Analytic description of the radio emission of air showers based on its emission mechanisms Christian Glaser, Sijbrand de Jong, Martin Erdmann, Jörg Hörandel, Erik Willems

Analytic description of the radio emission of air showers based on its emission mechanisms Christian Glaser, Sijbrand de Jong, Martin Erdmann, Jörg Hörandel, Erik Willems radio signal distribution sensitive to cosmic-ray energy mass e.g. Aab et al., PRL 116 241101 (2016) e.g. Buitink et al., Nature 531 70-73 (2016)

Radio Emission from Extensive Air Showers geomagnetic charge-excess Challenge: Access information with sparse grid of antennas Aab et al., PRL 116 241101 so far: described with empirical function (2 Gaussian's) successfully used to reconstruct radiation energy cosmic-ray energy no use of polarization information no direct physical interpretation of fit parameters Nelles et al., Astropart. Phys., 60 13f (2015) Pierre Auger Collaboration, PRL 116 241101 & PRD 93 122005 (2016) now: describe the two emission mechanisms separately

New Model of Radio Signal Distribution now: describe the two emission mechanisms separately explicitly use polarization of radio signal doubles usable information per station goal: analytic model with minimal number of parameters develop model with full Monte-Carlo air-shower simulation (CoREAS) radio emission calculated via first-principles from particle movement excellent agreement btw. data and simulation no explicit modelling of geomagnetic and charge-excess Trick: use 𝑣 ×( 𝑣 × 𝐵 ) axis

Decomposition: Geomagnetic – Charge-Excess Xmax 361 g/cm²

Decomposition: Geomagnetic – Charge-Excess Xmax 556 g/cm²

Decomposition: Geomagnetic – Charge-Excess Xmax 1024 g/cm²

Geomagnetic Parameters radiation energy 𝐸′𝑔𝑒𝑜 width 𝜎𝑔𝑒𝑜 Cherenkov ring 𝑅𝑔𝑒𝑜 cosmic-ray energy distance to Xmax  cosmic-ray mass

Geomagnetic Charge-Excess Parameters radiation energy 𝐸′𝑔𝑒𝑜 width 𝜎𝑔𝑒𝑜 Cherenkov ring 𝑅𝑔𝑒𝑜 Parameters radiation energy 𝐸′𝑐𝑒 width 𝜎𝑐𝑒 shape 𝑘 cr energy Cherenkov ring 𝑅𝑐𝑒=𝜎𝑐𝑒 𝑘 / 𝑘+1 distance to Xmax

Geomagnetic Charge-Excess Parameters radiation energy 𝐸′𝑐𝑒 width 𝜎𝑐𝑒 shape 𝑘 Cherenkov ring 𝑅𝑐𝑒=𝜎𝑐𝑒 𝑘 / 𝑘+1 Geomagnetic Charge-Excess Parameters radiation energy 𝐸′𝑔𝑒𝑜 width 𝜎𝑔𝑒𝑜 Cherenkov ring 𝑅𝑔𝑒𝑜 Parameters radiation energy 𝐸′𝑐𝑒 width 𝜎𝑐𝑒 shape 𝑘 cr energy distance to Xmax

Behaviour at Large Distances geomagnetic Xmax 1024 g/cm²

Behaviour at Large Distances signal falloff of function too strong modelled via modification of exponent geomagnetic Xmax 1024 g/cm²

Example 3 geomagnetic charge-excess Xmax 1024 g/cm²

Example 2 geomagnetic charge-excess Xmax 556 g/cm²

Example 1 reduction of fit parameters geomagnetic charge-excess Xmax 361 g/cm² reduction of fit parameters

Dependence on Air-Shower Parameters radiation energy scales with cosmic-ray energy all other parameters depends on 𝐷𝑋𝑚𝑎𝑥 only two free parameters: radiation energy and 𝐷𝑋𝑚𝑎𝑥 (+ core position) Glaser et al. JCAP 09(2016)024 geomagnetic charge-excess air shower has emitted all radiation energy at 𝐷𝑋𝑚𝑎𝑥 ~ 450 g/cm²

Combination to full 2D LDF Interference results in asymmetry Glaser et al. JCAP 09(2016)024

Combination to full 2D LDF

Summary new model of spatial radio signal distribution that models geomagnetic and charge-excess emission separately uses polarization information → uses full information per station fit parameters with direct physical meaning radiation energy scales with cosmic-ray energy width and radius of Cherenkov ring scales with Xmax → cosmic-ray mass

backup

Dependence of Fit Parameters on the Distance to Xmax radiation energy scales with cosmic-ray energy p(r) variation parametrized as function of DXmax air shower has emitted all radiation energy at DXmax ~ 450 g/cm² Glaser et al. JCAP 09(2016)024 geomagnetic charge-excess