The Transit Method
• When a planet crosses in front of its star as viewed by an observer,
the event is called a transit. Transits produce a very small change in
a stars brightness.
• If this change is caused by a planet it must be periodic and each
transit must have the same change in brightness.
• The transit method can be used to gain information about the
planet as well as just detecting it. The planet’s size, transit time and
radius of the orbit can all be determined from the data collected.
Transit Method
• It is possible to study the atmosphere of the transiting
planet.
• When the planet transits the star, light from the star passes
through the planets atmosphere.
• By studying the high resolution stellar spectrum carefully,
you can deduce what elements are present in the planet’s
atmosphere (by spectroscopy of absorption lines from its
atmosphere while it is transiting) and check it for indicators
of life - such as the presence of free oxygen in the
atmosphere.-
• The main disadvantage of the transit method is that for us to
detect a planet, the orbit must be precisely aligned with our
point of view.
We used reference stars so we can capture the
“noise”(darks, flats, biases)and subtract them
from the images of the object taken.
More reference stars= more accurate data
Theory
•Many characteristics determined through calculation, not
observation
•Radius mass of star, as well as planet’s period, are easily estimated
through observation
•You can then find:
1) semi-major axis
2) orbital speed
3) radius
4) transit duration
5) impact parameter
6) Inclination
• The maths used is based around Kepler’s Laws and Newton’s
Laws of Motion and of Gravitation.
Newton’s + Kepler’s Laws
•Newton’s Third Law states: when one
body exerts a force on another body,
the second body exerts equal &
opposite force on the first body.
•This leads to Newton’s Law of Universal
Gravitation
•We can then apply Kepler’s Third Law of Planetary Motion:
P2 ∝ a3
•If we assume circular orbit, this becomes:
M* is m1
Mp is m2
•However, Mp is negligible compared to M* , leading to
G
gravitational constant
r
radius.
•Finally, finding transit duration.
•Once you know R* , RP, P, and a, you can find ttrans.
•Two factors affect ttrans : impact parameter and
inclination of the planet’s orbit (i).
•In this diagram, b is the impact parameter and a
is the semi-major axis.
•We can obviously see that the longest transit
duration will occur when b is 0, and as b increases
ttrans decreases.
•Trigonometry tells us that b =a cos(i)
•Finally, we can use Pythagoras to
find l, the length of the transit (from
Earth POV)
GJ-1214 b
•Mass of 6.55 M⊕
•Radius of 2.68 R⊕
•Intermediate between
Earth-like planets and gas
giants.
•13 parsecs / 42 light
years away
•Mainly H2O
composition.
•Measurements indicate
period of 1.58 days
Our analysis of the light-curve shows:
• t trans of 0.039 days
• Dip in brightness: 0.0144
• Rp - R* ratio: 0.12 (using
)
•
•
•
•
Qatar-1b
Planet name: Qatar 1b
Planet Mass: 1.09±0.08 MJ
Planet radius: 1.17±0.06 RJ
Planet temp: 1380±45 Kelvin
•Hot Jupiter
•Gas giant
•Located 550 light years away from Earth
•Planet orbits its star every 34 hours, making it
one of the shortest period planets yet found
orbiting a star less massive than the sun
.
•Detected by transit method
• Duration of transit: 0.06 days
• Dip in brightness: 0.025
• Ratio of planet to star radius:
0.16
WASP-2bSP-2b
Jupiter compared to WASP-2b size
Mass
(m)
0.847 ± 0.045 MJ
Radius
(r)
1.079 ± 0.033 RJ
Surface gravity
(g)
3.279 ± 0.036 g
Temperature
(T)
1300 ± 54 K
•Orbits WASP 2
Distance
470 ly
•In constellation of Delphinus
Constellation
Delphinus
•that WASP
2b was a planet.
Giant
•Planet’sType
mass and radius indicate that it is a gasGas
giant
with a similar bulk composition to Jupiter.
Duration of
transit
0.060 days
using your final
lightcurve
Dip in brightness 0.019
using your final
lightcurve
Ratio of planet
to star radius
calculated from
your final
lightcurve
0.14
TrES-3b
Jupiter compared to TrES-3b size
Mass
(m)
1.92 ± 0.23 MJ
Radius
(r)
1.341 ± 0.081 RJ
Density
(ρ)
1172 kg m-3
Surface gravity
(g)
2.7 g
The planet’s home star is slightly smaller and cooler than the Sun
and is about 6 times larger than the planet. TrES-3b is a gas giant
and TrES-3 is very close to its parent star and orbits it in 31 hours.
TrES-3b- Experimental data
The light curve shows a drop in the brightness of the light between around 4:30
and 5:30 which is when the planet is transiting the star.
brightness of 2.54%.
The measurements suggest the planet has a radius roughly 0.16 times that of the
host star.
TrES-3b- Actual data
Transit time ≈ 1.015 hours
Mass
(m)
1.92 ± 0.23 MJ
Radius
(r)
1.341 ± 0.081 RJ
Density
(ρ)
1172 kg m-3
Surface gravity
(g)
2.7 g
Dip in
brightness
≈ 2.54%
Detecting - radial velocity.ppt