UHECR propagation from Centaurus A
Sarka Wykes, Andrew M. Taylor, Justin D. Bray, Martin J. Hardcastle, Michael Hillas
NNuclear and Particle Physics Proceedings 00 (2018) 1–8
Nuclear andParticle PhysicsProceedings
UHECR propagation from Centaurus A
Sarka Wykes a, ∗ , Andrew M. Taylor b , Justin D. Bray c , Martin J. Hardcastle d , Michael Hillas e a Department of Physics and Astronomy, University of Manitoba, Winnipeg R3T 2N2, Canada b Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin, Ireland c JBCA, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK d School of Physics, Astronomy and Mathematics, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB, UK e School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK
Abstract
In the light of the recently predicted isotopic composition of the kpc-scale jet in Centaurus A, we re-investigatewhether this source could be responsible for some of the ultra-high energy cosmic rays detected by the Pierre AugerObservatory. We find that a nearby source like Centaurus A is well motivated by the composition and spectral shape,and that such sources should start to dominate the flux above ∼ Fe energy fixed at 250 EeV, are of intermediate mass, C to O, while the best-fitting particleindex is 2 . Keywords: ultra-high energy cosmic rays, composition, galaxies: active, galaxies: individual (Centaurus A), galaxies: jets
1. Introduction
Ultra-high energy cosmic rays (UHECRs) are thehighest-energy particles found in nature. Good recentreviews are o ff ered by [28] and in the publications fromthe Cosmic ray origin – beyond the standard mod-els (these proceedings). No conclu-sive signal revealing the origin(s) of UHECRs has yetemerged.The interpretation of the Pierre Auger Observatorydata [e.g. 4, 5] strongly hints at a varying cosmic-raycomposition as a function of energy, and an Auger X max width-based study now also shows that the compositiontends towards intermediate masses [1] at the highest en-ergies, at least for the part of the sky covered by theAuger Observatory. Most recently, based on a corre-lation between the depth of shower maximum and thesignal in the water Cherenkov stations of air showers ∗ Corresponding author
Email address: [email protected] (Sarka Wykes) registered simultaneously by the fluorescence and thesurface detectors of the Auger Observatory, i.e. via amethod relatively robust to uncertainties in the hadronicmodels , [3] have shown that the observed correlation inthe energy range 3 . ∼
30 Mpc [e.g. 6, 15].A strong need for local sources of CRs around 1 EeVcomes from gamma-ray fluxes [20]. For CRs abovethese energies, the
Fermi -LAT extragalactic gamma-raybackground limits [6] demonstrate that if the EeV cos-mic rays are protons, their contribution to the extra-galactic gamma-ray background is problematic. Thegeneral requirement for relatively flat particle spectra[e.g. 11, 23, 24] is also alleviated for nearby sources.Photodisintegration of nuclei from nearby sourceswill not have a significant e ff ect – except for He andpossibly for N, O and Ne which are more fragile[e.g. 18, Section 2.4] – on a propagated spectrum, sup- a r X i v : . [ a s t r o - ph . H E ] J un . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 porting local objects as promising candidates.Of the local objects, ‘radio-loud’ active galacticnuclei (AGN) have long been considered potentialUHECR sources for their radio flux densities and di-mensions. Looking at radio flux alone to say somethingabout cosmic-ray power is probably not correct, becausewe also require physically large lobes in the model inwhich the UHECR are accelerated and confined there.[16] has investigated this issue, concluding that therewould be only ∼
20 objects within 100 Mpc distance(and thus a handful within 30 Mpc) capable of acceler-ating particles to the same energies as the radio galaxyCentaurus A. Hosted by the closest elliptical galaxy NGC 5128,Centaurus A is the nearest (3 . ± . ∼ . × − M (cid:12) yr − suggests jet deceleration on kpcscales, and a low-density ( ∼ × − cm − ) particle con-tent of the giant lobes of the radio galaxy. This materialis solar-like, with protons, He, O, C, N and Neas the principal ingredients.[29] have argued that most likely only nuclei above acharge threshold can be accelerated to ≥
55 EeV energiesin Centaurus A. The maximum Fe energy achievedin this model with final energisation by stochastic pro-cesses in the large-scale lobes translates to a proton cut-o ff energy at the source of ∼
10 EeV. Here, we followup on those studies, asking whether the input rate of theintermediate-mass nuclei can give the output in terms ofthe flux of UHECRs from Centaurus A and reproducethe spectrum measured by the Auger Observatory.The plan of the paper is as follows. In Section 2, wediscuss the overall model and the relevant astrophysi-cal parameters. In Section 3, we examine the energet-ics of the source and the fraction of the all-sky fluxwhich Centaurus A might be contributing, and lay outthe flux normalisation scheme. Section 4 is focused Although the model discussed in that work was a proton-onlyone, the conclusions should still be valid. That would only increaseCentaurus A’s dominance of the sky since many of the faint sourcesin the so far best attempt at a homogeneous all-sky radio survey [26]should not be considered as possible UHECR sources. Protons, while not a product of stellar nucleosynthesis, are themost abundant component of stellar winds by number, and in mostcases also by mass. around the composition-dependent and composition-independent spectral fits. The key findings are sum-marised in Section 5.Throughout the paper, we define the energy spectralindices α in the sense S ν ∝ ν − α and particle indices p as n ( E ) ∝ E − p .
2. Model and astrophysical inputs
We consider three stages through which particles maybe produced and energised to UH energies in Centau-rus A.Stage 1: The jet-enclosed stars in Centaurus A releasematerial, of a range of species .Stage 2: Some fraction of this material is injected intothe accelerator. This fraction is species-dependent .Stage 3: The injected material is accelerated. Thisprocess is rigidity-dependent , not conditional uponspecies.
We assume the cosmic-ray emission from Centau-rus A to originate from material entrained into its jetsand transported to its giant lobes, where it is availablefor further boosting to UH energies. From the quantityand isotopic composition of material released by starsenclosed within the northern jet of Centaurus A calcu-lated by Wykes et al. [31], we compute for each iso-tope the rate of particle entrainment for both lobes (Ta-ble 1). The He / Fe number rate ratio here is ∼ He / C ratio is ∼ He / O is 325.
The injection process into the accelerator, and rela-tive rates for di ff erent nuclear species, is a long-standingproblem [e.g. 21, 13]. We propose a phenomenologicalprescription for obtaining a multi-species energy spec-trum which scales the spectra in energy per nucleon by Z / A : E dNdE per A = f A E dNdE , (1)where f A = f SW Z / A , (2)with f SW being the stellar wind abundance value, A theatomic number, E per A the energy per nucleon and p theparticle index. This is equivalent, for a power law, toscaling the spectra in energy per particle by Z A ( p − .For an index of p = .
3, this will change the He / Fenumber rate ratio to 24 . He / C . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 N A , ent . isotope mass entrained mass rate number rate(single lobe) (twin lobes) (twin lobes)( M (cid:12) ) ( M (cid:12) yr − ) (s − ) H 7 . × . × − . × He 3 . × . × − . × He 2 . × . × − . × C 9 . × . × − . × N 7 . × . × − . × O 3 . × . × − . × Ne 5 . × . × − . × Ne 5 . × . × − . × Mg 1 . × . × − . × Mg 2 . × . × − . × Si 2 . × . × − . × S 1 . × . × − . × Fe 4 . × . × − . × and He / O ratios to 2 . .
9, respectively. The pre-scription defines the relative injection fraction of eachspecies, but does not define the absolute fraction of thematerial that is accelerated.
Once the particles are injected into the giant lobes,at su ffi cient energy to be accelerated further, we as-sume that all remaining processes are solely rigidity-dependent. This ignores any further species-dependentcollisional energy-loss processes, as the environmentin the lobes is su ffi ciently sparse that such collisionsshould be rare. We assume that each species A is ac-celerated to a power-law distribution d ˙ N A , inj dE = f A E − p e − E / E max for E > E min , (3)where ˙ N A , inj is the rate at which particles of this speciesare injected into the acceleration mechanism, f A is anormalisation constant, and the energy limits E max = E Fe , max × Z / Z Fe E min = E H , min × Z / Z H are purely rigidity-dependent. Based on the outcomefrom the stochastic acceleration model for the giantlobes by [29], we adopt E Fe , max = . eV (250 EeV). Particle spectra from plausible acceleration scenariosin the jet – magnetic reconnection (pc scales), di ff usiveshock acceleration (pc and kpc scales), shear accelera-tion (kpc scales) and stochastic acceleration (kpc scales)– might lead to power-law spectra in the close proxim-ity of the acceleration region with a particle index in therange 1 . − .
4. The spectrum will steepen due to radia-tive losses as particles move away from the accelerationspot.The giant lobes can either show power-law spectraor, in special cases, peaked spectra, from stochasticacceleration. The peaked spectrum is as much a re-sult of energy-dependent escape from the lobes as theenergy-dependent acceleration rate; the peak representsthe balance between the two rates. The injection of par-ticles might occur at the centre of the accelerator forthe peaked spectrum to be apposite, which is plausiblewhen the jet is driving the turbulence (for Centaurus A,jet driving the turbulence has been considered by [29]and [30]).
The model of the source by [29] and [31] does notlead to measurable ultra-high energy neutrino and pho-ton fluxes: both the jet-stellar wind interaction re-gions in the jet as well as the turbulent environmentof the giant lobes for the final acceleration to UH en-ergies are media with too small a cross section forproton-proton or proton-photon collisions to be impor-tant, which means that a non-detection of ultra-high en-ergy neutrinos and photons from the direction of Cen-taurus A does not rule out the radio galaxy as a sourceof UHECRs.
To investigate the various decay channels of the pho-todisintegration, we convolved cross-sections from [19]with the CMB and EBL radiation fields, which gives theinteraction length (i.e. energy-loss length). The EBL ra-diation field used is from [14].There are various exceptions to the general trendthat nuclei are more robust at higher charge Z . Fig. 1shows that of the intermediate-mass nuclei, C to Ne, C is relatively robust, with an interaction length of ∼ . N, Oand Ne are more fragile at 100 EeV; however, the ro-bustness is higher at lower energies with, for example,the interaction length of 15 . O and12.6 Mpc at 50 EeV for Ne. The robustness of N isvery comparable to Ne at 10 . to 10 . eV; it is morerobust than Ne outside these limits. . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 L i n t [ M p c ] log E [eV]
HeCNONe
Figure 1: Interaction length for five nuclei species (abundant at thesource) due to photodisintegration on CMB and EBL, with the Khanphotodisintegration cross section.
Given the proximity of our source, we focus on theinitial steps of the disintegration. Our modelling showsthat the second most important decay channel in thefirst photodisintegration step for O is feeding into Cvia O → C + He. For Ne, the most important(among many) decay channel in the first photodisinte-gration step leads again to stripping o ff an alpha parti-cle, i.e. to a reaction Ne → O + He. The nitrogenisotope N feeds in the first step again into C, via N → C + H.Thus, nuclei may reach the Earth largely una ff ected.A marginally lighter arrival composition, enhanced in C and He levels (at the cost of Ne and O) is pos-sible.
3. Absolute flux and energetics
To examine the overall energetics of cosmic-ray ac-celeration in Centaurus A, we first consider the case inwhich all material entrained in the jets is acceleratedto high energies in its lobes, neglecting the species-dependent injection described in Section 2.2; i.e. assum-ing that ˙ N inj = ˙ N ent . Taking ˙ N A , ent for each species fromTable 1, we can then calculate the normalisation f A ofits spectrum from equation 3. The particle index p andthe minimum energy E H , min of the accelerated particlesremain free variables, but we can constrain the latter, atleast, to be greater than the mean thermal energy in thelobes at a temperature T ∼ . × K [29], being E th = kT ∼ .
26 GeV (4) where k is the Boltzmann constant.From these parameters we can then obtain the totalpower used to accelerate particles of all species, P acc = (cid:88) A (cid:90) dE d ˙ N A dE E , (5)and compare it to the combined power supplied byboth jets P jets = erg s − , based on the higherend of the historical jet power for a single jet of1 − × erg s − [29, 22]. Fig. 2 shows the ratiobetween these two values: the acceleration e ffi ciency P acc / P jets . For a minimum energy close to E th , the par-ticle index may be close to p = . ffi ciency is close to 100%; however, if the acceleratione ffi ciency is limited to ∼ (cid:38) . d ˙ NdE = (cid:88) A π d d ˙ N A dE , (6)where d is the distance to Centaurus A. This is a simplis-tic treatment, but for a close source, particle interactionsare minimised (see also Section 2.4), and the most en-ergetic particles experience relatively small deflections,so it gives an approximate absolute normalisation to thecosmic-ray flux from Centaurus A. We have briefly ex-amined the resulting fluxes and found that, for p (cid:38) . To investigate the conditions under which Centau-rus A could contribute a significant fraction of the all-sky cosmic-ray flux, we next consider the case in whicha small, species-dependent fraction of the material en-trained in the jets is accelerated to high energies in thelobes, as described in Section 2.2. We fix the parti-cle index to p = .
63, matching the spectrum observedat energies above 10 . eV (4 EeV, traditionally calledthe ‘ankle’ ) by the Auger Observatory [27], and deter-mine the resulting cosmic-ray flux at Earth, assuming We move away from this traditional nomenclature as it has nolonger a su ffi cient physical basis. . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 p E H , m i n ( e V ) E th E Fe , max =10 . eV ˙ N inj / ˙ N ent =1 log ( P acc /P jets ) Figure 2: Fraction of jet power P jets required for particle accelera-tion P acc , under the assumptions described in Section 3.1, for di ff er-ent values of the particle index p and the minimum energy E H , min ofthe spectrum of accelerated particles. Lines follow parameter valueswith a constant acceleration e ffi ciency P acc / P jets ; the dotted line cor-responds to the common assumption of 10% acceleration e ffi ciency.The shaded region at the top of the plot is excluded, as it requires morepower for particle acceleration than is available from the jets. The hor-izontal line corresponds to the mean thermal energy E th of particlesin the lobes; the shaded region below this is excluded as it requiresparticles to be actively cooled below this energy. lossless, ballistic propagation per equation 6, as a frac-tion of the observed all-sky flux. For simplicity, we let E max → ∞ , which will have little e ff ect on the energet-ics for this steep spectrum.Results are displayed in Fig. 3. For this particle in-dex p , for Centaurus A to contribute significantly to theall-sky cosmic-ray flux, without exceeding the poweravailable for acceleration from its jets, requires that onlya small fraction ˙ N inj / ˙ N ent (cid:46) − of the entrained parti-cles are injected into the acceleration mechanism, andthat they all be accelerated above a minimum energy E min (cid:38) eV. These limits may be relaxed if the ac-celeration mechanism results in spectral curvature, witha flatter spectrum at higher energies than at lower ener-gies; or if non-rectilinear di ff usion leads to a significantenhancement of the flux from this source.A simple rectilinear flux normalisation as aboveseems challenged by the fact that any Centaurus A-related anisotropy of the Auger Observatory events isweak [e.g. 2]. A large fraction of the particles thereforemay appear to be di ff using, which invariably also mayalter the flux level (away from rectilinear). However,random deflections up to ∼ ◦ would be su ffi cient toconceal a ∼
10% contribution from Centaurus A to theall-sky flux, while only altering the flux level by a fac-tor ∼ -6 -5 -4 -3 -2 -1 ˙ N H , inj / ˙ N H , ent E H , m i n ( e V ) P a cc / P j e t s = . P a cc / P j e t s = . E th ˙ N Fe , inj > ˙ N Fe , ent E Fe , max →∞ p =2 . Fraction of all-sky fluxfrom Centaurus A
Figure 3: Fraction of the all-sky cosmic-ray flux beyond 4 EeV thatwould originate from Centaurus A, for the model laid out in Sec-tion 3.2, for di ff erent values of the injection fraction ˙ N inj / ˙ N ent andthe minimum energy E min of the spectrum of accelerated particles.Lines follow parameter values which result in a constant fraction ofthe all-sky cosmic-ray flux originating from Centaurus A, as describedin the legend. The shaded region at the bottom of the plot is ex-cluded, as in Fig. 2, because it requires particles to be cooled belowthe mean thermal energy in the lobes. The dark-shaded region in theupper right is closed out because it requires an acceleration e ffi ciency P acc / P jets >
1; the light-shaded region corresponds to acceleration ef-ficiencies exceeding 10%. Within the shaded region in the centre ofthe plot, it is not possible to strictly meet the prescription describedin Section 2.2, as it leads to a disproportionately high iron content ex-ceeding that available from entrained material. a minimum an order-of-magnitude estimate for the nor-malisation.
4. Propagated spectra and composition
To determine the particle spectrum and compare thiswith the measurements of the Auger Observatory, weused a 3D Monte Carlo description of UHECR prop-agation as per [25]. Here, UHECR protons and nu-clei are propagated through the cosmic microwave back-ground (CMB) and cosmic infrared background (CIB)radiation fields, undergoing energy losses via photodis-integration, pair production, photo-pion collisions andlosses due to cosmological redshift. In the present pa-per, we utilise the Khan photodisintegration cross sec-tion, based on phenomenological and microscopic mod-els by [19], and the description of the CIB spectral en-ergy distribution by [14]. We implemented the hadronicmodels QGSJet II-4, EPOS-LHC and Sybill 2.1 into theanalysis and fitting routines. . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 Fe, max =10 eVp=2.25 E d N / d E [ e V c m - s - s r - ] log Energy [eV]
HeCONe
Figure 4: Propagated spectra with He, C, O and Ne (solidlines), with the maximum energy at the source fixed at Fe max =
250 EeV, and with zero propagation magnetic field. Here, the overallflux is normalised to the Auger data (from [27]). The errors on thedata points shown are 1 σ errors. The vertical dashed line indicatesthe point in the data where a spectral hardening occurs. The assumed maximum Fe energy at the source [29,Section 2.3] of 250 EeV (not inconsistent, within the 1 σ error margins, with the so far highest-energy event, ob-served by Fly’s Eye, of 320 ±
93 EeV; [12]) translatesto a proton cuto ff energy at the source of 9 . χ minimised for spectral data fit in the en-ergy region > . eV (4 EeV). No parameters werescanned over for this result which we discuss in Sec-tion 4.3.Note that while understanding the low-energy abun-dances at a given energy is paramount, we need to nor-malise to as high an energy as possible to minimise thecomplications arising from propagation through extra-galactic and Galactic magnetic fields. The normalisa-tion is therefore a best fit to the data above 10 . eV. Below, we describe the e ff ect of normalising to theAuger data, i.e. a case without physically justified nor-malisation. Apart from the overall normalisation, alsothe composition ratios and the injection particle index Fe, max =10 eVp=2.30 E d N / d E [ e V c m - s - s r - ] log Energy [eV]
HeOSiFe
Figure 5: As in Fig. 4, but for propagated spectra with He, O, Siand Fe.
Fe, max =10 eVp=2.27 E d N / d E [ e V c m - s - s r - ] log Energy [eV]
HeCOFe
Figure 6: As in Fig. 4, but for propagated spectra with He, C, Oand Fe. were left free in the Monte Carlo scan. Each plot adoptsa particular admixture abundant species set. For eachadmixture case considered, the global best-fit result isshown. We did not include N in the analysis as only ∼ − Cand / or O is required to match the Auger data at en-ergies ∼ . eV (32 EeV). It is not possible to makea strong statement about C and O in particular: thespecies are too closely spaced in mass number to dis-tinguish between them. The C spectrum has a breakslightly ‘earlier’ than the O spectrum, making a largerfraction of C than O preferable in the admixture inorder to find agreement with the downturn feature from10 . and 10 . eV. The earlier downturn of C than O is a Lorentz factor e ff ect here; it is not due to,for example, the O → C + He photodisintegration . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 Fe, max =10 eVp=2.30 E d N / d E [ e V c m - s - s r - ] log Energy [eV]
A=1-2A=3-6A=7-19A=20-39A=40-56
Figure 7: Propagated spectra with He, O, Si and Fe (solidlines), with the maximum energy at the source fixed at Fe max =
250 EeV and the spectral index fixed at 2 .
3, and with zero propaga-tion magnetic field. Here, the overall flux is normalised based onthe injection prescription (Section 2.2). The errors on the data pointsshown are 1 σ errors. The vertical dashed line indicates the point inthe data where a spectral hardening occurs. The kink at high energiesis an artefact of the Monte Carlo method employed; due to the lowstatistics, the results are liable to Poisson noise. (which could potentially lead to additional C fluxes,see Section 2.4). Essentially, for a given energy, C hasa slightly larger Lorentz factor than O, so can interactwith somewhat lower-energy photons. The downturn isdue to onset when interactions with CMB + CIB pho-tons become possible.The vertical dashed line in Figs 4 − . eVis overlaid to stress that the data itself shows a new(harder) component that starts at these energies. Oursource results begin to dominate there since our fluxesare power laws, and the lack of break in our (ballistic)results naturally has the e ff ect that the power-law domi-nates at energies above the dashed line. The results from Section 4.2, in which the composi-tion ratios are left free to float and where the interme-diate to heavy ratios appear favoured, together with thesolar low-energy cosmic-ray composition data, suggesta selective injection process.Fig. 7 depicts the spectral outcome when Centaurus Ais adopted as the dominant source of UHECRs above10 . eV (4 EeV), for species in the ratios obtained byour injection prescription (Section 2.2). The slight de-partures from the Auger data demonstrate the need forother species, in the intermediate to heavy range, to beconsidered as well. The entrained composition, afterscaling per our injection prescription (Section 2.2) doesnot contain relatively enough intermediate-mass nuclei to fit the observed spectrum. Protons and He exceedthe spectrum at low energies, and Fe exceeds the spec-trum at high energies, and the CNO in between is not asabundant as it needs to be.The inclusion of plausible intergalactic magneticfields of ∼ . ff ect the fits at the highest energies in a strongway.Centaurus A as discussed throughout this work couldbe representing nearby UHECR sources, in which casethe total CR luminosity would be shared out amongstthe di ff erent sources. This would also help alleviate theCR anisotropy concerns.
5. Summary
The main results of this paper are as follows.(1) Centaurus A and other nearby objects are wellmotivated as a source of UHECRs by the compositionand spectral shape and start to dominate the CR fluxabove ∼ Fe energy at the sourcefixed at 250 EeV, are of intermediate mass, C to O,although we cannot make a strong statement on C ver-sus O (or N) due to close spacing in mass number.(2) Photodisintegration of nuclei is largely unimpor-tant for a quasi-rectilinear particle transport from thesource, except for a modest disintegration of N, Oand Ne which will marginally enhance C and Helevels at lower energies.(3) The best-fitting power-law particle spectral in-dices, from an approach which considers composition-dependent spectra and artificially normalises to theAuger data, cluster around 2 .
3, compatible with plau-sible acceleration scenarios at the source. The quantityof material accelerated to the highest energies in Cen-taurus A must be less than the material entrained fromjet-enclosed stars, otherwise the particle spectral indexis required to be too steep.(4) Composition-independent spectra, with normali-sation relying on our phenomenological prescription forinjection, demand that additional isotopes, in the inter-mediate to heavy range, be considered.In the next paper, we will also consider a range ofextragalactic magnetic fields and the e ff ects of Galacticfields on the propagation. . Wykes et al. / Nuclear and Particle Physics Proceedings 00 (2018) 1–8 Acknowledgements
We thank T. Jones, L. Drury, D. Ryu, P. Blasi, C.O’Dea, D. Caprioli and R. Gleisinger for helpful dis-cussions. AMT acknowledges a Schr¨odinger Fellow-ship at DIAS. JDB acknowledges support from ERC-StG 307215 (LODESTONE).
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