Diffuse origin of the high-energy IceCube neutrinos

Xmas Workshop 2014 Bari, December 22, 2014

Irene TamborraGRAPPA Center of Excellence, University of Amsterdam

Diffuse origin of the high-energy IceCube neutrinos

Outline

! High-energy IceCube neutrino flux

! Gamma-ray and neutrino backgrounds from star-forming galaxies

! Gamma-ray and neutrino backgrounds from clusters of galaxies

! Conclusions

High-energy IceCube excess

* IceCube Collaboration, Science 342 (2013) 6161, PRL 113 (2014) 101101, arXiv: 1410.1749.

! IceCube observed 37 events over three years (~ 10 events expected from conventional atmospheric contributions).

! Mostly showers. 3 events with energy above 1 PeV, 12 above 100 TeV.

! Zenith Distribution compatible with isotropic flux. ! E^(-2) spectrum with potential cutoff around 2-5 PeV [new data sample: E^(-2.46)].

! Flavor distribution consistent with . νe : νµ : ντ = 1 : 1 : 1

evidence for astrophysical flux 5.7 σ

Where are these neutrinos coming from?

! Galactic origin

! Extragalactic origin:• Gamma-ray bursts, blazars• Active galactic nuclei • Star-forming galaxies• Galaxy clusters

! New physics processes (i.e., superheavy dark matter, exotic neutrino models, ...).

* L. A. Anchordoqui et al., JHEAp 1-2 (2014) 1.

Warning: More statistics needed! No strong preference so far.

Hadronic interactions

gamma-rays

neutrinos

γ

γ

with Eγ 2Eν

α

Iνα(Eν) 6 Iγ(Eγ)

Gamma-ray and neutrino intensities are related by a simple relation.

Star-forming galaxies (galaxy clusters) produce neutrinos by cosmic rays colliding with the dense interstellar (intra-cluster) medium. Proton-proton collisions also produce high-energy gamma rays.

* L.A. Anchordoqui et al., PLB 600 (2004) 202.

Diffuse background ingredients

time

z = 0

z = 1

z = 5

neutrinos, gamma-rays

neutrinos, gamma-rays

• Gamma-ray and neutrino energy fluxes

• Distribution of sources with redshift

• Comoving volume (cosmology)

Gamma-ray diffuse background from star-forming galaxies

* C. Gruppioni et al., MNRAS 432 (2013) 23. Credits for images: ESA, Hubble, NASA web-sites.

Herschel provides IR luminosity function for each population X of star-forming galaxies.

Normal galaxies(i.e., Milky Way, Andromeda)

Injection spectral index in our canonical model (E> 600 MeV):

ΓNG = 2.7

Starburst galaxies (i.e., M82, NGC 253)

ΓSB = 2.2

Injection spectral index in our canonical model (E > 600 MeV):

SF-AGN(galaxies with dim/low

luminosity AGN)

Injection spectral index in our canonical model (E > 600 MeV):

SB-like or NG-like according to z.

Gamma-ray background from star-forming galaxies

Herschel PEP/HerMES survey provides IR luminosity function for each population X of star-forming galaxies (up to z > 4).

* C. Gruppioni et al., MNRAS 432 (2013) 23. M. Ackermann et al., Astrophys. J. 755 (2012) 164.

luminosity function gamma-ray flux comoving volume

ΦX(Lγ , z) = d2NX/dV dLγ

EBL correction

2.1 Infrared luminosity function and multi-wavelength luminosity comparison

Up to now, the total emissivity of IR galaxies at high redshifts has been poorly known, dueto the scarcity of Spitzer galaxies at z > 2, the large spectral extrapolations to derive thetotal IR-luminosity from the mid-IR and the incomplete information on the z-distributionof mid-IR sources. Herschel is the first telescope which allows us to detect the far-IR popu-lation to high redshifts (z ! 4 − 5) and to derive its rate of evolution through a luminosityfunction analysis [42]. From stellar mass function studies, one finds a clear increase with zof the relative fraction of massive star-forming objects (with mass M > 1011M!), startingto contribute significantly to the massive end of the mass functions at z > 1.

The IR population does not evolve all together as a whole, but it is composed by differentgalaxy classes evolving differently and independently. Following [42], IR observations report38% of NG, the 7% of SB and the remaining goes in star-forming galaxies containing AGN(SF-AGN). Here we consider spiral galaxies, starburst and star-forming galaxies containing anAGN as gamma-ray sources. The γ-ray intensity is defined through the luminosity function

I(Eγ) =

∫ zmax

0

dz

∫ Lγ,max

Lγ,min

dLγd2V

dΩdz

∑

X

ΦX(Lγ , z)dNX (Lγ , (1 + z)Eγ)

dEγ, (2.1)

where ΦX(Lγ , z) = d2NX/dV dLγ is the luminosity function for each galaxy family X =SG,SB, SF − AGN , dNX(Lγ , (1 + z)Eγ)/dEγ is the γ-ray flux, d2V/dΩdz the comovingvolume [43], and we assume zmax # 5.

For each population, we adopt a parametric estimate of the luminosity function in theIR range at different redshifts [42]:

ΦX(LIR)d logLIR = Φ∗X

(

LIR

L∗X

)1−αX

exp

[

−1

2σ2X

log2(

1 +LIR

L∗X

)]

d log LIR , (2.2)

that behaves as a power law for LIR $ L∗X and as a Gaussian in logLIR for logLIR for

LIR $ L∗X . The four parameters (αX , σX , L∗

X and Φ∗X) are different for each population X

and are defined as in Table 8 of [42].The data show a linear correlation between gamma-ray luminosity and IR luminosity

(8− 1000 µm). We adopt the fit scaling relationship given in [39],

log

(

L0.1−100 GeV

erg s−1

)

= α log

(

LIR

1010L!

)

+ β , (2.3)

with L! the Sun luminosity, α = 1.17 and β = 39.28 [39]. Note that this equationparametrizes the relationship between gamma-ray and total IR luminosity up to z # 2,we assume that it is also valid at higher redshifts (up to zmax # 5) and assume 108L! ≤LIR ≤ 1014L!.

2.2 Gamma-ray luminosity flux

As for the distribution of γ as a function of the energy, we here adopt a broken power-lawfit to the GALPROP conventional model of energy diffuse γ-ray emission and parametrize itas [6]

dNX(Lγ , Eγ)

dEγ= aX(Lγ)

(

Eγ

600 MeV

)−1.5s−1MeV−1 for Eγ < 600 MeV

(

Eγ

600 MeV

)−ΓX

s−1MeV−1 for Eγ > 600 MeV(2.4)

– 4 –

2 Extragalactic gamma-ray diffuse background from star-forming galaxies

In this Section, we compute the EGRB adopting the Herschel PEP/HerMES IR luminosityfunction up to z ! 4 [31] and the relation connecting the IR luminosity to the gamma-rayluminosity presented by the Fermi Collaboration [6]. The luminosity function provides afundamental tool to probe the distribution of galaxies over cosmological time, since it allowsus to access the statistical nature of galaxy formation and evolution. It is computed atdifferent redshifts and constitutes the most direct method for exploring the evolution of agalaxy population, describing the relative number of sources of different luminosities countedin representative volumes of the universe. Moreover, if it is computed for different samples ofgalaxies, it can provide a crucial comparison between the distribution of galaxies at differentredshifts, in different environments or selected at different wavelengths.

2.1 Gamma-ray luminosity function inferred from infrared luminosity function

Up to now, the total emissivity of IR galaxies at high redshifts had been poorly known becauseof the scarcity of Spitzer galaxies at z > 2, the large spectral extrapolations to derive the totalIR luminosity from the mid-IR, and the incomplete information on the redshift distribution ofmid-IR sources [27]. Herschel is the first telescope that allows to detect the far-IR populationto high redshifts (z < 4–5) and to derive its rate of evolution [31]. From stellar mass functionstudies, one finds a clear increase of the relative fraction of massive star-forming objects(with mass M > 1011M!) as a function of redshifts, starting to contribute significantly tothe massive end of the mass functions at z > 1 [31–35].

The IR population does not evolve all together as a whole, but it is composed of differentgalaxy classes evolving differently and independently. According to Ref. [31], among detected

star-forming galaxies, IR observations report 38% of normal spiral galaxies (NG), the 7% ofstarbursts (SB), and the remaining goes in star-forming galaxies containing AGN (SF-AGN)at 160µm, being the latter ones star-forming galaxies containing either an obscured or alow-luminosity AGN that still contributes to the cosmic star-formation rate. (Note that,in general, the intrinsic fractions are functions of redshifts.) Here we consider all of themas gamma-ray (and neutrino) sources. The galaxy classification has been done with the IRspectral data, where those that have the far-IR excess with significant ultraviolet extinctionare interpreted as the activities associated with star formation (hence classified as SB), andthose who exhibit mid-IR excess can be attributed to the obscured or low-luminosity AGNs(SF-AGN). The SB selected this way will feature high star-formation rate as well as highgas density, where both these features make the production of gamma rays and neutrinosefficient. The specific star-formation rate obtained for the SB population is shown to be onaverage 0.6 order of magnitude higher than that for the NG population [31].1

The gamma-ray intensity is calculated with the gamma-ray luminosity function as

I(Eγ) =

∫ zmax

0dz

∫ Lγ,max

Lγ,min

dLγ

ln(10)Lγ

d2V

dΩdz

∑

X

Φγ,X(Lγ , z)dFγ,X (Lγ , (1 + z)Eγ , z)

dEγe−τ(Eγ ,z) ,

(2.1)where Φγ,X(Lγ , z) = d2NX/dV d logLγ is the gamma-ray luminosity function for each galaxyfamily X = NG, SB, SF-AGN, dFγ,X(Lγ , (1 + z)Eγ , z)/dEγ is the differential gamma-ray flux at energy Eγ from a source X at the redshift z, d2V/dΩdz the comoving volume

1Some literature adopts the values of the specific star-formation rate in order to define NG and SB popu-lations. But we note that both conventions are consistent with each other as shown in Fig. 15 of Ref. [31].

– 4 –

Table 1. Local values of the characteristic luminosity (L!IR,X) and density (Φ!

IR,X) for each populationX .

X L!IR,X(z = 0) Φ!

IR,X(z = 0)

NG 109.45L! 10−1.95 Mpc−3

SB 1011.0L! 10−4.59 Mpc−3

SF-AGN 1010.6L! 10−3.00 Mpc−3

per unit solid angle per unit redshift range. The factor e−τ(Eγ ,z) takes into account theattenuation of high-energy gamma rays by pair production with ultraviolet, optical and IRextragalactic background light (EBL correction), τ(Eγ , z) being the optical depth. In ournumerical calculations we assume zmax ! 5 and adopt the EBL model in Ref. [63].

For each population X, we adopt a parametric estimate of the luminosity function forthe IR luminosity between 8 and 1000 µm at different redshifts [31]:

ΦIR,X(LIR, z)d logLIR = Φ!IR,X(z)

(

LIR

L!IR,X(z)

)1−αIR,X

× exp

[

−1

2σ2IR,X

log2(

1 +LIR

L!IR,X(z)

)]

d logLIR , (2.2)

which behaves as a power law for LIR $ L!IR,X and as a Gaussian in logLIR for LIR % L!

IR,X .We adopt the redshift evolution of L!

IR,X(z) and Φ!IR,X(z) for each population as in Table 8

of Ref. [31], as well as the values of αIR,X and σIR,X . We then fix the normalization by fittingthe data for L!

IR,X(z) and Φ!IR,X(z) from Fig. 11 of Ref. [31]. Table 1 shows the local (z = 0)

values of these parameters as the result of such a fitting procedure.2

By integrating the luminosity function, one obtains the IR luminosity density ρIR(z):

ρIR(z) =

∫

d logLIRLIR

∑

X

ΦIR,X(LIR, z), (2.3)

which is believed to be well correlated to the cosmic star-formation rate density. The adoptedfitting functions for the luminosity function of each family X reproduce the total IR lumi-nosity density data summarized in Fig. 17 of Ref. [31].

The Fermi data show a correlation between gamma-ray luminosity (0.1–100 GeV) andIR luminosity (8–1000 µm). Although such correlation is not conclusive at present due to thelimited statistics of starbursts found in gamma rays, we adopt the following scaling relation:

log

(

Lγ

erg s−1

)

= α log

(

LIR

1010L!

)

+ β , (2.4)

with L! the solar luminosity, α = 1.17 ± 0.07 and β = 39.28 ± 0.08 [6]. While this parame-terization is calibrated in a local volume, we assume that it is also valid at higher redshifts

2We note that adopting for these parameters the values directly from Table 8 of Ref. [31] results inoverestimate of the gamma-ray intensity, since the table summarizes the values of L

"IR,X and Φ"

IR,X for0 < z < 0.3, which are different from the values at z = 0 shown in Table 1.

– 5 –

Gamma-ray-IR linear relation from Fermi data.

Gamma-ray diffuse background from star-forming galaxies

* I. Tamborra, S. Ando, K. Murase, JCAP 09 (2014) 043.

Differential contributions to the EGRB intensity

Normal galaxies leading contribution up to z=0.5. SF-AGN and SB dominate at higher z.

Gamma-ray and neutrino backgrounds from star-forming galaxies

* I. Tamborra, S. Ando, K. Murase, JCAP 09 (2014) 043. See also: Strong et al. (1976), Thompson et al. (2006), Fields et al. (2010), Makiya et al. (2011), Stecker&Venters(2011). Loeb&Waxman (2006), Lacki et al. (2011), Murase et al. (2013).

Diffuse gamma-ray intensity

Fermi data

gamma-IR uncertainty band

Diffuse neutrino intensity

Neutrino intensity with its astrophysical uncertainty band within IceCube band for E<0.5 PeV.

The SB spectral index matching simultaneously Fermi and IceCube data is .ΓSB 2.15

Constraints from Fermi and IceCube dataFermi and IceCube data can constrain starburst abundance and their injection spectral index.

3 Results: Diffuse Neutrino Flux from Star-forming galaxies

Neutrino production at TeV to PeV energies is thought to proceed via pion production viaproton-photon (p − γ) or proton-gas (pp) interactions. Such interactions produce γ-rays aswell as neutrinos. However the relative flux of neutrinos and γ-rays depend on the ratio ofcharged to neutral pions, Nπ±/Nπ0 , and the relative neutrino flux per flavor depends on theinitial mix of π+ to π− [38]. In this work we focus on pp interactions, that are thought tobe the main hadronic process. Therefore Nπ± " 2Nπ0 and the flavor ratio after oscillationsis νe : νµ : ντ = 1 : 1 : 1 (and the same is for antineutrinos) [38]. Hence, following [48] andassuming the source at a much larger distance with respect to the typical interaction length,the relative differential fluxes of γ-rays and neutrinos are related as

∑

να

Iν(Eν) " 6 Iγ(Eγ) , (3.1)

with Eγ " 2Eν .The expected neutrino spectrum is plotted in Fig. 2 as a function of the energy. The

magenta line is the flux obtained adopting the luminosity function approach, the pink banddefines the uncertainty band coming from Eq. 2.3. The black line is the diffuse neutrinointensity obtained adopting the SFR, while the blue line is the IceCube measured flux withits error band as in Eq. 1.1. Our computed flux is comparable within the astrophysicaluncertainties with the IceCube one especially at low energies.

4 Fermi and IceCube Bounds on the Starburst Injection Spectral Indexand Abundance

The injection spectral index of the gamma-ray spectrum of starbursts is poorly constrainedas well as the fraction of SF-AGN that behaves similarly to SB. Here we consider as freeparameters ΓSB as well as the fraction of galaxies containing AGN that behaves similarly tostarbursts (0 ≤ fSB−AGN ≤ 1), and compute their allowed variation region compatible withboth the Fermi and Icecube data. Therefore Eq. 2.1 becomes

Iγ(Eγ) = Iγ,NG(Eγ)+Iγ,SB(Eγ ,ΓSB)+[fSB−AGN Iγ,SB(Eγ ,ΓSB) + (1− fSB−AGN) Iγ,NG(Eγ)] .(4.1)

Note as it recovers Eq. 2.1 and our previous results for fSB−AGN = 0.Figure 3 shows the exclusion regions by Fermi and IceCube data in the plane defined by

the injection spectral index (ΓSB) and the fraction of starburst (fSB−AGN), compatible withthe Fermi data [39] and IceCube ones as in Eq. 1.1. Note as the Fermi data at the momentexclude a larger region of the parameter space than the IceCube ones. We can concludethat very hard spectra for SB (i.e., ΓSB < 2.2) are excluded from present data and there isa tendency to allow more abundant starbursts as much as the spectral index is softer sincethey give a lower contribution to the high energy tail of the spectrum.

5 Extragalactic gamma-ray diffuse background adopting the star forma-tion rate

In this Section, for comparison to previous results, the γ-ray and neutrino diffuse backgroundadopting the cosmological star formation rate is derived adopting, as template galaxies, theMW as normal galaxy and M82 and NGC 253 as examples of starbursts.

– 6 –* I. Tamborra, S. Ando, K. Murase, JCAP 09 (2014) 043.

SB spectral index and SB-AGN fraction compatible with Fermi and IceCube data

Gamma-ray background from galaxy clusters

* G. Giovannini, M. Tordi, L. Ferretti, New A 4 (1999) 141. F. Zandanel, S. Ando, MNRAS 440 (2014) 663. MAGIC Collaboration A&A 541 (2012) A99. Credits for images: Hubble, CMSO web-sites.

Radio counts constraints from NVSS + Coma and Perseus gamma-ray upper limits need to be respected.

Coma galaxy cluster

Perseus galaxy cluster

Gamma-ray background from galaxy clusters

Cluster of galaxies give a negligible contribution to the diffuse backgrounds for z > 2.5.

Zandanel et al.: Gamma-ray and neutrino backgrounds from galaxy clusters

with Aγ enclosing the spectral information (Pfrommer et al.2008).

In the following, we will make use of Equations (1) and (2) tocalculate the hadronic-induced emission in galaxy clusters at ra-dio and gamma-ray frequencies. The spectral multipliers Af andAγ were obtained in Pfrommer & Enßlin (2004) as analytical ap-proximations of full proton-proton interaction simulations. Theanalytical expressions for Af and Aγ well reproduce the resultsof numerical simulations from energies around the pion bump(∼100 MeV) up to a few hundred GeV. A more precise formal-ism has been derived by Kelner et al. (2006) for the TeV–PeVenergy range, relevant to calculate the neutrino fluxes. Therefore,we correct the gamma-ray spectra obtained adopting the analyt-ical approximations with the recipe in Kelner et al. (2006) forenergies above ∼0.1–1 TeV. The transition energy between thetwo approximations is dependent on αp and it has been chosenas the energy at which the two models coincide.

We compute the corresponding neutrino spectra as pre-scribed in Kelner et al. (2006). Note that, assuming that proton-proton interactions are the main interactions producing neutri-nos and gamma-rays, the neutrino intensity for all flavours couldalso be approximately obtained as a function of the gamma-ray flux (Ahlers & Murase 2014; Anchordoqui et al. 2004):Lν(Eν) ≈ 6 Lγ(Eγ), with Eν ≈ Eγ/2, where we ignored theabsorption during the propagation of gamma-rays for simplic-ity. From this approximation, one gets that, at a given energy,Lν/Lγ ∼ 1.5 for αp = 2. However, detailed calculations byBerezinsky et al. (1997) and Kelner et al. (2006) show that thisratio is slightly smaller for spectral indices αp > 2 and slightlyhigher for αp < 2.

Note that we do not assume any CR spectral cut-off at high-energies, nor any spectral steepening due to the high-energy pro-tons that are no longer confined into the cluster (Volk et al. 1996;Berezinsky et al. 1997; Pinzke & Pfrommer 2010), and thus, asdiscussed in the following, our results should be considered asconservative. While this is not relevant when comparing withthe Fermi data, it might be relevant for the high-energy neutrinoflux.

Since the larger contribution to the total diffuse intensitycomes from nearby galaxy clusters (see Figure 5 and commentstherein), we will additionally neglect the absorption of high-energy gamma-rays due to interactions with the extragalacticbackground light as this becomes relevant only at high redshifts(see, e.g., Domınguez et al. 2011). We remark that our conclu-sions do not change even relaxing any of the above approxima-tions.

3. Phenomenological luminosity-mass relationIn this section, we estimate the maximum possible contributionto the extragalactic gamma-ray and neutrino backgrounds fromhadronic interactions in galaxy clusters using a simplified phe-nomenological approach for the luminosity-mass relation.

3.1. Modelling of the diffuse gamma-ray intensity

The total gamma-ray intensity, from all galaxy clusters in theUniverse, at a given energy, is

Iγ =∫ z2

z1

∫

M500, lim

Lγ(M500, z) (1 + z)2

4πDL(z)2 (3)

×d2n(M500, z)dVc dM500

dVc

dz dz dM500 ,

where the cluster mass M∆ is defined with respect to a densitythat is ∆ = 500 times the critical density of the Universe atredshift z. Vc is the comoving volume, DL(z) is the luminositydistance, and d2n(M500, z)/dVc dM500 is the cluster mass func-tion for which we make use of the Tinker et al. (2008) formal-ism and the Murray et al. (2013) on-line application. The lowerlimit of the mass integration has been chosen to be M500, lim =1013.8 h−1 M%, to account for large galaxy groups. The redshiftintegration goes from z1 = 0.01, where the closest galaxy clus-ters are located, up to z2 = 2. Where not otherwise specified,we assume Ωm = 0.27, ΩΛ = 0.73 and the Hubble param-eter H0 = 100 h70 km s−1 Mpc−1 with h70 = 0.7. Note thatwhere we explicitly use h in the units, as for M500, lim, we assumeH0 = 100 h km s−1 Mpc−1 with h = 1. As shown in Figure 1 (andlater in Figure 5), our conclusions are not affected by the specificchoice of z2 and M500, lim.

0.0 0.5 1.0 1.5 2.0 2.5z

10-9

10-8

10-7

10-6

10-5

10-4

n(>

M50

0,lim

) [h

3 Mpc

-3]

WMAPPlanck

Fig. 1. Total number density of galaxy clusters for masses aboveM500, lim = 1013.8 h−1M% as a function of redshift. We show thenumber density obtained assuming the WMAP (Komatsu et al.2011), our standard choice if not otherwise specified, and thePlanck (Planck Collaboration 2013) cosmological data. At red-shift z = 2, the number density is already negligible with respectto the lowest redshift.

We calculate the total number of detectable galaxy clustersat f = 1.4 GHz, above the flux Fmin, in the following way:

N1.4(> Fmin) =∫ z2

z1

∫ ∞

Fmin

d2n(F1.4, z)dVc dF1.4

dVc

dzdz dF1.4 , (4)

where F1.4 = L1.4(1 + z)/4πDL(z)2, and we compare it with theradio counts from the National Radio Astronomy ObservatoryVery Large Array sky survey (NVSS) of Giovannini et al.(1999).2 The flux Fmin is defined as in equation (9) ofCassano et al. (2012) by adopting a noise level multiplier ξ1 = 1,

2 We use the cumulative number density function as in Cassano et al.(2010). Note that Cassano et al. (2010) do not use the fluxes ofGiovannini et al. (1999), but the ones from follow-up observations ofthe same sample of galaxy clusters, which are higher than the NVSSones (R. Cassano, private communication).

3










Iγ =∫ z2

z1

∫

M500, lim

Lγ(M500, z) (1 + z)2

4πDL(z)2 (3)


dVc

dz dz dM500 ,


0.0 0.5 1.0 1.5 2.0 2.5z

10-9

10-8

10-7

10-6

10-5

10-4

n(>

M50

0,lim

) [h

3 Mpc

-3]

WMAPPlanck



N1.4(> Fmin) =∫ z2

z1

∫ ∞

Fmin


dVc

dzdz dF1.4 , (4)



3

cluster mass function gamma-ray flux comoving volume










Iγ =∫ z2

z1

∫

M500, lim

Lγ(M500, z) (1 + z)2

4πDL(z)2 (3)


dVc

dz dz dM500 ,


0.0 0.5 1.0 1.5 2.0 2.5z

10-9

10-8

10-7

10-6

10-5

10-4

n(>

M50

0,lim

) [h

3 Mpc

-3]

WMAPPlanck



N1.4(> Fmin) =∫ z2

z1

∫ ∞

Fmin


dVc

dzdz dF1.4 , (4)



3

Number density of galaxy clusters

* F. Zandanel, I. Tamborra, S. Gabici, S. Ando, arXiv: 1410.8697.

Gamma-ray and neutrino backgrounds from galaxy clusters

* F. Zandanel, I. Tamborra, S. Gabici, S. Ando, arXiv: 1410.8697.


1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9log10 F1.4 GHz [mJy]

0.8

1.0

1.2

1.4

1.6

1.8

log 1

0 N(>

F1.

4 G

Hz)

[#/s

ky]

NVSS (0.044 < z < 0.2)

!p = 2!p = 2.2!p = 2.4

B >> BCMB

0.0 2.0 4.0 6.0Log10 E [GeV]

-11.0

-10.0

-9.0

-8.0

-7.0

-6.0

-5.0

Log 1

0 E2 d

N/d

E [G

eV c

m-2

s-1 sr

-1]

!p=2!p=2.2!p=2.4!p=1.5

gammaneutrinos B >> BCMB

Fermi-LAT

IceCube

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9log10 F1.4 GHz [mJy]

0.8

1.0

1.2

1.4

1.6

1.8

log 1

0 N(>

F1.

4 G

Hz)

[#/s

ky]

NVSS (0.044 < z < 0.2)

!p = 2!p = 2.2B = 1 µG

0.0 2.0 4.0 6.0Log10 E [GeV]

-11.0

-10.0

-9.0

-8.0

-7.0

-6.0

-5.0

Log 1

0 E2 d

N/d

E [G

eV c

m-2

s-1 sr

-1]

!p=2!p=2.2!p=2.4!p=1.5

gammaneutrinos B = 1 µG

Fermi-LAT

IceCube

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9log10 F1.4 GHz [mJy]

0.8

1.0

1.2

1.4

1.6

1.8

log 1

0 N(>

F1.

4 G

Hz)

[#/s

ky]

NVSS (0.044 < z < 0.2)

!p = 2B = 0.5 µG

0.0 2.0 4.0 6.0Log10 E [GeV]

-11.0

-10.0

-9.0

-8.0

-7.0

-6.0

-5.0

Log 1

0 E2 d

N/d

E [G

eV c

m-2

s-1 sr

-1]

!p=2!p=2.2!p=2.4!p=1.5

gammaneutrinos B = 0.5 µG

Fermi-LAT

IceCube

Fig. 2. Total gamma-ray and neutrino intensities (right) due to hadronic interactions in galaxy clusters, for 100% of loud clusters,and corresponding radio counts due to synchrotron emission from secondary electrons (left). From top to bottom, we plot thecases with B ! BCMB, B = 1 µG and 0.5 µG, respectively. For comparison, the Fermi (The Fermi LAT collaboration 2014) andIceCube (Aartsen et al. 2014b) data are shown in the panels on the right. The neutrino intensity is meant for all flavours. All theplotted intensities respect NVSS radio counts and the gamma-ray upper limits on individual clusters. In the case with B = 1 µGand αp = 2.4, B = 0.5 µG and αp = 2.2, 2.4, and for αp = 1.5, the radio counts respecting the gamma-ray and neutrino limits,respectively, are below the y-scale range adopted for the panels on the left.

6

Diffuse gamma-ray and neutrino backgrounds

Radio counts due to synchrotron emission from secondary electrons

Galaxy clusters contribute by less than 1-10% to the total EGRB observed by Fermi and to the IceCube neutrino flux.

Conclusions

! Origin of high-energy IceCube neutrinos unknown.

! Diffuse neutrino flux from star-forming galaxies is one natural possibility.

! Multi-messenger approach: Starburst spectral index matching simultaneously Fermi and IceCube data close to .

! Galaxy clusters cannot explain the IceCube events, unless very hard (and speculative) spectral index is adopted.

ΓSB 2.15

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Documents

Diffuse origin of the high-energy IceCube neutrinos