Triple-alpha Reaction Research Articles

Fully Nonadiabatic Analysis of Vibrational Instability of Population III Stars due to the ɛ-Mechanism

Abstract A linear nonadiabatic analysis of the vibrational stability of population III main-sequence stars was carried out. It was demonstrated that, in the case of massive stars with $M$$\gtrsim$ 5 $M_\odot$, helium burning (triple alpha reaction) starts during the main-sequence stage and produces $^{12}$C, leading to the activation of a part of the CNO-cycle. It was found that, despite of that, those stars with $M$$\lesssim$ 13 $M_\odot$ become unstable against the dipole g$_1$- and g$_2$-modes due to the $\varepsilon $-mechanism, during the early evolutionary phase at which the pp-chain is still the dominant nuclear energy source. The instability due to the $\varepsilon $-mechanism occurs against g-modes having a large amplitude in the off-centered $^3$He accumulation shell in the deep interior, and the growth time is much shorter than the evolutionary timescale. This instability is therefore likely to induce mixing in the stellar interior, and have a significant influence on the evolution of these stars.

Variation of fundamental constants and the triple-alpha reaction in Population III stars and BBN

The effect of variations of the fundamental constants on the thermonuclear rate of the triple alpha reaction, 4He(αα, γ)12C, that bridges the gap between 4He and 12C is investigated. We have followed the evolution of 15 and 60 M⊙ zero metallicity stellar models, up to the end of core helium burning. The calculated oxygen and carbon abundances resulting from helium burning can then be used to constrain the variation of the fundamental constants. To investigate the effect of an enhanced triple alpha reaction rate in Big-Bang Nucleosynthesis, we first evaluated Standard Big-Bang Nucleosynthesis CNO production with a network of more than 400 reactions using the TALYS code to calculate missing rates.

STELLAR EVOLUTION CONSTRAINTS ON THE TRIPLE-α REACTION RATE

We investigate the quantitative constraint on the triple-alpha reaction rate based on stellar evolution theory, motivated by the recent significant revision of the rate proposed by nuclear physics calculations. Targeted stellar models were computed in order to investigate the impact of that rate in the mass range of 0.8 < M / Msun < 25 and in the metallicity range between Z = 0 and Z = 0.02. The revised rate has a significant impact on the evolution of low- and intermediate-mass stars, while its influence on the evolution of massive stars (M >~ 10 Msun) is minimal. We find that employing the revised rate suppresses helium shell flashes on AGB phase for stars in the initial mass range 0.8 < M / Msun < 6, which is contradictory to what is observed. The absence of helium shell flashes is due to the weak temperature dependence of the revised triple-alpha reaction cross section at the temperature involved. In our models, it is suggested that the temperature dependence of the cross section should have at least nu > 10 at T = 1 - 1.2 x 10^8 K where the cross section is proportional to T^{nu}. We also derive the helium ignition curve to estimate the maximum cross section to retain the low-mass first red giants. The semi-analytically derived ignition curves suggest that the reaction rate should be less than ~ 10^{-29} cm^6 s^{-1} mole^{-2} at ~ 10^{7.8} K, which corresponds to about three orders of magnitude larger than that of the NACRE compilation. In an effort to compromise with the revised rates, we calculate and analyze models with enhanced CNO cycle reaction rates to increase the maximum luminosity of the first giant branch. However, it is impossible to reach the typical RGB tip luminosity even if all the reaction rates related to CNO cycles are enhanced by more than ten orders of magnitude.

Three-body calculation of triple-alpha reaction at low energies

The reaction rate of the triple-alpha (3α) process at low temperatures, where resonant reaction is not dominant, is calculated through the inverse process, the photodisintegration of a 12C nucleus. For this, Schrödinger equations in a three-alpha (3-α) model of 12C are directly solved by a Faddeev method, which has been successfully applied to three-nucleon problem so far. The nuclear Hamiltonian consists of an α-α potential, which reproduces the 8Be resonance state, together with three-body potentials to reproduce 12C properties. Our results of the 3α reaction rate are about 103 times larger at low temperature (T = 107 K) than a standard rate from the Nuclear Astrophysics Compilation of Reaction Rates (NACRE), which means our results are remarkably smaller than recent results of quantum-mechanical three-body calculations by Ogata et al.

HELIUM IGNITION ON ACCRETING NEUTRON STARS WITH A NEW TRIPLE-α REACTION RATE

We investigate the effect of a new triple-alpha reaction rate from Ogata et al. (2009) on helium ignition conditions on accreting neutron stars and on the properties of the subsequent type I X-ray burst. We find that the new rate leads to significantly lower ignition column density for accreting neutron stars at low accretion rates. We compare the results of our ignition models for a pure helium accretor to observations of bursts in ultra-compact X-ray binary (UCXBs), which are believed to have nearly pure helium donors. For mdot > 0.001 mdot_Edd, the new triple-alpha reaction rate from Ogata et al. (2009) predicts a maximum helium ignition column of ~ 3 x 10^9 g cm^{-2}, corresponding to a burst energy of ~ 4 x 10^{40} ergs. For mdot ~ 0.01 mdot_Edd at which intermediate long bursts occur, the predicted burst energies are at least a factor of 10 too low to explain the observed energies of such bursts in UCXBs. This finding adds to the doubts cast on the triple-alpha reaction rate of Ogata et al. (2009) by the low-mass stellar evolution results of Dotter & Paxton (2009).

The triple alpha reaction rate and the [formula omitted] resonances in 12C

The triple alpha rate is obtained from the three-body bound and continuum states computed in a large box. The results from this genuine full three-body calculation are compared with standard reference rates obtained by two sequential two-body processes. The fairly good agreement relies on two different assumptions about the lowest 2+ resonance energy. With the same 2+ energy the rates from the full three-body calculation are smaller than those of the standard reference. We discuss the rate dependence on the experimentally unknown 2+ energy. Substantial deviations from previous results appear for temperatures above 3 GK.

Effects of a New Triple- Reaction Rate on the Helium Ignition of Accreting White Dwarfs

Effects of a new triple-alpha reaction rate on the ignition of carbon-oxygen white dwarfs accreting helium in a binary systems have been investigated. The ignition points determine the properties of a thermonuclear explosion of a Type Ia supernova. We examine the cases of different accretion rates of helium and different initial masses of the white dwarf, which was studied in detail by Nomoto. We find that for all cases from slow to intermediate accretion rates, nuclear burnings are ignited at the helium layers. As a consequence, carbon deflagration would be triggered for the lower accretion rate compared to that of $dM/dt\simeq 4\times10^{-8} M_{\odot} \rm yr^{-1}$ which has been believed to the lower limit of the accretion rate for the deflagration supernova. Furthermore, off-center helium detonation should result for intermediate and slow accretion rates and the region of carbon deflagration for slow accretion rate is disappeared.

Nuclear reaction rates and opacity in massive star evolution calculations

Nuclear reaction rates and opacity are important parameters in stellar evolution. The input physics in a stellar evolution code determines the main theoretical characteristics of the stellar structure, evolution and nucleosynthesis of a star. For different input physics, in this work we calculate stellar evolution models of very massive first stars during the hydrogen and helium burning phases. We have considered 100 and 200M⊙ galactic and pregalactic stars with metallicity Z = 10−6 and 109, respectively. The results show important differences from old to new formulations for the opacity and nuclear reaction rates, in particular the evolutionary tracks are significantly affected, that indicates the importance of using up to date and reliable input physics. The triple alpha reaction activates sooner for pregalactic than for galactic stars.

First stars. I. Evolution without mass loss

The first generation of stars was formed from primordial gas. Numerical simulations suggest that the first stars were predominantly very massive, with typical masses M > 100 Mo. These stars were responsible for the reionization of the universe, the initial enrichment of the intergalactic medium with heavy elements, and other cosmological consequences. In this work, we study the structure of Zero Age Main Sequence stars for a wide mass and metallicity range and the evolution of 100, 150, 200, 250 and 300 Mo galactic and pregalactic Pop III very massive stars without mass loss, with metallicity Z=10E-6 and 10E-9, respectively. Using a stellar evolution code, a system of 10 equations together with boundary conditions are solved simultaneously. For the change of chemical composition, which determines the evolution of a star, a diffusion treatment for convection and semiconvection is used. A set of 30 nuclear reactions are solved simultaneously with the stellar structure and evolution equations. Several results on the main sequence, and during the hydrogen and helium burning phases, are described. Low metallicity massive stars are hotter and more compact and luminous than their metal enriched counterparts. Due to their high temperatures, pregalactic stars activate sooner the triple alpha reaction self-producing their own heavy elements. Both galactic and pregalactic stars are radiation pressure dominated and evolve below the Eddington luminosity limit with short lifetimes. The physical characteristics of the first stars have an important influence in predictions of the ionizing photon yields from the first luminous objects; also they develop large convective cores with important helium core masses which are important for explosion calculations.

Astrophysical reaction rates for 6He and 9Be production by electromagnetic radiative capture and four-body recombination

The triple alpha reaction α+α+α → 12C + γ is considered to be the most relevant one in stars at the helium burning stage, since it permits to bridge the A=5 and A=8 instability gaps. However, at higher temperatures and neutron rich environments, other reactions can also play a relevant role. In this work we investigate the astrophysical reaction and production rates for the two-particle radiative capture processes α+n+n → 6He+γ and α+α+n → 9Be+γ. The hyperspherical adiabatic expansion method is used. With this method no assumption is made about the capture mechanism. The four-body recombination reactions α+α+n+n → 6He + α, α + n + n + n → 6He + n, α+α+n+n → 9Be + n and α + α + α + n → 9Be + α are also investigated as a possible alternative as a source of 6He and 9Be.

Constraints on the variations of fundamental couplings by stellar models

AbstractThe effect of variations of the fundamental constants on the thermonuclear rate of the triple alpha reaction, 4He(αα,γ)12C, that bridges the gap between 4He and 12C is investigated. We follow the evolution of 15 and 60 M⊙ zero metallicity star models, up to the end of core helium burning. They are assumed to be representative of the first, Population III stars undergoing a very peculiar evolution due to the absence of initial CNO elements (zero metallicity). The calculated oxygen and carbon abundances resulting from helium burning can then be used to constrain the variations of the fundamental constants.

Screened Thermonuclear Reaction Rates on Magnetar Surfaces

Improving Salpeter's method, we discuss the effect of superstrong magnetic fields (such as those of magnetars) on thermonuclear reaction rates. These most interesting reactions, including the hydrogen burning by the CNO cycle and the helium burning by the triple alpha reaction, are investigated as examples on the magnetar surfaces. The obtained result shows that the superstrong magnetic fields can increase the thermonuclear reaction rates by many orders of magnitude. The enhancement may have significant influence for further study research of the magnetars, especially for the x-ray luminosity observation and the evolution of magnetars.

Effect of superstrong magnetic fields on thermonuclear reaction rates on the surface of magnetars

A simple and efficient screening model for studying the effects of superstrong magnetic fields (such as those of magnetars) on thermonuclear reaction rates on magnetar surfaces is proposed in this paper. The most interesting thermonuclear reactions, including hydrogen burning by the CNO cycle and helium burning by the triple alpha reaction, are investigated on the surface of magnetars. We find that the superstrong magnetic fields can increase the thermonuclear reaction rates by many orders of magnitude. The enhancement may have a dramatic effect on the thermonuclear runaways and bursts on the surfaces of magnetars.

Influence of two updated nuclear reaction rates on the evolution of low and intermediate mass stars

Two key reactions of hydrostatic nuclear burning in stars have recently been revised by new experimental data - the 14N(p,gamma)15O and triple alpha reaction rates. We investigate how much the new rates influence the evolution of low-mass, metal-poor and metal-free, stars and of an intermediate-mass star of solar-type composition. We concentrate on phases of helium ignition or thermally unstable helium burning. Our global result is that the new triple alpha rate has no significant influence on such stars, but that there is a noticable, though small, effect of the new 14N(p,gamma)15O rate, in particular on the core helium flash and the blue loop during core helium burning in the intermediate-mass star.

Stellar production rates of carbon and its abundance in the universe.

The bulk of the carbon in our universe is produced in the triple-alpha process in helium-burning red giant stars. We calculated the change of the triple-alpha reaction rate in a microscopic 12-nucleon model of the (12)C nucleus and looked for the effects of minimal variations of the strengths of the underlying interactions. Stellar model calculations were performed with the alternative reaction rates. Here, we show that outside a narrow window of 0.5 and 4% of the values of the strong and Coulomb forces, respectively, the stellar production of carbon or oxygen is reduced by factors of 30 to 1000.

Nuclear reaction rates governing the nucleosynthesis of 44Ti

It appears that the main mechanism of 44Ti nucleosynthesis in supernovae involves an alpha-rich freezeout of hot matter. Late assembly of 12C nuclei via triple alpha reactions is followed by a rapid sequence of captures upward to the 44Ti. Considering that radioactive 44Ti is one of the premier targets of gamma astronomy, having already been detected in the Cas A remnant by COMPTEL, and considering that this sequence appears to be responsible for the large 44Ca abundance in solar matter and for the huge 44Ca excesses found within meteoritic SUNOCONs, we have surveyed the nuclear reaction rate uncertainties that govern this abundance. Our purpose is to identify for the nuclear physics community those reaction rates that have the greatest astrophysical importance. Using a large nuclear reaction network, we have systematically varied cross sections and groups of cross sections in an experimental test for astrophysical significance. We will identify these most important nuclear rates and explain our understanding of the overall rate dependencies that we have found.

Pycnonuclear triple-alpha fusion rates

Pycnonuclear triple-alpha reaction rates are calculated for mass densities from 10 exp 8 to 5 x 10 exp 9 g/cu cm. The plasma is assumed to be a fluid phase of alpha particles interacting through both nuclear and Coulomb potentials. It is described by Jastrow-type two-body correlations. The many-body wave function is determined variationally within a space of trial two-body wave functions that reproduce the expected long- and short-range behaviors of the correlations. The resulting three-body fusion rates are compared to previous calculations. 16 refs.

The anthropic significance of the existence of an excited state of 12C

Were it not for the presence of an excited state of 12C at 7.6 MeV, at the endpoint of the triple-alpha reaction, it would be difficult for stars to manufacture carbon and heavier elements. Calculations using modified triple-alpha rates test the sensitivity of stellar nucleosynthesis to the exact position of this excited state, and allow an empirical assessment of its importance in the anthropic principle in cosmology.

S-matrix calculation of the triple-alpha reaction

An S-matrix formalism is developed which can be applied to reactions in which electron screening is important, including three-body reactions and reactions involving weak interactions. The various regimes of the triple-alpha reactions are systematically discussed, and a new nonresonant regime at high densities is identified. Using the S-matrix formalism, an analytic expression is obtained for the screened triple-alpha reactions which is accurate for all temperatures and densities. The results are compared with those of Cameron (1959) and Nomoto et al. (1985), and the latter's expression for the unscreened reaction rate is verified. However, it is shown that the reaction rate in the pycnonuclear regime cannot be obtained from the unscreened rate using a screening factor, and that the results of Nomoto et al. therefore cannot be used in this regime.

The evolutionary behaviour of population III intermediate mass stars

Assuming the Big-Bang nucleosynthesis was responsible for the formation of helium, the evolution of first-generation intermediate-mass stars of 5, 7, and 9M⊙ with no metals have been studied from the threshold of stability through the stage of helium exhaustion in the cores of the stars. Hydrogen Main-Sequence positions are marked at effective temperatures higher than those of normal stars. The evolutionary tracks during the hydrogen burning phase start to be similar to those of normal stars when the CN-cycle reactions, which are controlled by the triple-alpha reactions, become operative for hydrogen depletion. Helium Main Sequence of Population III stars of intermediate mass occurs at the high effective temperature region of the H-R diagram and stars stay as blue stars until the end of the core helium exhaustion phase. The total time elapsed is in the range of 3×107 and 108yr. The stars with the initial masses of 5, 7, and 9M⊙ developed a moderately electron degenerate complete hydrogen-exhausted region with masses of 0.77, 1.06, and 1.42M⊙, respectively, in which the most abundant element is carbon.