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, tE, and bulge season
respectively.
4 x tE
0.8 x tE
M
H
L
0.08 x tE
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 umin negative solutions were considered.
Low resolution maps were used, with
accuracy in chi2 ~ 20.
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.
q2 = 10-5 search results
q1
b1
a2
q=1
b2
q2
Delta chi2 values
(from 1-planet
minimum)
< -600
-600<x<-500
-500<x<-400
-400<x<-300
-300<x<-200
-200<x<0
>0
q2 =
10-4
q1
b1
a2
q=1
b2
q2
Delta chi2 values
(from 1-planet
minimum)
< -600
-600<x<-500
-500<x<-400
-400<x<-300
-300<x<-200
-200<x<0
>0
q2 =
10-3
q1
b1
a2
q=1
b2
q2
Delta chi2 values
(from 1-planet
minimum)
< -600
-600<x<-500
-500<x<-400
-400<x<-300
-300<x<-200
-200<x<0
>0
q2 =
10-2
q1
b1
a2
q=1
b2
q2
Delta chi2 values
(from 1-planet
minimum)
< -600
-600<x<-500
-500<x<-400
-400<x<-300
-300<x<-200
-200<x<0
>0
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.
Method of including parallax
Ecliptic
March
Earth at December
Z
Sun
Y
X
23.5ｺ
n
June
September
(RA = 0)
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)
Non-parallax track of source
where rE = AU/|E|,
and the direction of


Lens
E is the direction of
Parallax track of source
u
motion of the source.
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 (umin negative)
Planet parameters: q1 = 0.0003841; b1 =
0.80689; q2 = 1.3x10-5; b2 = 0.73; a2 = 194
Track parameters
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)
Planet parameters: q1 = 0.000397; b1 = 0.794;
q2 = 7x10-6; b2 = 0.955; a2 = -3.5
Track parameters
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)
Planet parameters: q1 = 0.000395; b1 = 0.794;
q2 = 8.5x10-6; b2 = 0.952; a2 = 183.5
Track parameters
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)
Planet parameters: q1 = 0.0003851; b1 =
0.80569; q2 = 0.0010; b2 = 0.2; a2 = 213
Track parameters
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 wings
Only OGLE and MOA data used (older reduction)
Consistent with all solutions so far (negative umin)
3
3
1
2
1
2
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 umin, t0
converted to US system; b1, b2 not converted
q1
b1
Lens
star
umin
q1
b1
Lens
star
Centre of mass
umin
Source at t0
Source at t0
NZ system
US system
Sol # q1
1
b1
0.0003841 0.80689
q2
b2
a2
1.3x10-5
0.73
194
3
0.0003791 0.8073938 0.504x10-5 0.871897 193.1
(Subo)
umin

ssr
t0
-0.00210
0.325
0.00062
4348.7472
-0.0020802
0.322
0.0006177
4348.7471829
tE
E,E
E,N
2
111.61
0.11
0.21
902
112.12765
0.119
0.107
796.67
Sol # q1
b1
q2
b2
a2
2 (-ve) 0.000397
0.794
7x10-6
0.955
-3.5
5
0.0004034 0.7962501 8.10x10-6 0.9526577 -3.51
(Subo)
umin

ssr
t0
-0.00210
0.317
0.000615
4348.7447
-0.0021945
0.321
0.0006444
4348.7460743
tE
E,E
E,N
2
110.66
0.11
0.11
870
106.61081
0.117
0.009
769.09
Sol # q1
b1
q2
b2
a2
2
0.000395 0.794
8.5x10-6 0.952
183.5
(+ve)
5
0.0003731 0.7946362 8.68x10-6 0.9454526 183.72
(Subo)
umin

ssr
t0
0.00210
-0.315
0.00062
4348.7447
0.0020265
-0.321
0.0005883
4348.7459452
tE
E,E
E,N
2
110.41
0.12
-0.06
873
115.31758
0.114
-0.256
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