"Discrepant hardenings" in cosmic ray spectra: a first estimate of the effects on secondary antiproton and diffuse gamma-ray yields

0.16 MB·English

by  Fiorenza Donato

“Discrepant hardenings” in cosmic ray spectra: a first estimate of the effects on
secondary antiproton and diffuse gamma-ray yields.
Fiorenza Donato∗
Dipartimento di Fisica Teorica, Universita` di Torino and INFN–Sezione di Torino, Via P. Giuria 1, 10122 Torino, Italy
Pasquale D. Serpico†
LAPTh, UMR 5108, 9 chemin de Bellevue - BP 110, 74941 Annecy-Le-Vieux, France
Recent data from CREAM seem to confirm early suggestions that primary cosmic ray (CR)
spectra at few TeV/nucleon are harder than in the 10-100 GeV range. Also, helium and heavier
1 nuclei spectra appear systematically harder than the proton fluxes at corresponding energies. We
1 noteherethatif themeasurementsreflect intrinsicfeatures in theinterstellar fluxes(asopposed to
0 local effects) appreciable modifications are expected in thesub-TeVrange for thesecondary yields,
2 such as antiprotons and diffuse gamma-rays. Presently, the ignorance on the origin of the features
representsasystematicerrorintheextractionofastrophysicalparametersaswellasforbackground
n
estimatesforindirectdarkmattersearches. Wefindthatthespectralmodificationsareappreciable
a
J above100 GeV, and can be responsible for ∼30% effects for antiprotons at energies close to 1 TeV
orforgamma’satenergiescloseto300GeV,comparedtocurrentlyconsideredpredictionsbasedon
9
simple extrapolation of input fluxes from low energy data. Alternatively, if the feature originates
1
from local sources, uncorrelated spectral changes might show up in antiproton and high-energy

] gamma-rays, with the latter ones likely dependentfrom the line-of-sight.
E
H PACSnumbers: 98.70.Sa LAPTH-043/10
.
h
p I. INTRODUCTION TeV scale, inferring accurate spectra is challenging due
- the scarce statistics and experimental difficulties, mak-
o
ingtheaboveargumentsatbestbasedonshakyobserva-
r A more accurate determination of primary cosmic ray
t tional evidence. Also, for assessing uncertainties in sec-
s spectra at the top of the atmosphere has obvious im-
a ondary yields, the usual practice is to fit primary data
plications for the understanding of the acceleration and
[ to some power-law parameterization and extrapolate to
propagation of Galactic cosmic rays. It is also crucial
high energies. While this is a reasonable prescription
2 for other fields of investigations in astroparticle physics,
v two notable examples being atmospheric neutrino stud- for most applications given the present level of under-
9 standing, these simplified approaches and assumptions
ies (e.g. [1]) and the calculation of the backgrounds for
7 might hide a systematic error when searching for signa-
indirectdarkmatter(DM)searches(seeforexample[2]).
6 tures showing peculiar energy features. For example, for
5 Inthe specific case ofindirectDM searches,animpor-
antiprotons this is the case involving contributions from
. tant implicit assumption is that fluxes measured at the
0 DM annihilation [3] or production at the sources [4].
top of the atmosphere, at sufficiently high energies to
1
Obviously, the standard prescriptions do not usually
0 avoid solar modulation effects, are representative of in-
account for the possibility that a systematic departure
1 terstellarmedium(ISM)spectra. Or,morecorrectly,one
(rather than statisticalscattering)is presentin the spec-
: oftenassumes universalityfor the injection termandthe
v tral shape of the fitting formula, which is mostly cali-
propagation properties, fitting the free parameters (like
i
X injectionanddiffusionpower-lawindex)insuchawayto bratedonlowenergydata,neitherofthepossibilitythat
observed spectra might not be fair representative of the
r reproduce the observed spectra. It is those “universal”
a interstellarones. RecentdatafromtheCREAMballoon-
interstellar spectra which in turn enter as source termof
borne experiment [5] seem to confirm earlier suggestions
secondaryyields(likeantiprotonsordiffusegammarays)
(see e.g.[6])that cosmicrayspectra atfew TeV/nucleon
due to inelastic collisionsin the ISM. This assumption is
are harder than in the 10-100 GeV range, and that he-
usually supported by the apparent featureless nature of
lium (He) and heavier nuclei fluxes are harder than the
the observed cosmic ray fluxes (suggesting, at least in
proton (p) flux at corresponding energies. Preliminary
average, some universal mechanism for production and
data from PAMELA also suggest a hardening in p and
propagation) as well as by the check a posteriori that
Hespectraatarigidityofabout250GV,withaHespec-
the diffuse gamma-ray radiation of hadronic origin has
trum having an index ∼ 0.1 lower than the proton one
a spectrum consistent with the hypothesis, within the
overallenergiesabovea few GeV [7]. All this motivated
errors. However, especially at energies larger than the
us to have a more careful look at the errors potentially
committed when estimating secondary yields in the in-
terstellar medium.
∗Electronicaddress: [email protected] In this article, we refrain from discussing possible as-
†Electronicaddress: [email protected] trophysical interpretations of the above mentioned fea-
2
−2.74
tnuortees,haolwthevoeurghthsaotmief hthaevembeeaesnurpermopeonstesdr,esfleeect[5i,n8t]r.inWsiec φL2(T) = 5.04×103 (4T +m2He)2−m2He (4.)
properties of the interstellar spectra, appreciable mod- p !
ifications (i.e. above ∼ 10%) of very specific spectral
Thehighenergyfluxes“H”aretakenfromCREAMwith
shape are expected for the secondaryyields in the 0.1 to
the following criteria: i) power-laws in T are assumed,
1 TeV range, which is directly accessible (with growing
with the spectral indexes fixed to the best-fit values re-
precision) to present and forthcoming experiments like
portedin[5],i.e. 2.66forpand2.58forHe;ii)theproton
PAMELA, FERMI, and AMS-02. On the other hand,
spectrum normalization is taken from the first CREAM
if the hardenings reflect local phenomena/sources, sec-
point in Fig. 3 of [5]; iii) the Helium spectrum normal-
ondary yields which probe a large volume of the ISM,
izationfollowsfromimposingthatatT =9TeV/nucleon
likeantiprotons,mightnotshowrelevantdeparturesfrom
the proton to helium flux ratio is equal to 8.9 [5]. As a
naive expectations, while the diffuse gamma-rays along
result, in units of (GeV/nm2ssr)−1,
different lines of sight might reveal different hardenings
reflectingtheprimaryspectrapresentindifferentregions
φH(T) = 7.42×103T−2.66, (5)
of the ISM. Clearly, this provides an important test for 1
theories about the origin of the breaks. To the best of φH2 (T) = 4.03×102T−2.58. (6)
our knowledge, present data in high energy astrophysics
are either unrelated to the hardenings discussed here or The crossoverenergiesB1, B2 for the brokenpower-laws
aresimplyobtainedbycontinuity,andareapproximately
stilloftoolimited precisiontoprovideacrucialtest, but
the situation is likely to change in the near future. Bp = 1000GeV, BHe = 30GeV/n for the parameters
above1. A comparison with the predictions following
This article is structured as follows: in Sec. II we dis-
fromthe extrapolationofthe AMS-01 fits (i.e. the φL of
cuss the input fluxes and parameterization used to pro- i
Eqs.(3,4)) to arbitrarily high energy will be presentedto
vide a first estimate of the effect. In Sec. III we present
provideanestimateoftheimpactofhigh-energyspectral
the results for antiprotons and γ-rays, finally in Sec. IV
uncertainty on the secondary yield flux.
we discuss some implications of our findings, and con-
clude.
III. RESULTS
II. INPUT FLUXES
Discrepant hardenings of primary cosmic ray fluxes,
In the present exploratory study, we refrain from the possibly of non-universal nature, would obviously affect
ambitious goal of analyzing the whole body of cosmic all the yields of e+, p¯ and γ secondaries produced by
ray flux data in the 10−104GeV/n range. Rather we collisions in the interstellar medium (ISM). Here we do
limit ourselves to provide a first assessment of the sys- not discuss charged leptons simply because the primary
tematic effect potentially introduced by deviations from flux effects do not provide the major uncertainty in the
the power law behaviour at high energy, in general with flux shape (even fixing the average propagationparame-
different spectral indexes for different species. To this ters): very likely recent data [10–12] indicate that addi-
purpose, we explore the effects of combining the fits of tional sources of “primary” positrons exist for which the
“low-energy”(namelyintherangeabout10-100GeV/n) above mentioned effects are expected to be sub-leading
proton (i = 1) and helium (i = 2) flux data, φL, taken (seee.g.[13]). Additionally,energylossesmaketherange
i
fromAMS-01[9](inturn,tolargeextentconsistentwith shorter and the computation of the actual flux at the
what reported by other experiments), with the “high- Earth non-trivial, so it would be more difficult to dis-
energy” (above about 1 TeV/n) fluxes φH inferred by entangle the effects due to the break in primary spectra
i
CREAM [5]. We adopt broken power-laws to connect from a complicated interplay of effects involving the dis-
the two sets, using the following flux parameterizations creteness of local sources, inhomogeneities in the radia-
(differential fluxes with respectto kinetic energy per nu- tion field, etc. as illustrated for instance in [14]. The
cleon T): effect of universal primary CR hardening should be ap-
preciable in the predicted shape of the antiprotonor dif-
φ1(T) = φL1(T)Θ(B1−T)+φH1 (T)Θ(T −B1), (1) fuse gamma-ray signal. Here we report a careful com-
φ2(T) = φL2(T)Θ(B2−T)+φH2 (T)Θ(T −B2). (2) putationof the effect onthe antiprotonspectrum, where
the impactis expectedto be thelargestinviewoffuture
Thefluxes“L”arethebestfitvaluestakenfromAMS- high-statistics results from AMS-02, and an estimate of
01 [9], rewritten in terms of kinetic energy T per nu-
cleon (in GeV/n) instead of rigidity and asymptotically
decreasing as ∼T−2.78 for p and T−2.74 for He. In units
of (GeV/nm2ssr)−1, they write 1 Assumingarelativeuncertaintyinthefluxnormalizationofthe
<
two experiments of ∼20%—certainly consistent with published
φL1(T) = 1.71×104 (T +mp)2−m2p −2.78 , (3) tveanluceys—wiwthouthldersiugffiidcietyt∼o b2r5i0ngGVthehsientcerdostsoobvyerPvAaMlueEsLiAn,croenf.s[i7s-]
(cid:16)q (cid:17)
3
we plot the ratio of antiproton fluxes obtained with two
differentprimaryspectra. Thefluxatthenumeratorhas
beenobtainedwiththespectrainEqs.(1,2),whileinthe
denominator we employ the fit to AMS data arbitrarily
extrapolated to the highest energies. The modification
of the antiproton flux clearly reflects in its shape. The
effect of the hardening of primary spectra at hundreds
of GeV/n starts to be visible on the antiproton flux at
around100 GeV. It is near 15%at 200 GeV and reaches
30% at 1 TeV. Given the weak dependence of the sec-
ondary antiproton flux on the B/C selected transport
parameters, our results can be considered nearly inde-
pendent of the propagation model. If the hardening of
primarynucleiwillbeconfirmedathighenergies,aspec-
tral distortion of the secondary antiproton flux has to
be expected. This effect could be potentially observable
by a future high precision space-based mission, such as
FIG.1: Ratioofantiprotonfluxesfrom hardsources(Eqs.(1,
AMS-02.
2)) to the same flux obtained with p and He extrapolated
from AMS data to all energies (see text for details).
B. Effects on hadronic diffuse gamma-rays.
theeffectonthehadronicgamma-raydiffusebackground,
of some interest for the interpretation of FERMI data. The cosmic gamma ray flux observed in our Galaxy
is expected to be mainly due to the inelastic scattering
of incoming CRs on the nuclei of the ISM. The involved
A. Effects on secondary antiprotons. hadronic reactions produce gamma rays mostly via π0
decays. In addition to this hadronic component, other
contributionsareexpected—atdifferentlevelsdepending
Thecomputationofthesecondaryp¯fluxhasbeenper-
on the specific model— to Inverse Compton and brems-
formed as described in Refs. [2, 3], to which we refer
strahlungradiation. Thebasicmodelsfortheproduction
for all the details. The only component which we will
of gamma rays from π0 decays, considered for example
modify in the present calculation is the input p and He
by the Fermi-LAT Collaboration [16], do not introduce
spectra. We briefly remind that secondary p¯are yielded
by the spallation of cosmic ray proton and helium nu- high-energy spectral breaks in the proton spectrum φ1,
and account for nuclear effects (both in CR spectra and
clei over the H and He nuclei in the ISM, the contribu-
in target composition) in the π0 yield simply by rescal-
tion of heavier nuclei being negligible. The framework
ing the pp production via a constant “nuclear enhance-
used to calculate the antiproton flux is a two–zone dif-
ment factor”, taken from the value at the reference en-
fusion model with convection and reacceleration,as well
ergy T ≡10 GeV/n reported in [17]. This enhancement
as spallations on the ISM, electromagnetic energy losses ∗
encodes the relative yield of gamma-rays from nucleus-p
and the so–called tertiary component, corresponding to
and nucleus-Helium collisions compared with that from
non–annihilating inelastic scatterings on the ISM. The
p-p collisions via appropriate factors m , m , basically
relevant transport parameters are constrained from the ip iα
constant at T > 10GeV/n (the effects discussed in this
boron-to-carbon (B/C) analysis [15] and correspond to:
paper are only relevant at high energy, so it’s enough to
i) the half thickness of the diffusive halo of the Galaxy
focusonquantitiesatT >10GeV/n). Thisenhancement
L; ii) the normalization of the diffusion coefficient K0
and its slope δ (K(E)=K0βRδ); iii) the velocity of the is defined as
cV~ocn=sta±nVtcwe~zin;danddireivct)etdhpeerrepaecncdeilceuralatirotnoitnhteengsaitlayctpiacrdaimsk- ǫM(T)= mi1φφ1i((TT)) + mi2φφ1i((TT)) × 1−r r , (7)
i i
eterized by the the Alfv´enic speed V . The above pa- X X
a
rameters show significant degeneracies when confronted where the index i runs over all CR species (including
to B/C data [15]. Nevertheless, the impact on the sec- protons, i = 1), r ≃ 0.096 is the He/H fraction in the
ondary p¯ flux is marginal [2]. The fluxes presented be- ISM and φi being the CR spectrum of the species i. If
low have been obtained for the B/C best fit propagation allthenucleihaveroughlyidenticalT dependenceoftheir
parameters, i.e. L = 4 kpc, K0 = 0.0112 kpc2Myr−1, spectra, as suggested in [5], one can write
δ =0.7, V =12. km s−1 and V =52.9 km s−1 [15].
c a m12r m22r φ2 φN
We are interested in the effect of primary p and He ǫM(T)=1+ 1−r + m21+ 1−r φ1+kN φ1 , (8)
hardening at high energies on the p¯ flux and therefore (cid:18) (cid:19)
concentrate onthe relativeshape effect throughantipro- where φ (T) is any nuclear-like CR flux, and k is a
N N
ton flux ratios. Our results are reported in Fig. 1, where normalization factor. In Fig. 2 we show ǫM(T) for three
4
1.50
Naive Naive
2.20 He break 1.40 p break
All p+He break
All
1.30
u.]
a.
εM2.00 φ [γ 1.20
2.78 Eγ 1.10
1.00
1.80
0.90
10.0 100.0 1000.0 10.0 100.0
T [GeV/n] E [GeV]
γ
FIG. 2: Enhancement factor, see Eqs. (7,8), for the three FIG.3: γ-rayspectrum: thestandarddeparturefromequality
representative cases described in Sec. IIIB. of power-law with parent flux (dot-dashed, black), of adding
the hardening in the p spectrum at TeV scale as suggested
by CREAM (long-dashed, purple), of assuming the CREAM
hardening for both p and He (short-dashed, blue), and of in-
cases: i) the constant value ǫM = 1.84, adopted for ex-
cluding the small effect of other nuclei as well (solid, red).
ample in [16] (long-dashed,black); ii) the fluxes ofp and
He are set to the broken power-law functions described
above, while the last term kNφN/φ1 is taken constant
in energyandfixedso thatǫM(T∗)=1.84(short-dashed, bluecurve);overall,thespectrumaround300GeVis30%
blue). iii) As in ii) for p and He, but assuming for nu- higher with respect to naive expectations.
clei heavier than He a constant contribution to ǫ below
Theeffectdiscussedhereisalready“anestimate ofer-
200GeV/n (so that ǫM(T∗) = 1.84), then rising as T0.1, ror”: assessing the error on this quantity goes beyond
as suggested by CREAM data (solid, red).
our purpose. However, we can safely conclude that our
In Fig. 3, we show the result of computing the diffuse results are not significantly affected by the statistical er-
gamma ray spectrum (via the kernel provided in [18]2) rorswithwhichthenormalizationsorspectralindicesare
using the AMS-01 spectral fits φLi , extrapolated to arbi- known. We have checkedthis explicitly as follows: while
trarily high energy (long-dashed, black curve). The flux keepingtheHeliumfluxesatlowandhighenergiesatthe
has been multiplied by Eγ2.78 to underline the departure valuesdescribedabove,wehavevariedthenormalization
fromidenticalpower-lawbehaviourbetweenphotonsand ofthe p fluxes atlow/highenergyinsucha waythat the
parent CR due to production cross section/multiplicity p to He ration varies within ±1 (i.e. twice the statistical
effects. Instead, if one keeps ǫM = 1.84, but introduces error) of 18.8 at 100 GeV/nucleon [9], and within ±0.6
the broken power-law spectrum for the protons only as of 8.9 at 9 TeV/nucleon [5]. The resulting variations in
from Eq. (1), around 300 GeV one would obtain ∼ 10% the shape of secondary radiation are negligible (i.e. at
higher gamma fluxes, as shown by the long-dashed, pur- mostat a few percent level). This is due to the fact that
ple curve in Fig. 3. This case is introduced in order to the (relativelysmall)effect ofpflux renormalizationand
gaugevisuallytheeffectofthebreakof2.78−2.66≃0.12 the change in ǫM anti-correlate, and tend to cancel each
in the spectral index, between AMS and CREAM de- other. Onthe otherhand,theexactvalueofthespectral
termination of proton spectra (to be compared with the hardening is more important: Fig. 3 shows that more
∼ 0.01 and 0.02 fit errors, respectively, reported by the than 1/3 of the hardening is due to the assumed “best
experiments). The solid, red curve shows the effect of fit” spectral index difference of ±0.12 between low and
“discrepant hardenings” of the spectra, namely the T highenergy. Thisshouldbecomparedwiththestatistical
dependence of ǫM. This constitutes the major distortion errors of about ∼ ±0.01 and ±0.02 quoted by the AMS
and is mostly due to He (as shown by the short-dashed, and CREAM collaborations,respectively.
IV. DISCUSSION AND CONCLUSIONS
2 Notethatweareonlyinterestedintheeffectsthatdifferenthigh-
energy CR spectra have on the gamma-ray spectrum at Eγ ≫
In this article we have argued that departure at high
1GeV,sothesimplifiedformalismpresentedin[18]andvalidin
thehigh-energyregimeissufficientforourpurposes. energyfromasimpleanduniversalpower-lawforallcos-
5
micrayspectra,assuggestedbyrecentdata,shouldcause phenomena, should they be detected.
a spectral distortion in the spectra of secondary cosmic Even in a conservative scenario, the detection of such
ray yields (like diffuse photons and antiprotons) com- spectral signatures in secondary channels would provide
pared to the predictions obtained extrapolating the best awaytocheckthe interstellar natureofthe spectralfea-
fits to low-energy data sets. We have illustrated this ef- turesinthecosmicrayfluxattheEarthsuggestedbythe
fectusingthebestfitresultsofAMS-01dataatlowener- presentexperiments. Webelievethatsecondariesprovide
giesandthe CREAMdataathigh-energy,findingeffects an important handle for an empirical cross-check. One
exceeding10%above∼100GeV,andreachingabout30% shouldalsoconsiderthepartialdegeneracyofsucheffects
for photons around 300 GeV and for p¯close to TeV en- with the extraction of propagation parameters, in order
ergy; this figure is somewhat sensitive to the systematic to fully exploit the statistical power of forthcoming data
erroronthespectralindexathighenergyaswellasother sets. Knowing better the primary flux shapes would al-
eventualsystematics whichdo notcanceloutin ratiosof low one to set strategies minimizing these effects. Last
species(likep/He). Ifthehardeninginnucleidatawould but not least, a multi-messenger approach would allow
be due to local effect and not representative of the ISM onetodisentanglethesefeaturesfromalternativesources
average, the effect on the antiproton yield may be small of spectral distortions: features similar to the ones dis-
whilethe hadronicdiffuse gamma-rayspectrumcouldbe cussed in this article arise e.g. in models where high en-
modified differently according to the line-of-sight. No- ergy p¯are produced in sources [4], but in that case also
tice that the effect of a possible harder nuclear spectra associatedsignaturesinsecondary/primary“metals”[24]
on atmospheric neutrinos was already estimated in [1]. (andpossiblyinhighenergyneutrinos[25])areexpected,
Onemightwonderhowrelevantis ahigh-energyeffect which are absent for the process described here.
of a few tens of percent in a field where data are usu- While we are entering a much higher precision era
ally plagued by larger errors. We think that, at present, in cosmic ray studies, it is important to keep in mind
this level of accuracy is becoming crucial for at least a a couple of points: i) that multi-messenger and multi-
couple of reasons: First, space experiments like FERMI channel analyses are mandatory, if one is to gain some
or the future AMS-02 [19] are introducing us to a new deeper knowledge of cosmic ray astrophysics. ii) That
era of large exposures,which can revealmore subtle fea- any hope for the detection of new physics (not to speak
tures than previous cosmic ray or gamma-ray experi- of extracting new physics parameters) requires a more
ments. Fermi data errors at Eγ ≃ 100GeV are already robust understanding of the possible range of astrophys-
∼±20%[20],andforecaststhathavebeenpresentedsug- ical yields. In that respect, a natural development of
gest that AMS-02 (if performing close to specifications) this initial investigation would be to (re)assess how the
willbecertainlysensitivetoeffectsofthismagnitude,see errors on primary flux knowledge map into the predic-
for example [21]. Second, both diffuse gamma-rays [22] tions for secondaries (including their normalization), as
andthecombinationofhadronicdata[23]areconsistent, muchaspossibleinaparameterization-independentway.
at least at leading order, with a “standard” scenario for
the production and propagation of cosmic rays in the
Galaxy. It is very likely that any departure from base-
linemodels,ifdetectable,isgoingtobepresentatsucha
Acknowledgments
sub-leadinglevel. Modellingthustheastrophysicalback-
ground for indirect DM searches as a simple power law,
as often done in the literature, might lead to wrong con- We warmly acknowledge David Maurin for the agree-
clusions about the evidence of a signal, or to a bias in ment to use the USINE code for the calculation of the
the inferred values of the parameters describing the new antiproton flux.
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