1. Measurement of Cosmic-Ray Electrons with H.E.S.S.
Kathrin Egberts, Christopher van Eldik, Jim Hinton
for the H.E.S.S. Collaboration

2. Cosmic-Ray Electrons I
M. Aguilar et al. 2002
S.W. Barwick et al. 1998
DuVernois et al. 2001
S.Torii et al. 2001
Kobayashi et al. 2004
J.Chang et al. 2006
Spectrum of cosmic rays – hadronic component measured over a huge energy range (~7 decades)
Electron flux lower and only measured up to ~1TeV -> zoomed in picture on electron flux, flux scaled by energy to the power of 3!, compilation of different experiments that have measured the electron component of the CRs -> all balloon or satellite experiments -> can‘t measure up to higher energies because of small detector areas (~1m^2) and rapidely declining electron flux
electrons only measured up to ~1 TeV by balloon/satellite experiments: limited detector area (~1 m2) – problem with the low fluxes
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

3. Cosmic-Ray Electrons II
Energy losses via inverse Compton scattering and synchrotron radiation
Steep spectrum (makes measurement difficult)
Limit on the lifetime t 1/E and hence propagation distance
Sources of TeV electrons must be local and recent!
What is special about the electron flux?
-> energy losses by inverse compton and symchrotron radiation go with dE/dt~E² -> fast energy losses at high energies, step spectrum
dE/dt~E²  1/E² dE ~ dt 1/Einitial-1/ Efinal ~tinitial –tfinal ,if at time tinitial=0 Einitial= inf, then the time tfinal ~ 1/Efinal describes the lifetime of the electron after which it got decelerated to an energy Efinal
-> sets a limit on lifetime and propagation distance of high energy electrons, therefore their sources must be local and recent!
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

4. Cosmic-Ray Electrons III
Ec=, =0, D0=21029cm2s-1
Ec=20 TeV, =0, D0=21029cm2s-1
Ec=20 TeV, =1104yr, D0=21029cm2s-1
Production: shock acceleration in SNRs
Output energy of e- above 1 GeV: 1048 ergs/SN
Injection spectrum: power law with exp. cutoff at energy Ec
Diffusion coefficient D = D0(E/TeV)0.3 cm2s-1
Consequences of this implication:
Plots taken from the paper from Kobayashi et al., show the contributions of single nearby sources of high energy electrons to the electron spectrum.
Model calculations, the used assumptions are listed
In the different plots the cutoff energy of the injection spectrum, time of release and the diffusion coefficient are varied
Contributions can be seen from Vela SN, Monogem and Cygnus Loop
-> high energy end of the electron spectrum can give an exciting insight in the production mechanisms as well as their propagation (diffusion)
T. Kobayashi et al., The Astrophysical Journal, 601: , 2004
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

5. Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg
Measurement Method I
Indirect measurement of cosmic-ray electrons with ground based imaging atmospheric Cherenkov telescopes
Advantage: large collection area (~105 m2)
Challenge: separation of electrons from much more numerous hadronic background (also a problem for direct measurement!)
Measurement with the High Energy Stereoscopic System (H.E.S.S.), a -ray experiment consisting of four 13 m diameter Cherenkov telescopes in Namibia
As direct measurements can‘t measure at such high energies: different approach: imaging atmospheric cherenkov telescopes
Their large collection area can deal with low fluxes, main difficulty is the separation from the hadronic background
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

6. Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg
Measurement Method II
Principle: Primary particle produces air shower, shower particles emit Cherenkov light
Works the same way for electrons and gammas
Data selection criteria:
Data taken from extragalactic fields
Excluding 0.4° region around any -ray source
Zenith angle < 28°
Only events that triggered all four telescopes are used
194 hours, total effective exposure at 1 TeV ~1.4108 m2 sr s
HESS is gamma-ray experiment! But: gammas and electrons both produce electromagnetic showers and therefore the same principles apply to gamma and electron analysis!
Data selection criteria:
Only events that triggered the full 4 telescope array in order to get only best measured events -> improved separation from hadronic background
Only observation runs targeting extragalactic objects -> no contamination of diffuse gamma rays from galactic plane
Excluding any known or potential gamma-ray source
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

7. Measurement Method III
Electron-hadron separation done with a Random Forest (RF) approach (algorithm based on decision trees)
RF trained with simulated electrons and off-source data, converts image parameters into output parameter [0,1]:
=1: electron-like
=0: background
Highly efficient background rejection (only 0.5-2% of the protons passing previous cuts end up in the >0.6 regime)
Simulated background
data
electron excess
In order to achieve the necessary electron-hadron separation, a Random Forest –approach is chosen -> uses image parameters (16 per camera – total of 52) to make a decision about the „electron-likeness“ of the event: zeta=0 background, zeta=1: event looks like an electron
Plot shows the distribution of RF output parameter zeta: black histogram line data, shaded simulated background (composition of typical elements like H, He, N, Si, Fe). Huge peak at 0: all the hadronic background events -> nice match between distribution in data and simulation. Also, a good demonstration for the excellent separation power of the method! (Note the log scale!)
( %: varies due to energy dependence: separation is better for higher energies)
For zeta -> 1: peak in the data that cannot be explained by background simulations: electrons!
But still, even with superior background supression, in a signal region of ~ in zeta distribution, a high background level that needs to be estimated correctly to extract an electron spectrum
Background estimation done by fitting simulated protons and electrons to data in the  distribution ( > 0.6)
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

8. Electrons measured with H.E.S.S.
GeV
 distribution of the signal region >0.6:
Clear signal of an electron peak at =1
Good match between model and data
Proton simulations used: CORSIKA with SIBYLL as interaction model
data
electron-proton combination
simulated electrons
simulated protons 
Background estimation is done by fitting electron and proton simulations to the data in the zeta distribution.
In the plot: zeta distribution in the signal region of for different energy bands. data in black shows a peak in all 4 energy bands for zeta close to 1, background, estimated by simulated protons (in green) shows a flat zeta distribution, electrons (blue) always rise for zeta->1, in red the model curve of the combination of simulated electrons and protons -> matches the data very well
From these fits now a spectrum can be calculated...
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

9. Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg
Systematics
Background estimation relies strongly on the proton simulations
Compare two different interaction models: QGSJET & SIBYLL
Electrons and gammas give very similar air showers, can be distinguished on a statistical basis by depth of shower maximum Xmax (occurs ~1/2 radiation length higher in the atmosphere for electrons)
A significant contribution of gamma rays cannot be excluded
Energy scale uncertainty of the H.E.S.S. telescopes ~15%
A few remarks to the systematics of this measurement:
- Problem of the background estimation: hadron simulations have big uncertainties
Estimation of the effect done by comparing simulations with two different hadronic interaction models: QGSJET & SIBYLL
- It cannot be excluded that signal is due to gammas (with ½ radiation length, shower maxima are too close together), BUT: even though no measurements of extragalactic diffuse gamma-ray flux, theoretical predictions are much lower than electron flux (paper by Coppi, Aharonian, 1997, ApJ)
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

10. Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg
Electron Spectrum
PRELIMINARY
systematic error due to hadronic interaction model used for proton simulations
Shows the power of the method, analysis still ongoing
A VERY PRELIMINARY first version of the H.E.S.S. spectrum of cosmic ray electrons shown together with the spectral points measured by balloon and satellite experiments as comparison
Small statistical errors (much smaller than for the balloon experiments) the shaded band indicates the error due to proton simulations used for background estimation.
H.E.S.S. energy scale uncertainty is indicated by the blue arrows.
The spectrum is NOT meant as final answer, analysis is still ongoing, but it already shows the possibilities this method offers.
Especially interesting the high energy end of the spectrum above a few TeV, accessible to H.E.S.S., but analysis of these energies not yet finished...
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg

11. Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg
Summary
First ground based measurement of cosmic-ray electrons
Low statistical errors, systematics dominate
General agreement with satellite/balloon experiments within systematic uncertainties
Analysis ongoing, still room for improvements
ICRC Mérida, July 3-11, 2007
Kathrin Egberts, Max-Planck-Institut für Kernphysik, Heidelberg