Title: Triple-lens analysis of event OB07349/MB07379
1Triple-lens analysis of event OB07349/MB07379
- Yvette Perrott, MOA group
2Magnification 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.
3Three 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
4A typical high-resolution map and track
5Advantages 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.
6Cluster 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.
7First analysis of OB07349/MB07379
- Started with one-planet solution found by Dave
Bennett, and searched for second planet to fit
visible deviation.
82nd 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.
92nd 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.
10q2 10-5 search results
11q2 10-4
12q2 10-3
13q2 10-2
142nd 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.
15Method 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.
16Parallax 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.
17Terrestrial parallax - similar
- Add the small displacement from the Earths
centre to the position and velocity functions,
taking into account the Earths translation and
rotation.
18Results 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
19Track 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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21Results 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
22Track 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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24Results 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
25Track 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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27Results 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
28Track 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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30Parallax 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
31Comparison 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
32Sol 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
33Sol 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
34Sol 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
35Sol 3, ?2 881
Doesnt appear to correspond to any of Subos
solutions.
36Future plans
- Finish analysing the remaining minima
- Use MCMC for track parameters for speed and
better ?2 accuracy - Include HST data to identify lens
37Thanks
- 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