Detection of Extrasolar Planets throughthrough Gravitational Microlensing

and Timing MethodTiming Method

Technique & Results

A Brief History of Light Deflection

In 1911 Einstein derived:

Einstein in 1911 was only half right !

α = 2 GMּס

c2Rּס

= 0.87 arcsec

In 1916 using General Relativity Einstein derived:

α = 4 GMc2r

= 1.74 arcsec

Light passing a distance r from object

Factor of 2 due to spatial curvature which is missed if light is treated like particles

Eddington‘s 1919 Eclipse expeditionconfirmed Einstein‘s result

A Brief History of Light Deflection

In 1924 Chwolson mentioned the idea of a „factious double star.“ In thesymmetric case of a star exactly behind a star a circular image would result

In 1936 Einstein reported about the appearance of a „luminous“ circle of perfectalignment between the source and the lens: „Einstein Ring“

In 1937 Zwicky pointed out that galaxies are more likely to be gravitationallylensed than a star and one can use the gravitational lens as a telescope

Einstein Cross

Einstein Ring

Evidence for gravitational lensing first appeared in extragalactic work

Basics of Lensing:

Source

Lens

SS2 S1

Observer

Basics of Lensing: The Einstein Radius

θs

θE

S1

S2

Lens

Source off-centered

θE

Source centered

≈ 1 milli-arcsecond

=> Microlensing

β = 0

β = θ – α(θ)

Magnification due to Microlensing:

Typical microlensing events last from a few weeks to a few months

Time sequence: single star

• Top panel shows stellar images at ~1 mas resolution centered on lens star

• Einstein ring in green• Magnified stellar

images shown in blue• Unmagnified image is

red outline• The observable total

magnification is shown in the bottom panel

Animation by Scott Gaudi:

http://www.astronomy.ohio-state.edu/~gaudi/movies.html

Time sequence: star + planet

• A planet in the shaded (purple) region gives a detectable deviation

A planet lensing event lasts10-30 hours

Mao & Paczynski (1992) propose that star-planetsystems will also act as lenses

Successful Microlensing Programs

• OGLE: Optical Gravitational Lens Experiment (http://www.astrouw.edu.pl/~ogle/)

• 1.3m telescope looking into the galactic bulge

• Mosaic of 8 CCDs: 35‘ x 35‘ field

• Typical magnitude: V = 15-19

• Designed for Gravitational Microlensing

• First planet discovered with the microlensing method

Problem:Only 4 points!

Solution: Multi-site Campaigns

Microlensing Results:

12 Planets so far

Rumor has it that there are another ~20 planet candidates

The First Planet Candidate: OGLE-235-MOA53

OGLEalert

Lightcurve close-up & fit (from Bennet)• Cyan curve is the

best fit single lens model– ∆χ2 = 651

• Magenta curve is the best fit model w/ mass fraction ε≥ 0.03– ∆χ2 = 323

• 7 days inside caustic = 0.12 tE– Long for a

planet,– but ∆mag = only

20-25%– as expected for

a planet near the Einstein Ring

1st definitive µlensing planetary discovery

- complete coverage not required for characterization

Real-time data monitoring was critical!

S. Gaudi video

The First Planet Candidate: OGLE-235-MOA53

OGLE 2005-BLG-071

Udalski et al. 2005

The Star:

BASED ON GALACTIC MODEL

M = 0.46 Mּס

d = 3300 pc

I-mag = 19.5

The Planet:

M = 3.5 MJup

a = 3.6 AU

OGLE-06-109L

The Star:M = 0.5 Mּס

d = 1490 pcI-mag = 17.17

The Planets:M1 = 0.71 MJupa1 = 2.3 AUM2 = 0.27 MJupa2=4.6 AU

Features 1,2,3,5 are caused by Saturn massplanet near Einstein radius. Feature 4 byanother Jovian planet

Gaudi et al. 2008, Science, 319, 927

From The Astrophysical Journal Letters 644(1):L37–L40.© 2006 by The American Astronomical Society.For permission to reuse, contact journalpermissions@press.uchicago.edu.

Fig. 1.—Top: Data and best-fit model for OGLE-2005-BLG-169. Bottom: Difference between this model and a single-lens model with the same (t0, u0, tE, ρ). It displays the classical form of a caustic entrance/exit that is often seen in binary microlensing events, where the amplitudes and timescales are several orders of magnitude larger than seen here. MDM data trace the characteristic slope change at the caustic exit (∆t = 0.092) extremely well, while the entrance is tracked by a single point (∆t = −0.1427). The dashed line indicates the time t0. Inset: Source path through the caustic geometry. The source size ρ is indicated.

OGLE-2005-BLG-169

The Star:

M = 0.49 Mּס

d = 2700 pc

I-mag = 20.4

The Planet:

M = 0.04 MJ

a = 2.8 AU

Microlensing planet detection of a Super Earth?

OGLE-2005-BLG-390Mass = 2.80 – 10 Mearth

Best binarysource

a = 2.0 – 4.1 AU

q = 7.6 x 10–5 Ratio between planet and star

MOA-2007-BLG-192-L

The Star (brown dwarf):

M = 0.06 M ּס

d = 1000 pc

J-mag = 19.6

The Planet:

M = 3.3 Mearth

a = 0.62 AU

Is it or isn‘t it a Super Earth?

Best fit stellar binary

OGLE-2007-BLG-368

Mass star ~ 0.2 Msun

Mass planet ~ 2.6 MJupiter

To get the mass of the host star one must once again rely on statisticsincluding a galactic model of the distribution of stars in the galaxy

Stellar mass ranges from0.05 Msun (brown dwarf) to 0.2 Msun (star)

Mplanet = 0.07 – 0.49 MJupiter

Semi-major axis = 1.1 – 2.7 AU

Both at only the 90% confidencelevel.

Red line: constraints from galactic model

Black: constraints from observations with the Very Large Telescope

Microlensing PlanetsPlanet Mass

(MJ)Period(yrs)

a(AU)

e M*

(Msun)Dstar

(pcs)OGLE235-MOA53 b ~2.6 ~15 ~5 ? 0.63 5200

OGLE-05-071L b ~3.5 ~10 ~3.6 ? 0.64 3300

OGLE-05-169L b 0.04 ~9 ~2.8 ? 0.49 2700

OGLE-05-390L b 0.017 ~9.6 ~2.1 ? 0.22 6500

MOA-2007-BLG-192-L b 0.01 ~2 0.62 ? 0.06 1000

OGLE-06-109L b 0.71 ~5 2.3 ? 0.5 1490

OGLE-06-109L c 0.27 ~14 4.6 0.11 0.5 1490

MOA-2007-BLG-400-L b 0.9 - 0.5 0.35 6000

OGLE-2007-BLG-368L b 0.07 - 3.3

MOA-2008-BLG-310-L b 0.23 - 1.25 0.67 >6000

MOA-2008-BLG-387-L b 2.6 -1.8 3.6 0.19 ~5700

• Microlensing has discovered 4-5 cold Neptunes/Superearths

• Neptune-mass planets beyond the snowline are at least 3 times more common than for Jupiter- mass planets

But….this is based on small number statistics

The Advantages of Microlensing Searches

• No bias for nearby stars, planets around solar-type stars

• Sensitive to Earth-mass planets using ground-based observations: one of few methods that can do this

• Most sensitive for planets in the „lensing zone“, 0.6 < a < 2 AU forstars in the bulge. This is the habitable zone!

• Can get good statistics on Earth mass planets in the habitable zoneof stars

• Multiple systems can be detected at the same time

• Detection of free floating planets possible

Microlensing is complementary to other techniques

From The Astrophysical Journal Letters 644(1):L37–L40.© 2006 by The American Astronomical Society.For permission to reuse, contact journalpermissions@press.uchicago.edu.

Fig. 3.— Exoplanet discovery potential and detections as functions of planet mass and semimajor axis. Potential is shown for current ground-based RV (yellow) and, very approximately, microlensing (red) experiments, as well as future space-based transit (cyan), astrometric (green), and microlensing (peach) missions. Planets discovered using the transit (blue), RV (black), and microlensing (magenta) techniques are shown as individual points, with OGLE-2005-BLG-169Lb displayed as an open symbol. Solar system planets are indicated by their initials for comparison.

The Disadvantages of Microlensing Searches• Probability of lensing events small but overcome by looking at lots of stars

• One time event, no possibility to confirm, or improve measurements

• Duration of events is hours to days. Need coordinated observations frommany observatories

• Planet hosting star is distant: Detailed studies of the host star verydfficult

• Precise orbital parameters of the planet not possible

• Light curves are complex: only one crossing of the caustic. No unique solution and often a non-planet can also model the light curves

• Final masses of planet and host stars rely on galactic models and statistics and are poorly known

• Future characterization studies of the planet are impossible

2. The Timing Method

The Technique:

If you have a very stable “clock” that sends a signal with a constant pulse rate andthe capability to measure the time of arrival (TOA) of the signal with very high precision⇒Search for systematic deviations in the TOAs that indicate different light travel

times due to orbital motion

Timing Variations:

time

Due to the orbital motion thedistance the Earth changes. This causes differences in the light travel time

Change in arrival time = apmpsini

M*c

ap, mp = semimajor axis, mass of planet

time

Don’t forget to takeinto account yourown motion!!!

A Pulsar: a very stable astronomical clock!

radiation

Strong magnetic field

Rotation periods of pulsars < 10 second

The fastest rotators are millisecond pulsars:PSR1257+12: P = 0.00621853193177 +/- 0.00000000000001 s

Acts like a cosmiclighthouse

The (Really) First Exoplanets:in 1992

Arecibo Radio-telescope

98 d orbit removed, 66 d orbit remains

66 d orbit removed, 98 d orbit remains

PSR 1257+12 system:

Planet A:M = 0.02 M_EarthP = 25.3 d ; a = 0.19 AU

Planet B:M = 4.3 M_EarthP = 66.5 d ; a = 0.36 AU

Planet C:M = 3.9 M_EarthP = 98.2 d ; a = 0.46 AU

fourth companion with very low mass and P~3.5 yrs

Interaction between B & CConfirms the planets andEstablishes true masses!

Other applications ofthe timing method:

• Stably pulsating white dwarfs (P~200s)• Pulsating sdB stars (P~500s)• Eclipse timing • Transit time variations

NN Ser eclipses

Kepler-9 transits

Timing Method Summary:

• First successful detection technique!• Requires a suitable target (clock) • Lack of large sample => not efficient• In best case (very short periods) is sensitive to

sensitive to Earth-mass planets