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 axis2) orbital speed3) radius4) transit duration5) 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

G gravitational constant

r radius.

•We can then apply Kepler’s Third Law of Planetary Motion: P2 a∝ 3

•If we assume circular orbit, this becomes:

•However, Mp is negligible compared to M* , leading to

M* is m1

Mp is m2

•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

•Orbits WASP 2•In constellation of Delphinus•that WASP 2b was a planet.•Planet’s mass and radius indicate that it is a gas giant with a similar bulk composition to Jupiter.•Binary star

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

Distance 470 ly

Constellation Delphinus

Type Gas Giant

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 0.14

calculated from your final lightcurve

TrES-3b

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. That means that the year on TrES-3 lasts less than one and one-third Earth days.

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

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

Dip in brightness ≈ 2.54%

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

Detecting - radial velocity.ppt