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Information about Why radiodetection of UHECR still matters ? Karlsruhe Institute of...

In the field of radiodetection in astroparticle physics, the Codalema experiment is devoted to the detection of ultra high energy cosmic rays by the radio method. The main objective is to study the features of the radio signal induced by the development of extensive air showers (EAS) generated by cosmic rays in the energy range of 10 PeV-1 EeV. After a brief presentation of the recent results of UHECR, a description the CODALEMA II and III experiments characteristics is reported.

Next, a study of the response in energy of the radio-detection method is presented. The analysis of the CODALEMA II experiment data shows that a strong correlation can be demonstrated between the primary energy and the electric field amplitude on the axis shower. Its sensitivity to the shower characteristics suggests that energy resolution of less than 20% can be achieved. It suggests also that, not only the geomagnetic emission, but also another contribution proportional to all charged particles number in the shower, could play a significant role in the radio emission measured by the antennas (as Askaryan charge-excess radiation or a Cherenkov like coherence effect).

Finally, the transition from small-scale prototype experiments, triggered by particle detectors, to large-scale antenna array experiments based on standalone detection, has emerged new problems. These problems are related to the localization, recognition and the suppression of the noisy background sources induced by human activities (such as high voltage power lines, electric transformers, cars, trains and planes) or by stormy weather conditions (such as lightning). In this talk, we focus on the localization problem which belongs to a class of more general problems usually termed as inverse problems. Many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio wavefront time of arrival on antennas TOA), such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina, TREND in China and LUNASKA in Australia, we demonstrate the ill-posed character of this problem in the sense of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation of the problem. A comparison between the experimental results and the simulations have been made, to support the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.

Next, a study of the response in energy of the radio-detection method is presented. The analysis of the CODALEMA II experiment data shows that a strong correlation can be demonstrated between the primary energy and the electric field amplitude on the axis shower. Its sensitivity to the shower characteristics suggests that energy resolution of less than 20% can be achieved. It suggests also that, not only the geomagnetic emission, but also another contribution proportional to all charged particles number in the shower, could play a significant role in the radio emission measured by the antennas (as Askaryan charge-excess radiation or a Cherenkov like coherence effect).

Finally, the transition from small-scale prototype experiments, triggered by particle detectors, to large-scale antenna array experiments based on standalone detection, has emerged new problems. These problems are related to the localization, recognition and the suppression of the noisy background sources induced by human activities (such as high voltage power lines, electric transformers, cars, trains and planes) or by stormy weather conditions (such as lightning). In this talk, we focus on the localization problem which belongs to a class of more general problems usually termed as inverse problems. Many studies have shown the strong dependence of the solution of the radio-transient sources localization problem (the radio wavefront time of arrival on antennas TOA), such solutions are purely numerical artifacts. Based on a detailed analysis of some already published results of radio-detection experiments like : CODALEMA 3 in France, AERA in Argentina, TREND in China and LUNASKA in Australia, we demonstrate the ill-posed character of this problem in the sense of Hadamard. Two approaches have been used as the existence of solutions degeneration and the bad conditioning of the mathematical formulation of the problem. A comparison between the experimental results and the simulations have been made, to support the mathematical studies. Many properties of the non-linear least square function are discussed such as the configuration of the set of solutions and the bias.

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1 This work has been made a part under a grant from Region Pays de la Loire France and CNRS/IN2P3 (Centre national de la recherche scientifique). I would also like to thank Dr. Andreas Haungs and Dr. Tim Huege for the invitation and Dr. Sabine Bucher for her administrative collaboration

2 Introduction Recent Results in Ultra High Energy Cosmic Rays physics and their interpretation Radiodetection of UHECR The CODALEMA Experiment The measurement of the energy of the primary particle ● Localization of the radio-emission source

3 Ultra High Energy Cosmic Rays puzzles Knee Power law: Flux ~ E-2.7 Transition ??? Many regions : GZK or SOMETHING ELSE? - Low energies - Knees - ankle Gaisser T. K. et al. Front. Phys. China. 8 (2013) Many origins : - solar - galactic -extragalactic and ? Many techniques : Direct: satellites, balloons Indirect: ground base arrays (fluorescence, particle detectors and antennas) Open questions: Origin ? Nature ? Limit ?

4 Current results on the Ultra High Energy Cosmic Rays Physics

5 UHECR Origins Question: How to reach 100 EeV (1020 eV)? Cosmological origin (top-down mechanism) Massive particles decay (M.c2 ~ 1024 eV) Signature: photons/neutrinos Excluded by the Pierre Auger Experiment (The Astrophysical Journal Letters, 755:L4 (7pp), 2012 August 10) Astrophysic origin (bottom-up mechanism) Accélération de Fermi des particules chargées (Fermi: Phys. Rev. 75, 1169, 1949) => Limite ~ 1018 eV Proximité d'objets astrophysiques => Now, need to find sources

6 South hemisphere : Auger UHECR sources Sky maps @ Ep>55 EeV North hemisphere : TA/Hires TA/Hires : directional correlation 44% (Astrophys.J. 757 (2012) 26) Auger :increase of statistics and decrease of statistical correlation (61% to 33%) (Science 318 (2007) no. 5852, 938–943) Propagation: effect of the Intergalactic magnetic fields?

7 UHECR propagation : GZK effect Interaction of UHECR with the Cosmic Microwave Background CMB During the 90s => disagreement between AGASA (Japan)-Hires1 (USA) experiments 2008: GZK cut confirmed by TA/Hires (Phys, Rev. Lett. 101 (2008) 061101) by Auger in 2010 (Phys. Lett. B 685 (2010) 239–246) Auger =>limit the observable universe at 100 Mpc => depends on the primary nature => @3.119 eV : Max energy of acceleration or propagation ?

8 UHECR Nature Xmax : depth of the shower maximum development => related to the nature of the primary Auger : Heavy composition favoured (Phys.Rev.Lett.104:091101,2010) TA/Hires : lightening of the composition in function of the energy (Phys.Rev.Lett.104:161101,2010) Difficulties on measurements and interpretations and strongly increasing cross-section

9 Proton interaction cross section @57TeV Constrained the hadronic models (QGSJET, Sibyll, Epos) used in particle physics (Phys.Rev.Lett. 109 (2012) 062002)

10 UHECR detection methods Particle detection on the ground : Cerenkov detectors Scintillators Detection of the fluorescence light Advantages Disadvantages Ground based detectors Duty cycle near to 100% Dependence on hadronic models Deployed large surfaces > 1000 km2 Fluorescence telescopes Low dependence on hadronic models Large volume detection Low duty cycle near to 10%

11 Radio-detection of Extensive Air Shower: A complementary detection method in evaluation Spectrum remains understood @UHE Ill-defined chemical composition @UHE Unknown astrophysical origin @UHE Low statistics at extreme energies

z First interaction Extensive Air Shower 2n(Κ±π± ...hadrons) nπ° e e e e γ e γ Nmax Nucleons cascade Near shower axis Hadrons Sol γ γ e Xmax 12 Pions cascade π± desintegration µ µ µ µ Electromagnetic cascade e γ e γ e γ ~90% of γ (>50 keV) ~9% electrons (>250 keV) ~1% µ (>1 GeV) small hadron fraction 13

13 Radio-detection of EAS Radio emission mechanisms 9% electrons/positrons Geomagnetic effect => deviation of electrons/positrons under the geomagnetic field effect => bipolar emission, transverse current, synchrotron emission => linear polarisation Askaryan Negative charge-excess radiation => temporal variation of the negative charge excess => monopolar emission => radial field + Cherenkov-like coherence effect? (2010) Distance shower-antenna Forme du signal radio Radio signal shape

14 Radio emission theoretical models Comprehension of the radio signal => Intense theoretical efforts => several models available : ● Microscopic : use of CORSIKA and AIRES codes ● Macroscopic : simplistic assumptions on the EAS phenomenology Unipolar pulse models : ● REAS1, REAS2, ReAIRES Bipolar pulse models: ● MGMR, REAS3, SELFAS2 The total electric field +

15 MHz radio-detection experiments EASIER LOPES AUGER AERA LOFAR TREND

16 CODALEMA experiment @Nançay • Radio-astronomy environment • Electromagnetic quiet environment ~1 Km ~2 Km • Far from big cities => Non-existence of strong transmitter • But no possibility for end-to-end calibration.

17 CODALEMA Actual Setup Array of 24 short antennas 21 polar. E-W 4 detector arrays Decametric array 18 groups of 8 logperiodic phased antennas 30 selftriggered Antennas 2 polar. (E-W + N-S) Objective : 60 on 1.5 km2 Array of 17 scintillator Experiment Trigger Energy Estimator Shower core location Arrival direction

18 CODALEMA II : method of detection recording of the radio sky state Sla ve t recording of the radio sky state r ig ge rm od e

19 Radio transient selection Recording radio waveforms in 0-200 MHz: Sampling frequency 1Gs / s on 2520 Points

20 Filtered radio transients Digital filtering in the [20-83] MHz band Corrections : +Cables delays +Attenuation +Antennas gain Event = 2 physical quantities/antenna (transient maximum amplitude and time of maximum transient )

21 Reconstruction of physical observables Event = 2 physical quantities - Maximum amplitude of the transient - Time of maximum transient Arrivals direction : θ zenith angle ϕ azimuth angle Hypothesis : a plane wave front with equation : u.x+v.y+w.z+cte = 0 (u,v,w) normal vector coordinates Electric field profile Allan model: exponential function with 4 parameters Ε = ε 0 exp(-d/d0(xc,yc)) => ε 0 electric field on the shower axis => d0 radio shower lateral distance => (xc,yc) shower core on the ground

CODALEMA Results 22 Evidence of a geomagnetic effect in the electric field generation mechanisms B CODALEMA model |vXB|EW Deficit of events near the magnetic axis =>Est-West Polarisation of the electric field => Signal amplitude ~ |vXB|EW D. Ardouin et al. Astro.ph 31 2009

Primary particle energy Ep 23 Correction factors: + Geomagnetic emission? + Askaryan charge-excess radiation? + Cherenkov-like coherence effect? ε0 The primary particle energy measurement with ε 0 radio observable + A. Rebai et al. ArXiv:1210.1739, Oct. 2012 (submitted to Astro.Ph) + ARENA2012, AIP Conf. Proc. 1535, 99-104 (2013)

24 Study of correlation between Ep and ε 0 Fit function : 3 assumptions : * Linear-linear fit * Gaussian error * Independence relation between ε 0 and Ep σ(Ep)/Ep ~ 30% σ(ε 0)/ε 0 ~ 22% (Monte-Carlo) (Only statistical errors No systematics for this study) E0 ~ Ep^alpha avec alpha ~ 1.0=> dépendance linéaire Goodness of fit study => Standard deviation of the distribution of Ep and E0 residual Corrélation dépend : Erreurs sur Ep Erreurs sur e0 Existence of outlier events

25 1st correction factor : geomagnetic emission Geomagnetic effect : ε 0 ~ Ep.|(vXB)EW| ε'0 ~ Ep.|(v'XB)EW| => ε 0 → ε 0 /|(vXB)EW| Overestimation of the energy of the events near to the geomagnetic axis But no effect in Ep => The existence of a second contribution

Additional mechanism 26 ε 0 ~ Ep.|(vXB)EW| + Ep.c => ε 0 → ε 0 / ( |(vXB)EW| + c ) 0 < |(vXB)EW| < 1 c>0 Quality criteria An simple assumption : Contribution proportional to the energy (i.e. total charge produced in the shower) 70 events per window Best resolution for |(vXB)EW| close to 1 and c=0 => Geomagnetic effect dominance For small |(vXB)EW| => improvement in resolution when c increase => Ep.c dominates

27 Additional mechanism Can we combine this new contribution to an existing electric field emission mechanism ? Shower axis perpendicular component Shower axis parallel component ε 0 ~ Ep.|(vXB)EW|+Ep.c.|sin(θ).sin(ϕ)| Resolution degradation=> we reject the hypothesis Interpretations with the current data set of 315 events: ε 0 ~ Ep.|(vXB)EW|+Ep.c 1st term depends on the geomagnetic effect 2nd term depends on the shower total charge => Askaryan charge-excess mechanism ? ε 0 ~ Ep.|(vXB)EW|(1+c/|(vXB)EW|+d/|(vXB)EW|2+ ….) (partial fraction expansion...) Analogy with a magnetic field deflection created by a dipole => Charged particles deflection increases with |(vXB)EW| => distance between the particles increases => Is there a limit imposed by the emission coherence??

28 Summary of the analysis Our interpretation with only 315 events : ε 0 ~ Ep.|(vXB)EW| + Ep.c 1st term depends in the geomagnetic emission 2nd term depends in the shower charge => Askaryan negative charge-excess mechanism ? ε 0 ~ Ep.|(vXB)EW|.(1+c/|(vXB)EW|)

29 Energy resolution Radio energy “Particle” energy Radio energy spectrum after calibration Monte Carlo: Construction (E0, EP) distributions for fixed (∆E0, ∆EP) => Construction of the abacus σ(EPE0)/EP => σ(E0) ~ 20% => Adopting a better parametrization RLDF (Gaussian) => Improving the analysis chain + including systematic errors

30 Tarek Salhi Applied Math. Engineer Now is working as a Field Engineer @General Electric in Algeria Localization of radio emission sources ➢ Motivations ➢ Experimental observations ➢ Mathematical framework ➢ Ill-posedness formulation ➢ Convex hull concept A. Rebai, Tarek Salhi et al. arXiv:1208.3539 (rejected by Astropart Because of the mathematical concepts) + ARENA2012, AIP Conf. Proc. 1535, 99-104 (2013) . Phy.

31 Towards a self-radio trigger Objective : avoid to trigger the antenna array by another array Transition from prototype experiments triggered by a particle detector arrays to selftriggered antenna arrays deployed on large surfaces Antenna trigger Antennas triggered by scintillators In 4 days : 107 events In 3 years : 2030 events Noise sources appearance

32 Study of the radio interference (RFI) Need to accurately locate interference sources to remove it => spherical emission assumption Anthropogenic sources: Aircraft, power lines, transformers, electric motors ... Natural sources: Atmospheric storm discharges... This is the crucial problem to be fixed in order to make radiodetection auto-triggering mode (radio trigger)!

33 Why a spherical wavefront hypothesis ? ● The near field and far field are regions of the radio emission around the source ● Near field => spherical wavefront (airplanes, electric transformers …) ● Far field => planar wavefront (the sun during solar flare periods cf. J. Lamblin for the CODALEMA collab.. Radiodetection of astronomical phenomena in the cosmic ray dedicated CODALEMA experiment. In Proceeding of the 30 th ICRC 2008) 2*D2/λ Near field Far field source Electric gate of a farm Near to Lofar array EDF electric transformer

RFI localization 34 CODALEMA III AERA ►Correct localization expected for a spherical reconstruction: ● immobile sources ● Large number of detected events + Source/array position effect TREND ►► localization problem ? ►►numerical simulation

35 Model and simulation of the spherical wave Test array Spherical Propagation 1-Source at distance Rs 2- Arrival times distribution Computing 3-Introduction of errors 4-Generation of 1000 events 5-Reconstruction of the emission centre by minimizing an objective function with Simplex and Levenberg Marquardt (LVM) algorithms

Time resolution effect 36 Simplex algorithm: direct search (no gradient calculation) Effect of temporal error : ● σ =0 ns : good localization with a t statistical estimator ● σ =3, 10 ns : Degradation of t reconstruction: spread of the Rs distribution σ t=0 ns σ t=3 ns σ t=10 ns Elongated distribution points : but θ, ϕ => good estimation !!!

37 Initial conditions effect LVM algorithm Sensibility in initial conditions : Rini >> Rs => False results Small modification in Rini => unpredictable results => Need to refine the analysis: apply other selection criteria

38 Simulation conclusions When the temporal resolution increases: : Reconstruction degradation=> distribution points spread Bias appearance But the temporal resolution is not the only factor ● ✔ ✗ Source position relative to the array : Source outside the array => bad reconstruction Source inside the array => good reconstruction Localization sensitive to the minimization algorithms (simplex and Levenberg-marquardt, linear search) Initial conditions dependence Multiple solutions (degeneration) ==> Need for a detailed study of this spherical minimization

39 The followed approach The minimization algorithms based on f descent direction search to reach the minimum (local or global) ● ● ● ● Solution = function minimum found Global minimum => convex function => unicity of the solution Local minimum => non-convexe function=> degeneration of the solution Need to watch the first differential (minima) and second (convexity) Study the convexity of f: Jacobian and Hessian Classification of the localization problem in a more general framework ● Coercivity of the objective function ● Sylvester criterion ● Ill-posed problem in the sense of Hadamard ● Ill-conditioned problem

40 Convexity of the objective function symbolic calculus: With M is the Minkowski matrix Sylvester Criterion : f is convex ⇔ All Hessian minors are positive Reasoning on the principal Hessian minor of order 4: We choose => a negative minor => f is not convex => existence of several minimum

41 Distribution of f minima symbolic calculus: Search of minima: => Analogy with the barycentre formula: => Importance of the barycentre of the spatio-temporal variations of tagged antennas ● Existence of a privileged direction of barycentre-source Importance of the closest antennas to the source Difficulties in resolution => use of an empirical method

1D array case 42 3 hypothesis : ● Source inside the array ● Source outside the array ● Source outside the array but off-line Source externe Particular role for the segment => convex hull Role of the nearest antenna to the source Source interne

43 1D array case (external source) Source outside the segment and off-line Constraints => light cones Unconstrained Minimization results => Solutions lie on a half-line

44 2D array case (internal source) Real case : source inside the antenna array Convex hull role

45 2D array case (external source) Real case : source on the ground and outside the array convex hull (RFI sources) Presence of local minima Distribution on a line Role of the convex hull Existence of privileged half-line

46 2D array case : source in the sky source Antenna array on the ground Good estimation of the arrivals direction

47 Ill-conditioned problem Condition number : measure how sensitive a function is to changes or errors in the input κ(H)=||H-1||*||H|| ~ λ max(H)/λ min(H) (eignevalues of H) (F. Delprat-Jannaud and P. Lailly, Ill-Posed and Well-Posed Formulation of the Reflection Travel Time Tomography Problem, J. of Geophysical Research, vol. 98, No. B4, p. 6589, April 10, 1993.) Low condition number (~1) => well-conditioned problem High condition number (>>1) => ill-conditioned problem

48 Classification of the localization problem Jacque Hadamard (1902) A physics problem is ill-posed if: 1 – no solution or 2 – has many solutions or 3 – the solution has a strong dependence In the different parameters of the problem (initial conditions, boundary conditions, data errors) (2) et (3) => localization problem is ill-posed in the case of a source external to the tagged antenna convex hull localization problem is well posed in the case of an internal source to the convex hull of antenna

49 Direct search attempt Best method to circumvent the problem is not yet found 1 - Quantification of the phase space in a cubic grid: step ~ 50 m in space, time step ~ 10 ns 2 - Using the planar fit to determine the search directions in the phase space 3 - Calculate the value of f on a grid 4 - Search absolute minimum R(estimated)=4000 m R(estimated)=9700 m

50 Direct search attempt Best method to circumvent the problem is not yet found Source on the ground PhD of Diego Torres But in the case of a source in the sky => Bias

And now EAS ? 51 Dimensions of the charged particles pancake: + Longitudinal spreading ~ few meters (J. Linsley, "Thickness of the particle swarm in cosmic-ray air showers," Journal Phys G vol. 12, No. 1., P. 51, 1986) + Lateral spreading: limited by the effect of coherence => band [2383] MHz => ~ 3 - ~ 13 m Apparent point source localized in space => spherical emission Hypothesis : the signal maximum amplitude linked To the development region of the shower (Xmax ?) Data Observation of a time shift relative to the plane wavefront assumption But only one realization per event ► Problem for a statistical estimation of the source position

52 3D detectors in the water and in the ice Volume detector array (not a new idea) : Askaryan during the 70s and DUMAND array during 90s. Slide from ARENA 2010 presentation “H. Ralf”

53 3D detectors in the water and the ice

54 3D convex hull: Towards 3D antenna array Exposure of high altitude antennas (mountains, ballons, satellite) P. Motloch, N. Hollon, P. Privitera, On the prospects of ultra-high energy cosmic rays detection by high altitude antennas (arXiv:1309.0561) accepted in Astro. Part. i.e. Forte satellite i.e Anita Our idea A. Rebai, T. Salhi and Ramzi Boussaid Formulation of the emission sources localization problem in the case of a selftriggered radio-detection experiment: Between Ill-posedness and Regularization (to be submitted)

55

56 Conclusions + Energy analysis was improved indication of the presence of several radio emission mechanisms Estimation of the energy resolution of ~ 20% + Perspective: More accurate LDF (Gaussian) => resolution enhancement + RFI observations and simulations => difficulties in interpretations Study the objective function Role of the convex hull Role of the half-line that binds the antennas barycentre and the source We need to work with mathematicians (multidisciplinary approach)

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