Angular distributions of Cherenkov photons in the geomagnetic field

Transcription

1 Angular distributions of Cherenkov photons in the geomagnetic field P. Homolaa, R. Engelb, H. Wilczyńskia a) Institute of Nuclear Physics PAN, Kraków, Poland b) Karlsruhe Institute of Technology, Germany Azimuthal Cherenkov distribution in air showers is asymmetric. This asymmetry significantly depends on the local geomagnetic field and air density. 1/12

2 Motivation None of the presently used parameterizations of the angular Cherenkov distribution in high-energy air showers accounts for the influence of the geomagnetic field (GMF). GMF deflects charged particles asymmetry of lateral distributions of Cherenkov photons is expected, especially pronounced for events developing in small air densities and arriving transversely to the direction of the local GMF vector. The azimuthal asymmetry is important for air shower reconstruction the source of uncertainty that has never been checked. 2/12

3 B tr e- sh a x ow e r is Cherenkov photons in air showers: situation e+ i em X=const st og ra m e- hi st og ra m m in g le ve l s( M C) shower axis iss =2o ion hi j =10o histogramming level Existing parameterizations g (M of angular distributions C) of Cherenkov photons: dn/d d = F( ) (axial symmetry assumed) e+ This work: F( ) F(, ) account for axial asymmetry m in 3/12

4 Does the Cherenkov asymmetry make a difference? MC example of Cherenkov lateral distribution: p, 10 EeV, 0=60o, 0=90o (from East), s 0.7, Btr=0.5 G, Yes, it does. e.g. max/min=5 at =15o 4/12

5 Cherenkov azimuthal distribution is asymmetric MC example of normalized Cherenkov azimuthal distribution: p, 10 EeV, 0=60o, 0=90o (from East), s=1, viewing angle 8o< <10o strong Btr strong asymmetry e e+ no Btr no asymmetry 5/12

6 Let's parameterize the Cherenkov azimuthal asymmetry Assumption I (Hillas '82; Giller '04, '05; Nerling '06): reasonable universality of e+/e- lateral profiles: - for a wide range of primary energies - for nuclear primaries - around shower maximum: 0.7 < shower age < 1.2 Assumption II (Elbert '83): - azimuthal distribution of Cherenkov photons is determined only by a Btr / and viewing angle Btr : GMF component transverse to shower axis; : air density - shape of the azimuthal distribution approximated by F(a,, ) = A + B(a, )sin4 A: normalization constant; B(a, ): asymmetry amplitude 6/12

7 Average asymmetric azimuthal Cherenkov profiles Example: p, 10 EeV, 0=70o, 0=0o (from South), s=0.86, 8o< <10o vertical bars: RMS, 10 histograms; horizontal bars: bin size 10o e Be+(a, ) Be (a, ) e+ 7/12

8 Heights of asymmetry peaks increase with a Example: a Btr / 8/12

9 Parameterization of the Cherenkov azimuthal asymmetry F(a,, ) = A + F+(a, )[1+F-(a, )sin ]sin4 A=1/2-3F+/8; F+=(Be + Be+)/2; F =(Be - Be+)/(Be + Be+); Be+/ (a, )=B1( )a+b2; B1( )=B11 2+B12 +B13 Be+(a, ) Be (a, ) MC Fit: F(a,, ) average: F( ) B2(e+)= B11(e+)=( )10-5 deg-2 B12(e+)= deg-1 B13(e+)= B2(e-)= B11(e-)=( )10-5 deg-2 B12(e-)= deg-1 B13(e-)= This work: F( ) F(a,, ) 9/12

10 Validation 1. MC simulations used for validation: random 0< 70o; E0 = 1014, 1015, 1016, 1017, 1018, 1019 ev; primary mass: p, Fe; B=0.6 G (TUNKA site, B value according to IGRF 11) 2. Validation: histograms compared to parameterization with 2 test around 90% histograms pass the test at 95% confidence level 3. Application range (limited simulation statistics): 0.3 Gm3kg-1 < a < 2.5 Gm3kg-1 10/12

11 Cherenkov light in strong B dnch/d Example: Monte Carlo for Btr = 0.6 G, (e.g. TUNKA site) max. ~ E0=1015eV 0=70o s=0.8 0 =15o average ~ min. ~ [deg] max/min 30 (!) max/average 3 min/average /12

12 Summary Azimuthal Cherenkov distribution is asymmetric due to the GMF. Parameterization of this asymmetry has been derived. The asymmetry effect increases with a B / and with the viewing angle; is most significant for inclined events at early stages of development; azimuthal profile is independent of the nuclear primary mass, energy and shower age. The derived parameterization has been validated for 0.3 Gm3kg 1 < a < 2.5 Gm3kg 1 2o < viewing angle < 20o. Looking forward to experimental verification! 12/12

13 Detection possible? Experiment TUNKA-133 at lake Baikal Optical detectors (PMTs), area of 1 km2, 1015< Eo/eV <1018, strong local geomagntic field: B 0.6 G (acc. to the IGRF 11, close to geomagnetic anomaly) look forward to testing the predictions of this work 13/12