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Detection of Extrasolar Planets through
Gravitational Microlensing
and Timing Method
Timing Method
Technique & Results
A Brief History of Light Deflection
In 1911 Einstein derived:
a=
2 GM‫סּ‬
c2R‫סּ‬
= 0.87 arcsec
Einstein in 1911 was only half right !
In 1916 using General Relativity Einstein derived:
a=
4 GM
c2r
Light passing a distance r from object
= 1.74 arcsec
Factor of 2 due to spatial curvature which is missed if light is treated like particles
Eddington‘s 1919 Eclipse expedition
confirmed Einstein‘s result
A Brief History of Light Deflection
In 1924 Chwolson mentioned the idea of a „factious double star.“ In the
symmetric 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 perfect
alignment between the source and the lens: „Einstein Ring“
In 1937 Zwicky pointed out that galaxies are more likely to be gravitationally
lensed than a star and one can use the gravitational lens as a telescope
Evidence for gravitational lensing first appeared in
extragalactic work
Einstein Cross
Einstein Ring
Basics of Lensing:
S2
Source
Lens
Observer
S
S1
Basics of Lensing: The Einstein Radius
≈ 1 milli-arcsecond
Lens
=> Microlensing
S1
qE
qE
qs
S2
Source off-centered
Source centered
b = q – a(q)
b=0
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 lasts
10-30 hours
Mao & Paczynski (1992) propose that star-planet
systems 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
OGLE
alert
Lightcurve close-up & fit (from Bennet)
• Cyan curve is the
best fit single lens
model
–2 = 651
• Magenta curve is
the best fit model
w/ mass fraction e
 0.03
–2 = 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
The First Planet Candidate: OGLE-235-MOA53
1st definitive
lensing planetary
discovery
- complete coverage
not required for
characterization
Real-time data
monitoring was
critical!
S. Gaudi video
OGLE 2005-BLG-071
Udalski et al. 2005
The Star:
BASED ON
GALACTIC MODEL
M = 0.46 M‫סּ‬
d = 3300 pc
I-mag = 19.5
The Planet:
M = 3.5 MJup
a = 3.6 AU
OGLE-06-109L
Features 1,2,3,5 are caused by Saturn mass
planet near Einstein radius. Feature 4 by
another Jovian planet
The Star:
M = 0.5 M‫סּ‬
d = 1490 pc
I-mag = 17.17
Gaudi et al. 2008, Science, 319, 927
The Planets:
M1 = 0.71 MJup
a1 = 2.3 AU
M2 = 0.27 MJup
a2=4.6 AU
From The Astrophysical Journal Letters 644(1):L37–L40.
© 2006 by The American Astronomical Society.
For permission to reuse, contact [email protected].
OGLE-2005-BLG-169
The Star:
The Planet:
M = 0.49 M‫סּ‬
M = 0.04 MJ
d = 2700 pc
a = 2.8 AU
I-mag = 20.4
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 (Δt = 0.092) extremely well, while the entrance is tracked
by a single point (Δt = −0.1427). The dashed line indicates the time t0. Inset: Source path through the caustic geometry. The source size ρ is indicated.
Microlensing planet detection of a Super Earth?
Best binary
source
OGLE-2005-BLG-390
Mass = 2.80 – 10 Mearth
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 M‫סּ‬
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 statistics
including a galactic model of the distribution of stars in the galaxy
Stellar mass ranges from
0.05 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% confidence
level.
Red line: constraints from galactic model
Black: constraints from observations with the Very Large Telescope
Microlensing Planets
Planet
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
OGLE-2007-BLG-368L b
0.07
-
3.3
MOA-2008-BLG-310-L b
0.23
-
MOA-2008-BLG-387-L b
2.6
-1.8
0.35
6000
1.25
0.67
>6000
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 for
stars in the bulge. This is the habitable zone!
• Can get good statistics on Earth mass planets in the habitable zone
of 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 [email protected].
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 from
many observatories
• Planet hosting star is distant: Detailed studies of the host star very
dfficult
• 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 and
the 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:
Don’t forget to take
into account your
own motion!!!
Due to the orbital motion the
distance the Earth changes.
time This causes differences in
the light travel time
time
Change in arrival time =
apmpsini
M *c
ap, mp = semimajor axis, mass of planet
A Pulsar: a very stable astronomical clock!
radiation
Strong magnetic field
Acts like a cosmic
lighthouse
Rotation periods of pulsars < 10 second
The fastest rotators are millisecond pulsars:
PSR1257+12: P = 0.00621853193177 +/- 0.00000000000001 s
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_Earth
P = 25.3 d ; a = 0.19 AU
Planet B:
M = 4.3 M_Earth
P = 66.5 d ; a = 0.36 AU
Planet C:
M = 3.9 M_Earth
P = 98.2 d ; a = 0.46 AU
fourth companion with very
low mass and P~3.5 yrs
Interaction between B & C
Confirms the planets and
Establishes true masses!
Other applications of
the 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
Earth-mass planets