ЖЭТФ, 2020, том 158, вып. 2 (8), стр. 295-299
© 2020
SELF-CONSISTENT MODEL OF EXTRAGALACTIC NEUTRINO
FLUX FROM EVOLVING BLAZAR POPULATION
A. Neronova,b*, D. Semikoza
a APC, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris Cité
75205, Paris, France
b Astronomy Department, University of Geneva, Ch. d’Écogia 16
Versoix, 1290, Switzerland
Received December 20, 2019,
revised version December 20, 2019
Accepted for publication December 25, 2019
DOI: 10.31857/S0044451020080064
galactic source for which evidence for neutrino signal
was found is a blazar TXS 0506 + 056 [38, 39]. As it is
The origin of astrophysical neutrino signal [1] de-
discussed in Ref. [20] not all blazars are expected to
tected in “high-energy starting events” (HESE) [2] and
be “neutrino-loud”. Differences in overall gamma-ray
muon neutrino [3] channels by IceCube telescope is un-
and neutrino emission power are generically expected
certain. The overall flux and spectral slope of the HESE
because neutrinos are efficiently produced only in the
signal are consistent with the high-energy extrapolation
presence of dense matter and radiation backgrounds
of the gamma-ray flux detected by Fermi telescope up
[20, 21, 23, 24, 29].
to the TeV band [4-9]. However, the anisotropy pat-
We explore constraints on neutrino emitting blazar
tern of the signal does not reveal strong excess toward
population imposed by observational properties of the
the Galactic Plane [10-12]. The neutrino signal at en-
neutrino signal: the absence of event clustering in neu-
ergies higher than several hundred TeV sampled from
trino arrival directions, a problem first noticed in the
the Northern hemisphere with muon neutrinos reveals
analysis of Ref. [40], and the fact that nearby blazars
harder spectrum compared to that of the HESE neu-
are not strong neutrino sources, with the nearest identi-
trino flux [3, 13]. This hardening could be due to the
fied neutrino emitted blazar TXS 0506+056 at redshift
presence of extragalactic component of the astrophysi-
≈ 0.3 [41] which is by a factor ∼ 10 further away than
cal neutrino flux. The overall flux of the hard compo-
the closest gamma-ray blazar (Mrk 421).
nent is at the level consistent with the observed ultra-
We consider standard candle type sources with lu-
high-energy cosmic ray (UHECR) flux [14-19].
minosity function ρ(LE , z) dLE (the comoving number
Radio-loud Active Galactic Nuclei (AGN) are
density of sources at a given redshift z having spectral
among astronomical source classes in which physical
luminosities LE to LE + dLE at an energy E) which is
conditions which enable acceleration of protons and
proportional to a δ function
nuclei to energies up to UHECR range are realised
[20-22]. Neutrino emission from AGN, and in particu-
ρ(LE , z) = ρ∗(1 + z)ζ δ(LE - LE∗(E)),
lar from blazars, is widely discussed in the context of
hadronic models of AGN activity [20, 21, 23-35]. This
where LE∗(E) ∝ E1-γ is assumed to be a powerlaw
neutrino emission is expected to be accompanied by
with the slope γ. We allow the standard candle lu-
the γ-ray emission produced in result of development
minosity to evolve with redshift as (1 + z)ζ. Models
of electromagnetic cascade inside the neutrino emitting
considered in Monte-Carlo simulations described below
source. In this respect, it is surprising that brightest
assume either positive evolution up to z∗ followed by
and/or nearest gamma-ray blazars do not appear as
no-evolution period between z∗ and zmax = 3. Such
brightest neutrino sources [36, 37]. The only extra-
evolution patterns are characteristic for blazar popu-
lations: flat spectrum radio quasars (FSRQ) [42] and
* E-mail: andrii.neronov@gmail.com
BL Lacs [43] as well as to the parent populations of
295
A. Neronov, D. Semikoz
ЖЭТФ, том 158, вып. 2 (8), 2020
FSRQs and BL Lacs, Fanaroff-Riley radio galaxies of
assume “pure luminosity” evolution model, rather than
type I and II [44, 45] and to X-ray selected AGN [46].
“luminosity dependent density evolution” model which
Assuming that neutrino flux is emitted into a jet
better suits the description of population of blazars
with an opening angle θjet one could find that the ave-
[42, 43]). Fixing the position and luminosity of each
rage number of neutrino events detectable with a tele-
source, we calculate its expected relative contribution
scope with effective collection area Aeff within expo-
to the neutrino flux at Earth as a function of (properly
sure time Texp is related to the luminosity LE as
redshifted) neutrino energy, assuming that all sources
have powerlaw type spectra with the slope γ = 2. Our
Aeff TexpLE(E∗)
Nν(E∗) = (1 + z)2-γ
,
(1)
calculation takes into account the source position on
πθ2jetd2
L
the sky, and the declination dependence of the IceCube
effective area Aeff (E) [3,13]. We simulate the neutrino
where dL is the luminosity distance. If the jet direc-
signal with total statistics Nν,tot ≈ 24 that corresponds
tions are randomly distributed, the probability to find
to the published IceCube sample of muon neutrinos [3]
a given source with a jet pointing in the direction of
with muon energy proxies above 200 TeV, if the resid-
an observer is pobs = θ2jet/2 so that the “effective” den-
ual atmospheric neutrino background (approximately
sity of sources visible for an observer is ρeff (LE , z) =
one third of the muon neutrino sample) is removed.
= θ2jetρ(LE, z)/2.
We assume that detected muons have experienced an
The number of observable sources in the redshift
order-of-magnitude energy loss before entering the Ice-
range z to z + dz and producing given number of neu-
Cube detector. We retain only muons which arrive at
trino events between Nν and Nν + dNν is
the detector with energies above 200 TeV.
η(Nν , z) dNνdz = ρeff (LE , z) dLEdVC ,
(2)
Non-observation of sources producing multiplet
events in IceCube indicates that the effective source
where LE is expressed through Nν using Eq. (1), dVC
density is low enough so that typically there are no
is the comoving volume element per steradian of the
sources contained within a sphere of the radius at which
telescope field-of-view dVC = d2C /(H0E(z)) dz where
an individual source produces one event. Assuming
√
that zm ≪ 1 one could find that sources produce on
E(z) = Ω0,m(1 + z)3 + Ω0,Λ
average m events as a distance
√
with Ω0,m, Ω0,Λ being the present day dark matter and
dm = Aeff TexpLE∗/(πθ2jetm).
dark energy density parameters and dC is the comoving
distance.
The condition that there is less than one source within
Calculating LE from (1) and substituting the ex-
the volume of the sphere with radius dm is then
pression for the comoving volume element in the right
(
)3/2
hand side of Eq. (2) and integrating over the redshifts
ρ∗,eff ≲ (3/4π)
πθ2jetm/(Aeff TexpLE∗)
we find the differential source count (the number of
sources contributing between Nν and Nν+dNν counts):
imposes an upper bound on a combination ρ∗,eff L3/2E∗
of the source density and luminosity, as discussed in
∫∞
Ref. [40].
n(Nν ) = η(Nν , z) dz =
This analytical result which neglects the Poisson na-
0
ture of the signal is confirmed by the Monte-Carlo sim-
∞
∫
πθ4jet
d4Lρ(LE, z)
ulation results shown in Fig. 1. The boundary of the
=
dz.
(3)
2H0Aeff Texp
(1 + z)4-γ E(z)
dark grey shaded band follows the ρ∗,eff L3/2E∗ ∼ const
0
dependence at large source densities, but deviates from
The total number of sources producing at least m
it at low densities, where the sources become sparse
events within a given exposure is Ns(Nν
> m) =
and Poisson fluctuations of the signal becomes more
∫∞
=
n(Nν ) dNν .
important. The x axis on Fig. 1 shows the bolometric
m
∫∞
To properly deal with small m case, we use Mon-
luminosity L =
LEdE.
200 TeV/ϵ
te-Carlo simulations of the signal from a source popula-
Absence of identified sources at the distances closer
tion. We first generate source distribution which we as-
than z = 0.3 imposes an additional constraint which
sume to be uniform throughout the comoving volume.
becomes stronger than the constraint from the absence
For each source we ascribe a fixed luminosity depen-
of doublets at high source densities. Qualitative ex-
ding on the source distance/redshift (in this sense, we
planation for this fact is that as the source density
296
ЖЭТФ, том 158, вып. 2 (8), 2020
Self-consistent model of extragalactic neutrino flux. ..
*, Мрс-3
*, Мрс-3
10-7
10-7
Weak BL Lacs
10-8
Bright BL Lac
10-8
-9
10
10-9
FSRQ
Y
10-10
(1 + z) evolution0
10-10
(1 + z) up to z = 1.75
10-11
10-11
1044
1045
1046
1047
1043
1044
1045
1046
1047
L, erg/s
L, erg/s
Fig. 1. (Color online) 95 % confidence level constraints on
Fig. 2. (Color online) Same as in Fig. 1 but for sources evolv-
the properties of non-evolving standard candle neutrino source
ing with ζ = 5 up to redshift z = 1.7 [46]. For comparison,
population. Dark grey shading shows constraint from non-
luminosity dependent densities of FSRQs (blue shading) from
observation of doublets in the muon neutrino sample. Light
Ref. [42] and bright BL Lacs from Ref. [43] are shown
grey shows constraint from non-observation of neutrino-
emitting blazars within redshift z < 0.3. Red band shows the
source density required for production of the observed muon
neutrino flux. For comparison, luminosity dependent density
7
of weak BL Lacs from Ref. [43] (green shading) is shown
6
grows, it becomes more and more difficult not to no-
FSRQ
tice very nearby sources (which we assume are all iden-
5
tified as blazars using techniques of multi-wavelength
astronomy). Nevertheless, also this constraint shows
dependence on the source luminosity because the indi-
4
vidual sources get weaker and weak nearby sources on
average contribute with less than one neutrino to the
3
signal. The first identifiable source which occasionally
produces one event in a given exposure is not necessar-
2
BL Lac
ily the nearest one.
A combination of the absence of doublets and ab-
sence of nearby sources constraints rules out the possi-
1
bility that the IceCube muon neutrino flux is generated
by a population of non-evolving sources, like Low-lumi-
nosity BL Lac and Fanaroff-Riley type I (FR I) radio
0
0.5
1.0
1.5
2.0
2.5
3.0
z*
galaxies which show no or negative cosmological evo-
lution [43, 44]. This is clear from comparison of the
Fig. 3. (Color online) Allowed region of evolution parameters
constraints with the density of the sources required for
for source populations (white area) compared to the evolution
generation of the observed neutrino flux, shown as the
parameters of BL Lac [43] and FSRQ populations [42]
red band in Fig. 1. The red band is never found within
the allowed range of ρ∗, L.
The constraints from non-observation of doublets
Figure 2 shows that for fast enough evolution with
and nearby sources are relaxed if the source population
ζ ≥ 5 the combined constraint from non-observation of
is assumed to evolve positively with the redshift, sim-
doublets and nearby sources do not rule out a range
ilarly to high-luminosity BL Lacs and/or FSRQ (and,
of source densities needed to provide the observed
possibly their progenitors, high luminosity FR II type
IceCube muon neutrino flux. Figure 3 shows the al-
radio galaxies) [42-45] which evolve as fast as ζ = 5 up
lowed range of evolution parameters z∗, ζ within which
to z∗ ∼ 1 . . . 2.
source population could explain the IceCube muon neu-
297
A. Neronov, D. Semikoz
ЖЭТФ, том 158, вып. 2 (8), 2020
trino flux avoiding constraints from non-identification
10-10
of nearby sources and absence of doublets in IceCube
Fermi/LAT EGB
10-9
dataset.
Comparison of the properties of the populations of
10-11
IceCube
TXC 0506+056
astrophysical
gamma-ray and neutrino emitting blazars is shown in
TXC 0506+056
IceCube
neutrinos
Fermi/LAT
10-10
Figs. 1-3, and where we have overplotted the luminos-
ity function and evolution parameters of BL Lacs from
10-12
Ref. [43] and FSRQs from Ref. [42]. One could see that
sources evolving as weak BL Lacs could not explain the
10-11
IceCube signal, in spite of the fact that weak BL Lac
10-13
population avoids the constraint on the absence of cor-
103
105
107
109
1011
relation of source positions with IceCube neutrinos, as
E, MeV
discussed in Ref. [35].
Fig. 4. (Color online) Multi-messenger time-averaged spectrum
Only the evolution parameters of the highest lu-
of TXS 0506 + 056 measured by IceCube [39] (butterfly and
minosity BL Lacs (ζ > 4, z∗ > 1.5) become consis-
black horizontal line) and Fermi/LAT (grey data points)
tent with IceCube data. Such evolution is valid only
for BL Lacs with gamma-ray luminosities in excess of
1046-1047 erg/s. The density of those sources is very
trum which we have extracted from the LAT data
low, n ∼ 10-9-10-11 Mpc-3.
collected between 2008 and 2018 (fully covering the
Figure
3
shows that the evolution parameters
IceCube exposure). One could see that the time ave-
bright BL Lacs and FSRQ populations are consis-
raged gamma-ray flux of TXS 0506+ 056 is more than
tent with constraints on evolution parameters of neu-
an order-of-magnitude higher than the time-averaged
trino sources. From Fig. 2 one could judge that the
neutrino flux.
density of FSRQs and bright BL Lacs is comparable
Figure 4 also shows a comparison of the characteris-
with the density required for neutrino sources evolv-
tics of the multi-messenger spectrum of TXS 0506+056
ing as (1 + z)5, similarly to the FSRQ and bright BL
with those of the entire neutrino+gamma-ray extra-
Lacs. Low-lumnosity FSRQs and/or bright BL Lacs
galactic sky [3,51]. We have chosen the y axis range
could be considered as viable neutrino source candi-
in such a way that the TXS 0506 + 056 gamma-ray
dates [20, 47], provided that their neutrino luminosity
flux does not exceed the extragalactic gamma-ray flux
is much lower than γ-ray luminosity. Assumption of
range. With such y-axis range adjustments, it becomes
comparable γ-ray and neutrino luminosities would vi-
clear that neutrino-to-gamma-ray flux ratio measure-
olate constraints stemming from the absence of corre-
ments and upper limit for TXS 0506 + 056 is consistent
lations of neutrino arrival directions with γ-ray source
with the neutrino-to-gamma-ray flux ratio of entire ex-
positions on the sky [36,37,40,48]. One could also see
tragalactic sky.
that neutrino-to-γ-ray luminosity ratio has to be lower
Overall, we conclude that the hypothesis of the
for the brightest FSRQs, otherwise they would be in-
rapidly evolving part of blazar population (bright
dividually detectable neutrino sources.
BL Lacs, FSRQs) contribution to the extragalactic
FSRQs are less abundant in the low-redshift Uni-
neutrino flux is consistent with the observational data
verse than low-luminosity BL Lacs. The closest FSRQ,
(absence of doublets in IceCube muon neutrino sample
3C 273, is at the redshift z ≈ 0.16 [49]. There are only
and z ≈ 0.3 redshift of the nearest detected source),
about 10 FSRQs within the redshift < 0.3 detected by
once the details of cosmological evolution of the source
Fermi/LAT [50] and 3C 273 is brightest among them.
population and differences in the overall luminosity
The neutrino emitting blazar TXS 0506 + 056 is classi-
and anisotropy patterns of gamma-ray and neutrino
fied as BL Lac in SIMBAD astronomical database, but
emission are taken into account.
its luminosity scale is closer to that of FSRQs.
TXS 0506 + 056 multi-messenger detection could
The full text of this paper is published in the English
provide a useful insight into neutrino-to-gamma-ray lu-
version of JETP.
minosity ratio. Its multi-messenger gamma-ray + neu-
trino spectrum is shown in Fig. 4. To produce this fig-
ure, we have taken the estimate of the time-averaged
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