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.  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 M H 4 x t E 0.8 x t E 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.  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.  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.  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 2 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.  The search procedure used for the track parameters was neither steepest descent or MCMC. Chi 2 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.

q 2 = search results Delta chi 2 values (from 1-planet minimum) < <x< <x< <x< <x< <x<0 > 0 q1q1 q2q2 q=1 b1b1 b2b2 a2a2

q 2 = Delta chi 2 values (from 1-planet minimum) < <x< <x< <x< <x< <x<0 > 0 q1q1 q2q2 q=1 b1b1 b2b2 a2a2

q 2 = Delta chi 2 values (from 1-planet minimum) < <x< <x< <x< <x< <x<0 > 0 q1q1 q2q2 q=1 b1b1 b2b2 a2a2

q 2 = Delta chi 2 values (from 1-planet minimum) < <x< <x< <x< <x< <x<0 > 0 q1q1 q2q2 q=1 b1b1 b2b2 a2a2

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.  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  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):  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): To galactic bulge Sun June March September (RA = 0) 23.5 ｺ Z Y X n e Ecliptic Earth at December

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  E is the direction of motion of the source.  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  E is the direction of motion of the source. Non-parallax track of source Parallax track of source   Lens u min

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 1 = ; b 1 = ; q 2 = 1.3x10 -5 ; b 2 = 0.73; a 2 = 194

Track parameters  u min = ;  = 0.325; ssr = ; t 0 = ; t E = ;  E,E = 0.11;  E,N = 0.21 u min 

Results of 2nd stage - Sol #2,  2 = 870 (u min negative) Planet parameters: q 1 = ; b 1 = 0.794; q 2 = 7x10 -6 ; b 2 = 0.955; a 2 = -3.5

Track parameters  u min = ;  = 0.317; ssr = ; t 0 = ; t E = ;  E,E = 0.11;  E,N = 0.11 u min 

Results of 2nd stage - Sol #2,  2 = 873 (u min positive) Planet parameters: q 1 = ; b 1 = 0.794; q 2 = 8.5x10 -6 ; b 2 = 0.952; a 2 = 183.5

Track parameters  u min = ;  = ; ssr = ; t 0 = ; t E = ;  E,E = 0.12;  E,N = u min 

Results of 2nd stage - Sol #3,  2 = 881 (u min negative) Planet parameters: q 1 = ; b 1 = ; q 2 = ; b 2 = 0.2; a 2 = 213

Track parameters  u min = ;  = ; ssr = ; t 0 = ; t E = ;  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 )  Only OGLE and MOA data used (older reduction)  Consistent with all solutions so far (negative u min )  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  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 Centre of mass Source at t 0 US system u min b1b1 Lens star q1q1 Source at t 0 NZ system u min b1b1 Lens star q1q1

u min  ssrt0t Sol #q1q1 b1b1 q2q2 b2b2 a2a x (Subo) x tEtE  E,E  E,N 2

u min  ssrt0t Sol #q1q1 b1b1 q2q2 b2b2 a2a2 2 (-ve) x (Subo) x tEtE  E,E  E,N 2

u min  ssrt0t Sol #q1q1 b1b1 q2q2 b2b2 a2a2 2 (+ve) x (Subo) x tEtE  E,E  E,N 2

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  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  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