Gravitational lensing and neutrinos
Internal note: ANTARES-PHYS-2012-008
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 2007-2010 data next September
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Gravitational lensing
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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:
Deflection proportional to mass and
inverse proportional to min. distance
Lens equation:
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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
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Multiple images
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Magnification
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Gravitational light
deflection order of
tenth of arcsec
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Lens z=0.68
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Lens mass~1014Msun
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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 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:
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Einstein angle > 16”
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 * 1014 M_sun
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Selection cuts for different catalogs
Last two tables only used for crosscheck
Around 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 distribution
Take some conversion factor between
M_500 and M_vir or M_x (large errors)
Select only galaxy clusters with
M_500 > 10 * 1014 M_sun
Einstein angle and magnification
are proportional to M/z
Select only galaxy clusters with
M_500/z > 40
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Gravitational lensed neutrino source
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Take into account nature of source
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Electromagnetic information=>potential neutrino source
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Two blazars with bright flat spectrum and compact jets
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Both lensed by galaxy
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PKS 1830-211
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JVASB0218+357 at z=0.94, lens at z=0.68
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Both blazars are
at z=2.51, lens at z=0.89
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%
14 M_sun
 M_500 > 10 * 10
 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:
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Einstein angle?
(Done)
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Mass, even when no lensing? (Done)
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Magnifications?
(Not done)

Nature of source?
(Partially done)
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Outlook
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Finalize webpage
(http://antares.in2p3.fr/internal/dokuwiki/doku.php?id=gravitationallensing)
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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
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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
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Internal note written
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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. 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 misalignment
Probability very small
for huge amplification
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Selected galaxy clusters in
equatorial coordinates
(not final selection)
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Magnification Objects and Magnification power
Gravitational Lensing Objects:
1. Black Hole in Galactic Center
2. Galaxies
(CASTLES Catalog)
3. Galaxy clusters
(MCXC Catalog, etcetera)
For near perfect alignment (is very rare):
If finite source of radius R_s => Galaxy clusters have magnification of 10¹²
[Magnification of extended source given as
Order(10)]
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