The physics of radio emission from cosmic-ray induced air showers is shortly summarized. It will be shown that the radio signal at different distances from the shower axis provides complementary information on the longitudinal shower evolution, in particular the early part, and on the distribution of the electrons in the shower core. This complements the information obtained from surface, fluorescence, and muon detectors and is very useful in getting a comprehensive picture of an air shower

de Vries, Krijn D.

Scholten, Olaf

Werner, Klaus

EPJ Web of Conferences

English

arXiv

Dissertations of the University of Groningen

   University of GroningenWhat the radio signal tells about the cosmic-ray air showerScholten, Olaf; de Vries, Krijn D.; Werner, KlausPublished in:EPJ Web of ConferencesDOI:10.1051/epjconf/20135308005IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2013Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Scholten, O., de Vries, K. D., & Werner, K. (2013). What the radio signal tells about the cosmic-ray airshower. EPJ Web of Conferences, 53, [08005]. https://doi.org/10.1051/epjconf/20135308005CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 17-07-2023EPJ Web of Conferences 53, 08005 (2013)DOI: 10.1051/epjconf/20135308005C© Owned by the authors, published by EDP Sciences, 2013What the radio signal tells about the cosmic-ray air showerOlaf Scholten1,a, Krijn D. de Vries1 and Klaus Werner21KVI, University of Groningen, Groningen, The Netherlands2SUBATECH, Nantes, FranceAbstract. The physics of radio emission from cosmic-ray induced air showers is shortly summarized. Itwill be shown that the radio signal at different distances from the shower axis provides complementaryinformation on the longitudinal shower evolution, in particular the early part, and on the distribution of theelectrons in the shower core. This complements the information obtained from surface, fluorescence, andmuon detectors and is very useful in getting a comprehensive picture of an air shower.1. INTRODUCTIONThere are several approaches that are followed to model radio emission from extensive air showers.These can crudely be separated into two categories, Microscopic and Macroscopic. In a Microscopicapproach the tracks of the individual electrons are followed and the emitted radiation of each is summedto yield the total radiation of the extensive air shower. This approach is incorporated in the REAS [1]and the ZHAireS [2] codes. In the alternative, Macroscopic, approach the velocity distribution of theelectrons is summed locally to yield the macroscopic charge and current density distribution in theshower. From this four-current distributions the (relativistic) Maxwell equations [3] are used to generatethe radiated fields. This approach is followed in the MGMR [4, 5] and EVA [6] calculations. Up to afew years ago the two approaches showed large inconsistencies which were shown to be mainly due toa rather subtle term that was missing in the Microscopic calculations. By correcting this, consistencycould be reached [7] which is a major achievement and indicates that, based on first principles, webasically understand the emission process. It also shows that a dual approach is necessary to be able totrust the results. It should be noted that for coherent radiation the two approaches should give the sameresults, they differ in the incoherent contribution to the radiation field.The main advantage of a macroscopic approach is that it clearly indicates the aspects of the showerdynamics that are responsible for certain features of the detected radio signal. The macroscopic approachrequires a parametrization of the position and time dependence of the four-currents in the showerwhich can be performed at various levels of sophistication. In the following we use the Macroscopicapproach. Since radio emission is basically governed by wave mechanics any features in the frequencyspectrum of the pulse are directly related to critical length scales in the distribution of the particles in theshower.2. BASICS OF RADIO-WAVE EMISSIONTo understand radio emission from extensive air showers it is important to keep in mind that a constantcurrent (at a fixed distance) does not radiate. To create radiation one needs a varying current and/orae-mail: scholten@kvi.nlThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135308005EPJ Web of Conferencesa distance to this current that changes. In an air shower we have both, the charge/current distributionis concentrated in the shower which rushes towards the surface of the Earth with the velocity of lightin vacuum (denoted by c). In addition, the current and charge densities are (roughly) proportional tothe particle density in the shower which grows from the first collision to reach a maximum at Xmaxwhereafter it decreases rapidly again. Since the latter introduces a fast time dependence in the currentsthis is the dominant driving mechanism for the emission of MHz radiation.An equally important consideration is the fact that coherent radiation can only be emitted fromcurrent and charge densities, involving many particles, that have a typical spatial and temporal extentthat is smaller than the wave-length or the inverse-frequency of the radiation. With this simple principlethe main features of the pulse shape can be understood [8]. Here we will go a step further and focus onthe influence of the finite refractivity of air, N = n − 1, on the measured radio signal as this turns outto be essential to come to a correct interpretation.3. THE MACROSCOPIC MODELThe particles in the cosmic-ray shower move through the magnetic field of Earth with the light velocityc. The lighter ones, electrons and positrons, will receive a substantial acceleration due to the action ofthe Lorentz force. This acceleration is counteracted by the collisions with the ambient air molecules andresults in an (air-pressure dependent) drift velocity with opposite directions for electrons and positrons,vd ≈ 0.04 c. As a result a net electric current develops which is proportional to the number of particlesin the shower and oriented in the direction of the Lorentz force, x̂ = −v × B, where v is the direction ofthe original cosmic ray. This varying current is responsible for -so called- geomagnetic radiation whichis polarized along the direction of the emitting current, x̂.In addition to the electric current there is also a net charge excess in the shower due to the knock-out of electrons from air molecules by elastic positron-electron collisions and Compton scattering. Inshower simulations the charge excess is approximately equal to 20% of the number of particles and isthus substantial, and, equally important, varies with shower height z (the distance, measured along theshower, to the point of impact on Earth). Because of this variation there is also charge-excess radiationwhich is radially polarized and as such distinguishable from geomagnetic radiation [9–11].4. INDEX OF REFRACTIONOf particular importance to understand the effect of the finite refractivity of air is the relation betweenthe time, t , for an observer at a distance d from the shower core and the height, z, from which this partof the signal was emitted. For the simple geometry of a vertical shower it can be shown that t ≈ d2/2cz.This implies that signals emitted from the top part of the shower arrive earlier than those emitted fromlater stages. In Fig. 1 (l.h.s.) the red-colored curve shows the dependence between emission height andobserver time for the case of vanishing refractivity. It can easily be seen that this follows closely theapproximate formula t ≈ d2/2cz. The black curve drawn in Fig. 1 gives the vertical shower profile. Ascan be deduced from this picture the leading edge of the resulting pulse lies around t = 1 ns with a zerocrossing of the pulse (related to the shower maximum) near t = 4 ns, consistent with the pulse shownon the r.h.s. of Fig. 1.Including a realistic refractivity of air (n = nGD indicating a dependence on air density as givenby the law of Gladstone and Dale) changes the picture in an essential way as shown by the light bluedotted curves in Fig. 1. Due to the fact that the shower propagates faster than radio waves, much of theradiation emitted along a finite part of the shower arrives at the observer at the same time. This is clearfrom the l.h.s. of the figure by the fact that the blue curve maps all points with z > 4 km to the sameobserver time of t = 7 ns. As a result the pulse (on the r.h.s.) shows a very strong peak at this time. Thefinite but very narrow width of the peak (as compared to the one for n = 1) is due to the fact that theimportant-limiting length scale is no longer the projected length of the shower (which tends to zero at08005-p.2UHECR 2012012345678910z(km)0 5 10 15 20t(ns)0 4 8 12 16Ne 10-7d=100 mn=1n=1.0003n=nGDNe(z)-250-200-150-100-50050E(mV/m)0 1 2 3 4 5 6 7 8 9 10t(ns)d=112 mn=1n=nGDn=1.0003Figure 1. L.h.s.: the emission height z as function of the observer time t for three different values of the index ofrefraction for an observer at a distance of 112 m from the shower core (impact distance is 100 m). The dashed linegives the shower-profile as function of z for a E = 5 × 1017 eV proton-induced shower at  = 27◦. The calculatedpulses for the three cases of the index of refraction n (vacuum, constant Earth-surface value, realistic air-densitydependence) are shown on the r.h.s.012345678910z(km)0 50 100 150 200t(ns)0 4 8 12 16Ne 10-7d=400 mn=1n=1.0003n=nGDNe(z)-0.35-0.3-0.25-0.2-0.15-0.1-0.050.00.050.1E(mV/m)0 10 20 30 40 50 60 70 80 90 100t(ns)d=448 mn=1n=nGDn=1.0003Figure 2. Same as Fig. 1 but for an observer at a distance of 448 m from the shower core (impact distance is 400 m).this point) but the distribution of the particles in the shower front. Simulations show that close to theshower core the particles in the longitudinal direction are concentrated within length-scales of mm’swhile in the transverse direction this may be meters. Projecting this transverse distance along the line ofsight, because of the angles involved, very short dimensions emerge translating in a very narrow pulse.The picture is rather different at a distance of 448 m from the core (impact parameter equals 400 m)as shown in Fig. 2. At this observer distance the shower velocity projected on the line-of-sight is muchless than the propagation speed of radio waves, c/n, and as a result the influence of the air-refractivityis negligible. This is shown on the l.h.s. where the curves showing the mapping of shower height onobserver time lie almost on top of each other. As a result also the calculated pulses for the three differentcases are almost identical. The determining length scale is the longitudinal shower profile projectedalong the line-of-sight, compared to which the length scale of the distribution of particles in the showercore is negligible and thus can be ignored.To obtain a better insight in the implication of the pulse width for observations, the frequency spectraare shown in Fig. 3. This shows that at the Cherenkov distance (defined as the distance from the showercore where the inflection point of the curve giving shower height v.s. observer distance coincides withthe shower maximum) there are strong high frequency components in the signal ranging up to 5 GHz.This is in sharp contrast to the pulse at distances beyond the Cherenkov cone where the maximumfrequency is of the order of 10’s of MHz, dropping with distance.08005-p.3EPJ Web of Conferences1251025E(V/m/MHz)2 5 1022 5 1032 5(MHz)d=112 mn=1n=nGDn=1.0003512510E(V/m/MHz)2 5 10 2 5 102(MHz)d=448 mn=1n=nGDn=1.0003Figure 3. Frequency spectra for the calculated pulses at d = 112 m (l.h.s.) and d = 448 m (r.h.s.).The Cherenkov contribution to radio emission has distinct effects on the lateral distribution of thesignal strength as is discussed in the following section. In addition we are investigating to what extentthis gives us a novel and more accurate method to determine the position of the shower maximum andthus composition. An update of our previous study [12] (where Cherenkov effects were not included) isforthcoming [13].Cherenkov effects could possibly affect the separation of geomagnetic and charge excess radiationby the analysis of the polarization patters [5] as discussed in [11]. Even though Cherenkov effects arenot changing the polarization direction of the signal, the strength or the signal at a particular distancefrom the shower core depends directly on the optimal emission height which may be different for thetwo processes. Ongoing calculations [13] show that Cherenkov emission is important for certain aspect,but that the analysis of frequency filtered data, as discussed for example in [9, 11], is hardly affected.5. THE LATERAL DISTRIBUTIONRecently some preliminary results were reported [14] for the lateral distribution of the signal strengthas measured with the antenna’s in the core of LOFAR [15], see Fig. 4. LOFAR is a new generationradio-astronomy telescope which operates in the frequency regime of 30–240 MHz. The revolutionaryaspect of this telescope is that it deploys thousands of very simple wire antenna’s instead of largeparabolic dishes. All simple antennas can be phase-coupled to obtain the equivalent resolution of a dishwith a diameter of many hundreds kilometers and a collecting area of several thousand square meters.Apart from using this telescope for astronomical observations, because of the software coupling of theindividual antennas, it can also be used for observation of transient phenomena such as radio emissionfrom air showers.Due to the large number of antennas the ground pattern can be determined accurately for singleshowers. This is a major advantage with respect to sparse arrays where data of many showers have tobe combined. The data of Fig. 4 have been obtained using the low-band antennas that operate in thefrequency regime of 30–80 MHz. The figure shows that for distances less than about 100 m the intensityof the radiation is rather constant and starts to drop exponentially only at larger distances. Since thedistance where the Cherenkov radiation reaches a maximum is of the order of 100 m this structure in theLDF can be understood and it follows closely the predicted [16] trend made before the experiment.6. COMPLEMENTARITYThe strong point of cosmic-ray observations at the Pierre Auger Observatory is (besides its large surfacearea) the fact that it allows for hybrid observations. At present this is based on simultaneous observations08005-p.4UHECR 2012Figure 4. Figure from ref. [14] showing the (un calibrated) lateral distribution function (LDF) for two polarizationdirection for a single event as measured with LOFAR.with fluorescence (FD) and surface (SD) detectors where the two detectors yield complementaryinformation on the air shower induced by the cosmic ray. Radio detection (RD) will offer additionalcomplementarity.Depending on the distance from the shower core, the radio pulse is sensitive to different aspects ofthe shower evolution. Close to the shower core, especially at the Cherenkov distance, the frequencycontent of the pulse is determined by the distribution of particles in the shower front [16]. TheCherenkov distance itself is directly related to Xmax of the shower maximum. Therefore this yieldsa measurement of Xmax on an event-by-event basis, which is essential for the determination of thechemical composition. This constitutes an alternative determination of this important shower parameter,independent from FD observations. Also the fall-off of signal strength with distance to the showercore [12] depends on Xmax . The frequency content of the pulse at the Cherenkov angle is a directindication of the spatial distribution of the particles in the shower core [6]. At present little effort hasgone in the understanding of the significance of such a measurement as this could not be investigatedwith any other means. At larger distances the pulse shape is determined by the (derivative of) the showerprofile [8]. Because of the relation between shower height and observer time, the earlier part of theshower induces the higher frequency components (which are much lower than the frequencies seen atthe Cherenkov distance). This makes that the measured pulse is sensitive to the early stages of showerdevelopment which is an aspect that is not well covered by FD measurements.In general the radio signal is exclusively sensitive to the electron content of the shower in contrast tothe SD which are primarily sensitive to the muon content. In addition the polarization of the radio signalcan be used to distinguish the charge excess from the geomagnetic current. No other measurement isable to do so. This will serve as an additional constraint on shower simulations.References[1] M. Ludwig and T. Huege, Astrop. Phys. 34 (2011) 438[2] J. Alvarez-Muñiz, W.R. Carvalho Jr., and E. Zas, Astropart. Phys. 35 (2012) 325[3] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1999[4] O. Scholten, K. Werner, and F. Rusydi, Astropart. Phys. 29 (2008) 94[5] K. Werner and O. Scholten, Astropart. Phys. 29 (2008) 393[6] K. Werner, K.D. de Vries, and O. Scholten, arXiv:1201.4471, Submitted to Astropart. Phys[7] T. Huege, M. Ludwig, O. Scholten, and K.D. de Vries, Nucl. Inst. Meth. A 662 (2012) S17908005-p.5EPJ Web of Conferences[8] O. Scholten and K. Werner, Nucl. Inst. Meth. A 604 (2009) S24; O. Scholten, K.D. de Vries, andK. Werner, Nucl. Inst. Meth. A 662 (2012) S80[9] B. Revenu for the Pierre Auger Collaboration, Proc. 32nd ICRC (2011) 172[10] H. Schoorlemmer et al. [Pierre Auger Coll.], Nucl. Inst. Meth. A 662 (2012) S134[11] A.M. van den Berg, this conference[12] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Astropart. Phys. 34 (2010) 267[13] K.D. de Vries, et al., to be published[14] A. Corstanje et al., Proc. 32nd ICRC (2011) 916; arXiv:1109.5805v1[15] A. Horneffer et al. [LOFAR CR-KSP], Nucl. Inst. Meth. A 617 (2010) 482[16] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107 (2011)06110108005-p.6

What the radio signal tells about the cosmic-ray air shower

University of Groningen

   University of GroningenWhat the radio signal tells about the cosmic-ray air showerScholten, Olaf; de Vries, Krijn D.; Werner, KlausPublished in:EPJ Web of ConferencesDOI:10.1051/epjconf/20135308005IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2013Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Scholten, O., de Vries, K. D., & Werner, K. (2013). What the radio signal tells about the cosmic-ray airshower. EPJ Web of Conferences, 53, [08005]. https://doi.org/10.1051/epjconf/20135308005CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-11-2019EPJ Web of Conferences 53, 08005 (2013)DOI: 10.1051/epjconf/20135308005C© Owned by the authors, published by EDP Sciences, 2013What the radio signal tells about the cosmic-ray air showerOlaf Scholten1,a, Krijn D. de Vries1 and Klaus Werner21KVI, University of Groningen, Groningen, The Netherlands2SUBATECH, Nantes, FranceAbstract. The physics of radio emission from cosmic-ray induced air showers is shortly summarized. Itwill be shown that the radio signal at different distances from the shower axis provides complementaryinformation on the longitudinal shower evolution, in particular the early part, and on the distribution of theelectrons in the shower core. This complements the information obtained from surface, fluorescence, andmuon detectors and is very useful in getting a comprehensive picture of an air shower.1. INTRODUCTIONThere are several approaches that are followed to model radio emission from extensive air showers.These can crudely be separated into two categories, Microscopic and Macroscopic. In a Microscopicapproach the tracks of the individual electrons are followed and the emitted radiation of each is summedto yield the total radiation of the extensive air shower. This approach is incorporated in the REAS [1]and the ZHAireS [2] codes. In the alternative, Macroscopic, approach the velocity distribution of theelectrons is summed locally to yield the macroscopic charge and current density distribution in theshower. From this four-current distributions the (relativistic) Maxwell equations [3] are used to generatethe radiated fields. This approach is followed in the MGMR [4, 5] and EVA [6] calculations. Up to afew years ago the two approaches showed large inconsistencies which were shown to be mainly due toa rather subtle term that was missing in the Microscopic calculations. By correcting this, consistencycould be reached [7] which is a major achievement and indicates that, based on first principles, webasically understand the emission process. It also shows that a dual approach is necessary to be able totrust the results. It should be noted that for coherent radiation the two approaches should give the sameresults, they differ in the incoherent contribution to the radiation field.The main advantage of a macroscopic approach is that it clearly indicates the aspects of the showerdynamics that are responsible for certain features of the detected radio signal. The macroscopic approachrequires a parametrization of the position and time dependence of the four-currents in the showerwhich can be performed at various levels of sophistication. In the following we use the Macroscopicapproach. Since radio emission is basically governed by wave mechanics any features in the frequencyspectrum of the pulse are directly related to critical length scales in the distribution of the particles in theshower.2. BASICS OF RADIO-WAVE EMISSIONTo understand radio emission from extensive air showers it is important to keep in mind that a constantcurrent (at a fixed distance) does not radiate. To create radiation one needs a varying current and/orae-mail: scholten@kvi.nlThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135308005EPJ Web of Conferencesa distance to this current that changes. In an air shower we have both, the charge/current distributionis concentrated in the shower which rushes towards the surface of the Earth with the velocity of lightin vacuum (denoted by c). In addition, the current and charge densities are (roughly) proportional tothe particle density in the shower which grows from the first collision to reach a maximum at Xmaxwhereafter it decreases rapidly again. Since the latter introduces a fast time dependence in the currentsthis is the dominant driving mechanism for the emission of MHz radiation.An equally important consideration is the fact that coherent radiation can only be emitted fromcurrent and charge densities, involving many particles, that have a typical spatial and temporal extentthat is smaller than the wave-length or the inverse-frequency of the radiation. With this simple principlethe main features of the pulse shape can be understood [8]. Here we will go a step further and focus onthe influence of the finite refractivity of air, N = n − 1, on the measured radio signal as this turns outto be essential to come to a correct interpretation.3. THE MACROSCOPIC MODELThe particles in the cosmic-ray shower move through the magnetic field of Earth with the light velocityc. The lighter ones, electrons and positrons, will receive a substantial acceleration due to the action ofthe Lorentz force. This acceleration is counteracted by the collisions with the ambient air molecules andresults in an (air-pressure dependent) drift velocity with opposite directions for electrons and positrons,vd ≈ 0.04 c. As a result a net electric current develops which is proportional to the number of particlesin the shower and oriented in the direction of the Lorentz force, xˆ = −v × B, where v is the direction ofthe original cosmic ray. This varying current is responsible for -so called- geomagnetic radiation whichis polarized along the direction of the emitting current, xˆ.In addition to the electric current there is also a net charge excess in the shower due to the knock-out of electrons from air molecules by elastic positron-electron collisions and Compton scattering. Inshower simulations the charge excess is approximately equal to 20% of the number of particles and isthus substantial, and, equally important, varies with shower height z (the distance, measured along theshower, to the point of impact on Earth). Because of this variation there is also charge-excess radiationwhich is radially polarized and as such distinguishable from geomagnetic radiation [9–11].4. INDEX OF REFRACTIONOf particular importance to understand the effect of the finite refractivity of air is the relation betweenthe time, t , for an observer at a distance d from the shower core and the height, z, from which this partof the signal was emitted. For the simple geometry of a vertical shower it can be shown that t ≈ d2/2cz.This implies that signals emitted from the top part of the shower arrive earlier than those emitted fromlater stages. In Fig. 1 (l.h.s.) the red-colored curve shows the dependence between emission height andobserver time for the case of vanishing refractivity. It can easily be seen that this follows closely theapproximate formula t ≈ d2/2cz. The black curve drawn in Fig. 1 gives the vertical shower profile. Ascan be deduced from this picture the leading edge of the resulting pulse lies around t = 1 ns with a zerocrossing of the pulse (related to the shower maximum) near t = 4 ns, consistent with the pulse shownon the r.h.s. of Fig. 1.Including a realistic refractivity of air (n = nGD indicating a dependence on air density as givenby the law of Gladstone and Dale) changes the picture in an essential way as shown by the light bluedotted curves in Fig. 1. Due to the fact that the shower propagates faster than radio waves, much of theradiation emitted along a finite part of the shower arrives at the observer at the same time. This is clearfrom the l.h.s. of the figure by the fact that the blue curve maps all points with z > 4 km to the sameobserver time of t = 7 ns. As a result the pulse (on the r.h.s.) shows a very strong peak at this time. Thefinite but very narrow width of the peak (as compared to the one for n = 1) is due to the fact that theimportant-limiting length scale is no longer the projected length of the shower (which tends to zero at08005-p.2UHECR 2012012345678910z(km)0 5 10 15 20t(ns)0 4 8 12 16Ne 10-7d=100 mn=1n=1.0003n=nGDNe(z)-250-200-150-100-50050E(mV/m)0 1 2 3 4 5 6 7 8 9 10t(ns)d=112 mn=1n=nGDn=1.0003Figure 1. L.h.s.: the emission height z as function of the observer time t for three different values of the index ofrefraction for an observer at a distance of 112 m from the shower core (impact distance is 100 m). The dashed linegives the shower-profile as function of z for a E = 5 × 1017 eV proton-induced shower at  = 27◦. The calculatedpulses for the three cases of the index of refraction n (vacuum, constant Earth-surface value, realistic air-densitydependence) are shown on the r.h.s.012345678910z(km)0 50 100 150 200t(ns)0 4 8 12 16Ne 10-7d=400 mn=1n=1.0003n=nGDNe(z)-0.35-0.3-0.25-0.2-0.15-0.1-0.050.00.050.1E(mV/m)0 10 20 30 40 50 60 70 80 90 100t(ns)d=448 mn=1n=nGDn=1.0003Figure 2. Same as Fig. 1 but for an observer at a distance of 448 m from the shower core (impact distance is 400 m).this point) but the distribution of the particles in the shower front. Simulations show that close to theshower core the particles in the longitudinal direction are concentrated within length-scales of mm’swhile in the transverse direction this may be meters. Projecting this transverse distance along the line ofsight, because of the angles involved, very short dimensions emerge translating in a very narrow pulse.The picture is rather different at a distance of 448 m from the core (impact parameter equals 400 m)as shown in Fig. 2. At this observer distance the shower velocity projected on the line-of-sight is muchless than the propagation speed of radio waves, c/n, and as a result the influence of the air-refractivityis negligible. This is shown on the l.h.s. where the curves showing the mapping of shower height onobserver time lie almost on top of each other. As a result also the calculated pulses for the three differentcases are almost identical. The determining length scale is the longitudinal shower profile projectedalong the line-of-sight, compared to which the length scale of the distribution of particles in the showercore is negligible and thus can be ignored.To obtain a better insight in the implication of the pulse width for observations, the frequency spectraare shown in Fig. 3. This shows that at the Cherenkov distance (defined as the distance from the showercore where the inflection point of the curve giving shower height v.s. observer distance coincides withthe shower maximum) there are strong high frequency components in the signal ranging up to 5 GHz.This is in sharp contrast to the pulse at distances beyond the Cherenkov cone where the maximumfrequency is of the order of 10’s of MHz, dropping with distance.08005-p.3EPJ Web of Conferences1251025E(V/m/MHz)2 5 102 2 5 103 2 5(MHz)d=112 mn=1n=nGDn=1.0003512510E(V/m/MHz)2 5 10 2 5 102(MHz)d=448 mn=1n=nGDn=1.0003Figure 3. Frequency spectra for the calculated pulses at d = 112 m (l.h.s.) and d = 448 m (r.h.s.).The Cherenkov contribution to radio emission has distinct effects on the lateral distribution of thesignal strength as is discussed in the following section. In addition we are investigating to what extentthis gives us a novel and more accurate method to determine the position of the shower maximum andthus composition. An update of our previous study [12] (where Cherenkov effects were not included) isforthcoming [13].Cherenkov effects could possibly affect the separation of geomagnetic and charge excess radiationby the analysis of the polarization patters [5] as discussed in [11]. Even though Cherenkov effects arenot changing the polarization direction of the signal, the strength or the signal at a particular distancefrom the shower core depends directly on the optimal emission height which may be different for thetwo processes. Ongoing calculations [13] show that Cherenkov emission is important for certain aspect,but that the analysis of frequency filtered data, as discussed for example in [9, 11], is hardly affected.5. THE LATERAL DISTRIBUTIONRecently some preliminary results were reported [14] for the lateral distribution of the signal strengthas measured with the antenna’s in the core of LOFAR [15], see Fig. 4. LOFAR is a new generationradio-astronomy telescope which operates in the frequency regime of 30–240 MHz. The revolutionaryaspect of this telescope is that it deploys thousands of very simple wire antenna’s instead of largeparabolic dishes. All simple antennas can be phase-coupled to obtain the equivalent resolution of a dishwith a diameter of many hundreds kilometers and a collecting area of several thousand square meters.Apart from using this telescope for astronomical observations, because of the software coupling of theindividual antennas, it can also be used for observation of transient phenomena such as radio emissionfrom air showers.Due to the large number of antennas the ground pattern can be determined accurately for singleshowers. This is a major advantage with respect to sparse arrays where data of many showers have tobe combined. The data of Fig. 4 have been obtained using the low-band antennas that operate in thefrequency regime of 30–80 MHz. The figure shows that for distances less than about 100 m the intensityof the radiation is rather constant and starts to drop exponentially only at larger distances. Since thedistance where the Cherenkov radiation reaches a maximum is of the order of 100 m this structure in theLDF can be understood and it follows closely the predicted [16] trend made before the experiment.6. COMPLEMENTARITYThe strong point of cosmic-ray observations at the Pierre Auger Observatory is (besides its large surfacearea) the fact that it allows for hybrid observations. At present this is based on simultaneous observations08005-p.4UHECR 2012Figure 4. Figure from ref. [14] showing the (un calibrated) lateral distribution function (LDF) for two polarizationdirection for a single event as measured with LOFAR.with fluorescence (FD) and surface (SD) detectors where the two detectors yield complementaryinformation on the air shower induced by the cosmic ray. Radio detection (RD) will offer additionalcomplementarity.Depending on the distance from the shower core, the radio pulse is sensitive to different aspects ofthe shower evolution. Close to the shower core, especially at the Cherenkov distance, the frequencycontent of the pulse is determined by the distribution of particles in the shower front [16]. TheCherenkov distance itself is directly related to Xmax of the shower maximum. Therefore this yieldsa measurement of Xmax on an event-by-event basis, which is essential for the determination of thechemical composition. This constitutes an alternative determination of this important shower parameter,independent from FD observations. Also the fall-off of signal strength with distance to the showercore [12] depends on Xmax . The frequency content of the pulse at the Cherenkov angle is a directindication of the spatial distribution of the particles in the shower core [6]. At present little effort hasgone in the understanding of the significance of such a measurement as this could not be investigatedwith any other means. At larger distances the pulse shape is determined by the (derivative of) the showerprofile [8]. Because of the relation between shower height and observer time, the earlier part of theshower induces the higher frequency components (which are much lower than the frequencies seen atthe Cherenkov distance). This makes that the measured pulse is sensitive to the early stages of showerdevelopment which is an aspect that is not well covered by FD measurements.In general the radio signal is exclusively sensitive to the electron content of the shower in contrast tothe SD which are primarily sensitive to the muon content. In addition the polarization of the radio signalcan be used to distinguish the charge excess from the geomagnetic current. No other measurement isable to do so. This will serve as an additional constraint on shower simulations.References[1] M. Ludwig and T. Huege, Astrop. Phys. 34 (2011) 438[2] J. Alvarez-Muñiz, W.R. Carvalho Jr., and E. Zas, Astropart. Phys. 35 (2012) 325[3] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1999[4] O. Scholten, K. Werner, and F. Rusydi, Astropart. Phys. 29 (2008) 94[5] K. Werner and O. Scholten, Astropart. Phys. 29 (2008) 393[6] K. Werner, K.D. de Vries, and O. Scholten, arXiv:1201.4471, Submitted to Astropart. Phys[7] T. Huege, M. Ludwig, O. Scholten, and K.D. de Vries, Nucl. Inst. Meth. A 662 (2012) S17908005-p.5EPJ Web of Conferences[8] O. Scholten and K. Werner, Nucl. Inst. Meth. A 604 (2009) S24; O. Scholten, K.D. de Vries, andK. Werner, Nucl. Inst. Meth. A 662 (2012) S80[9] B. Revenu for the Pierre Auger Collaboration, Proc. 32nd ICRC (2011) 172[10] H. Schoorlemmer et al. [Pierre Auger Coll.], Nucl. Inst. Meth. A 662 (2012) S134[11] A.M. van den Berg, this conference[12] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Astropart. Phys. 34 (2010) 267[13] K.D. de Vries, et al., to be published[14] A. Corstanje et al., Proc. 32nd ICRC (2011) 916; arXiv:1109.5805v1[15] A. Horneffer et al. [LOFAR CR-KSP], Nucl. Inst. Meth. A 617 (2010) 482[16] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107 (2011)06110108005-p.6

Proceedings - University of Groningen

   University of GroningenWhat the radio signal tells about the cosmic-ray air showerScholten, Olaf; de Vries, Krijn D.; Werner, KlausPublished in:EPJ Web of ConferencesDOI:10.1051/epjconf/20135308005IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2013Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Scholten, O., de Vries, K. D., & Werner, K. (2013). What the radio signal tells about the cosmic-ray airshower. EPJ Web of Conferences, 53, [08005]. https://doi.org/10.1051/epjconf/20135308005CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 04-06-2022EPJ Web of Conferences 53, 08005 (2013)DOI: 10.1051/epjconf/20135308005C© Owned by the authors, published by EDP Sciences, 2013What the radio signal tells about the cosmic-ray air showerOlaf Scholten1,a, Krijn D. de Vries1 and Klaus Werner21KVI, University of Groningen, Groningen, The Netherlands2SUBATECH, Nantes, FranceAbstract. The physics of radio emission from cosmic-ray induced air showers is shortly summarized. Itwill be shown that the radio signal at different distances from the shower axis provides complementaryinformation on the longitudinal shower evolution, in particular the early part, and on the distribution of theelectrons in the shower core. This complements the information obtained from surface, fluorescence, andmuon detectors and is very useful in getting a comprehensive picture of an air shower.1. INTRODUCTIONThere are several approaches that are followed to model radio emission from extensive air showers.These can crudely be separated into two categories, Microscopic and Macroscopic. In a Microscopicapproach the tracks of the individual electrons are followed and the emitted radiation of each is summedto yield the total radiation of the extensive air shower. This approach is incorporated in the REAS [1]and the ZHAireS [2] codes. In the alternative, Macroscopic, approach the velocity distribution of theelectrons is summed locally to yield the macroscopic charge and current density distribution in theshower. From this four-current distributions the (relativistic) Maxwell equations [3] are used to generatethe radiated fields. This approach is followed in the MGMR [4, 5] and EVA [6] calculations. Up to afew years ago the two approaches showed large inconsistencies which were shown to be mainly due toa rather subtle term that was missing in the Microscopic calculations. By correcting this, consistencycould be reached [7] which is a major achievement and indicates that, based on first principles, webasically understand the emission process. It also shows that a dual approach is necessary to be able totrust the results. It should be noted that for coherent radiation the two approaches should give the sameresults, they differ in the incoherent contribution to the radiation field.The main advantage of a macroscopic approach is that it clearly indicates the aspects of the showerdynamics that are responsible for certain features of the detected radio signal. The macroscopic approachrequires a parametrization of the position and time dependence of the four-currents in the showerwhich can be performed at various levels of sophistication. In the following we use the Macroscopicapproach. Since radio emission is basically governed by wave mechanics any features in the frequencyspectrum of the pulse are directly related to critical length scales in the distribution of the particles in theshower.2. BASICS OF RADIO-WAVE EMISSIONTo understand radio emission from extensive air showers it is important to keep in mind that a constantcurrent (at a fixed distance) does not radiate. To create radiation one needs a varying current and/orae-mail: scholten@kvi.nlThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135308005EPJ Web of Conferencesa distance to this current that changes. In an air shower we have both, the charge/current distributionis concentrated in the shower which rushes towards the surface of the Earth with the velocity of lightin vacuum (denoted by c). In addition, the current and charge densities are (roughly) proportional tothe particle density in the shower which grows from the first collision to reach a maximum at Xmaxwhereafter it decreases rapidly again. Since the latter introduces a fast time dependence in the currentsthis is the dominant driving mechanism for the emission of MHz radiation.An equally important consideration is the fact that coherent radiation can only be emitted fromcurrent and charge densities, involving many particles, that have a typical spatial and temporal extentthat is smaller than the wave-length or the inverse-frequency of the radiation. With this simple principlethe main features of the pulse shape can be understood [8]. Here we will go a step further and focus onthe influence of the finite refractivity of air, N = n − 1, on the measured radio signal as this turns outto be essential to come to a correct interpretation.3. THE MACROSCOPIC MODELThe particles in the cosmic-ray shower move through the magnetic field of Earth with the light velocityc. The lighter ones, electrons and positrons, will receive a substantial acceleration due to the action ofthe Lorentz force. This acceleration is counteracted by the collisions with the ambient air molecules andresults in an (air-pressure dependent) drift velocity with opposite directions for electrons and positrons,vd ≈ 0.04 c. As a result a net electric current develops which is proportional to the number of particlesin the shower and oriented in the direction of the Lorentz force, x̂ = −v × B, where v is the direction ofthe original cosmic ray. This varying current is responsible for -so called- geomagnetic radiation whichis polarized along the direction of the emitting current, x̂.In addition to the electric current there is also a net charge excess in the shower due to the knock-out of electrons from air molecules by elastic positron-electron collisions and Compton scattering. Inshower simulations the charge excess is approximately equal to 20% of the number of particles and isthus substantial, and, equally important, varies with shower height z (the distance, measured along theshower, to the point of impact on Earth). Because of this variation there is also charge-excess radiationwhich is radially polarized and as such distinguishable from geomagnetic radiation [9–11].4. INDEX OF REFRACTIONOf particular importance to understand the effect of the finite refractivity of air is the relation betweenthe time, t , for an observer at a distance d from the shower core and the height, z, from which this partof the signal was emitted. For the simple geometry of a vertical shower it can be shown that t ≈ d2/2cz.This implies that signals emitted from the top part of the shower arrive earlier than those emitted fromlater stages. In Fig. 1 (l.h.s.) the red-colored curve shows the dependence between emission height andobserver time for the case of vanishing refractivity. It can easily be seen that this follows closely theapproximate formula t ≈ d2/2cz. The black curve drawn in Fig. 1 gives the vertical shower profile. Ascan be deduced from this picture the leading edge of the resulting pulse lies around t = 1 ns with a zerocrossing of the pulse (related to the shower maximum) near t = 4 ns, consistent with the pulse shownon the r.h.s. of Fig. 1.Including a realistic refractivity of air (n = nGD indicating a dependence on air density as givenby the law of Gladstone and Dale) changes the picture in an essential way as shown by the light bluedotted curves in Fig. 1. Due to the fact that the shower propagates faster than radio waves, much of theradiation emitted along a finite part of the shower arrives at the observer at the same time. This is clearfrom the l.h.s. of the figure by the fact that the blue curve maps all points with z > 4 km to the sameobserver time of t = 7 ns. As a result the pulse (on the r.h.s.) shows a very strong peak at this time. Thefinite but very narrow width of the peak (as compared to the one for n = 1) is due to the fact that theimportant-limiting length scale is no longer the projected length of the shower (which tends to zero at08005-p.2UHECR 2012012345678910z(km)0 5 10 15 20t(ns)0 4 8 12 16Ne 10-7d=100 mn=1n=1.0003n=nGDNe(z)-250-200-150-100-50050E(mV/m)0 1 2 3 4 5 6 7 8 9 10t(ns)d=112 mn=1n=nGDn=1.0003Figure 1. L.h.s.: the emission height z as function of the observer time t for three different values of the index ofrefraction for an observer at a distance of 112 m from the shower core (impact distance is 100 m). The dashed linegives the shower-profile as function of z for a E = 5 × 1017 eV proton-induced shower at  = 27◦. The calculatedpulses for the three cases of the index of refraction n (vacuum, constant Earth-surface value, realistic air-densitydependence) are shown on the r.h.s.012345678910z(km)0 50 100 150 200t(ns)0 4 8 12 16Ne 10-7d=400 mn=1n=1.0003n=nGDNe(z)-0.35-0.3-0.25-0.2-0.15-0.1-0.050.00.050.1E(mV/m)0 10 20 30 40 50 60 70 80 90 100t(ns)d=448 mn=1n=nGDn=1.0003Figure 2. Same as Fig. 1 but for an observer at a distance of 448 m from the shower core (impact distance is 400 m).this point) but the distribution of the particles in the shower front. Simulations show that close to theshower core the particles in the longitudinal direction are concentrated within length-scales of mm’swhile in the transverse direction this may be meters. Projecting this transverse distance along the line ofsight, because of the angles involved, very short dimensions emerge translating in a very narrow pulse.The picture is rather different at a distance of 448 m from the core (impact parameter equals 400 m)as shown in Fig. 2. At this observer distance the shower velocity projected on the line-of-sight is muchless than the propagation speed of radio waves, c/n, and as a result the influence of the air-refractivityis negligible. This is shown on the l.h.s. where the curves showing the mapping of shower height onobserver time lie almost on top of each other. As a result also the calculated pulses for the three differentcases are almost identical. The determining length scale is the longitudinal shower profile projectedalong the line-of-sight, compared to which the length scale of the distribution of particles in the showercore is negligible and thus can be ignored.To obtain a better insight in the implication of the pulse width for observations, the frequency spectraare shown in Fig. 3. This shows that at the Cherenkov distance (defined as the distance from the showercore where the inflection point of the curve giving shower height v.s. observer distance coincides withthe shower maximum) there are strong high frequency components in the signal ranging up to 5 GHz.This is in sharp contrast to the pulse at distances beyond the Cherenkov cone where the maximumfrequency is of the order of 10’s of MHz, dropping with distance.08005-p.3EPJ Web of Conferences1251025E(V/m/MHz)2 5 1022 5 1032 5(MHz)d=112 mn=1n=nGDn=1.0003512510E(V/m/MHz)2 5 10 2 5 102(MHz)d=448 mn=1n=nGDn=1.0003Figure 3. Frequency spectra for the calculated pulses at d = 112 m (l.h.s.) and d = 448 m (r.h.s.).The Cherenkov contribution to radio emission has distinct effects on the lateral distribution of thesignal strength as is discussed in the following section. In addition we are investigating to what extentthis gives us a novel and more accurate method to determine the position of the shower maximum andthus composition. An update of our previous study [12] (where Cherenkov effects were not included) isforthcoming [13].Cherenkov effects could possibly affect the separation of geomagnetic and charge excess radiationby the analysis of the polarization patters [5] as discussed in [11]. Even though Cherenkov effects arenot changing the polarization direction of the signal, the strength or the signal at a particular distancefrom the shower core depends directly on the optimal emission height which may be different for thetwo processes. Ongoing calculations [13] show that Cherenkov emission is important for certain aspect,but that the analysis of frequency filtered data, as discussed for example in [9, 11], is hardly affected.5. THE LATERAL DISTRIBUTIONRecently some preliminary results were reported [14] for the lateral distribution of the signal strengthas measured with the antenna’s in the core of LOFAR [15], see Fig. 4. LOFAR is a new generationradio-astronomy telescope which operates in the frequency regime of 30–240 MHz. The revolutionaryaspect of this telescope is that it deploys thousands of very simple wire antenna’s instead of largeparabolic dishes. All simple antennas can be phase-coupled to obtain the equivalent resolution of a dishwith a diameter of many hundreds kilometers and a collecting area of several thousand square meters.Apart from using this telescope for astronomical observations, because of the software coupling of theindividual antennas, it can also be used for observation of transient phenomena such as radio emissionfrom air showers.Due to the large number of antennas the ground pattern can be determined accurately for singleshowers. This is a major advantage with respect to sparse arrays where data of many showers have tobe combined. The data of Fig. 4 have been obtained using the low-band antennas that operate in thefrequency regime of 30–80 MHz. The figure shows that for distances less than about 100 m the intensityof the radiation is rather constant and starts to drop exponentially only at larger distances. Since thedistance where the Cherenkov radiation reaches a maximum is of the order of 100 m this structure in theLDF can be understood and it follows closely the predicted [16] trend made before the experiment.6. COMPLEMENTARITYThe strong point of cosmic-ray observations at the Pierre Auger Observatory is (besides its large surfacearea) the fact that it allows for hybrid observations. At present this is based on simultaneous observations08005-p.4UHECR 2012Figure 4. Figure from ref. [14] showing the (un calibrated) lateral distribution function (LDF) for two polarizationdirection for a single event as measured with LOFAR.with fluorescence (FD) and surface (SD) detectors where the two detectors yield complementaryinformation on the air shower induced by the cosmic ray. Radio detection (RD) will offer additionalcomplementarity.Depending on the distance from the shower core, the radio pulse is sensitive to different aspects ofthe shower evolution. Close to the shower core, especially at the Cherenkov distance, the frequencycontent of the pulse is determined by the distribution of particles in the shower front [16]. TheCherenkov distance itself is directly related to Xmax of the shower maximum. Therefore this yieldsa measurement of Xmax on an event-by-event basis, which is essential for the determination of thechemical composition. This constitutes an alternative determination of this important shower parameter,independent from FD observations. Also the fall-off of signal strength with distance to the showercore [12] depends on Xmax . The frequency content of the pulse at the Cherenkov angle is a directindication of the spatial distribution of the particles in the shower core [6]. At present little effort hasgone in the understanding of the significance of such a measurement as this could not be investigatedwith any other means. At larger distances the pulse shape is determined by the (derivative of) the showerprofile [8]. Because of the relation between shower height and observer time, the earlier part of theshower induces the higher frequency components (which are much lower than the frequencies seen atthe Cherenkov distance). This makes that the measured pulse is sensitive to the early stages of showerdevelopment which is an aspect that is not well covered by FD measurements.In general the radio signal is exclusively sensitive to the electron content of the shower in contrast tothe SD which are primarily sensitive to the muon content. In addition the polarization of the radio signalcan be used to distinguish the charge excess from the geomagnetic current. No other measurement isable to do so. This will serve as an additional constraint on shower simulations.References[1] M. Ludwig and T. Huege, Astrop. Phys. 34 (2011) 438[2] J. Alvarez-Muñiz, W.R. Carvalho Jr., and E. Zas, Astropart. Phys. 35 (2012) 325[3] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1999[4] O. Scholten, K. Werner, and F. Rusydi, Astropart. Phys. 29 (2008) 94[5] K. Werner and O. Scholten, Astropart. Phys. 29 (2008) 393[6] K. Werner, K.D. de Vries, and O. Scholten, arXiv:1201.4471, Submitted to Astropart. Phys[7] T. Huege, M. Ludwig, O. Scholten, and K.D. de Vries, Nucl. Inst. Meth. A 662 (2012) S17908005-p.5EPJ Web of Conferences[8] O. Scholten and K. Werner, Nucl. Inst. Meth. A 604 (2009) S24; O. Scholten, K.D. de Vries, andK. Werner, Nucl. Inst. Meth. A 662 (2012) S80[9] B. Revenu for the Pierre Auger Collaboration, Proc. 32nd ICRC (2011) 172[10] H. Schoorlemmer et al. [Pierre Auger Coll.], Nucl. Inst. Meth. A 662 (2012) S134[11] A.M. van den Berg, this conference[12] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Astropart. Phys. 34 (2010) 267[13] K.D. de Vries, et al., to be published[14] A. Corstanje et al., Proc. 32nd ICRC (2011) 916; arXiv:1109.5805v1[15] A. Horneffer et al. [LOFAR CR-KSP], Nucl. Inst. Meth. A 617 (2010) 482[16] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107 (2011)06110108005-p.6

The physics of radio emission from cosmic-ray induced air showers is shortly summarized. It will be shown that the radio signal at different distances from the shower axis provides complementary information on the longitudinal shower evolution, in particular the early part, and on the distribution of the electrons in the shower core. This complements the information obtained from surface, fluorescence, and muon detectors and is very useful in getting a comprehensive picture of an air shower.

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ARTS repository - University of Groningen

   University of GroningenWhat the radio signal tells about the cosmic-ray air showerScholten, Olaf; de Vries, Krijn D.; Werner, KlausPublished in:EPJ Web of ConferencesDOI:10.1051/epjconf/20135308005IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2013Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Scholten, O., de Vries, K. D., & Werner, K. (2013). What the radio signal tells about the cosmic-ray airshower. EPJ Web of Conferences, 53, [08005]. https://doi.org/10.1051/epjconf/20135308005CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 07-06-2022EPJ Web of Conferences 53, 08005 (2013)DOI: 10.1051/epjconf/20135308005C© Owned by the authors, published by EDP Sciences, 2013What the radio signal tells about the cosmic-ray air showerOlaf Scholten1,a, Krijn D. de Vries1 and Klaus Werner21KVI, University of Groningen, Groningen, The Netherlands2SUBATECH, Nantes, FranceAbstract. The physics of radio emission from cosmic-ray induced air showers is shortly summarized. Itwill be shown that the radio signal at different distances from the shower axis provides complementaryinformation on the longitudinal shower evolution, in particular the early part, and on the distribution of theelectrons in the shower core. This complements the information obtained from surface, fluorescence, andmuon detectors and is very useful in getting a comprehensive picture of an air shower.1. INTRODUCTIONThere are several approaches that are followed to model radio emission from extensive air showers.These can crudely be separated into two categories, Microscopic and Macroscopic. In a Microscopicapproach the tracks of the individual electrons are followed and the emitted radiation of each is summedto yield the total radiation of the extensive air shower. This approach is incorporated in the REAS [1]and the ZHAireS [2] codes. In the alternative, Macroscopic, approach the velocity distribution of theelectrons is summed locally to yield the macroscopic charge and current density distribution in theshower. From this four-current distributions the (relativistic) Maxwell equations [3] are used to generatethe radiated fields. This approach is followed in the MGMR [4, 5] and EVA [6] calculations. Up to afew years ago the two approaches showed large inconsistencies which were shown to be mainly due toa rather subtle term that was missing in the Microscopic calculations. By correcting this, consistencycould be reached [7] which is a major achievement and indicates that, based on first principles, webasically understand the emission process. It also shows that a dual approach is necessary to be able totrust the results. It should be noted that for coherent radiation the two approaches should give the sameresults, they differ in the incoherent contribution to the radiation field.The main advantage of a macroscopic approach is that it clearly indicates the aspects of the showerdynamics that are responsible for certain features of the detected radio signal. The macroscopic approachrequires a parametrization of the position and time dependence of the four-currents in the showerwhich can be performed at various levels of sophistication. In the following we use the Macroscopicapproach. Since radio emission is basically governed by wave mechanics any features in the frequencyspectrum of the pulse are directly related to critical length scales in the distribution of the particles in theshower.2. BASICS OF RADIO-WAVE EMISSIONTo understand radio emission from extensive air showers it is important to keep in mind that a constantcurrent (at a fixed distance) does not radiate. To create radiation one needs a varying current and/orae-mail: scholten@kvi.nlThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135308005EPJ Web of Conferencesa distance to this current that changes. In an air shower we have both, the charge/current distributionis concentrated in the shower which rushes towards the surface of the Earth with the velocity of lightin vacuum (denoted by c). In addition, the current and charge densities are (roughly) proportional tothe particle density in the shower which grows from the first collision to reach a maximum at Xmaxwhereafter it decreases rapidly again. Since the latter introduces a fast time dependence in the currentsthis is the dominant driving mechanism for the emission of MHz radiation.An equally important consideration is the fact that coherent radiation can only be emitted fromcurrent and charge densities, involving many particles, that have a typical spatial and temporal extentthat is smaller than the wave-length or the inverse-frequency of the radiation. With this simple principlethe main features of the pulse shape can be understood [8]. Here we will go a step further and focus onthe influence of the finite refractivity of air, N = n − 1, on the measured radio signal as this turns outto be essential to come to a correct interpretation.3. THE MACROSCOPIC MODELThe particles in the cosmic-ray shower move through the magnetic field of Earth with the light velocityc. The lighter ones, electrons and positrons, will receive a substantial acceleration due to the action ofthe Lorentz force. This acceleration is counteracted by the collisions with the ambient air molecules andresults in an (air-pressure dependent) drift velocity with opposite directions for electrons and positrons,vd ≈ 0.04 c. As a result a net electric current develops which is proportional to the number of particlesin the shower and oriented in the direction of the Lorentz force, x̂ = −v × B, where v is the direction ofthe original cosmic ray. This varying current is responsible for -so called- geomagnetic radiation whichis polarized along the direction of the emitting current, x̂.In addition to the electric current there is also a net charge excess in the shower due to the knock-out of electrons from air molecules by elastic positron-electron collisions and Compton scattering. Inshower simulations the charge excess is approximately equal to 20% of the number of particles and isthus substantial, and, equally important, varies with shower height z (the distance, measured along theshower, to the point of impact on Earth). Because of this variation there is also charge-excess radiationwhich is radially polarized and as such distinguishable from geomagnetic radiation [9–11].4. INDEX OF REFRACTIONOf particular importance to understand the effect of the finite refractivity of air is the relation betweenthe time, t , for an observer at a distance d from the shower core and the height, z, from which this partof the signal was emitted. For the simple geometry of a vertical shower it can be shown that t ≈ d2/2cz.This implies that signals emitted from the top part of the shower arrive earlier than those emitted fromlater stages. In Fig. 1 (l.h.s.) the red-colored curve shows the dependence between emission height andobserver time for the case of vanishing refractivity. It can easily be seen that this follows closely theapproximate formula t ≈ d2/2cz. The black curve drawn in Fig. 1 gives the vertical shower profile. Ascan be deduced from this picture the leading edge of the resulting pulse lies around t = 1 ns with a zerocrossing of the pulse (related to the shower maximum) near t = 4 ns, consistent with the pulse shownon the r.h.s. of Fig. 1.Including a realistic refractivity of air (n = nGD indicating a dependence on air density as givenby the law of Gladstone and Dale) changes the picture in an essential way as shown by the light bluedotted curves in Fig. 1. Due to the fact that the shower propagates faster than radio waves, much of theradiation emitted along a finite part of the shower arrives at the observer at the same time. This is clearfrom the l.h.s. of the figure by the fact that the blue curve maps all points with z > 4 km to the sameobserver time of t = 7 ns. As a result the pulse (on the r.h.s.) shows a very strong peak at this time. Thefinite but very narrow width of the peak (as compared to the one for n = 1) is due to the fact that theimportant-limiting length scale is no longer the projected length of the shower (which tends to zero at08005-p.2UHECR 2012012345678910z(km)0 5 10 15 20t(ns)0 4 8 12 16Ne 10-7d=100 mn=1n=1.0003n=nGDNe(z)-250-200-150-100-50050E(mV/m)0 1 2 3 4 5 6 7 8 9 10t(ns)d=112 mn=1n=nGDn=1.0003Figure 1. L.h.s.: the emission height z as function of the observer time t for three different values of the index ofrefraction for an observer at a distance of 112 m from the shower core (impact distance is 100 m). The dashed linegives the shower-profile as function of z for a E = 5 × 1017 eV proton-induced shower at  = 27◦. The calculatedpulses for the three cases of the index of refraction n (vacuum, constant Earth-surface value, realistic air-densitydependence) are shown on the r.h.s.012345678910z(km)0 50 100 150 200t(ns)0 4 8 12 16Ne 10-7d=400 mn=1n=1.0003n=nGDNe(z)-0.35-0.3-0.25-0.2-0.15-0.1-0.050.00.050.1E(mV/m)0 10 20 30 40 50 60 70 80 90 100t(ns)d=448 mn=1n=nGDn=1.0003Figure 2. Same as Fig. 1 but for an observer at a distance of 448 m from the shower core (impact distance is 400 m).this point) but the distribution of the particles in the shower front. Simulations show that close to theshower core the particles in the longitudinal direction are concentrated within length-scales of mm’swhile in the transverse direction this may be meters. Projecting this transverse distance along the line ofsight, because of the angles involved, very short dimensions emerge translating in a very narrow pulse.The picture is rather different at a distance of 448 m from the core (impact parameter equals 400 m)as shown in Fig. 2. At this observer distance the shower velocity projected on the line-of-sight is muchless than the propagation speed of radio waves, c/n, and as a result the influence of the air-refractivityis negligible. This is shown on the l.h.s. where the curves showing the mapping of shower height onobserver time lie almost on top of each other. As a result also the calculated pulses for the three differentcases are almost identical. The determining length scale is the longitudinal shower profile projectedalong the line-of-sight, compared to which the length scale of the distribution of particles in the showercore is negligible and thus can be ignored.To obtain a better insight in the implication of the pulse width for observations, the frequency spectraare shown in Fig. 3. This shows that at the Cherenkov distance (defined as the distance from the showercore where the inflection point of the curve giving shower height v.s. observer distance coincides withthe shower maximum) there are strong high frequency components in the signal ranging up to 5 GHz.This is in sharp contrast to the pulse at distances beyond the Cherenkov cone where the maximumfrequency is of the order of 10’s of MHz, dropping with distance.08005-p.3EPJ Web of Conferences1251025E(V/m/MHz)2 5 1022 5 1032 5(MHz)d=112 mn=1n=nGDn=1.0003512510E(V/m/MHz)2 5 10 2 5 102(MHz)d=448 mn=1n=nGDn=1.0003Figure 3. Frequency spectra for the calculated pulses at d = 112 m (l.h.s.) and d = 448 m (r.h.s.).The Cherenkov contribution to radio emission has distinct effects on the lateral distribution of thesignal strength as is discussed in the following section. In addition we are investigating to what extentthis gives us a novel and more accurate method to determine the position of the shower maximum andthus composition. An update of our previous study [12] (where Cherenkov effects were not included) isforthcoming [13].Cherenkov effects could possibly affect the separation of geomagnetic and charge excess radiationby the analysis of the polarization patters [5] as discussed in [11]. Even though Cherenkov effects arenot changing the polarization direction of the signal, the strength or the signal at a particular distancefrom the shower core depends directly on the optimal emission height which may be different for thetwo processes. Ongoing calculations [13] show that Cherenkov emission is important for certain aspect,but that the analysis of frequency filtered data, as discussed for example in [9, 11], is hardly affected.5. THE LATERAL DISTRIBUTIONRecently some preliminary results were reported [14] for the lateral distribution of the signal strengthas measured with the antenna’s in the core of LOFAR [15], see Fig. 4. LOFAR is a new generationradio-astronomy telescope which operates in the frequency regime of 30–240 MHz. The revolutionaryaspect of this telescope is that it deploys thousands of very simple wire antenna’s instead of largeparabolic dishes. All simple antennas can be phase-coupled to obtain the equivalent resolution of a dishwith a diameter of many hundreds kilometers and a collecting area of several thousand square meters.Apart from using this telescope for astronomical observations, because of the software coupling of theindividual antennas, it can also be used for observation of transient phenomena such as radio emissionfrom air showers.Due to the large number of antennas the ground pattern can be determined accurately for singleshowers. This is a major advantage with respect to sparse arrays where data of many showers have tobe combined. The data of Fig. 4 have been obtained using the low-band antennas that operate in thefrequency regime of 30–80 MHz. The figure shows that for distances less than about 100 m the intensityof the radiation is rather constant and starts to drop exponentially only at larger distances. Since thedistance where the Cherenkov radiation reaches a maximum is of the order of 100 m this structure in theLDF can be understood and it follows closely the predicted [16] trend made before the experiment.6. COMPLEMENTARITYThe strong point of cosmic-ray observations at the Pierre Auger Observatory is (besides its large surfacearea) the fact that it allows for hybrid observations. At present this is based on simultaneous observations08005-p.4UHECR 2012Figure 4. Figure from ref. [14] showing the (un calibrated) lateral distribution function (LDF) for two polarizationdirection for a single event as measured with LOFAR.with fluorescence (FD) and surface (SD) detectors where the two detectors yield complementaryinformation on the air shower induced by the cosmic ray. Radio detection (RD) will offer additionalcomplementarity.Depending on the distance from the shower core, the radio pulse is sensitive to different aspects ofthe shower evolution. Close to the shower core, especially at the Cherenkov distance, the frequencycontent of the pulse is determined by the distribution of particles in the shower front [16]. TheCherenkov distance itself is directly related to Xmax of the shower maximum. Therefore this yieldsa measurement of Xmax on an event-by-event basis, which is essential for the determination of thechemical composition. This constitutes an alternative determination of this important shower parameter,independent from FD observations. Also the fall-off of signal strength with distance to the showercore [12] depends on Xmax . The frequency content of the pulse at the Cherenkov angle is a directindication of the spatial distribution of the particles in the shower core [6]. At present little effort hasgone in the understanding of the significance of such a measurement as this could not be investigatedwith any other means. At larger distances the pulse shape is determined by the (derivative of) the showerprofile [8]. Because of the relation between shower height and observer time, the earlier part of theshower induces the higher frequency components (which are much lower than the frequencies seen atthe Cherenkov distance). This makes that the measured pulse is sensitive to the early stages of showerdevelopment which is an aspect that is not well covered by FD measurements.In general the radio signal is exclusively sensitive to the electron content of the shower in contrast tothe SD which are primarily sensitive to the muon content. In addition the polarization of the radio signalcan be used to distinguish the charge excess from the geomagnetic current. No other measurement isable to do so. This will serve as an additional constraint on shower simulations.References[1] M. Ludwig and T. Huege, Astrop. Phys. 34 (2011) 438[2] J. Alvarez-Muñiz, W.R. Carvalho Jr., and E. Zas, Astropart. Phys. 35 (2012) 325[3] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1999[4] O. Scholten, K. Werner, and F. Rusydi, Astropart. Phys. 29 (2008) 94[5] K. Werner and O. Scholten, Astropart. Phys. 29 (2008) 393[6] K. Werner, K.D. de Vries, and O. Scholten, arXiv:1201.4471, Submitted to Astropart. Phys[7] T. Huege, M. Ludwig, O. Scholten, and K.D. de Vries, Nucl. Inst. Meth. A 662 (2012) S17908005-p.5EPJ Web of Conferences[8] O. Scholten and K. Werner, Nucl. Inst. Meth. A 604 (2009) S24; O. Scholten, K.D. de Vries, andK. Werner, Nucl. Inst. Meth. A 662 (2012) S80[9] B. Revenu for the Pierre Auger Collaboration, Proc. 32nd ICRC (2011) 172[10] H. Schoorlemmer et al. [Pierre Auger Coll.], Nucl. Inst. Meth. A 662 (2012) S134[11] A.M. van den Berg, this conference[12] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Astropart. Phys. 34 (2010) 267[13] K.D. de Vries, et al., to be published[14] A. Corstanje et al., Proc. 32nd ICRC (2011) 916; arXiv:1109.5805v1[15] A. Horneffer et al. [LOFAR CR-KSP], Nucl. Inst. Meth. A 617 (2010) 482[16] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107 (2011)06110108005-p.6

Olaf Scholten

Krijn D. de Vries

Klaus Werner

Crossref

   University of GroningenWhat the radio signal tells about the cosmic-ray air showerScholten, Olaf; de Vries, Krijn D.; Werner, KlausPublished in:EPJ Web of ConferencesDOI:10.1051/epjconf/20135308005IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2013Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Scholten, O., de Vries, K. D., & Werner, K. (2013). What the radio signal tells about the cosmic-ray airshower. EPJ Web of Conferences, 53, Article 08005. https://doi.org/10.1051/epjconf/20135308005CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 09-09-2023EPJ Web of Conferences 53, 08005 (2013)DOI: 10.1051/epjconf/20135308005C© Owned by the authors, published by EDP Sciences, 2013What the radio signal tells about the cosmic-ray air showerOlaf Scholten1,a, Krijn D. de Vries1 and Klaus Werner21KVI, University of Groningen, Groningen, The Netherlands2SUBATECH, Nantes, FranceAbstract. The physics of radio emission from cosmic-ray induced air showers is shortly summarized. Itwill be shown that the radio signal at different distances from the shower axis provides complementaryinformation on the longitudinal shower evolution, in particular the early part, and on the distribution of theelectrons in the shower core. This complements the information obtained from surface, fluorescence, andmuon detectors and is very useful in getting a comprehensive picture of an air shower.1. INTRODUCTIONThere are several approaches that are followed to model radio emission from extensive air showers.These can crudely be separated into two categories, Microscopic and Macroscopic. In a Microscopicapproach the tracks of the individual electrons are followed and the emitted radiation of each is summedto yield the total radiation of the extensive air shower. This approach is incorporated in the REAS [1]and the ZHAireS [2] codes. In the alternative, Macroscopic, approach the velocity distribution of theelectrons is summed locally to yield the macroscopic charge and current density distribution in theshower. From this four-current distributions the (relativistic) Maxwell equations [3] are used to generatethe radiated fields. This approach is followed in the MGMR [4, 5] and EVA [6] calculations. Up to afew years ago the two approaches showed large inconsistencies which were shown to be mainly due toa rather subtle term that was missing in the Microscopic calculations. By correcting this, consistencycould be reached [7] which is a major achievement and indicates that, based on first principles, webasically understand the emission process. It also shows that a dual approach is necessary to be able totrust the results. It should be noted that for coherent radiation the two approaches should give the sameresults, they differ in the incoherent contribution to the radiation field.The main advantage of a macroscopic approach is that it clearly indicates the aspects of the showerdynamics that are responsible for certain features of the detected radio signal. The macroscopic approachrequires a parametrization of the position and time dependence of the four-currents in the showerwhich can be performed at various levels of sophistication. In the following we use the Macroscopicapproach. Since radio emission is basically governed by wave mechanics any features in the frequencyspectrum of the pulse are directly related to critical length scales in the distribution of the particles in theshower.2. BASICS OF RADIO-WAVE EMISSIONTo understand radio emission from extensive air showers it is important to keep in mind that a constantcurrent (at a fixed distance) does not radiate. To create radiation one needs a varying current and/orae-mail: scholten@kvi.nlThis is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20135308005EPJ Web of Conferencesa distance to this current that changes. In an air shower we have both, the charge/current distributionis concentrated in the shower which rushes towards the surface of the Earth with the velocity of lightin vacuum (denoted by c). In addition, the current and charge densities are (roughly) proportional tothe particle density in the shower which grows from the first collision to reach a maximum at Xmaxwhereafter it decreases rapidly again. Since the latter introduces a fast time dependence in the currentsthis is the dominant driving mechanism for the emission of MHz radiation.An equally important consideration is the fact that coherent radiation can only be emitted fromcurrent and charge densities, involving many particles, that have a typical spatial and temporal extentthat is smaller than the wave-length or the inverse-frequency of the radiation. With this simple principlethe main features of the pulse shape can be understood [8]. Here we will go a step further and focus onthe influence of the finite refractivity of air, N = n − 1, on the measured radio signal as this turns outto be essential to come to a correct interpretation.3. THE MACROSCOPIC MODELThe particles in the cosmic-ray shower move through the magnetic field of Earth with the light velocityc. The lighter ones, electrons and positrons, will receive a substantial acceleration due to the action ofthe Lorentz force. This acceleration is counteracted by the collisions with the ambient air molecules andresults in an (air-pressure dependent) drift velocity with opposite directions for electrons and positrons,vd ≈ 0.04 c. As a result a net electric current develops which is proportional to the number of particlesin the shower and oriented in the direction of the Lorentz force, x̂ = −v × B, where v is the direction ofthe original cosmic ray. This varying current is responsible for -so called- geomagnetic radiation whichis polarized along the direction of the emitting current, x̂.In addition to the electric current there is also a net charge excess in the shower due to the knock-out of electrons from air molecules by elastic positron-electron collisions and Compton scattering. Inshower simulations the charge excess is approximately equal to 20% of the number of particles and isthus substantial, and, equally important, varies with shower height z (the distance, measured along theshower, to the point of impact on Earth). Because of this variation there is also charge-excess radiationwhich is radially polarized and as such distinguishable from geomagnetic radiation [9–11].4. INDEX OF REFRACTIONOf particular importance to understand the effect of the finite refractivity of air is the relation betweenthe time, t , for an observer at a distance d from the shower core and the height, z, from which this partof the signal was emitted. For the simple geometry of a vertical shower it can be shown that t ≈ d2/2cz.This implies that signals emitted from the top part of the shower arrive earlier than those emitted fromlater stages. In Fig. 1 (l.h.s.) the red-colored curve shows the dependence between emission height andobserver time for the case of vanishing refractivity. It can easily be seen that this follows closely theapproximate formula t ≈ d2/2cz. The black curve drawn in Fig. 1 gives the vertical shower profile. Ascan be deduced from this picture the leading edge of the resulting pulse lies around t = 1 ns with a zerocrossing of the pulse (related to the shower maximum) near t = 4 ns, consistent with the pulse shownon the r.h.s. of Fig. 1.Including a realistic refractivity of air (n = nGD indicating a dependence on air density as givenby the law of Gladstone and Dale) changes the picture in an essential way as shown by the light bluedotted curves in Fig. 1. Due to the fact that the shower propagates faster than radio waves, much of theradiation emitted along a finite part of the shower arrives at the observer at the same time. This is clearfrom the l.h.s. of the figure by the fact that the blue curve maps all points with z > 4 km to the sameobserver time of t = 7 ns. As a result the pulse (on the r.h.s.) shows a very strong peak at this time. Thefinite but very narrow width of the peak (as compared to the one for n = 1) is due to the fact that theimportant-limiting length scale is no longer the projected length of the shower (which tends to zero at08005-p.2UHECR 2012012345678910z(km)0 5 10 15 20t(ns)0 4 8 12 16Ne 10-7d=100 mn=1n=1.0003n=nGDNe(z)-250-200-150-100-50050E(mV/m)0 1 2 3 4 5 6 7 8 9 10t(ns)d=112 mn=1n=nGDn=1.0003Figure 1. L.h.s.: the emission height z as function of the observer time t for three different values of the index ofrefraction for an observer at a distance of 112 m from the shower core (impact distance is 100 m). The dashed linegives the shower-profile as function of z for a E = 5 × 1017 eV proton-induced shower at  = 27◦. The calculatedpulses for the three cases of the index of refraction n (vacuum, constant Earth-surface value, realistic air-densitydependence) are shown on the r.h.s.012345678910z(km)0 50 100 150 200t(ns)0 4 8 12 16Ne 10-7d=400 mn=1n=1.0003n=nGDNe(z)-0.35-0.3-0.25-0.2-0.15-0.1-0.050.00.050.1E(mV/m)0 10 20 30 40 50 60 70 80 90 100t(ns)d=448 mn=1n=nGDn=1.0003Figure 2. Same as Fig. 1 but for an observer at a distance of 448 m from the shower core (impact distance is 400 m).this point) but the distribution of the particles in the shower front. Simulations show that close to theshower core the particles in the longitudinal direction are concentrated within length-scales of mm’swhile in the transverse direction this may be meters. Projecting this transverse distance along the line ofsight, because of the angles involved, very short dimensions emerge translating in a very narrow pulse.The picture is rather different at a distance of 448 m from the core (impact parameter equals 400 m)as shown in Fig. 2. At this observer distance the shower velocity projected on the line-of-sight is muchless than the propagation speed of radio waves, c/n, and as a result the influence of the air-refractivityis negligible. This is shown on the l.h.s. where the curves showing the mapping of shower height onobserver time lie almost on top of each other. As a result also the calculated pulses for the three differentcases are almost identical. The determining length scale is the longitudinal shower profile projectedalong the line-of-sight, compared to which the length scale of the distribution of particles in the showercore is negligible and thus can be ignored.To obtain a better insight in the implication of the pulse width for observations, the frequency spectraare shown in Fig. 3. This shows that at the Cherenkov distance (defined as the distance from the showercore where the inflection point of the curve giving shower height v.s. observer distance coincides withthe shower maximum) there are strong high frequency components in the signal ranging up to 5 GHz.This is in sharp contrast to the pulse at distances beyond the Cherenkov cone where the maximumfrequency is of the order of 10’s of MHz, dropping with distance.08005-p.3EPJ Web of Conferences1251025E(V/m/MHz)2 5 1022 5 1032 5(MHz)d=112 mn=1n=nGDn=1.0003512510E(V/m/MHz)2 5 10 2 5 102(MHz)d=448 mn=1n=nGDn=1.0003Figure 3. Frequency spectra for the calculated pulses at d = 112 m (l.h.s.) and d = 448 m (r.h.s.).The Cherenkov contribution to radio emission has distinct effects on the lateral distribution of thesignal strength as is discussed in the following section. In addition we are investigating to what extentthis gives us a novel and more accurate method to determine the position of the shower maximum andthus composition. An update of our previous study [12] (where Cherenkov effects were not included) isforthcoming [13].Cherenkov effects could possibly affect the separation of geomagnetic and charge excess radiationby the analysis of the polarization patters [5] as discussed in [11]. Even though Cherenkov effects arenot changing the polarization direction of the signal, the strength or the signal at a particular distancefrom the shower core depends directly on the optimal emission height which may be different for thetwo processes. Ongoing calculations [13] show that Cherenkov emission is important for certain aspect,but that the analysis of frequency filtered data, as discussed for example in [9, 11], is hardly affected.5. THE LATERAL DISTRIBUTIONRecently some preliminary results were reported [14] for the lateral distribution of the signal strengthas measured with the antenna’s in the core of LOFAR [15], see Fig. 4. LOFAR is a new generationradio-astronomy telescope which operates in the frequency regime of 30–240 MHz. The revolutionaryaspect of this telescope is that it deploys thousands of very simple wire antenna’s instead of largeparabolic dishes. All simple antennas can be phase-coupled to obtain the equivalent resolution of a dishwith a diameter of many hundreds kilometers and a collecting area of several thousand square meters.Apart from using this telescope for astronomical observations, because of the software coupling of theindividual antennas, it can also be used for observation of transient phenomena such as radio emissionfrom air showers.Due to the large number of antennas the ground pattern can be determined accurately for singleshowers. This is a major advantage with respect to sparse arrays where data of many showers have tobe combined. The data of Fig. 4 have been obtained using the low-band antennas that operate in thefrequency regime of 30–80 MHz. The figure shows that for distances less than about 100 m the intensityof the radiation is rather constant and starts to drop exponentially only at larger distances. Since thedistance where the Cherenkov radiation reaches a maximum is of the order of 100 m this structure in theLDF can be understood and it follows closely the predicted [16] trend made before the experiment.6. COMPLEMENTARITYThe strong point of cosmic-ray observations at the Pierre Auger Observatory is (besides its large surfacearea) the fact that it allows for hybrid observations. At present this is based on simultaneous observations08005-p.4UHECR 2012Figure 4. Figure from ref. [14] showing the (un calibrated) lateral distribution function (LDF) for two polarizationdirection for a single event as measured with LOFAR.with fluorescence (FD) and surface (SD) detectors where the two detectors yield complementaryinformation on the air shower induced by the cosmic ray. Radio detection (RD) will offer additionalcomplementarity.Depending on the distance from the shower core, the radio pulse is sensitive to different aspects ofthe shower evolution. Close to the shower core, especially at the Cherenkov distance, the frequencycontent of the pulse is determined by the distribution of particles in the shower front [16]. TheCherenkov distance itself is directly related to Xmax of the shower maximum. Therefore this yieldsa measurement of Xmax on an event-by-event basis, which is essential for the determination of thechemical composition. This constitutes an alternative determination of this important shower parameter,independent from FD observations. Also the fall-off of signal strength with distance to the showercore [12] depends on Xmax . The frequency content of the pulse at the Cherenkov angle is a directindication of the spatial distribution of the particles in the shower core [6]. At present little effort hasgone in the understanding of the significance of such a measurement as this could not be investigatedwith any other means. At larger distances the pulse shape is determined by the (derivative of) the showerprofile [8]. Because of the relation between shower height and observer time, the earlier part of theshower induces the higher frequency components (which are much lower than the frequencies seen atthe Cherenkov distance). This makes that the measured pulse is sensitive to the early stages of showerdevelopment which is an aspect that is not well covered by FD measurements.In general the radio signal is exclusively sensitive to the electron content of the shower in contrast tothe SD which are primarily sensitive to the muon content. In addition the polarization of the radio signalcan be used to distinguish the charge excess from the geomagnetic current. No other measurement isable to do so. This will serve as an additional constraint on shower simulations.References[1] M. Ludwig and T. Huege, Astrop. Phys. 34 (2011) 438[2] J. Alvarez-Muñiz, W.R. Carvalho Jr., and E. Zas, Astropart. Phys. 35 (2012) 325[3] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1999[4] O. Scholten, K. Werner, and F. Rusydi, Astropart. Phys. 29 (2008) 94[5] K. Werner and O. Scholten, Astropart. Phys. 29 (2008) 393[6] K. Werner, K.D. de Vries, and O. Scholten, arXiv:1201.4471, Submitted to Astropart. Phys[7] T. Huege, M. Ludwig, O. Scholten, and K.D. de Vries, Nucl. Inst. Meth. A 662 (2012) S17908005-p.5EPJ Web of Conferences[8] O. Scholten and K. Werner, Nucl. Inst. Meth. A 604 (2009) S24; O. Scholten, K.D. de Vries, andK. Werner, Nucl. Inst. Meth. A 662 (2012) S80[9] B. Revenu for the Pierre Auger Collaboration, Proc. 32nd ICRC (2011) 172[10] H. Schoorlemmer et al. [Pierre Auger Coll.], Nucl. Inst. Meth. A 662 (2012) S134[11] A.M. van den Berg, this conference[12] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Astropart. Phys. 34 (2010) 267[13] K.D. de Vries, et al., to be published[14] A. Corstanje et al., Proc. 32nd ICRC (2011) 916; arXiv:1109.5805v1[15] A. Horneffer et al. [LOFAR CR-KSP], Nucl. Inst. Meth. A 617 (2010) 482[16] K.D. de Vries, A.M. van den Berg, O. Scholten, and K. Werner, Phys. Rev. Lett. 107 (2011)06110108005-p.6

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What the radio signal tells about the cosmic-ray air shower

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