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

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

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

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

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

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 10 / 12 / 2008 Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

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

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

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

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

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

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

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

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

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

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 10 / 12 / 2008 Christopher Lindsay Naumann - Fluxes and Event Rates for KM3NeT Geometries

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