Star-forming galaxies as the origin of the IceCube PeV neutrinos
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29, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
STAR-FORMING GALAXIES AS THE ORIGIN OF THE ICECUBE PEV NEUTRINOS X IAO -C HUAN C HANG , R UO -Y U L IU , X IANG -Y U W ANG
School of Astronomy and Space Science, Nanjing University, Nanjing, 210093, China; [email protected] Key laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany
Draft version July 29, 2018
ABSTRACTStar-forming galaxies, due to their high star-formation rates and hence large number of supernova remnantstherein, are huge reservoirs of cosmic rays (CRs). These CRs collide with gases in the galaxies and producehigh-energy neutrinos through pp collisions. In this paper, we calculate the neutrino production efficiency instar-forming galaxies by considering realistic galaxy properties, such as the gas density and galactic wind instar-forming galaxies. To calculate the accumulated neutrino flux, we use the infrared luminosity function ofstar-forming galaxies obtained by Herschel
PEP/HerMES survey recently. The intensity of CRs producingPeV neutrinos in star-forming galaxies is normalized with the observed CR flux at EeV ( 1 EeV=10 eV),assuming that supernova remnants or hypernova remnants in star-forming galaxies can accelerate protons toEeV energies. Our calculations show that the accumulated neutrino emission produced by CRs in star-forminggalaxies can account for the flux and spectrum of the sub-PeV/PeV neutrinos under reasonable assumptions onthe CR confinement time in these galaxies. Subject headings: neutrinos- cosmic rays INTRODUCTION
The IceCube Collaboration recently announced the dis-covery of extraterrestrial neutrinos. With 37 events rang-ing from 60 TeV to 3 PeV within three years of opera-tion, the excess over the background atmospheric neutrinosand muons reaches 5.7 σ (Aartsen et al. 2014). The non-detection of events beyond 3 PeV suggests that the neu-trino flux follows either a hard power law spectrum witha break above 3 PeV, or an unbroken power law spectrumwith a softer index of Γ ≃ . - . pp collisions occur in such star-forming galaxies, so they are guaranteed factories of high-energy neutrinos.In the pioneering work of the starburst galaxy scenario,Loeb & Waxman (2006) assume that CRs in the starburst galaxies lose almost all the energy into pions and calibratethe GeV neutrino emissivity with the synchrotron radio emis-sivity. A simple power-law extrapolation is then used to es-timate the neutrino flux at PeV energies. On the other hand,we (Liu et al. 2014) studied the PeV neutrino emissions fromstar-forming/starburst galaxies, assuming that the intensity ofCRs producing PeV neutrinos in star-forming/starburst galax-ies matches the observed CR flux at EeV. This is motivatedby the possibility that PeV neutrinos could originate fromthe same sources responsible for extragalactic CRs (Liu et al.2014), as PeV neutrinos require ∼
50 PeV CRs, which isonly one order of magnitude lower than the energy of the"second knee" of CR spectrum (4 - × eV), where thetransition from Galactic CRs to extragalactic CRs may oc-cur (Berezinsky et al. 2006). It has been suggested that theremnants of hypernovae or other peculiar types of supernovaein star-forming galaxies may accelerate protons to EeV en-ergies due to their faster ejecta and larger explosion energy(Wang et al. 2007; Budnik et al. 2008; Chakraborti et al.2011; Liu & Wang 2012). In Liu et al. (2014), we assumethat all star-forming galaxies as well as all starburst galaxieshave uniform properties such as gas density, which lead to thesame neutrino production efficiency among all star-forminggalaxies, and among all starburst galaxies. However, the CRintensity and gas density should be different in galaxies of dif-ferent luminosities or types. In this paper, we attempt to im-prove our earlier calculation by considering realistic galaxyproperties and the galaxy luminosity function. The luminos-ity function describes the relative number of galaxies of dif-ferent luminosities, as well as the evolution of a galaxy pop-ulation with redshift. The Herschel PEP/HerMES survey hasrecently provided an estimate of the IR luminosity functionup to z ∼ In another model, the transition occurs at the "ankle" ( . eV)(Katz et al. 2009), where the spectral index flattens from -3.3 to -2.7 . galaxies containing obscured or low-luminosity AGNs, all ofwhich contribute to the star-formation rate in the Universe(Gruppioni et al. 2013). The gas density in a galaxy is ex-pected to relate to its star-formation rate and hence to the IRluminosity of the galaxy. Then, with these galaxy propertiesknown, we are able to calculate the neutrino fluxes producedin star-forming galaxies of different luminosities and popula-tions.In §2, we first outline the neutrino production process instar-forming galaxies. In §3, we describe the galaxy parame-ters that are needed for calculating the accumulated neutrinoflux from star-forming galaxies. In §4, we invoke the lumi-nosity function to calculate the accumulated neutrino flux pro-duced by all the star-forming galaxies in the Universe. Finally,we give our conclusions and discussions in §5. NEUTRINO PRODUCTION PROCESS IN STAR-FORMINGGALAXIES
Supernova remnants (SNRs)are widely discussed as accel-erators of CRs. Due to high star-formation rates (SFRs) instar-forming galaxies, large amount of SNRs reside in thesegalaxies and hence these galaxies are huge reservoirs of CRs.The total energy of CRs injected into a galaxy per unit timeis proportional to the total SFR of the galaxy, i.e., L p ∝ SFR,where L p represents the luminosity in CR protons. The totalinfrared luminosity of a galaxy is a good tracer for its SFR,and there exists a widely used relation between the total in-frared luminosity L TIR and SFR (Kennicutt 1998). Thus weexpect that L p ∝ L TIR , i.e. L p = C L
TIR L ⊙ (cid:18) E p (cid:19) - p , (1)where C is the normalization factor, L ⊙ is the bolometric lu-minosity of the Sun and E p is the proton energy in unit ofGeV. p is the index of the proton spectrum ( dn / dE p ∝ E - pp ),and we assume p = 2, as expected from the first-order Fermiacceleration in blastwaves of SNRs.Once the accelerated CRs are injected into interstellarmedium (ISM), hadronuclear collisions between CRs and nu-clei in ISM would produce charged pions, which will decayto neutrinos ( π + → ν µ ¯ ν µ ν e e + , π - → ¯ ν µ ν µ ¯ ν e e - ). On the otherhand, CRs can escape a galaxy through diffusion or galac-tic wind advection. These two competing processes regu-late the efficiency of the pion-production of CRs which canbe described by f π = 1 - exp (cid:0) - t esc / t loss (cid:1) , where t esc is the es-cape time of CRs and t loss is the energy-loss time of CRs viaproton–proton ( pp ) collisions.The energy-loss time t loss can be expressed as (cid:0) . n σ pp c (cid:1) - ,where 0.5 is the inelasticity factor, n is the particle numberdensity and σ pp is the inelastic pp collision cross section. Weconvert the particle number density to gas surface density by Σ g = m p nH , where m p is the mass of proton and H is theheight of the galaxy, the energy-loss time is t loss = 1 . × H (cid:16) σ pp (cid:17) - (cid:18) Σ g
1g cm - (cid:19) - yr . (2)There are basically two ways for CRs to escape from agalaxy, i.e. diffusion and advection. In the diffusion escapecase, CRs are scattered by small-scale inhomogeneous mag-netic fields randomly and diffuse out of the host galaxy. Thediffusive escape time is t diff = H / D . Here D = D (cid:0) E / E (cid:1) δ is the diffusion coefficient, where D and E = 3GeV are nor-malization factors, and δ = 0 - t diff = 7 . × (cid:18) H (cid:19) (cid:18) D cm s - (cid:19) - (cid:18) E p (cid:19) - δ yr . (3)Since galaxies with higher IR luminosities are observed tohave stronger magnetic fields (Thompson et al. 2006), andthe diffusion coefficient is expected to scale with the CRLarmor radius, these high luminosity galaxies could havea smaller diffusion coefficient. Thus, we allow lower val-ues of diffusion coefficient for galaxies with IR luminos-ity L TIR > L ⊙ in the calculation, while the diffusioncoefficient for galaxies with IR luminosity L TIR < L ⊙ is fixed to D , L = 10 cm - s - , the same value as that ofour Galaxy. The energy dependence of the diffusion coef-ficient is also unknown. We assume two cases, one is thecommonly-used value δ = 0 .
5, based on the measurementsof the CR confinement time in our Galaxy (Engelmann et al.1990; Webber et al. 2003), which is also consistent with theKraichnan-type turbulence. Another choice is δ = 1 /
3, as-suming the Kolmogorov-type turbulence.In the advection escape case, CRs are confined in the galac-tic wind and transported outward with the wind in a charac-teristic timescale t adv = H / v w = 1 . × H (cid:18) v w - (cid:19) - yr (4)where v w is the speed of galactic wind. The real escape timeshould involve both effects, and we parameterize it as t - = t - + t - .The flux of neutrinos produced in one galaxy is then calcu-lated by the following analytical formula L ν ( E ν ) ≃ Z ∞ E ν f π (cid:0) E p (cid:1) L p (cid:0) E p (cid:1) F ν (cid:18) E ν E p , E p (cid:19) dE p E p , (5)where F ν (cid:0) E ν / E p , E p (cid:1) is the spectrum of the secondary neu-trino emissions given in Kelner et al. (2006).CRs that escape their host galaxies contribute to the extra-galactic CRs observed by us. At higher energies, diffusionescape timescale is shorter and hence leads to a higher escapeefficiency of CRs, which can be estimated as f esc = 1 - f π . Thespectrum of these escaped CRs can then be simply expressedas f esc L p . GALAXY PARAMETERS
We have seen that the pion-production efficiency dependson galaxy parameters, such as gas surface density Σ g , galac-tic wind velocity v w , scale height of the galaxy H and etc. Inthis section, we try to give a description of these parameters,which are needed in calculating the accumulated neutrino fluxin §4. Since the infrared luminosity function is used to char-acterize the population of galaxies, we try to build relationsbetween these parameters and the total infrared luminosity ofthe galaxy.To determine the gas surface density Σ g , we employ thewidely used Kennicutt-Schmidt law, which relates the SFRsurface density Σ SFR with gas surface density, i.e., Σ SFR ∝ Σ . g (Kennicutt 1998). The Kennicutt-Schmidt law, althoughdiscovered for galaxies in the local Universe, is proven to bealso valid at high redshift (Genzel et al. 2010). In this paperwe use the classic form given by Kennicutt (1998), i.e. Σ SFR = (2 . ± . × - (cid:18) Σ g M ⊙ pc - (cid:19) . ± . M ⊙ yr - kpc - . (6)If the radius of each galaxy is known, we could derive theSFR surface density Σ SFR =SFR/ π R . Assuming the Chabrierinitial mass function (IMF) (Chabrier 2003), one hasSFR = L TIR L ⊙ M ⊙ yr - . (7)Substituting this relation into Kennicutt-Schmidt Law, we get Σ g = (7 . ± . × - (cid:18) L TIR L ⊙ (cid:19) . ± . (cid:18) R pc (cid:19) - . ± . g cm - . (8)There is a correlation between SFR and the total stel-lar mass for the majority of star-forming galaxies, whichare known as the Main Sequence (MS) galaxies. Therelation is quite tight in the local Universe (Peng et al.2010, 2012) and also works well at higher redshift(Elbaz et al. 2007; Daddi et al. 2007; Rodighiero et al. 2010).In this paper, we use the SFR-stellar mass relation pro-vided by Bouché et al. (2010) and Genzel et al. (2010), i.e.,SFR (cid:0) M ⊙ yr - (cid:1) = 150 (cid:0) M ⋆ / M ⊙ (cid:1) . [(1 + z ) / . . for z < . (cid:0) M ⊙ yr - (cid:1) = 163 (cid:0) M ⋆ / M ⊙ (cid:1) . for z > . z = 4, since the redshift evolution flattens above z ∼ - . / M ⋆ . Galaxies with higher sSFR arethought to be off-MS galaxies and in a merger mode. Accord-ing to Gruppioni et al. (2013), normal spiral galaxies, star-burst galaxies and SF-AGNs(spiral) are thought to be mostlyon-MS galaxies, while SF-AGNs(SB) are thought to be off-MS galaxies. In our calculation, the SFR-stellar mass relationis increased by 0.6 dex for off-MS galaxies. For the ChabrierIMF, the relation between the total stellar mass and the totalinfrared luminosity can be summarized as M ⋆ = (cid:16) L TIR . α × L ⊙ (cid:17) . (cid:0) + z . (cid:1) - . ( z < . × (cid:16) L TIR . α × L ⊙ (cid:17) . ( z > . , (9)where α is equal to 1 and 4 for on-MS galaxies and off-MSgalaxies respectively.The relation between stellar mass and galaxy radiushas been studied by different authors (Shen et al. 2003;Dutton et al. 2011; Mosleh et al. 2011; Law et al. 2012;Cebrián & Trujillo 2014). For local late-type galaxies,Shen et al. (2003) found a relation based on the Sloan Digi-tal Sky Survey, R SDSS = 0 . (cid:18) M ⋆ M ⊙ (cid:19) . (cid:18) + M ⋆ . × M ⊙ (cid:19) . kpc . (10)At high redshift galaxies tend to be more compact, whilethe scaling still works (Dutton et al. 2011; Mosleh et al. 2011; Law et al. 2012). Law et al. (2012) found a redshift-dependent relation, RR SDSS ≈ (cid:26) z < , + z ) - . ( z > . (11)Combining the SFR-stellar mass relation and the radius-stellar mass relation above, we can now derive the galaxyradius R from its SFR. As the star-forming galaxies at highredshift are more consistent with triaxial ellipsoids with mi-nor/major axis ratio ∼ . H =0 . R .Galactic-scale gaseous outflows or winds in star-forminggalaxies are ubiquitous at all cosmic epochs (Heckman et al.1990; Pettini et al. 2001; Shapley et al. 2003). Such outflowsare powered by supernova explosions or other processes. Thedependence of galactic wind speed on the galaxy’s SFR hasbeen studied. For ultraluminous infrared galaxies at lowredshifts, winds from more luminous starbursts have higherspeeds roughly as v w ∝ SFR . (Martin 2005). Similar rela-tion is found in star-forming galaxies at z = 1 .
4, showing v w ∝ SFR . with an error in v w being 34% (Weiner et al. 2009).Combining Eq. 1, we get v w ≈ (cid:18) SFR M ⊙ yr - (cid:19) . ≈ (cid:18) L TIR L ⊙ (cid:19) . km s - . (12)Once the galaxy parameters are known, we can calculate thepion-production efficiency f π of CRs in galaxies of differentluminosities.Fig.1 shows the efficiency f π for CRs producing1 PeV neutrinos in a galaxy at z = 1. One can see that the pp interaction is quite inefficient in low IR luminosity galaxies,due to low gas densities in these galaxies. As the IR luminos-ity increases, the pion-production efficiency increases. It alsoshows that the pion-production efficiencies are higher in off-MS galaxies, which is due to denser ISM in them. We alsogive the uncertainty of f π in Fig. 1 (the shaded region), tak-ing into account the uncertainties in the Kennicutt-SchmidtLaw (including the uncertainty in slope) and in the galacticwind velocity. We find the uncertainty of f π is about 50%which mainly results from the uncertainty in the slope of theKennicutt-Schmidt Law.In our calculation, we assumed that the column density ofgas in a galaxy is uniform out to a limiting radius in a galaxy.The realistic gas density distribution in a galaxy may have asmooth gradient outwards. Correspondingly, the CR injectionrate, which traces the SFR, may follow the same distribution.We employ an exponential density profile found by Kravtsov(2013) to re-calculate the pion-production efficiency and findthat the overall efficiency is decreased by a factor of about30%.The pion-production efficiency also depends on the energyof CRs. As the diffusion escape is faster at higher energywhile the advection and pp interaction timescales are energy-independent, the pion-production efficiency would break atsome energy and then decreases as the energy of CRs in-creases. As a result, the escape efficiency for CRs, f esc =1 - f π , increases with energy. That means CRs above 1 EeVare able to escape almost freely from their host galaxies andcontribute to the observed flux of extragalactic CRs. ACCUMULATED NEUTRINO FLUX WITH NORMALIZATION TOEEV CRS
In this section, we compute the accumulated neutrino fluxby adopting the Herschel PEP/HerMES luminosity function(Gruppioni et al. 2013). Herschel is the first telescope that al-lows to detect far-IR population up to z ≃
4. Gruppioni et al.(2013) estimate the luminosity functions of different galaxypopulations including normal spiral galaxies, starbursts andstar-forming galaxies containing obscured or low-luminosityAGNs. The galaxy classification is based on IR spectra, wherethose that have far-IR excess with significant ultraviolet ex-tinction are classified as starbursts and those that have mid-IR excess are classified as galaxies with obscured or low-luminosity AGNs (SF-AGN). The SF-AGN family includesSeyferts, LINERs and ULRIGs containing AGNs. SF-AGNsare further divided into two sub-classes: SF-AGN(SB) thatresembles starburst galaxies and SF-AGN(spiral)that resem-bles normal spiral galaxies. This family, although containingAGNs, is dominated by star-formation but not by AGN pro-cesses. The accumulated neutrino flux is the sum of the con-tribution from all the galaxies throughout the whole universe,i.e., E ν Φ accu ν i = E ν c π Z z max Z L TIR , max L TIR , min P i φ i ( L TIR , z ) L ν i [(1 + z ) E p , L TIR ] H p (1 + z ) Ω M + Ω Λ dL TIR dz . (13)where φ i ( L TIR , z ) is the luminosity function for each galaxyfamily i , H = 71 km s - Mpc - , Ω M = 0 . Ω Λ = 0 . i ) can be generally described as φ i ( L TIR , z ) = φ ∗ (cid:18) L TIR L ∗ (cid:19) - α exp[ - σ log (cid:18) + L TIR L ∗ (cid:19) ](14)where L ∗ evolves as (1 + z ) k L , at z < z b , L , and as (1 + z ) k L , at z > z b , L , while φ ∗ evolves as ∝ (1 + z ) k ρ , at z < z b , ρ and as (1 + z ) k ρ , at z > z b , ρ . For each population of galax-ies, the parameters in luminosity functions, such as L ∗ , φ ∗ , α , σ , z b , L , k L , , k L , , z b , ρ , k ρ , , k ρ , are provided in Ta-ble 8 in Gruppioni et al. (2013). The number ratio betweenthe two sub-classes of SF-AGNs (i.e. SF-AGN(spiral) andSF-AGN(SB))evolves with redshift, as given in Table 9 ofGruppioni et al. (2013).To compute the accumulated neutrino flux from all star-forming galaxies, we need to determine the normalization forthe CR intensity at EeV energy in each galaxy, i.e. the factor C in Eq.1. We assume that the CRs which escape from thesegalaxies are responsible for the extragalactic CR flux at EeV.As EeV CRs do not suffer significant attenuation during theirpropagations to the Earth, the expected CR flux at E p is E p Φ accu p = E p c π Z z max Z L TIR , max L TIR , min P i φ i ( L TIR , z ) f esc L p [(1 + z ) E p , L TIR ] H p (1 + z ) Ω M + Ω Λ dL TIR dz . (15)The observed flux at 1 EeV is about E p Φ p | E p =1EeV ≃ × - GeV cm - s - sr - , accord-ing to several CR experiments such as HiRes(High Resolution Fly’S Eye Collaboration et al. 2009) ,Auger (Pesce 2012), KASCADE-Grande (Chiavassa et al.2014) and TA (Abu-Zayyad et al. 2015). Then we get thenormalization factor C ≃ × eV - s - . The accumulated neutrino flux can then be obtained withEq.(13). Since the galaxy parameters are all determined,there are only two free parameters, i.e. the diffusion coef-ficient D and δ , which are not well-understood. We studywhether the theoretical flux agrees with the observations un-der reasonable values of these two parameters. We find thatfor δ = 1 / D , H ≃ . cm s - (the diffusion coefficient forgalaxies with high IR luminosity L TIR > L ⊙ ) leads to atotal neutrino flux that can fit the IceCube data, as shown inFig.2. Note that the diffusion coefficient for galaxies with lowIR luminosity L TIR < L ⊙ is fixed to D , L = 10 cm s - .The figure shows contributions from various types of galaxies.We find that star-forming galaxies with obscured AGNs andstarburst galaxies contribute significant fractions of the neu-trino flux, while the spiral galaxies contribute the least. Asexpected, the neutrino spectrum becomes softer at high en-ergies where the diffusion time is shorter than the advectiontime. The slope becomes steeper than Φ ( E ν ) ∝ E - . ν abovePeV energy.For δ = 0 .
5, a smaller values of D , H ≃ cm s - is neededto fit the IceCube data, as shown in Fig.3. With a large δ , the neutrino spectrum becomes softer than Φ ( E ν ) ∝ E - . ν above PeV energy, which could explain the non-detection ofneutrinos above 3 PeV (Anchordoqui et al. 2014a; Winter2014). The lower value of D , H leads to a diffusion coeffi-cient of D = 5 . × cm s - at E p = 100PeV. The confine-ment of 100 PeV protons requires E = eBl c > l c > . B - ( E p / D (100PeV) =(1 / l c c = 3 × cm s - (Tamborra et al. 2014). The diffu-sion coefficient obtained above in explaining the IceCube datasatisfies this condition.We calculate the diffuse gamma-ray flux accompanying theneutrino emission, following the approach of Chang & Wang(2014). The results are also shown in Fig. 2 andFig. 3 for the cases of δ = 1 / D , H ≃ . cm s - and δ = 0 . D , H ≃ cm s - , respectively. In thecalculation, we considered the synchrotron loss effect ofelectron-positron pairs produced by the absorbed gammarays in the galaxies. The strength of the magnetic fields inthe galaxies are assumed to be B = 400 µ G( Σ g / - ) . (Thompson et al. 2006; Lacki & Thompson 2010). We findthat the accompanying gamma-ray flux is below the diffuseisotropic gamma-ray background observed by the Fermi/LAT(The Fermi LAT collaboration et al. 2014).We also study the neutrino flux from star-forming galaxiesin different luminosity ranges. Figure 4 presents the result for δ = 0 . D , H ≃ cm s - , the same parameters as thosein Figure 3. We can see that most fraction of the neutrino fluxis contributed by the galaxies with total IR luminosity in therange of 10 - L ⊙ . This indicates that the accumulatedneutrino flux is dominated by high-luminosity starburst andSF-AGN galaxies.Figure 5 shows the flux contributed by on-MS galaxiesand off-MS ones separately. According to their locations onthe SFR-stellar mass plane, normal spiral galaxies, starburstgalaxies and SF-AGNs(spiral) are thought to be mostly on-MS galaxies, while SF-AGNs(SB) are thought to be off-MSgalaxies (Gruppioni et al. 2013). Fig.5 suggests that on-MSgalaxies dominate the contribution to the total neutrino fluxover off-MS galaxies.In above calculations, we have assumed that the CR diffu-sion coefficient in galaxies with IR luminosity L TIR < L ⊙ is fixed to D , L = 10 cm - s - , i.e. the same value as thatof our Galaxy. However, there is observational evidence fora smaller diffusion coefficient in high-redshift star-forminggalaxies (Bernet et al. 2013). Thus, we recalculate the neu-trino flux by taking D , L = 10 cm s - for galaxies with totalIR luminosity L TIR < L ⊙ , while keeping other parame-ters unchanged. The comparison between these two cases isshown in Fig.6. As is shown, the total neutrino flux changesonly a little. This is mainly because that low IR luminositygalaxies contribute sub-dominantly to the total neutrino fluxdue to lower pion-production efficiencies. DISCUSSIONS AND CONCLUSIONS
The proposed scenario above is based on the assumptionthat CR protons in star-forming galaxies are accelerated to en-ergy above 1 EeV. Though we suggest that remnants of hyper-novae or other peculiar types of supernova in these galaxiesare possible accelerators of these CRs, the estimate of the neu-trino flux presented in this paper does not depend on any spe-cific accelerator sources. If remnants of normal supernovaein star-forming galaxies are able to accelerate protons to en-ergy above 100 PeV due to higher magnetic fields in thesegalaxies, our calculations also apply. Nevertheless, the factthat normalizing the CR intensity in star-forming galaxies atEeV with the observed CR flux results in a neutrino flux com-parable to that observed by IceCube implies that star-forminggalaxies are potential origins of both IceCube PeV neutrinosand extragalactic EeV CRs.We note that Tamborra et al. (2014) have discussed the pos-sibility that star-forming galaxies are the main sources of Ice-Cube PeV neutrinos by adopting the IR luminosity functionof Gruppioni et al. (2013). They first calculated the diffusegamma-ray background produced by star-forming galaxiesusing the correlation between the gamma-ray intensity and in-frared luminosity reported by Fermi observations. They thenobtained the PeV neutrino flux assuming that all the gamma-rays are produced by hadronic pp collisions and used power-law extrapolation to PeV energy. However, the correlationbetween gamma-ray luminosities and infrared luminosities isbased on observations of nearby galaxies and it is unclearwhether this correlation applies to high-redshift star-forminggalaxies. Differently, we do not rely on this correlation, butcalculate the pion production efficiencies (and hence the neu-trino flux) in these galaxies using the available knowledgeabout high-redshift star-forming galaxies.To summarize, we have calculated the neutrino flux pro-duced by CRs in different populations of star-forming galax-ies considering realistic galaxy properties and the latest IR lu-minosity functions. By normalizing the CR intensity from thegalaxies with the observed flux of EeV CRs, we have foundthat the accumulated neutrino flux from star-forming galaxiescan explain the IceCube observations of sub-PeV/PeV neutri-nos.We thank Junfeng Wang and Yong Shi for useful discus-sions. This work is supported by the 973 program undergrant 2014CB845800, the NSFC under grants 11273016 and11033002, and the Excellent Youth Foundation of JiangsuProvince (BK2012011). REFERENCES Aartsen, M. 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TIR [L ] =0.5 off-MS galaxies =0.5 on-MS galaxies
Figure 1.
The pion-production efficiency f π for CRs producing 1 PeV neutrinos in star-forming galaxies with different total IR luminosities (assuming thesource is at the redshift z = 1). The shaded regions denote the uncertainties of f π resulted from the uncertainties in the galaxy properties (see the text for details). -9 -8 -7 -6 -5 E [ G e V c m - s - s r - ] E[GeV]
Total i SB i Spiral i SF-AGN(SB) i SF-AGN(Spiral) i Total Fermi 2010 Fermi 2014atm IceCube 2014
Figure 2.
Accumulated neutrino flux produced by star-forming galaxies of different populations. D , H = 10 . cm s - , D , L = 10 cm s - and δ = 1 / -9 -8 -7 -6 -5 E [ G e V c m - s - s r - ] E[GeV]
Total i SB i Spiral i SF-AGN(SB) i SF-AGN(Spiral) i Total Fermi 2010 Fermi 2014atm IceCube 2014
Figure 3.
Same as Figure 2, but with δ = 0 . D , H = 10 cm s - , and D , L = 10 cm s - . -10 -9 -8 -7 -6 -5 E [ G e V c m - s - s r - ] E[GeV]
Total i -10 L i -10 L i -10 L i atm IceCube 2014 Figure 4.
Accumulated neutrinos flux from star-forming galaxies of different IR luminosities. -9 -8 -7 -6 -5 E [ G e V c m - s - s r - ] E[GeV]
Total i On-MS galaxies Off-MS galaxiesatm IceCube 2014
Figure 5.
The same as Figure 3, but the contribution of the galaxies is divided into two subclasses, on-MS galaxies and off-MS galaxies. The black line showsthe total flux, while the red and blue lines show the flux contributed by off-MS and on-MS galaxies, respectively. -8 -7 E [ G e V c m - s - s r - ] E[GeV] D =10 cm s -1 D =10 cm s -1 atm IceCube 2014 Figure 6.
The accumulated neutrino flux of star-forming galaxies with different values of D , L , while the other parameters remain unchanged. The black andred lines shows the cases with D , L = 10 cm s - and D , L = 10 cm s -1