1. 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

2. 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 (2016)
e.g. Buitink et al.,
Nature (2016)

3. Radio Emission from Extensive Air Showers
geomagnetic
charge-excess
Challenge: Access information
with sparse grid of antennas
Aab et al., PRL
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 & PRD (2016)
now: describe the two emission mechanisms separately

4. 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

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

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

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

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

9. 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

10. 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

11. Behaviour at Large Distances
geomagnetic
Xmax
1024 g/cm²

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

13. Example 3
geomagnetic
charge-excess
Xmax
1024 g/cm²

14. Example 2
geomagnetic
charge-excess
Xmax
556 g/cm²

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

16. 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

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

18. Combination to full 2D LDF

19. 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

20. backup

21. 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