How bright can the brightest neutrino source be?

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1 TeV Particle Astrophysics Columbus, OH August, 2017 How bright can the brightest neutrino source be? Shin ichiro Ando University of Amsterdam Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017)

2 Lessons from gamma rays Fornasa et al. Phys. Rev. D 94, (2016)

3 Lessons from gamma rays Fornasa et al. Phys. Rev. D 94, (2016)

4 Lessons from gamma rays Fornasa et al. Phys. Rev. D 94, (2016) Is there signature of point sources here?

5 Angular power spectrum: Observations with Fermi sr] sr -2 s -2-4 [cm C l Energy bin [ ] GeV Masking sources in 3FGL Masking sources in 2FGL Poissonian fit (masking sources in 3FGL) Poissonian fit (masking sources in 2FGL) 2 Multipole Analysis 15 of Fermi data for the angular 15 power spectrum of the diffuse gammaray 5 background in 2012 Discovery 5 of small-scale anisotropies sr] sr -2 s -2-4 [cm C l Reanalysed in Energy bin [ ] GeV Masking sources in 3FGL Masking sources in 2FGL Poissonian fit (masking sources in 3FGL) Poissonian fit (masking sources in 2FGL) 11 Almost -20 constant excess compared -20 with 2 3 shot noise of the Multipole of the beam window function photons on the errorat bars 50 at < high l < multipoles, as in Fig. 7. The right panel shows the cross- 700 FIG. 7. Same as Fig. 6, but showing a wider range in multipole, going APS from between l =to2000. two high-energy Thetwodashedgreyverticallines bins. This combination indicate the lower and upper bounds of the multipole range used for the present analysis. Note the different scale of the y-axis does not correspond to a significant detection, as the in each panel. best-fit C P is compatible with zero at a 2σ level. sr] sr -2 s -2 χ 2 distribution with 1 degree of freedom and, thus, it can be used to estimate the significance associated to C P. For the default data set masking 3FGL sources, the significance of the measured auto-aps C P is larger than 3σ for all energy bins up to 21.8 GeV, except between 5.00 and.45 GeV. The significance of the detection Masking sources in 3FGL is reported in italics in Tabs. I and II. Inthecaseof Masking sources in 2FGL the mask around 3FGL sources, the highest significance in the auto-aps 1 is 6.3σ and it is reached 2 in the second energy bin, i.e. between 0.72 Energy and [GeV] 1.04 GeV. cm -4 2 [GeV -2 ( E) C P 4 E Data The best-fit are Cmore P for the consistent cross-aps between with the i-th and discrete The the way j-th the autoenergy point and bins cross-aps sources are shown depend inrather on Appendix energy than C, (i.e. multiplied the so-called by Ei 2 anisotropy energy spectrum ) is andiffuse informativecomponent E2 j / E i E j and for all the possible combinations of observable energy bins. that Cross-APS can(blazars; provide C P insight is detected Ando into et the in most al. emission combinations 2007) causing of the energy anisotropic bins, with signal. the ones In failing fact, in to the yield case a detection that the auto-aps mainly involving is produced the two by a highest single energy bins. Tabs. I and II report the detected cross-aps population of sources, the anisotropy energy spectrum allows with their their significance energy spectrum 9 The largest to be reconstructed detection significance [28, 43, is 7.8σ for the case of the cross-aps between the energy bin from 1.99 and 3.15 GeV and the energy bin between 3.15 and 5.0 GeV. The tables also report in bold the χ 2 associated with Fornasa et al. Phys. Rev. D 94, (2016) Ando et al. Phys. Rev. D 95, (2017)

6 Implications Anisotropy analyses have already been established for GeV gamma rays Solid measurement of angular power spectrum implies (sub-threshold) point-source contribution They can be identified, not individually but statistically Same technique can be used for high-energy neutrinos, to identify source population

7 High-energy neutrinos: Searches for point sources IceCube, Astrophys. J. 835, 151 (2017) Pre-trial (Disc. Potential) Pre-trial (Sensitivity) Post-trial Upper Limit (90%) ANTARES (Sensitivity) Upper Limits (90%) Hotspots h Equatorial 0h [ TeV cm 2 s 1 ] E ν 2 dφ deν log p sin δ Figure 8. Discovery potential (5σ, solidred)andsensitivity (dashed red) for a ν µ + ν µ unbroken Eνdφ/dE 2 ν flux shown against declination δ. Thegraylineshowsthere- sults of (Adrian-Martinez et al. 2014) inthesouth. Upper limits of source candidates in Tab. 2 and Tab. 3 are depicted by red crosses. The blue line represents the upper limit for the observed most significant spots in each half of the sky for all declinations, the actual declination position of the spots is indicated by a star. No excess over the atmospheric backgrounds Roughly ~ 11 TeV/cm 2 /s for the E 2 spectrum its position (α =1, δ =11.5 ), no significant cluster-

8 Significant signal clustering? Angular power! IceCube, Astropart. Phys. 66, 39 (2015) s -1 ] per source -2 dn/de [GeVcm 2 E signal spectrum: E 2pt analysis, uniform source distr., discovery flux, post-tr. multipole analysis, discovery flux, post-tr. 2pt analysis, uniform source distr., upper limit (90% CL), post-tr. multipole analysis, upper limit (90% CL), pre-tr. ps search, avg. discovery flux, pre-tr. ps search, avg. upper limit (90% CL), pre-tr. Converted HESE flux 1 number of sources in the northern sky No angular power was found (everything is consistent with diffuse the background model) It can exceed the point-source limit for more than 0 sources But it is assumed that all these sources have the same flux

9 Flux distribution and implications Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017) F +1 Flux distribution of any astrophysical sources will follow a power law Particularly F 2.5 for high-flux region (cf., Olbers paradox) First moment (mean): Intensity Second moment (variance): Angular power spectrum Procedure: 1. Pick N* as a parameter 2. From measured intensity I, calculate F* 3. Discuss what constraints we have on Fmax

10 One-source limit Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017) Radio galaxies If Fmax gets too large, the expected number of the source at this flux gets significantly smaller than 1 This one-source limit is much stronger than the point-source flux limit for N* > 4 Blazars Starbursts

11 Flux limit from the angular power spectrum: HESE Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017) High-Energy Starting Events (HESE): 14 tracks, 39 showers Particularly important for small N* So far it is not very constraining Given that there are only 14 track events (HESE; 1 deg angular resolution), this is not surprising The sensitivity will however improve as exposure squared Blazars

12 Flux limit from the angular power spectrum: Upgoing ν μ Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017) Projection for the current upgoing νμ events above 300 TeV: ~60 astro, atmospheric This doesn t change much even for 50 TeV threshold Constraints can already be very strong Critical test of a scenario of blazar-domination for the diffuse flux Thanks to much larger exposure and better angular resolution

13 Flux sensitivity for the next generation Ando, Feyereisen, Fornasa, Phys. Rev. D 95, 3003 (2017) Detector Strategy E/E today livetime psf (tracks) IceCube HESE 1 4 yr 1 upgoing µ 1 6 yr 0.5 IceCube-Gen2 HESE 8 yr 0.5 upgoing µ 12 yr 0.3 KM3NeT HESE 4 8 yr 0.2 upgoing µ 4 12 yr 0.1 The angular power spectrum can test cases of any sources with N* < 5 6 (blazars and radio galaxies) Similar sensitivities expected for KM3NeT and IceCube-Gen2

14 Relation with physical representation Flux representation Luminosity representation [Mpc -3 ]) log(n 0 eff Murase, Waxman, Phys. Rev. D 94, 3006 (2017) LL AGN SBG, GC/GG-int IceCube Line Point Source Limits (IceCube) Point Source Limits (IceCube-Gen2) RQ AGN GC-acc RL AGN BL Lac -11 Muon Neutrino Constraints FSRQ eff log(e L E µ [erg s -1 ]) Phenomenological, but model-independent Contribution to the diffuse flux has to be assumed in advance Power spectrum constraints nicely integrated Physical, but model dependent No assumption needed for fraction to the diffuse flux Power spectrum constraints not well integrated (so far) Conversion between the two straightforward (but model dependent)

15 Figure 3: top: Probability distribution P (I) of the SFG intensities as observable at 0 Te Beyond variance: One-point fluctuation analysis Flux PDF is highly non-gaussian, featuring long power-law tail Power spectrum does not capture all the statistical information One-point fluctuation analysis utilise all the information contained in full PDF Benefit is slim for now, but in the future will be large E.g., test of Galactic component in the future KM3NeT data (Feyereisen, Gaggero, Ando, in preparation) Probability log(i*p(i)) Probability log(i*p(i)) Feyereisen, Tamborra, Ando, JCAP 03, 057 (2017) SB, showers SB, tracks SF-AGN(SB), showers SF-AGN(SB), tracks Intensity log(i / cm² sec rad² GeV) FHL, tracks 2FHL, showers Intensity log(i / cm² sec rad² GeV)

16 Conclusions IceCube s detection of TeV-PeV neutrinos has launched highenergy neutrino astrophysics The next question to be answered: What are the sources? Given that there will be many more events (KM3NeT, IceCube- Gen2, etc.), it is important to go beyond the mean of the flux PDF (i.e., intensity energy spectrum) Simple discussions of the PDF such as the angular power spectrum already show good prospects; e.g., testing blazar contribution Full usage of one-point PDF will be important to further constrain neutrino sources

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