The radio signal from extensive air showers
TTHE RADIO SIGNAL FROM EXTENSIVE AIR SHOWERS
BENOˆIT REVENU
Subatech, ´Ecole des Mines de Nantes, CNRS/IN2P3, Universit´e de Nantes4 rue Alfred Kastler, BP20722, 44307 Nantes C ´EDEX 3, FRANCE
The field of ultra-high energy cosmic rays made a lot of progresses last years with largearea experiments such as the Pierre Auger Observatory, HiRes and the Telescope Array. Asuppression of the cosmic ray flux at energies above 5 . × eV is observed at a veryhigh level of significance but the origin of this cut-off is not established: it can be due tothe Greisen-Zatsepin-Kuzmin suppression but it can also reflect the upper limit of particleacceleration in astrophysical objects. The key characteristics to be measured on cosmic raysis their composition. Upper limits are set above 10 eV on primary photons and neutrinosand primary cosmic rays are expected to be hadrons. Identifying the precise composition(light or heavy nuclei) will permit to solve the puzzle. It has been proven that the radio signalemitted by the extensive air showers initiated by ultra-high energy cosmic rays reflects theirlongitudinal profile and can help in constraining the primary particle. We review in this paperthe emission mechanisms as a function of the frequency of the electric field. In the current large area ultra-high energy cosmic rays experiments (Auger , and TA , ),extensive air showers are studied through the secondary particles reaching the ground level andby collecting the fluorescence light emitted by the atmospheric diazote molecules excited bythe passage of the charged particles. Surface detectors (SD) arrays are composed of particledetectors (Cerenkov water tanks, scintillators...) having a high duty cycle (around 100 %) andthat allow to estimate the arrival direction of the shower and its core position. During darknights (duty cycle of 14 % in Auger), the fluorescence detectors (FD) detect the longitudinalprofile of the showers through a calorimetric measurement during their development in the air.A FD directly measures the shower energy and estimates the nature of the primary cosmic rayby the determination of the atmospheric depth X max corresponding to the maximum numberof secondary particles in the shower. Hybrid events, detected by both SD and FD, allow tocalibrate the SD using the FD reconstruction of the energy. The need for a better event-by-eventidentification of the nature of the primary particle have speed up the research and developmentof additionnal detection techniques such as the measurement of the radio signal emitted by theelectrons and positrons of the showers. The radio signal associated to cosmic rays was detected for the first time in 1965 but thedetailed characteristics of the electric field have been understood in the last years using thedata from several experiments (CODALEMA , LOPES , LOFAR , AERA ...). It has beenshown that the emission is coherent for wavelengths larger than or of the order of the typicaldimensions of air showers: the scale of their longitudinal development (10 km, 30 kHz), their a r X i v : . [ a s t r o - ph . H E ] N ov ateral spread (1 km, 0 . >
80 MeV) electrons and positrons of air shower (weneglect the emission from muons and ions, being much heavier) interfere with each other: if theobservation wavelength is larger than the size of the emitting region, the fields add-up coherentlyso that the total electric field is proportionnal to the number of electrons and positrons, andthen, to the primary energy. On the contrary, if the wavelength is smaller than the size of theemitting region, the fields interfere destructively. We should therefore expect a cut-off frequencyin the full frequency spectrum. The radio signal has a clear coherent contribution over a largefrequency range: from tens of kHz up to some hundreds of MHz. It has been shown that thesignal in the frequency range 30-80 MHz allows to reconstruct precisely the incoming directionof the shower (angular resolution below 1 ◦ , see ). The deep understanding of the radio signalwe reached today allows to use simulations to estimate the X max and LOFAR obtained aresolution on this parameter of 20 g cm − , similar to the resolution achieved by the FD. Theenergy estimation is underway, for instance in the AERA experiment. In 1967, Kahn and Lerche studied the dominant mechanism: the emission from the timevarying transverse currents induced by the interaction between the geomagnetic field and thecharged particles (hereafter the geomagnetic mechanism). The systematic opposite drift of elec-trons and positrons when they propagate in the geomagnetic field associated to the interactionswith the medium results into an average transverse current (with respect to the shower axis).This current induces a macroscopic electric field linearly polarized along the a × B direction,where a is the direction of the shower axis and B the direction of the geomagnetic field. Theorientation of this electric field is independent on the observer’s location.A secondary emission process is due to the excess of electrons with respect to positrons inair showers (Askaryan ). This net negative charge excess is due to the fast in-flight positronsannihilation and to direct enrichment in electrons extracted from the medium by the Compton,Bhabha and Moeller diffusions. The charge-excess mechanism leads to a radial polarizationpattern of the electric field in the plane transverse to the shower axis.An observer will detect the superposition of both electric fields. These fields depend on timethrough the varying number of electrons and positrons in the showers during its developmentin the air. This superposition leads to an asymetry in the total electric field strength accordingto the observer’s location with respect to the shower core and explains the departure from theradially symetric lateral distribution function proposed by Allan in 1971. The electric fieldvalue cannot be simply modelized by a 1D lateral function. Figure 1 presents the superpositionof both mechanisms. Note that other mechanisms can also lead to the emission of electric fields: Figure 1 – Left: in green, electric field generated by the geomagnetic mechanism. The polarization is linearand the same for all observers. Center: in red, electric field generated by the charge-excess mechanism. Thepolarization is linear with a radial pattern with respect to the shower core in the plane transverse to the showeraxis. Right: in blue, total electric field measured by an observer. Its value and direction depends on the observer’slocation. he presence of electric dipoles in the shower, the emission from the ions that are left behindthe shower, the individual geosynchrotron emission but all of them are largely subdominant.
The simulation of the electric field emitted by air showers recently reached a mature and robuststate. Different approaches were chosen in the past, using microscopic or macroscopic descrip-tions, in the time or frequency domains. The codes MGMR and EVA use the macroscopictransverse current as the main ingredient to the Maxwell’s equations. The code SELFAS , uses the energy, impulsion, angular, position distributions of electrons and positrons from theshower universality description and computes the resulting electric field as the summation of allindividual contributions (see Eq. 1). The code ZHAireS uses the ZHS formalism and computesthe electric field in both time and frequency domains. CoREAS uses the end-point formalismand computes all individual electric fields directly inside a full CORSIKA simulated shower. Asan example, the following formula used in SELFAS gives the electric field emitted by a singleparticle of charge q and lifetime τ = t − t (its charge q is taken as 0 before t and after t ): E ( r , t ) = 14 πε (cid:18) q n R (1 − η β · n ) + 1 c ∂∂t q n R (1 − η β · n ) − c ∂∂t q β R (1 − η β · n ) (cid:19) ret (1)where r is the observer’s position, n is the unit vector between the particle and the observer, η isthe air refractive index, β the particle velocity and R the distance between the particle and theobserver. The field is evalutated at time t ret = t − η R/c . We obtain the complete electric fieldafter summation over all electrons and positrons of the shower. The first term corresponds to theCoulombian contribution; it is negligible with respect to the two others. The global contributionof the second term for a system with equal numbers of electrons and positrons vanishes. Due tothe net excess of electrons in air showers, this term is not negligible and constitutes the chargeexcess contribution. The third term contains the particle velocity and its time derivative isproportionnal to the Lorentz force: this is the geomagnetic term. The particle velocity directionis close, at first order, to the shower axis direction. We note the presence of the air refractiveindex η leading to a boost of the electric field when the angle between the particle velocity andthe line of sight is close to the Cherenkov angle. This is not actual Cherenkov radiation butthis effect is important for observers located close to the shower axis. For these observers, inthe time domain, the electric field pulse is sharpened making it dominant at higher frequencies(above 100 MHz) and still important below 100 MHz and this explains the flat electric profilesobserved by LOPES and CODALEMA in the past. The electric field is amplified along aring of radius R C = (cid:96) sin θ C ∼
140 m, (cid:96) ∼ ∼ eV primary energies and θ C = arccos(1 /η ) ∼ . ◦ is the Cherenkov anglein air. Observation of this ring would be of great interest because it probes the distance to thesource of the electric field and therefore could help in differentiating proton or iron initiatedshowers. The ring radius being small, it would be necessary to detect shower with a dense arrayof radio stations which is not a good solution (not cheap). −
200 MHz
The frequency band 30 −
200 MHz is intensively studied since the beginning of years 2000.It has been established that the main emission mechanism in this band is the geomagneticcontribution. Beside this contribution, the CODALEMA and AERA experiments observed thesecondary electric field emitted by the charge excess mechanism using different observables.The CODALEMA experiment compared the shower core positions obtained using the datafrom the radio array to the core positions obtained using the particle array. A significantstatistical discrepancy between the two core positions was found: on average, the radio corepositions is shifted by ∼
25 m to the east with respect to the particle core position. The radioore position is estimated using a radio lateral distribution function (LDF) of the electric fieldamplitude depending only on the distance to the shower axis; ie a radially symmetric LDF.Using SELFAS simulations including only the geomagnetic contribution, it has been shown thatthe core positions estimated from the radio and particle arrays were in good agreement. UsingSELFAS with both mechanisms permitted to reproduced the same shift toward the east. Thiswas the first strong indication of the presence of the charge excess mechanism in the data .The AERA experiment used the polarization information to exhibit the charge excess con-tribution. Following Figure 1, an observer measures the superposition of two electric fields withdifferent polarization patterns. If we consider only the geomagnetic mechanism, we can computethe polarization angle φ P (pr . ) (with respect to the geographic east) in the horizontal plane usingthe north-south (NS) and east-west (EW) components of the predicted electric field: φ P (pr . ) = arctan ( a × B ) NS ( a × B ) EW Using the data, we can compute for each radio station i in a given event the measured polarizationangle in the horizontal plane (the antennas used in AERA do measure the electric field in bothEW and NS directions). This angle φ iP (me . ) is given by: φ iP (me . ) = arctan ε NS ε EW where ε is the electric field amplitude in both EW and NS directions. The correlation between φ P (pr . ) and φ iP (me . ) in the case of a pure geomagnetic contribution is presented in Figure 2(left).For a given event with a known incoming direction ( ie we know the axis direction a ) involving N radio stations, we have a single value for φ P (pr . ) but we have N values of the measuredpolarization angles φ iP (me . ). This explains the bunches of different values of φ iP (me . ) at agiven value of φ P (pr . ). The correlation is very clear: the Pearson correlation coefficient is ρ P = 0 . +0 . − . at 95% CL (with χ / ndf = 27) which demonstrates that the geomagnetic isindeed dominant. As we know that the charge excess mechanism is also there, we can refine ourpredicted value of the polarization angles φ P (pr . ). As discussed before, the electric field fromthis mechanism has a radial linar polarization in the plane transverse to the shower axis. Thepredicted polarization angle at each radio station i can be deduced using the following formula: φ iP (me . ) = arctan (cid:18) sin φ G sin α + a sin φ i A cos φ G sin α + a cos φ i A (cid:19) , where φ G is the azimuth of the geomagnetic contribution, α the angle between the shower axis a and the geomagnetic field B and φ i A is the azimuth of the charge excess contribution at thelocation of the radio station i . The parameter a is the ratio of the amplitude of the electric fieldfrom the charge excess contribution ε A to the amplitude of the electric field from the geomagneticcontribution ε G , modulated by sin α (in order to cancel the geomagnetic contribution when theshower incoming direction is parallel to the geomagnetic field): a = | ε A || ε G | sin α The average value of a was computed using showers detected by AERA and we obtained: a =0 . ± .
02 (see ). This value should not be considered as the fraction of charge excess in theshower, as it depends also on the angular distance between the shower axis and the geomagneticfield through sin α . Using this value for a , we can finally compute the predicted polarization angle φ iP (me . ) for each radio station i involved in a given event, taking into account both geomagneticand charge excess contributions. The correlation between φ iP (me . ) and φ P (me . ) is presented inFigure 2(right). The Pearson correlation coefficient rises up to ρ P = 0 . +0 . − . at 95% CL (with (cid:176) (pr.) [ p f -50 0 50 ] (cid:176) ( m e . ) [ p f -50050 a = 0 ] (cid:176) (pr.) [ p f -50 0 50 ] (cid:176) ( m e . ) [ p f -50050 a = 0.14 Figure 2 – Left: correlation between the measured polarization angle and the predicted polarization angle in thecase of a pure geomagnetic contribution. Right: same than the left figure but adding the contribution of thecharge excess mechanism. χ / ndf = 2 . −
200 MHz is very well described by thesuperposition of two mechanisms of electric field emission: the geomagnetic and the chargeexcess contributions.
The first signal we can think about in this frequency region is the GHz counterpart of the usualsignal made of the geomagnetic and charge excess mechanisms, enhanced by the Cherenkov-likeeffect due to the air index effect as discussed in section 2.2; this emission has a steeply fallingspectrum due the the incoherence of the fields at these frequencies. The Cherenkov-like effectresults in a highly forward-beamed emission. As seen previously, this electric field is polarizedaccordingly to the superposition of both mechanisms. Figure 3(left) presents the Fourier spectraof the simulated electric field for a vertical shower at 10 eV and antennas located at differentdistances from the shower axis. For the antennas located at 100 and 200 m from the axis, wesee the coherent part of the spectrum; this corresponds to the coherent geomagnetic and chargeexcess electric field between 30 MHz and some hundreds of MHz. The signal is incoherent athigher frequencies because these frequencies corrresponds to wavelength much smaller than theemittive zone. Figure 3(right) shows the electric field amplitude between 300 MHz and 1 . etal . in 2004 using a test beam at Argonne and SLAC: it is the molecular Bremsstrahlungradiation (MBR). This emission is due to the deceleration of the low-energy electrons ( ∼
10 eV)in the plasma created by the high energy electrons and positrons of the shower. We remindthat the electrons and positrons of the shower mainly loose energy by exciting or ionizing themedium. The excited N then emits UV light detected by fluoresence telescopes but the ionizedmolecules provide low energy electrons forming a weakly ionized and stationary plasma. Theseelectrons emit a Bremsstrahlung radiation that is expected to be non-polarized, isotropic whichis potentially an excellent feature for a detection at large distance from the shower axis (theradiation is not focalized). The MBR implies a microwave continuum emission at the GHz level igure 3 – Contribution at high frequencies of the electric field from the geomagnetic and charge excess mecha-nisms. Left: electric field power as a function of frequency. The coherent part lies at smaller frequencies as canbe seen for antennas close to the shower axis (100 m and 200 m). Right: amplitude of the same electric fieldbetween 300 MHz and 1 . eV. and is expected to have a direct relationship with the shower energy. Finally, this radiationis detectable with a duty cycle close to 100%. The experiment of Gorham et al . measured anon-polarized flux density of 4 × − W m − Hz − for a setup corresponding to a shower at3 . × eV at 0 . σ of 1 . × eV and 8 . × eV assuminga quadratic or linear dependence of the power with respect to the shower energy respectively.The MAYBE (electron beam) and AMY (electron or positron beam) experiments also aimedat detecting and characterizing the MBR. The results disagree with those of Gorham. Recently,Conti et al. , using a low energy electron beam (in order to be below the Cherenkov threshold),obtained a linear scaling of the signal with the number of electrons and an asymmetric emissionpattern, in opposition to the isotropic feature reported by Gorham et al . In conclusion on thebeam experiments, the situation is very unclear but the high MBR signal reported by Gorham et al. is not confirmed by any of the other experiments.AMBER , MIDAS and EASIER are three prototypes installed at the Pierre Auger Ob-servatory aiming at detecting the GHz emission from air showers. MIDAS excludes at quadratic(resp. linear) scaling of the power flux with the primary energy as reported in at a confidencelevel of 5 σ (resp. 4 σ ). EASIER detected five (up to summer 2014) GHz events, in 3 years ofdata acquisition. All of those were detected by a single antenna and at a small distance fromthe shower axis (below 270 m) and for high-energy showers. The simulation with SELFAS ofthe first detected EASIER shower was in good agreement with the data: it shows that the GHzsignal can be explained with the usual geomagnetic and charge excess mechanisms in the GHzrange, for this event. The others have not been simulated.The CROME experiment, installed at the KASCADE experiment detected showers in theGHz range. The 35 detected showers in coincidence with the KASCADE setup after 18 monthsof data taking presented an east-west asymmetry in their electric field strength. High valuesof the electric field strength were measured following a ring pattern at the ground level. Thedetected GHz emission is strongly polarized with a pattern in agreement with the geomagneticand charge excess expectations. The conclusion of CROME is that the GHz signal associated toair showers is fully consistent with geomagnetic and charge excess mechanisms as sole emissionprocesses at these frequencies and the data rule out the MBR mechanism.In conclusion, the GHz signal strength and characteristics as reported in are not confirmedEAM EXPERIMENTSName location year freq. (GHz) scaling emission patternGorham SLAC 2004 1-8 quadratic isotropicMAYBE Argonne 2012 1-15 linear isotropic, (cid:28) Gorham fluxAMY Frascati 2012 1-20 MBR much smaller than CherenkovConti et al. Padova 2014 11 linear peaked forwardPARABOLA IN CR EXPERIMENTSAMBER Auger 2011 no CR detectionMIDAS Auger 2012 no CR detectionEASIER Auger 2011-2012 3 . . . . Table 1: Summary of the results obtained in the GHz domain, seeking for the characteristics of the molecularBremsstrahlung radiation (MBR). by any other experiments. The GHz emission from showers is compatible with the GHz coun-terpart of the usual geomagnetic and charge excess mechanisms. No MBR emission associatedwith EAS is clearly observed up to now and clearly, detecting EAS using the GHz signal is notefficient.
On the other side of the frequency spectrum, below 20 MHz, we can of course think to thecontributions of the geomagnetic and charge excess mechanisms. Nevertheless, these contribu-tions have not been carefully measured at the MHz level because of the atmospheric noise whichincreases with decreasing frequency, this explains why people favoured higher frequencies. Inthe past, several experiments reported the observation of radio pulses in coincidence with EAS.A complete review of the experimental status can be found in Revenu & Marin . The frequen-cies probed at that time were between some hundreds of kHz up to 9 MHz. The conclusionswere that a very strong signal (1 or 2 orders of magnitude higher than in the usual band 30-80 MHz) associated to air showers was undoubtly detected. People thought about several newmechanisms to explain this signal: the interaction between the ionization electrons in the airwith the atmospheric electric field, the transition radiation front the electrons when the showerfront hits the ground or the longitudinal and transverse emissions assuming full coherence butnone of them could explain the reported huge values of the electric field. In , we propose anew emission mechanism: the coherent deceleration of the electrons and positrons of the showerfront when it hits the ground level. The sudden deceleration of these particles when hitting theground (which we call the sudden death of the shower) produces a coherent Bremsstrahlungemission for wavelengths larger than the typical size of the shower front, or equivalently forfrequencies smaller than 20 MHz. We can also understand this emission using a macroscopicpoint of view. When the shower front disappears below the ground level, the macroscopic chargedensity ρ ( r , t ) and current J ( r , t ) vary very quickly and their space and time derivatives, pro-viding electric fields according to Maxwell’s equations, reach strong values. We therefore expecta significant electric field emission and we suspect that the previous experiments did measurethis signal. We used the simulation code SELFAS to characterize the electric field emitted bythe sudden death mechanism. The basic formula, derived from Eq. 1 and using the Coulombauge reads: E tot ( r , t ) = 14 πε c ∂∂t N t (cid:88) i =1 q i ( t ret ) (cid:20) β i − ( n i . β i ) n i R i (1 − η β i . n i ) (cid:21) ret (2)where, as in Eq. 1, η is the air refractive index, n i and R i are the line of sight and the distancebetween the observer and the particle i , β i the velocity of this particle and q i its electric charge.The summation is done over the total number N t of particles that emitted an electric fielddetected by the observer at time t . All these quantities are evaluated at the retarded time t ret ,related to the observer’s time t through t = t ret + η R i ( t ret ) /c . Figure 4 presents the verticalcomponent of the electric received by two observers located at 500 m and 600 m of the showeraxis for vertical showers with a primary energy of 3 × eV and 10 eV. The origin of time t = 0 corresponds to the time when the shower front hits the ground. In this figure, the electric Figure 4 – Vertical component of the electric field as a function of time for two observers located at 500 m and600 m of the shower core for vertical simulated showers with primary energy of 3 × eV and 10 eV. Theelectric field emitted during the shower development in the air is clearly visible around t = 100 −
200 ns. Thesudden death pulse, generated when the shower front hits the ground, appears at t ∼ t ∼ field pulse created by the disappearance of the shower front in the ground has a very specificshape. Its maximum is located at a time corresponding to the time needed for the signal toreach the observer from the shower core. The reception time of this signal is therefore delayedby t = d/c with respect to the time at the shower core, ie a − ( n · a ) n because at first order, the β i of the particlesat the ground level is parallel to the shower axis a . The vertical component should therefore beimportant. The sudden death pulse amplitude scales linearly with the primary energy and, avery important feature, is that this amplitude decreases as 1 /d where d is the distance to theshower core. It means that it should be possible to detect showers up to some kilometers fromthe core, contrarily to the signal in 30-80 MHz. Figure 5 summarizes our current understandingof the emission mechanisms as a function of the frequency. At the time of this conference, the radio signal emitted by extensive air showers is understood ata very high level of precision. This signal, between 30 MHz and 80 MHz, allows to reconstructprecisely the arrival direction of the primary cosmic ray. It also allows to estimate its naturefollowing the results from the LOFAR experiment which claims a resolution of 20 g cm − . Thisvalue is comparable to the resolution of a fluorescence detector but with an uptime close to 100% igure 5 – Summary of the current status of the experiments and of the understood mechanisms of electric fieldemission in showers, as a function of the frequency. which is very interesting for improving our knowledge on ultra-high energy cosmic rays. Thedrawback of this signal is the relatively small range of the order of some hundreds of meters. Thecontribution from the geomagnetic and charge excess mechanisms can explain the data in a largerange of frequencies, between 30 MHz up to some GHz. At low frequency, below 20 MHz, showershave already been observed in the past. A very large electric field amplitude was observed withno satisfactory underlying mechanism. We are currently installing the EXTASIS experiment inNan¸cay, dedicated to the low frequency signal of the showers when the front hits the ground.The range of this sudden death signal is much higher than the range in 30-80 MHz; this couldbe a very important feature for the detection of cosmic ray with a large efficiency. References
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