4. Einstein Angle and MagnificationThe angular deflection for a relativistic neutrino with mass mʋ that passes by a compact lens of mass M with impact parameter b is

where Eʋ is the energy of the neutrino, G is the gravitational constant and c is the speed of light in vacuum. For astrophysical neutrinos with mʋ~1 eV and Eʋ~1 TeV, the value mʋ

2/2Eʋ2 <<1 and

the deflection angle difference between photon and neutrino is negligible. Therefore this Equation simplifies to the deflection angle known from photons and the neutrino is treated as a massless particle.

The Figure above shows a general lensing configuration. The Einstein angle for such a configuration is given by

The observed magnification μs of a finit-size source is

Galaxy clusters can enhance the photon flux observed from sources behind them through gravitational lensing. Neutrino fluxes would also be enhanced by this effect, and this could allow the observation of sources otherwise below the detection threshold. Neutrinos, contrary to photons, would not be absorbed by the gravitational lens. Therefore, sources with a moderate observed gamma-ray flux could be interesting candidates for neutrino telescopes. This paper presents the outcome of a search for cosmic neutrinos in the direction of a selected sample of eleven of the most promising gravitational lenses using the data collected from 2007 to 2010 by the ANTARES telescope. The result of this search shows no excess of neutrino events over the background for the directions considered.

Gravitational Lensing and Neutrinos with the ANTARES Deep Sea Telescope

Salvatore Mangano (manganos@ific.uv.es)IFIC (Instituto de Física Corpuscular) CSIC – University of Valencia, Spain

on behalf of the ANTARES Collaboration

ICRC2013, 33RD INTERNATIONAL COSMIC RAY CONFERENCE, RIO DE JANEIRO 2013

1.Gravitational Lensing of Electromagnetic Radiation Gravitational lensing of electromagnetic radiation from distant

astrophysical sources is a well-known prediction of Einstein's general relativity. The gravitational bending of light generated by mass or energy concentrations along a light path produces magnification, distortion and multiple images of a background source. The following picture shows a spectacular image taken by the Hubble Space Telescope, where a quasar and a galaxy are lensed by a galaxy cluster.

6. Search for Neutrino Emission from Gravitational Lensed SourcesThe search for neutrino emission from gravitational lensed sources has been performed using an unbinned maximum likelihood method. The likelihood function is maximized with respect to the number of signal events, ns,for a fixed direction for each source in the list. The ratio between the value of the likelihood given by the maximization and the likelihood computed for the only-background case is used as a test statistic, λ. In the absence of a significant excess of neutrinos above the expected background an upper flux limit is calculated. The flux upper limits are calculated at 90% confidence level using the approach from Feldman & Cousins.

The results from the search for neutrino emission from the direction of the eleven gravitationally lensed systems for ANTARES data corresponding to the 2007-2010 period are presented in the Table on the right. No excess of neutrino events is found at any of the selected locations and upper limits on the neutrino flux intensity are presented in the Figure on the right.

3. ANTARES Neutrino TelescopeThe ANTARES neutrino telescope is located on the bottom of the Mediterranean Sea (42050´ N, 6º10´ E) at a depth of 2.5 km. The detector consists of 885 photomultiplier tubes mounted on twelve lines. Sea water is used as the detection medium of the Cherenkov light induced by the muons produced in the interactions of neutrinos. The design of ANTARES is optimized for the detection of up-going muons produced by neutrinos which have traversed the Earth, in order to limit the background from down-going atmospheric muons.

2. Gravitational Lensing of NeutrinosCosmic neutrinos are expected to be emitted along with gamma-rays by astrophysical sources in processes involving the interaction of accelerated hadrons. Both gamma-rays and neutrinos will be similarly deflected by any sufficiently massive object interposed between the source and the observer. While the limited angular resolution of neutrino telescopes prevents the observation of multiple-image patterns, the telescopes could be sensitive to an overall enhancement of the neutrino flux from lensed sources.

The Table shows the eleven selected gravitational lensing systems. The equatorial coordinates, the ANTARES visibility, the source redshift (if applicable), the lens redshift, the Einstein angle and the minimal and maximal estimated total magnification are listed. The first nine objects are gravitationally lensed quasars. PKS 1830 and B0218 are gravitationally lensed quasars with bright flat radio spectrum and compact jets and have gamma emission.  B1422 and B1030 are BL Lac objects. J1131, J1004, J0924 and J0911 have quadruple images with large magnifications and with X-ray emission.  J1029 is the largest separation image quasar with X-ray emission. The galaxy clusters A1689 and A370 are well known gravitational lenses with large Einstein angles and large estimated masses.

The following Table shows the results from the search for high-energy neutrinos from sources behind gravitational lenses. The equatorial coordinates, the observed test statistics value, λobs ,the fitted number of signal events, ns ,the p-value and the 90% CL upper limit on the E-2 flux in units of 10-8GeV-1cm-2s-1 are given for the eleven directions.

Upper limits (at 90% CL) on the E-2 neutrino flux from the eleven selected gravitational lensed sources as a function of their declination. Upper limits from other experiments for other sources are also shown.

The colour code means the visibility of the ANTARES telescope for detecting upward going particles, where 1 indicates a visibility of 100%.

5. Gravitational Lensing of NeutrinosA list of very promising neutrino lensing systems has been established on the basis of known systems where lensing has been observed in photons, and where the lensed object is a potential neutrinos source.

The selection criteria are:

- the system is in the field of view of ANTARES.- the lensed object is a known AGN.- the system was detected in X-ray and/or gamma-ray observations.- if the object has not been identified as a gamma-ray emitter, a magnification factor larger than 20 for at least one of the images is required.

These criteria allow the identification of nine gravitational lenses, including four blazars and five strongly amplified AGNs. The sample covers a source redshift range, 0.6<zs<3.6, a lens redshift range, 0.2<zl<0.9, and Einstein angle from 1 arcsecond to 50 arcseconds. Two galaxy clusters with particularly large Einstein angles and estimated masses were also added. These eleven structures are listed in the Table on the right and shown in the following sky map in equatorial coordinates.