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Studying the microlens mass function from statistical analysis of the caustic concentration

Studying the microlens mass function from statistical analysis of the caustic concentration. Teresa Mediavilla Gradolph Octavio Ariza Sánchez Evencio Mediavilla Gradolph. Introduction

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Studying the microlens mass function from statistical analysis of the caustic concentration

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  1. Studying the microlens mass function from statistical analysis of the caustic concentration Teresa Mediavilla Gradolph Octavio Ariza Sánchez Evencio Mediavilla Gradolph

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

  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. Magnification

  13. Inverse lens mapping

  14. Point like source magnification map

  15. Binary lens magnification map

  16. Magnification maps

  17. Simulation and statistical analysis • Comparison between observed and simulated microlensed effect allows 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.

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

  19. Simplify the problem reducing microlensing to a series of discrete events, the caustics 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 Objectives

  20. Statistical analysis of the caustic concentration based on caustic crossing counts. Application to QSO 2237+0305

  21. Caustic concentration analysis

  22. Application to QSO 2237+0305

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

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

  25. Comparison with the binomial distribution (D image)

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

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

  28. Results (II)

  29. Results (II) D imagemicrolensesdistributedin 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

  30. 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

  31. Conclusions

  32. Conclusions • Caustic crossing statistics is affected by the microlenses mass function and by the shear. • For QSO 2237+0305D the detection of a small number of events will allow to distinguish between the unimodal and distributed in a range mass distributions • We could determinate the size of the observing window

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