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Progress report on the detector optimization
& Progress report on observation strategies
and estimation techniques (part B)
Apostolos Tsirigotis, Antonis Leisos, Spyros Tzamarias
Physics Laboratory H.O.U
Outline
• Discovery Potential using the Un-Bin method in extended sources
• Comparison of different detector layouts
• Stack of galactive sources
• Analysis strategy taking into account the source structure
KM3NeT General Meeting
20-23 February 2012
LNS Catania
Reminder of the Un-bin method
angle
energy
Psignal  x , y , Em , m ;    Psignal
( x , y )  Psignal
( Em , m ;  )
energy
Pbck  Pbckangle ( x , y )  Pbck
( Em , m )
Pi  x , y , Em , m ;  , N s  

Ns
N 
 Psignal  x , y , Em , m ;    1  s  Pbck  x , y , Em , m 
Ntotal
 Ntotal 
N  N   m N
mB 
e

L  , N s  

Ntotal  N s ! i 1
total
s
  2  ln
B
total

Pi  x , y , Em , m ;  , N s

L0 N s  0 
L   2, N s 

Extended Source
1
angle
Psignal
(θx , φy ) 
Point source 
1 e

R max
s2x s2y

Psignal ( x ,  y ) 
angle
1
1 e

1
d
sx2  s y2
2 x y

e
1
e
2πσ x σ y

1  x t
 
2 
s x2

  
2

y
t
sy2
 
2
1  θx2 φy 


 
2  s2x s2y 


2


1
d d
d2 t t
d
Rm
R 2

angle
angle
m
Psig n a l ( x ,  y ) Psig n a l   ,cos  t 
 d 


cos θ=0 -0.05
Comparison of the Discovery Potentials
Number of events (N) – Angular profile (S) – Energy (E)
5.00
Discovery Potential in units of the
reference flux
RXJ1713
T180 NES
T180 NS
T180 N
T180(A)
0.50
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
years
Energy distribution of signal (RXJ1713) and
background (atmospheric)
cos θ=0 - -0.05
Signal
Background
Signal
Background
(R/d)2
cos θ=-0.95 - -1.
logE, E in GeV
(R/d)2
Comparison of the Discovery Potentials
Number of events (N) – Angular profile (S) – Energy (E)
Number of sets
Background samples
15 y 12 y 8 y 10y
S100
Only the Poisson term (total number of events)
Total number of events + Angular profile + Energy
21 signal
events on top
of bck
Cumulative
Probability
distribution of the test statistic λ
S100
Only Background
  2  ln
L0  N s  0 
L Nˆ
 
s
  2  ln
L0  N s  0 
L Nˆ
 
s
Comparison of the Discovery Potentials
Cumulative
Probability
Number of events (N) – Angular profile (S) – Energy (E)
S100
21 signal
events on top
of background
  2  ln
L0  N s  0 
L Nˆ
 
s
22% improvement in DP
FOM 7.2y  5.6y
Comparison of the Discovery Potentials
For different detector layouts
308 Towers with vertical separation of 130 m (T130)
308 Towers with vertical separation of 150 m (T150)
308 Towers with vertical separation of 180 m (T180)
616 Strings with vertical separation of 100 m (S100)
616 Strings with vertical separation of 130 m (S130)
5-σ DISCOVERY POTENTIAL @ 50% C.L.
Discovery Potential in units of the
reference flux
5.00
T180
T150
T130
S130
S100
0.50
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16
years
FOM (years of observation time)
5-σ DISCOVERY @ 50% C.L.
0.70
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
T180
8.4y
T150
7.6y
T130
6.4y
S130
6.0y
S100
5.6y
Size (degrees) *
Source
Flux
RXJ1713.7-3496
Radius
0.65
1.68*10-11*(E-1.72)*exp(-sqrt(E/2.1))
RXJ0852.0-4622
Radius
1.00
1.676*10-11*(E-1.78)*exp(-sqrt(E/1.19))
HESSJ1616-508
Gaussian σ
0.16
0.42*10-11*(E-2.2)*exp(-sqrt(E/2,1)) **
HESSJ1614-518
Gaussian σ
0.25
0.46*10-11*(E-2,2)*exp(-sqrt(E/2.1)) **
dN/dE (TeV-1 cm-2 s-1 )
* ApJ 636 (2006) 777 , A&A 437-L7
HESSJ1616-508
HESSJ1614-518
Energy (TeV)
** approximation (red line) of the ApJ
656 (2007) fluxes (black line) in order to
incorporate the same energy cut-off as in
the RXJ1713.7 case.
Modeling the Spatial Distribution of the Sources
generated
neutrinos
φ
Reconstructed
neutrino
directions
generated
neutrinos
Reconstructed
neutrino
directions
θ
WPD Full Detector – 308 Towers – 180 m horizontal separation
Source
Wide Ring
Selection
Optimum Ring
Selection *
FoM (y)
bin
FoM (y)
un-bin**
Signal
per year
Backgr.
per year
Signal
per year
Backgr.
per year
RXJ1713.73496
3.3
5.9
2.9
3.7
11
8.4*** (3σ:
3.3)
RXJ0852.04622
2.6
12.4
2.1
7.4
41
33 (3σ: 11)
HESSJ1616-508
0.9
2.8
0.7
1.2
68
57 (3σ: 19)
HESSJ1614-518
0.82
6.26
0.6
2.7
-
-
* Optimum Sensitivity and cuts to reject all the atm. muon-background
** Tracking and Energy Information is used
*** Only with tracking information the FoM is 9.6 y
SOURCE STACKING
In case of: K sources, Ntotal observed tracks from all the sources and MB total expected
background
Psignal  x ,  y , Em ,  m ;     wn  Psignal  x ,  y , Em ,  m ;   and
n
Pbck    n Pback
 x , y , Em ,m 
K
K
n
n 1
where : wn 
exp. signal n
K
 exp. signal 
n
n 1
n 
exp. bck n
K
 exp . bck 
n 1
Pi  x ,  y , Em ,  m ;  , N s  
or 
n
or 
n 1
observation time n
K
 observation time 
1
K
n
n 1
observation time n
K
 observation time 
n 1
or 
or 
1
K
n
 N
N s total
 Psignal  x ,  y , Em ,  m ;    1  s total
N total
N total


 Pbck  x ,  y , Em ,  m 

WPD Full Detector – 308 Towers
Stacking Sources
Assuming 6 years of observation, the 50% discovery potential of
RXJ1713.7-3496 corresponds to 1.33* 1.68*10-11*(E-1.72)*exp(-sqrt(E/2.1))
RXJ0852.0-4622 corresponds to 2.55*1.676*10-11*(E-1.78)*exp(-sqrt(E/1.19))
HESSJ1616-508 corresponds to 3.3*0.42*10-11*(E-2.2)*exp(-sqrt(E/2,1))
HESSJ1614-518 corresponds to 5.3*0.46*10-11*(E-2,2)*exp(-sqrt(E/2.1))
STACKING TOGETHER 6 years simultaneous observations of the RXJ1713.7-3496 and the
RXJ0852.0-4622 , the 50 % discovery potential of observing neutrino from these sources
corresponds to:
1.22* [1.68*10-11*(E-1.72)*exp(-sqrt(E/2.1))+1.676*10-11*(E-1.78)*exp(-sqrt(E/1.19))] using as
weights the relative source strength
In this case the FoM is less than 7.5 years whilst for the RXJ1713.7-3496 alone is 8.4 y
Events/bin (a.u.)
Taking into account the source structure…
R
Decl.
R.A
Events/deg**2
fraction
R [Degrees]
R [Degrees]
Simulate the ν emission to follow the (raw) VHE gamma emission topology
(just a toy model)
3D angular distribution of the reconstructed (ν) signal induced muons
1
angle
Psignal
( x , y ) 
1e
1
angle
Pbck
( x , y ) 


1
R max
sx2 sy2

2 x y
e
2 
 2
1  x  y 
 

2
2 
2 
 sx sy 
101
angle
Psignal ( x ,  y , E)   E   wi  Psignalbini
( x ,  y )
i 1
Ptotal ( x ,  y , E) 
ns
n 

Psignal   1  s  Pback

N
N
Each bin of the source-model contributes as

Psignalbin ( x ,  y ) 
angle
1
1 e

1
2
Rmax
sx2  sy2
2 x y


e

1   x t

2 
sx2

  
2
y
t
sy2
 
2


1
d d
d2 x y
Back (15y)
166.4 μ
Back (8y)
88.7 μ
20 signal
events
Back (6 y)
66.6μ
Back (1y)
11.1 μ