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Microlensing
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Do curso por Princeton University
Imagining Other Earths
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Einstein and the Search for Planets
Einstein’s theory of General Relativity tells us that mass curves space and deflects light. Thus, observations of light deflection can tell us about the distribution of mass. Microlensing observations use this effect to detect planets around distant stars. We discuss how these observations have shown us that planets are as common as stars and imply the existence of “orphan planets”, planets that were ejected by their Suns and are now wandering the Galaxy.
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David SpergelCharles Young Professor of Astronomy on the Class of 1897 Foundation and Chair
Department of Astrophysics
Welcome back.
Now let's take this general relativity idea and apply it and
see how we can use it as astronomers.
Einstein himself realized that the fact that light was going to be curved
by stars and galaxies would mean that you could use these objects as telescopes.
And we use these objects today in extra galactic astronomy studying the universe,
and galaxies beyond our own and we use them, we used galaxies as a lens.
So here, is light, traveling to us, from a distant object.
This object was here.
The light travels to us,
it gets deflected because this galaxy here curves space around it.
So light gets deflected and comes towards us.
So when we observe, this distant galaxy, we see it here.
But, we also see light deflected this way.
And light deflected that way.
So if the distribution of mass in this foreground galaxy
is very close to spherical, then this acts as a nearly perfect lens.
And the distant galaxy here gets distorted into what we call an Einstein ring.
Now, if this galaxy's mass distribution isn't circular,
it's a more imperfect lens, and instead we see multiple images.
But one of the very dramatic observations by the Hubble telescope was
the detection of this galaxy-sized lens where you see an Einstein Ring.
This is a nearby galaxy here.
It has distorted space.
The light from the galaxy behind it has been stretched into a nearly perfect ring.
And this imperfection here is due to
the fact that the mass distribution in this galaxy is not completely symmetric.
And that asymmetry means that things have not been focused to us perfectly.
But the fact that we see something like this means we have a system where
our telescope, the Hubble telescope, a foreground galaxy and
a distant galaxy, are nearly perfectly aligned.
Now, this can happen not only with galaxies, as we see here, but with stars.
What happens with stars is what we call gravitational microlensing.
So, if we can have a really nearly perfect alignment or
a background star, and a foreground star line up with our telescope,
the foreground star can focus light from the background star.
So, its mass can serve as a gravitational lens that makes
the background star brighter.
So as the foreground star moves, across the sky,
we will go from the star having a normal appearance, to getting brighter,
when they line up, to when the foreground star has passed this way,
so it's no longer serving as an effective lens, it gets dimmer again.
And there's a very characteristic pattern of brightening and
dimming that's predicted for gravitational microlensing.
This pattern will have a characteristic time,
and will be the same regardless of wavelength, so
now let's use our generalitivity workout that characteristic time.
So here's our background star, our foreground lens.
It's curving light around it, and here we are as the observer.
We can ask, how big is this characteristic Einstein ring?
How big is the scale on which lensing takes place?
Well, light is bent on the scale of the Shwartzshield radius.
That sets this bending angle here, we know this angle, we
know this distance, d, we can solve for the Einstein radius.
And it turns out to be the geometric mean between the Schwartzshield radius and
the distance between the source and the lens.
We can then ask, how long does it take the lens to move out of focus,
to move where it's no longer deflecting light to us?
We can call that the Einstein lensing time,
and that's the Einstein radius divided by the velocity.
And that will be the ratio of the Schwartzshield radius to the 1/2 times
the distance to the 1/2, divided by velocity.
So what I can observe is how long that, is the duration of that event.
How long did the microlensing event take place?
Once I measure how long it takes, I can figure out,
if I know approximately the distance to the lens, and its velocity.
How much space is curved, hence I can infer the mass.
And because the Einstein radius goes as the 1/2 power to the Schwartzfield radius,
the duration of the event goes as mass to the 1/2.
So if I can see these microlensing events, I can infer how, the mass of the lens,
the mass of a star, and potentially, as we'll see soon, the mass and planets.
This seemed like a very difficult task.
In order to get this kind of perfect alignment,
you'd have to look at more than a million stars at once.
My late colleague, Bohdan Paczynski, had the vision that this could be done.
And Bohdan working at Princeton with his colleagues in Warsaw,
built a dedicated experiment that stared at the sky, stared at the,
towards the center of our galaxy where there are many stars.
And looked for these events,
waiting to see a foreground star pass in front of a background star.
And this is one of the events they saw, here you can see the star having normal
brightness, getting brighter, getting dimmer, returning to normal brightness.
The points here are the observations.
This red curve here is the theory line.
And the theory is determined entirely by geometry.
It's just going back to this picture,
looking at how the brightness changes as the lens moves.
So there really is only two parameters in this fit, the height,
where it occurred, and the duration of the lensing of that.
And they're determined basically by the, properties of the system.
And the theory makes a very, nice fit to the data.
What we, what Bohdan and his colleagues realized is they were seeing just the kind
of gravitational microlensing events that were predicted by Einstein's theory.
They also recognized that this could be used to measure the mass of the stars, and
to measure the mass of the objects causing the lensing.
Bohdan and Shuday now,
then realized that they can use this as a way to discover planets around stars.
If you have a star and a planet orbiting around it,
the light gets deflected both by the star, and by the planet.
And what happens as a result is a much more complicated magnification problem.
When you have the star, the planet and
the lens star here, it looks like an ordinary lens.
Until, the planet's position lies just at the right location
to deflect light so we actually have multiple images.
That causes, as soon as the planet crosses this,
it causes a sudden jump in the brightness of the star.
The star' brightness then drops, and again, when things line up again,
it jumps again, and then returns to the classical stellar microlensing.
So, by detecting these sudden jumps,
astronomers could then detect the planet around the star.
They could see light lensed by this much more complex lens.
Not just a single star curving space, but a star and a planet around it.
This is just that event.
Here are our observations, of a star,
a foreground star passing in front of a background star.
The background star getting brighter, and then dimmer.
And now, this little blip here is when a planet around
the foreground star also passes in front of the background star.
So this blip occurs when you have gravitational lensing by both
a star and a planet.
And by taking this complex, more complex light curve,
astronomers are able to infer the planetary mass.
And what you see here are, these are observations done by multiple telescopes
around the world, in order to constantly monitor the star over time.
To carry out a program like this, you need to have telescopes distributed
around the planet, because you want to be able to observe,
say the star when it's daytime in Chile and nighttime in Australia.
And then perhaps, you know, so you'll look at it in Perth, and
you'll look at it in Chile, and you'll look at it in New Zealand, and you have
telescopes around the world doing this monitoring, in order to see this event.
These discoveries of planets have actually now become routine.
There are now many planets that have been discovered through these
microlensing events.
And here's another rather dramatic event and
here is a very bright sudden jump in a star's brightness.
What's plotted here is the star's brightness versus time.
And as you can see, as we've gotten more and more discoveries, there are more and
more groups working together collaboratively to
provide very detailed monitoring of the light curve.
Detailed enough that we can zoom in and
look at these brightening events in detail.
This actually tells us a lot about the the background star.
And, this data has meant that we can now use microlensing as another tool for
studying and detecting extrasolar planets.
These observations have taught us a number of important things about
extra solar planets.
The statistics of these events have led astronomers to
suggest that there are one or more bound planets around every star.
now, this, these events, as we'll get to soon,
are very complementary to the kind of measurements done by Kepler.
And, these measurements here show for some of the events,
the inferred mass, and the inferred distance of these events, and
you'll notice that microlensing events occur at larger distances
from the host star, than the transit or radial velocity measurements.
And you see these are the different events, and
estimates of mass and distance.
And some of the uncertainties here for individual events, are associated with,
that we don't know the distance to the lens, and
we often don't know its velocity.
However, we can combine these observations together, and the microlensing events
provide an important complement to the other techniques that we've talked about.
This plot here shows some of the planets that have been discovered up to,
to now, on download this file.
What's shown in red are the transits.
You'll notice transit events are mostly due to planets that are very close
to the star, because those are the planets that are easiest to detect by transits.
So transits work best on this part of the diagram.
And with Kepler, we're able to push down and see fairly well-masked planets.
The blue points in this diagram are radial velocity measurements.
And the radial velocity technique works best when the planet's most massive,
because that's where it,
when the planet exerts the largest possible pull on the host star.
So the my, the radial velocity data really helps fill in this part of the diagram.
Microlensing lets us find planets out near the orbits of Jupiter, Uranus, Neptune.
It lets us get beyond the orbit of the Earth.
So that's why microlensing has become an important technique for
studying the outer regions of solar systems.
Now, one, to me one of the most exciting observations done by the micro
lensing measurements are the observations of what seems to be free-floating planets.
So there are microlensing events of very short duration.
These are events that they have relatively little data on.
You can see here's one point, another, and
then down again, because these events happen so quickly.
Now remember what we talked about earlier.
The duration of a microlensing event depends on the planet's,
the mass of the lens.
So we can look at the duration of the events, and
what's plotted here is the rate of events versus its duration.
So these are one day events, ten-day events, 100-day events, and
stars will produce characteristically ten or 100-day events.
And the events shown here in this curve here with this dash line,
these are two different estimates of the number of events we expect,
due to the stars that we know about.
And you can see stars should produce a fairly broad distribution of events, but
with characteristic durations of ten to 20 days, and
very few events of durations less than a day.
These very rapid events aren't expected by stars,
because the stars have fairly large Einstein ring radii.
Yet, what the astronomers have found, are a number of very
short duration events, with some events lasting just about half a day.
What are producing these short events?
Our current best guess on what that is,
is these short duration events are due to low mass objects.
And we think what we're seeing are orphan planets,
planets that are wandering freely through space.
And one of the things that we're hoping to learn about in the next few years is by
getting more data to be convinced that these orphan planets are there,
you see the error bars are still quite large, and
to get an accounting of how many there are.
What many of us view as the next step in this direction is carrying out
a dedicated experiment in space looking for microlensing.
And what's shown here in this plot is the region that
the Kepler experiment has covered, in terms of planetary mass and
Earth mass versus distance from the sun and astronomical units.
Here's one AU, the earth's distance from the sun, and kind of the characteristic
Earth mass, and the Kepler experiment has probed this region here.
We'd like to complement these observations of Kepler by looking for
more distant planets.
And, what we want to do is make use of this microlensing method.
One of the things we're hoping to do, and this is something that the US
astronomy community views as part of its top priority for the next big mission in
space, a mission called W First, which is something that I've been working on.
Is that mission will carry out a dedicated microlensing survey.
In doing so, it'll be able to count the number of planets out there, not just like
Venus and Earth, but also like Mars and Jupiter and Saturn, Uranus and Neptune.
It'll be able to cover this whole region of parameter space, complement the Kepler
measurements, and give us a complete demographic census of what's out there.
This however, lies in the future, we're hoping though that when you come back,
take a new version of this course ten years from now,
this will not be filled with theoretical points, but with real observations.
So let me stop at this point, for
a moment, and let you think about the question of,
if planets form around stars, why are we finding free-floating planets?
How did they get there?
That's going to be the subject of the next section of our talk.
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