Triple-lens analysis of event OB07349/MB07379

Triple-lens analysis of event OB07349/MB07379

Yvette Perrott, MOA groupYvette Perrott, MOA group

Magnification map technique

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

Three maps - high, medium, low resolution

The three maps cover roughly the FWHM, tE, and bulge season respectively.

The three maps cover roughly the FWHM, tE, and bulge season respectively.

L

M

H4 x tE0.8 x tE

0.08 x tE

A typical high-resolution map and track

A typical high-resolution map and track

Advantages and disadvantages of the

method

Advantages and disadvantages of the

methodIt 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 usageCluster 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

First analysis of OB07349/MB07379

Started with one-planet solution found by Dave Bennett, and searched for second planet to fit visible deviation.

Started with one-planet solution found by Dave Bennett, and searched for second planet to fit visible deviation.

2nd planet search procedure(1st stage)

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.

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.

2nd planet search procedure cont’d2nd 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.

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.

q2 = 10-5 search resultsq2 = 10-5 search results

Delta chi2 values (from 1-planet

minimum)

< -600

-600<x<-500

-500<x<-400

-400<x<-300

-300<x<-200

-200<x<0

> 0

q1

q2

q=1

b1

b2

a2

q2 = 10-4q2 = 10-4

Delta chi2 values (from 1-planet

minimum)

< -600

-600<x<-500

-500<x<-400

-400<x<-300

-300<x<-200

-200<x<0

> 0

q1

q2

q=1

b1

b2

a2

q2 = 10-3q2 = 10-3

Delta chi2 values (from 1-planet

minimum)

< -600

-600<x<-500

-500<x<-400

-400<x<-300

-300<x<-200

-200<x<0

> 0

q1

q2

q=1

b1

b2

a2

q2 = 10-2q2 = 10-2

Delta chi2 values (from 1-planet

minimum)

< -600

-600<x<-500

-500<x<-400

-400<x<-300

-300<x<-200

-200<x<0

> 0

q1

q2

q=1

b1

b2

a2

2nd stage of search2nd 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.

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.

Method of including parallax

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.

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.

To galactic bulge

Sun

June

March

September(RA = 0)

23.5 ｺ

Z

Y

X

n

e

EclipticEarth at December

Parallax method cont’dParallax method cont’d

The corrections to the track of the source star are then given by

(,) = (Es, Es)

where rE = 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

(,) = (Es, Es)

where rE = 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

umin

Terrestrial parallax - similar

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.

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 (umin

negative)

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

Planet parameters: q1 = 0.0003841; b1 = 0.80689; q2 = 1.3x10-5; b2 = 0.73; a2 = 194

Track parametersTrack parametersumin = -0.00181; = 0.325; ssr = 0.00062; t0

= 4348.7366; tE = 111.61; E,E = 0.11; E,N = 0.21

umin = -0.00181; = 0.325; ssr = 0.00062; t0 = 4348.7366; tE = 111.61; E,E = 0.11; E,N = 0.21

umin

Results of 2nd stage - Sol #2, 2 = 870 (umin

negative)

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

Planet parameters: q1 = 0.000397; b1 = 0.794; q2 = 7x10-6; b2 = 0.955; a2 = -3.5

Track parametersTrack parametersumin = -0.00181; = 0.317; ssr = 0.000615;

t0 = 4348.7341; tE = 110.66; E,E = 0.11; E,N = 0.11

umin = -0.00181; = 0.317; ssr = 0.000615; t0 = 4348.7341; tE = 110.66; E,E = 0.11; E,N = 0.11

umin

Results of 2nd stage - Sol #2, 2 = 873 (umin positive)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

Planet parameters: q1 = 0.000395; b1 = 0.794; q2 = 8.5x10-6; b2 = 0.952; a2 = 183.5

Track parametersTrack parametersumin = 0.00181; = -0.315; ssr = 0.00062; t0

= 4348.7341; tE = 110.41; E,E = 0.12; E,N = -0.06

umin = 0.00181; = -0.315; ssr = 0.00062; t0 = 4348.7341; tE = 110.41; E,E = 0.12; E,N = -0.06

umin

Results of 2nd stage - Sol #3, 2 = 881 (umin

negative)

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

Planet parameters: q1 = 0.0003851; b1 = 0.80569; q2 = 0.0010; b2 = 0.2; a2 = 213

Track parametersTrack parametersumin = -0.00192; = -0.341; ssr = 0.000625;

t0 = 4348.7521; tE = 111.31; E,E = 0.10; E,N = 0.38

umin = -0.00192; = -0.341; ssr = 0.000625; t0 = 4348.7521; tE = 111.31; E,E = 0.10; E,N = 0.38

umin

Parallax from the wingsParallax from the wingsOnly OGLE and MOA data used (older

reduction)Consistent with all solutions so far (negative

umin)

Only OGLE and MOA data used (older reduction)

Consistent with all solutions so far (negative umin)

1 1

2 2

33

2 levels are at 1, 4, 9, 16,

25

Comparison with Subo Dong’s results (Ohio State)

Comparison with Subo Dong’s results (Ohio State)6 solutions, of which 2 correspond to oursNote different conventions: our results for

umin, t0 converted to US system; b1, b2 not converted

6 solutions, of which 2 correspond to oursNote different conventions: our results for

umin, t0 converted to US system; b1, b2 not converted

Centre of mass

Source at t0

US system

umin

b1

Lens star

q1

Source at t0

NZ system

umin

b1 Lens star

q1

umin ssr t0

-0.00210 0.325 0.00062 4348.7472

-0.0020802 0.322 0.0006177 4348.7471829

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

tEE,E E,N 2

111.61 0.11 0.21 902

112.12765 0.119 0.107 796.67

umin ssr t0

-0.00210 0.317 0.000615 4348.7447

-0.0021945 0.321 0.0006444 4348.7460743

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

tEE,E E,N 2

110.66 0.11 0.11 870

106.61081 0.117 0.009 769.09

umin ssr t0

0.00210 -0.315 0.00062 4348.7447

0.0020265 -0.321 0.0005883 4348.7459452

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

tEE,E E,N 2

110.41 0.12 -0.06 873

115.31758 0.114 -0.256 758.10

Sol #3, 2 = 881 Sol #3, 2 = 881

Doesn’t appear to correspond to any of Subo’s solutions.

Future plansFuture 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

ThanksThanks

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 discussionTo the IT department at Auckland University

for use of the clusterTo 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 discussionTo the IT department at Auckland University

for use of the clusterTo the North Harbour Club who helped to

fund my trip