MHD decomposition explains diuse -ray emission in Cygnus X Ottavio Fornieri1 2 3and Heshou Zhang1 4 5y 1Deutsches Elektronen-Synchrotron DESY Platanenallee 6 15738 Zeuthen Germany

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MHD decomposition explains diﬀuse γ-ray emission in Cygnus X

Ottavio Fornieri1, 2, 3, ∗and Heshou Zhang1, 4, 5, †

1Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany

2Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100 L’Aquila, Italy

3INFN-Laboratori Nazionali del Gran Sasso (LNGS), Via G. Acitelli 22, 67100 Assergi (AQ), Italy

4Institut f¨ur Physik und Astronomie, Universit¨at Potsdam,

Haus 28, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany.

5Istituto Nazionale di Astroﬁsica (INAF) - Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate(LC), Italy.

Cosmic-ray (CR) diﬀusion is the result of the interaction of such charged particles against magnetic

ﬂuctuations. These ﬂuctuations originate from large-scale turbulence cascading towards smaller

spatial scales, decomposed into three diﬀerent modes, as described by magneto-hydro-dynamics

(MHD) theory. As a consequence, the description of particle diﬀusion strongly depends on the model

describing the injected turbulence. Moreover, the amount of energy assigned to each of the three

modes is in general not equally divided, which implies that diﬀusion properties might be diﬀerent

from one region to another. Here, motivated by the detection of diﬀerent MHD modes inside the

Cygnus-X star-forming region, we study the 3D transport of CRs injected by two prominent sources

within a two-zone model that represents the distribution of the modes. Then, by convolving the

propagated CR-distribution with the neutral gas, we are able to explain the γ-ray diﬀuse emission

in the region, observed by the Fermi-LAT and HAWC Collaborations. Such a result represents

an important step in the long-standing problem of connecting the CR observables with the micro-

physics of particle transport.

I. INTRODUCTION

More than one hundred years after the discovery

of cosmic rays (CRs), the debate about their origin

is still largely ongoing. According to the standard

paradigm, CRs are accelerated at the shock fronts of Su-

pernova Remnants (SNRs) via diﬀusive shock accelera-

tion (DSA) [1] and then transported across our Galaxy,

undergoing all the physical processes that are eﬀectively

described by the transport equation [2]. The fact that

the bulk of CRs is originated at SNRs was ﬁrst proposed

in Baade and Zwicky [3] and since then motivated by en-

ergy considerations. In particular, comparing the power

injected by the sources of CRs in the Galaxy with that of

a typical SNR, we obtain a reasonable ∼10% eﬃciency

for the conversion of their energy budget into CRs [4].

A limitation in such a paradigm is represented by the

maximum energy Emax that CRs from SNRs can reach.

This Emax is regulated by the number of accelerating cy-

cles that particles undergo bouncing back and forth at the

shock front before escaping, and is therefore eventually

limited by the eﬃciency of conﬁnement in the region up-

stream of the shock. The excitation of resonant instabili-

ties [5] can help in this sense, but hardly allows to achieve

energies of the order ∼ O(100 TeV) [6,7]. This value,

however, needs to face the experimental evidence of an

all-particle spectrum that extends up to a few PeV’s. For

this reason, massive stellar clusters (MSCs) have been in-

voked as alternative accelerating sites for galactic CRs.

On the theory side, MSCs have been studied for this

purpose since long time ago [8]. The engine causing the

∗ottavio.fornieri@gssi.it, ORCID: 0000-0002-6095-9876

†heshou.zhang@desy.de, ORCID: 0000-0003-2840-6152

acceleration process could come from the collection of

∼ O(100) stellar winds conﬁned in the compact cluster

(Rcluster ∼1−5 pc), injecting kinetic energy at a rate

Lw∼1034 −1038 erg ·s−1[9,10], forcing charged par-

ticles to undergo multiple shocks before being released

into the Interstellar Medium (ISM). Whether this mech-

anism results in a continuous injection of particles [11] or

a burst, once the shell excavated by the winds is dissi-

pated [12], is still matter of debate, and depends on the

adopted acceleration mechanism (see Bykov et al. [13] for

a recent review on the topic). Regardless, considering all

the stars contributing to the wind luminosity across the

Galaxy, a (possibly) sizeable but not dominant contribu-

tion to the CR ﬂux at Earth could come from MSCs [10].

From the experimental point of view, the observations

of Very High Energy (VHE) (100 GeV ≤Eγ≤100 TeV)

γ-ray emission in compact star clusters — such as West-

erlund 1 [14], Westerlund 2 [15] and the Cygnus-X star-

forming region [9,16] — have been interpreted as sig-

natures of local PeV accelerators. Since they are com-

patible with the decay of neutral pions originated by the

scattering of CR-hadrons oﬀ the molecular clouds — this

process generates photons with energy hEγi ' 0.1ECR

— these ﬁndings have opened the way in the search for

PeV accelerators, the so-called PeVatrons. Among the

above-mentioned observations, the cocoon at the center

of the Cygnus-X region has recently received much at-

tention in a broader multi-messenger sense. In fact, the

LHAASO [17] Collaboration reported the 7σ-detection of

∼530 photons with Eγ≥100 TeV from twelve regions

with overlapping known sources, including the Cygnus

cocoon, where the highest-energy event (Emax

γ'1.4 PeV)

was originated. Similarly, Tibet-ASγ[18] reports 10 γ-

ray events from the Galactic plane with Eγ≥398 TeV

of clear hadronic origin, 4 of which — including the one

arXiv:2210.15542v2 [astro-ph.HE] 28 Oct 2022

at the highest energy, again (Emax

γ'957 TeV) — are

coming from the Cygnus region. These observations rep-

resent the ﬁrst direct evidence that stellar clusters may

be acceleration sites for PeV CRs.

The last important piece of information comes from

the identiﬁcation, within Cygnus X, of regions where

diﬀerent magneto-hydro-dynamic (MHD) modes domi-

nate the turbulent spectrum [19]. Indeed, as it is well

known [20], after turbulence is injected, energy is trans-

ferred to smaller spatial scales, and it is decomposed

into Alv´en (incompressible), fast- and slow-magnetosonic

(compressible) modes. The amount of energy transferred

to each of these modes depends on the driving force that

turbulence experiences [21], with also the possibility of

mode mixing, in speciﬁc environments [22]. Based on the

calculation in Makwana and Yan [21] and on the anal-

ysis of the polarized synchrotron light, in Zhang et al.

[19] it is found that the turbulent energy is diﬀerently

partitioned among the modes in diﬀerent locations of the

Cygnus-X region. Since Alfv´en modes cascade anisotrop-

ically in wave number [23,24] and, consequently, are not

able to conﬁne particles below ECR ∼10 TeV [25], this

evidence has signiﬁcant implications on CR transport,

that is therefore inhomogeneous.

In this paper, we consider the Cygnus-X region and

study the detailed propagation of particles injected by

the OB2 cluster and a nearby SNR (γ-Cygni) in a two-

zone diﬀusion model, where the values of the diﬀusion

coeﬃcients are regulated by the diﬀerent MHD modes

dominating the transport. The resulting CR distribu-

tion will serve to reproduce the γ-ray morphology ob-

served in the region. The paper is organized as follows.

First, we describe the details of the model that we use in

the simulations and show the resulting CR distributions.

Then, we convolve such distributions with the neutral

gas in the molecular clouds, the targets generating the

observed γ-rays. Finally, we discuss the results and de-

rive our conclusions.

II. SIMULATION SETUP

A. Sources of CRs in the region

As mentioned in the introduction, much attention has

been given to the Cygnus-X region, especially motivated

by the possible presence of an accelerator of PeV CRs.

The invoked acceleration mechanism involves the dynam-

ics of stellar winds [8,12] driven by the presence of the

OB2 cluster, a young (tOB2

age ∼1−4 Myr) globular clus-

ter of ∼ O(100) type-O stars dominating the emission

in the region — ∼90% of the emission is estimated

to come from this association, at TeV energy as well

as in the lower Fermi domain. This region is identi-

ﬁed to be HAWC J2030+409 by the HAWC Collabora-

tion [16] and is considered to be the counterpart of the

GeV cocoon observed by Fermi [9]. Another source con-

tributes in the region to the γ-ray analysis, γ-Cygni —

2HWC J2020+403 [16] likely associated with the VER-

ITAS source VER J2019+407 [26] —, a young SNR

whose age is estimated from its internal pulsar to be

tSNR

age '77 kyr. The SNR accelerates CRs at the forward

shock and releases them into the ISM at the beginning of

the Sedov-Taylor phase (tSed ≤103yr) as a delta func-

tion in time [27]. For what concerns the star cluster, on

the other hand, the responsible acceleration mechanism

considers a reverse shock that traps particles in the inner

region for as long as ∼1 Myr, until the shock is dissipated

and CRs of all energies are released in the ISM [12]. In

what follows, we consider the physical situation where the

OB2 cluster — with Galactic coordinates (lOB2, bOB2) =

(80◦,1◦) — has an age tOB2

age = 2 Myr and it injected

particles tOB2

rel = 1.2 Myr ago. Additionally, the SNR —

with coordinates (lSNR, bSNR) = (78◦,2.3◦) — injects

particles as well after a long time, tSNR

age 'tSNR

rel = 77 kyr

ago, normalized such that nOB2nSNR = 100.

B. Transport properties

In order to reproduce the γ-ray diﬀuse emission ob-

served by Fermi-LAT [9] — in the range 1 GeV ≤Eγ≤

100 GeV — and HAWC [16] — above Eγ= 1 TeV —, we

propagate parent CRs with energies 10 GeV ≤ECR ≤

10 TeV, since we expect the main photon production to

be of hadronic origin (see details below), due to neutral

pion decay, for which hEγi ' 0.1ECR. Due to the de-

clining source spectra of the type dNCR/dE ∝E−Γinj ,

with Γinj >2, the contribution to the ﬁnal maps coming

from more energetic CRs can be considered negligible.

For what concerns the nature of the particles respon-

sible for the photon emission, there are clues pointing

towards a hadronic origin. Above the TeV scale this is

well-established, as discussed for instance in Aharonian

et al. [11], Amenomori et al. [18]. In the GeV domain the

situation is diﬀerent: the Radio and X-ray emission con-

strains the higher-energy γ-ray data to be not of leptonic

origin, as clearly shown in Abeysekara et al. [16]. It is

worth noticing however that, although this implies that

a single lepton population cannot be responsible for the

whole spectrum from Radio to γ-rays, still it cannot rule

out the possibility of an additional leptonic component

contributing below Eγ∼100 GeV and then becoming

subdominant due to the large magnetic ﬁeld in the re-

gion (see details below) and the consequent rapid loss

rates. In what follows, we investigate the hadronic sce-

nario and its implications, leaving the study of a possible

lepton contamination to a future work.

In order to propagate CR-protons in the region, we use

the ﬁndings discussed in Zhang et al. [19], in particular

regarding (i) the emerging magnetic ﬁeld directions and

(ii) the diﬀerent modes dominating diﬀerent regions in

the Cygnus-X area. (i) Regarding the former, there is

evidence for a randomly distributed direction of the total

ﬁeld Btot =B0+δB, being B0and δBthe regular and

the turbulent ﬁelds, respectively. This implies a 3D par-

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MHDdecompositionexplainsdiuse-rayemissioninCygnusXOttavioFornieri1,2,3,andHeshouZhang1,4,5,y1DeutschesElektronen-SynchrotronDESY,Platanenallee6,15738Zeuthen,Germany2GranSassoScienceInstitute,VialeFrancescoCrispi7,67100L'Aquila,Italy3INFN-LaboratoriNazionalidelGranSasso(LNGS),ViaG.Acitelli22,67100A...

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MHD decomposition explains diuse -ray emission in Cygnus X Ottavio Fornieri1 2 3and Heshou Zhang1 4 5y 1Deutsches Elektronen-Synchrotron DESY Platanenallee 6 15738 Zeuthen Germany

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