ЖЭТФ, 2021, том 160, вып. 3 (9), стр. 366-371
© 2021
GAMMA-RAYS AND NEUTRINOS FROM PROTON-PROTON
INTERACTIONS IN GAMMA-RAY BURSTS
A. Neronova,b*, Y. Gateleta
a APC, University of Paris, CNRS/IN2P3, CEA/IRFU
75205, Paris, France
b Astronomy Department, University of Geneva
CH-1290, Versoix, Switzerland
Received November 9, 2020,
revised version December 18, 2020.
Accepted for publication December 21, 2020
DOI: 10.31857/S0044451021090030
[8,9] afterglows might potentially carry such signatures.
The VHE γ-ray flux can hardly be attributed to the
Expansion of relativistic outflows of gamma-ray
synchrotron emission that presumably forms the bulk
bursts (GRB) into medium created by the winds or
of the GRB prompt and afterglow flux
[3, 4, 10, 11],
their progenitor stars is accompanied by interactions
because the synchrotron spectrum can hardly extend
of picked-up protons with the medium. These in-
into the VHE band. Alternatively, the inverse Comp-
teractions produce neutrinos and γ-rays with ener-
ton emission [9,12,13] produced by electrons with ex-
gies in the TeV-PeV range. We study if such neu-
tremely high Lorentz factors possibly accelerated at the
trinos and γ-rays are detectable with neutrino and γ-
forward shock of the GRB outflow is also not directly
ray telescopes. We find that neutrino signal can be
sensitive to the matter content of the medium through
detectable with IceCube-Gen2 type telescope(s) if the
which the GRB outflow propagates.
GRB progenitor has been a low-metallicity star with
It
is
also possible that in exceptional
initial mass (40-100)M⊙, or if the progenitor system
VHE-γ-ray-bright GRBs part of the γ-ray emis-
has been a binary with dense circumstellar environment
sion is produced by high energy proton interactions.
(∼ 1013 cm-3) within the binary system extent. γ-ray
Such emission is also not directly sensitive to the
emission from pion decays is detectable only in the af-
circumstellar environment if proton interact with
terglow phase, because of the pair production opacity
radiation field through photo-pion production, as
of the prompt emission. This emission can contribute
suggested in a range of hadronic models of GRBs
to the TeV afterglow flux of GRBs. Detection of the
[14]. To the contrary, proton-proton interactions are
pion decay γ-ray and neutrino emission can serve as a
directly sensitive to the density of the circumstellar
diagnostic of the GRB progenitor evolution during the
medium.
last years of its life.
Proton-proton interactions are conventionally not
considered in the GRB afterglow physics because of the
Before the gravitational collapse, massive stars ex-
assumption of collisionless propagation of the GRB out-
perience significant wind-like and explosive mass loss
flow through external medium. However, Refs. [15-18]
[1]. These stars are perhaps progenitors of long gam-
show that even if particle collisions do not affect the
ma-ray bursts (GRB) [2-4]. GRB relativistic outflow
dynamics of the GRB outflow and particle acceleration
might propagate through matter-rich circumstellar en-
processes, proton interactions still generate secondary
vironment created by the stellar wind and interact with
particles taking small fraction of the blast wave energy.
this environment [5].
If the progenitor stellar system of the GRB has pro-
Recent detection of very-high-energy (VHE) γ-ray
duced strong wind or evolved as a binary system just
emission from GRB 180720B [6, 7] and GRB 190114C
before the explosion, signatures of the pp interactions
could be present in the GRB prompt-emission and/or
* E-mail: andrii.neronov@gmail.com
afterglow spectral and timing properties. In what fol-
366
ЖЭТФ, том 160, вып. 3 (9), 2021
Gamma-rays and neutrinos from proton-proton interactions. . .
lows we explore these signatures. We show that γ-ray
this energy is set by the overall energy liberated in the
and neutrino emission from pp interactions can reach
gravitational collapse, estimated as the gravitational
detectable levels and provide a diagnostic of the pres-
binding energy of material forming the black hole con-
ence of dense wind environment around the collapsed
fined to its horizon Rbh ∼ GN Mbh/c2:
star generated by the mass loss prior to the collapse
or by interactions with a companion star in a binary
Egrav ∼ GN M2bh/Rbh = Mbhc2 ∼ 10M⊙c2 ∼ 2·1055 erg.
system.
The density of the circumstellar medium at the dis-
As soon as the kinetic energy of the picked up material
tance r is determined by the mass loss rate at the time
becomes comparable to the energy of the outflow, it
starts to decelerate.
[
]-1 [r
]
The “coasting” phase of the GRB outflow continues
r
vw
tw =
≃ 10
yr
(1)
up to the distance r0 at which E(r0) ∼ E0:
vw
300 km/s
1016 cm
before the collapse, where vw is the wind velocity, cf.
(
)1/(3-γ)
Refs. [19-23]. Emission from GRB outflow propagating
(3 - γ)E0
r0 =
(3)
at the distances ∼ 1016 cm from the collapsed star can
Γ20mpn0ΩR∗
potentially probe the history of mass ejection over the
The signal from within this distance is expected to ar-
last decade of the progenitor star life.
rive within the time interval
GRB outflow expanding into the circumstellar
medium initially goes through the “coasting” stage.
r0
During this stage, even if the GRB outflow is not ini-
t0 ∼
(4)
2Γ2
0
tially loaded with protons, it starts to pick up and ac-
celerate protons from the wind. The amount of mate-
from the GRB start, possibly by the end of the prompt
rial picked up after expansion to the distance r is
emission phase of the GRB. During the subsequent
deceleration stage the outflow dynamics follows the
∫r
3-γ
Blandford-McKee solution [25] for an adiabatic rela-
n0ΩR∗r
N (r) = Ω n(r′)r′2dr′ =
,
(2)
tivistic blast wave. The bulk Lorentz factor of the blast
3-γ
R∗
wave decreases with distance r and new particles picked
up by the outflow gain energy Γ(r)2mp. The particles
where n0 is the central wind density, R∗ ∼ 1012 cm and
which were initially picked up still might retain their
γ ≈ 2 are the characteristic scale and the power-law ex-
energy ∼ Γ0mp in the comoving frame, but in the col-
ponent of the density profile. In the reference frame of
lapsar frame their energy decreases down to maximum
the outflow, protons from the medium arrive all from
Er ∼ ΓΓ0mp (as could be found from the Lorentz trans-
radial direction with energy E′ = Γ0mp where Γ0 is
formation between the collapsar and comoving frames).
the initial bulk Lorentz factor of the outflow. The
As a result, there is a specific spectrum of protons
picked up particles initially form a nearly monoener-
which establishes in the comoving frame in the absence
getic isotropic distribution sharply peaked at the en-
of additional shock acceleration. Most of the energy
ergy E′. Shock acceleration process may produce pro-
distributed among the freshly picked up particles so
tons with still higher energies, so that the spectrum of
that E0 ≃ Γ2mpN = Γ2mpn0R2∗r for Γ ≪ Γ0. The
protons may extend as a powerlaw above the energy E′.
distance dependence of the gamma-factor can be con-
A conventional assumption is that the acceleration pro-
verted into time dependence for the observer’s time t
cess results in a powerlaw spectrum f′(E′) ∝ (E′)-p,
using a relation r(t) found from dr = 2Γ2dt which gives
p ≃ 2 for E′ > Γ0mp. Uncertainties in the physics
r = 2Γ2 ((4 - γ)t - t0) so that
of relativistic shock acceleration yield large scatter of
possible spectral slopes deviating from p = 2 [24].
(
)1/(2(4-γ))
If most of the kinetic energy of the picked up mate-
(3 - γ)E0
Γ=
(5)
rial is contained in particles with energies E′ ∼ Γ0mp
23-γmpn0R∗Ω [(4-γ)t-t0]3-γ
in the comoving frame, the energy distribution of pro-
tons in the collapsar frame is peaked at the energy
scales at t-1/4 in the case γ = 2.
E ∼ Γ20mp. The total kinetic energy of the outflow
The picked up protons carry the energy of the GRB
grows as [25] E(r) ∼ Γ20mpN. The total energy of the
outflow. They dissipate a part of this energy in pp in-
picked up protons gradually gets comparable to the to-
teractions. The energy output from these interactions
tal energy release of the GRB, E0. The upper limit on
is
367
A. Neronov, Y. Gatelet
ЖЭТФ, том 160, вып. 3 (9), 2021
{
dEpp
Γ20mpN, r < r0,
Flux, erg/cm2 . s
= κσppn
(6)
–
dr
E0,
r>r0,
1
3
GBM, 10 - 10
keV
–
where σpp ≃ 5 · 10-26 cm2 is the cross-section of pp
1
MAGIC, > 0.3 TeV
interactions and κ ≃ 0.5 is the average inelasticity of
–
1
pp collisions [26,27].
–
We obtain the luminosity of
1
-8
10
Lpp = 2κΓ2σppnE0 =
[
]1/2 [
]-3/2 [
]1/2
–
1
Ω
t
E0
= 2 · 1048
×
0.1
7s
1054 erg/s
10-10
]3
[
]3/2 [R
3
n0
∗
erg
100
101
102
10
×
(7)
t, s
1013 cm-3
1012 cm
s
Fig. 1. (Color online) Fermi/GBM (grey solid line) and MAGIC
The flux decreases as t3/(4-γ) at late times. If γ = 2
(blue data points) lightcurves of GRB 190114C. Vertical
(environment created by the wind with constant mass
dashed line marks the suggested time scale t0 given by Eq. (4).
loss rate) then the flux decrease is t-3/2.
Dotted blue line shows possible 0.3-1 TeV γ-ray flux for the
If the radial density profile of the medium has a
reference π0 decay model of GRB outflow propagating through
shallower slope, e.g. γ = 1, the overall time dependence
the wind environment
of Lpp changes. The luminosity grows as t3-2γ = t dur-
ing the coasting phase and decreases as t-3/(4-γ) = t-1
during the deceleration phase (see (7)). The shallower
profile of the stellar wind density can be e. g. due to
systems, with density n0 ∼ 1013 cm-3 across large re-
the decrease of the mass loss rate of the progenitor star
gion of the size about the binary separation distance,
over the last 10 years before the gravitational collapse.
R∗ ∼ 3·1012 cm can yield Nν ∼ 1 neutrino signal. Oth-
The luminosity Lpp deposited by the proton-proton
erwise, the dense circumstellar environment can also
interactions into neutrinos and electromagnetic channel
be found around low-metallicity progenitor stars in the
is detectable by neutrino and gamma-ray telescopes.
mass range 40M⊙ - 100M⊙ for which the central wind
Most of the neutrino and γ-ray flux is initially con-
densities can exceed 3 · 1014 cm-3 [21].
centrated in a decade-wide energy range at the energy
≲ 10 % of the proton energy [28], i.e. at
Pion decay γ-rays which are initially produced in
[
]2
the same energy band as neutrinos do not escape from
Γ0
Eγ,ν ≲ 0.1Γ20mp ≃ 4
TeV
(8)
the source because of the pair production opacity of
200
the GRB outflow, cf. Ref. [29-31]. TeV photons from
pp interactions produced in the prompt emission zone
if there is no significant acceleration of protons.
are immediately converted into e+e- pairs which con-
Otherwise, if the shock acceleration process is ef-
tribute to the pair loading of the GRB outflow and ul-
ficient, the spectrum extends to higher energies as a
timately contribute to the prompt flux in the energy
powerlaw with the slope nearly identical to that of the
range in which the pair production optical depth is
accelerated proton spectrum.
τγγ ≲ 1.
The number of neutrino events per GRB in a detec-
tor of volume V is
γ-rays produced in pp interactions during the de-
[
]2 [
]-2 [
]
A
D
Vdet
celeration phase of the GRB outflow lag behind the
Nν ≃ 10-2
region occupied by the pulse of the prompt emission.
1037 cm-1
1 Gpc
1 km3
Thus, they never interact with the prompt emission
for a GRB at the distance D, where A = n0R2∗. This es-
photons. During the deceleration phase the luminosity
timate shows that only exceptional GRBs occurring in
Lϵ drops by several orders of magnitude, as illustrated
dense extended circumstellar environment might yield
by GRB 190114C (Fig. 1). This makes the GRB out-
Nν ∼ 1 neutrino event statistics in neutrino detectors
flow transparent to the VHE γ-rays. If the luminosity
like IceCube, Baikal-GVD, or Km3NET. This might
Lϵ decreases as Lϵ = Lϵ,0(t/t0)-δ during the afterglow
be the case e. g. for GRBs occurring in binary stellar
phase, the optical depth scales as
368
ЖЭТФ, том 160, вып. 3 (9), 2021
Gamma-rays and neutrinos from proton-proton interactions. . .
count
-ray count
log[E /(1 GeV)]
log[E /(1 GeV)]
–
–
a
1
b
1
4.0
4.0
3.5
10-10
3.5
10-10
3.0
3.0
10-11
10-11
2.5
2.5
10-12
10-12
2.0
2.0
1.5
1.5
0
0.5
1.0
1.5
2.0
2.5
3.0
10-13
0
0.5
1.0
1.5
2.0
2.5
3.0
10-13
log[t/(1 s)]
log[t/(1 s)]
Fig. 2. (Color online) Spectral evolution of neutrino (a) and γ-ray (b) emission from pp interactions. Y axes show the neutrino
or photon energy, X axis is time. Color shows the spectral energy density. White vertical line marks the end of the coasting
phase. White piece-wise straight lines show the evolution of the peak energy. White horizontal lines mark the energy range of
MAGIC detection of GRB 190114C
[
][
]
Lϵ,0
Eγ
Using the estimate D ≈ 2.4 Gpc for the luminosity
τγγ ≃ 1
×
1051 erg/s
300 GeV
distance to the GRB190114C at z = 0.4245 as a refer-
[
]-6 [
]-(1+δ)
ence, we find an estimate of the flux of the VHE γ-ray
Γ
t
×
(9)
signal from the decelerating phase
200
10 s
[
]-1/2
and the outflow is transparent to the TeV γ-rays.
Lpp
Ω
Fpp =
≃ 10-8
×
The requirement that opacity for TeV γ-rays de-
ΩD2
0.1
[
]-3/2 [
creases to τγγ ≲ 1 by the time of Cherenkov tele-
]1/2 [
]3/2
t
E0
n0
scope observations (say, at t ∼ 102 s into the afterglow
×
×
102 s
1054 erg/s
1013 cm-3
phase) imposes a restriction on the energy budget of the
[
]3 [
]-2
R∗
D
erg
GRB propagating through relatively dense medium (or,
×
(12)
1012 cm
2.4 Gpc
cm2 · s
equivalently, on the density of the medium for a GRB
with a fixed energy budget) [30]. Re-interpreting the
This level of γ-ray flux is not far from the observed
condition τγγ ≤ 1 from Eq. (9) as a lower bound on
flux of GRB190114C in the 102 < t < 103 s time in-
Γ0 ≥ Γ,
terval, as can be seen from Fig. 1 [32] for the reference
[
]1/6 [
]-1/6
parameters of the wind density and overall energy out-
Lϵ
t
put in our reference model. The VHE γ-ray flux of
Γ > 200
,
(10)
1051 erg/s
7s
GRB190114C has decreased as t-1.5 during the after-
glow phase. This is close to the expected luminosity
and using a measurement of t0, one can use Eqs. (3),
from pp interactions for a GRB outflow expanding into
(4) to estimate a lower bound on the total energy of
environment with radial density profile with γ = 2.
the outflow E0:
Figure 2 shows a model of expected time evolution of
3-γ
[
][
]1/3
the VHE γ-ray spectrum of pion decay flux based on
t
Γ40mpn0ΩR2∗
Ω
t0
0
E0 =
> 1054
×
AAfrag parameterisation of the differential production
(3 - γ)3-γ
0.1
7 s
cross-sections of pp interactions [27]. The model γ-ray
]2
[
][R
n0
∗
lightcurve in fixed energy range 0.3-1 TeV extracted
×
×
1013 cm-3
1012 cm
from the the numerical calculation with AAfrag for
[
]2/3
the reference model considered in the text is shown
Lϵ
×
erg,
(11)
in Fig. 1. It shows deviation from the t-3/2 powerlaw
1051 erg/s
behavior.
where we have assumed t ∼ t0 for the time moment
Even though the pion decay emission is not the only
when τγγ ∼ 1 (in general the two times are not neces-
possible contribution to the VHE band γ-ray luminos-
sarily equal).
ity, the VHE band detection can serve as a selection
369
5
ЖЭТФ, вып. 3 (9)
A. Neronov, Y. Gatelet
ЖЭТФ, том 160, вып. 3 (9), 2021
criterion of GRBs that might be expanding into dense
The full text of this paper is published in the English
circumstellar environment and thus can be considered
version of JETP.
as candidate neutrino sources. This can be used in the
multi-messenger neutrino + γ-ray analysis: the sensi-
tivity of the neutrino searches can be improved if only
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