First Orbital Parameters for a Planet Found by Microlensing the Jupiter/Saturn analog system OGLE-2006-BLG-109Lb,c

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First Orbital Parameters for a Planet Found by
Microlensingthe Jupiter/Saturn analogsystem
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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The Physics of Microlensing

• Foreground lens star planet bend light of
  source star
• Multiple distorted images
• Only total brightness change is observable
• Sensitive to planetary mass
• Low mass planet signals are rare not weak
• Stellar lensing probability a few ?10-6
• Planetary lensing probability 0.001-1 depending
  on event details
• Peak sensitivity is at 2-3 AU the Einstein ring
  radius, RE

Einsteins telescope
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Microlensing Target Fields are in the Galactic
Bulge
Galactic center
Sun
8 kpc
1-7 kpc from Sun
Light curve
Source star and images
Lens star and planet
Telescope
10s of millions of stars in the Galactic bulge in
order to detect planetary companions to stars in
the Galactic disk and bulge.
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Lensed images at ?arcsec resolution
View from telescope
A planet can be discovered when one of the lensed
images approaches its projected position.
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Magnification Determined by Caustics
Planetary caustic Lower magnification Larger area
Host star (lens)
Planet (lens)
Central caustic High magnification

• Deviation from single-lens is largely determined
  by caustics. Multiple planet sensitivity in
  high magnification events.

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Properties of Microlensing Events

• At any given time in the Galactic bulge, 2 stars
  in a million are being microlensed
• So, wed like to monitor 100 million star to
  look for microlensing events
• The OGLE and MOA projects survey many 10s of
  millions of Galactic bulge stars and announce
  events in progress on the web.
• Stellar microlensing events typically last 1-2
  months
• Planetary microlensing events have durations from
  several hours to several days (duration
  )
• 24 hour light curve coverage is needed
• Global telescope networks
• PLANET (Probing Lensing Anomalies NETwork)
• MicroFUN (Microlensing Follow-Up Network)
• Includes amateurs

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Microlensing Observation Network
Survey Groups
Follow-up Groups
Micro- lensing Alert ?

• PLANET
• ?FUN
• (MOA)
• Pointing each candidate
• High cadence - to catch planetary deviations
• Strategy based on public photometry

• MOA(NewZealand)
• OGLE(Chile)
• Wide field
• Low cadence (until 2006)
• Continuous survey
• Each group discovers 500-600 events per year
• probably 700-800 events total with duplications

Anomaly Alert ??
Anyone who wants alert is welcome to sign up on
the websites.
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High Magnification Microlensing

• Disadvantage
• High magnification planet signals are more rare.
• Advantages
• Decent photometry is possible with small
  telescopes - including amateur astronomers.
• Long duration high magnification events can be
  predicted in advance, which allows high planet
  detection efficiency per observing hour.
• Sensitivity to planets over a wide range of
  separations - multiple planets can be detected or
  excluded
• But, event modeling is a bit more challenging.
• Events announced by OGLE MOA
• Monitored by PLANET ?FUN, which concentrates on
  high magnification events

12 Meade LX200R
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Microlensing Telescope Locations
Survey Telescopes
PLANET Network
MOA
OGLE
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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
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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
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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).

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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 planetary
event Model includes planet-star relative
velocity and acceleration
Feature due to Jupiter
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OGLE-2006-BLG-109Lb,c Caustics

• Curved source trajectory due to Earths orbital
  motion microlensing parallax
• Caustic curves plotted at 3-day intervals
• 0.2 of 14-yr orbit completed during planetary
  event
• Model includes planet-star relative velocity and
  acceleration

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Effect of Parallax Orbital Motion
Binary model similar to OGLE-06-109

• 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.

ratio to single lens light curve
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Characterization of Microlensing Planet Host
Stars with Light Curve Details and Follow-up
Observations
I dont understand. You are looking for planets
you cant see around stars you cant see.

• Debra Fischer
• RV planet hunter
• 2000 Microlensing Workshop

Microlensing events might only give mass ratio,
q, and separation, d/RE, in Einstein radius
units. We want more info on the planetary events
than this!
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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, , with
  the microlensing parallax effect (due to Earths
  orbital motion).

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Lens System Properties

• Einstein radius ?E ?tE/t and projected
  Einstein radius,
• ? the angular radius of the star
• from the microlensing parallax effect (due
  to Earths orbital motion).

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Finite Source Effects Microlensing Parallax
Yield Lens System Mass

• If only ?E or is measured, then we have a
  mass-distance relation.
• Such a relation can be solved if we detect the
  lens star and use a mass-luminosity relation
• This requires HST or ground-based adaptive optics
• With ?E, , and lens star brightness, we have
  more constraints than parameters

mass-distance relations
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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
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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 lenssource
  stars from the brighter star.
• But, sourcelens 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

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Implications of Light Curve Modelcircular orbit
case

• 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

• Other parameter values
• Jupiter mass mb 0.71 ? 0.08
  MJup semi-major axis
• Saturn mass mc 0.27 ? 0.03 MJup
  0.90 MSat semi-major axis
• Saturn orbital velocity vt 9.5 ?
  0.5 km/sec

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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

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Full Orbit Determination forOGLE-2006-BLG-109Lc

• Series of fits with fixed orbital acceleration
  (weight with fit ?2)
• Each fit corresponds to a 1-parameter family of
  orbits parameterized by vz
• unless
• 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.
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Full Orbit Determination forOGLE-2006-BLG-109Lc

• Full calculation using Markov chains run at fixed
  a.
• Include only Hill-stable orbits
• preliminary results

• RV follow-up w/ 30m telescope
• K 13 km/sec

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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 gt 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.

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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 arent stable.

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OGLE-2006-BLG-109Lb,c Summary

• 1st JupiterSaturn 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
  non-transiting planet (?)
• RV confirmation possible in 10yrs lt ?t lt 100 yrs
• an improvement over next microlensing
  confirmation in 106 yrs
• hard, but easier than TPF or Darwin