1 Gravitational lensing and neutrinos Why not look where natural lenses exist? Proposal of an additional candidate list in point source search: 1. Motivation 2. Theory 3. Strong lenses and Galaxy clusters 4. Candidate List 5. Ask collaboration to reunblind data

2 Gravitational lensing ● Magnification of cosmic signals (higher fluxes) ● Same geodesic for photons and neutrinos ● Advantage: neutrinos not absorbed by lensed object

3 Lensing geometry and Lens equation Deflection angle: (for spheric sym. Mass distribution) From Figure: (small angles) Reduced deflection angle: Lens equation: Deflection proportional to mass and inverse proportional to min. distance

4 Einstein angle and Magnification Einstein angle: (derived from lens equation) Magnification: (for near perfect alignment) Both Einstein angle and Magnification are proportional to M/D_OL

5 Highest massive objects in universe: Galaxy clusters Multiple images and magnification of two Galaxy clusters CL Abell 1689 One of the most massive cluster known with many lensed images Size around one arcmin

6 Typical values for Galaxy clusters ● Abell 383 ● z=0.189 ● Gravitational light deflection order of tenth of arcsec ● 27 multiple images of 9 systems ● Mass ~ M sun ● Magnification for light between 1 to 20

7 Gravitational Lensing Objects: 1. Black Hole in Galactic Center 2. Galaxies (CASTLES Catalog) 3. Galaxy clusters (MCXC Catalog, etcetera) Magnification Objects and Magnification power If finite source of radius R_s => Galaxy clusters have magnification of 10¹² [Magnification of extended source given as Order(10)] For near perfect alignment (is very rare):

8 Summary of existing cluster catalogs Telescopes: - Optical - X-ray - Earth based - In space

9 Selection 1: Einstein angle Most of best studied galaxy clusters are also strongest gravitational lenses Strong lensing objects show good constellation between observer, lens and source Mass derived from strong and weak lensing Selection: Einstein angle > 16”

10 If no info about Einstein angle Selection 2: Mass Planck selected galaxy clusters Mass proportional to various other physical quantities like: X-ray temperature or luminosity M_500 > 10 * M_sun

11 Selection cuts for different catalogs Last two tables only used for crosscheck Around 50 galaxy clusters selected

12 Distance and Einstein angle distribution Redshift between 0.15 and 0.9 Einstein angle between 16” and 55”

13 Mass and mass/z distribution Take some conversion factor between M_500 and M_vir or M_x Einstein angle and magnification are proportional to M/z

14 Selected galaxy clusters in equatorial coordinates (not final selection) Sky map produced by Juan Pablo

15 Possible final candidate list Selection criteria: ● Einstein angle > 16´´ ● M_500 > 10 * M_sun ● ANTARES visibility >20% ● M_500/z > 40 List with 12 galaxy clusters

16 Outlook ● Gravitational lensing expert Jose Muñoz suggests to use isothermal sphere instead of point mass lenses ● Referee suggests to find in addition to galaxy clusters also some known neutrino sources which are lensed ● Apply same candidate list search method used in point source paper (assume E -2 spectrum) ● Internal note ● Ask Collaboration to reunblind data ● Ask Juan Pablo to apply his well tested candidate list search method

17 Conclusion ● Gravitational lensing used to enhance hypothetical cosmic neutrino flux ● Select Galaxy Clusters with large Einstein angle or mass ● Internal note in preparation ● Ask Collaboration to reunblind data ● Publish gravitational lensing and neutrino results

18 Backup

19 Three different G ravitational lensing regimes 1.Microlensing (change in brightness of observed lensed object) 2.Weak lensing (distortion of observed lensed objects) 3.Strong lensing 3.Strong lensing (multiple images and high flux magnification of observed lensed object) Select strong lensing objects

20 Magnification and Probability (arXiv: v1) Magnification up to for small misalignment Probability very small for huge amplification

21 Backup (Clash paper)

22 Backup

23 Referees and Discussions ● Referees: - Véronique: Author of gravitational lensing paper - Juande: Profound knowledge on point source searches ● Two phone meetings (in February) - Reasonable assumptions (point-like, near perfect alignment) - Reliable magnification formula (factor 2) - Optimize in a first step for Mass and in a second step for M/z - Started to send questions