1. Detecting Exoplanets by Gravitational Microlensing
© Center for Astronomy Education
University of Arizona
2015
The development of this slide set and the accompanying materials was funded through the generous contributions of NASA's Exoplanet Exploration Program.
The development of these materials was funded through the generous contributions of NASA's Exoplanet Exploration Program.

2. Warped Spacetime Bends Light
The blue streaks are lensed images of background galaxies caused by the central cluster.
Image courtesy of NASA:

3. Why It Happens
A mass causes the region of spacetime around itself to become warped.
A light ray traveling through warped spacetime travels on a curved path.
This slide is a brief reminder for students about the nature of gravity.
It is expected that the students have already had an introduction to the concepts of spacetime and gravity as curvature.

4. Gravitational Lensing
A massive object located between Earth and a distant source of light will warp spacetime, which can bend light rays toward Earth that would not normally reach Earth.
Image courtesy of NASA’s Goddard Spaceflight Center
Image courtesy of NASA’s Goddard Spaceflight Center

5. In The Real World
Hubble Space Telescope image of an Einstein cross.
Image courtesy of NASA’s HubbleSite:

6. Gravitational Microlensing
When a single nearby star passes between us and a distant object, it can cause gravitational lensing as well. But the effect is not large enough to produce separate images of the distant object.
We call this gravitational microlensing.
The following slides help students understand how microlensing causes an increase in brightness.
We suggest not giving away that answer yet!

7. These slides represent a set of light rays coming from a distant object (top) toward Earth (bottom).
As a nearby star moves through our field of view, the light is gravitationally lensed.

10. At this point we can clearly see that light is being bent toward Earth that would not have otherwise arrived at Earth.
This means the observed brightness of the distant object increases.

11. The observed brightness of the distant object reaches a maximum when the nearby star is directly between it and Earth.
(Note that in real situations, the alignment is rarely 100% perfect; the background object will be slightly above or below the nearby star.
This explains the light ray that appears to be going through the nearby star in this image.)

16. Which graph below best represents the observed brightness of the distant background star over time as the nearby star moves between the distant star and Earth? A B
Brightness
Brightness
Time
Time
Answer B is correct.
Answer A may incorrectly appeal to students using the representation from Slide 5 that showed two lensed images of the distant object on either side of the real object.
Answer C may incorrectly appear to students who do not consider that the lensing effect gradually increases over time. C
Brightness D
Brightness
Time
Time

17. Earth
The correct graph of brightness vs. time is hidden on the bottom half of the slide.
As the nearby star moves to the right, the graph will be revealed in synchronization with the star’s motion.

18. Brightness Graph due to Microlensing
Peak Height – represents the amount of light bent toward Earth that we wouldn’t normally receive
Taller peak = more massive lensing object
Peak Width – represents the amount of time during which the region of spacetime between Earth and the distant star is warped
Wider peak = more massive lensing object

19. Alignment of the Lens
When the nearby star passes between Earth and the distant star, it usually won’t come exactly between Earth and the distant star.
As seen from Earth:
The images on this slide and the next are “As seen from Earth” – i.e. this is what you would observe if you looked into the sky.

20. Alignment Affects Brightness
The more closely the nearby star (the lensing object) is aligned with the distant source of light, the more it will bend the light from the distant source.
You can do a quick call-and-response with students here after the animation. If the stars are the same, which one will produce a taller brightness peak, left or right? (answer: right)

21. Only Use the Width
In doing real astronomy, we aren’t able to tell how much of the peak’s height is due to the mass of the lensing object, and how much of the height is due to the alignment.
Because of this, we only use the width of the peak to learn about the mass of the lensing object.

22. Application
When we observe changes in the brightness of real stars caused by microlensing, sometimes we get a graph like this:

23. Detecting Planets with Microlensing
When an exoplanet is orbiting a star, the planet causes an additional warping of spacetime, which can cause additional microlensing (bending of light).
So, planets can be found by looking for bumps on the brightness curve of the light from distant stars that are microlensed.

24. Question for You
Based on the graph below, did the planet move into our field of view before or after its companion star?
This is a good opportunity for student voting and/or discussion, to provide the chance to begin working with time as the horizontal axis.

25. This Is Totally On The Test
If the exoplanet moves into the region of spacetime between Earth and the distant star ahead of the parent star the exoplanet is orbiting, then the brightness bump caused by the planet occurs at an earlier time on the brightness vs. time graph than the main brightness peak caused by the parent star.
This slide addresses a key reasoning difficulty encountered by many students.
When students see a planet to the left/right of a star, they will automatically map this to a bump on the left/right side of the graph.

26. Peak caused by parent star
Earth
Bump caused by planet
Peak caused by parent star
The correct graph of brightness vs. time is hidden on the bottom half of the slide.
As the nearby star moves to the right, the graph will be revealed in synchronization with the star’s motion.
It is important to note that the “planet bump” appears to the right of the “star peak” even though the planet is located to the left of the star!
It can be helpful to point out to students the moment when the planet bump appears (when the planet comes between Earth and the distant object).

27. The Exoplanet Bump
Would you expect a high-mass planet to create a taller or shorter bump than a low-mass planet? Why?
Would you expect a high-mass planet to create a wider or narrower bump than a low-mass planet? Why?
This is just a quick check to reaffirm that planets follow the same rules as those already explained for stars.

28. Planets Far From Their Stars
When the exoplanet and its parent star are very close together (as seen from Earth) it is not always possible to distinguish the brightness bump caused by the exoplanet from the peak caused by its parent star.
So the microlensing method is better at finding exoplanets that orbit their stars at a large distance.

29. This slide is optional. If you choose to skip this slide, please remove Slide 32 also.
You can point at different locations where a planet can be in its orbit and ask whether the planet’s lensing effect could be resolved from that of the star based on their apparent separation from our point of view.
We recommend using the same reference points as on the previous graphic: Earth below the bottom of the frame and the distant object at
Feel free to hide the slide if you are not interested in having your students consider this type of reasoning.

30. Planet Bumps Happen Quickly
The brightness bumps caused by planets only last for very short amounts of time, so we can’t learn about the planet’s orbital speed or period by the microlensing method.
If you teach other methods of exoplanet detection (such as radial velocity or the transit method), this slide is a good time to compare and contrast the methods.
In a class for science majors, one can also consider how our viewing angle affects the apparent exoplanet-star distance and whether we can determine the planet’s orbital radius using this method.

31. But, Bump Width Does Matter
As with the brightness peak caused by the star, we can’t tell how much of the height of the planet bump is due to the planet’s mass and how much is due to its alignment with the distant source.
So, we use only the width of the planet bump to learn about how massive the planet is.

32. Which of the four star-exoplanet systems shown below would be easiest to detect by gravitational microlensing? A B
The correct answer is A.
This slide and the next will help assess your students’ understanding of the content before the Lecture-Tutorial. C D

33. A star-exoplanet system moves from left to right as seen from Earth
A star-exoplanet system moves from left to right as seen from Earth. The exoplanet is to the right of the star when the system crosses between Earth and a background object. Which of the following statements best describes the brightness vs. time graph for the background object?
The bump caused by the planet will occur earlier than the peak caused by the star.
The bump caused by the planet will occur later than the peak caused by the star.
The bump caused by the planet will occur at the same time as the peak caused by the star.
The correct answer is A.

34. Lecture Tutorial – Detecting Exoplanets with Gravitational Microlensing (handout)
Work with a partner!
Read the instructions and questions carefully.
Discuss the concepts and your answers with one another.
Come to a consensus answer you both agree on.
If you get stuck or are not sure of your answer, ask another group.
If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask one of us for help.

35. Debrief
Let’s address any questions you have about the tutorial.

36. C. Not enough information
A nearby star-exoplanet system passes between Earth and a distant star as shown below. Is it possible to detect the presence of the exoplanet by gravitational microlensing?
A. It is possible
B. It is not possible
C. Not enough information
Exoplanet
Earth
Please remove this slide if you did not use Slide 26 to discuss the ability to resolve the planet’s microlensing effect from the star’s microlensing effect based on their positions.
Correct answer is B.

37. Which of the four brightness vs
Which of the four brightness vs. time graphs below best represents the microlensing caused by a high-mass planet orbiting a low-mass star?
Correct answer is D.

38. How many of the below graphs are reasonable representations of the microlensing that is caused by the star-exoplanet system shown at right?
Earth
Correct answer is C. (The two graphs with the bump to the left of the peak are correct).
Students may choose B, thinking that a planet cannot make a taller bump than the peak caused by the star. However, we are only considering the width of the features. In these two graphs, the planet bump is indeed narrower than the star peak, as is correct for a planet less massive than its star. These two graphs also show the planet bump occurring earlier in time than the star peak, which matches the diagram shown for the motion of the bodies.
A. None B. Only one C. Two D. Three E. All four

39. Which of the below graphs correctly represents the observed brightness vs. time of the background star, as a result of the microlensing caused by the extrasolar planet system shown at right?
Earth
Correct answer is C.

40. Microlensing Works
This method for detecting exoplanets really works – so far 19 discoveries have been confirmed and more are expected!
Detection efforts are ongoing as of August 2014.
Students enjoy knowing that they are learning about real, cutting-edge science!