Who would have guessed that from simply measuring brightness changes in a star, we could find not only whether the star has a planet, but a host of interesting properties of that planet as well. Even whether or not the planet might be inhabitable by life forms!
Using SalsaJ image processing software and telescopic images of stars, we can make measurements of star brightness, then plot a light curve
(graph of brightness vs time) for a planet transit and analyze it to find out those interesting properties hadn't dreamed of knowing before before 1995.
This Investigation has five parts:
- Plot a Transit Light Curve
- Examine the Light Curve
- Find the Planet's Size
- Find the Distance of the Planet from its Star
- Is the Planet Habitable?
This is a rather idealized light curve—most are quite a bit more rough or difficult to discern the brightness drop.
Salsa J V. 2.1 Image Processing software, available from European HOU site.
Images — four possible sets:
These are observations of four different stars (HD189733, TrES-3, HD209458, GJ436) each containing a transit event—the dimming of the star as a planet passes in front of it.
First let’s have another look at graph E of the light curves near the
end of chapter 6.
What would determine how much dimming occurs during a transit of a
planet in front of a star?
What would affect how long the transit lasts?
What would determine how often a transit occurs?
What properties of a planet could we tell from observations of
I. Plot a Transit Light Curve
In order for a planet transit (and corresponding dimming of the star's light) to be observed:
The planet’s orbital plane must be in line with our view of the star
(as with eclipsing binary stars). Geometrically, less than 2% of exoplanets would satisfy this condition. (See illustration of Geometry for Transit Probability on the NASA Kepler About Transits page.)
The planet must be large enough for us to detect a drop in
brightness. Earth based observations can detect a drop of 1% from a
transit of a Jupiter sized planet.
image is really 20 or so images “stacked” on one another so that “noise”
in the resulting image is kept to a minimum.
Comments about each image set:
- HD189733 (20 images) - The exoplanet orbiting the star HD 189733 was discovered on October 5, 2005 by transit method in France. It was the very first star for which planet transits were observed.
The planet had already been discovered by the spectroscopic method.
planet is known as HD189733b. Planets around a star are designated by a lower case
letter of the alphabet, with the star taking the letter “a” and each
orbiting body taking a letter in the order of their discovery.
HD189733b was the first planet discovered around star HD189733.
The images in this set were taken with the NASA Spitzer satellite. We list this set first because a macro is automatically included with SalsaJ software that can Open all 20 images and tile them. (Images are also available by downloading this file: 20 image_spitzer 4.77 Mb .
- TrES-3 - The TrES-3 images were provided by Todd Klaus who worked in the Kepler Science Operations Center as Lead Software Engineer at NASA Ames Research Center in Mountain View CA. The telescope used was at the Zen Observatory.
- HD209458 (19 images) - As is common HD209458 has multiple names for the same star, another being SAO 107623. This is part of the Astronomical Image Set for A Changing Cosmos, the Hands-On Universe high school course, part of Global Systems Science.
- GJ436 - The 102 GJ436 images were provided by Bareket Observatory. This set, being so large, lends itself to teams of students dividing the task into smaller batches of images and pooling the results.
For any given set of images, use the following
procedure (like the Finding Supernova investigation—Chapter 6).
Find the time of each image from the Image Header Info. Find the
difference, in minutes, between the observation time and the time of the
first image (i.e. 10/20/2001, 3:06 UT for HD209458).
Identify the correct star on the image. Use your judgment or a
finder map. For all the image sets except for one (HD 209458), there is a special labelled star finder image with reference stars marked. For HD 209458 (SAO 107623), it's the star
that is the brightest. Take some Counts measurements
using the Aperture tool to make sure you've found the brightest star.
Find reference star(s). The bright star about 45° to the upper
right of HD 209458 (x = 564, y = 266) can be a reference star. Even
better reference stars are at (x = 185, y = 181) or (x = 311, y = 276).
Using Aperture, measure and record the Counts of the star as well as the
reference star. Then divide the Counts for the star by the Counts for the
reference star to get the Count Ratio for each image. Make a light
curve for the star by plotting the Count Ratio versus time (in min).
Before graphing, look at the range of Count Ratios and optimize the
range of y-axis values (maximum value just above the highest Count Ratio
and the minimum value just below the lowest Count Ratio on the axis).
II. Examine the Light Curve
If you do not have data for a full transit, is there any way you
could still determine the transit duration?
What was the duration of the transit you plotted in Part I?
Would the duration be the same for all transits of a given
Transit Depth is the dip in the light curve. This is the drop in
brightness of the star as a planet passes in front of it.
What is the Transit Depth (TD)—the maximum dip in brightness— of
the transit you plotted in Part I, expressed as the ratio between the
brightness before the transit and the brightness at the deepest point in
TD = fraction decrease in brightness of the star due to the
= (B1- B2)/B1 or (C1- C2)/C1 [B = brightness; C = Counts]
What makes it difficult to find the Transit Depth for this planet?
III. Find the Planet’s Size
The transit depth (TD) is related to the size of the planet in a very
simple way: the area of light blocked when the planet transits is
exactly the area of the apparent disk of the planet. So, the ratio of
area of planet disk to star disk should directly determine the drop in
TD = (area planet)/(area star)
Since area = πr 2
TD = (πrplanet 2
TD = (rplanet
What is the radius of planet? [First find the radius of
the star (from Internet or clues from teacher or colleagues), and
then use the transit depth equations in both II and III to find the
radius of the planet]
The size of the planet gives us crucial information about its possible
habitability. It’s a little like the Goldilocks story.
If the planet is too small (like Mercury or Mars), it will not have
enough gravity to hold on to an atmosphere—gas molecules will escape the
planet over a time-span of not many years in the lifetime of the
If the planet is too large, it will retain a huge amount of atmosphere
and have crushing atmospheric pressure, like the giant planets Jupiter
What does Kepler’s Third Law tell us about how the period of a
planet is related to its distance from a star?
One light curve cannot show the period of the planet. The star must
be observed for many days, weeks or months in order to establish that
the transits occur in a regular period.
What is the period of the planet? (Use library or Internet
search, e.g. the NASA Exoplanet Archive or exoplanet catalog.)
IV. Find the Distance of the Planet from its Star
Using Kepler’s Third Law, what is the orbit radius of the planet in Astronomical Units (AU)?
The distance of the planet from its star gives us crucial
information about its possible habitability. Again, it’s like the
Goldilocks story, but an even closer analogy, since the “soup” will be
either too hot or too cold for life. More precisely, the temperature
must be in the range to allow for liquid water, which is an essential
ingredient for nearly all life forms that we know of. If the planet is
too close to its star, all water vaporizes, and if the planet is too far
from its star, water is all frozen.
V. Conclusion—Is the Planet Habitable?
8.16. What factors besides distance from star might impact the
temperature of a planet?
8.17 Is the planet habitable? Justify your answer with results
from parts I through IV of this investigation. Check your results against an exoplanet catalog.
More advanced exoplanet investigation
Visit the NASA Kepler website and find Instructions for Getting Kepler Light Curves. Then analyze those light curves.
Visit the TransitSearch website - http://www.transitsearch.org - to find
and download data on exoplanets with observed transits. Find the time
between consecutive transit observations to find period. Find the
transit depth. If possible, get information about the parent star to
determine the size of the planet and its orbit radius.
Visit the Sloan Digital Sky Survey (SDSS) web page on Calculating the
radius of a star -
http://cas.sdss.org/dr6/en/proj/advanced/hr/radius1.asp. See the meaning
and derivation of a formula that can be used to compute a star’s radius
in relation to our Sun’s radius:
R = star radius
Rs = Sun’s radius
T = Temperature of the star
Ts = Temperature of the Sun
M = absolute magnitude of the star
ms = absolute magnitude of the Sun = 4.83
Relationship of b-v magnitude and temperature is in chart at left.
Absolute magnitude is
M = m - 5 log d + 5
Where d = distance to the star in parsecs.
Use the Hipparchos skyplot to find parallax, distance to star, and
compute absolute magnitude -
Finally, visit the AAVSO website (http://www.aavso.org) and look for any
exoplanet “campaigns” that are there (e.g on
Also, try getting names of stars known to have transiting exoplanets
from http://exoplanet.eu/catalog-transit.php (52 as of July 2008) and
then do a search on the AAVSO website for any light curves they have for
any of those stars.
To find out about the NASA mission to find Earth-size exoplanets, see
the Kepler mission website - http://kepler.nasa.gov.
* See explanation of temperature scales