Young and massive stellar clusters are a promising source class for the acceleration of galactic cosmic rays to PeV energies. Supernova explosions of massive stars lead to semi-continuous injection of cosmic rays into the cluster environment. Collective stellar winds form a wind-blown bubble with a termination shock at which further particle acceleration may occur. Interactions of such energetic hadronic particles with target material - such as molecular clouds - will generate signature gamma-ray and neutrino emission. We apply a model of cosmic ray acceleration in stellar clusters to catalogues of known stellar clusters, identifying the most promising targets to search for evidence of PeVatron activity. Predictions for the secondary fluxes of gamma-ray and neutrino emission are derived based on particle acceleration at the collective wind termination shock. Our results are compared to data available from the H.E.S.S. Galactic Plane Survey, and we estimate the detection prospects for current and future generation neutrino experiments

A. M. W. Mitchell

A. Specovius

G. Morlino

S. Celli

S. Menchiari

English

Archivio della ricerca- Università di Roma La Sapienza

PoS(ICRC2023)611Searching for evidence of PeVatron activity from stellarclusters via gamma-ray and neutrino signaturesA. M. W. Mitchell,𝑎,∗ S. Celli,𝑏,𝑐,𝑑 A. Specovius,𝑎 G. Morlino𝑒 and S. Menchiari𝑒, 𝑓𝑎Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen Centre for Astroparticle PhysicsNikolaus-Fiebiger-Str. 2, 91058 Erlangen, Germany𝑏Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy𝑐Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Piazzale Aldo Moro 5, 00185, Rome, Italy𝑑Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Roma,Monte Porzio Catone, Rome, Italy𝑒Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Arcetri,L.go E. Fermi 5, Firenze, Italy𝑓 INFN - Sezione di Pisa, Edificio C – Polo Fibonacci Largo B. Pontecorvo, 3 – 56127 PisaE-mail: alison.mw.mitchell@fau.deYoung and massive stellar clusters are a promising source class for the acceleration of galacticcosmic rays to PeV energies. Supernova explosions of massive stars lead to semi-continuousinjection of cosmic rays into the cluster environment. Collective stellar winds form a wind-blownbubble with a termination shock at which further particle acceleration may occur. Interactions ofsuch energetic hadronic particles with target material - such as molecular clouds - will generatesignature gamma-ray and neutrino emission. We apply a model of cosmic ray acceleration instellar clusters to catalogues of known stellar clusters, identifying the most promising targets tosearch for evidence of PeVatron activity. Predictions for the secondary fluxes of gamma-ray andneutrino emission are derived based on particle acceleration at the collective wind terminationshock. Our results are compared to data available from the H.E.S.S. Galactic Plane Survey, andwe estimate the detection prospects for current and future generation neutrino experiments.38th International Cosmic Ray Conference (ICRC2023)26 July - 3 August, 2023Nagoya, Japan∗Speaker© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. Mitchell1. IntroductionIn recent years, very-high-energy (𝐸 > 100 GeV) 𝛾-ray astronomy has begun detecting sourcesreaching 𝛾-ray energies above 100 TeV [1]. Whether produced through hadronic mechanisms suchas neutral pion-decay or leptonic mechanisms such as inverse Compton scattering, the parent particlepopulation must have energies ≳ 1 PeV. This implies that the astrophysical particle accelerators are‘PeVatrons’, the long sought-after sources responsible for Cosmic Rays (CRs) up to and beyond theso-called ‘knee’ feature occurring in the CR spectrum at ∼ 3 PeV. Whilst supernova remnants havelong been considered prime PeVatron candidates, due to theoretical and observational difficultiesin reconciling such a scenario, attention has recently turned to other candidate source classes, suchas stellar clusters.Young stellar clusters drive a collective wind into the surrounding medium, producing a WindTermination Shock at which particle acceleration can occur. Beyond this distance, a wind blownbubble further expands into the surrounding interstellar medium, a scenario depicted schematicallyin figure 1. In this work, we use the model of [2] to predict the expected 𝛾-ray (and neutrino)emission from the wind-blown bubble associated with stellar clusters. We investigate how theexpected spectral energy distributions depend on properties of the stellar cluster, subsequentlyapplying the model to known stellar clusters as listed in either the Milky Way Stellar Cluster(MWSC) catalogue, or the open cluster sample from the Gaia DR2 [3, 4]. The systems with thehighest predicted energy flux are then listed in ranked order and compared to available data, togenerate a list of possible PeVatron candidates. Such a target list can be used to motivate futureobservations, to either constrain or verify the predictions of this model.2. Properties of Stellar ClustersA stellar cluster of radius 𝑅𝑐 is thought to drive a wind into the surrounding ISM of density 𝜌,resulting in both a termination shock of the cluster wind with radius 𝑅𝑠 and a forward shock of thewind-blown bubble with radius 𝑅𝑏. These are expected to depend on the age of the stellar cluster 𝑡and the wind luminosity of the cluster, 𝐿w,c = 12 ¤𝑀c𝑣2w,c, which is determined by the mass-loss rate¤𝑀c and wind speed 𝑣w,c. Expressions for 𝑅𝑠 and 𝑅𝑏 are given by equations (1) and (2) respectively.𝑅𝑠 (𝑡) =48.6( 𝜌cm−3)−0.3 ( ¤𝑀c10−4M⊙yr−1)0.3 (𝑣w,c1000 km s−1)0.1 (𝑡10 Myr)0.4pc (1)𝑅𝑏 (𝑡) = 174( 𝜌cm−3)−0.2 ( 𝐿w,c1037 erg s−1)0.2 (𝑡10 Myr)0.6pc (2)The cold wind region between 𝑅𝑐 and 𝑅𝑠 is expected to have a constant wind velocity 𝑢1, whereasin the shocked wind region between 𝑅𝑠 and 𝑅𝑏 the velocity is expected to drop ∝ 𝑟2. At the windtermination shock, the velocity becomes suppressed by a factor 𝜎 such that 𝑢2 = 𝑢1/𝜎. The fullradial dependence of the cluster wind velocity is:𝑢(𝑟) =𝑢1 𝑟 < 𝑅𝑠𝑢2(𝑅𝑠𝑟)2𝑅𝑠 < 𝑟 < 𝑅𝑏0 𝑟 > 𝑅𝑏(3)2PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellFigure 1: Schematic of the wind-blown bubble formed around a young stellar cluster, based on [2]. Subscripts1, 2 and 3 refer to the cold wind, shocked wind and interstellar medium regions respectively.Within the wind region, the density drops as 𝑛𝑤 ∝ 𝑟2, whereas within the bubble, the density 𝑛𝑏 isassumed constant and can be obtained from the mass-loss rate and the cluster age. To derive 𝑛𝑏,the total mass output by the cluster to date ¤𝑀𝑐𝑡, is assumed to be uniformly distributed throughoutthe bubble volume, 43𝜋(𝑅3𝑏− 𝑅3𝑠).Corresponding to these regions with distinct properties, we use diffusion coefficients 𝐷1, 𝐷2and 𝐷3 for the cold wind region, the shocked wind (bubble) and the ISM respectively.3. Particle acceleration at the stellar cluster wind termination shockParticle acceleration occurs at the wind termination shock, such that the particle distributionfunction 𝑓2(𝑟, 𝑝) as a function of distance 𝑟 and particle momentum 𝑝 is:𝑓2(𝑟, 𝑝) = 𝑓𝑠 (𝑝)𝑒𝛼(𝑟 )1 + 𝛽(𝑒𝛼(𝑅𝑏 )𝑒−𝛼(𝑟 ) − 1)1 + 𝛽(𝑒𝛼(𝑅𝑏 ) − 1)+ 𝑓Gal(𝑝)𝛽(𝑒𝛼(𝑟 ) − 1)1 + 𝛽(𝑒𝛼(𝑅𝑏 ) − 1)(4)where 𝑓Gal(𝑝) takes the Galactic sea of cosmic rays into account in the overall particle distributionfunction within the bubble. The functions 𝛼(𝑟, 𝑝) and 𝛽(𝑝) are:𝛼(𝑟, 𝑝) = 𝑢2𝑅𝑠𝐷2(𝑝)(1 − 𝑅𝑠𝑟); 𝛽(𝑝) = 𝐷3(𝑝)𝑅𝑏𝑢2𝑅2𝑠(5)and 𝑓𝑠 (𝑝) is the particle distribution at the termination shock:𝑓𝑠 (𝑝) =𝜒CR2𝜎𝑛1𝑢214𝜋Λ𝑝 (𝑚𝑝𝑐)3𝑐2(𝑝𝑚𝑝𝑐)−𝑠𝑒−Γ (𝑝) , (6)where 𝜒cr is the CR acceleration efficiency, 𝑛1 the wind numerical density, 𝑚𝑝 the proton mass,𝑠 = 4 the spectral slope of acceleration, and Λ𝑝 a normalisation constant. By fitting the pure3PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellFigure 2: Particle distribution function of the stellar cluster wind. Left: the ratio of the particle distributionat a given energy to that at the wind termination shock 𝑅𝑠 , as a function of distance from the shock. Right:the particle energy flux as a function of energy at 𝑅𝑠 and just prior to 𝑅𝑠 , compared to that for the sea ofgalactic CRs 𝑓gal .Figure 3: Left: 𝛾-ray energy flux from different components of the stellar cluster environment. Due to thehigher average density, the bubble dominates over the cold wind region. Right: Energy flux of secondariesproduced via hadronic interactions.exponential part of the solution with the following analytical expression:exp−Γ (𝑝) = (1 + 𝐴(𝑝/𝑝𝑚)𝑏) exp−𝑘 (𝑝/𝑝𝑚 )𝑐, (7)we derive 𝑘 = 12.52, 𝐴 = 5, 𝑏 = 0.448549 and 𝑐 = 0.064266 for a Kraichnan-like diffusioncoefficient, i.e. 𝐷1 = 𝑣3 𝑟1/3𝐿𝐿2/3𝑐 ≡ 𝑘1𝑝 𝛿1 with 𝛿1 = 0.5, 𝑣 the particle velocity, 𝑟𝐿 its Larmor radius,and 𝐿𝑐 ≃ 2 pc the coherence length of the magnetic field. Finally, 𝑝𝑚 can be obtained from thecondition 𝐷1 = 𝑢1𝑅𝑠.Figure 2 shows how the particle distribution function varies with distance and energy, where theratio 𝑓 (𝑟, 𝑝)/ 𝑓 (𝑅𝑠, 𝑝) is set equal to unity at 𝑅𝑠. Within the bubble region, the particle distributiondrops off more rapidly with distance for higher energies, and more slowly at lower energies. Asa function of energy, the particle distribution at 𝑅𝑠 provides the peak of the particle accelerationprocess.4PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellFigure 4: Variation in 𝛾-ray energy flux with properties of the stellar cluster wind. Left: variation withmass-loss rate. Right: variation with wind velocity.Figure 3 shows that as a consequence of the radial density profile of the cluster environment,the bubble region dominates the 𝛾-ray emission from hadronic particles accelerated in the clusterwind. The average ambient density within the wind-blown bubble is assumed to be provided byan isotropic distribution of the integrated mass lost via the wind over the age of the stellar cluster.Hence, the contribution of the wind region to the total 𝛾-ray flux is negligible. The energy flux ofsecondaries (neutrinos, gamma-rays) from the same parent particle population has a consistent shapeover the energy range as also shown in Figure 3, where the muon neutrino flux is approximatelyone third of the all flavour neutrino flux [5].4. Dependence of emission on stellar cluster propertiesFrom the particle distribution functions given in equations (4) and (6), we obtain the 𝛾-rayflux Φ𝛾 produced as these energetic particles interact with target material in the bubble region (ofdensity 𝑛𝑏). Following the prescription of Kelner et al. [6]:Φ𝛾 (𝐸𝛾 , 𝑅′, 𝑡′) = 𝑐𝑛∫ ∞𝐸𝛾𝜎inel(𝐸) 𝑓 (𝐸, 𝑅′, 𝑡′)𝐹𝛾(𝐸𝛾𝐸, 𝐸)𝑑𝐸𝐸, (8)where we use the parameterisation of [7] for the inelastic cross-section 𝜎inel(𝐸) for proton-protoninteractions. Analogous expressions to (8) apply to evaluate the expected neutrino flux Φa , using𝐹a(𝐸a𝐸, 𝐸)in place of 𝐹𝛾 . Over long distances (≳ pc) the neutrino oscillation probabilities averageto a constant, such that the flux of muon neutrinos is approximately one third that of the all-flavour neutrino flux [5]. Muon neutrinos are of particular interest, as they are the neutrino specieswhich is most easily detected by modern neutrino experiments and with the most accurate directionreconstruction. Figure 3 shows the energy fluxes of secondaries (𝛾, a and a`) for a given (canonical)set of stellar cluster properties.Figure 4 illustrates how the energy flux varies with mass-loss rate and wind velocity. Asexpected, both increasing ¤𝑀𝑐 and increasing 𝑣𝑤,𝑐 - corresponding to the wind luminosity - yieldlarger resulting 𝛾-ray fluxes. With this model, we can determine which combination of propertieswill yield the most promising stellar cluster targets for detection by current and future experiments.5PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellCluster GLON GLAT Age Distance 𝑅𝑠 𝑅𝑏 𝑅𝑏(◦) (◦) (Myr) (kpc) (pc) (pc) (◦)1 Danks 2 305.390 0.089 2.0 2.2 45.8 181 4.632 NGC 3603 291.624 -0.518 1.0 7.2 32.5 115 0.923 Danks 1 305.342 0.074 1.0 1.9 31.6 113 3.454 Juchert 3 40.354 -0.701 1.0 1.5 25.7 98 3.805 DC 5 286.795 -0.502 1.1 4.4 25.9 103 1.336 Berkeley 59 118.230 5.019 1.3 1.0 24.5 103 5.877 NGC 6357 353.166 0.890 1.0 1.8 22.6 90 2.928 NGC 6611 16.962 0.811 2.1 1.6 28.5 134 4.669 Andrews Lindsay 5 27.733 -0.667 1.0 2.3 20.7 85 2.1410 UBC 344 18.354 1.820 3.5 1.9 30.3 159 4.74Table 1: Properties of the stellar clusters with the brightest predicted emission (integrated over the wind-blown bubble) in ranked order.5. Predictions for emission from known stellar clustersTo obtain predictions for specific stellar clusters, we use the Milky Way Stellar Cluster (MWSC)catalogue and the open cluster sample from Gaia data release 2 [3, 4]. The energetics of stellarclusters are dominated by winds only within approximately the first 3 Myr, thereafter supernovaremnant shocks start to contribute. Beyond ages of ∼ 10 Myr, the cluster energetics can no longer beconsidered to be dominated by winds. Therefore, we applied selection criteria to the stellar clustersfor which we evaluated the predicted 𝛾-ray (and neutrino) energy flux. We required the clusters tobe young, with an age < 10 Myr; to be compact, with a core radius (50% containment) less thanthe radius of the wind termination shock; and to have a reported effective temperature available,ensuring that a sufficient proportion of the member stars have been sampled by the respectivecatalogue.For each stellar cluster in the selected sample, the required free parameters of the model (𝑡, ¤𝑀 ,𝑣𝑤 and 𝑛𝑏) could be either obtained directly from the catalogues or derived from known quantities.1This enabled the expected 𝛾-ray emission to be evaluated using the model outlined above, togetherwith the calculation of the expected 𝑅𝑠 and 𝑅𝑏 (see equations (1) and (2)). We sort the clustersaccording to the integral of the predicted 𝛾-ray flux over the wind blown bubble and list the brightestten in Tables 1 and 2. The corresponding spectral energy distributions are shown in figure 5.Table 1 provides properties of these brightest ten clusters, amongst which the oldest (in tenthplace) is UBC 344 with an age of 3.5 Myr, whilst all others are young with ages ≲ 2.1 Myr. Thewind termination shock radii are typically a few tens of pc, whilst the radii of the wind-blownbubbles are around 100 − 200 pc, which - at distances ≤ 5 kpc, correspond to angular diameters ofup to ∼ 10◦ on the sky.The spectral energy distributions for the ten clusters with the highest integrated energy fluxabove 1 TeV are shown in figure 5. It should be noted that given our model, the ranked order interms of energy flux also corresponds to the ranked order in terms of the maximum energy. This1Full details will be given in a forthcoming publication6PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellFigure 5: Stellar clusters with the brightest predicted 𝛾-ray flux according to this model, integrated over thebubble region.Cluster 𝐹𝛾 (> 1 TeV) 𝐹ul𝛾 (> 1 TeV) Emax(TeV cm−2 s−1) (TeV cm−2 s−1) (PeV)1 Danks 2 8.497e-11 1.217e-12 4.99982 NGC 3603 4.563e-11 2.446e-12 3.36123 Danks 1 3.887e-11 1.255e-12 3.11184 Juchert 3 1.208e-11 8.298e-12 1.79785 DC 5 1.02e-11 3.553e-12 1.69566 Berkeley 59 5.903e-12 – 1.34977 NGC 6357 5.669e-12 3.734e-12 1.27668 NGC 6611 4.822e-12 2.376e-12 1.30339 Andrews Lindsay 5 3.369e-12 3.063e-12 1.014610 UBC 344 2.021e-12 2.33e-12 0.8983Table 2: Stellar clusters with the brightest predicted gamma-ray fluxes integrated above 1 TeV and properties,together with upper limits from the HGPS where available, corresponding to an angular size of 0.6◦. Gamma-ray spectral energy distributions for the 10 brightest clusters are depicted in figure 5 [8].can be seen in figure 5 and values for the maximum achievable energy, Emax are given in table 2.Despite all listed clusters achieving an Emax ≳ 1 PeV, this is likely an overestimate as the influenceof magnetic turbulence on the diffusion has not been taken into account, which would reduce Emax.Table 2 also provides the total integrated 𝐹𝛾 above 1 TeV over the whole wind-blown bubble,together with an upper limit extracted from the H.E.S.S. Galactic Plane Survey (HGPS) at thelocation of the stellar cluster yet with a radius of 0.6◦. This is the largest angular radius out towhich the HGPS data can be considered valid for the analysis of extended regions. Whilst in severalcases the upper limits are lower than the predicted fluxes, due to the integration over the full bubbleregion (see Table 1) the surface brightness of these clusters will be much lower over an angular sizeof 0.6◦.7PoS(ICRC2023)611Stellar Clusters as PeVatrons A. M. W. MitchellThe presence of target material such as molecular clouds in the vicinity of such an energeticparticle population may act to enhance the detectable gamma-ray flux. Corresponding predictions,based on this model together with that of [9] and catalogues of known molecular clouds are givenin a companion proceedings [10].6. ConclusionsSeveral stellar clusters are predicted to have properties of PeVatrons according to the modelapplied in this study. Whilst the maximum energy achieved is likely a generous over-estimate, thepredicted energy fluxes and 𝐸max are promising for future observations. Nevertheless, the predictedemission is integrated over the wind-blown bubble, that may occupy a large region of space suchthat the surface brightness will be correspondingly reduced.The detection of 𝛾-ray emission from stellar cluster bubbles with angular sizes of the order of∼ 6◦ − 10◦ will be challenging for Imaging Atmospheric Cherenkov Telescopes due to their limitedfield-of-view, however may be nevertheless detectable in suitably obtained survey datasets, and/orby virtue of the surface brightness profile, which will likely peak towards the wind terminationshock (at much smaller radii than 𝑅𝑏). Survey instruments such as HAWC, LHAASO or the futureSWGO are however well-suited to search for and study such extended sources. For the unambiguousdetection of emission from bubble regions and association to stellar clusters, a robust treatment ofsource confusion effects and 3D analysis approaches will be of paramount importance.Due to the hadronic processes, cluster environments producing bright 𝛾-ray emission are alsopredicted to be strong neutrino emitters. Here, the large angular size of bubbles, may be beneficial,compared to the PSF of current and future generation neutrino instruments.7. AcknowledgementsAM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foun-dation) – Project Number 452934793. SC gratefully acknowledges the support from SapienzaUniversità di Roma through the grant ID RG12117A87956C66.References[1] Z. Cao et al. [LHAASO Coll.], Nature 594 (2021) 33;[2] G. Morlino, P. Blasi, E. Peretti & P. Cristofari, MNRAS 504 (2021) 6069;[3] T. Cantat-Gaudin et al. [Gaia Coll.], A&A 640 (2020) A1;[4] R. Kharchenko et al. A&A 558 (2013) A53;[5] C. Mascaretti & F. Vissani, JCAP 08 (2019) 004;[6] S.R. Kelner, F.A. Aharonian, V.V. Bugayov, Phys.Rev.D 74, (2006) 034018;[7] E. Kafexhiu, F. Aharonian, A. M. Taylor & G. S. Vila, Phys. Rev. D 90 (2014) 123014;[8] H.E.S.S. Collaboration, A&A 612, (2018) A1;[9] A.M.W. Mitchell et al. MNRAS 503, (2021) 3522;[10] S. Celli et al. PoS(ICRC2023) 775 (2023)8

Searching for evidence of PeVatron activity from stellar clusters via gamma-ray and neutrino signatures

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Searching for evidence of PeVatron activity from stellar clusters via gamma-ray and neutrino signatures

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