_. Notice that the first bin on the left represents stellar mass between 0 and 0.1M_. The second bin represents stellar mass between 0.1M_ and 0.2M_. The third bin represents stellar mass between 0.2M_ and 0.3M_, and so on. The last bin on the right is stellar mass between 9.9M_ and 10M_. The height of the bar in each bin represents how many stars exist within a specific range of stellar masses. The total number of stars represented in this histogram is approximately 10,000,000.

G. How many stars exist with masses between 0.2 M_ and 0.5 M_? How many of these stars could support complex life?

H. Based on the data represented in this histogram, what is a more accurate answer to question E?

I. According to this histogram, how many stars are there in the galaxy that can support complex life?

J. What fraction of all main sequence stars can support complex life? Express you answer as a fraction, a decimal and a percentage.

The histogram shown in Graph 3 provides an estimate of the total number of stars with main-sequence lifetimes. These main sequence stars make up approximately 70% of all stars in the galaxy. The remaining stars fall into four broad classes: those with too little mass (e.g., brown dwarfs); those with too much mass (e.g., blue giants); those that are too young (e.g., T Tauri stars); and those that are too old (e.g., red giants, white dwarfs, and neutron stars.)

K. Using Graph #3, out of all the stars in our galaxy, how rare (what percentage) are stars that could support complex Earth-like life?

Challenge Questions:

A. If you were studying a star that has a stellar mass that is a little larger than the sun, how will the luminosity and main-sequence lifetime compare to that of the sun? Explain your reasoning.

B. Consider the following debate between three students.

Student #1: If a star is too bright the star is too hot and there is no chance life could be found on the star.

Student #2: I disagree, if the luminosity is too high there is not enough UV radiation for life to be found on the star.

Student #3: I disagree, if L is too high then the lifetime of the star is too short for complex life to develop on the star.

For each student response, state whether you agree or disagree with the student statement. State explicitly which ideas you think are correct and which are incorrect.

C. Is it possible for complex life to exist on a planet that is near a star that has a main sequence lifetime that is shorter than t_? If not, why not? If so, what is the smallest main sequence lifetime the star could have? Explain your reasoning.