Statistical analysis of caustic crossings in multiply imaged quasars

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Statistical analysis of caustic crossings in
multiply imaged quasars

• Teresa Mediavilla Gradolph
• Octavio Ariza Sánchez
• Evencio Mediavilla Gradolph
• Pilar Álvarez Ruíz

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Index

• Introduction
• Statistical analysis of the caustics
  concentration based on caustic crossings counts.
  Application to QSO 22370305
• Conclusions

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Introduction
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Terrestrial mirage
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Light deflection by the Sun 1919 eclipse
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Gravitational mirage
Without gravity
With gravity
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First discovered gravitational lens
(QSO 0957561)
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QSO 22370305
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Microlensing
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One Source several imagesMagnification
X
Y
T. LIOUVILLE
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Pixels-magnification map
X
Y
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Point-like lens magnification map
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Binary lens magnification map
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Magnification maps
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Simulation and statistical analysis

• Comparison between observed and simulated
  microlensed effect allows us to study
• Source
• Size at different wavelengths.
• Quasar luminosity profile
• Lens galaxy
• Mass distribution
• Microlenses
• Abundance
• Mass
• Lens system
• Transversal velocity
• Determination of these parameters can be only
  statistically done.

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Statistical study problems

• Experimental errors and intrinsical variability
  can affect data and results

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Objectives

• Simplify the problem reducing microlensing to a
  series of discrete events, caustic crossings. If
  the source size is small enough
• They appear well separated
• They are of high magnification
• They are difficult to mistake with other
  variability features

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Statistical analysis of caustics concentration
based on caustic crossings counts. Application to
QSO 22370305
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Caustics concentration analysis
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Analysis steps

• Simulate magnification maps for different
  densities of matter, different mass distribution
  and shear.
• Identify caustic curves
• Count the number of caustics detected in a
  one-dimensional window of certain size in pixels
  for each axis
• Estimate probability of detecting a caustic in a
  pixel for each axis
• Compare experimental distributions obtained in
  simulations with theoretical binomial
  distribution.
• We have used the method of Inverse Polygon
  Mapping to carry out two first steps.

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Application to QSO 22370305
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Magnification Maps
1 solar mass microlenses
A Y B
C
D
Microlenses distributed in a range of masses
A Y B
C
D
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Caustics
1 solar mass microlenses
C
D
A Y B
Microlenses distributed in a range of masses
A Y B
C
D
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Comparison with the binomial distribution (D
image)
Masses in a range Peak Centroid
400 pixels X axis 6 7
200 pixels X axis 3 3
400 pixels Y axis 9 10
200 pixels Y axis 3 4
Unimodal distribution Peak Centroid
400 pixels X axis 1 1
200 pixels X axis 0 0
400 pixels Y axis 0 2
200 pixels Y axis 0 0
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Results (I)
D IMAGE
X AXIS X AXIS
n7, error 3 P(7 3/A)0.63 P(7 3/B)0.22 n1, error 1 P(1 1/A)0.049 P(1 1/B)0.66
P(A/7)0.75 P(B/7)0.25 P(A/1)0.07 P(B/1)0.93
Y AXIS Y AXIS
n10, error 3 P(10 3/A)0.37 P(10 3/B)0.12 n2, error 1 P(2 1/A)0.12 P(2 1/B)0.38
P(A/10)0.76 P(B/10)0.24 P(A/2)0.24 P(B/2)0.76
We can distinguish between A and B hypothesis
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Results (II)
Can we solve the size / transversal velocity
degeneracy?
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Results (II)
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Results (II)
D image microlenses distributed in a range of
masses Number of caustics (X axis) gt 6
Window gt 1.2 Einstein radii Number of caustics
(X axis) lt 3 Window lt 1.2 Einstein
radii Number of caustics (Y axis) gt 9
Window gt 1.2 Einstein radii Number of caustics
(Y axis) lt 3 Window lt 1.2 Einstein radii
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Bayesian Analysis
D image
400 pixels X axis
400 píxels Y axis
In a 76 of cases we can distinguish between both
hypothesis with more than 80 of likelihood
In a 77 of cases we can distinguish between
both hypothesis with more than 70 of likelihood
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Conclusions
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Conclusions

• Caustic crossing statistics is affected by the
  microlenses mass function and by shear.
• For QSO 22370305D detection of a small number of
  events will allow us to distinguish between
  unimodal and distributed in a range mass
  distributions.
• We could determinate the size of the observing
  window