Fluxes and Event rates in
KM3NeT detectors
-flux and rate calculation
-examples
-exploration of systematic effects
-provocation?
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
1
Flux calculations and rate predictions – introduction
Motivation:
For detector design not Aeff important but event rates and significances !
--> try to answer:
-what is the effect of improved low-E / high-E acceptance?
-how important is good angular / energy resolution?
-what are the best sources for KM3NeT?
Assumptions:
•neutrino effective areas from Monte-Carlo, mean value for all upgoing 
•angular resolution, Gaussian energy resolution, search cone efficiency
•located in the middle of the Mediterranean (avg. over sites)
•sources: point-like (AGNs,…) and extended sources (SNRs,…)
•atmospheric neutrino background (here: Volkova)
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
2
Event rate calculation – quick guide
1. take search cone around source -> background expectation
B and S fluxes inside cone
Background
3. integrate above energy cut-off
10 16
Signal
10 22
integrated event rates above cut off
10 28
100
100
10 34
10 40
1
2
1
3
2
3
4
4
55
66
77
log 10 E GeV
log
10E [GeV]
2. fold with effective area and Tobs
> Ecut)
<Nevt> N(E
evt
1 -22 -11
-1cm
flux GeV
cm ss ]
Φ [GeV
10 10
10
Signal
11
0.1
0.01
.01
differential event rates 1 GeV
100
0.001
Background
1 -1
dN dE GeV
[GeV
dN/dE
]
1
1
3
3
4
4
5
5
6
6
7
7
log 10 E cut GeV
log10Ecut [GeV]
1
expectation value for S and
B above Ecut
S+B
0.01
Signal
10 4
10 6
2
2
4. estimate significance…
1
1
2
2
3
3
4
4
5
6
5
6
7
7
10 E GeV
loglog
10E [GeV]
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
3
Significance (1): S / √B
S / √B
Significance
“how many standard deviations is
my S+B above B ?”
-> significant… but will never be
measured !
B
21.0
10.5
00.0
1
1
2
2
CEA DSM Irfu
Christopher Lindsay Naumann
-
44
55
66
77
signalsignal
significance
significance aboveabove
cut off Ecut
significance [σ]
44
33
<S> <<1
?
22
11
00
11
22
 need better criterion.
10 / 12 / 2008
3
3
log 10 E cut GeV
log10
Ecut [GeV]
but: works well only if number of
events large enough !
for hard fluxes without cut-off,
S / √B highest for large E, where
<S> << 1!
S
31.5
significance [σ]
Simple significance estimator:
signalsignal
significance
significance aboveabove
cut off Ecut
Significance
to estimate significance of a
signal, calculate probability that it
could come from background
Fluxes and Event Rates for KM3NeT Geometries
33
44
55
66
77
GeV
cut [GeV]
loglog1010EEcut
4
Alternative approach: nσ - detection probability in 5 years
event
counts needed for 3σ
signal events needed for at least 3
Ex: “Probability to get at least 3
sigma from source in 5yrs”:
S+B
NS B 3
N(S-B>3σ)
100
calculate min. number of events
needed to be over <B>+3σ
50
30 evts
10
5
S
only
Pdet:= Poissonian prob. to get these
from μ=<B+S>
1
11
22
33
44
55
66
log 10 E cut GeV
log10E [GeV]
77
Here: 18% at E > 2.5TeV
(30 events at <B> = 17,  3.13σ)
3σ margin
probability
for
probability for at
least3σ
3
18%
“1-event
spike”
0.15
P(>3σ)
PS 3
S+B
B only
0.10
0.05
0.00
1
1
2.5TeV
2
33
2
event counts
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
44
55
66
77
log 10 E cut GeV
log
10Ecut [GeV]
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Fluxes and Event Rates for KM3NeT Geometries
5
Example results – HESS sources
take several HESS sources from paper Kappes et al. (astro-ph/0607286v3)
Parameterisation of neutrino spectra from measured  spectrum:
dN
dE
E
k
exp
1 TeV
E
k : flux amplitude
 : spectral index
 : cut-off energy
B and S fluxes inside cone
B and S fluxes inside cone
log flux
flux GeV 1 cm 2 s 1
log flux
flux GeV 1 cm 2 s 1
background
with cut-off
log 10 E
without cut-off
GeV
log 10 E
log E
GeV
log E
put in string-type and tower-type detectors, calculate:
•number of events and background above fixed cuts (1 and 5 TeV)
•optimum energy cut to maximise 3-σ probability
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
6
Some results – Supernova Remnants
TD-6
Name
RXJ1713 .7
RXJ0852 .0
HESSJ1640
HESSJ1745
HESSJ1834
HESSJ1713
S 5TeV
3946 2.46397
4622 2.36735
465 0.435377
290 0.471034
087 0.257473
381 0.168825
B 5TeV
6.13524
16.5521
0.164971
0.105013
0.206909
0.182713
angular res. 0.1°
ΔlogE= 0.5
TD-4
SorB 5TeV
0.994762
0.581884
1.07192
1.45356
0.566033
0.394958
Name
RXJ1713 .7
RXJ0852 .0
HESSJ1640
HESSJ1745
HESSJ1834
HESSJ1713
3946
4622
465
290
087
381
maxProb
10.2885
9.26692
37.8793
41.9812
25.6713
20.0787
S 5TeV
1.90104
1.78442
0.390052
0.427284
0.226749
0.152718
MaxProbE
158.489
251.189
7.94328
5.01187
10.
10.
B 5TeV
4.13608
11.176
0.111432
0.0703376
0.139317
0.123379
highest 3σ
prob. (%)
SorB 5TeV
0.934754
0.53377
1.16847
1.6111
0.607497
0.43478
maxProb
13.0085
8.34935
35.8439
40.466
24.3304
20.6617
optimum
energy
cut (TeV)
MaxProbE
125.893
251.189
6.30957
3.16228
7.94328
6.30957
SD-ANT
Name
RXJ1713 .7
RXJ0852 .0
HESSJ1640
HESSJ1745
HESSJ1834
HESSJ1713
3946
4622
465
290
087
381
S 5TeV
3.08682
3.0018
0.491211
0.527662
0.294194
0.189523
B 5TeV
8.20272
22.1138
0.220364
0.140816
0.276774
0.244101
SorB 5TeV
1.07779
0.638338
1.0464
1.40614
0.559205
0.383598
maxProb
11.5617
6.86554
36.4598
42.0943
26.2467
20.5899
MaxProbE
158.489
316.228
12.5893
7.94328
12.5893
12.5893
- all significances for Ecut=5 TeV less than 2 !
12% at Ecut≈160 TeV
42% at Ecut ≈ 8 TeV
ΣPi = “1.4 sources
per 5 years at 3 σ”
- several sources with 3σ probability > 1/3 in 5 years
- optimum energy cut varies from <10 TeV to >100 TeV
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
7
Systematic studies
•
•
•
•
Study systematic effects of:
energy resolution
realistic angular resolution
modified effective area
• Use CDR reference detector as basis
from Kappes et al.
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
8
Systematic effects: Influence of energy resolution
treat energy resolution by smearing of differential fluxes with Gaussian
distribution in log(Ereco/Etrue)
int.integrated
event
event rate
rate
0.08
1515
0.04
10
10
N E Ecut
N(E>Ecut)
0.06
(ΔlogE=0)
ΔlogE=0.5
ΔlogE=1.0
5
5
0.02
logE
0.00
0
2
-2
-11
00
11
0 22
22
3
3
log E reco
E true
log
10Ereco/Etrue
significance
significance
77
3-sigma
probability
3 probability
0.15
.15
P(>3σ)
P3
1.5
1.5
SS / √B
B
44
55
66
loglog1010EEcutcutGeV[GeV]
1
1.0
0.5
.5
0.10
.1
0.05
.05
0
0
22
0.00
0.0
2
2
3
3
44
55
66
log 10 E GeV
log10Ecut [GeV]
77
33
44
55
66
log 10 E GeV
log10Ecut [GeV]
7
7
additional energy smearing -> loss of significance, stronger energy cut
needed ! -> loss of “S>1” significance region
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
9
Discussion: Single-event sources
If energy smearing is taken into account, background dominates up to
higher energies
-> higher energy cut necessary
-> NEARLY ALL sources are most significant with a single event!
event
counts needed for 3σ
signal events needed for at least 3
probability
for
atleast
least
3σ
probability
for at
3
0.4
50
single event
significant!
20
10
5
many 2
events 11
necessary
P(>3σ)
PS 3
N(S-B>3σ)
NS B 3
100
1 event
0.3
0.2
0.1
0.0
2
3
4
5
6
log 10 E cut GeV
log10Ecut [GeV]
7
1
2
3
4
5
6
7
log10Ecut [GeV]
log 10 E cut GeV
in principle, single event in direction window would be significant…
but: risk of unknown contamination too high?
move to 2-event peak? -> lower probability !
this problem is always there for sources without cut-off!
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
10
Source independent energy cut ?
with realistic energy resolution, ≈all sources most significant with 1 event !
-> optimum energy cut independent of source flux:
set Ecut such that
P(μ=<B>, 0) > 0.997
already 1 event is significant
-> depends only on source size, position and detector Aeff
-> for this Ecut, calculate the expected source signal => Pdet,3σ
min events for 3σ
probability for 3σ
13 TeV
3.0
PS 3
NS B 3
5.0
2.0
1.5
1.0
2
3
4
5
6
7
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
2
3
4
5
6
7
log10 Ecut GeV
log10 Ecut GeV
but: how robust is a single event???
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
11
Systematics: Variation of low-energy effective area
Naïve approach (assume perfect
energy reconstruction):
1000
100
Aeff+
Aeff m2
10
variations
of Kuch
“CUBOID”
1
0.1
Aeff-
0.01
general improvement of low-E
significances…
=> better detection capabilities???
0.001
2
3
4
log 10 E
5
6
7
GeV
NO energy ×flux
smearing! integrate E>E
cut
but: must include realistic
energy reconstruction !
integrated event rate
3 probability
25
0.20
Aeff+
Aeff+: 22%
0.15
Aeff-: 16%
15
P3
N E Ecut
20
0.10
10
Aeff-
5
0.05
0.00
0
2
3
4
5
6
7
2
3
10 / 12 / 2008
CEA DSM Irfu
log10Ecut [GeV]
Christopher Lindsay Naumann
-
4
log 10 E
log 10 Ecut GeV
Fluxes and Event Rates for KM3NeT Geometries
5
6
7
GeV
log10Ecut [GeV]
12
low-E effective areas (2): realistic energy reconstruction
higher Aeff at low energies:
example: Vela-X
•energy cut loses efficiency!
1
cm 2 s
S dominant
1
•this leaks into higher-energy region
due to energy smearing
B and S fluxes inside cone
flux GeV
•increased sensitivity where
background dominates (bad S-to-N)
B dominant
log10 E GeV
 reduced significances!
B
S
generally: all acceptance below energy
cut-off decreases signal quality!
small low-E Aeff “automatically” cuts
most of the background !
smaller Aeff
 maximise Aeff above Ecut, keep
small below (there it only does harm!)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
A- 2.9σ
A+ 2.3σ !
larger Aeff
2
3
4
5
6
7
log10 E GeV
due to bad E-reco, higher low-E Aeff can decrease physics potential !
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
13
Conclusion and Outlook
Calculate expected neutrino event rates from candidate sources to
establish “physics potential” of KM3NeT designs
•Use realistic energy resolution and angular cone size
•calculate significances and detection probabilities
optimum energy cuts
candidate sources for each geometry
optimisation of detector for maximum expected discoveries!
Outlook:
•Add other types of sources (extragalactic, diffuse, transient…)
•establish limits for generic source types
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
14
Additional material
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
15
Search cone optimisation
radial distribution of events around source
fraction of events inside search cone
0.7
1.0
0.6
0.8
0.4
N R Ntot
dN dr
0.5
0.3
0.865
0.715
0.6
0.4
0.393
0.2
0.2
0.1
0.0
0.0
1
0.5
1.0
2
1.5
2.0
2.5
3.0
0.0
0.0
1.585
0.5
distance r
2.5
3.0
maximise S/√B as function of Rcone
0.20
R
2.0
assumption: 2D Gaussian PSF and
source distribution, σpsf and σsrc .
0.25
R
1.5
R cone
relative significance for search cone size R
Result: optimum cone radius
0.15
0.10
Ropt = 1.585 (σpsf2 + σsrc2)1/2
0.05
ex: σpsf =0.3°, σsrc=0° => Ropt=0.48°
0.00
0.0
1.585
0.5
1.0
1.5
2.0
2.5
R cone
10 / 12 / 2008
1.0
CEA DSM Irfu
Christopher Lindsay Naumann
3.0
ext. source, σsrc=1° => Ropt =1.65°
optimum “source efficiency”: ε=0.72
-
Fluxes and Event Rates for KM3NeT Geometries
16
Effect of kinematic angular error (example RXJ1713)
search cone efficiency
assume muon angular resolution 0.3°
cone
1.00
0.50
source diameter 1.3°
search cone
efficiency
0.20
0.10
0.05
take fixed search cone radius 1.13°
0.02
1
2
3
4
5
6
7
log 10 E
compare without and with nu-mu angle
GeV
significance
2.00
S
median angular error Deg
1.00
B
0.50
0.20
1.5
0.10
0.05
significance
0.02
1.0
0.01
2
3
4
log 10 E
5
6
0.5
GeV
2
integrated source counts
3
4
5
6
E GeV
log7 10logE10cut
[GeV]
5
6
E GeV
log7 10logE10cut
[GeV]
integrated event rate
3 probability
N E E cut
P3
15
3-sigma
probability
10
0.15
0.10
5
0.05
2
3
4
5
6
GeV
log710log
E10cutE [GeV]
2
10 / 12 / 2008
CEA DSM Irfu
Christopher Lindsay Naumann
-
Fluxes and Event Rates for KM3NeT Geometries
3
4
17