Download Detecting Extrasolar Planets

Detecting Extrasolar Planets
I hope you enjoyed this activity, which began to explore one of the most important areas of
modern astrophysics. Extrasolar planets are planets which orbit other stars and make up other
solar systems in our Galaxy. It is hard to directly view these planets with telescopes, as they are
so faint compared to their star. In fact, Autumn 2008 saw the first two direct detections of
extrasolar planets. In general, astronomers measure the influence of extrasolar planets on their
parent stars. This activity specifically looked at the transit method for detecting extrasolar
planets, which is one of the simplest methods for determining the presence of a planet. Here is
some guidance to approaching the activity and a summary of the key points.
The Transit Method for Detecting Extrasolar Planets
Some of you may have witnessed the transit of Venus in 2004, where Venus passed across the
face of the Sun. If you missed the event itself, you can see a movie of the transit at:
http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=35225. We can look for the same
effect on other stars in the Galaxy. By monitoring the brightness of these stars, we can identify
when the brightness dips – a signature of the transit. As a planet passes in front of the star, the
brightness from the star reduces because the planet blocks a small portion of the light from the
star. Astronomers plot lightcurves, which show the brightness of a star as a function of time, and
this can be used to see if a transit has occurred.
The transit method is therefore quite
simple. However, it has two key
disadvantages, which we will look at in the
“Going Further” section later.
As the planet passes across the face of the
star, the amount of light it blocks is directly
proportional to its area. We can use this
information to determine by how much the
light from the Sun drops (as viewed by a
distant observer) when the Earth transits.
This is simply equal to the ratio of the area
of the Earth to the area of the Sun.
Image from: http://www.astro.keele.ac.uk/~dw/images/transit.gif
Therefore, we only need to know the radius of the Sun and the radius of the Earth. You can find
these out using Google:
Radius of Sun = 695 500km
Radius of Earth = 6378.1km
Area of visible Sun = πrSun2
Area of Earth = πrEarth2
Fractional change in brightness during transit = πrEarth2 / πrSun2
= rEarth2 / rSun2
= (6378.1)2 / (695500)2
= 8.4x10-5
= 0.008%
To detect an Earth, we would need to be able to measure a change in brightness of about 1/10000!
Detecting Extrasolar Planets
The Kepler Mission
The Kepler mission has been designed to specifically detect Earth-like (and smaller) planets orbiting
other stars. These types of planets have not really been investigated, as it is very hard to detect
them. Measurements to date have been of large, Jupiter-mass planets. Our previous calculation
shows how difficult it is to detect an Earth-like planet using the transit method. This is one of the
main reasons for Kepler being a satellite, and not a ground-based instrument. To detect such small
changes in brightness would be impossible through the Earth's turbulent atmosphere.
The scientific motivation for the Kepler mission is to understand more about the different types of
planetary system. At the moment, our Solar System is a bit of an odd-ball, with many extrasolar
planetary systems having 'hot Jupiter' planets. These are planets the mass of Jupiter that reside
very close to their stars, so that the period of their orbit is only a few days. The detection of these
kinds of systems may be due to the sensitivity of our detection methods, so looking for smaller
planets may uncover solar systems more like our own. Another of the key motivations of Kepler is to
determine how many planets fall in the so-called 'habitable zone'. This is a region around a star
where the temperature is suitably low to allow planets in this region to harbour liquid water, the
essential compound required for life (as we know it). Discovery of such planets would lead to an
improved understanding of the possibilities for life in our Galaxy.
The aim of Kepler is to monitor the same patch of sky for three and a half years, studying a huge
number of stars. One of the difficulties with the transit method is being sure you have detected a
planet, and the easiest way to check is to look for another transit with the same characteristics. In
fact, astronomers use three transits, which must all be of the same dip in brightness and the same
duration, before they conclude that they have detected a planet.
Lightcurve Analysis
The lightcurve data that you have downloaded is from a transit study of the star HD209458. The
planet in question is called HD209458b. The star is very similar to the Sun, in terms of its
temperature, radius and mass. On the next page I have plotted the lightcurve, using the first column
as the x axis, and the second column as the y axis. The x axis shows the time as the fraction of a
day after the transit (so negative numbers are before the transit) and the y axis shows the relative
flux, or relative brightness of the star. When the observer is receiving all the light from the star, this
value is 1. Any reduction in the brightness due to the transit therefore reduces this number. I have
included the error bars on the y data points, which show the accuracy with which the data has been
taken (column 3 in the data table).
We can use the lightcurve to determine information about the planet. On the Kepler website,
following the 'In-depth Science' link gives information about the characteristics of transits. We can
use this information to determine the radius of the planet. We have already used one relation when
calculating the brightness drop of the Sun when the Earth transits:
Fractional change in brightness
=
Rplanet2 / Rstar2
You are given that the radius of the star is 1.46 times the radius of the Sun. We can use the
lightcurve to measure the fractional change in the brightness of the star during the transit.
Detecting Extrasolar Planets
Lightcurve of HD209458
1.015
1.01
Relative Flux
1.005
1
0.995
0.99
0.985
0.98
0.975
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time (fraction of a day)
To measure the fractional change in brightness, we need to measure the depth of the transit. You
may have done this is different ways, but here let's make an estimate. We know that before and
after the transit, the relative flux is 1. During the transit, we can see that the data points scatter
around the line 0.985, so fractional change in brightness is approximately 1 – 0.985 = 0.015. We
can rearrange our equation (and using F to denote the fractional change in brightness) we find:
Rplanet2 = F x Rstar2
= 0.015 x 1.46 x 695 5002
= 1.06x109
(radius of the Sun = 695 500 km)
and taking the square root gives the radius of the planet = 102925 km. We can compare this with
the radius of Jupiter (71300 km), which gives a radius of the planet of 1.4 times the radius of
Jupiter.
We can in fact go further and establish more of the planet's properties, such as the period of the
orbit and the mass of the star. We can estimate the duration of the transit from the lightcurve,
shown on the next page in red. This is approximately 0.1 days. The planet transits across the star
in this time, and so the distance it travels is equal to the diameter of the star (as viewed by a
distant observer, as in reality its path is curved).
Detecting Extrasolar Planets
Lightcurve of HD209458
1.015
Therefore we can use the
relationship between speed,
distance and time to estimate
the speed (v) of the planet.
1.01
Relative Flux
1.005
1
0.995
v = 2Rstar / duration
0.99
0.985
0.1 days is equivalent to 8640s,
0.98
therefore v = 23.8 km / s
0.975
-0.2
-0.15
Duration
of transit
is about
0.1 days
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Time (fraction of a day)
Can you determine the period of the orbit from the speed? What about the
mass of the star (hint - think about Kepler's third law)? You can find more
information about HD 209458 here, to use in your calculation or to check
your answers: http://exoplanet.eu/star.php?st=HD+209458.
Going Further
I have already mentioned one of the limitations of the transit method, and that is the need to
repeat observations to confirm a transit. Transits are not the only phenomenon to cause a change
in brightness of a star. Certain types of stars (for example cataclysmic variable stars) show
periodic changes in their brightness, and many stars are in binary star systems which also affect
the measured lightcurve. It is therefore necessary to confirm a transit using at least three
observations that show an equal change in brightness and transit length. The downside of this is
the time taken to make the observations, as planets can orbit their stars only once every few
years. The Kepler mission is designed to last three and a half years, as during this time, Earth-like
planets will transit their star three times. Here is an example of something a bit more wacky
affecting
a
transit,
in
this
case
the
transit
of
Venus
(image
from
http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=35224):
The other important limitation of the transit method is the required
geometry of a system. For us to see a transit, the orbit of the planet
has to be inclined such that it crosses the surface of the star. In fact
the probability of seeing a transit for a randomly orientated orbit is
equal to the diameter of the star divided by the diameter of the orbit
(see http://kepler.nasa.gov/sci/basis/character.html for a diagram).
Different methods exist to detect extrasolar planets, and the most successful to date has been the
radial velocity method. The star and planet orbit a common centre of mass, which is located within
the star but not at is centre. Consequently, the star 'wobbles' and this motion can be detected by the
Doppler shift of the light from the star. This method is particularly successful at finding massive
Jupiter-like planets orbiting very close to their stars. You can investigate the types of planets found by
the different methods at http://exoplanet.eu/catalog.php. This shows that we need to use multiple
methods of planet detection to uncover all the different planetary systems – one method alone is not
enough.