1. Fluxes and Event rates in KM3NeT detectors
flux and rate calculation
examples
exploration of systematic effects
provocation?
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

2. 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
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

3. Event rate calculation – quick guide
1. take search cone around source -> background expectation
Background
3. integrate above energy cut-off
Signal
Φ [GeV-1cm-2s-1]
100
Signal 1 2 3 4 5 6 7
<Nevt> (E > Ecut) 1
log10E [GeV]
2. fold with effective area and Tobs
.01
Signal
Background
S+B 1 2 3 4 5 6 7
log10Ecut [GeV]
expectation value for S and B above Ecut
dN/dE [GeV-1]
4. estimate significance… 1 2 3 4 5 6 7
log10E [GeV]
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

4. Significance (1): S / √B
signal significance above Ecut
to estimate significance of a signal, calculate probability that it could come from background
Simple significance estimator:
S / √B
“how many standard deviations is my S+B above B ?” 3
significance [σ] 2 1 1 2 3 4 5 6 7
log10Ecut [GeV]
signal significance above Ecut
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!
-> significant… but will never be measured ! 4
<S> <<1 ? 3
significance [σ] 2 1 1 2 3 4 5 6 7
log10Ecut [GeV]
 need better criterion.
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

5. Alternative approach: nσ - detection probability in 5 years
event counts needed for 3σ
Ex: “Probability to get at least 3 sigma from source in 5yrs”:
calculate min. number of events needed to be over <B>+3σ
Pdet:= Poissonian prob. to get these from μ=<B+S>
S+B
30 evts
N(S-B>3σ)
S only 1 2 3 4 5 6 7
Here: 18% at E > 2.5TeV
(30 events at <B> = 17,  3.13σ)
log10E [GeV]
3σ margin
probability for 3σ
18%
2.5TeV
“1-event spike”
S+B B only
P(>3σ) 1 2 3 4 5 6 7
event counts
log10Ecut [GeV]
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

6. Example results – HESS sources
take several HESS sources from paper Kappes et al. (astro-ph/ v3)
Parameterisation of neutrino spectra from measured  spectrum:
k : flux amplitude  : spectral index  : cut-off energy
background
log flux
log flux
with cut-off
without cut-off
log E
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
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

7. Some results – Supernova Remnants
TD-6
optimum energy cut (TeV)
highest 3σ prob. (%)
angular res. 0.1°
ΔlogE= 0.5
TD-4
SD-ANT
12% at Ecut≈160 TeV
42% at Ecut ≈ 8 TeV
ΣPi = “1.4 sources per 5 years at 3 σ”
- all significances for Ecut=5 TeV less than 2 !
- several sources with 3σ probability > 1/3 in 5 years
- optimum energy cut varies from <10 TeV to >100 TeV
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

8. Study systematic effects of: energy resolution
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
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

9. Systematic effects: Influence of energy resolution
treat energy resolution by smearing of differential fluxes with Gaussian distribution in log(Ereco/Etrue)
int. event rate 15
(ΔlogE=0) ΔlogE=0.5 ΔlogE=1.0 10
N(E>Ecut) 5 -2 -1 1 2 2 3 4 5 6 7
log10Ereco/Etrue
log10Ecut [GeV]
significance
3-sigma probability
1.5
.15
S / √B 1
P(>3σ) .1 .5
.05 2 3 4 5 6 7 2 3 4 5 6 7
log10Ecut [GeV]
log10Ecut [GeV]
additional energy smearing -> loss of significance, stronger energy cut needed ! -> loss of “S>1” significance region
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

10. 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
probability for at least 3σ
1 event
single event significant!
N(S-B>3σ)
P(>3σ)
many events necessary
log10Ecut [GeV]
log10Ecut [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
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

11. 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
but: how robust is a single event???
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

12. Systematics: Variation of low-energy effective area
Naïve approach (assume perfect energy reconstruction):
general improvement of low-E significances…
=> better detection capabilities???
Aeff+
variations of Kuch “CUBOID”
Aeff-
×flux
integrate E>Ecut
NO energy smearing!
but: must include realistic energy reconstruction !
Aeff+: 22%
Aeff-: 16%
Aeff+
Aeff-
log10Ecut [GeV]
log10Ecut [GeV]
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

13. low-E effective areas (2): realistic energy reconstruction
higher Aeff at low energies:
increased sensitivity where background dominates (bad S-to-N)
this leaks into higher-energy region due to energy smearing
energy cut loses efficiency!
 reduced significances!
example: Vela-X
S dominant
B dominant
smaller Aeff
generally: all acceptance below energy cut-off decreases signal quality!
small low-E Aeff “automatically” cuts most of the background !
 maximise Aeff above Ecut, keep small below (there it only does harm!)
A- 2.9σ A+ 2.3σ !
larger Aeff
due to bad E-reco, higher low-E Aeff can decrease physics potential !
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

14. 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
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

15. Additional material 10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

16. Search cone optimisation
assumption: 2D Gaussian PSF and source distribution, σpsf and σsrc .
maximise S/√B as function of Rcone
Result: optimum cone radius
Ropt = (σpsf2 + σsrc2)1/2
ex: σpsf =0.3°, σsrc=0° => Ropt=0.48°
ext. source, σsrc=1° => Ropt =1.65°
optimum “source efficiency”: ε=0.72
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries

17. Effect of kinematic angular error (example RXJ1713)
assume muon angular resolution 0.3°
source diameter 1.3°
take fixed search cone radius 1.13°
compare without and with nu-mu angle
search cone efficiency
significance
log10Ecut [GeV]
integrated source counts
3-sigma probability
log10Ecut [GeV]
log10Ecut [GeV]
10 / 12 / 2008
Christopher Lindsay Naumann Fluxes and Event Rates for KM3NeT Geometries