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Triple-lens analysis of event OB07349/MB07379

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Magnification map technique. This technique was developed at Auckland, by Lydia ... It was developed for high magnification events with multiple lenses. ... – PowerPoint PPT presentation

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Title: Triple-lens analysis of event OB07349/MB07379


1
Triple-lens analysis of event OB07349/MB07379
  • Yvette Perrott, MOA group

2
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.

3
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
4
A typical high-resolution map and track
5
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.

6
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.

7
First analysis of OB07349/MB07379
  • Started with one-planet solution found by Dave
    Bennett, and searched for second planet to fit
    visible deviation.

8
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.

9
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.

10
q2 10-5 search results
11
q2 10-4
12
q2 10-3
13
q2 10-2
14
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.

15
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.

16
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.

17
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.

18
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

19
Track parameters
  • umin -0.00181 ? 0.325 ssr 0.00062 t0
    4348.7366 tE 111.61 ?E,E 0.11 ?E,N 0.21

20
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21
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

22
Track parameters
  • umin -0.00181 ? 0.317 ssr 0.000615 t0
    4348.7341 tE 110.66 ?E,E 0.11 ?E,N 0.11

23
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24
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

25
Track parameters
  • umin 0.00181 ? -0.315 ssr 0.00062 t0
    4348.7341 tE 110.41 ?E,E 0.12 ?E,N -0.06

26
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27
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

28
Track parameters
  • umin -0.00192 ? -0.341 ssr 0.000625 t0
    4348.7521 tE 111.31 ?E,E 0.10 ?E,N 0.38

29
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30
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
31
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
32
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
33
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
34
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
35
Sol 3, ?2 881
Doesnt appear to correspond to any of Subos
solutions.
36
Future plans
  • Finish analysing the remaining minima
  • Use MCMC for track parameters for speed and
    better ?2 accuracy
  • Include HST data to identify lens

37
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
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