Gamma-Rays from Heavy Nuclei Accelerated in Supernova Remnants

Abstract

We investigate the theoretical and observational implications of the acceleration of protons and heavier nuclei in supernova remnants (SNRs). By adopting a semi-analytical technique, we study the non-linear interplay among particle acceleration, magnetic field generation and shock dynamics, outlining a self-consistent scenario for the origin of the spectrum of Galactic cosmic rays as produced in this class of sources. Moreover, the inferred chemical abundances suggest nuclei heavier than Hydrogen to be relevant not only in the shock dynamics but also in the calculation of the gamma-ray emission from SNRs due to the decay of neutral pions produced in nuclear interactions. Comment: To appear on the proceedings of ICATPP Conference on Cosmic Rays for Particle and Astroparticle Physics, Villa Olmo, Como 7-8 October 2010

Full text

Page 1

arXiv:1011.6527v1 [astro-ph.HE] 30 Nov 2010
December 1, 2010 1:9WSPC - Proceedings Trim Size: 9in x 6in Como10
1
γ-RAYS FROM HEAVY NUCLEI ACCELERATED IN
SUPERNOVA REMNANTS
D. CAPRIOLI∗, P. BLASI and E. AMATO
INAF/Osservatorio Astrofisico di Arcetri,
50125 Firenze, Italy
∗E-mail: caprioli@arcetri.astro.it
We investigate the theoretical and observational implications of the accelera-
tion of protons and heavier nuclei in supernova remnants (SNRs). By adopting
a semi-analytical technique, we study the non-linear interplay among particle
acceleration, magnetic field generation and shock dynamics, outlining a self-
consistent scenario for the origin of the spectrum of Galactic cosmic rays as
produced in this class of sources. Moreover, the inferred chemical abundances
suggest nuclei heavier than Hydrogen to be relevant not only in the shock dy-
namics but also in the calculation of the γ-ray emission from SNRs due to the
decay of neutral pions produced in nuclear interactions.
Keywords: cosmic rays, acceleration of particles, SNR, γ-rays
1. Cosmic rays and supernova remnants
For more than 70 years scientists have been regarding supernova remnants
(SNRs) as the most plausible sources for Galactic cosmic rays (GCRs), but
only in recent times the theoretical comprehension of the ongoing processes
have made important steps forward (see also P. Blasi’s contribution in this
volume). Once a model for CR propagation in the Milky Way is assumed, it
is possible to infer from observations at Earth the spectra of single chemical
species expected at the sources. In this work we investigate a scenario in
which Galactic SNRs are responsible for the acceleration of protons and
heavier nuclei (hereafter HN), trying to disentangle the solid, physical in-
gredients and the phenomenological recipes which have to be included in
order to account for many observational constraints. In particular we show
that, according to this SNR paradigm for the origin of GCRs, HN may
play a fundamental role in the shock dynamics and also contribute in a
non-negligible way to the γ-ray emission from SNRs.
We consider here a semi-analytical approach to the problem of non-

Page 2

December 1, 2010 1:9 WSPC - Proceedings Trim Size: 9in x 6inComo10
2
linear diffusive acceleration of particles at shocks (NLDSA) following the
basic implementation put forward in Ref. 1–3, also including the effects
of the magnetic field amplification on the shock dynamics4and the pres-
sure of the most abundant CR species.5The evolution of a remnant in a
homogeneous circumstellar medium is followed in a quasi-stationary way
as in Ref. 6 and coupled with the acceleration of particles at the forward
shock as in Refs. 5,7. For the details of the computational apparatus, the
reader may refer to the papers above. Here, we only would like to highlight
how such a semi-analytical approach to NLDSA is typically much faster
than, and as much rigorous as, other fully numerical or Monte Carlo meth-
ods for non-relativistic shocks,8and therefore it is very useful for including
multi-specie CRs or, in general, for studying problems with a wide range
of environmental parameters.
In our calculations protons are injected into the acceleration process
from the thermal bath through a “thermal-leakage” mechanism,9which
is sensitive to the shock dynamics and tends to suppress the number of
injected particles when the the acceleration becomes more and more effi-
cient. The amounts of injected HN are tuned by hand relatively to pro-
tons to reproduce the abundances measured at Earth. This recipe, while
including a reasonable feedback which self-regulates the efficiency of the
injection, has to be regarded as a necessary phenomenological description
since, unfortunately, the HN injection at SNR shocks is still poorly un-
derstood for two main reasons. First, injection strongly depends on the
charge/mass ratio and it is very difficult to follow the degree of ionization
of heavy atoms during their acceleration; second, refractory elements (Mg,
Si, Fe,...) are thought to be injected as a result of sputtering of acceler-
ating dust grains.10,11The latter phenomenon, though very hard to deal
with quantitatively, is however expected to produce largely suprathermal
(but still non-relativistic) ions able to cross the shock from downstream to
upstream because of their large gyroradii. For the same reason, partially
ionized heavy atoms are expected to be preferentially injected, in agree-
ment with the relative abundances measured in GCRs.10,11Nevertheless,
since our abundances are tuned on the relativistic region of the GCR spec-
trum, we can bypass the problem above and make safe predictions about
the role of HN in the shock dynamics and in the SNR γ-ray emission.
At any given time the shock dynamics is regulated by the non-linear in-
terplay between particle acceleration, occurring via first-order Fermi mech-
anism, and magnetic field amplification, which we model as due to resonant
streaming instability excited by all the accelerated particles.12On one hand,

Page 3

December 1, 2010 1:9WSPC - Proceedings Trim Size: 9in x 6in Como10
3
the pressure in CRs diffusing around the shock leads to the formation of a
precursor which slows down the incoming fluid and tends to make the shock
weaker while, on the other hand, the pressure in the shape of self-generated
magnetic turbulence may become comparable to, or even larger than, the
gas pressure upstream, preventing an excessive modification of the velocity
profile. This magnetic feedback13has proved itself to be a very common
mechanism able to account, at the same time, for both the level of mag-
netization and the hydrodynamics inferred by multi-wavelength studies of
young SNRs.4In addition, when the velocity of the scattering centres, which
we assume to be transverse Alfv´ en waves as predicted by the quasi-linear
theory of resonant streaming instability, becomes a non-negligible fraction
of the fluid velocity, the compression ratios actually felt by the fluid and
by the accelerated particles are no longer the same. A physically motivated
account for the relative velocity between the fluid and the waves leads to
conclude that the more efficient the magnetic field amplification (the larger
the Alfv´ en velocity) is, the steeper the spectra of the accelerated particles
are (see e.g. §7 of Ref. 5).
2. Particle escape from SNRs
In order to explain the observations at Earth, one has to account for when
and how accelerated particles leave the source and become CRs. There
are three main mechanisms playing a potential role in the problem: escape
from upstream, escape from downstream and release at the “death” of the
remnant (after having undergone adiabatic losses). In general, the total CR
flux provided by a single source is given by the convolution over its life of
these three contributions. Let us discuss them in some more detail.
During the ejecta-dominated stage the shock velocity Vsh is roughly
constant: the magnetic field is expected to increase, in turn leading to more
and more energetic particles. In such a situation no particle can diffuse away
from upstream. During the Sedov-Taylor stage, instead, both the shock ve-
locity and the magnetization level decrease: the diffusion length increases
as 1/Vsh∝ t3/5and hence the highest-energy particles are no longer able
to make it back to the shock, since it moves as Rsh∝ t2/5.14Quantitatively
speaking, we assume that at any moment the system can confine only par-
ticles with diffusion length D(E,δB)/Vsh≤ χRsh, where D(E,δB) is the
Bohm diffusion coefficient in the amplified field δB, by imposing the distri-
bution function of the accelerated particles to vanish for radii larger than
(1 + χ)Rsh(see also Ref. 3).
Clearly, most of accelerated particles are advected behind the shock

Page 4

December 1, 2010 1:9 WSPC - Proceedings Trim Size: 9in x 6inComo10
4
and, trapped in the expanding shell, cannot do but losing energy adiabati-
cally. If, for any reason (like, for instance, the presence of strong density or
magnetic patterns in the circumstellar medium), the SNR shell were “bro-
ken”, preferential conduits might channel particles from downstream into
the Galaxy. Such a contribution is in principle very hard to model, thus we
assume that, at any given time, a 10% of the downstream accelerated parti-
cles is injected into the Galaxy, contributing to the diffuse GCRs.7Finally,
the remainder of the advected particles should be released at the “death”
of the SNRs, which is also quite difficult to define: it might coincide with
the beginning of the radiative stage, but actually it should be more closely
related to the damping of the magnetic field and hence to the transition
from a SNR-like to a Galactic-like regime for the particle diffusion.
We consider here a “benchmark” SN explosion releasing 1.4 solar masses
with total kinetic energy 1051erg in the homogeneous circumstellar environ-
ment, taken with temperature 106K and particle density ρ0= 0.01mHcm−3.
The remnant evolution is thus followed as in Ref. 6, Tab. 7, and the SNR
is imposed to die at the end of the Sedov stage. The transport in the
Galaxy is then calculated within a simple leaky-box model, assuming a
halo height of 3.5 kpc, a Galaxy radius of 10 kpc and a residence time
τesc(R) = 20(R/10GV)−0.55Myr, where R is the nucleus rigidity. When
spallation (mainly relevant at low energies and for HN) is also included,15
the spectra of the GCRs is recovered in terms of slope, normalization and
cut-off (see Figs. 3,4 in Ref. 5).
It is however worth keeping in mind that the recipe linking magnetic
field amplification and the velocity of the scattering centers is rather phe-
nomenological and it has not been thoroughly calculated from first princi-
ples, yet. Remarkably, at the moment it represents the only proposed effect
able to produce source spectra steeper than E−2(see also Ref. 16) and
therefore consistent with the inferred value of δ = 0.3 − 0.6 for the scaling
of the Galactic residence time τesc∝ E−δ. In fact, in Ref. 17 such an effect
is not included and δ = 0.75 is required to recover the GCR spectrum.
3. The role of heavy nuclei
The chemical abundances fitting the GCR data at Earth are self-
consistently put in the computational apparatus in a recursive way un-
til consistency is reached, since the non-linear nature of the acceleration
process does not allow an a priori exact determination of the proton/HN
ratios. Provided that the relative abundances do not depend on time, such
a process allow us to investigate the role of HN at any given time of the

Page 5

December 1, 2010 1:9WSPC - Proceedings Trim Size: 9in x 6in Como10
5
SNR evolution.
In the left panel of Fig. 1 a snapshot of the shock profile at the age
t = 2000 yr (beginning of the Sedov phase) is shown, in units of x0 =
χRsh ≃ 0.2Rsh, i.e. the distance of the free-escape boundary from the
shock. U(x) is the local velocity in units of Vsh, Pg(Pw) is the gas (magnetic
field) pressure and the other curves correspond to the contributions to the
pressure by accelerated particles of different species, as in the legend; all
pressures are normalized to ρ0V2
sh.
Fig. 1.
the different curves. Right panel: γ-ray spectrum from π0decay produced in nuclear
collisions, in arbitrary units. Both panels correspond to a SNR age of about 2000 yr.
Left panel: spatial profile of the modified shock. See text for the details of
It is easy to see that more than 10% of the bulk pressure is channelled
into accelerated particles, and that HN contribute as much as the protons to
the shock dynamics. Most of their contribution comes from He nuclei, but
heavier elements still account for about 25% of PALL. As outlined above, the
pressure in magnetic turbulence Pwturns out to be larger than the gas pres-
sure Pg < 10−4, and thus the precursor is dynamically dominated by the
interplay between CRs and magnetic field.4,13Moreover, since Pw∝ PALL,
we can postulate that HN play a non-negligible role also in the amplification
of the background magnetic field via streaming instability.
Another interesting consequence of the acceleration of HN is that they
may make an impact on the hadronic γ-ray emission from SNRs, i.e. the
emission due to the decay of neutral pions produced in nuclear collisions
between relativistic particles and background gas.18For distributions of
accelerated particles ∝ E−2, the contribution to the γ-ray flux by different
chemicals is simply proportional to their relative abundances (see also §5 in
Ref. 5). This means that, for the chemical composition determined above,
HN contribute in a substantial way to the γ-ray flux from a SNR (more