Download Towards event-by-event studies of the ultrahigh-energy cosmic

Towards event-by-event studies of the
ultrahigh-energy cosmic-ray composition
6th Rencontres du Vietnam,
Challenges in Particle Astrophysics
Hanoi, 6-12 August, 2006
Dmitry S. Gorbunov
astro-ph/0601449
astro-ph/0606442
astro-ph/06xxxxx
In collaboration with G.I. Rubtsov, S.V. Troitsky, MSU, Yakutsk Collaboration
[email protected]
Institute for Nuclear Research, Moscow
D. Gorbunov
Towards event-by-event composition studies
– p. 1/19
Motivation
What can we learn from GZK-studies,
if the cutoff would be observed?
Astrophysics
sources:
accelaration mechanism,
local backgrounds
space:
-background,
magnetic fileds
D. Gorbunov
Particle physics
interactions at Ecm 300 TeV:
cross section,
inelasticity,
multiplicity,
PT -distribution,
new physics phenomena?
Towards event-by-event composition studies
– p. 2/19
Motivation
What can we learn from GZK-studies,
if the cutoff would be observed?
Astrophysics
sources:
accelaration mechanism,
local backgrounds
space:
-background,
magnetic fileds
Particle physics
interactions at Ecm 300 TeV:
cross section,
inelasticity,
multiplicity,
PT -distribution,
new physics phenomena?
chemical composition
D. Gorbunov
Towards event-by-event composition studies
– p. 2/19
Plan
The main idea: event-by-event analysis
The probability of a given particle (p, , . . . ) to
be a primary of a given observed event
Chemical composition from observed events
with “estimated” primary type
Several Examples: highest energy AGASA and
Yakutsk events, low energy Yakutsk events
What else?
D. Gorbunov
Towards event-by-event composition studies
– p. 3/19
Event-by-event analysis
It is obviously important for studies of:
highest energy tail
evolution of chemical compoistion with energy
global anisotropy (direction-dependent composition)?
Problems with poor statistics:
just several parameters of EAS are measured
significant fluctuations
degeneracy: similar values for different primaries
azimuth angle dependence
D. Gorbunov
Towards event-by-event composition studies
– p. 4/19
Interesting questions: a given event
For a given observed event (several parameters of EAS are
measured):
conservative study (negative knowledge): what is the
probability, that it could not be initiated by the primary A?
(positive knowledge): what is the probability, that it could be
initiated by a primary of a given type Ai (say, Ai = p, , . . . ,
Fe)?
...
D. Gorbunov
Towards event-by-event composition studies
– p. 5/19
What is the primary of an observed event?
energy-related parameters of EAS (S600 ,. . . )
composition-related parameters of EAS ( 1000 ,. . . )
E-parameters
c-parameters
Both parameters are reconstructed with some errors
The probability distribution that the primary particle which
produced an actual shower with the observed E-parameters equal
to Eobs would rather produce a shower with these parameters equal
to Erec :
gE (Erec , Eobs )
The probability distribution that a shower with measured
c-parameters equal to c could produce detector readings
corresponding to c :
gc (c , c).
D. Gorbunov
Towards event-by-event composition studies
– p. 6/19
Steps
1. for each primary one generates a library of
simulated
showers : the same direction, Es Eobs , e.g.
0.5Eobs < Es < 2Eobs
2. following the experimental procedure for each event one finds
rec
)
Erec (e.g., S600
3. one assigns to each simulated shower a weight
w1 = gE (Eobs , Erec )
4. one assigns to each simulated shower an additional weight
w2 = (Es /Eobs ) to mimic the real power-law spectrum
Output:
The distribution of the c-parameters for the showers consistent
with the real one by E-parameters is given by
fA(c) =
D. Gorbunov
1
gc (c, ciA)w1,iAw2,iA
i
Towards event-by-event composition studies
– p. 7/19
Example
The highest energy AGASA event 2.46 1020 eV:
(1000)
c=
0.5
0.4
log 2 (Erec /Eobs )
2 2
l
e
2
l
c )2
2 2
c
(c c )2
2 2
c
(c
0.3
l
= 0.104
E/E = 0.25
gE (Eobs , Erec ) =
e
0.2
gc (c , c) =
e
dc
0
c
0.1
5
10
15
20
Ρ Μ H1000L
25
= 0.4c
30
Distributions of muon densities fA of simulated events: thin dark line,
A = ; thick gray line, A = p; dashed line, A =Fe.
D. Gorbunov
Towards event-by-event composition studies
– p. 8/19
Results
If the event is unlikely being initiated by the primary A, one can
estimate the probability of it could be initiated by the primary A:
fA(c)dc
pA = FA(cobs )
fA (c) fA(cobs )
one can test the hypothesis that the primary was either A1 or A2 .
Then pA1 + pA2 = 1 and
0.5
pAk =
0.4
fAk (cobs )
fA1 (cobs )+fA2 (cobs )
,
k = 1, 2
0.3
0.2
0.1
5
D. Gorbunov
10
15
20
Ρ Μ H1000L
25
30
Towards event-by-event composition studies
– p. 9/19
Interesting questions: combined set
Chemical composition of UHECR within a given energy interval
) (within a given solid angle, etc.):
Emin < E < Emax (
(negative knowledge): the upper limit on the primary A
(positive knowledge): what is the most probable chemical
composition (the set of possible primaries is fixed)?
...
D. Gorbunov
Towards event-by-event composition studies
– p. 10/19
Procedure to estimate the chemical composition
1. one selects the set of N observed events (E- , c-parameters
have been measured) — experimental cuts (z < 45 ), quality
cuts,. . .
2. for each event j one compares the parameters of simulated
EAS of various primaries to parameters of observed EAS and
estimates the probabilities pi (j) that it could (not) be initiated
by a primary Ai of energy within
3. pi (j) enables one to estimate the probability that among N
events ni were (not) initiated by primary Ai — combinatorics
4. one estimates the most probable chemical composition i or
set the upper bound on a primary Ai , which are consistent
with selected set of observed events — likelihood
5. one takes into account possible corrections because of cuts
on initial set, detector acceptance, etc. — lost events
D. Gorbunov
Towards event-by-event composition studies
– p. 11/19
The upper limit on a fraction of primary A
1. Input
set of N observed events with energies ,
(+)j
(+)j
(+)j
( )j
generally pA + pA = 1
pA , pA ,
Steps
2. Probability (n1 , n2 ): among N observed events, n1 initiated by
A with and n2 initiated by A with :
A
pA(+)mn
,
A
mn =ij ,kl
-
,
,
kl
(n1 , n2 ) one sums over all subsets ( ij , kl )
ij , kl , mn
/
&
%
#
1
N
D. Gorbunov
.
.
.
'
.
,
.
.
i1 <i2 < <in
1
k1 <k2 < <kn ,ij =kl
2
ij , kl
/
(n1 , n2 ) =
%
# "
+
To calculate
p(+)mn
'
ij
*
1
)
p(+)kl
pA
-
#
=
)
(+)ij
&
%
ij , kl
%
$#"
(
!
The probability to have i1 -th, . . . , in1 -th events (i1 <
< in1 ) induced by
< kn2 , ij = kl ) induced by A
A with and k1 -th, . . . , kn2 -th events (k1 <
with :
Towards event-by-event composition studies
– p. 12/19
The upper limit on a fraction of primary A
Let A be the fraction of A in
3. Let ( A) be the probability that the observed results are
reproduced for a given A. Hence
n1 +n2 N
A)
(1
)
n1
A
(n1 , n2 )
( A) =
n2
n1 ,n2
P( A)
1
0
0
at a given confidence level :
)
A
1
4. Upper limit on
D. Gorbunov
+
1
2
A
2
A, true
=
)
mlost
,
=
m
2
5. Correction because of cuts:
A
Towards event-by-event composition studies
– p. 13/19
Example
all AGASA events with known muon content
and energies Eobs > 8 1019 eV: N=6
p(+)
1.000
0.998
0.921
0.887
0.580
0.565
1
3
p(+)
0.000
0.001
0.013
0.003
0.000
0.000
3
Event
1
2
3
4
5
6
0.8
P
0.6
0.4
68% C.L.
0.2
95% C.L.
0.2
0.4
0.6
0.8
1
< 0.50 at 95% C.L.
,true < 0.36
,true
3
3
Result:
AGASA+Yakutsk, E > 1020 eV, muons:
ΕΓ
Rubtsov et al, astro-ph/0601449
D. Gorbunov
Towards event-by-event composition studies
– p. 14/19
Low energy Yakutsk data
0.8
ΕΓ
0.6
0.4
D. Gorbunov
4
EY > 2 1019 eV, NY = 47
Z-burst
PRELIMINARY
A
HP
PA
19
Y
A
A
0.2
0
EY > 4 1019 eV, NY = 15
4
AY: Rubtsov et al, astro-ph/0601449
Y: D.G, Rubtsov, Troitsky, Yakutsk Coll., astro-ph/06xxxxx
RH
HP
AY
SHDM
TD
Y
19.5
Log E
20
20.5
Towards event-by-event composition studies
– p. 15/19
The most probable chemical composition
1. Input
set of N observed events with energies ,
(+)j
(+)j
(+)j
( )j
generally pA1 + pA2 = 1
pA1 , pA2 ,
Steps
2. Probability (n1 , n2 ): among N observed events, n1 initiated by
A1 with and n2 initiated by A2 with :
*
n
pA(+)m
1
mn =ij ,kl
kl
-
,
,
(n1 , n2 ) one sums over all subsets ( ij , kl )
ij , kl , mn
/
&
%
#
1
N
D. Gorbunov
.
.
.
'
.
,
.
.
i1 <i2 < <in
1
k1 <k2 < <kn ,ij =kl
2
ij , kl
/
(n1 , n2 ) =
%
# "
+
To calculate
n
pA(+)m
;,
2
'
ij
1
)
l
pA(+)k
2
pA1
-
#
=
)
(+)ij
&
%
ij , kl
%
# "
(
!
The probability to have i1 -th, . . . , in1 -th events (i1 <
< in1 ) induced by
< kn2 , ij = kl ) induced by
A1 with and k1 -th, . . . , kn2 -th events (k1 <
A2 with :
Towards event-by-event composition studies
– p. 16/19
The most probable chemical composition
)
Let us suppose that A1,2 are the fractions of A1,2
3. Let ( A1 ) be the probability that the observed results are
reproduced for a given set ( A1 , A2 = 1
A1 ). Hence
A1
)
1
"
n1
A1
(n1 , n2 )
A1 ) =
(
&
n1 +n2 N
n2
n1 ,n2
0
at a given confidence level :
1
0
(
D. Gorbunov
A2 )
2
A1 ( A1
2
+
)
A1
1
)
=
A2 )
A1 )
2
A1 (1
2
true
A1
)
mlost
,
=
m
2
4.b The most probable composition: maximization of
5. Correction because of cuts:
A1 )
)
P(
1
A1
4.a The allowed
.
Towards event-by-event composition studies
– p. 17/19
Example
Two AGASA and two Yakutsk events with known muon content
and energies Eobs > 1.5 1020 eV:
N=4 , A1 = p, A2 = F e
0.5
Event
1
2
7
8
pp(+)
(+)
pFe
0.254
0.295
0.186
0.413
0.136
0.135
0.814
0.587
0.4
P
0.3
0.2
68% C.L.
95% C.L.
0.1
0.2
0.4
0.6
0.8
1
D. Gorbunov
= 0.35 , Fe = 0.65
< 0.54 at 68% C.L.
most probable
0.15 <
p
Result:
Εp
p
Towards event-by-event composition studies
– p. 18/19
What else?
With this method one can consider
Many types of c-parameters
Many types of primaries
Only
0.8
ΕΓ
0.6
0.4
depends on energy systematics
Z-burst
PRELIMINARY
RH
A
HP
PA
19
D. Gorbunov
Y
A
A
0.2
0
Unknown primary
HP
AY
SHDM
TD
Y
19.5
Log E
20
20.5
Towards event-by-event composition studies
– p. 19/19