Photodisintegrated Gamma Rays and Neutrinos from Heavy Nuclei

Home , Photodisintegration

arXiv:1512.02434v3 [astro-ph.HE] 10 Feb 2016 LT Zue l 03.TeGMlcto fGB130427A GRB of location the GBM with The consistent 2013). was al. et (Zhu (LAT) ue2021 June 8 03 n twsfloe-pb the by followed-up was it and 2013) n oeta 0tlsoe usqetyosre hsextr of this redshift a observed at subsequently Located telescopes burst. dinary 50 than more and us oio GM ttime at (GBM) Monitor Burst o.Nt .Ato.Soc. Astron. R. Not. Mon. am-a us GB 347 rgee the triggered 130427A (GRB) burst Gamma-ray INTRODUCTION 1 htcr-olpeo asv tr r osbyteprogen the possibly isotropic-equivalent The are GRBs. stars long-duration massive of evi of further providing supernov core-collapse thus type-Ic 2014), that a al. with et (Melandri associated 2013cq be SN to found is 130427A GRB R 347 is 130427A GRB h am-a us e fGB130427A GRB of jet nuc burst heavy gamma-ray from the neutrinos and rays gamma Photodisintegrated is o lotady(cemn ta.21)wieteGM10- GBM the for while 2014) lasted al. emission et (Ackermann keV day 1000 a almost for Rsee eetd(ael ta.2014). al. et (Maselli detected ever GRBs ego hs at phase terglow hs at phase Fermi ‡ † ⋆

2 1 c ads .Joshi C. Jagdish [email protected] [email protected] eateto hsc,Uiest fJhnebr,P o 5 Box PO Johannesburg, of University Physics, of Department aa eerhIsiue aahvngr aglr 5600 Bangalore Sadashivanagar, Institute, Research Raman [email protected] L 00RAS 0000 γ, Fermi LTdtcin fa7 e htndrn h prompt the during photon GeV 73 a of detections -LAT iso 2 = T LThsdtce e msinfo R 130427A GRB from emission GeV detected has -LAT 0 . 19 + 7 × E 10 T γ, n fa9 e htndrn h af- the during photon GeV 95 a of and s 0 53 iso 244 + 000 r/,mkn toeo h otenergetic most the of one it making erg/s, 8 = Swift 1 0–0 00)Pitd8Jn 01(NL (MN 2021 June 8 Printed (0000) 000–000 , , . 2 1 T BTlcto Mslie l 2013) al. et (Maselli location -BAT ⋆ × 0 r atclryrmral as remarkable particularly are s obrRazzaque Soebur , 74:64 T vnKienlin (von UTC 07:47:06:42 = 10 ∼ 53 nryi h rnnce o hshdoi oe o e emis GeV for model hadronic this for nuclei Ob Iron Neutrino the IceCube in the energy by 130427A GRB of non-detection with h hsclpoesso GeV of processes physical the eeto of Detection ABSTRACT e words: Key emission. keV-MeV prompt the in released energy total con o h adpwrlwcmoeto h pcr nth in spectra the of component power-law hard the for account hre hnti uain efidthat f find We scale duration. time this than photodisintegration com shorter The spectral trigger. hard keV-Me additional, after an observed second explain with to nuclei order in Oxygen 130427A and Iron of interactions us GB 347 ythe by 130427A (GRB) burst the a eeitdwt nrisu to up energies with emitted secondary be the can from antineutrinos Electron photons. energy z Fermi 350 r n h ekluminosity peak the and erg 0 = γγ . Pec ta.2014). al. et (Preece s LreAe Telescope Area -Large 34 → Lvne l 2013), al. et (Levan Fermi e ± γ ∼ am a us htdsnerto am as–Neutrin – rays Gamma – Photodisintegration : Burst Ray Gamma arpouto ihlweeg htn eeeyattenuat severely photons low-energy with production pair ryeeg of energy -ray -Gamma-ray 0 . 0 India 80, 1 7 e prompt GeV -70 4 ukadPr 06 ot Africa South 2006, Park Auckland 24, dence 2 itors aor- † a n etnaiMoharana Reetanjali and Fermi γ rcs o rdcino hseegtcpoo nteafter the in photon 2014). strong energetic al. et provides this ph (Ackermann of phase the GRB, production as a for emission photon, from process electron-synchrotron GeV yet the 95 on detected constraints The energetic 2014). most al. the et (Ackermann scenario shocks 347,asmn msino h 3GVpoo sunatten- is photon GeV 73 the the by of uated emission assuming 130427A, esadeiso rcse Akrane l 04.Amini- A parame- 2014). of jet al. factor et Lorentz (Ackermann GRB bulk processes jet the mum emission on and constraints ters meaningful provide they A 2 Zhang & Kumar reviews, for also, c (see been literature have the in 2009), ered al. et et Pe’er (Asano 2009; interactions 20 al. photohadronic al. et Boˇsnjak et (Razzaque proton-synchrotron 2009; hadronic, and al. 2012) et C (Wang inverse emission primarily leptonic, mech ton the Both is emission. what GeV clear di prompt from far for also is 2014 it al. as 2014); et al. Ackermann 2010) et 2013; Beloborodov al. Razzaque et (Tam 2010; 130427A GRB Du is for al. Barniol cussed et & over, Ghisellini Kumar emiss e.g., 2010; is (see, Compton 2009, blastwave emission inverse decelerating keV-MeV a and/or from the synchrotron after afterglow likely long emission, GeV neatn ihteosre e-e htn nteprompt the in photons keV-MeV observed the with interacting ryeiso rmteGBjt.I hswr ediscuss we work this In jets. GRB the from emission -ray A ∼ + LreAe eecp rvdsa potnt oexplore to opportunity an provides Telescope Area -Large T γ E tl l v2.2) file style X hl ti eeal cetdnwta temporally-extende that now accepted generally is it While nti etrw ou npooiitgaino ev nucl heavy of photodisintegration on focus we letter this In γ ryeiso rmteecpinlybih gamma-ray bright exceptionally the from emission -ray 2 γ e.Teflxo hs etio slwadconsistent and low is neutrinos these of flux The TeV. → asrsligfo h rnnce iitgaincan disintegration nuclei Iron the from resulting rays A ∗ γγ → ( → A − e ± )+ 1) arpouto rcs nteinternal- the in process pair-production rIo ulii oprbet or to comparable is nuclei Iron or γ eto ea,o h te hand, other the on decay, neutron oetosre uig11.5-33 during observed ponent + inis sion Γ 2 n/p, htn ntejto GRB of jet the in photons V e min ‡ evtr.Terqie total required The servatory. ∼ ∼ 1 . 7 e ag,before range, GeV -70 450 10 seiso fhigher of emission es ie h observed the times snee o GRB for needed is os e in lei 0 and 10) onsid- anism ysical omp- 015). glow ran ion (1) ei al. s- d ; 2 Joshi et al. phase of GRB 130427A, to produce the observed GeV emission scale (Wang et al. 2008) that is detected as an additional power-law component during the ′ ′ 2πEA T0 + 11.5 s to T0 + 33 s interval (Ackermann et al. 2014). Heavy t = η acc ZeB′c nuclei such as the Iron (Fe) and Oxygen (O) can be entrapped − ′ − ′ − η Z 1 B 1 E in the GRB jet from the stellar envelope as the jet propagates in- ≈ 2 × 10 6 A s, (4) side the GRB progenitor star (Zhang et al. 2003). It was discussed 10 26 130 kG TeV ′ by Wang et al. (2008) that these heavy nuclei can survive nuclear where EA is energy of the nuclei and η = 10 is a fiducial value for spallation due to nucleon-nucleon collisions and photodisintegra- the number of gyroradius required for acceleration. The maximum tion while interacting with the thermal photons in the GRB jet at the energy is limited from comparing this time scale with the shorter stellar Fe core radius of ∼ 109 cm. In particular, the first ∼ 10 s of the jet dynamic time scale, given by of the GRB jet could be rich in heavy nuclei (Wang et al. 2008). −1 ′ Rin Rin Γ Non-thermal photons created in the internal-shocks, e.g., from syn- tdyn = = 0.7 s, (5) Γc 2 × 1013 cm 103 chrotron radiation of shock-accelerated electrons, outside the stellar envelope, however, can break down the shock-accelerated heavy and the energy loss time scales, which we discuss next. nuclei (Wang et al. 2008) and lead to high-energy gamma-ray Photodisintegration by interacting with the observed keV- emission (Murase & Beacom 2010). MeV photons in the GRB jet is the main and most interesting pro- We discuss photodisintegration process using parameters of cess for energy losses by heavy nuclei. The observed differential −1 −1 −2 GRB 130427A in Sec. 2 and resulting γ-ray flux in Sec. 3. We photon flux at the Earth, fγ (ǫ), e.g., in (MeV s cm ) units, calculate neutrino flux from the photodisintegration process and its can be converted to photon density per unit energy and volume ′ ′ −1 −3 detectability in Sec. 4, discuss our results and conclude in Sec. 5. nγ (ǫ ), e.g., in (MeV cm ) units, in the comoving jet frame by the relation (see, e.g., Razzaque 2013),

2 2 ′ ′ ′ 2d 2d Γǫ n (ǫ )= L f (ǫ)= L f , (6) γ R2 c γ R2 c γ 1+ z 2 PHOTODISINTEGRATION IN THE GRB JET in in where dL is the luminosity distance to the source. For In this calculation we have used four frames of references: (i) The GRB 130427A redshift of z = 0.34, dL = 1.8 Gpc using the stan- comoving GRB jet frame or wind rest frame denoted with super- dard ΛCDM cosmology. These photons interact with the heavy nu- script ‘′’, (ii) the lab frame or GRB source frame denoted with clei by the Giant Dipole Resonance (GDR) process (Stecker 1969; superscript ‘∗’, (iii) the rest-frame of the nuclei denoted with su- Puget et al. 1976a; Stecker & Salamon 1999; Anchordoqui et al. perscript ‘′′’, and (iv) the observer frame with no superscript. The 2007) and the rate of such interactions is given by (Stecker 1968), energies in the observer frame, lab frame and comoving jet frame ∞ ∞ ′ ′ are related by the Lorentz boost factor Γ of the bulk GRB outflow ′ −1 ′ c ′′ ′′ ′′ nγ (ǫ ) ′ ∗ ′ tA (γA)= ′ 2 εγ σA(εγ )dεγ ′2 dǫ . (7) and redshift z by the relation Eγ = E /(1 + z)=ΓE /(1 + z). 2γ Z ′′ Z ′′ 2 ′ ǫ γ γ A εth εγ / γA 3 For calculation, we use fiducial parameter values Γ = 10 , ′ ′ 13 52 Here γ = E /m c2 is the Lorentz boost factor of the ener- Rin = 2 × 10 cm and Lγ,iso = 10 erg/s for the 11.5-33.0 s A A A getic nuclei, ′′ ′ ′ is the photon energy in interval of GRB 130427A, where Rin is the dissipation radius εγ = γAǫ (1 − βA cos θ) the rest frame of the nuclei with an angle θ between their ve- and Lγ,iso is the isotropic-equivalent γ-ray luminosity in the keV- ′′ locity vectors, εth is the threshold photon energy for the nuclei MeV range. We calculate magnetic field in the shocks as (see, e.g., ′′ excitation, βA ≈ 1 and σA(εγ ) is the photodisintegration cross Razzaque et al. 2004) ′′ section. We use the threshold energy εth = 10 MeV and cross 1/2 ′ 2ǫB Lγ,iso/ǫe sections given in Puget et al. (1976b); Anchordoqui et al. (2007); B = 2 2 RincΓ Wang et al. (2008). We use the same rate formula in equation (7) ′′ 1 2 −1 2 1 2 ǫ / ǫ / L iso / for the related photopion interactions with ε = 145 MeV per nu- ≈ 130 B e γ, th 0.1 0.01 1052 erg/s cleon and the delta resonance cross section given in Mücke et al. 2/3 −1 −1 Rin Γ (2000) scaled by a factor A for a nuclei with mass number × kG, (2) 2 × 1013 cm 103 A (Wang et al. 2008). The observed prompt flux from GRB 130427A has been mea- where ǫe = 0.01 is a fraction of the shock energy that is carried sured by the Fermi-GBM and Fermi-LAT in three time intervals, by the relativistic electrons, which promptly radiate most of this labelled ‘a’, ‘b’ and ‘c’ (Ackermann et al. 2014) as also listed energy in γ rays (so-called fast-cooling scenario), and ǫB = 0.1 in Table 1. The γ-ray spectra in these intervals are fitted by a is a fraction of the shock energy that is carried by the magnetic ′2 smoothly-broken power-law (SBPL) model (interval ‘a’), a power- field. Magnetic energy density, B /8π, in this scenario far exceeds law (PL) model (interval ‘b’), and a SBPL+PL model (interval the radiation energy density and synchrotron radiation is the most 1 ‘c’) in the energy ranges as indicated by Eγ in the table (in in- effective energy loss channel for the relativistic electrons. Only a terval ‘c’ the upper line is for SBPL and the lower line is for modest electron Lorentz factor PL). The corresponding luminosities in the intervals ‘a’ and ‘b’ 1/2 ′ −1/2 −1/2 ′ E B Γ are also listed. Note that the GBM detectors were saturated in γ ≈ 244 γ , (3) e 100 keV 130 kG 1000 the interval ‘b’and a full spectrum at lower energies is not avail- able (Ackermann et al. 2014). The PL component in the interval is required to explain the observed Eγ ≈ 100 keV peak photon ‘c’ is particularly hard, with photon index −1.66 ± 0.13, extending energy from GRB 130427A in this scenario. up to ∼ 73 GeV (Ackermann et al. 2014). The Table 1 also shows A large fraction of the jet energy, however, is carried by the heavy nuclei in our scenario. Heavy nuclei, with atomic number 1 −8 −2 −1 Z, can be accelerated quickly in this magnetic field within a time with flux νFν > 2 × 10 erg cm s

c 0000 RAS, MNRAS 000, 000–000 Photodisintegrated γ and ν from GRB 130427A 3

Table 1. Observed prompt γ-ray emission properties for GRB 130427A and Fe-dis Fe type p-γ Acc-time O-dis O type p-γ Fe-cooling-time corresponding Fe-photodisintegration properties. See main text for details. p-γ Dyn-time 107 106 5 Parameters Time intervals 10 104 3 ‘a’ ‘b’ ‘c’ 10

(sec) 2 ′ 10 1 Interval (s) −0.1 to 4.5 4.5 to 11.5 11.5 to 33.0 10 100 Spectral model SBPL PL SBPL+PL -1 52 51 10 Lγ,iso (erg/s) 1.1 × 10 – 3.7 × 10 (SBPL) -2 50 10 – – 5.3 × 10 (PL) -3 Γ = 1000, Rin = 2.0e+13 cm Timescale t 10 5 5 7 -4 Eγ (keV) 10 − 10 (0.3 − 8) × 10 8 − 5 × 10 10 – – 200 − 7.3 × 107 10-5 ′ 5 5 10-6 γFe 3 × 10 − 30 100 − 4 4 × 10 − 1 0 1 2 3 4 ′ 10 10 10 10 10 5 5 ′ γO 7 × 10 − 75 250 − 9 9 × 10 − 1 5 6 2 γA Eγ (GeV) [Fe] 9 × 10 − 90 300 − 11 10 − 3 10 6 3 6 Eγ (GeV) [O] 6 × 10 − 560 2 × 10 − 70 7 × 10 − 7 Fe-disint 1 O-disint 10 Dynamic-time

100 ′ the ranges of Fe-nuclei Lorentz boost factor γFe that will be inter- -1 10 acting with the observed photons and the photodisintegrated γ rays with energy 10-2

′′ ′ t (sec) Timescale ¯ -3 Eγ = 2Eγ,AγAΓ/(1 + z), (8) 10 ′′ ′′ ¯ ¯ -4 where Eγ,Fe ∼ 2-4 MeV and Eγ,O ∼ 5- 10 3 4 5 6 7 7 MeV (Anchordoqui et al. 2007). Thus heavy nuclei in the 10 10 10 10 10 interval ‘c’ can be disintegrated most effectively to produce a Eγ (MeV) broad γ-ray spectrum in the Fermi-LAT energy range. We have ¯′′ ¯′′ used Eγ,Fe = 2 MeV and Eγ,O = 5 MeV in Table 1. The absence Figure 1. Top: Comparison of different timescales per nucleon energy in of an additional PL in the intervals ‘a’ and ‘b’ is compatible the GRB jet frame using the properties in interval ‘c’ (see Table 1). Bot- with inefficiency of photodisintegration in those time intervals to tom: Comparison of the observed timescales for photodisintegrated γ-ray produce GeV γ rays. emission for observed γ-ray energy and the dynamic time. We have used ¯′′ The top panel of Fig. 1 shows the jet-frame photodisintegra- Eγ,A = 1 MeV in these plots. ′ tion timescale tA for Fe and O nuclei as functions of the Lorentz ′ factor of the nuclei γA for the time interval ‘c’. Also shown are the timescales for photopion (p-γ) interactions for Fe and O nuclei, as as “Fe-cooling-time” and is too long to be significant in the energy ′ ′ well as the dynamic time tdyn. The acceleration timescale tacc is range of our interest. shown as the dotted line with positive slope. Iron nuclei can be ac- 20 celerated to an energy EFe ∼ 3×10 eV within the dynamic time scale. However, photodisintegration limits the maximum nuclei en- ′ ′ 3 GEV γ-RAY FLUX AT THE EARTH ergy, from the condition tA = tdyn, to EFe,max ≈ 120 PeV and EO,max ≈ 110 PeV, respectively for Iron and Oxygen. The bottom The nuclear γ-ray emission (number per unit volume per unit time panel of Fig. 1 shows the photodisintegration time scale as a func- per unit energy) from photodisintegration of a given nucleus can be tion of the observed secondary γ-ray energy in equation (8) with written as (see Anchordoqui et al. 2007, and references therein) ¯′′ Eγ,A = 1 MeV. Note that the Fe photodisintegration time scale in 2 ′ ′ the GeV energy range matches with the time interval ‘c’ in Table 1 ′ ′ n¯AmN c dnA ′ ′ dEN qγ (Eγ )= ′′ 2 ′ ′ RA(EN ) ′ , (10) ¯ mN c Eγ when Fermi-LAT detected the hard power-law component in the 2E Z ′′ dEN EN γ,A 2E¯ ∼ 1-70 GeV range. Photopion (p-γ) losses are not significant for γ,A our model parameters, as also found by Crumley & Kumar (2013) ¯′′ where Eγ,A is the average γ-ray energy from the nuclei de- for protons in realistic GRB environment. excitation when it is assumed that the γ-ray spectrum is monochro- Apart from photodisintegration and photopion losses, heavy matic, and n¯A is the average multiplicity of these γ rays, with nuclei can also lose energy through synchrotron radiation. The time n¯Fe = 1-3 and n¯O = 0.3-0.5 (Anchordoqui et al. 2007). The scale for this process is given by (Wang et al. 2008) ′ ′ first term inside the integration in equation (10), dnA/dEN = ′ ′−α AN EN is the nucleon spectrum per nucleon energy, with ′ ′ ′ 4 3 ′ 6πm c A 4 AN being a normalization constant. Of course dnA/dEA = t = p ′ ′ ′ syn 2 ′ ′2 (1/A)dnA/dEN in terms of the nucleus energy EA. The second σT m E B Z e A term inside the integration in equation (10), R′ (E′ )= t′−1, with ′ −2 ′ −1 A N A 6 B EA ′ ′ 2 ≈ 5.7 × 10 EN = γAmN c , is the scattering rate of the GDR interactions. 130 kG TeV The emission coefficient (number per unit volume per unit A 4 Z −4 × s. (9) time) of the photodisintegration γ-rays in the wind rest frame is 56 26 ′ ′ ′ ′ ′ jγ (Eγ ) = Eγ qγ (Eγ ), which can be related to the emission co- ∗ ∗ ∗ ′ 2 ′ ′ This time scale for Fe nuclei is shown in Fig. 1 top panel labelled efficient in the lab frame as jγ (Eγ ) = (Eγ /Eγ ) jγ (Eγ ) =

c 0000 RAS, MNRAS 000, 000–000 4 Joshi et al.

‘c’ is ≈ 4 × 1051 erg/s, which is less than two orders of magnitude lower than the luminosity in the Fe nuclei. However, LFe,iso is -0.1 to 4.5 sec:interval(a SBPL) of the same order as the peak γ-ray luminosity of Lγ,iso = 2.7 × 4.5 to 11.5 sec:interval(b PL) 53 11.5 to 33.0 sec:interval(c SBPL) 10 erg/s (Maselli et al. 2014) and the magnetic luminosity, LB = 10-5 2 ′2 2 53

) 11.5 to 33.0 sec:comp(c PL) 4πRinc(B /8π)Γ ≈ 10 erg/s. The total energy in the relativis-

1 54

− Γ =1000 Photo-disint model flux ( ) tic Fe nuclei is EFe,iso ≈ ∆tcLFe,iso/(1+z) ≈ 5×10 erg, where Electron-synchrotron

sec ∆tc = 21.5 s is the interval ‘c’ duration. A comparison with the 2 − total isotropic-equivalent gamma-ray energy released from the 10-6 53 GRB 130427A, Eγ,iso = 8.1 × 10 erg (Maselli et al. 2014), we ﬁnd that EFe,iso is only a factor . 10 times higher. This is a very conducive situation for the hadronic model from the total energy

flux (erg cm perspective. 10-7 The maximum γ-ray energy from Fe-disintegration is Eγ ≈ 5 TeV for EFe,max ≈ 120 PeV, following equation (8) with ¯′′ Eγ,Fe = 1 MeV. Photons of this energy cannot escape the GRB 1 2 3 4 5 6 7 8 9 10 10 10 10 10 10 10 10 10 jet due to e± pair creation by interacting with the same low-energy Energy (keV) photons in the SBPL component which are responsible for photo- ± Figure 2. Observed prompt γ-ray energy flux (solid lines) from disintegration. We calculate the γγ → e pair-production opacity, GRB 130427A in 3 different time intervals (Ackermann et al. 2014). The following Gould & Schréder (1967), as thick-dashed line corresponds to our fit to the PL component (photon index 2 4 2 −1.66 ± 0.13) in the interval ‘c’ using the Fe-photodisintegration model Rin 2 mec Γ τγγ (Eγ ) = πr0 in equation (12). The turnover of the model flux above ∼ 70 GeV is due Γ (1 + z)Eγ ± to the γγ → e pair production with the low-energy photons in the SBPL (1+z)Eγ ′ ′ Γ n (ǫ ) ′ ′ component. The uncertainty in the observed PL flux component, where it (15) × 2 4 ′2 ϕ[S0(ǫ )]dǫ , dominates over the SBPL component, is shown with shaded region. The Z mec Γ ǫ (1+z)E thin-dashed line corresponds to the synchrotron flux from the secondary γ ± ′ ′ e pairs. where r0 is the classical electron radius and n (ǫ ) is the isotropic distribution of photons in the GRB jet given by the equation (6). ′ ′ ′ 2 4 2 ′ ∗ The function ϕ[S0(ǫ )], with S0(ǫ ) = (1+ z)ǫ Eγ /Γmec , is Γ jγ (Eγ /Γ) (Rybicki & Lightman 1986). Similarly the four vol- ∗ defined by Gould & Schréder (1967) and corrected by Brown et al. ume invariance gives the volume in the lab frame as V = 3 13 ′ ∗ (1973). For the fiducial values of Γ = 10 and Rin = 2 × 10 cm, ΓV (Dermer & Menon 2009), where V = 4πR3 /3. The flux in we calculate τ ≈ 1 at E ≈ 70 GeV for the time-interval ‘c’ in in the lab frame is therefore given by γγ γ Table 1 for GRB 130427A. Figure 2 shows the photodisintegrated ∗ ∗ ∗ ∗ ∗ ∗ ∗ j (Eγ )V ΓEγ V ′ ∗ γ-ray flux model (thick-dashed curve) using the opacity in equa- Eγ fγ,A(Eγ )= 2 = 2 qγ (Eγ /Γ), (11) 4πdL 4πdL tion (15) to modify the flux in equation (12) in the slab approxima- −1 −1 −2 tion (Dermer & Menon 2009). and finally the differential flux in, e.g., (MeV s cm ) units ± The secondary e pairs from γγ interactions will be pro- at the Earth is given by ′ ¯′′ ′ duced with a maximum energy of Ee ≈ Eγ,FeγFe ≈ 3 GeV. 2 ′ Γ V ′ Eγ (1 + z) The characteristic synchrotron photon energy from these pairs, with fγ,A(Eγ )= qγ . (12) 13 2 BQ = 4.414 × 10 G, is given by 4πdL Γ ′ In Fig. 2 we fit the photodisintegration model flux (thick- 3B ′2 2 Γ Eγ,syn = γe mec dashed line) in equation (12) for the Iron nuclei, with parameters 2BQ 1+ z ¯′′ ′ n¯Fe = 2 and Eγ,Fe = 1 MeV, to the observed additional PL B Γ ≈ 60 MeV. (16) component in the interval ‘c’ during the prompt emission phase of 130 kG 103 GRB 130427A (Ackermann et al. 2014). To model the ∼ 1-70 GeV ± component in the interval ‘c’ we need a parent Fe-nuclei spectrum The e pairs are essentially in the fast-cooling regime, and their in the GRB jet-frame which is given by synchrotron emission flux is shown (thin-dashed line) in Fig. 2, ′ which is below the primary SBPL component. dnFe 20 ′ −3.05 −3 −1 ′ = 1.3 × 10 EFe cm MeV . (13) dEFe This corresponds to an isotropic-equivalent luminosity of the Fe- nuclei in the jet of GRB 130427A as given by 4 BETA-DECAY NEUTRINOS

′ ′ EFe,max A secondary neutron is produced approximately every other GDR 2 2 ′ dnFe ′ LFe,iso = 4πRincΓ ′ 2 EFe ′ dEFe interactions, see equation (1), which will decay to produce an elec- Eγ mFec Z ′′ dEFe 2E¯ γ,Fe tron antineutrino. Due to relativistic effect (Razzaque & Mészáros − 2006), the time scale for the neutron decay neutrino emission in ≈ 3.2 × 1053 erg s 1, (14) the observer frame is of the same order as the interval ‘c’. Since where the lower limit of the integration follows from the equa- the multiplicity of photodisintegrated γ rays is 2 and the energy tion (8). As for comparisons, the isotropic-equivalent luminosity of ν¯e is roughly 1/2 of the energy of the γ-ray in equation (8) as in the PL component of 1-70 GeV γ-rays is ≈ 5 × 1050 erg/s, i.e., given by Anchordoqui et al. (2007), the neutrino source flux can be about three orders of magnitude lower. The isotropic-equivalent γ- estimated as fν¯e (Eν )=(1/2)fγ,A(2Eγ ). ray luminosity in the SBPL component in the same time-interval After neutrino flavor oscillation over cosmological distance,

c 0000 RAS, MNRAS 000, 000–000 Photodisintegrated γ and ν from GRB 130427A 5 the flux will be modified and the oscillation probability can be ACKOWLEDGMENTS written for a given production flavor α and an observable flavor 2 2 This work was supported in part by the National Research Foun- β as P (ν → ν ) = |U | |U | , where U is the PMNS α β i βi αi αi dation (South Africa) grants no. 87823 (CPRR) and no. 93273 mixing matrix (Olive et al. 2014). The fluxes on the Earth are mod- P (MWGR) to SR. JCJ is thankful to SR and the Raman Research ified by this probability as f (E ) = P (ν → ν )f (E ). For β ν α β α ν Institute for supporting a visit to the University of Johannesburg the current best-fit oscillation parameter values (Fogli et al. 2012) where most of this work was done. the ratios of fluxes of different flavors at the source, fν¯e : fν¯µ : fν¯τ =1:0:0 from the beta decay neutrinos, will be modified to fν¯e : fν¯µ : fν¯τ ≈ 0.55 : 0.27 : 0.18, at the Earth. We calculate the number of neutrino events expected from REFERENCES GRB 130427A in our photodisintegration model, using the IceCube Abbasi R. et al., 2012, Nature, 484, 351 effective area in Abbasi et al. (2011) scaled to the full IceCube, as Abbasi R. et al., 2011, Phys. Rev. D, 83, 012001

2.5 TeV Ackermann M. et al., 2014, Science, 343, 42 fν¯µ ∆tc Anchordoqui L. A., Beacom J. F., Goldberg H., Palomares-Ruiz S., Weiler Nν¯µ = Aeff (Eν )fγ,Fe(2Eν )dEν . (17) fν¯e 2 Z100 GeV T. J., 2007, Phys. Rev. D, 75, 063001 The expected neutrino events from GRB 130427A in our model Asano K., Guiriec S., Mészáros P., 2009, ApJ, 705, L191 Beloborodov A. M., Hascoët R., Vurm I., 2014, ApJ, 788, 36 is N¯ ≈ 0.003, which is consistent with IceCube non- νµ Boˇsnjak Z.,ˇ Daigne F., Dubus G., 2009, A&A, 498, 677 detection (Abbasi et al. 2012). Therefore no constraints can be de- Brown R. W., Mikaelian K. O., Gould R. J., 1973, Astrophys. Lett., 14, rived on our model, as was done by Gao et al. (2013) for a primary 203 p-γ model, using non-detection of neutrinos from GRB 130427A. Crumley P., Kumar P., 2013, MNRAS, 429, 3238 Dermer C. D., Menon G., 2009, High Energy Radiation from Black Holes: Gamma Rays, Cosmic Rays, and Neutrinos Fogli G. L., Lisi E., Marrone A., Montanino D., Palazzo A., Rotunno 5 SUMMARY AND CONCLUSIONS A. M., 2012, Phys. Rev. D, 86, 013012 GRB 130427A is one of the brightest and energetic GRBs detected Gao S., Kashiyama K., Mészáros P., 2013, ApJ, 772, L4 Ghisellini G., Ghirlanda G., Nava L., Celotti A., 2010, MNRAS, 403, 926 at a relatively low redshift of 0.34. Detection of a hard PL com- Gould R. J., Schréder G. P., 1967, Physical Review, 155, 1404 ponent in the prompt phase by the Fermi-LAT, that extends up to Kumar P., Barniol Duran R., 2009, MNRAS, 400, L75 73 GeV, is very interesting and beg explanation of its origin. We Kumar P., Barniol Duran R., 2010, MNRAS, 409, 226 have modeled this spectral component using photodisintegrated γ- Kumar P., Zhang B., 2015, Phys. Rep., 561, 1 ray emission from an Iron-rich GRB jet. The observed keV-MeV Levan A. J., Cenko S. B., Perley D. A., Tanvir N. R., 2013, GRB Coordi- γ rays, presumably produced by synchrotron radiation from pri- nates Network, 14455, 1 mary electrons or by another process, provide the necessary tar- Maselli A., Beardmore A. P., Lien A. Y., Mangano V., Mountford C. J., get photons required for this model. The time scale required for Page K. L., Palmer D. M., Siegel M. H., 2013, GRB Coordinates Net- Fe photodisintegration with target photons is compatible with the work, 14448, 1 11.5-33.0 s interval of GRB 130427A when the hard PL spectral Maselli A. et al., 2014, Science, 343, 48 Melandri A. et al., 2014, A&A, 567, A29 component was detected by the Fermi-LAT. Non-detection of a PL Mücke A., Engel R., Rachen J. P., Protheroe R. J., Stanev T., 2000, Com- component at earlier times can be interpreted as inefficiency of the puter Physics Communications, 124, 290 photodisintegration process to produce γ rays in the LAT range. Murase K., Beacom J. F., 2010, Phys. Rev. D, 82, 043008 The total isotropic-equivalent energy required in the relativis- Olive K. A., et al., 2014, Chin. Phys., C38, 090001 54 tic Fe nuclei in this model, ≈ 5 × 10 erg, is relatively modest Pe’er A., Zhang B.-B., Ryde F., McGlynn S., Zhang B., Preece R. D., for a hadronic model and is only . 10 times the total isotropic- Kouveliotou C., 2012, MNRAS, 420, 468 equivalent energy released in γ rays from GRB 130427A. This is Preece R. et al., 2014, Science, 343, 51 due to relatively higher efficiency of the photodisintegration pro- Puget J. L., Stecker F. W., Bredekamp J. H., 1976a, ApJ, 205, 638 cess than other hadronic processes, such as the photopion produc- Puget J. L., Stecker F. W., Bredekamp J. H., 1976b, ApJ, 205, 638 tion. A more challenging issue, however, is to explain the origin of Razzaque S., 2010, ApJ, 724, L109 Razzaque S., 2013, Phys. Rev. D, 88, 103003 heavy nuclei in the GRB jet. Wang et al. (2008) suggested a pos- Razzaque S., Dermer C. D., Finke J. D., 2010, The Open Astronomy Jour- sibility that the GRB jet could be rich in heavy nuclei initially, as nal, 3, 150 the subrelativistic jet deep inside the GRB progenitor star can en- Razzaque S., Mészáros P., 2006, J. Cosmology Astropart. Phys., 6, 6 trap core material (Zhang et al. 2003). This is the scenario we have Razzaque S., Mészáros P., Zhang B., 2004, ApJ, 613, 1072 adopted to explain the observed prompt GeV γ-rays by Fe disinte- Rybicki G. B., Lightman A. P., 1986, Radiative Processes in Astrophysics gration. In case the Fe is a subdominant component in the GRB jet, Stecker F. W., 1968, Phys. Rev. Lett., 21, 1016 the required total energy will increase. For example, in case of so- Stecker F. W., 1969, Physical Review, 180, 1264 lar composition the jet will be dominated by proton and light nuclei Stecker F. W., Salamon M. H., 1999, ApJ, 512, 521 and the total jet energy will need to be ∼ 103 times the value we Tam P.-H. 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