1. Reconstruction of the altitude of the shower maximum.
…Towards the shower reconstruction
Pierre Colin (Petr Sudakov)
(LAPP)
Dmitry Naumov
(LAPP/JINR)
3-5 Febrary

2. To reconstruct the shower energy
Why should we know hmax?
To reconstruct the shower energy
we need to know the attenuation
2. To do physics
transform hmax into xmax and identify
neutrinos, protons, iron and all that
How can we measure hmax?
Using Cherenkov echo information
If not… try to use Fluoresence only
3-5 Febrary

3. Can we do something to save the rest showers?…
How often we can use the Cherenkov echo?
We do not expect a Cherenkov signal for large 
Golden events
Fluorescence only
Energy, eV
, deg.
1020eV
Can we do something to save the rest showers?…
3-5 Febrary

4. A qualitative example: 2 horizontal showers at different altitudes
 N =  x yield x attenuation x efficiency x NeL
E=1020 eV, proton
SLAST N
 N  NeL = Ne x/(h)
Ntot =   N
Nmax/Ntot  (h)
20km
5km
t, ms
Therefore, Nmax/Ntot is sensitive to
the air density for horizontal
showers …
Look also Eric’s remark
on the duration of
horizonthal showers
3-5 Febrary

5. What about inclined showers?
Using GIL parametrization we found that hmax can
be reconstructed in general case
(see details in our memo):
tmax = a+b (ln(E/E1) + ln(A))
Hi is the slope in exp(-h/Hi)
Unit vector pointing to EUSO from
the shower maximum
Very weak dependence of the shower energy and nature!
3-5 Febrary

6. With SLAST we generated 10000 proton initiated Showers with
eV < E < 1021 eV
0 <  < 100
0 <  < 360
We tryied to reconstruct that data with
Space Telescope Reconstruction Program (STrecon)
written within ROOT/C++ (stored under CC)
applying the following cuts to have «good showers»:
N > Threshold = 30 photons
Existence of the shower maximum (Nleft > 0 && Nright > 0)
Number of hits around maximum > 25
3-5 Febrary

7. (today we implement and develop the algorithms to reconstruct them)
We assumed currently:
 That angles are known
(today we implement and develop the algorithms to reconstruct them)
 Energy is known
(it will be reconstructed later in an iterative scheme. We have to implement the atmosphere response (LOWTRAN, etc), Fluorescence Class and some other technical points)
 Optics is perfect (important only for angles)
 Statistical fluctuations of the number of photons in the shower development are neglected
(it is easy to simulate within SLAST but needs a special algorithms to reconstruct).
3-5 Febrary

8. Results: Hmax(rec)- Hmax(sim) in km
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9. Results: (Hmax(rec)- Hmax(sim))/ Hmax(sim )
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10. Results: (Hmax(rec)- Hmax(sim))/ Hmax(sim ) vs 
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11. We can reconstruct Hmax relying on the Fluorescent light only.
A Short summary:
We can reconstruct Hmax relying on the Fluorescent
light only.
 Our procedure is weakly dependent on the
shower Energy and its Nature
 Effect of clouds have to be studied, however
we expect it to be small
 A good check is to work with other
generators as well
Technical details:
STrecon is a self-documented system (ROOT “trucs”)
CVS allows interested people to:
 write/test the code (author login)
 to be systematically and automatically informed
who and what has been commited (euso guest login)
3-5 Febrary

12.  Internal Note explaing all the details
We are working on:
Reconstruction of:
 angles, energy, Hmax
 particle type
 Internal Note explaing all the details
Optional Future
Implement all that inside ESAF to have the
whole chain:
 simulation of the shower, optics, electronics
 analysis
3-5 Febrary