Neutrinos, supernovae, and the origin of the heavy elements
SSCIENCE CHINA
Physics, Mechanics & Astronomy
Vol. No. : xdoi: c (cid:13) Science China Press and Springer-Verlag Berlin Heidelberg 2014 phys.scichina.com link.springer.com
Neutrinos, supernovae, and the origin of the heavy elements
QIAN YONG-ZHONG *1,2 School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA Tsung-Dao Lee Institute, Shanghai 200240
Received ; accepted ; published online
Stars of ∼ M (cid:12) end their lives as core-collapse supernovae (SNe). In the process they emit a powerful burst of neutrinos,produce a variety of elements, and leave behind either a neutron star or a black hole. The wide mass range for SN progenitorsresults in diverse neutrino signals, explosion energies, and nucleosynthesis products. A major mechanism to produce nuclei heavierthan iron is rapid neutron capture, or the r process. This process may be connected to SNe in several ways. A brief review ispresented on current understanding of neutrino emission, explosion, and nucleosynthesis of SNe. neutrino; supernova; nucleosynthesis; the r processPACS number(s): Citation:
Qian Y Z. Neutrinos, supernovae, and the origin of the heavy elements. Sci China-Phys Mech Astron, , : x, doi:
After baryogenesis in the early universe and when the tem-perature drops to T ∼
100 MeV, the only baryons presentare neutrons and protons. Because matter at such a high tem-perature is in thermal equilibrium, the neutron-to-proton ratio n / p is determined by their mass di ff erence ∆ = m n − m p = .
293 MeV through the Boltzmann factor: n / p = exp( − ∆ / T ) . (1)It is a remarkable achievement of the standard model of par-ticle physics that this mass di ff erence can now be calculatedfrom first principles to within 20% [1]. Because a neutron isheavier than a proton, the equilibrium abundance shifts moreand more towards protons as T drops. This shift is accom-plished by the competition among the weak interactions in-terconverting neutrons and protons: ν e + n (cid:10) p + e − , (2)¯ ν e + p (cid:10) n + e + . (3) Because the rates of these interactions also decrease with T , the neutron-to-proton ratio eventually freezes out at T ∼ H, H, He, He, Li, and Be.Under the influence of gravity, big bang debris contain-ing mostly protons condenses into stars, which shine byburning protons into heavier nuclei and provide the newly-synthesized products to the interstellar medium when theydie. Therefore, the next generation of stars formed from thismedium are enriched beyond the big bang composition. Thiscycle repeats as generation after generation of stars are born,lead luminous lives, die glorious deaths, and in the processconvert primordial baryons into nuclei of the entire periodictable. To quantify this picture of cosmic alchemy, we cancompare the composition of big bang debris with that in thesun, which formed ≈ He with mass fractions of ≈
75% and ≈ He, and nuclei for the rest ofthe elements in the sun are ≈ . ≈ . ≈ . a r X i v : . [ a s t r o - ph . H E ] J a n IAN Y. Z.
Sci China-Phys Mech Astron () Vol. No. x-2 respectively. Clearly, the net e ff ect of stellar processing is toconvert protons into nuclei containing both protons and neu-trons. Although the actual processes involve many steps, wecan state in general that this end result must be achieved withthe help of weak interactions of the following types:( Z , N ) → ( Z − , N + + e + + ν e , (4) e − + ( Z , N ) → ( Z − , N + + ν e , (5)¯ ν e + ( Z , N ) → ( Z − , N + + e + , (6)where ( Z , N ) indicates a nucleus with Z protons and N neu-trons.The following examples serve to illustrate the criticalroles of the above weak interactions in providing neutronsfor making nuclei. The β + decay of N is of the typein Eq. (4) and is the crucial step in the reaction sequence C( p , γ ) N( e + ν e ) C( α, n ) O that provides a major neutronsource for s -process nucleosynthesis in stars of ∼ M (cid:12) (see e.g., Ref. [2] for a review). The reverse reaction inEq. (2) is of the type in Eq. (5) and is responsible for con-verting the Fe core of a massive ( (cid:38) M (cid:12) ) star into a neutronstar (NS). If the NS is formed in a binary with another NSor a black hole (BH) as its companion, then it can be tappedas a powerful neutron source for r -process nucleosynthesisthrough its disruption during the merger with its companion(see Sec. 2.5). The forward reaction in Eq. (3) is of the typein Eq. (6) and plays an important role in supernova nucle-osynthesis (see Sec. 2.3). The above discussion shows thatneutrinos are intimately associated with the origin of the ele-ments. r process and supernovae Before further discussing the roles of neutrinos in nucleosyn-thesis, we first describe how heavy nuclei are made by cap-turing neutrons. There are two prominent sets of peaks in theabundance distribution of nuclei heavier than Fe in the so-lar system. One set contains nuclei such as
Ba and
Pbwith magic neutron numbers 82 and 126, respectively. Theseare produced by the so-called slow neutron-capture ( s ) pro-cess. Once stable nuclei with magic neutron numbers areproduced by the s process, they are hard to destroy due totheir small neutron-capture cross sections. So they pile upand form peaks. In contrast to the s process whose path staysclose to stable nuclei, the so-called rapid neutron-capture ( r )process initially produces nuclei far from stability. This isbecause the neutron density in the r -process environment isso high that neutron capture on the unstable nuclei producedoccurs much faster than their β decay. Unstable nuclei withmagic neutron numbers also form peaks because they are rel-atively more stable. On exhaustion of neutrons, these nuclei β decay to stability and give rise to the peaks at mass num-bers A ∼
130 and 195, respectively, in the solar abundancedistribution.The r process (see e.g., Refs. [3–6] for reviews) has a lot to do with the death of a massive star in a core-collapse su-pernova (SN). The connection between such an SN and theformation of an NS was proposed by Baade and Zwicky [7]shortly after the discovery of the neutron by Chadwick in1932. They observed an extremely bright SN and found thatthe net energy of radiation was enormous [8]. They alsofound that a comparable amount of energy from each past SNcould power the cosmic rays [7]. To account for the requiredenergy in each case, they made the following proposal [7].“With all reserve we advance the view that a super-nova rep-resents the transition of an ordinary star into a neutron star ,consisting mainly of neutrons. Such a star may possess a verysmall radius and an extremely high density. As neutrons canbe packed much more closely than ordinary nuclei and elec-trons, the ‘gravitational packing’ energy in a cold neutron starmay become very large, and, under certain circumstances,may far exceed the ordinary nuclear packing fractions.”We now know that the total amount of energy emitted inphotons by a typical SN is ∼ ergs and the kinetic energyof the SN debris is ∼ ergs. By comparison, the gravita-tional binding energy E G of an NS is E G ∼ GM R NS ∼ × (cid:32) M NS . M (cid:12) (cid:33) (cid:32)
10 km R NS (cid:33) ergs , (7)where nominal values of the NS mass M NS and radius R NS are indicated. Although Baade and Zwicky did not give anexplicit estimate of E G , which they referred to as the “grav-itational packing” energy, they correctly suggested that thisenergy may far exceed the binding energy released in nuclearreactions, which they meant by “ordinary nuclear packingfractions.” Indeed, E G corresponds to ∼
100 MeV / nucleon,which is much higher than the typical nuclear binding energyof ∼ / nucleon. Furthermore, the insightful associa-tion of NS formation and cosmic-ray production with SNe byBaade and Zwicky has been put on much firmer grounds. Only massive stars of (cid:38) M (cid:12) can become SNe. A star of ∼ M (cid:12) develops an O-Ne-Mg core at the end of its life.The density in the core is so high that the electrons thereare relativistically degenerate. Capture of these electrons byNe and Mg nuclei reduces the electron degeneracy pressureand triggers the collapse of the core. In contrast, a star of > M (cid:12) develops an Fe core, which collapses when thermalenergy is lost due to photo-dissociation of Fe-group nuclei.In both cases, the inner core bounces due to the repulsive nu-clear force at very short range when supra-nuclear density isreached. This bounce launches a shock wave into the still-collapsing outer core. However, the shock quickly loses en-ergy on its way out by dissociating nuclei into free nucleonsand is stalled before exiting the outer core. The inner core isnow a proto-NS and material falling onto it releases the gravi-tational binding energy by emitting mostly ν e and ¯ ν e . Some ofthese ν e and ¯ ν e are captured by neutrons and protons through IAN Y. Z.
Sci China-Phys Mech Astron () Vol. No. x-3 the forward reactions in Eqs. (2) and (3), respectively, to heatthe material behind the stalled shock. In some cases, this neu-trino heating provides su ffi cient energy to revive the shock,which proceeds to make an explosion. This is the so-calledneutrino-driven SN mechanism [9].The above SN mechanism has been consistently demon-strated by several groups for a star of 8 . M (cid:12) [10–12]. How-ever, the same mechanism is harder to operate in more mas-sive stars, which have more extended envelopes with largergravitational binding energies. For these more massive stars,the shock is required to do extra work and sometimes neutri-nos fail to deliver an explosion. At the present time, whetherneutrino-driven explosion works for stars of > M (cid:12) and ifso, how exactly it works are under intense study by many SNmodelers around the world [13]. An exploratory study bythe Garching group in Germany found that whether neutrino-driven explosion works is not a simple function of the SNprogenitor mass [13]. In addition, when a neutrino-drivenSN occurs, it takes ∼ . ∼ ∼ to ∼ ergs. Neither the time nor theenergy of explosion is a monotonic function of the progenitormass.A successful explosion typically leaves behind an NS ofa few M (cid:12) , while a failed SN produces a BH that swallowsthe entire progenitor star most of the time. In some cases, anaccretion disk may form around the BH and powers a jet thatdrives an explosion ejecting part of the progenitor star. In rarecases, this jet-driven mechanism gives rise to the so-calledhypernovae associated with long gamma-ray bursts [14]. The ν e and ¯ ν e potentially driving the explosion are emit-ted dominantly through the reverse reactions in Eqs. (2) and(3), respectively, by material falling onto the proto-NS. Theso-called accretion phase associated with this emission lasts ∼ . ∼ ν e , ¯ ν e , ν µ , ¯ ν µ , ν τ , and¯ ν τ during the so-called cooling phase, for which the impor-tant neutrino production mechanisms are processes such as e + + e − → ν + ¯ ν . The cooling phase lasts ∼
10 s becauseneutrinos must di ff use out of the extremely hot and dense in-terior of the proto-NS. Detection of the neutrino burst fromSN 1987A [15, 16], which lasted ≈
13 s, confirmed this over-all picture of SN neutrino emission.The characteristics of neutrino emission di ff er greatly be-tween the accretion and cooling phases. Figure 1 shows theevolution of neutrino luminosities and average neutrino en-ergies as functions of time for an 18 M (cid:12) SN model [12, 17].During the accretion phase (Fig. 1b, time post core bounce t pb ∼ . ν e luminosity L ¯ ν e is approximatelythe same as the ν e luminosity L ν e . Both follow nearly thesame time evolution and are much higher than the luminos-ity L ν x ≈ L ¯ ν x ( x = µ, τ ) of any other species. In addition,the average neutrino energies (Fig. 1e) follow a clear hierar- chy (cid:104) E ν e (cid:105) < (cid:104) E ¯ ν e (cid:105) < (cid:104) E ν x (cid:105) ≈ (cid:104) E ¯ ν x (cid:105) , with (cid:104) E ν e (cid:105) ≈ (cid:104) E ¯ ν e (cid:105) ≈ (cid:104) E ν x (cid:105) ≈ (cid:104) E ¯ ν x (cid:105) ≈ L ν x ≈ L ¯ ν x is close to L ν e ≈ L ¯ ν e during the coolingphase (Fig. 1c, t pb > . (cid:104) E ν e (cid:105) remains the low-est, the di ff erence between (cid:104) E ¯ ν e (cid:105) and (cid:104) E ν x (cid:105) ≈ (cid:104) E ¯ ν x (cid:105) becomessmaller and smaller. Note that Figs. 1a and 1d correspondto the so-called shock-breakout phase. As the shock breaksthrough the neutrino-trapping surface formed by nuclei of theFe group, the protons released from the dissociation of thesenuclei rapidly capture electrons to produce a strong ν e pulse.Therefore, the shock-breakout phase is characterized by pow-erful emission of predominantly ν e . L u m i no s it y ( e r g / s ) L ν / 100(a) 5 10 15-0.05 0.00 A v e r a g e e n e r gy ( M e V ) ν / 10(b)0.1 0.2 0.3 0.4 0.5 0.6 t pb (s) (e) (c) ν e − ν e ν µ / τ Figure 1
Evolution of neutrino luminosities and average neutrino energiesas functions of time for an 18 M (cid:12) SN model [12, 17]. Panels (a) and (d) cor-respond to the shock-breakout phase, panels (b) and (e) the accretion phase,and panels (c) and (f) the cooling phase. (Figure from Ref. [17])
For SNe with di ff erent progenitors, the shock-breakoutpulse is a common feature that signifies the launch of theprompt shock. A ν e pulse with L ν e ≈ (4–5) × erg / s anda width of ∼
10 ms is typical of all SNe. For those SNewith neutrino-driven explosion, the duration of the accretionphase depends on the progenitor. For example, this phaselasts ∼ . M (cid:12) model described above, which is ∼ . M (cid:12) model discussed inRef. [13]. The cooling phase is similar for all SNe that leavebehind NS remnants. For SNe producing BHs, when the BHforms depends on the progenitor structure and the nuclearequation of state. If a BH forms during the first ∼
10 s aftercore bounce, neutrino emission from the proto-NS is abruptlyterminated (e.g., [18]). However, if there is an accretion disk
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Sci China-Phys Mech Astron () Vol. No. x-4 surrounding the BH, significant neutrino emission from thisdisk might continue for some time (e.g., [19]).
Subsequent to a successful SN explosion, material in thevicinity of the proto-NS is still heated by ν e and ¯ ν e through theforward reactions in Eqs. (2) and (3), respectively. When thismaterial acquires su ffi cient energy from neutrino heating, itovercomes the gravitational potential of the proto-NS and es-capes as the so-called neutrino-driven wind. The neutron-to-proton ratio in the wind is determined by the competition be-tween neutron production by ¯ ν e and proton production by ν e through the same reactions that provide the heating [20, 21].The rates for these reactions at radius r are λ ¯ ν e p = L ¯ ν e π r (cid:104) σ ¯ ν e p (cid:105)(cid:104) E ¯ ν e (cid:105) ∝ L ¯ ν e (cid:104) E ν e (cid:105)(cid:104) E ¯ ν e (cid:105) − ∆ , (8) λ ν e n = L ν e π r (cid:104) σ ν e n (cid:105)(cid:104) E ν e (cid:105) ∝ L ν e (cid:104) E ν e (cid:105)(cid:104) E ν e (cid:105) + ∆ , (9)where the angular brackets indicate averaging over the rel-evant neutrino energy spectrum, σ ¯ ν e p ∝ ( E ¯ ν e − ∆ ) and σ ν e n ∝ ( E ν e + ∆ ) are the cross sections for the correspondingreactions, and we have ignored terms proportional to ∆ . Theneutron-to-proton ratio in the wind can be estimated as n / p ≈ λ ¯ ν e p λ ν e n ≈ L ¯ ν e L ν e (cid:32) (cid:15) ¯ ν e − ∆ (cid:15) ν e + ∆ (cid:33) , (10)where (cid:15) ν ≡ (cid:104) E ν (cid:105) / (cid:104) E ν (cid:105) . For L ¯ ν e ≈ L ν e , n / p > (cid:15) ¯ ν e − (cid:15) ν e > ∆ .Because neutrino energy spectra are determined by neu-trino opacities in the surface layers of the proto-NS, whetherthe wind is neutron rich is sensitive to neutrino interactionsin hot and dense matter. Using various approximate neutrinoopacities, earlier studies found the wind to be mostly neutronrich (e.g., [21, 22]), whereas later ones obtained only proton-rich winds (e.g., [23]) with neutrino emission parameters sim-ilar to those shown in Fig. 1. Recently, two groups [24, 25]studied ν e and ¯ ν e opacities in some detail and found that thewind may be neutron rich for a significant period of time.A number of groups (e.g., [21, 22, 26–31]) have studiedother conditions such as the entropy and expansion timescalein the neutrino-driven wind and surveyed the resulting nucle-osynthesis. The general consensus is that elements such as Sr,Y, and Zr with A ∼
90 can be readily produced for somewhatneutron-rich winds. It is likely that the production can beextended to Pd and Ag with A ∼ n , γ ), ( p , γ ), ( n , p ), ( α, γ ), ( α, n ), ( α, p ), and their re-verse reactions, in contrast to the classical r process whereneutron capture plays a dominant role. With extreme condi-tions such as associated with a massive proto-NS [33], a clas-sical r process can occur to produce nuclei up to A ∼ ffi cult to justify conditions for making r -process nuclei with A ∼
195 in the wind. r process in helium shells In addition to driving a neutron-rich wind, neutrino interac-tions in SNe can provide neutrons in other ways as well. Forexample, neutral-current reactions on He nuclei can produceneutrons through He( ν, ν n ) He( n , p ) H and He( ν, ν p ) Hfollowed by H( H , n ) He. In the helium (He) shell of anearly SN, these neutrons are captured by the few Fe nucleipresent in the birth material of the progenitor, but not by thepredominant He nuclei. This scenario was proposed as amodel for the r process [34]. It was critically examined byRef. [35], which constrained it to be viable only for somespecial metal-poor SNe with He shells at very small radii andhence, exposed to large neutrino fluxes for neutron produc-tion.A recent study [36] reexamined the above scenario for aneutrino-induced r process. Using updated models of metal-poor massive stars, it found that the H nuclei produced byneutral-current neutrino reactions on He lead to productionof Li through He( H , γ ) Li instead of generating neutronsas in the original scenario. However, the charged-current re-action ¯ ν e + He → H + n + e + (11)may provide a new neutron source, especially in the presenceof ¯ ν e (cid:10) ¯ ν x oscillations. The reaction in Eq. (11) has a thresh-old of 21.6 MeV, which is significantly above the average ¯ ν e energy in the absence of flavor oscillations. Earlier SN neu-trino transport calculations (e.g., [22]) gave a very hard ¯ ν x spectrum with (cid:104) E ¯ ν x (cid:105) ∼ ν x is significantlyharder than that of ¯ ν e at least for a few seconds (see Fig. 1).For an inverted neutrino mass hierarchy, ¯ ν e (cid:10) ¯ ν x oscillationscan occur before neutrinos reach the He shell, thereby givingrise to a harder e ff ective ¯ ν e spectrum for neutron production.The neutron production rate per He nucleus is λ ¯ ν e α, n = π r (cid:34) L ¯ ν e (cid:104) σ ¯ ν e α, n (cid:105)(cid:104) E ¯ ν e (cid:105) (cid:35) e ff ∝ ( L ¯ ν e T p ¯ ν e ) e ff r , (12)where (cid:104) σ ¯ ν e α, n (cid:105) is the cross section for the charged-current re-action in Eq. (11) averaged over the ¯ ν e spectrum, the subscript“e ff ” denotes e ff ective quantities for ¯ ν e in the presence of¯ ν e (cid:10) ¯ ν x oscillations, T ¯ ν e is the temperature for a Fermi-Diracspectrum with zero chemical potential, and the power index p is ∼ ν e (cid:10) ¯ ν x oscillations, Ref. [36] showed that an r process can occur and produce nuclei up to A >
200 in theHe shell of an 11 M (cid:12) SN model with an initial metallicity of[Fe / H] ≡ log (Fe / H) − log (Fe / H) (cid:12) ∼ − . Fe in thebirth material. As the metallicity of the SN progenitor in-creases, more Fe nuclei are available to capture neutrons,
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Sci China-Phys Mech Astron () Vol. No. x-5 which results in lower neutron densities and less e ffi cient pro-duction of nuclei heavier than Fe. Consequently, the aboveneutrino-induced r process ceases to operate at [Fe / H] (cid:38) −
30 34 38 42 46 50 54 58 62 66 70 74 78 82 86−15−14−13−12−11−10 Z l og Y Z Pb A ∼ Figure 2 E ff ect of SN progenitor metallicity on neutrino-induced r -processnucleosynthesis in He shells [36,37]. Final elemental abundance patterns areshown as functions of atomic number Z for 11 M (cid:12) models with metallicitiesof [Fe / H] ∼ − − − / H] ∼ − ff erent abundances of S and Si in the He shell( ∼
10 times smaller for the red curve). (Figure from Ref. [37]) r process The NS left behind by an SN is a great source of neutron-richmaterial. This source can be tapped to drive a robust r processduring mergers of an NS with another NS or a BH. The pro-genitor system of such a merger is a binary consisting of twomassive stars, which explode as SNe without disrupting thesystem. Energy loss through radiation of gravitational wavesleads to the eventual merger of the two compact remnantsleft by the SNe. Pioneering work on r -process nucleosynthe-sis during decompression of cold NS matter was carried outin Ref. [38]. More recently, detailed hydrodynamic simula-tions of an NS-NS merger were performed (e.g., [39, 40]). Itwas shown that r -process nuclei with A (cid:38)
130 including tho-rium and uranium are produced in the extremely neutron-richejecta. In addition, the less neutron-rich material ejected fromthe accretion disk surrounding the merger remnant has sim-ilar nucleosynthesis (e.g., [41]) to the neutron-rich neutrino-driven winds from a proto-NS (see Sec. 2.3).The production of r -process nuclei with A (cid:38)
130 and theassociated production of lighter nuclei in an NS-NS mergerreceived strong support from the observations of such anevent, GW170817, through gravitational waves [42] and elec-tromagnetic radiation. In this regard, the most dramatic ob-servation of this event is the detection of the so-called kilo-nova [43], which was powered by the decay of the nuclei syn-thesized by the r process (e.g., [44]). Eight decades after Baade and Zwicky proposed the connec-tion between SNe and NS formation, we are still figuringout the mechanisms through which SNe occur. It has beenshown that neutrino-driven explosion works for stars of ∼ M (cid:12) . While neutrinos may also play important roles in ex-plosions of more massive stars, the detailed mechanisms inthese cases are rather uncertain but under intense investiga-tion at the present time. Nevertheless, it appears that SNefrom stars of ∼ M (cid:12) have a wide range of neutrino sig-nals, explosion energies, nucleosynthesis products, and com-pact remnant (NS or BH) masses.With formation of an NS and the associated profuse emis-sion of neutrinos, SNe can provide neutrons for making heavynuclei, especially through the r process, in several ways. Firstof all, neutrino-driven winds from a proto-NS can be neutronrich due to the dominance of the forward reaction in Eq. (3).These winds can produce elements from Sr, Y, Zr ( A ∼ A ∼ A ∼
130 through the r process. In addition, ¯ ν e can pro-duce neutrons through the reaction in Eq. (11). This maygive rise to a neutrino-induced r process in the He shell of anearly SN where neutrons are captured by the few Fe nucleipresent in the birth material of the progenitor star. As neutronproduction is sensitive to the e ff ective ¯ ν e energy spectrum inthe He shell, this neutrino-induced r process can be enhancedgreatly by ¯ ν e (cid:10) ¯ ν x oscillations, the occurrence of which mostlikely requires an inverted neutrino mass hierarchy. In the op-timal case, nuclei with A >
200 can be produced. However,the neutrino-induced r process ceases to operate when metal-licities of SN progenitors exceed [Fe / H] ∼ −
3. Finally, asmall fraction of binary systems consisting of two massivestars can evolve into NS-NS or NS-BH binaries after surviv-ing two SNe. Cold NS matter ejected from mergers of thetwo compact remnants in such binaries serves as the best sitefor making r -process nuclei with A (cid:38)
130 including thoriumand uranium.
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