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Gravitational lensing and neutrinos

Why not look where natural lenses exist?

Proposal of an additional candidate list in point source search:1. Motivation and Theory2. Strong lenses and Galaxy clusters3. Candidate List4. Ask collaboration to reunblind 2007-2010 data next September

Internal note: ANTARES-PHYS-2012-008

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Gravitational lensing

Magnification of cosmic signals (higher fluxes)

Same geodesic for photons and neutrinos

Advantage: neutrinos not absorbed by lensed object

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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 andinverse proportional to min. distance

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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

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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)

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Galaxy and quasar lensed by galaxy cluster

Multiple images

Magnification

Gravitational light deflection order of tenth of arcsec

Lens z=0.68

Lens mass~1014Msun

Magnification for light between 1 to 20

Field of view: arcmin => Point like for us

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Summary of existing cluster catalogs

Telescopes:- Optical- X-ray- Earth based- In space

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Selection 1: Einstein angle Most of best studiedgalaxy clusters are also strongest gravitational lenses

Strong lensing objectsshow good constellationbetween observer,lens and source

Mass derived from strong and weak lensing

Selection:Einstein angle > 16”

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Selection 2: MassIf no info about Einstein angle

Planck selected galaxy clusters

Mass proportional to various other physical quantities like:X-ray temperature or luminositySelected only objects with M_500 > 10 * 1014 M_sun

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Selection cuts for different catalogs

Last two tables only used for crosscheckAround 50 galaxy clusters selected (remove multiple entries)

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Distance and Einstein angle distribution

Redshift between 0.15 and 0.9 Einstein angle between 16” and 55”

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Mass and mass/z distributionTake 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 * 1014

M_sun

Select only galaxy clusters with M_500/z > 40

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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 1830-211 at z=2.51, lens at z=0.89 JVASB0218+357 at z=0.94, lens at z=0.68 Both blazars are

not in gamma-ray flaring blazars paper

not in point source paper

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Final candidate list

Selection criteria: Einstein angle > 16´´ ANTARES visibility >20% M_500 > 10 * 1014 M_sun M_500/z > 40

Ten galaxy clusters +Two lensed blazars

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Skymap in equatorial coordinates of ten galaxy clusters and two lensed

quasars

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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)

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Outlook Finalize webpage

(http://antares.in2p3.fr/internal/dokuwiki/doku.php?id=gravitationallensing)

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 2007-2010 data Ask Juan Pablo to apply his well tested

candidate list search method Show results in Bologna

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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

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Images of galaxy clusters and gravitational lensed blazars

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Questions and answers

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Backup

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Three different Gravitational lensing regimes

1.Microlensing (change in brightness of observed lensed object)

2.Weak lensing (distortion of observed lensed objects)

3.3.Strong lensing Strong lensing (multiple images and high flux magnification of observed lensed object)

Select strong lensing objects

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Magnification and Probability (arXiv:0610918v1)

Magnification up to 1012

for small misalignmentProbability very smallfor huge amplification

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Selected galaxy clusters in equatorial coordinates

(not final selection)

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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):