Neutrino-Accelerated Hot Hydrogen Burning: Realistic Astrophysical Sites, Ejection of Processed Material, and Nucleosynthetic Yields

Kishimoto & Fuller (2007) showed that a prodigious electron-antineutrino flux can replace the slow weak-interaction bottlenecks of the pp chain and the hot CNO cycle with much faster antineutrino-capture reactions, raising hydrogen-burning energy generation by orders of magnitude and shifting the breakout condition into the rp-process, and they explicitly left open whether any realistic astrophysical environment realizes this regime. The problem is to determine whether neutrino-accelerated hot hydrogen burning actually occurs in nature: identify (or robustly exclude) environments — high-entropy accretion disks around forming black holes, or the general-relativistic collapse of very- and super-massive stars — that supply antineutrino fluxes of order $10^{39}$–$10^{40}\ \mathrm{cm^{-2}\,s^{-1}}$ at MeV-scale mean energies to matter still in a hydrogen-burning state; decide by fully relativistic multidimensional simulations with coupled burning and neutrino transport whether the processed material escapes the nascent black hole; quantify the nucleosynthetic yields by coupling the antineutrino-capture weak rates to reaction networks; and establish whether supermassive stars massive enough to provide the required fluxes ever existed.

Background

Hydrogen burning converts four protons into a helium-4 nucleus, and in every known variant the pace is set by a weak-interaction step that converts a proton into a neutron. In the proton–proton (pp) chain, dominant in cool stars like the Sun, this is the extremely slow fusion reaction $p+p\rightarrow d+e^{+}+\nu_e$. In the carbon–nitrogen–oxygen (CNO) cycle, dominant in more massive stars, carbon acts as a catalyst and the weak conversion happens through positron decays of radioactive oxygen isotopes. At the higher temperatures of explosive hydrogen burning ($T\gtrsim10^{8}\ \mathrm{K}$) the cycle becomes the 'hot CNO' cycle: proton captures are fast, and the cycle rate is set by the positron decays of $^{14}\mathrm{O}$ (half-life 71 s) and $^{15}\mathrm{O}$ (half-life 122 s). Still hotter, denser hydrogen-rich matter can break out into the rp-process — a sequence of rapid proton captures on seed nuclei toward heavy proton-rich isotopes, limited by the positron decays of 'waiting-point' nuclei.

Kishimoto & Fuller (2007) pointed out that an intense flux of electron antineutrinos opens a competing weak channel: capture on free protons, $\bar{\nu}_e+p\rightarrow n+e^{+}$, and on the bottleneck nuclei themselves, $^{14}\mathrm{O}(\bar{\nu}_e,e^{+})^{14}\mathrm{N}$ and $^{15}\mathrm{O}(\bar{\nu}_e,e^{+})^{15}\mathrm{N}$. Antineutrino–nucleus cross sections are tiny but grow steeply with neutrino energy, and neutrinos escape freely from deep, hot regions and stream to where burning occurs. To dominate the pp-chain bottleneck requires prodigious fluxes $\phi_{\bar{\nu}_e}\gtrsim10^{40}\ \mathrm{cm^{-2}\,s^{-1}}$ at mean energies $\langle E_{\bar{\nu}_e}\rangle\gtrsim$ a few MeV; to accelerate the hot-CNO bottlenecks the capture rates need only rival the 71 s and 122 s positron decays, which for a Fermi–Dirac spectrum with $\langle E_{\bar{\nu}_e}\rangle=10\ \mathrm{MeV}$ happens at fluxes of order $10^{39}\ \mathrm{cm^{-2}\,s^{-1}}$, the threshold scaling approximately as $\langle E_{\bar{\nu}_e}\rangle^{-2}$. Where these conditions hold, the energy generation rate rises by several orders of magnitude and becomes nearly temperature-independent; the free neutrons produced are diverted by the fast strong reactions $^{15}\mathrm{O}(n,p)^{15}\mathrm{N}$ and $^{14}\mathrm{O}(n,p)^{14}\mathrm{N}$ into the CNO cycle; and the breakout criterion into the rp-process, $\rho X\,\lambda_{p\gamma}(^{19}\mathrm{Ne})>\lambda_{w}(^{19}\mathrm{Ne})$ (with $\rho$ the density, $X$ the hydrogen mass fraction, and $\lambda_{w}$ the total weak rate of $^{19}\mathrm{Ne}$), shifts because antineutrino capture raises $\lambda_{w}$, so a higher temperature is needed for breakout at a given density.

Only violent environments can supply such fluxes. Kishimoto & Fuller suggested two: high-entropy accretion disks around forming black holes, and the collapse of a supermassive star ($M\gtrsim5\times10^{4}\,M_\odot$) triggered by the Feynman–Chandrasekhar instability — the general-relativistic radial instability of a radiation-dominated star. For the supermassive-star case they used the calculations of Shi & Fuller (1998), who found that the collapsing homologous core — the inner region of the star that falls inward self-similarly, with infall velocity linear in radius — emits neutrinos of all flavors with a total luminosity $L_\nu\approx2.8\times10^{57}(M_{\rm HC}/10^{5}M_\odot)^{-1.5}\ \mathrm{erg\,s^{-1}}$; evaluating the capture rates in the envelope at a radius of 100 Schwarzschild radii, the antineutrino-capture rate scales as $M_{\rm HC}^{-4}$, so the effect on the hot-CNO bottlenecks dies away for homologous core masses $\gtrsim4\times10^{4}\,M_\odot$ (i.e., $M_{5\rm HC}\gtrsim0.4$ in units of $10^{5}\,M_\odot$), leaving only the lower end of the supermassive-star mass range interesting (for primordial, metal-free stars the pp-chain boost would still apply). The environment must satisfy a sharp dual requirement: prodigious in antineutrinos yet quiescent enough that ordinary hydrogen burning — not a slide to nuclear statistical equilibrium (NSE), the high-temperature equilibrium state whose yield carries no memory of the burning path — is the relevant physics; and the processed material must be ejected rather than swallowed by the forming black hole. The authors stated they were 'skeptical that these conditions can be met' and that only fully relativistic numerical simulations could settle the question.

Two adjacent lines of work frame but do not answer this question. First, concurrently with the source paper, the νp-process was discovered (Fröhlich et al. 2006; Pruet et al. 2006; Wanajo 2006): in the proton-rich, neutrino-heated ejecta of ordinary core-collapse supernovae, antineutrino capture on protons supplies free neutrons that bridge the minutes-long waiting points of the rp-process, and this is now the standard explanation for light p-nuclei. That regime differs from the one posed here: the ejecta are hot, freely expanding matter near a proto-neutron star, in no sense a quiescent hydrogen-burning state, and the relevant competition is with waiting-point beta decays rather than with the pp or hot-CNO bottlenecks. Second, relativistic simulations of supermassive-star collapse exist — including models with thermonuclear burning (Montero et al. 2012; Chen et al. 2014; Nagele et al. 2023) — but in every case neutrinos enter only as cooling channels, never as capture reactions coupled to the burning. The source's question therefore stands.

Problem Statement

Determine whether neutrino-accelerated hot hydrogen burning — the regime identified by Kishimoto & Fuller (2007) in which electron-antineutrino capture replaces the weak bottlenecks of the pp chain and the hot CNO cycle — is realized in nature. The single overarching objective is to establish, or robustly exclude, an astrophysical environment in which this process operates with observable nucleosynthetic consequences, and it decomposes into four jointly supporting parts: (i) Site identification: find a realistic environment, or show that none can exist, that simultaneously supplies to matter undergoing hydrogen burning an electron-antineutrino flux $\phi_{\bar{\nu}_e}$ of order $10^{39}$–$10^{40}\ \mathrm{cm^{-2}\,s^{-1}}$ (the pp-chain threshold being $\gtrsim10^{40}$ and the hot-CNO threshold $\sim10^{39}$ for $\langle E_{\bar{\nu}_e}\rangle=10\ \mathrm{MeV}$, scaling approximately as $\langle E_{\bar{\nu}_e}\rangle^{-2}$) with $\langle E_{\bar{\nu}_e}\rangle\gtrsim$ a few MeV, while the gas remains in a hydrogen-burning regime rather than nuclear statistical equilibrium; the candidate sites suggested by the source are high-entropy accretion disks around forming black holes and collapsing very- or super-massive objects, with the hot-CNO effect confined to homologous core masses $\lesssim4\times10^{4}\,M_\odot$ because the capture rate scales as $M_{\rm HC}^{-4}$. (ii) Ejecta survival: determine, by fully relativistic multi-dimensional hydrodynamic simulations that include both hydrogen burning and neutrino transport, whether material at radii where the antineutrino flux suffices can avoid incorporation into the nascent black hole and be ejected into the interstellar or intergalactic medium. (iii) Nucleosynthetic yields: quantify how the antineutrino-accelerated weak rates and the altered neutron-capture branching (diversion of free neutrons through $^{15}\mathrm{O}(n,p)^{15}\mathrm{N}$ and $^{14}\mathrm{O}(n,p)^{14}\mathrm{N}$) change the detailed nucleosynthetic output — including changes to the rp-process breakout condition $\rho X\,\lambda_{p\gamma}(^{19}\mathrm{Ne})>\lambda_{w}(^{19}\mathrm{Ne})$ and to final abundance distributions — by coupling the antineutrino-capture weak rates to nuclear reaction networks within realistic dynamical simulations. (iv) Supermassive-star prevalence: clarify whether supermassive stars — objects with masses $M\gtrsim5\times10^{4}\,M_\odot$ collapse on the general-relativistic Feynman–Chandrasekhar instability in the source — ever existed at any cosmic epoch, and under what accretion or collapse conditions. An answer that establishes a site must carry through parts (i)–(iii) for that site, and part (iv) is required whenever the claimed site is a supermassive star; an answer that excludes all sites must do so by an explicit physical argument covering every candidate environment named in (i).

References

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