Table Of ContentDraft version April 27, 2015
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
EXTRAGALACTIC STAR-FORMING GALAXIES WITH HYPERNOVAE AND SUPERNOVAE
AS HIGH-ENERGY NEUTRINO AND GAMMA-RAY SOURCES:
THE CASE OF THE 10 TEV NEUTRINO DATA
Nicholas Senno1, Peter Me´sza´ros1, Kohta Murase1,2, Philipp Baerwald1, and Martin J. Rees3
Draft version April 27, 2015
ABSTRACT
InlightofthelatestIceCubedata,wediscusstheimplicationsofthecosmicray(CR)
energyinputfromhypernovaeandsupernovaeintotheUniverse,andtheirpropagation
in the hosting galaxies and galaxy clusters or groups. The magnetic confinement of
CRs in these environments may lead to efficient neutrino production via pp collisions,
resulting in a diffuse neutrino spectrum extending from PeV down to 10 TeV energies,
5
with a spectrum and flux level compatible with that recently reported by IceCube. If
1
0 the diffuse 10 TeV neutrino background largely comes from such CR reservoirs, the
2 corresponding diffuse γ-ray background should be compatible with the recent Fermi
data. In this scenario, the CR energy input from hypernovae should be dominant over
r
thatofsupernovae,implyingthatthestarburstscenariodoesnotworkifthesupernova
p
A energy budget is a factor of two larger than the hypernova energy budget. Thus, this
strong case scenario can be supported or ruled out in the near future.
4 Subjectheadings: cosmicrays—galaxies: clusters: general—neutrinos—supernovae:
2 general
]
E
1. INTRODUCTION & Ioka 2013; Liu & Wang 2013), radio-loud ac-
H tive galactic nuclei (Stecker et al. 1991; Alvarez-
The detection of PeV and sub-PeV astrophysi-
. calneutrinosbyIceCube(Aartsenetal.2013;Ice- Mun˜iz & M´esz´aros 2004; Murase et al. 2014;
h
Dermer et al. 2014; Kalashev & Troitsky 2014),
p Cube Collaboration 2013; Aartsen et al. 2014b),
galaxy clusters and groups (Murase et al. 2008a,
- which more recently has been extended down
o to 10 TeV energies (Aartsen et al. 2015), is a 2013) with accretion shocks (Keshet et al. 2004;
r major development. The origin of these neu- Inoue et al. 2005) that may accelerate cosmic
t rays (CRs) to higher energies (Hillas 1984; Bier-
s trinos is a matter of intense interest (for recent
a mann & Strittmatter 1987) or other CR sources
reviews, see e.g., M´esz´aros 2014; Murase 2014).
[ suchasgalaxymergersinclusters(Kashiyama&
Star-forming galaxies, especially starbursts, are
M´esz´aros 2014).
3 promising candidates (Loeb & Waxman 2006;
Inthiswork,wewillconcentratemainlyonthe
v Murase et al. 2013; Katz et al. 2013; Tamborra
HN/SN origin of neutrinos from pp interactions
4 et al. 2014; Chang & Wang 2014; Anchordoqui
in the starburst and normal star-forming intra-
3 et al. 2014), in which the major contributing
galacticmaterialandtheintraclustermedium. In
9 sourcesmaybesupernovae(SNe),aswellastheir
4 hyper-energetic equivalent the so-called hyper- particular, we discuss their implications in light
0 novae (HNe) (Sveshnikova 2003; Fox et al. 2013; of the latest IceCube data in the 10 TeV range.
1. He et al. 2013; Murase et al. 2013; Liu et al. Constraints from the diffuse γ-ray background
measured by Fermi are even more pronounced in
0 2014; Ahlers & Murase 2014) or active galac-
this case.
5 tic nuclei (AGN) (Murase et al. 2014; Tamborra
1 et al. 2014). Other possible candidates include
: low-luminosity classes of γ-ray bursts (Murase 2. HYPERNOVA AND SUPERNOVA
v
ENERGY INPUT RATE
i
X [email protected] HNe typically belong to a sub-class of broad-
1Dept. of Physics, Dept. of Astronomy & As-
r line Type Ib/c SNe with ejecta kinetic ener-
a trophysics, Center for Particle and Gravitational As-
trophysics, Pennsylvania State University, University gies of order Ek = 1052Ek,52 erg, representing
Park,PA16802,USA a fraction ξ (cid:39) 4 × 10−2ξ of all core-
2InstituteforAdvancedStudy,Princeton,NJ08540, hn hn,−1.4
collapse SNe, with substantial uncertainties (Ar-
USA
3Institute of Astronomy, University of Cambridge, cavi et al. 2010; Guetta & Della Valle 2007;
CambridgeCB30HA,U.K. Smith et al. 2011). The rate of all core-collapse
2
SNe is 1.06×10−4Mpc−3yr−1 (e.g., Taylor et al. e.g., CR-streaming instabilities, but in any case
2014), which implies a local HN rate of R ∼ the stronger magnetic fields in starburst galaxies
hn
4 × 10−6ξ Mpc−3yr−1. If the fraction of may also be enough (Murase et al. 2013). Diffu-
hn,−1.4
HN remnant kinetic energy transferred to CRs is sive shock acceleration in the blast wave leads to
Ecr,hn (cid:39) 2.8×1051 ergs, the CR energy density a power law spectrum distribution N(εp)∝ε−pΓ,
input rate in the Universe is U˙ (cid:39)E R (cid:39) typically with Γ >∼ 2, up to a maximum energy
cr cr,hn hn
1.2×1046ξ E erg Mpc−3yr−1. Fur- εp,max (cid:39)(3/20)ZeBsRdecβej (Drury 1983), or
hn,−1.4 cr,51.4
thermore, if the CRs are protons with a power
ε (cid:39)1017Zn1/6 E M−2/3 eV (3)
law distribution N(ε ) ∝ ε−Γ between ε ∼ p,hn,max g,2.3 k,hn,52 ej,0.5
p p p,min
1 GeV and ε <∼ 1017ε eV, the energy for CRs with charge Z. However, in the follow-
p,max p,17
density input rate per logarithmic interval of en- ingworkweonlyconsiderCRprotons. Theabove
ergyisε Q (cid:39)U˙ /C ergMpc−3yr−1,wherethe equation implies that the CRs are accelerated to
bolometpricεpcorrecctrion is C = ln(ε /ε ) ∼ 100PeV as the shock slows and enters the so-
p,max p,min
called Sedov-Taylor phase. The maximum CR
for a spectral index Γ=2†. Assuming Γ∼2 and
energy is expected to decrease with time during
taking C ∼18C the local (z =0) CR energy in-
18 this deceleration phase (Drury 2011). Also note
put per logarithmic interval in the Universe due
that while many SNe and HNe may happen in
to hypernovae is
relatively low-density regions such as superbub-
(cid:0)εpQεp(cid:1)hn (cid:39)6.4×1044erξghnM,−p1c.4−C31−y8r1−E1c,r,hn,51.(41) mblaesl,StNhee, duespinegndtehnecesaomnenpgariasmweteearks.exFcoerptnoforr-
E = 1051 erg, the maximum energy would be
k
which is larger than the typical value expected ε (cid:39) 1.1 × 1016Zn1/6 E M−2/3 eV.
for γ-ray bursts. Conventional SNe will also con- p,sn,max g,2.3 k,51 ej,0.5
As we will show below, HNe that occur in star-
tribute significantly to lower-energy CRs, hav-
burstgalaxiescanacceleratethemajorityofCRs
ing a smaller kinetic energy input E (cid:39)
k,sn which produce detectable high-energy neutrinos.
1051Eksn,51 erg but a larger rate Rsn. The typi- Although we use typical numbers for HNe for
cal CR energy of SNe is uncertain and could be our estimates, in star-forming galaxies hosting
less(e.g. Ecr,sn =4.8×1049 erg). Ingeneral, the an AGN the latter may be also contribute as a
energy injection rate for SNe is given by 10-100 PeV CR accelerator (Murase et al. 2014;
(cid:0)ε Q (cid:1) = (1−ξhn) Chn Ecr,sn (cid:0)ε Q (cid:1) . TaCmRbsorsruaffeetrale.n2e0rg1y4).losses both during accel-
p εp sn ξ C E p εp hn
hn sn cr,hn eration and after escaping their source. Syn-
(2)
chrotron losses are negligible at the energies con-
It is believed that SNe can typically accelerate
sidered here, the dominant loss mechanism being
CRs to a maximum energy ε ∼ 1015 eV
p,max hadronuclear (pp) collisions. The effective op-
resulting in C ∼ 13.8. The energy input due
sn tical depth to pp collisions undergone while ad-
to conventional SNe would be typically larger
vected downstream of the blast wave is τ ∼
than that of HNe at lower energies. However, pp,s
t /t ∼ κσ R(c/V), where κ ∼ 0.5 is the
with the parameters given above, Eq. (2) im- dyn pp pp
inelasticity and σ (ε =100PeV) ∼ 10−25 cm2
plies the energy input rate of SNe for CRs with pp p
< (in the numerical calculations presented below,
ε ∼ ε is roughly half that of HNe. Be-
p p,max,sn we use the energy dependent inelastic pp cross
low, we leave this ratio as a free parameter.
section presented in Kelner et al. 2006). Thus
3. SHOCK ACCELERATION τpp,s ∼1.3×10−6Ek−,h1/n2,52Me5j/,60.5n−g,12/.33, which is
A typical Type Ibc SN has a bulk ejecta negligible compared to losses during the subse-
mass of M (cid:39) 3M M , and a HN has quent propagation. Similar considerations apply
ej ej,0.5 (cid:12)
an average velocity β = (V /c) = 6.1 × also to the supernovae.
ej ej
10−2Ek1,/h2n,52Me−j,10/.25. The postshock random 4. PROPAGATION EFFECTS AND PP
magnetic field strength is expected to be ampli- OPTICAL DEPTH
fiedtoafraction(cid:15) ofthepostshockthermalen-
B The propagation of the CRs in the turbulent
ergy, B ∼(16π(cid:15) n m c2β2 )1/2, with n being
s B g N ej g magneticfieldofthehostgalaxyandgalaxyclus-
the interstellar particle number density. The up- ter depends, in the diffusion approximation, on
streammagneticfieldshouldalsobeamplifiedby thestrengthofthemagneticfieldB,theCRLar-
mor radius r , and the coherence length (cid:96) of
†ItwouldbeC=(cid:2)1−(εp,max/εp,min)2−Γ(cid:3)ε2p−,mΓin(Γ− the magneticLfield fluctuations. At the highcest
2)−1 ifΓ(cid:54)=2. energies ε , where r (ε ) (cid:29) (cid:96) , the CR diffu-
p L p c
3
sion coefficient is D(ε ) ∝ r (ε )2. At lower n κσ c min[t ,t ] or
p L p g pp d,g w,g
<
energies, where r (ε ) ∼ (cid:96) , the diffusion coef-
ficient is D(εp) ∝LrLp(εp)α, wc here α = 1/3 (1/2) τpp,g∼4.9×10−3 ng,2.3Hg2,21(cid:96)g,20Bg2,−3.7ε−p,219
for a Komolgoroff (Kraichnan) fluctuation power τ ∼0.55 n H2 (cid:96) B2 ε−1/3
spectrum (e.g., Berezinsky et al. 1997). The two pp,g g,2.3 g,21 g,20 g,−3.7 p,17.2
regimes can be interpolated as τ ∼1 n H V (6)
pp,g g,2.3 g,21 w,3.2
(cid:104) (cid:105)
D(ε )=D (ε /ε )α+(ε /ε )2 (4) in the ranges (εp >εp∗,g), (εw <εp <εp∗,g) and
p ∗ p p,∗ p p,∗
(ε <ε ), respectively.
p w
One can see that starburst galaxies are effi-
where r (ε ) = (cid:96) /5 with D (cid:39) (1/4)cr (ε )
L p∗ c ∗ L p∗ cient neutrino factories via pp interactions due
(Parizot2004). Belowweshalluseα=1/3asan
to their high interstellar gas density. As seen
example,butthediscussioncanbegeneralizedto
in Fig. 1-4, normal star-forming galaxies have
a general positive α value.
lower values of ε , ε , and τ resulting in
After leaving the source (e.g. HNe or SNe), p∗,g w pp,g
only a modest amount of neutrinos produced at
the CRs first propagate diffusively through the
high energies. We will show below that if the
host galaxy or are advected away by a strong
starburst fraction is high and CRs with energies
galactic wind, with typical velocities of V ∼
w up to ∼ 10−100 PeV are sufficiently confined,
1500 km/s in starburst galaxies (Strickland &
the majority of the observed high-energy diffuse
Heckman 2009) and V ∼ 500 km/s for normal
w neutrinofluxcanbeexplainedusingHNeorother
star-forminggalaxies(Crocker2012;Keeneyetal.
sources in starburst galaxies.
2006). Forastarburstgalaxy(SBG)thegasscale
For the subsequent propagation in the
heightH ∼30−300pcmaybeparameterizedas
g galaxy cluster or group, the average mag-
H ∼300pc(cid:39)1021H cm. We assume a mag-
sbg 21 netic field and coherence length are pa-
netic field strength of Bg ∼ 200×10−6Bg,−3.7G rameterized as Bcl ∼ 10−6Bcl,−6G and
and a coherence length parameterized here as
(cid:96) ∼ 30kpc = 1023(cid:96) cm. This im-
(cid:96) ∼ 10−1H ∼ 30pc (cid:39) 1020(cid:96) cm. Both c,cl 23
c,g g g,20 plies ε ∼ 5.6 × 1018Z(cid:96) B eV
quantities are subject to large uncertainties p∗,cl 23 cl,−6
and D ∼ 1.4 × 1032Z(cid:96) cm2 s−1. For
and variations, so that the diffusion coefficient ∗,cl 23
adopted here corresponds to the optimistic case. a cluster of 1015M(cid:12) the virial radius is
For our fiducial starburst galaxy parameters, we R ∼ 2.6M1/3Mpc (cid:39) 8×1024M1/3 cm and the
oDb∗t,agin∼εp1∗.,4g×∼1012.91(cid:96)1g,2×0 c1m0128/(cid:96)gs,2.0BTgo,−3e.n7seuVre aCnRd dmicufflmusipornottoimn15eenisertgdy,clth=is Risc2lt/d,6cDl(ε.1p5,mAatxt)h∼e m2.a3x×i-
csaotnifisfnyemε ent,>∼w1e0r−eq1u0i0rePetVhe(cMouhrearesneceetaleln.g2t0h13t)o. 1017M115/3(cid:96)−232/3Bc1l/,−36Z1/3n−cl,1−/148(cid:15)−B1,−/62Ek−,512/.35Me2j/,91
p∗,g
Foranormalstar-forminggalaxy(SFG),wetake ε−1/3 s. Similarly to the galactic component
p,16.94
the typical scale height to be Hg ∼1000pc, with mentioned above, there is a spectral break
(cid:96) ∼ 10−1H , a magnetic field of B ∼ 6µG when the diffusion time exceeds the injection
c,g g g
(Beck 2008) and interstellar medium density of time of CRs (Murase et al. 2008a). Assum-
n ∼1cm−3. ing CR injection effectively occurs during the
g
Given the above, the time for CR diffusive es- Hubble time at the corresponding redshift (i.e.
cfoarpestfarorbmurtshteggaallaaxxiyescaisn tbe ca=lculHat2e/d6,Dwhic(cid:39)h taatger(ezd)sh=ift (cid:82)zz∞=dz1(cid:48)(cid:12)(cid:12)ddstzu∗(cid:48)c(cid:12)(cid:12)h),afobrreaakcluosctceurrsloactataend
d,g g g
1.5 × 1012H2 (cid:96) B2 ε−1/3 s. The time energy εp,cl ∼ 4 × 1017Z eV. If the cluster
g,21 g,20 g,−3.7 p,17.2 break energy is higher than the maximum
for advective escape is t = H /V (cid:39) 6.2 ×
w,g g w HNe energy, CR diffusion does not significantly
1012Hg,21Vw−,31.2 s regardless of the CR energy. affect the fraction of CRs that interact in the
Notice that advective escape dominates diffu- intracluster medium. The cluster pp optical
sive escape from the galaxy for CRs with energy depth is again τ = n κσ c min[t ,t ],
< pp,cl cl pp d,cl age
ε ∼ε with assuming a typical intracluster gas density
p w
n (cid:39) 10−4n cm−3, at high redshifts (e.g.
cl cl,−4
ε = ZeBlc1−1/α (cid:18)10VwHg(cid:19)1/α, (5) z =1) tage <∼td,cl(εp,max) so that
w 5 3c
τ (ε )∼2.7×10−2n (t /5.8 Gyr)
pp,cl p,max cl,−4 age
yielding ε ∼ 5.1×1015 eV for the fiducial pa- (7)
w
rameters used here. For more nearby clusters τ increases as the
pp,cl
The effective pp optical depth undergone dur- cluster age approaches the local Hubble time, al-
ing propagation in a starburst galaxy is τ (cid:39) though the density is also redshift-dependent.
pp,g
4
For a diffusion exponent α different from the
value 1/3 used as an example above, the values
ofτ ,τ ,etc.,arecalculatedsimilarlyand
pp,g pp,cl,H
are somewhat different, as can be seen in the nu- 10-6
merical results discussed in the next section. 1]−
sr
Further pp collisions occur in the intergalac- 1−
s
tic medium after the CRs escape the cluster, 2−10-7
m
but with the intergalactic target density nigm = Vc
2.5×10−7(Ωbh2/0.022) cm−3, and a total flight [Ge
time limited by t ∼ 1010yr, the corresponding Φε10-8
τ isnegligiblHecomparedtotheprevioustwo 2ε
pp,igm
contributions.
5. DIFFUSE NEUTRINO FLUX 10-9 100 101 102 103 104 105 106 107
ε [GeV]
Whenhigh-energyCRsundergoppinteractions
with the ambient intragalactic and intracluster
medium, charged and neutral pions are created
whichsubsequentlydecaytoneutrinosandγ-rays 10-6
respectively. On average, the resulting neutrino 1]−
sr
and parent CR energies can be related by εν ∼ 1s−
0.03−0.05εp. As a result, the diffuse neutrino 2m−10-7
flux(perflavorperlogarithmicintervalofenergy) c
V
can be estimated using the CR energy injection Ge
[
ratesimilarlytowhatisdoneforGRBs(Waxman Φε10-8
& Bahcall 1997; Murase et al. 2013), as 2ε
ε2νΦεν = 4cπ (cid:90)0z(cid:88)i fi6,pp(cid:0)ε(p1Q+εpz(cid:1)(cid:48)p)h4ys (cid:12)(cid:12)(cid:12)(cid:12)ddzt(cid:48)(cid:12)(cid:12)(cid:12)(cid:12)dz(cid:48), 10-9 100 101 102 1ε03[GeV]104 105 106 107
(8) Fig. 1.—Diffusefluxperflavorofneutrinos(solidblack)
where the physical CR energy injection rate per andγ-rays(dash-dot)fromHNeandSNe, foradiffusion
energy bandwidth at a given redshift z is related coefficient (top): D ∝ ε1p/3, (bottom): D ∝ ε1p/2, in
to Eq.(1, 2), cosmological evolution is taken into both the host galaxy and cluster. For both figures HNe
andSNereleaseonaverage2.8×1051 and4.8×1049ergs
accountbythescalefactorS(z)sothenormalized
ofCRenergyrespectively,andtheprotonspectralindexis
physical star formation rate is Γ=2. Theblacklinewithwhitecirclesdenotesthemea-
(cid:0) (cid:1) sured flux of atmospheric neutrinos (Abbasi et al. 2011).
εpQεp phys(z)= The starburst galaxy scale height, density, and magnetic
(cid:2)(cid:0)ε Q (cid:1) +(cid:0)ε Q (cid:1) (cid:3) (1+z)3S(z) (9) field strength are Hsbg = 300pc, nsbg = 200cm−3, and
p εp hn p εp sn Bsbg = 200µG and are represented by red lines. For
normal star-forming galaxies H = 1000pc, n =
with sfg sfg
1cm−3, and B = 6µG; they are represented by blue
sfg
S(z)=(cid:34)(1+z)aη+(cid:18)1+z(cid:19)bη+(cid:18)1+z(cid:19)cη(cid:35)1/η, lliinneess.coTlhoreecdonwthriilbeuttihoonsefrformomHtNheeaSrNeemaarrekeddaswheitdh. sTolhide
solidgreenlinedenotesthetotalclustercontribution(i.e.
B C
HNe and SNe from both types of galaxies). Green data
(10) points correspond to the Fermi measurements of the ex-
where a = 3.4, b = −0.3, c = −3.5, η ≈ tragalactic diffuse γ-ray background (Ackermann et al.
2014). Black points correspond to the IceCube measure-
−10, B (cid:39) 5000, andC (cid:39) 9 (Hopkins & Beacom
ments of astrophysical neutrinos (Aartsen et al. 2015) ,
2006; Yu¨ksel et al. 2008). notethattwoofthelowenergydatapointsarewithinthe
The sum in Eq. (8) is over the different galac- graylinesoftheerrorbarsoftheatmosphericflux.
tic and cluster/group contributions. We assume
a fraction ξsbg of neutrinos are produced in star- (cid:2)ξsbge−τpp,g,sbg +ξsfge−τpp,g,sfg(cid:3)
burst galaxies with the rest ξ = 1−ξ pro-
sfg sbg
duced in normal starforming galaxies: Note that in the last line of Eq. (11) only CRs
which escape from the galaxies can contribute to
fpp,sbg=ξsbg(cid:0)1−e−τpp,g,sbg(cid:1) the cluster component.
fpp,sfg=ξsfg(cid:0)1−e−τpp,g,sfg(cid:1) (11) For our cluster/group parameters and the av-
erage galaxy parameters taken in §4, the diffuse
neutrino flux per flavor for a D ∝ ε1/3 diffusion
fpp,cl =(cid:0)1−e−τpp,cl(cid:1) × coefficient is shown in Fig. 1 (top ppanel). Here
5
10-6 10-6
1]− 1]−
sr sr
1− 1−
s s
2−10-7 2−10-7
m m
c c
V V
Ge Ge
[ [
Φε10-8 Φε10-8
2ε 2ε
10-9 100 101 102 103 104 105 106 107 10-9 100 101 102 103 104 105 106 107
ε [GeV] ε [GeV]
Fig. 2.—Diffusefluxperflavorofneutrinos(solidblack)
and γ-rays (dash-dot) from HNe and SNe which release
on average 7.5×1051 and 5×1049 ergs of CR energy
respectively, with a phenomenologically motivated diffu- 10-6
sthioenMcoilekffiycWieanyt bgaalsaexdyo(nseoebtseexrtvaftoirondsetoafilsC)R. Idniffthuissiocnasien, 1sr]−
clustercontributionsaredominantathighenergies. 1−
s
2−10-7
m
c
the contributions of the pp interactions in the GeV
galaxiesareindicatedbothforthesupernovaand [
hypernova components. In the same figure, the Φε10-8
2ε
resultingdiffuseγ-rayfluxisalsoshown,resulting
fromthecorrespondingπ0decaysandsubsequent
pair cascades in the intergalactic medium, which 10-9 100 101 102 103 104 105 106 107
are discussed in §6. A similar calculation for a ε [GeV]
D ∝ ε1p/2 Komolgoroff type diffusion coefficient Fig. 3.— Same as Fig. 1, with D ∝ ε1p/3 but top:
is shown in the bottom panel of Fig. 1. ξsbg = 0.01 with Ecr,hn = 5×1051 erg, and Ecr,sn =
Thesituationdependsstronglyonthediffusion 2.2×1050ergbottom: ξ =0.5withE =1051erg,
sbg cr,hn
coefficients of both galaxies and clusters, which andEcr,sn=2.5×1049erg
areuncertainespeciallyathighenergies;and,due
in large part to uncertainties in the magnetic co-
cluster contribution at the same energy. For this
herence length. For example, the diffusion coeffi-
combination of parameters the cluster and group
cientfornormalgalaxiesusedinFig.1is10times
contribution should be dominant, and it is pos-
lowerthanthevalueobtainedforourMilkyWay.
sible to explain the hard spectrum of the diffuse
While this discrepancy is alleviated by inhomo-
neutrino background. Note that the parameters
geneities, the diffuse Galactic emission suggests
used for the cluster/group contribution to the
that the CR spectral break is much lower since
diffuse neutrino flux are optimistic, and massive
the observed γ-ray spectrum is already steep at
clusters are only a fraction of the total cluster
GeVenergies(Ackermannetal.2012a). InFig.2,
population.
weconservativelyusethediffusioncoefficientsug-
Returning to the parameters used in Fig. 1,
gested for our Milky Way by Blasi & Amato
thefluxresultingfromaveragehostgalaxieswith
(2012)fornormalstar-forminggalaxies. Wethen
a smaller (top) and larger (bottom) fraction of
use the scaling relation D ∝ r (ε )α (see §4) to
L p CRs produced in starburst galaxies is shown in
determine the diffusion coefficient in starbursts.
Fig. 3. Here the fraction of HN/SN CR en-
Since the break energy is sensitive to the diffu-
ergy was adjusted ad-hoc in order to fit the ob-
sioncoefficient,oneseesthatthediffuseneutrino served neutrino flux with E = 5×1051 erg
background cannot be explained by star-forming cr,hn
and E = 2.2×1050 erg for ξ = 0.01, and
galaxies in this case, even with an optimistically cr,sn sbg
E = 1051 erg and E = 2.5 × 1049 erg
high fraction of HN kinetic energy converted to cr,hn cr,sn
CRs (i.e. 7.5×1051 erg). At high energies the for ξsbg = 0.5 respectively. The diffusion coeffi-
galaxy contribution may not be appreciable. At cient was taken to be D ∝ε1/3 while leaving the
p
and below ε (cid:39) 1.11 × 1018(cid:96) B eV, remaining parameters unchanged.
p∗,g g,20 g,−3.7
however, the galactic contribution becomes con- The Fig. 1 and 3 were calculated for “typical”
siderable, τ (ε ) (cid:39) 0.33, overcoming the star-forming galaxies with parameters as given
pp,g p∗,g
6
neticcascade. Theresultingcascadedγ-rayspec-
trum takes a universal form, (e.g., Berezinskii &
Smirnov 1975; Murase et al. 2012):
10-6
211Vcmssr]−−−10-7 (cid:15)γddN(cid:15)γγ ∝G(cid:15)γ = (cid:16)(cid:16)(cid:15)(cid:15)(cid:15)bγγγr(cid:17)(cid:17)−1−1/s2 (cid:15)(cid:15)γbr≤<(cid:15)(cid:15)bγr ≤(cid:15)cut
[Ge (cid:15)bγr γ γ γ
Φε10-8 (12)
2ε The characteristic energies (cid:15)cγut and (cid:15)bγr given
above are defined by 1 = τ (cid:2)(cid:15)cut,z(cid:3) and (cid:15)br=
γγ γ γ
10-9 100 101 102 103 104 105 106 107 0.0085(1 + z)2 (cid:16) (cid:15)cγut (cid:17)2 respectively and the
ε [GeV] 0.1TeV
high-energy spectral index is generally taken to
be s ∼ 2. Here τ is the optical depth for a
γγ
high energy photon traveling through intergalac-
10-6 tic space, the values for which are from model C
1]− of Finke et al. (2010).
sr
1− There is also an attenuated component to the
s
2−10-7 observed γ-ray flux from photons with energy
cm (cid:15) <∼ (cid:15)cutwhich can be calculated similarly to eq.
V γ γ
Ge (8)
[
2εΦε10-8 (cid:15)2Φunatt = c (cid:90) dz(cid:12)(cid:12)(cid:12)dt(cid:12)(cid:12)(cid:12)e−τγγ[(1+z)(cid:15)γ,z] ×
γ γ 4π (cid:12)dz(cid:12)
10-9 100 101 102 1ε03[GeV]104 105 106 107 1 (cid:34)2Γ−2 (cid:88)f (cid:0)ε Q (cid:1) (cid:35) (13)
(1+z)4 3 i,pp p εp phys
EFcrig,h.n4.=—3S.5am×e1a0s5F1ige.rg1,,abnudtfEorcra,spnro=ton10in50deexrgΓ.=t2o.p1:, i ε(cid:48)cr=10(1+z)(cid:15)γ
D∝ε1p/3 ,bottom: D∝εp1/2. which combined with Eq. (12) can be compared
withFermi-LATmeasurementsoftheextragalac-
tic diffuse γ-ray background (Ackermann et al.
above,andforaprotoninjectionspectrumΓ=2.
2014). Figures 1 through 4 show our calculated
WeconsidernexttheSFGandSBGcontributions
diffuse flux of neutrinos and γ-rays along with
usingthesameparameters,butwithaprotonin-
data from IceCube and Fermi.
jection index Γ = 2.1, results are shown in Fig.
4.
7. DISCUSSION AND SUMMARY
Theeffectofpγ interactionsinthegalacticand
intracluster medium is sub-dominant relative to In this work, we discuss the starburst sce-
the pp collisions in the relevant energy range, al- nario in light of the new 10 TeV neutrino data.
thoughitbecomesdominantatveryhighenergies Although there are large systematic uncertain-
(Kotera et al. 2009). ties involved in removing the atmospheric muon
background at such low energies (Aartsen et al.
6. GAMMA-RAY CASCADES 2014a), it may be challenging to explain the
diffuse neutrino flux in the whole energy range
The same pp interactions which produce neu-
with a single power-law component with Γ ∼ 2.
trinos also produce high-energy γ-rays with typ-
Adding the SNe contribution enables us to ex-
ical energy (cid:15) ∼ ε /10. Note that because of
γ p plain the low-energy data, but we find that con-
this connection, their resulting flux can be re-
(cid:12) straints from the diffuse γ-ray background are
lated by (cid:15)2γΦ(cid:15)γ = 2Γ−1ε2νΦεν(cid:12)εν=0.5(cid:15)γ. When quite stringent (Murase et al. 2013). If the CR
γ-rays with energy (cid:15)(cid:48) >∼ 100 GeV are injected energyinputbySNeisafactoroftwolargerthan
γ
intointergalacticspacesufficientlyfarfromEarth thatbyHNe,thediffuseγ-raybackgroundisvio-
(i.e. ∼ few Mpc), they undergo γγ interactions lated. Additional constraints could be placed on
with extragalactic background light (EBL) pho- the cluster contribution by considering the con-
tonsproducingelectron/positionpairs. Thepairs comitant radio emission, although in the strong
scatter additional EBL photons via the inverse evolution case these limits are weaker than the
Compton mechanism generating an electromag- ones imposed by the accretion shock scenario
7
(Zandanel et al. 2014). From the γ-ray limits, Joshi et al. 2014), some extended sources such
we conclude that if the diffuse neutrino back- as the Fermi Bubbles (Ahlers & Murase 2014;
ground in the PeV range originates mainly from Lunardini et al. 2014) or nearby HN remnants
HNe (and their host galaxies), the HN contribu- (Foxetal.2013;Ahlers&Murase2014)couldbe
tionshouldbelargerthanoratleastcomparable viable. Alternatively, the diffuse neutrino back-
to the SN contribution. However, interestingly, groundmightbeproducedmainlybyhiddenneu-
in cases where the cluster/group contribution is trino sources via pγ processes (Murase & Ioka
mainly responsible for the diffuse neutrino flux, 2013; Kalashev & Troitsky 2014; Kimura et al.
itisstillpossiblefortheSNcontributiontoover- 2014). The advantage of the strong case consid-
whelm the HN contribution (e.g. the top panel eredhereisthatitcanbetestedbymultimessen-
of Fig. 3). ger approaches. It has been commonly believed
The strong case scenario, where the ∼ 10 TeV that Galactic CRs come from SN remnants. If
neutrinodataareexplainedbyCRreservoirs,has the diffuse neutrino background is dominated by
an interesting feature that can be tested soon. star-forminggalaxies,ourresultsimplythateven
As proposed by Murase et al. (2013), CR reser- Galactic CRs may include significant contribu-
voirscangiveacommonexplanationforboththe tions from past HN remnants.
diffuse neutrino and γ-ray backgrounds. In gen- CR acceleration to energies >∼ 1016 −1017 eV
eral, the contributions from starbursts and other has also been proposed in other accelerators,
sources to the neutrino flux above 100 TeV re- such as shocks in AGN jets, (e.g., Hillas 1984;
sult in subdominant contributions to the diffuse Biermann & Strittmatter 1987; Dermer et al.
γ-ray background. However, as we show above 2014),AGNwinds(Muraseetal.2014;Tamborra
any source which contributes significantly to the et al. 2014), and AGN cores (Stecker et al. 1991;
10 TeV diffuse neutrino flux in the pp scenario Alvarez-Mun˜iz & M´esz´aros 2004; Kimura et al.
must also account for almost all of the diffuse γ- 2014). While in such cases neutrinos can come
raybackground. Itiscommonlybelievedthatthe fromAGNsthemselves,CRsescapingfromAGNs
diffuse γ-ray background is dominated by unre- canalsoproduceneutrinosinintergalacticspace,
solvedblazars(Inoue2014;DiMauroetal.2014), which may give a significant contribution to the
implying a comparatively smaller starburst con- diffuseneutrinobackground(Muraseetal.2013).
tribution. Although there are still significant un- Otherpossibilitiesareaccretionshocksontoclus-
certainties in the modeling of both blazar (e.g., ters of galaxies (Murase et al. 2008a; Dobardzic
Ajello et al. 2014, 2012) and starburst contribu- & Prodanovic 2014), galaxy mergers in clusters
tions (e.g., Ackermann et al. 2012b; Tamborra (Kashiyama & M´esz´aros 2014), and γ-ray bursts
et al. 2014), our results imply that the strong includingtrans-relativisticSNeorlow-luminosity
casescenariocanbetestedbyanimprovedunder- γ-ray bursts (Murase et al. 2008b; Wang et al.
standing or characterization of the diffuse γ-ray 2007). In principle, the discussion of the clus-
background. ter/group propagation effects discussed above
If, for example, it is proven that blazars are also applies to any intracluster sources. The
>
responsible for ∼ 50% of the observed diffuse main difference between these other sources and
γ-ray background, the starburst contribution to SNe/HNe (or sources inside galaxies in general)
the diffuse neutrino background at low energies is that the CRs accelerated in the former do not
should be small, especially if the CR energy in- undergo pp interactions in the galactic gas, but
putfromSNeiscomparabletoorlargerthanthat only in the intracluster gas; whereas CRs from
fromHNe. Specifically,tighterconstraintsonthe HNeandgalacticsourcesundergoppinteractions
theunresolvedblazarfractionofthediffuseγ-ray in both the host galaxy and the cluster/group.
background measured by Fermi and possibly the This disparity may be relevant at sub-PeV and
High Altitude Water Cherenkov (HAWC) obser- TeV energies, where the spectral shape of the
vatory (BenZvi 2015), as well as the low energy neutrino flux can provide clues to the source. In
(ε <∼ 100 TeV) spectral shape of the astrophys- this energy range we expect the advective escape
ν
ical neutrino flux as analyzed by Aartsen et al. and Hubble times to dominate the galactic and
(2014a), will impose limits to the corresponding cluster diffusion times respectively, and at differ-
fluxes from galaxy clusters/groups. If there is ent critical energies (i.e. εw and εp,cl as in §4).
little room for the CR reservoirs, other sources Therefore, for galactic sources (that are extra-
need to be responsible for the low-energy neu- galactic),asoftspectrumistypicallyexpectedat
trino component. For instance, there might be energiesbelowthemaximumaccelerationenergy,
a significant contribution from Galactic sources. with ε2νΦν ∝ ε−να (for a diffusion time ∝ ε−να),
Although the Galactic diffuse emission by CRs withalevelingoffoftheslopetoε2Φ ∼constant
ν ν
propagating in our Milky Way cannot provide below about ε ∼ 130 (2/(1+z)) TeV (assum-
ν,g
the main contribution (Ahlers & Murase 2014; ing, e.g., a galactic magnetic field strength of
8
<
200µG and diffusion exponent α=1/2). Sources is flat at low energies ε ∼ 130 TeV and soft-
ν
which release their CRs directly into the intra- ens to ε2Φ ∝ ε−α slightly before the Glashow
ν ν ν
cluster medium on the other hand, are expected resonance, while the corresponding diffuse γ-ray
toproducerelativelyflatneutrinospectrabelowa spectrum is below the Fermi measured flux.
break around ε ∼few (2/(1+z)) PeV, steep- We have shown in §5 that the high-energy dif-
ν,cl
ening above that. Such a spectral softening of fuse neutrino flux could potentially be explained
the cluster contribution is not seen for the HNe by HNe, predominantly those located in dense
model considered here (e.g. in Fig. 2) because starburst galaxies (e.g. the red solid curve in the
the break energy due to diffusion is lower than bottom panel of Fig. 1) especially for ε >∼ 50
ν
the cutoff energy imposed by maximally acceler- TeV. For neutrinos with this energy and be-
atedCRs. Whilebothεν,g andεν,claresubjectto low, the SNe in both starburst and normal star-
largeuncertaintiesinparameters,thepresenceof forming galaxies contribute significantly to the
their corresponding features could be suggestive diffuse flux and produce a “bump” in the spec-
ofsourceswhichareembeddedinstar-formingor trum‡. Reasonable fits by eye are obtained for
starburst galaxies. thediffuseneutrinofluxmeasuredbyIceCubein-
As shown by Murase et al. (2013), in the pp cluding the latest TeV data by using reasonable
scenario, the neutrino spectrum cannot be softer parameters for the sources as well as the diffu-
than about ε2νΦν ∝ ε−ν0.2 at low energies for the sion properties in hosting structures. Such a flux
correspondingγ-raycomponentnottoviolatethe also approximates but does not violate the dif-
Fermi measurements of the diffuse γ-ray back- fuse γ-ray background measured by Fermi. This
ground (Ackermann et al. 2014). At the same does not mean that SNe and HNe are necessar-
time, a flat spectrum at moderate to high en- ily the only sources contributing to the neutrino
ergies creates tension with the non-detection of and γ-ray diffuse backgrounds. Itsupports, how-
neutrinos with energies near the Glashow res- ever, the case for CR reservoirs such as clus-
onance at εν ∼ 6 PeV, which necessitates a ters and groups being promising sources which
neutrino spectral shape near that energy steeper could contributes at least a significant fraction
than ε2νΦν ∝ ε−ν0.3 (Laha et al. 2013). Such a of these backgrounds, without violating both CR
spectral break can occur if acceleration stops or (Yoshida & Takami 2014) and γ-ray constraints.
there is a transition in the diffusive escape time
(i.e. D(ε ) ∝ εα → D(ε ) ∝ ε2 ) around
cr cr cr cr
ε ∼ 240 ((1+z)/2) PeV (e.g., Murase et al.
cr
2013; Anchordoqui et al. 2014). As can be seen This work was partially supported by NASA
in Fig. 1 and 3, the model presented here can NNX13AH50G. We are grateful to J. van Santen
also resolve this tension. The neutrino spectrum for providing the IceCube data points.
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