The primary proton spectrum of the hadronic PeVatron candidate HAWC J1825-134
aa r X i v : . [ a s t r o - ph . H E ] J a n Draft version January 27, 2021
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The primary proton spectrum of the HAWC J1825-134 source
Timur Dzhatdoev
1, 2, 3 Federal State Budget Educational Institution of Higher Education, M.V. Lomonosov Moscow State University, Skobeltsyn Institute ofNuclear Physics (SINP MSU), 1(2), Leninskie gory, GSP-1, 119991 Moscow, Russia Institute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospect 7a, Moscow 117312, Russia Institute for Cosmic Ray Research, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Japan
ABSTRACTThe γ -ray spectrum of the source HAWC J1825-134 measured with the High Altitude WaterCherenkov (HAWC) observatory extends beyond 200 TeV without any evidence for a steepening orcutoff. There are some indications that the γ -rays detected with HAWC were produced by cosmicray protons or nuclei colliding with the ambient gas. Assuming primary protons, we inquire whichshape of the primary proton spectrum is compatible with the HAWC measurements. We find thatthe primary proton spectrum with the power-law shape of γ p = 2 . E c − p > γ p down to 1.3 and E c − p as low as200 TeV also do not contradict the HAWC measurements. The former option might be realized if theaccelerator is inside or very near to the γ -ray production zone. The latter option is viable for the caseof a cosmic ray source which effectively confines low-energy ( E p <
100 TeV) accelerated protons.
Keywords: γ -ray astronomy — galactic sources — individual: HAWC J1825-134 INTRODUCTIONCosmic rays up to the so-called “knee” — a steep-ening in the all-nuclei spectrum measured at Earth(Kulikov & Khristiansen 1959) — are widely believedto have a Galactic origin. The acceleration and propa-gation of cosmic ray (CR) protons and nuclei collidingwith the ambient gas is accompanied by the productionof γ -rays. Therefore, Galactic hadronic PeVatrons —the objects accelerating protons up to the knee — couldbe searched for and studied with γ -astronomical meth-ods.Very recently, the High Altitude Water Cherenkov(HAWC) collaboration reported a measurement of the γ -ray spectrum of the source HAWC J1825-134 up to theenergy of 300 TeV (Albert et al. 2020). The spectrumdoes not reveal any steepening or cutoff. Albert et al.(2020) argue that the observed γ -rays were produced bythe hadronic mechanism.In the present paper we put constraints on the pa-rameters of the primary CR spectrum, assuming thatall γ -rays detected by HAWC from this source were pro- Corresponding author: Timur [email protected] duced by primary protons. In Section 2, we provide afew examples of a plausible primary proton spectrumthat could explain the HAWC data reasonably well. Weperform a scan on the parameters of the primary protonspectrum in Section 3. Finally, we discuss the obtainedresults in Section 4 and conclude in Section 5. EXAMPLES OF THE PRIMARYPROTON SPECTRUMThe spectral energy distribution (SED= E γ dN γ /dE γ )of HAWC J1825-134 according to Albert et al. (2020) isshown in Figure 1. Three model γ -ray SEDs are alsoshown in this Figure, assuming a hadronuclear (moreprecisely, proton-proton) mechanism of γ -ray produc-tion on an optically thin matter. These SEDs were calculated using approximations ofKelner et al. (2006) under the assumption of the pri-mary proton spectrum ∝ E − γ p exp ( − E p /E p − c ). Blackcurve corresponds to the case of γ p = 2 . E p − c = 3PeV, green curve — γ p = 2 .
06 and E p − c = 1 PeV, bluecurve — γ p = 1 . E p − c = 500 TeV. that is, neglecting the contribution of cascade γ -rays to the ob-servable γ -ray spectrum; given that the average gas column den-sity from the region of HAWC J1825-134 is N H = 3 × cm − (Albert et al. 2020), this assumption is justified Dzhatdoev
For simplicity, we neglect bremsstrahlung of electronsproduced together with γ -rays and γ -ray absorption. Wenote that the mean free path of γ -rays on cosmic mi-crowave background (CMB) photons exceeds 50 kpc forthe energy below 300 TeV. Given that the estimateddistance to the source is 3.9 kpc, the effect of pair pro-duction on CMB photons could be neglected at suchenergies. The absorption on extragalactic backgroundlight (EBL) photons is also negligible. However, someadditional γ -ray absorption is expected on the infraredGalactic background. [TeV] γ E1 10 ] - s - [ T e V c m γ / d E γ d N γ E − − − Figure 1.
SED of HAWC J1825-134 measured with HAWC(red circles with statistical uncertainties) together with threemodel curves calculated for various proton spectrum param-eters (see text for more details).3.
SCAN OVER PARAMETERSWe performed an exhaustive scan over the values ofthe primary proton spectrum parameters ( γ p , E p − c ) inthe range γ p = 1 − E p − c = 10 − eV. Forevery set of the parameters, a model histogram of theobservable SED was computed in the HAWC energybins. After that, the optimal normalization of the modelSED was determined that minimizes the value of the χ form. The optimized χ value was converted to p-valueand then to Z-value (statistical significance) accordingto the prescriptions of Zyla et al. (2020). The resulting100 ×
100 matrix of the Z-value vs. ( γ p , E p − c ) is shown inFigure 2. All values of the Z-value below 1.0 are shownin Figure 2 in the same color.In particular, it turns out that the primary protonspectrum with parameters γ p = 2 . E p − c = 3 PeVdescribes the HAWC data well. However, some harderspectra with relatively low values of E p − c (such as γ p =2 .
06 and E p − c = 1 PeV; γ p = 1 . E p − c = 500 TeV;or even γ p = 1 . E p − c = 200 TeV) formally do notcontradict the HAWC data. [eV] p-c E p γ Figure 2.
Significance (Z-value) vs. the primary protonspectrum parameters.4.
DISCUSSION4.1.
The acceleration spectrum and the effective γ -rayproduction spectrum It is widely believed that a typical Galactic hadronicPeVatron has a spectrum of protons with γ p = 2 . − . E p − c = 1 − γ -ray produc-tion zone is not necessarily spatially coincident with theparticle acceleration zone. The primary proton spec-trum may be significantly modified by propagation ef-fects associated with escape from the accelerator (e.g.Moskalenko et al. (2008)), diffusion from the accelera-tor to the γ -ray production zone, etc. Therefore, a hard“effective” spectrum of protons with γ p = 1 . γ p = 1 . Statistical considerations
The results of this study could be somewhat influencedby several statistical effects, including a) migration ofevents between the energy bins of the HAWC spectrum,b) a possible Eddington bias (Eddington 1913) in thelast energy bin. An account of the first effect is likelyto result in an increase of the minimal value of E p − c compatible with the HAWC data. The Eddington biaswould lead to an overestimation of the observable fluxat the last energy bin. Therefore, a correction for thisstatistical effect would decrease the minimal value of E p − c compatible with the HAWC data. To some extent,these two effects partially compensate each other. AWC J1825-134 as hadronic PeVatron CONCLUSIONSThe HAWC data alone do not allow one to ex-clude the hypothesis of E p − c < γ p , E p − c ) values is allowed, down to γ p = 1 . E p − c = 200 TeV. Relatively low-energy( E <1 TeV) data, as well as observations with theLHAASO (Bai et al. 2019) and CTA (Actis et al. 2011;Acharya et al. 2013) detectors will be crucial in estab-lishing the nature of this source. ACKNOWLEDGMENTSThe author acknowledges helpful discussions with E.I.Podlesnyi and Prof. S.V. Troitsky. This work is sup-ported in the framework of the State project “Science”by the Ministry of Science and Higher Education of theRussian Federation under the contract 075-15-2020-778.This research has made use of the NASA ADS biblio-graphical system.REFERENCES