Triple-lens analysis of event OB07349/MB07379 Yvette Perrott, MOA group.
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Transcript of Triple-lens analysis of event OB07349/MB07379 Yvette Perrott, MOA group.
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