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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.

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Triple-lens analysis of event OB07349/MB07379

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  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 cont’d • 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. q1 b1 a2 Delta chi2 values (from 1-planet minimum) q=1 b2 < -600 q2 -600<x<-500 -500<x<-400 -400<x<-300 -300<x<-200 -200<x<0 > 0 q2 = 10-5 search results

  11. q1 b1 a2 Delta chi2 values (from 1-planet minimum) q=1 b2 < -600 q2 -600<x<-500 -500<x<-400 -400<x<-300 -300<x<-200 -200<x<0 > 0 q2 = 10-4

  12. q1 b1 a2 Delta chi2 values (from 1-planet minimum) q=1 b2 < -600 q2 -600<x<-500 -500<x<-400 -400<x<-300 -300<x<-200 -200<x<0 > 0 q2 = 10-3

  13. q1 b1 a2 Delta chi2 values (from 1-planet minimum) q=1 b2 < -600 q2 -600<x<-500 -500<x<-400 -400<x<-300 -300<x<-200 -200<x<0 > 0 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. Ecliptic March Earth at December Z Sun Y X 23.5ｺ n September (RA = 0) June To galactic bulge e Method of including parallax • 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.

  16. Non-parallax track of source   Lens Parallax track of source umin Parallax method cont’d • 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 Earth’s centre to the position and velocity functions, taking into account the Earth’s 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. umin  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. 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

  21. umin  Track parameters • umin = -0.00181;  = 0.317; ssr = 0.000615; t0 = 4348.7341; tE = 110.66; E,E = 0.11; E,N = 0.11

  22. 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

  23. umin Track parameters • umin = 0.00181;  = -0.315; ssr = 0.00062; t0 = 4348.7341; tE = 110.41; E,E = 0.12; E,N = -0.06

  24. 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

  25. umin  Track parameters • umin = -0.00192;  = -0.341; ssr = 0.000625; t0 = 4348.7521; tE = 111.31; E,E = 0.10; E,N = 0.38

  26. 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

  27. q1 q1 b1 b1 Lens star Lens star umin umin Source at t0 Source at t0 NZ system US system Comparison with Subo Dong’s 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

  28. Sol #3, 2 = 881 Doesn’t appear to correspond to any of Subo’s solutions.

  29. Future plans • Finish analysing the remaining minima • Use MCMC for track parameters for speed and better 2 accuracy • Include HST data to identify lens

  30. 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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