Transcript BENNETT, Constraints on the Orbital Motion of OGLE-2006

First Orbital Parameters for a Planet
Found by Microlensing
the Jupiter/Saturn analog
system OGLE-2006-BLG-109Lb,c
MicroFUN
Microlensing Follow-Up Network
David Bennett
University of Notre Dame
for the MicroFUN, OGLE,
MOA and PLANET
collaborations
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Double-Planet Event: OGLE-2006-BLG-109
• 5 distinct planetary
light curve features
• Source trajectory
crosses long axis of
planetary caustic
feature
• Feature #4 requires
an additional planet
• Planetary signals
visible for 11 days
• Features #1 & #5
cannot simultaneously
be fit without including
the orbital motion of
the Saturn-mass
planet and the Earth
FUN, OGLE, MOA & PLANET
OGLE-2006-BLG-109 Light Curve Detail
• OGLE alert on feature
#1 as a potential
planetary feature
• FUN (Gaudi)
obtained a model
approximately
predicting features #3
& #5 prior to the peak
• But feature #4 was not
predicted - because it
is due to the Jupiter not the Saturn
Gaudi et al (2008)
published in Science
OGLE-2006-BLG-109 Light Curve Features
• The basic 2-planet
nature of the event
was identified
during the event,
• But the final model
required inclusion
of orbital motion,
microlensing
parallax and
computational
improvements (by
Bennett).
OGLE-2006-BLG-109Lb,c Caustics
Curved source trajectory due
to microlensing parallax
Caustic curves plotted at 3-day intervals
0.2% of 14-yr orbit completed during
Feature
planetary event
due to
Model includes planet-star relative
Jupiter
velocity and acceleration
Effect of Parallax & Orbital Motion
• black curve is the full model
• red curve: neither orbital motion nor parallax.
• blue curve: orbital motion, but no parallax
• green curve: constant velocity approx.
• cyan curve: parallax and the constant velocity
approx.
Binary model similar to OGLE-06-109
ratio to single lens
light curve
Lens System Properties
• For a single lens event, 3 parameters (lens mass,
distance, and velocity) are constrained by the
Einstein radius crossing time, tE
• There are two ways to improve upon this with light
curve data:
– Determine the angular Einstein radius : E= *tE/t* = tErel
where * is the angular radius of the star and rel is the
relative lens-source proper motion
– Measure the projected Einstein radius, r%
E , with the
microlensing parallax effect (due to Earth’s orbital motion).
Lens System Properties
• Einstein radius : E= *tE/t* and projected Einstein radius, r%
E
– * = the angular radius of the star
– r%
E from the microlensing parallax effect (due to Earth’s orbital motion).
2
r%
4GM
c
RE   E DL , so   E  2
. Hence M 
 E r%
E
DL c  E DL
4G
OGLE-2006-BLG-109 Source Star
Apparent source
In image
The model indicates
that the source is
much fainter than
the apparent star at
the position of the
source. Could the
brighter star be the
lens star?
source from model
OGLE-2006-BLG-109Lb,c Host Star
• OGLE images show that the source is offset from the bright star by 350 mas
• B. Macintosh: Keck AO images resolve lens+source stars from the brighter star.
• But, source+lens blend is 6 brighter than the source (from CTIO H-band light
curve), so the lens star is 5 brighter than source.
– H-band observations of the light curve are critical because the lens and source and not
resolved
• Planet host (lens) star magnitude H  17.17
– JHK observations will help to constrain the extinction toward the lens star
Implications of Light Curve Model
circular orbit case
Host star mass: M L  0.52 0.18
0.07 M e from light curve model.
• Apply lens brightness constraint: HL 17.17.
• Correcting for extinction: HL0= 16.93  0.25
– Extinction correction is based on preliminary HL-KL color
– Error bar includes both extinction and photometric uncertainties
• Lens system distance: DL= 1.49  0.13 kpc
Host star mass: M L  0.50  0.05M e from light curve and
lens H-magnitude.
Other parameter values:
• “Jupiter” mass:
semi-major axis:
• “Saturn” mass:
semi-major axis:
• “Saturn” orbital velocity
mb= 0.71  0.08 MJup
ab  2.3  0.3AU
mc= 0.27  0.03 MJup= 0.90 MSat
ac  4.6  0.5AU
vt = 9.5  0.5 km/sec
Orbital Motion Modeling
• 4 orbital parameters are well determined from the light
curve
– 2-d positions and velocities
– Slight dependence on distance to the source star when
converting to physical from Einstein Radii units
• Masses of the host star and planets are determined
directly from the light curve
– So a full orbit is described by 6 parameters (3 relative positions &
3 relative velocities)
– A circular orbit is described by 5 parameters
• Models assume planetary circular motion
– 2-d positions and velocities are well determined
– Orbital period is constrained, but not fixed by the light curve
– The orbital period parameter can be interpreted as acceleration
or 3-d Star-Saturn distance (via a = GM/r2)
• Details in Bennett et al (2009) in preparation
Full Orbit Determination for
OGLE-2006-BLG-109Lc
• Series of fits with fixed orbital
acceleration (weight with fit 2)
• Each fit corresponds to a 1parameter family of orbits
parameterized by vz


– unless 1 v 2  v 2  GM  0
x
y
2
r
• Assume the Jupiter orbits in the
same plane and reject solutions
crossing the Jupiter orbit or that
are Hill-unstable
• Weight by prior probability of
orbital parameters
– planet is unlikely to be near
periastron if   0
Families of solutions corresponding to
best models at various values of a.
Full Orbit Determination for
OGLE-2006-BLG-109Lc
• Full calculation using Markov
chains run at fixed a.
• Include only Hill-stable orbits
• preliminary results:
M LA  0.54 0.02
0.03 M e
M Lc  0.29 0.01
0.02 M J
M Lb  0.77 0.02
0.04 M J
a Lc  4.0 2.3
0.7 AU
a Lb  2.0 0.4
0.2 AU
inclination  62 o 4
6
  0.14
0.13
0.10
• RV follow-up w/ 30m telescope
–K = 13 km/sec
Complication
• New models include terrestrial parallax - unlike the
results presented in Gaudi et al (2008)
• 2 improves by  2 = 12 - so orbital parallax is
“confirmed” by terrestrial parallax
• but, the best dJ > 1 models improve by  2 = 22, so they
are disfavored by only  2  1
• Fortunately, these models are almost entirely inconsistent
with stable, co-planar orbits
• So, the previous interpretation of a Jupiter orbiting inside
a Saturn remains unchanged.
Limits on Additional Planets
• Jupiter-mass planets excluded from projected separations
of 0.5-8.0 AU
• Planets with the same mass as OGLE-2006-BLG-109Lc
(0.27 Jupiter-masses) are excluded from projected
separations of 0.8-6.6 AU
• Planets of 10 Earth-masses are excluded from projected
separations of 1.8-2.8 AU, but such orbits probably aren’t
stable.
OGLE-2006-BLG-109Lb,c Summary
• 1st Jupiter+Saturn analog system
• 1st planets and host star with geometrically measured
masses
• 1st non-transiting, non-astrometric exoplanet with a
known orbital inclination
• Probably the first microlensing planetary system with a
host star brighter than the source
– ~ 5 brighter in H
• Best determined planetary parameters for a nontransiting planet (?)
• RV confirmation possible in 10yrs < t < 100 yrs
– an improvement over next microlensing confirmation in ~106 yrs
– hard, but easier than TPF or Darwin