Nucleosynthesis in the Outflows Associated with Accretion Disks Of

arXiv:1309.0954v1 [astro-ph.HE] 4 Sep 2013 ai aeegh hc nrosyhle oestablish to and helped optical X-ray, enormously the which wavelengths in gamma of radio Besides sub- observed detection a were astronomers. afterglows the remained the to rays, origin since interest and great Ever nature of were ject their 1974). which satel- GRBs, Konus first 1973), al. Soviet the et the (Mazets al. from sev- lites data et by published (Klebesadel strictly confirmed were However, quickly later is satellites Vela treaty years nations. the ban other eral from and test results track nuclear U.S.S.R. the keep the the to by that USA, followed fact the by the launched of satellites Vela long- the causing disk to the material to GRBs. of duration jets perpendicular drive outward that holes blast black surround- mass disks one accretion the stellar to ing is explaining stars massive models 2001) of theoretical collapse Woosley core promising al. & most et the MacFadyen MacFadyen of Col- MW99, 1993; hereafter infancy. (Woosley their 1999, governing in model still theories are lapsar underlying well- bursts the are short-duration driving the now, bursts the by long-duration completely Although sec- understood by the two caused behind are to phenomena. mechanisms they milliseconds that physical few believed different dura- is a short It last from while onds. bursts range minutes, bursts several Long-duration to tion seconds (GRBs) two increased. bursts from drastically gamma-ray long-duration has studying for [email protected] [email protected] , [email protected] India; 012, 560 1 by 1960s late the in accidentally discovered were GRBs data of availability the decades two last the Over rpittpstuigL using 2018 typeset 15, Preprint October version Draft eateto hsc,Ida nttt fSine Bangal Science, of Institute Indian Physics, of Department ULOYTEI NTEOTLW SOITDWT ACCRETION WITH ASSOCIATED OUTFLOWS THE IN NUCLEOSYNTHESIS fmn fteehayeeet aebe bevdi h -a a X-ray the de in not observed have silico to been in headings: seems have rich Subject Swift remains elements etc., disk XMM-Newton heavy the BeppoSAX, these of Chandra, of zone many Si-rich of the from outflow However, h uflw rmteedssi aoiyo ae illa oa obs an He-rich, to the lead from will considered cases is of outflow majority when a present in mainly disks is these It from outflows the tdigti efidta aynweeet ieiooe ftitanium, of disk isotopes the like in elements new synthesized outflows. many spher thus the that adiabatic, in elements find an we these outflo using this and of by studying winds which disks via understand these disk s from to the are launched from elements outflows ejected heavy nucleosynthes the are Several the elements past. and heavy the hydrodynamics these in driven. The extensively t is studied gets fallback. sta explosion been star massive massive supernova neutron formed via collapsars, mild newly hole a these this subsequently In and and initially momentum collapsars. star II proto-neutron Type a the by formed eivsiaencesnhssisd h uflw rmgamma-ray from outflows the inside nucleosynthesis investigate We 1. A INTRODUCTION T E tl mltajv 03/07/07 v. emulateapj style X 56 ii bnatysnhszdi oto h ae nteoto which outflow the in cases the of most in synthesized abundantly is Ni abundance — crto,aceindss—gmary:brt olpas—nuc — collapsars — bursts rays: gamma — disks accretion accretion, nrn Banerjee Indrani .in rf eso coe 5 2018 15, October version Draft 1 COLLAPSARS n airt Mukhopadhyay Banibrata and ABSTRACT ore eio Hgre l 03 aFde ose 1999; Woosley pro- 2006). & MacFadyen Heger, the 2003; & from Woosley al. loss) mass et momentum reduces (Heger angular metallicity genitor develops hence low disk and (and accretion hole loss black necessary an black the the that form star around so the to very momentum endows collapse only rotation angular rapid core because ro- The undergo is rapidly holes. This can most stars and stars. massive massive metallicity 2006). low most (Zhang tating from asso- 060614 result GRB not are GRBs e.g. supernovae GRBs with with long-duration hy- ciated associated all their not Similarly, losing are GRBs. after envelope, stars helium massive and/or very drogen of and collapse lines core 2010). oxygen al. weak et with (Nomoto SN (XRF) as Flashes dimmer exception X-Ray a an con- exhibited be in to it appears 2006aj are GRB060218 SN they with Nevertheless, hence junction ‘hypernova’. and supernovae as magni- typical of termed orders than several larger energies tude possessed oxy- and strong lines Most exhibited 2005; gen supernovae 2004). mentioned above al. al. et the Höflich Nomoto et of 2005; 2005; Bloom 2005; Matheson Valle Bloom Della & 2005; Woosley Piran (see, 021211; 031203 2006; GRB GRB with with 2002lt 2003lw SN SN 2003), and events GRB al. with et such 2003dh (Hjorth more 030329 SN SN1998bw many of that seen, association After the ever namely, followed, SNe 1998). conjunction unusual al. research in most et GRB 980425 (Galama the of GRB of history of one the discovery with the in with point arose turning co- A in (Mészáros occur 2002). (SNe) GRBs observations supernovae several core-collapse Many that with reveal incidence GRBs. years recent the the of in hypothesis working a olpa oeswihepantefraino ac- of formation the explain which models Collapsar the to due occur which Ibc, Type of SNe all However, nhszdi h ikadmc of much and disk the in ynthesized asomdt tla asblack mass stellar a to ransformed 56 sudrocr olpet form to collapse core undergo rs s esuyncesnhssin nucleosynthesis study We ws. clyepnigoto model, outflow expanding ically Ni/ etdteelnsyet. lines these tected uvv nteoto.While outflow. the in survive si hs crto ik has disks accretion these in is trlw fsvrlGB by GRBs several of fterglows us GB crto disks accretion (GRB) burst ral uenv explosion. supernova ervable opr icec r present are etc. zinc copper, 54 .Atog,eiso lines emission Although, n. h uenv jcalack ejecta supernova The erc oe ftedisks. the of zones rich Fe 1 IK FTP II TYPE OF DISKS mle that implies leosynthesis 2 Banerjee & Mukhopadhyay cretion disks around stellar mass black holes as a result neutrino-driven jets have too much baryon loading (Lei of core collapse of rapidly rotating massive stars can be et al. 2013). Nucleosynthesis in the jets has been studied categorized broadly into two kinds, namely, Type I and extensively in the past (Fujimoto et al. 2008, Fujimoto et Type II collapsars. In Type I collapsar, the star under- al. 2007; Beloborodov 2003; Inoue et al. 2003; Lemoine going core collapse is very massive with mass in the main 2002; Pruet et al. 2002). 56Ni is abundantly synthe- 56 sequence (MMS ) at least greater than 40M⊙. When sized in the jets. Additionally, Ni is also synthesized these stars undergo core collapse they directly form stel- in copious amounts in the outflows from the collapsar lar mass black holes. No observed supernova explosion is accretion disks (MW99; Pruet et al. 2003, Milosavl- associated with such core collapse events and hence they jevićet al. 2012,) and also in explosive burning as a are often termed as “failed supernovae” (Fryer 1999). shock wave propagates out through the star (Maeda & If the progenitor star has sufficient angular momentum Nomoto 2003; Fryer et al. 2006; Maeda & Tominaga (MW99), which is in a reasonable range of progenitor 2009). Apart from accreting black holes, protomagne- model predicted by Heger et al. (2000), an accretion tars which can serve as another possible central engine disk develops around the black hole. The disk stays for for long-duration GRBs are also capable of producing 10 − 20 s (MW99) and during this time very high accre- neutron-rich outflows (Metzger et al. 2008). MacFadyen −1 tion rate (M˙ ) with M˙ > 0.1M⊙s is maintained. Due & Woosley (1999) showed that as collapsar disks accrete to such high M˙ the temperature of the disk rises signif- matter on to the black hole, they also eject substantial icantly above 1010K, specially in the inner region of the amount of matter through outflows. These outflows of- disk close to the black hole, which enables the photo- ten result in stellar explosions which may be observable disintegration of all the heavy nuclei (which might have as Type Ibc supernovae (Kumar et al. 2008). SN1998bw been formed in the outer disk) into free nucleons. While and SN1997ef are examples of such supernovae (Mac- nucleosynthesis is not so important in order to produce Fadyen 2003). It has been suggested that these explo- heavy elements in such accretion disks itself (Banerjee & sions may take place independent of any jet resulting Mukhopadhyay 2013a), there may be outflows from the in GRBs. It is worth mentioning that a stellar explosion neutron-proton rich regions (Surman et al. 2011; Surman does not necessarily lead to a supernova. For a stellar ex- et al. 2006) where due to appropriate lowering of tem- plosion to be observable as a supernova, there has to be a perature and density, the free nucleons may recombine continuous source of energy to power the observable light to give rise to 56Ni and other heavy elements. Since, curve for long times, of the order of weeks to months. nucleosynthesis in the context of outflows from Type I The time evolution of the light curve of Type Ibc supernovae results from the decay of 56Ni to 56Co which subse- collapsars has been studied extensively in the past (e.g., 56 Surman et al. 2006; Surman et al. 2011 etc.), we do not quently decays to Fe. The half-lives of these decays are repeat it in the present context. 6 days and 77 days respectively. Once these nuclei un- Type II collapsars are formed from the core collapse of dergo beta decay, their daughter nuclei emit gamma rays progenitors with mass which eventually come in thermal equilibrium with the matter ejected in the outflow. The energy from these de- 20M⊙ . MMS < 40M⊙. In this case, first a proto- neutron star is formed after the core collapse and a mild cays is later re-emitted in the optical band and observed supernova explosion is driven. However, a strong reverse as the supernova light curve. Hence the temporal evo- shock causes the supernova ejecta to fall back onto the lution of the supernova light curve is directly dependent on the amount of 56Ni produced in the outflow. If suffi- newly formed neutron star which then immediately col- 56 lapses into a black hole. The increase in progenitor mass cient amount of Ni is not produced in the outflow, the enhances the amount of supernova ejecta falling back stellar explosion would still take place but it would not onto the nascent neutron star (Woosley & Weaver 1995; be observable and hence there will be no supernova. In this work we have found that 56Ni is abundantly syn- Fryer 1999; Fryer & Heger 2000). M˙ is also lower in −4 −2 −1 thesized in most of the cases in the outflow which signifies this case, 10 to 10 M⊙s (Fujimoto et al. 2003), that the outflows from these disks in a majority of cases and this accretion may continue for hundreds to thou- ˙ will lead to an observable supernova explosion. Apart sands of seconds (MacFadyen et al. 2001). Lower M from 56Ni, some other isotopes of nickel (57Ni, 58Ni) and decreases the density and temperature in these accretion 44Ti, 60Zn, 62Zn and 59Cu are synthesized abundantly disks compared to collapsar I disks which makes them in the outflow. 28Si, 32S, 36Ar and 40Ca are also synthe- ideal sites for the nucleosynthesis of heavy elements. sized in the outflow in some of the cases. By investigating Nucleosynthesis in the accretion disks of Type II col- nucleosynthesis in the outflow, we can conclusively say lapsars has already been studied in detail (Banerjee & that which of the elements leave their signatures in the Mukhopadhyay 2013a,b). Here we examine nucleosyn- observation. This is important because, emission lines of thesis in the outflows launched from them considering many of these heavy elements have been observed in the an adiabatic, one-dimensional and spherically expand- X-ray afterglows of several GRBs by BeppoSAX, Chan- ing outflow model (Fujimoto et al. 2004). As matter ac- dra, XMM-Newton etc., e.g. iron lines in GRB 970828 cretes onto the central object, some fractions of the ac- (Yoshida et al. 1999), GRB 970508 (Piro et al. 1999), creting gas could be ejected from the disk through out- and GRB 000214 (Antonelli et al. 2000); magnesium, flows and jets. Jets can be driven by neutrino processes silicon, sulphur, argon and calcium lines in GRB 011211 (MW99; Fryer & Mészáros 2003) and/or magnetohydro- (Reeves at al. 2003); sulphur lines in GRB 991216 (Piro dynamic (MHD) processes (Mizuno et al. 2004; Proga et al. 2000) and GRB 020813 (Butler et al. 2003). We et al. 2003) with relativistic velocities which exhibit as also present the nuclear reactions responsible for the syn- GRBs. It has been recently proposed that a large frac- thesis of such heavy elements. tion of GRBs should have a magnetically driven jet, since The paper is organized as follows. In the next section, Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 3 we briefly mention the hydrodynamic model adopted to Table 1 study the collapsar accretion disk and discuss the main Various disk models results we have obtained while studying the nucleosynthesis in the accretion disk. In §3 we give the details of Model M˙ Initial abundance the outflow model chosen for the present purpose. §4 is I 0.001 He − rich − devoted to the nucleosynthesis in the different outflow II 0.001 Si rich III 0.01 He − rich models with the details of the underlying nuclear reac- − tions and finally we end with a summary and discussion IV 0.01 Si rich in §5. 2. DISK MODEL AND INPUT PHYSICS efficient, then most of the incoming gas will be accreted, else it will be ejected from the system in the form of We adopt height-averaged equations based on a outflows. The cooling processes depend on temperature pseudo-Newtonian framework (Mukhopadhyay 2002). which in turn depend on the angular momentum of the The accretion disk formed in a Type II collapsar is stellar progenitor (MacFadyen 2003). The virial temper- modelled within the framework suggested by previous ature and the angular momentum at the Keplerian radius authors (Kohri et al. 2005; Chen & Beloborodov 2007) are inversely proportional to each other. The production where the electron degeneracy pressure and the evolv- of a supernova corresponding to a GRB thus depends ing neutron to proton ratio are appropriately calculated. on the angular momentum of the disk. If the angular The details of the hydrodynamics and the nucleosynthe- momentum is low enough so that the virial temperature sis in the disk are described by Banerjee & Mukhopad- reaches above 1010K, then all the heavy elements will hyay (2013a,b). Here we recall some of the salient fea- be photodisintegrated to free nucleons which will initi- tures of the nucleosynthesis in the disk for completeness. ate the pair capture reactions onto the free protons and Table 1 describes the various disk models we use for our neutrons which in turn will lead to the emission of neu- work. While analysing the nucleosynthesis in the disk trinos. Thus, subsequently the system will be cooled effi- we choose that the disk is once He-rich and then it is ciently. Hence, low angular momentum progenitors may Si-rich in the outer region. In Banerjee & Mukhopad- produce a GRB but not an observable supernova. When hyay (2013a,b), we have reported synthesis of several un- the angular momentum is large enough so that the virial 31 39 43 35 usual nuclei like P, K, Sc, Cl and various uncom- temperature falls below 5 × 109K, photodisintegration mon isotopes of titanium, vanadium, chromium, man- and pair capture reactions get suppressed, as a result of ganese and copper in the disk, apart from isotopes of which the matter remains heated up subject to be ejected iron, cobalt, nickel, silicon, sulphur, argon and calcium from the disk in the form of outflows. In the intermedi- which have already been reported earlier. Moreover, ate range, there is a partial photodisintegration; hence analysing the disk results we have found that several although photodisintegration cools the system, cooling zones, characterized by dominant elements, are formed due to pair capture is still suppressed. Thus photodisin- in the disk. For example in the He-rich disk the region tegration aids accretion in this regime. 40 44 48 between 1000 − 300Rg is rich in Ca, Ti and Cr. In- The winds/outflows can be driven by various processes, side this region between 300−80Rg there is a zone which e.g. neutrino process, mechanisms related to viscosity is overabundant in 56Ni, 54Fe, 28Si and 32S. Finally in- and magnetic centrifugal force. We first briefly describe side 80Rg all the heavy elements get photodisintegrated the mechanism driving winds via each of the processes. to 4He and some free nucleons are also synthesized. For When the proto-neutron stars are formed after the core the Si-rich disk the outermost zone from 1000 − 250Rg is collapse of their progenitors, a region of low density and rich in 28Si and 32S. Inside this region there is a narrow high entropy is formed behind the supernova ejecta which 54 56 zone rich in Fe and Ni which extends upto 70Rg and is steadily heated up by the neutrinos emanating from the finally the innermost region of the disk is again overabun- proto-neutron star. Due to the deposition of the heat, the dant in 4He with the presence of some free nucleons. It is ejecta gains kinetic energy which accelerates the material to be noted here that by overabundant we mean the mass in it resulting in an outflow known as the neutrino-driven fractions of the elements like 56Ni, 54Fe, 28Si, 32S and 4He wind (Fischer et al. 2010). However the geometry of are many orders of magnitude higher compared to their this process is quite different from the collapsar scenario initial mass fractions at the outer disk. The elemental (MW99). When the accretion rate is high mainly in the distribution in the He- and Si-rich disks starts appear- context of Type I collapsars, the inner regions of the ac- ing identical once threshold density and temperature are cretion disk become very hot to emit copious amounts of reached irrespective of the initial abundances. On in- neutrinos. But as the neutrino luminosity increases, neu- creasing M˙ the respective zones shift outwards. Under- trino annihilation also becomes efficient and large energy lying nuclear reactions were also described in detail by deposition can occur in the polar regions which creates Banerjee & Mukhopadhyay (2013a). a pressure gradient that has a component away from the disk. This pressure gradient pushes the gas of radiation 3. OUTFLOWS FROM ACCRETION DISKS OF TYPE II and pairs which drives the outflow. Thus, close to the COLLAPSARS black hole neutrino annihilation may lead to energy depo- The production of outflows depends on the degree to sition which can drive polar relativistic outflows contain- which the disk is cooled by neutrino emission and pho- ing expanding bubbles of radiation, pairs and baryons todisintegration of heavy nuclei. Since M˙ is very high, (MW99). it is always possible that the matter may get deposited High differential rotation in the accretion disks leads onto the accretion disk which favors outflow unless cool- to enhanced viscous interaction which heats up the disk, ing plays an important role to aid accretion. If cooling is raises its entropy and drives a wind off the disk. This 4 Banerjee & Mukhopadhyay explains how outflows can be driven by viscosity. How- accretion disk. The radial velocity and the disk scale ever, since the temperature in these accretion disks is height are known from the disk hydrodynamics and hence very high, the gas is completely ionized which generates vej at Rej can be calculated. Once vej is calculated, the electric currents, that in turn produces magnetic fields. temperature profile can be obtained from equation (1), Galeev et al. (1979) showed that rotational shear and where we choose γ =5/3. convection which are present in these disks can amplify Adiabaticity ensures no entropy change during the the seed magnetic field to very large values, B & 1015G. propagation of the outflow. The entropy per baryon, The magnetic field can subsequently drive an outflow S, of the ejecta is given by (Pruet et al. 2003, Qian & transferring a part of the Poynting flux to matter (Bland- Woosley, 1996) ford & Payne 1982). For further details of how winds can 3 3/2 be driven by viscosity and MHD processes, see, MW99 S TMeV TMeV ≈ 0.052 +7.4+ ln ≈ S0, (7) and Daigne & Mochkovitch (2002) respectively. Also see k ρ10 ρ10

Levinson (2006) where general relativistic MHD driven where S0 is the entropy per baryon of the accretion disk outflows were comprehensively studied in the context of in units of k at Rej , TMeV is the temperature of the out- GRBs. Barzilay & Levinson (2008) investigated nucle- flow in units of MeV and ρ10 is the density of the outflow osynthesis in the above mentioned outflows. in units of 1010 g cm−3. The first term on the right hand side of equation (7) is the contribution to the entropy 3.1. Formulation of the outflow model per baryon due to the relativistic particles like photons Abundance of various elements synthesized in the disk and electron-positron pairs, while the last two terms rep- usually evolves in the outflow. The change in the abun- resent the contribution due to the heavy nonrelativistic dance not only depends on the initial conditions of the particles. Assuming that outflows are unlikely from a ejecta (e.g. density, temperature and abundance at the very large distance of the black hole, we consider out- radius from where the outflow is launched), but also on flow from Rej . 200Rg (Fujimoto et al. 2004) for our the detailed hydrodynamics of the wind. spherical outflow. The temperature profile is already ob- Various outflow models have been suggested by several tained from equations (1) and (6). Therefore, assuming authors. For the present purpose, we choose a hydrody- a fixed entropy for the outflow, we obtain the density namic model which is assumed to be adiabatic and freely profile from equation (7). Once the hydrodynamics of expanding (Fujimoto et al. 2004), which was already im- the outflow is determined, the abundance evolution of plemented in past for the purpose of nucleosynthesis in various elements in the ejecta can be obtained in the collapsars. The temperature of the ejecta, based on this same way as it has been done for the disk (Banerjee & model, is given by Mukhopadhyay 2013a) such that the initial composition 3(γ−1) of the ejecta to begin with is the same as that in the disk Rej Tej (t)= T0 . (1) at Rej . Rej + vej t In the following sections, the abundance evolution Here, R is the radius of the accretion disk at which of various elements and the subsequent reactions lead- ej ing to change of abundances will be systematically dis- the outflow is launched, vej is the velocity of the ejecta at that radius which is assumed to be constant during cussed considering the possibility that the outflow may be launched from different radii of the disk with differ- the ejection, T0 is the temperature at Rej and γ is the adiabatic index. T at R is known from the disk hy- ent velocities of ejection, and the entropy of the outflow 0 ej being once same as that of the disk and once double the drodynamics. We calculate vej from the ratio of the rate at which matter is ejected from the disk to the matter entropy of the disk. accreted in. Let us assume that M˙ ej be the rate at which 4. INVESTIGATION OF ABUNDANCE EVOLUTION IN THE matter is ejected from the disk. Then if we assume that OUTFLOW the gas is spherically expanding, In order to study the abundance evolution in the out- M˙ =4πr2ρv , (2) flow, we use well tested nuclear network code, which ej ej has been implemented for more than two decades where, by, e.g., Chakrabarti et al. (1987) and Mukhopad- 2 2 2 r = Rej + Hej , (3) hyay & Chakrabarti (2000) in the context of accretion disks. Cooper et al. (2006) used it to study super- Hej being the disk height at which the outflow is launched and ρ the outflowing matter density. On the bursts on the neutron star surface. We have modi- fied this code further by increasing the nuclear net- other hand at Rej , the rate at which the matter accretes is, work and including reaction rates from the JINA Reaclib Database, https://groups.nscl.msu.edu/jina/reaclib/db/ M˙ =4πR ρH v , (4) acc ej ej R (Cybert et al. 2010). when total accretion rate, As already shown by Banerjee & Mukhopadhyay ˙ ˙ ˙ (2013a), the disk has several zones characterized by dom- M = Macc + Mej = constant. (5) inant elements. We investigate abundance evolution in Thus, the outflow from all the zones in the accretion disks men- M˙ v R H tioned in Table I that lie within Rej . 200Rg. We focus ej = ej ej + ej , (6) ˙ our attention mainly on the outflows from disks with Macc vR Hej Rej −1 M˙ = 0.001M⊙s where initially the accreting matter where vR is the radial velocity of the inflow at Rej We was chosen to be once He-rich and then Si-rich. Then we assume a given M˙ ej /M˙ acc at the ejection radius of the briefly mention the main results for the outflows from Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 5 relatively high M˙ disks, because outflows from those underlying reactions taking place in the outflow. 28Si, disks do not yield any new result. While considering 32S, 36Ar, 40Ca, 44Ti and 48Cr all react with excess 4He the outflow from the disks, we must keep in mind that present in the outflow to give rise to 56Ni. Apart from the material may be heated as it leaves the disk due 56Ni, these α-elements also give rise to some amount of to viscous heating and/or neutrino energy deposition. 54Fe, 55Co, 56Co and 58Ni. The reactions are mainly However, heating due to neutrino energy deposition is a series of (α,p) and (α,n) reactions starting with the mainly important in the context of Type I collapsar ac- α-elements. For example, 28Si gives rise to 56Ni via cretion disks. Most of the heating occurs when the out- 28Si(α, p)31P(α, p)34S(α, n)37Ar(α, p)40K(α, n)43Sc(α, p) flow is being launched from the disk, while it evolves 46Ti(α, n)49Cr(α, p)52Mn(n,γ)53Mn(p, n)53Fe(α, n)56Ni. almost adiabatically during its way away from the disk By means of similar reactions, 56Ni is obtained by (Pruet et al. 2004a). However, in an MHD driven wind starting with the other α-elements as well. the entropy in the outflow remains almost similar to that 56Ni, which is the chief nucleosynthesis product in of the disk at the point of ejection as there is no efficient these cases, is obtained from two processes, first, from heating source inside the wind (Fujimoto et al. 2004). the direct recombination of α-s and second from the Therefore, we consider outflows for both the cases, when (α,p), (α,n) reactions starting with the α-elements. once the entropy in the outflow remains close to that of The density and velocity of the outflow decide which the disk and then the entropy in the outflow becomes out of the two processes plays the dominant role in double than that of the disk. In each of the high en- the synthesis of 56Ni. While both the above processes 4 tropy and the low entropy cases we consider two vej , lead to a decrease in the abundance of He, the only one ∼ 105cm s−1 and the other ∼ 108cm s−1, depend- process by which 4He can be synthesized is the re- ing on the outflow rate with respect to the inflow rate combination of neutrons and protons to α-particles, (Fujimoto et al. 2004). The major nucleosynthesis prod- which is also not very effective in this case as the ucts obtained and the underlying nuclear reactions tak- mass fraction of neutrons is quite different from that ing place in the outflows are discussed in the subsequent of protons (Surman et al. 2011). Thus, the abundance subsections. of α-particles declines quite rapidly in the outflow (even more rapidly when the velocity of ejection is 4.1. Outflow from the He-rich disk low). Once the mass fraction of the α-elements be- Here we consider the disk flow with pre-SN He-rich comes lower than a certain threshold, the rates of composition at the outer region, which surrounds a 3M⊙ (α,p) and (α,n) reactions decrease significantly and −1 their reverse reactions gain prominence to give rise Schwarzschild black hole accreting at M˙ =0.001M⊙s . to the α-elements from 54Fe, 55Co, 56Co and 58Ni.

4.1.1. Outflow from 40Rg This marks the beginning of the rising arm of the α- elements. For instance, 58Ni gives rise to 28Si via, Rej ∼ 40Rg lies primarily in the He-rich zone of the 58Ni(n, α)55Fe(p, α)52Mn(p, α)49Cr(n, α)46Ti(n, α) disk, but apart from 4He it also contains substantial 43 40 37 34 31 28 54 Ca(p, α) K(p, α) Ar(p, α) Cl(p, α) S(n, α) Si. amount of Fe. The entropy of the disk at Rej ∼ 40Rg Once the (α,p), (α,n) reactions and their inverses is S ∼ 15k, which can be calculated from equation (7) attain equilibrium, the mass fractions of the α-elements knowing the underlying disk hydrodynamics. The en- become constant and then recombination of 4He is tropy of the outflow is fixed once to S ∼ 15k and then the only source of synthesizing 56Ni. Production of to S ∼ 30k, and for each of these entropies we con- 56Ni in copious amounts in the outflow is important ˙ ˙ sider Mej /Macc = 0.1 and 100 which correspond to because the temporal evolution of the light curve of core 5 −1 8 −1 56 vej ∼ 10 cm s and 10 cm s respectively. With collapse supernovae is driven by the decay of Ni to this information, the hydrodynamics of the outflow can 56Co and subsequently to 56Fe. Hence, synthesis of 56Ni be solved with which the abundance evolution can be in the outflow signifies that there will be an observable studied, provided the initial composition of the ejecta is supernova explosion. known. The initial composition is same as that in the Apart from 56Ni, other isotopes of nickel (57Ni, 58Ni), 59 60 62 accretion disk at Rej . and Cu, Zn and Zn are also synthesized in copi- Figure 1 depicts the abundance evolution of the most ous amounts in the outflow which is illustrated in Fig. important elements in the outflow from Rej ∼ 40Rg with 1. Similar results were also obtained by Pruet et al. the entropy of the outflow S ∼ 15k. If we examine the (2004b). Surman et al. (2006) studied nucleosynthesis abundances of 4He and 56Ni for both the high velocity in the outflow from GRB accretion disks and obtained and the low velocity cases in Fig. 1(a) and Fig.1(d) re- several unusual nuclei. Kizivat et al. (2010) also ob- spectively, we notice that 4He has a lesser mass fraction tained several light p-nuclei in the outflows from GRB 56 but the yield of Ni in the outflow is higher when vej is accretion disks. However, all of them investigated nu- low. This is because when vej is low, it is easier for the cleosynthesis in the outflows associated with Type I col- 56 α-particles to recombine to form Ni. Also, elements lapsar accretion disks. When vej is low, the yields of like 28Si, 32S, 36Ar, 40Ca, 44Ti and 48Cr experience a 59Cu, 60Zn and 62Zn are also lower compared to the dip and then rise in their mass fraction while evolving high vej case (see Figs. 1(c) and 1(d)). In fact, as the in the outflow which is shown for 28Si, 44Ti and 48Cr outflow advances, 59Cu and 60Zn are found to have a in Fig. 1(b). This characteristic behavior is observed decreasing trend in the mass fraction when vej is low. in many more outflow cases and we are reporting this This is because the reactions like 59Cu(n, α)56Co and for the first time in the literature. In order to explain 60Zn(γ, α)56Ni(n, α)53Fe(α, p)56Co are favored in the low why this feature is observed in the mass fractions of the vej case. Thus, we also notice gradual rise in the mass aforementioned elements, we have to understand the 6 Banerjee & Mukhopadhyay

Fig. 1.— Abundance evolution in the ejecta while moving away from the disk, when outflow is being launched from Rej ∼ 40Rg of −1 the accretion disk for a 3M⊙ Schwarzschild black hole with M˙ = 0.001M⊙s with pre-SN He-rich abundance at the outer disk and the entropy of the ejecta being same as that of the disk. The variations of mass fraction of the elements shown by the solid lines correspond to M˙ ej /M˙ acc = 100 and the same elements when shown by linestyles other than solid correspond to M˙ ej /M˙ acc = 0.1. fraction of 56Co as the ejecta evolves away from the ac- which explains the rise in the mass fraction of 4He during cretion disk which is evident from the long-dashed line the launching of the outflow. Note that 4He was also not of Fig. 1(c). destroyed in the beginning of launching in the high en- Figure 2 illustrates the abundance evolutions of the tropy case. However, the mass fractions of all the heavy important elements in the ejecta when the outflow has elements start rising thereafter and the trough-like fea- double the entropy of the disk. On increasing the entropy ture, which was there for the α-elements in the previous of the outflow, the density of the ejecta declines (which is figure, is also seen here. In fact, Fig. 1 and Fig. 2 have illustrated in Fig. 3) and hence there are lesser chances qualitatively the same features which implies that the for the direct recombination of the α-s to 56Ni. How- underlying nuclear physics taking place in both the cases ever, we assume, in the framework of the outflow model is similar. Thus, to avoid repetition, we are not going under consideration, that with the decrease of density into the detailed description of Fig. 2. at the launching radius of the disk, the base of the out- 4.1.2. Outflow from 120R flow expands keeping it isothermal (maintaining T to g 0 56 54 be the same as that with lower entropy). In such a case, This Rej lies in the zone overabundant in Ni, Fe, the abundances of most of the heavy nuclei experience a 32S and 28Si. The entropy of the disk is calculated in the sharp decline compared to the low entropy case in Fig. same way as done earlier and in this case it is S ∼ 24k. 1 when the outflow is being launched. Since the mass We assume that the outflow has, once the entropy same fractions of neutrons and protons are very similar in the as that of the disk and then double the entropy of the outflow to begin with (see Fig. 2(a)), they efficiently disk, and while considering each of these entropy cases combine to give rise to α-particles (Surman et al. 2011) we assume the same values for M˙ ej /M˙ acc as done earlier. Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 7

Fig. 2.— Same as in Fig. 1, except that the entropy of the ejecta being double than that of the disk.

Figure 4. illustrates the evolutions of mass fraction of among the elements which finally enables them to syn- some of the most abundant elements in the outflow when thesize 56Ni. This explains why the mass fraction of 56Ni the outflow has the same entropy as that of the disk. is higher when vej is lower. This is one of the cases Although increasing the entropy decreases the density of where many elements like 28Si, 32S, 36Ar, 40Ca, 54Fe, the outflow, there is qualitatively not much change in 55Co, 56Ni, 57Ni, 58Ni, 44Ti, 48Cr etc. survive in the the abundance evolution pattern for high entropy case outflow. Thus, these elements should leave their signa- compared to the low entropy case and hence we do not tures in the outflow. Here we emphasize that although present a separate plot for the high entropy case in this emission lines of many of these heavy elements have been situation. seen in the X-ray afterglows of several GRBs by XMM- We do not observe any trough-like feature in the mass Newton, Chandra, BeppoSAX etc., Swift is yet to detect fraction of α-elements in this case. Rather the elements these lines. One possible resolution to this is that out- which were abundant during the launching of the outflows may be mainly launched from the inner disk so flow almost maintain their high abundance e.g., 28Si, 32S, that 56Ni is the primary component in it and the above 36Ar, 40Ca, 54Fe, 55Co, 56Ni, 57Ni and 58Ni etc. The mentioned elements will thus not be present in outflows. abundance evolution of some of these elements are plot- ted in Fig. 4. Whatever 4He was present in the disk to 4.2. Outflow from the Si-rich disk begin with, they recombine almost entirely to give rise 56 Now we analyze the abundance evolution in the outflow to Ni. When vej is low, the abundances of most of from the Si-rich disk, keeping other parameters of the the elements decrease more as the ejecta evolves away disk unchanged. from the disk, compared to the high vej case, because lower velocity of the ejecta ensures greater interaction 8 Banerjee & Mukhopadhyay

Fig. 3.— Typical density profiles of the outflow illustrating that the density increases on decreasing the entropy of the outflow. The solid line corresponds to the case where the entropy is same as that of the disk, while the dotted line denotes the case where the entropy is double than that of the disk.

4.2.1. Outflow from 30Rg also high, as the entropy of the outflow is low (see, e.g., Fig. 3) which favors greater recombination of α-particles in the ejecta (Fujimoto et al. 2004; Witti et al. 1994). Rej ∼ 30Rg lies primarily in the He-rich zone of the disk. The entropy of the disk at this Rej is S ∼ 13k. 4.2.2. Outflow from 75R Here also we consider two cases, once we assume that g the outflow has the same entropy as that of the disk and Here we study outflow from Rej ∼ 75Rg, when the then double the entropy of the disk. For each of the cases entropy chosen to be, once the same as that in the disk ˙ ˙ (which is ∼ 22k) and then double than that in the disk. we again assume that Mej /Macc =0.1 and 100. 54 56 The abundance evolution of the elements, when the en- This Rej chiefly lies in the Fe/ Ni rich zone of the disk. tropy of the outflow is high compared to that of the disk, However, 4He is also present abundantly in this part of have very similar trend to the case of Rej ∼ 40Rg for the disk. The abundance evolutions of the elements in He-rich disk. Hence we do not discuss the high entropy the ejecta resemble the abundance evolution trend of the outflow from this radius of the disk in detail. However, elements in the outflow from Rej ∼ 40Rg of the He-rich the outflow having the same entropy as that of the disk disk. Hence, we do not go into the detailed discussion of this particular case. has some different features. When M˙ ej /M˙ acc = 100, i.e. v is high, as shown by Fig. 5, the abundance evolutions ej 4.2.3. Outflow from 180R of the elements resemble Fig. 1 qualitatively. Hence, the g underlying nuclear physics governing both the cases are In this case we investigate outflow from Rej ∼ 180Rg. similar. However, when M˙ ej /M˙ acc = 0.1, i.e. vej is When the entropy of the disk at Rej is S ∼ 28k and, low, we find that the abundance evolution of the ejecta as done before, we once assume that the outflow has the exhibits a markedly different trend. The most impor- same entropy as that of the disk and then assume that it tant difference is that, the α-elements do not exhibit a has double the entropy of the disk. This Rej lies chiefly in trough in their abundance evolution pattern, although the 28Si/32S rich zone of the disk. 4He is hardly present their mass fractions decrease slightly and then become in the disk during the launching of the outflow. The constant. Thus, in this situation the (α,p) and (α,n) abundance evolution of various elements present in the reaction chains are not the dominant source for the syn- outflow is shown in Fig. 6. The outflow from this partic- 56 4 thesis of Ni, rather the direct recombination of He to ular Rej almost retains the composition of the disk. We 56Ni is more important, as a result of which 4He gets note that this is one case where 56Ni is hardly synthe- substantially depleted in this case, which is quite clear sized in the outflow and hence outflow from this Rej will from Fig. 1(a). The recombination of α-particles gains not lead to an observable supernova. Elements chiefly 28 32 36 40 54 so much of prominence because the vej of the ejecta is present in the outflow are Si, S, Ar, Ca, Fe, the lowest in this case and the density of the ejecta is 56Fe and 52Cr and their mass fractions remain roughly Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 9

Fig. 4.— Same as in Fig. 1, except that Rej ∼ 120Rg . constant throughout the outflow. As an example, we consider outflow from Rej ∼ 80Rg of the Si-rich disk. Thus, to begin with, the outflow had 4.3. Outflow from the disks with high accretion rate plenty of α-particles apart from substantial amounts of 56 Here we consider outflow from the accretion disks sur- free nucleons. As before Ni is abundantly synthesized 4 56 4 rounding a 3M⊙ Schwarzschild black hole accreting at at the expense of He. The yields of Ni and He in the −1 outflow by varying the entropy and velocity of ejection of M˙ =0.01M⊙s . In these disks, inside 500Rg, the abundance evolutions of the elements start appearing identi- the outflow are illustrated in Fig. 8. Of all the four cases considered here, the mass fraction of 56Ni is highest and cal irrespective of the initial abundance at the outer disk. 4 The region 90R . R . 500R forms the He-rich zone He is lowest when the outflow has low entropy and low g g velocity of ejection. This is because when the entropy of the disk. For R . 90Rg the α-particles break down into neutrons and protons. Thus, in the innermost re- is low, the density is high (see, e.g., Fig. 3) and the gion of the disk, as is evident from Fig. 7, the electron low velocity of expansion in the dense outflow medium favors greater recombination of α-s to 56Ni. Note that fraction Ye gets reduced from the value 0.5 (unlike the −1 lower vej is a more important factor than higher density case of the disk with M˙ = 0.001M⊙s ). Moreover, in for the conversion of α-s to 56Ni and hence next to the the outflow from this region, the neutrons and protons case with low entropy and low v , the yield of 56Ni is recombine to form alpha particles and further away from ej higher when vej is low but entropy is high. The relative the disk the alpha particles recombine among themselves 56 to ultimately form 56Ni (Surman et al. 2011). Hence, if yields of α-s and Ni in the remaining two cases can be explained in similar fashions. we consider outflows from Rej < 200Rg of both the He- rich and Si-rich disks, the abundance evolutions of the elements in the outflow will exhibit similar behavior. 10 Banerjee & Mukhopadhyay

Fig. 5.— Abundance evolution of the ejecta while moving away from the disk, when outflow is being launched from Rej ∼ 30Rg of −1 the accretion disk for a 3M⊙ Schwarzschild black hole with M˙ = 0.001M⊙s with pre-SN Si-rich abundance at the outer disk and the entropy of the ejecta being same as that of the disk. The variation of mass fraction of the elements shown by the solid lines correspond to M˙ ej /M˙ acc = 100 and the same elements when shown by linestyles other than solid correspond to M˙ ej /M˙ acc = 0.1. 5. DISCUSSIONS AND CONCLUSIONS the outflow, although the final abundance of the elements We have studied nucleosynthesis in outflows from ac- may slightly vary. cretion disks associated with the fallback collapsars using We have shown in our previous works (Banerjee & already established outflow model and the nuclear reac- Mukhopadhyay 2013a,b) that the accretion disks formed tion network. While studying the abundance evolution by the Type II collapsars have several zones characterized in the outflow, we have considered different velocities of by dominant elements and we have considered outflows from each of these zones. Outflow from the He-rich and expansion and entropies of the outflow. We once con- 54 56 sidered that the entropy of the outflow is same as that the Fe- Ni-rich zones of the disk always leads to the synthesis of copious amounts of 56Ni. The synthesis of of the disk which is the case for an MHD-driven out- 56 flow and subsequently assumed that the entropy is dou- Ni is important because it signifies that the outflow will drive a supernova explosion. Apart from 56Ni, the iso- ble than that of the disk, because the entropy of the 57 58 59 44 60 62 outflow may get enhanced due to viscous heating. The topes like Ni, Ni, Cu, Ti, Zn and Zn are also entropy of the outflow is mostly raised when it is being synthesized abundantly in the outflow from these zones launched from the disk and after that it remains roughly of the disk (see, for e.g., Fig. 1). If the velocity of ejec- constant (Fujimoto et al. 2004; Pruet et al. 2004a). We tion is higher than a certain threshold, the α-elements have found that the nucleosynthesis products do not in the outflow from the aforementioned zones of the disk change by varying the entropy of the outflow. In fact, exhibit a trough like feature in their abundance evolu- the abundance evolution patterns of the elements also tion pattern. However, if the velocity of expansion is too do not change qualitatively by changing the entropy of low then this feature vanishes. The reason is explained Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 11

Fig. 6.— Same as in Fig. 5, except Rej ∼ 180Rg . in great detail in §4.1.1 & 4.2.1 and we are reporting this in GRB 970508 (Piro et al. 1999), GRB 970828 (Yoshida very feature for the first time in the literature. Although et al. 1999) and GRB 000214 (Antonelli et al. 2000); we are not yet aware of any observational consequences of magnesium, silicon, sulphur, argon, calcium lines in GRB this feature, it certainly bears significance in terms of the 011211 (Reeves et al. 2003), these results should be taken underlying nuclear physics governing it. It reveals that with caution as a more recent satellite Swift has not de- certain chain of nuclear reactions becomes important un- tected these lines yet (Zhang et al. 2006, Hurkett et al. der the specific hydrodynamic conditions of the outflow 2008). Nevertheless, if we observe these elements in the and therefore is important in the context of nuclear as- outflow, we can have an idea about the nature of the ac- trophysics. We have shown that if we consider outflow cretion disks from where they are ejected, based on the from the Si-rich zone of the disks, the abundance in the present computations. outflow is not much changed from that of the disk, i.e, It has been recently speculated that the Ultra High the outflow remains rich in silicon. There may be stellar Energy Cosmic Rays (UHECRs) may be composed of explosions in these cases, but since there is no 56Ni to heavy nuclei like 56Ni. The Yakutsk data analysed the begin with, it cannot decay to 56Fe and hence there is muon component of the UHE air showers and reported nothing to power the supernova light curve. Thus there the presence of heavy nuclei component in the UHECR will be no observable supernova. spectrum (Glushkov et al. 2007). Moreover, the elonga- We expect that those elements which survive in the tion rate measurements done by the Pierre Auger Ob- outflow will leave their signatures in the observations. servatory team indicate the possible presence of heavy Although emission lines of many of these elements have or intermediate mass nuclei in the UHECRs. Wang et been discovered in the X-ray afterglows of GRBs by al. (2008) explored under what conditions these UHE XMM-Newton, BeppoSAX, Chandra etc., e.g., iron lines heavy nuclei synthesized in a GRB scenario survive pho- 12 Banerjee & Mukhopadhyay

0.5

0.498

0.496

0.494 e

Y 0.492

0.49

0.488

0.486

10 100 1000 R/Rg

−1 Fig. 7.— Evolution of the electron fraction inside the disk with M˙ = 0.01M⊙s irrespective of the initial abundance.

56 4 Fig. 8.— Yields of Ni and He in the outflow which is being launched from Rej ∼ 80Rg of the accretion disk for a 3M⊙ Schwarzschild −1 black hole with M˙ = 0.01M⊙s with pre-SN Si-rich abundance at the outer disk. The solid lines correspond to high velocity and low entropy cases, dotted lines correspond to high velocity and high entropy, short-dashed lines correspond to low velocity and low entropy and long-dashed lines correspond to low velocity and high entropy cases. Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 13 todisintegration and become a major component of UHE- place in every 100 years and the typical change in the CRs. They investigated the survival of these heavy nu- mass fraction of the i-th species during one such super- clei both in the context of internal shock and external nova event is 10−3, then the average change of mass frac- shock GRB scenarios. In the internal shock scenario, tion of the i-th species in entire galaxy in its lifetime can the outflows, which are collimated as jets, themselves be given by are the sources of heavy nuclei, whereas in the situation 11 −6 ∆Xi 100 TG 10 of external shocks the jet interacts and entrains heavy h∆Xii = 10 −3 10 . (8) nuclei as it passes through the surrounding interstellar 10 TS 10 MG medium. In the present work, we show to have synthe- As an example let us consider 60Zn. Of all the cases sized copious amounts of 56Ni and other heavy elements considered here the mass fraction of 60Zn at largest dis- in the outflow. These heavy elements once synthesized tance from the accretion disk is maximum when the ve- in the outflow spread out and contaminate the interstel- locity of ejection is high and the entropy of the ejecta is lar medium. Therefore, if the supernovae we discussed same as that of the He-rich accretion disk at Rej ∼ 40Rg. are associated with GRBs, there are possibilities that the The maximum mass fraction of 60Zn in the outflow is nuclei synthesized in the outflows resulting in stellar ex- ∼ 0.0365. If we put ∆Xi = 0.0365 in equation (8) 10 11 plosions may be entrained with the jet of material in the with TS = 100, TG = 10 and MG = 10 , we obtain −5 burst and be plausible components of UHECRs. Note h∆Xii =3.65 × 10 . This gives the maximum contami- that Metzger et al. (2011) discussed the possibility of nation of 60Zn in the galaxy. Similarly for 28Si, 32S, 59Cu, 48 44 −4 heavy nuclei synthesized in the outflows from GRBs (in- Cr and Ti the value of h∆Xii obtained are 7 × 10 , cluding disk winds) as components of UHECRs. This 1.7 × 10−4, 6 × 10−6, 1.5 × 10−6 and 7 × 10−7 respec- possibility was further studied by Horiuchi et al. (2012). tively. If the mass of the galaxy is chosen to be smaller, 9 Metzger (2012) studied one-dimensional models of nu- say 10 M⊙, then above values of h∆Xii will increase by clear burning in accretion disks with outer composition two orders of magnitude which appear quite significant. similar to those of collapsars and M˙ similar to those con- We can proceed in the similar fashion for other ele- −1 sidered in this work ∼ 0, 001M⊙s . He found that the ments as well. For every element we have to consider the outer region of the disk could be thermally unstable, due outflow model giving rise to the maximum mass fraction to high nuclear energy generation. Hence, if the disk is of the element generally away from the disk. This gives unstable, then the steady flow assumption for either disk an upperbound of the contamination of the element in or outflow is not valid. This work was followed up by the galaxy during its lifetime. two-dimensional numerical simulations by Fernandez & We now attempt to estimate the possible mass of vari- Metzger (2013), where the authors actually found that ous elements ejected in the outflow which will eventually detonations could occur in the disk miplane, possibly un- enable us to predict whether the emission lines of these binding the disk material dynamically. However, these elements should be observed or not in the afterglow. In a −4 −2 −1 concerns are not so important in our case, when we find collapsar II accretion disk, M˙ of 10 −10 M⊙s is ap- that the viscous energy is at least two orders of magni- proximately maintained for hundreds to thousands of sec- tude higher than the nuclear energy even in the outer onds (MacFadyen et al. 2001). In our case, when matter −1 regions. This may be due to the difference in the disk is being accreted in the disk at the rate of 0.001M⊙s , model for our case (Banerjee & Mukhopadhyay 2013a) the accretion continues for approximately 100s. Thus compared to the case of Metzger (2012). Moreover, Met- the total amount of matter supply is 0.1M⊙. A part zger (2012) considered disks formed by mergers of white of this matter is ejected from the disk producing out- dwarfs with neutron stars or black holes, while we dis- flow. Hence, we can calculate the mass of the various cuss about collapsar accretion disks. Hence, the tem- individual elements like 44Ti, 48Cr, 59Cu, 60Zn, 62Zn etc. perature and the density profiles of the two disk models present in the outflow. We estimate, as an example, the are expected to be different, which might affect the nu- mass of 62Zn in the outflow. clear energy generation. Further, the central object in 62Zn is synthesized abundantly in the outflow from our case is always a stellar mass black hole and not a 40Rg of the He-rich disk (see Fig. 1 and Fig. 2). We neutron star, which brings in a deeper potential well and evaluate the amount of 62Zn being ejected in the outflow potentially lower angular momentum (and hence smaller from Fig. 1. In the outflow, we have already chosen that 8 −1 5 −1 outer radius) in our disks. Finally, in the inner region of vej is once ∼ 10 cm s and then ∼ 10 cm s . When the disk, the nuclear reactions become endothermic. All vej is high, M˙ ej /M˙ acc ∼ 100. If M˙ = M˙ ej + M˙ acc = of them argue for stable collapsar disks. Nevertheless, −1 ˙ −4 −1 one should check with the possible nuclear instability (as 0.001M⊙s , then Mej ∼ 9.9 × 10 M⊙s . If we as- was done by one of us in the context of low density disks, sume that the outflow continues for 100s, i.e, as long as Mukhopadhyay & Chakrabarti 2000, 2001) in collapsar steady accretion is maintained, then we obtain an upper limit of the total amount of mass ejected ∼ 0.099M⊙. disks itself based on different disk models, which might 62 prevent us from choosing steady accretion flows. Now the maximum mass fraction of Zn as the ejecta evolves away from the disk is ∼ 0.0082 (see Fig. 1). Thus We now roughly estimate the change in the mass frac- 62 −4 tion of a particular species due to these supernova events the amount of Zn ejected would be 8 × 10 M⊙. ˙ ˙ during the lifetime of a galaxy. If we assume that the When vej is low, Mej /Macc ∼ 0.1. In that case, for −1 −5 −1 mass of the galaxy where these supernova events take M˙ = 0.001M⊙s , M˙ ej ∼ 9.09 × 10 M⊙s . Assum- 11 place is typically about 10 M⊙, the typical age of the ing, as before, that the outflow continues as long as ac- galaxy is approximately 1010 years, during the lifetime cretion takes place, i.e, for ∼ 100s, the upper limit of the of the galaxy on an average one supernova event takes total amount of matter ejected in this case is ∼ 0.009M⊙. The maximum mass fraction of 62Zn as the ejecta evolves 14 Banerjee & Mukhopadhyay away from the disk is ∼ 0.0035 (as is evident from Fig. tained similar masses of the ejecta from our calculations 62 1). Thus, the the total mass of Zn ejected in this case above (e.g. 0.009M⊙ and 0.099M⊙ when vej in low and −5 is 3.15 × 10 M⊙. high respectively). From similar calculations, we obtain the amount of Lazzati et al. (1999) evaluated the iron mass required 44Ti, 48Cr, 59Cu, 60Zn, 32S and 28Si in the outflow to to obtain an emission line of iron in the GRB after- be 7 × 10−5, 1.5 × 10−4, 6 × 10−4, 4 × 10−3, 1.7 × 10−2 glow. According to them, the required amount of iron −2 −5 2 and 6.9 × 10 M⊙ respectively when vej is high, some mass MF e & 2.3 × 10 F(F e,−13)t5R16/(qE52) M⊙. See of which may be sufficient to be observed in the emis- Lazzati et al. (1999) for the definition of various sym- 28 32 sion lines. However, for low vej , apart from Si, S and bols. Assuming F(F e,−13) ∼ 1 (Lazzati et al. 1999), 60Zn the masses of all the other elements are much less q ∼ 0.1 at most (Ghisellini et al. 1999), and the re- and hence not sufficient to be observed in the emission maining parameters in the expression of MF e to be ∼ 1 lines, as will be argued below. The masses of 28Si, 32S (Lazzati et al. 1999), the required mass of iron should 60 −3 −4 and Zn in the outflow when vej is low are 6.5 × 10 , be ∼ 2.3 × 10 M⊙. If this is roughly true for other −3 −4 1.35 × 10 and 1 × 10 M⊙ respectively. elements, then our model predicts that there is a pos- According to Fujimoto et al. (2004), the amount of sibility of observing silicon, sulphur, zinc, copper and matter ejected from the disk in a Type II collapsar can chromium lines in the GRB afterglow as the masses of go upto 0.1M⊙, depending on the amount of explo- these elements, as calculated above, represent a value −4 sion energy in the mild supernova explosion associated & 2.3 × 10 M⊙. with it. According to them, if the explosion energy is 51 & 1 × 10 ergs, the ejecta mass will be less than 0.01M⊙ and if the explosion energy is less than 1 × 1051ergs, ACKNOWLEDGMENTS the yields in the outflow will be ∼ 0.1M⊙. Although we This work was partly supported by the ISRO grant have not calculated the explosion energy, we have ob- ISRO/RES/2/367/10-11.

REFERENCES Antonelli, L. A., et al. 2000, ApJ, 545, L39 Hurkett, C. P., et al. 2008, ApJ, 679, 587 Banerjee, I., & Mukhopadhyay, B. 2013a, RAA, 13, 1063; Inoue, S., Iwamoto, N., Orito, M., Terasawa, M. 2003, ApJ, 595, arXiv:1305.1755 294 Banerjee, I., & Mukhopadhyay, B. 2013b, Proceedings of 13th Kizivat, L.-T., Mart´ınez-Pinedo, G., Langanke, K., Surman, R. & Marcel Grossman Meeting, Stockholm, Sweden, 1-7 July 2012 McLaughlin, G. C. 2010, PRC, 81, 025802 (to appear); arXiv:1302.3067 Klebesadel, R., Strong, I., Olson, R. 1973, ApJ, 182, L85 Barzilay, Y., Levinson, A. 2008, NewA, 13, 386 Kohri, K., Narayan, R., & Piran, T. 2005, ApJ, 629, 341 Beloborodov, A. M. 2003, ApJ, 588, 931 Kumar, P., Narayan, R. & Johnson, J. L. 2008, MNRAS, 388, 1729 Blandford R. D., Payne D. G. 1982, MNRAS, 199, 883 Lazzati, D., Campana, S. & Ghisellini, G. 1999, MNRAS, 304, L31 Bloom J. S. 2005, In IAU Colloq. 192: Cosmic Explosions, on the Lei, W.-H., Zhang, B. & Liang, E.-W. 2013, ApJ, 765, 125 10th Anniv. SN1993J, p. 411 Lemoine, M. 2002, A&A, 390, L31 Butler, N. R., et al. 2003, ApJ, 597, 1010 Levinson, A. 2006, ApJ, 648, 510 Chakrabarti, S. K., Jin, L., & Arnett, W. D. 1987, ApJ, 313, 674 MacFadyen, A.I. 2003, in AIP. Conf. Proc. 662, pp. 202-205 Chen, W.-X., & Beloborodov, A. M. 2007, ApJ, 657, 383 MacFadyen, A.I., & Woosley, S. E. 1999, ApJ, 524, 262; MW99 Cooper, R. L., Mukhopadhyay, B., Steeghs, D., & Narayan, R. MacFadyen, A.I., Woosley, S. E., & Heger, A. 2001, ApJ, 550, 410 2006, ApJ, 642, 443 Maeda, K. & Nomoto, K. 2003, ApJ, 598, 1163 Cybert, R. H., Amthor, A. M., Ferguson, R. 2010 ApJS, 189, 240 Maeda, K. & Tominaga, N. 2009, MNRAS, 394, 1317 Daigne F. & Mochkovitch R. 2002, A & A, 388, 189 Matheson, T. 2005. In ASP Conf. Ser. 332: The Fate of the Most Della Valle M. 2005., Nuovo Cimento C, 28, 563 Massive Stars, p. 416 Fernandez, R. & Metzger, B. D. 2013, ApJ, 763, 108 Mazets, E.P., Golenetskii & S.V., Ilinskii, V.N. 1974, JETP Lett, Fischer, T., Whitehouse, S. C., Mezzacappa, A., Thielemann, F.- 19, 77 K., & Liebendörfer, M. 2010, A & A, 517, A80 Mészáros, P. 2002, ARA&A, 40, 137 Fryer, C. L. 1999, ApJ, 522, 413 Metzger, B. D. 2012, MNRAS, 419, 827 Fryer, C. L., & Heger, A. 2000, ApJ, 541, 1033 Metzger, B. D., Giannios, D., Horiuchi, S. 2011, MNRAS, 415, 2495 Fryer, C. L., & Mészáros, P. 2003, ApJ, 588, L25 Metzger, B. D., Thompson, T. A. & Quataert, E. 2008, ApJ, 676, Fryer, C. L., Young, P.A. & Hungerford, A.L. 2006, ApJ, 650, 1028 1130 Fujimoto, S.-I., Hashimoto, M., Arai, K., & Matsuba, R. 2004, ApJ, Milosavljević, M., Lindner, C. C., Shen, R., Kumar, P. 2012, ApJ, 614, 847 744, 103 Fujimoto, S.-I., Hashimoto, M., Koike, O., Arai, K., & Matsuba, Mizuno, Y., Yamada, S., Koide, S., & Shibata, K. 2004, ApJ, 606, R. 2003, ApJ, 585, 418 395 Fujimoto, S.-I.,Hashimoto, M., Kotake, K., Yamada, S. 2007, ApJ, Mukhopadhyay, B. 2002, ApJ, 581, 427 656, 382 Mukhopadhyay, B., & Chakrabarti, S. K. 2000, A&A, 353, 1029 Fujimoto, S.-I., Nishimura, N.,Hashimoto, M. 2008, ApJ, 680, 1350 Mukhopadhyay, B., & Chakrabarti, S. K. 2001, ApJ, 555, 816 Galama, T., et al. 1998, Nature, 395, 670 Nomoto, K., Maeda, K., Mazzali, P.A., Umeda, H., Deng, J. & Galeev, A. A., Rosner, R., & Vaiana, G. S. 1979, ApJ, 229, 318 Iwamoto, K. 2004, In Stellar Collapse, ed. C Fryer, p. 277. Ghisellini, G., Haardt, F., Campana, S., Lazzati, D. & Covino, S. Amsterdam: Kluwer Academic 1999, ApJ, 517, 168 Nomoto, K., Masaomi, T., Nozomu, T. & Maeda, K. 2010, NewAR, Glushkov, A. V., et al. 2007, preprint (arXiv:0710.5508) 54, 191 Heger, A., Fryer, C. L.,Woosley, S. E., Langer, N., & Hartmann, Piran, T. 2005, Rev. Mod. Phys., 76, 1143 D. H. 2003, ApJ, 591, 288 Piro, L., et al. 1999, ApJ, 514, L73 Heger, A., Langer, N., & Woosley, S. E. 2000, ApJ, 528, 368 Piro, L., et al. 2000, Science, 290, 955 Hjorth, J., et al. 2003, Nature, 423, 847 (Kyoto: Kyoto Univ. Press), Proga, D., MacFadyen, A. I., Armitage, P. J., & Begelman, M. C. 245 2003, ApJ, 599, L5 Höflich, P., Baade, D., Khokhlov, A., Wang, L., Wheeler, J.C. 2005. Pruet, J., Guiles, S., Fuller & G. M. 2002, ApJ, 580, 368 In IAU Colloq. 192: Cosmic Explosions, on the 10th Anniv. Pruet, J., Surman, R., McLaughlin, G.C. 2004b, ApJ 602, L101 SN1993J, p. 403 Pruet, J., Thompson, T. A. & Hoffman, R. D. 2004a, ApJ, 606, Horiuchi, S., Murase, K., Ioka, K. & Mészáros, P. 2012, ApJ 753,69 1006 Nucleosynthesis in the outflows associated with accretion disks of Type II collapsars 15

Pruet, J., Woosley, S. E., & Hoffman, R. D. 2003, ApJ, 586, 1254 Woosley, S. E. 1993, ApJ, 405, 273 Qian, Y.-Z., & Woosley, S. E. 1996, ApJ, 471, 331 Woosley, S. E., & Bloom, J. S. 2006, ARA&A, 44, 507 Reeves, J. N., Watson, D., Osborne, J. P., Pounds, K. A., & Woosley, S. E., & Heger, A. 2006, ApJ, 637, 914 O’Brien, P. T. 2003, A&A, 403, 463 Woosley, S. E., & Weaver, T. A. 1995, ApJS, 101, 181 Surman, R., McLaughlin, G.C., Hix, W.R. 2006, ApJ 643, 1057 Yoshida, A., et al. 1999, A&AS, 138, 433 Surman, R., McLaughlin, G.C. & Sabbatino, N. 2011, ApJ 743, Zhang, B. 2006, Nature, 444, 1010 155 Zhang, B., et al. 2006, ApJ, 642, 354 Wang, X. -Y., Razzaque, S. & Mészáros, 2008, ApJ 677, 432 Witti, J., Janka, H.-Th., Takahashi, K. 1994, A&A 286, 841