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Statistical Analysis of Caustic Crossings in Multiply Imaged Quasars

This study presents a statistical analysis of caustic crossings in multiply imaged quasars, focusing on the concentration of caustics based on counts of caustic crossings. Applications to QSO 2237+0305 are explored through simulations and comparisons between observed and simulated microlensed effects. The study aims to simplify microlensing to discrete events and address statistical study problems related to experimental errors and variability. Methods include simulating magnification maps, identifying caustic curves, and estimating detection probabilities. Results show the impact of microlenses mass function and shear on caustic crossing statistics.

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Statistical Analysis of Caustic Crossings in Multiply Imaged Quasars

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  1. Statistical analysis of caustic crossings in multiply imaged quasars Teresa Mediavilla Gradolph Octavio Ariza Sánchez Evencio Mediavilla Gradolph Pilar Álvarez Ruíz

  2. Index Introduction Statistical analysis of the caustics concentration based on caustic crossings counts. Application to QSO 2237+0305 Conclusions

  3. Introduction

  4. Terrestrial mirage

  5. Light deflection by the Sun –1919 eclipse

  6. Gravitational mirage Without gravity With gravity

  7. First discovered gravitational lens (QSO 0957+561)

  8. QSO 2237+0305

  9. Microlensing

  10. One Source several imagesMagnification X Y T. LIOUVILLE

  11. Pixels-magnification map X Y

  12. Point-like lens magnification map

  13. Binary lens magnification map

  14. Magnification maps

  15. 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.

  16. Statistical study problems Experimental errors and intrinsical variability can affect data and results

  17. 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

  18. Statistical analysis of caustics concentration based on caustic crossings counts. Application to QSO 2237+0305

  19. Caustics concentration analysis

  20. 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.

  21. Application to QSO 2237+0305

  22. Magnification Maps 1 solar mass microlenses A Y B C D Microlenses distributed in a range of masses A Y B C D

  23. Caustics 1 solar mass microlenses C D A Y B Microlenses distributed in a range of masses A Y B C D

  24. Comparison with the binomial distribution (D image)

  25. Results (I) D IMAGE We can distinguish between A and B hypothesis

  26. Results (II) Can we solve the size / transversal velocity degeneracy?

  27. Results (II)

  28. Results (II) D image microlenses distributed in a range of masses Number of caustics (X axis) > 6 Window > 1.2 Einstein radii Number of caustics (X axis) < 3 Window < 1.2 Einstein radii Number of caustics (Y axis) > 9 Window > 1.2 Einstein radii Number of caustics (Y axis) < 3 Window < 1.2 Einstein radii

  29. 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

  30. Conclusions

  31. Conclusions Caustic crossing statistics is affected by the microlenses mass function and by shear. For QSO 2237+0305D 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

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