Transcript Triple-lens analysis of event OB07349/MB07379
Triple-lens analysis of event OB07349/MB07379 Yvette Perrott, MOA group
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.
Three maps - high, medium, low resolution The three maps cover roughly the FWHM, t E , and bulge season respectively.
L 4 x t E 0.8 x t E M H 0.08 x t E
A typical high-resolution map and track
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.
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.
First analysis of OB07349/MB07379 Started with one-planet solution found by Dave Bennett, and searched for second planet to fit visible deviation.
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 u min negative solutions were considered.
Low resolution maps were used, with accuracy in chi 2 ~ 20.
2nd planet search procedure cont’d The search procedure used for the track parameters was neither steepest descent or MCMC. Chi found.
2 values are calculated over a grid of track parameter values until a minimum not using an edge value in any parameter is 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.
q 2 = 10 -5 search results q=1 b 1 q 1 b 2 a 2 q 2 Delta chi 2 values (from 1-planet minimum) < -600 -600
q 2 = 10 -4 q 1 q=1 b 1 a 2 b 2 q 2 Delta chi 2 values (from 1-planet minimum) < -600 -600
q 2 = 10 -3 q 1 q=1 b 1 a 2 b 2 q 2 Delta chi 2 values (from 1-planet minimum) < -600 -600
q 2 = 10 -2 q 1 q=1 b 1 a 2 b 2 q 2 Delta chi 2 values (from 1-planet minimum) < -600 -600
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 chi 2 ~ a few.
u min positive and negative solutions explored.
Method of including parallax Ecliptic March Earth at December
Z
Sun
Y
23.5
ｺ
X n
September (RA = 0) June To galactic bulge
e
The sun’s 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.
Parallax method cont’d The corrections to the track of the source star are then given by ( , ) = (
E
s,
E
s) where r E = AU/| E |, and the direction of Non-parallax track of source E is the direction of motion of the source.
Lens u min Parallax track of source
Terrestrial parallax - similar Add the small displacement from the Earth’s centre to the position and velocity functions, taking into account the Earth’s translation and rotation.
Results of 2nd stage - Sol #1, 2 = 902 (u min negative) Planet parameters: q 0.80689; q 2 1 = 0.0003841; b 1 = 1.3x10
-5 ; b 2 = 0.73; a 2 = = 194
Track parameters u min = -0.00181; 4348.7366; t E = 0.325; ssr = 0.00062; t 0 = 111.61; E,E = 0.11; E,N = = 0.21
u min
Results of 2nd stage - Sol #2, 2 = 870 (u min negative) Planet parameters: q q 2 = 7x10 -6 ; b 2 1 = 0.000397; b 1 = 0.955; a 2 = -3.5
= 0.794;
Track parameters u min = -0.00181; 4348.7341; t E = 0.317; ssr = 0.000615; t 0 = 110.66; E,E = 0.11; E,N = 0.11
= u min
Results of 2nd stage - Sol #2, 2 = 873 (u min positive) Planet parameters: q q 2 = 8.5x10
-6 ; b 2 1 = 0.000395; b = 0.952; a 2 1 = 0.794; = 183.5
Track parameters u min = 0.00181; 4348.7341; t E = -0.315; ssr = 0.00062; t 0 = 110.41; E,E = 0.12; E,N = = -0.06
u min
Results of 2nd stage - Sol #3, 2 = 881 (u min negative) Planet parameters: q 0.80569; q 2 1 = 0.0003851; b 1 = 0.0010; b 2 = 0.2; a 2 = = 213
Track parameters u min = -0.00192; 4348.7521; t E = -0.341; ssr = 0.000625; t 0 = 111.31; E,E = 0.10; E,N = 0.38
= u min
Parallax from the wings Only OGLE and MOA data used (older reduction) Consistent with all solutions so far (negative u min ) 3 1 2 3 2 1 2 levels are at 1, 4, 9, 16, 25
Comparison with Subo Dong’s results (Ohio State) 6 solutions, of which 2 correspond to ours Note different conventions: our results for u min , t 0 converted to US system; b 1 , b 2 not converted q 1 q 1 b 1 b 1 Lens star u min Lens star Centre of mass u min Source at t 0 Source at t 0 NZ system US system
Sol # q 1 1 3 (Subo) b 1 0.0003841 0.80689
q 2 1.3x10
-5 0.0003791 0.8073938 0.504x10
-5 b 2 0.73
a 2 194 0.871897 193.1
u min -0.00210
-0.0020802
0.325
0.322
ssr 0.00062
0.0006177
t 0 4348.7472
4348.7471829
t E 111.61
112.12765
E,E 0.11
0.119
E,N 0.21
0.107
2 902 796.67
Sol # q 1 2 (-ve) 0.000397
b 1 0.794
q 2 7x10 -6 b 2 0.955
a 2 -3.5
5 (Subo) u min -0.00210
0.0004034 0.7962501 8.10x10
-6 0.317
ssr 0.000615
-0.0021945
0.321
0.0006444
0.9526577 -3.51
t 0 4348.7447
4348.7460743
t E 110.66
106.61081
E,E 0.11
0.117
E,N 0.11
0.009
2 870 769.09
Sol # q 1 2 (+ve) 0.000395
5 (Subo) b 1 0.794
q 2 8.5x10
-6 0.0003731 0.7946362 8.68x10
-6 b 2 0.952
a 2 183.5
0.9454526 183.72
u min 0.00210
0.0020265
-0.315
-0.321
ssr 0.00062
0.0005883
t 0 4348.7447
4348.7459452
t E 110.41
115.31758
E,E 0.12
0.114
E,N -0.06
-0.256
2 873 758.10
Sol #3, 2 = 881 Doesn’t appear to correspond to any of Subo’s solutions.
Future plans Finish analysing the remaining minima Use MCMC for track parameters for speed and better 2 accuracy Include HST data to identify lens
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