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Fluxes and Event rates in KM3NeT detectors

Fluxes and Event rates in KM3NeT detectors. flux and rate calculation examples exploration of systematic effects provocation?. Flux calculations and rate predictions – introduction. Motivation:. For detector design not A eff important but event rates and significances !

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Fluxes and Event rates in KM3NeT detectors

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

  3. Background S+B 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 Signal 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 <Nevt> (E > Ecut) 1 log10E [GeV] 2. fold with effective area and Tobs .01 log10Ecut [GeV] expectation value for S and B above Ecut dN/dE [GeV-1] 4. estimate significance… log10E [GeV] Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

  4. 1 1 2 2 3 3 4 4 5 5 6 6 7 7 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 2 significance [σ] 1 0 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 0 log10Ecut [GeV]  need better criterion. Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

  5. 1 1 2 2 3 3 4 4 5 5 6 6 7 7 18% “1-eventspike” 2.5TeV 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 Here: 18% at E > 2.5TeV (30 events at <B> = 17,  3.13σ) log10E [GeV] 3σ margin probability for 3σ S+BB only P(>3σ) event counts log10Ecut [GeV] 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/0607286v3) 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 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 Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

  8. Systematic studies • Study systematic effects of: • energy resolution • realistic angular resolution • modified effective area • Use CDR reference detector as basis from Kappes et al. Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

  9. 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 Systematic effects: Influence of energy resolution treat energy resolution by smearing of differential fluxes with Gaussian distribution in log(Ereco/Etrue) int. event rate (ΔlogE=0)ΔlogE=0.5ΔlogE=1.0 15 10 N(E>Ecut) 5 0 -2 -1 0 1 2 log10Ecut [GeV] log10Ereco/Etrue significance 3-sigma probability .15 1.5 1 .1 S / √B P(>3σ) .5 .05 0 0 log10Ecut [GeV] log10Ecut [GeV] additional energy smearing -> loss of significance, stronger energy cut needed ! -> loss of “S>1” significance region 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! 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??? 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+ variationsof 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] 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 acceptancebelow 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- 2.9σA+2.3σ ! larger Aeff due to bad E-reco, higher low-E Aeff can decrease physics potential ! 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 Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

  15. Additional material 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 = 1.585 (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 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 coneefficiency significance log10Ecut [GeV] integrated source counts 3-sigma probability log10Ecut [GeV] log10Ecut [GeV] Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

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