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

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 Galaxy or galaxy cluster acting as lens Singular isothermal sphere (SIS) SIS-model takes into account the extended mass distribution Mass distribution (sigma=velocity dispersion) (sigma² ~ mass) Einstein angle Magnification Multiple images only if source inside Einstein ring: Solutions of the lens equation: (Again Einstein angle and Magnification are proportional to M)

6 Galaxy and quasar lensed by galaxy cluster Multiple images Magnification Gravitational light deflection order of tenth of arcsec Lens z=0.68 Lens mass~10 14 M sun Magnification for light between 1 to 20 Field of view: arcmin => Point like for us

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

8 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”

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

10 Selection cuts for different catalogs Last two tables only used for crosscheck Around 50 galaxy clusters selected (remove multiple entries)

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

12 Mass and mass/z distribution Take some conversion factor between M_500 and M_vir or M_x (large errors) Einstein angle and magnification are proportional to M/z Select only galaxy clusters with M_500 > 10 * M_sun Select only galaxy clusters with M_500/z > 40

13 Gravitational lensed neutrino source Take into account nature of source Electromagnetic information=>potential neutrino source Two blazars with bright flat spectrum and compact jets Both lensed by galaxy PKS at z=2.51, lens at z=0.89 JVASB at z=0.94, lens at z=0.68 Both blazars are not in gamma-ray flaring blazars paper not in point source paper

14 Final candidate list Selection criteria: Einstein angle > 16´´ ANTARES visibility >20% M_500 > 10 * M_sun M_500/z > 40 Ten galaxy clusters + Two lensed blazars

15 Skymap in equatorial coordinates of ten galaxy clusters and two lensed quasars

16 Discuss decisions For the selection should we take into account: Einstein angle? (Done) Mass, even when no lensing? (Done) Magnifications? (Not done) Nature of source? (Partially done)

17 Outlook Finalize webpage ( Finalize questions and answers note Apply same candidate list search method used in point source paper (assume E -2 spectrum) Beginning of September ask Collaboration to reunblind data Ask Juan Pablo to apply his well tested candidate list search method Show results in Bologna

18 Conclusion Gravitational lensing can increase by order of magnitude the signal from a source. Several papers on the subject. Selection criteria of candidate sources based on: 1. Einstein angle 2. Mass 3. Distance => ten galaxy cluster Two lensed quasars with compact jets Internal note written Unblinding request for beginning of September

19 Images of galaxy clusters and gravitational lensed blazars

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26 Questions and answers

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31 Backup

32 Three different G ravitational lensing regimes  Microlensing (change in brightness of observed lensed object)  Weak lensing (distortion of observed lensed objects)  Strong lensing  Strong lensing (multiple images and high flux magnification of observed lensed object) Select strong lensing objects

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

34 Selected galaxy clusters in equatorial coordinates (not final selection)

35 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):