Triple-lens analysis of event OB07349/MB07379

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Triple-lens analysis of event OB07349/MB07379

• Yvette Perrott, MOA group

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Magnification map technique

• This technique was developed at Auckland, by
  Lydia Philpott, Christine Botzler, Ian Bond, Nick
  Rattenbury and Phil Yock.
• It was developed for high magnification events
  with multiple lenses.

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Three maps - high, medium, low resolution

• The three maps cover roughly the FWHM, tE, and
  bulge season respectively.

L
M
4 x tE
H
0.08 x tE
0.8 x tE
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A typical high-resolution map and track
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Advantages and disadvantages of the method

• It is straightforward conceptually, and can be
  applied to any combination of lens and source
  geometries.
• Many tracks can be laid across the same map.
• It is not the fastest way.

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Cluster usage

• We use a cluster of teaching computers during
  weeknights, weekends and holidays. This keeps
  the cost down, but they are not always available
  or reliable.
• The codes are written in C for reliability, at
  the cost of speed.

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First analysis of OB07349/MB07379

• Started with one-planet solution found by Dave
  Bennett, and searched for second planet to fit
  visible deviation.

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2nd planet search procedure(1st stage)

• Searched for low mass planets fairly near to the
  ring, and higher mass planets further away.
• Only solutions with both planets inside the ring
  were considered.
• Only umin negative solutions were considered.
• Low resolution maps were used, with accuracy in
  chi2 20.

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2nd planet search procedure contd

• The search procedure used for the track
  parameters was neither steepest descent or MCMC.
  Chi2 values are calculated over a grid of track
  parameter values until a minimum not using an
  edge value in any parameter is found.
• Three trials are conducted using randomised
  starting points and coarse step sizes, then the
  best minimum found in this way is used as a
  starting point for a final minimisation using
  fine step sizes.

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q2 10-5 search results
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q2 10-4
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q2 10-3
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q2 10-2
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2nd stage of search

• Mass and position of both planets varied.
• Orbital and terrestrial parallax effects
  included.
• Higher resolution maps used to increase accuracy
  to chi2 a few.
• umin positive and negative solutions explored.

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Method of including parallax

• The suns apparent motion around the Earth is
  calculated as in
• Gould, A. Resolution of the MACHO-LMC-5
  Puzzle the Jerk-Parallax Microlens Degeneracy.
  Astrophys.J. 606 (2004) 319-325.

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Parallax method contd

• The corrections to the track of the source star
  are then given by
• (??,??) (?E??s, ?E??s)
• where rE AU/?E,
• and the direction of
• ?E is the direction of
• motion of the source.

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Terrestrial parallax - similar

• Add the small displacement from the Earths
  centre to the position and velocity functions,
  taking into account the Earths translation and
  rotation.

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Results of 2nd stage - Sol 1, ?2 902 (umin
negative)

• Planet parameters q1 0.0003841 b1 0.80689
  q2 1.3x10-5 b2 0.73 a2 194

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Track parameters

• umin -0.00181 ? 0.325 ssr 0.00062 t0
  4348.7366 tE 111.61 ?E,E 0.11 ?E,N 0.21

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Results of 2nd stage - Sol 2, ?2 870 (umin
negative)

• Planet parameters q1 0.000397 b1 0.794 q2
  7x10-6 b2 0.955 a2 -3.5

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Track parameters

• umin -0.00181 ? 0.317 ssr 0.000615 t0
  4348.7341 tE 110.66 ?E,E 0.11 ?E,N 0.11

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Results of 2nd stage - Sol 2, ?2 873 (umin
positive)

• Planet parameters q1 0.000395 b1 0.794 q2
  8.5x10-6 b2 0.952 a2 183.5

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Track parameters

• umin 0.00181 ? -0.315 ssr 0.00062 t0
  4348.7341 tE 110.41 ?E,E 0.12 ?E,N -0.06

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Results of 2nd stage - Sol 3, ?2 881 (umin
negative)

• Planet parameters q1 0.0003851 b1 0.80569
  q2 0.0010 b2 0.2 a2 213

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Track parameters

• umin -0.00192 ? -0.341 ssr 0.000625 t0
  4348.7521 tE 111.31 ?E,E 0.10 ?E,N 0.38

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Parallax from the wings

• Only OGLE and MOA data used (older reduction)
• Consistent with all solutions so far (negative
  umin)

??2 levels are at 1, 4, 9, 16, 25
3
3
1
1
2
2
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Comparison with Subo Dongs results (Ohio State)

• 6 solutions, of which 2 correspond to ours
• Note different conventions our results for umin,
  t0 converted to US system b1, b2 not converted

Centre of mass
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Sol q1 b1 q2 b2 a2
1 0.0003841 0.80689 1.3x10-5 0.73 194
3 (Subo) 0.0003791 0.8073938 0.504x10-5 0.871897 193.1
umin ? ssr t0
-0.00210 0.325 0.00062 4348.7472
-0.0020802 0.322 0.0006177 4348.7471829
tE ?E,E ?E,N ?2
111.61 0.11 0.21 902
112.12765 0.119 0.107 796.67
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Sol q1 b1 q2 b2 a2
2 (-ve) 0.000397 0.794 7x10-6 0.955 -3.5
5 (Subo) 0.0004034 0.7962501 8.10x10-6 0.9526577 -3.51
umin ? ssr t0
-0.00210 0.317 0.000615 4348.7447
-0.0021945 0.321 0.0006444 4348.7460743
tE ?E,E ?E,N ?2
110.66 0.11 0.11 870
106.61081 0.117 0.009 769.09
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Sol q1 b1 q2 b2 a2
2 (ve) 0.000395 0.794 8.5x10-6 0.952 183.5
5 (Subo) 0.0003731 0.7946362 8.68x10-6 0.9454526 183.72
umin ? ssr t0
0.00210 -0.315 0.00062 4348.7447
0.0020265 -0.321 0.0005883 4348.7459452
tE ?E,E ?E,N ?2
110.41 0.12 -0.06 873
115.31758 0.114 -0.256 758.10
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Sol 3, ?2 881
Doesnt appear to correspond to any of Subos
solutions.
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Future plans

• Finish analysing the remaining minima
• Use MCMC for track parameters for speed and
  better ?2 accuracy
• Include HST data to identify lens

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Thanks

• To the observatories and groups that provided
  data OGLE, Bronberg, FTN, CTIO, MOA, Palomar,
  UTAS, Perth, VintageLane
• To Ian Bond and Subo Dong for data reductions
• To Andy Gould and Subo Dong for discussion
• To the IT department at Auckland University for
  use of the cluster
• To the North Harbour Club who helped to fund my
  trip