Pycnonuclear Reactions Research Articles

Impact of Pycnonuclear Fusion Uncertainties on the Cooling of Accreting Neutron Star Crusts

The observation of X-rays during quiescence from transiently accreting neutron stars provides unique clues about the nature of dense matter. This, however, requires extensive modeling of the crusts and matching the results to observations. The pycnonuclear fusion reaction rates implemented in these models are theoretically calculated by extending phenomenological expressions and have large uncertainties spanning many orders of magnitude. We present the first sensitivity studies of these pycnonuclear fusion reactions in realistic network calculations. We also couple the reaction network with the thermal evolution code dStar to further study their impact on the neutron star cooling curves in quiescence. Varying the pycnonuclear fusion reaction rates alters the depth at which nuclear heat is deposited although the total heating remains constant. The enhancement of the pycnonuclear fusion reaction rates leads to an overall shallower deposition of nuclear heat. The impurity factors are also altered depending on the type of ashes deposited on the crust. These total changes correspond to a variation of up to 9 eV in the modeled cooling curves. While this is not sufficient to explain the shallow heat source, it is comparable to the observational uncertainties and can still be important for modeling the neutron star crust.

Synthesis of Elements in Compact Stars in Pycnonuclear Reactions with Carbon Isotopes: Quasibound States vs. States of Zero-Points Vibrations

(1) Purpose: Conditions of formation of compound nuclear systems needed for synthesis of heavy nuclei in pycnonuclear reactions in compact stars are studied on a quantum mechanical basis. (2) Methods: The method of multiple internal reflections is applied for pycnonuclear reactions in compact stars with new calculations of quasibound spectra and spectra of zero-point vibrations. (3) Results: Peculiarities of the method are analyzed for reaction with isotopes of Carbon. The developed method takes into account continuity and conservation of quantum flux (describing pycnonuclear reaction) inside the full spacial region of reaction, including the nuclear region. This gives the appearance of new states (called quasibound states) in which compound nuclear systems of Magnesium are formed with the largest probability. These states have not been studied yet in synthesis of elements in stars. Energy spectra of zero-point vibrations and spectra of quasibound states are estimated with high precision for reactions with isotopes of Carbon. For the first time, the influence of plasma screening on quasibound states and states of zero-point vibrations in pycnonuclear reactions has been studied. (4) Conclusions: The probability of formation of a compound nucleus in quasibound states in pycnonuclear reaction is essentially larger than the probability of formation of this system in states of zero-point vibrations studied by Zel’dovich and followers. Therefore, synthesis of Magnesium from isotopes of Carbon is more probable through the quasibound states than through the states of zero-point vibrations in compact stars. Energy spectra of zero-point vibrations are changed essentially after taking plasma screening into account. Analysis shows that from all studied isotopes of Magnesium, only 24Mg is stable after synthesis at an energy of relative motion of 4.881 MeV of the incident nuclei 12C.

Квантові ефекти пікноядерних реакцій у компактних зорях: Нові квазізв’язані стани та спектроскопія

Quantum effects in pycnonuclear reactions in compact stars at zero temperatures are studied with high precision. The reaction 16O + 16O was analyzed using the method of multiple internal reflections. The study of such reactions requires full consideration of quantum fluxes in the internal nuclear region. This reduces the rate and number of pycnonuclear reactions up to 1.8 times. This leads to the appearance of new states (which we call quasibound states) where the compound nuclear system is formed with maximal probability. As shown, the minimal energy of such a state is slightly higher than the energy of zero-mode oscillations in the lattice nodes in the pycnonuclear reaction, however, the probability of the formation of a compound system in a quasibound state is significantly greater than the corresponding probability in a state of zero-mode oscillations. It is reasonable to say that the frequency of reactions in quasi-bound states is more likely than in states of zero-mode oscillations. This can lead to significant changes in estimates of reaction rates in stars.

Nuclear physics with TriSol at Notre Dame’s Nuclear Science Laboratory

The detailed study of radioactive nuclei has resulted in opportunities for addressing many open questions in low-energy nuclear physics. For over three decades, the TwinSol separator at the University of Notre Dame has produced high-quality in-flight radioactive beams at low-energy for light isotopes that have been used in experiments aimed at nuclear structure, astrophysics, and fundamental symmetries studies. We have recently upgraded the TwinSol separator by adding additional elements: a dipole magnet, and a third solenoid. This new TriSol separator will improve the quality and purity of future radioactive beams. This improvement will enable the use of heavier beams and address beam contamination that has hindered past experiments. The current status of TriSol and its science program will be presented along with the role the TriSol program plays in the current landscape of nuclear physics user facilities. The TriSol program includes plans for studies of 11C(p, p)11C reaction for investigating the nature of the first stars, 14O(α, p)17F and its influence on reaction networks in X-ray bursts, the measurement of fusion reactions on Ne isotopes important for pycnonuclear reactions, precision half-life measurements for fundamental symmetries studies, and the use of TriSol as a magnetic spectrometer.

Quantum design in study of pycnonuclear reactions in compact stars

Pycnonuclear reactions in the compact stars at zero temperatures are studied on quantum mechanical basis in the paper. Formalism of multiple internal reflections is generalized for analysis, that was developed for nuclear decays and captures by nuclei with high precision and tests. For the chosen reaction $^{12}$C + $^{12}$C = $^{24}$Mg, we find the following. A quantum study of the pycnonuclear reaction requires a complete analysis of quantum fluxes in the internal nuclear region. This reduces rate and number of pycnonuclear reactions by 1.8 times. This leads to the appearance of new states (called as quasibound states) where the compound nuclear system is formed with maximal probability. As shown, minimal energy of such a state is a little higher than energy of zero-point vibrations in lattice sites in pycnonuclear reaction, however probability of formation of compound system at the quasibound state is essentially larger than the corresponding probability at state of zero-point vibrations. Hence, there is a sense to tell about reaction rates in such quasibound states as more probable, rather than states of zero-point vibrations. This can lead to the essential changes in estimation of the rates of nuclear reactions in stars.

Screening Effects in Stars and in the Laboratory

Nuclear reactions are the driver of the evolution of many astrophysical objects. In the astrophysical environment their respective reaction rates are, however, modified due to the presence of other charges. The effects depend on the relative importance of Coulomb energy versus thermal energy and are distinguished between weak and strong screening. In the extreme case of pycnonuclear reactions, fusion reactions can be induced by the zero-point motion of nuclei in a Coulomb crystal. This paper reviews the various screening situations and discusses important applications. We also briefly review laboratory approaches to study screening effects.

Static and rotating white dwarf stars at finite temperatures

Static and rotating, cold and hot white dwarf stars are investigated both in Newtonian gravity and general theory of relativity, employing the well-established Chandrasekhar equation of state. The Hartle formalism is involved to construct and study uniformly rotating configurations of white dwarfs. The mass-radius, mass-central density, radius-central density and other basic relations of stable white dwarfs, consisting of pure helium and iron, are constructed for different temperatures at mass shedding limit. Stability of white dwarfs is analyzed with respect to the inverse beta decay process, pycnonuclear reactions and instabilities of general relativity. It is found that for a fixed mass hot white dwarfs consisting of pure iron are smaller in size, correspondingly denser with respect to the ones composed of light elements. In addition, it is shown that near the Chandrasekhar mass limit the mass of hot rotating white dwarfs is slightly less than for cold ones, though for low mass rotating white dwarfs and static ones in all mass range the situation is opposite.

Mass limits of the extremely fast-spinning white dwarf CTCV J2056–3014

CTCV J2056–3014 is a nearby cataclysmic variable with an orbital period of approximately 1.76 h at a distance of about 853 light-years from the Earth. Its recently reported X-ray properties suggest that J2056–3014 is an unusual accretion-powered intermediate polar that harbors a fast-spinning white dwarf (WD) with a spin period of 29.6 s. The low X-ray luminosity and the relatively modest accretion rate per unit area suggest that the shock is not occurring near the WD surface. It has been argued that, under these conditions, the maximum temperature of the shock cannot be directly used to determine the mass of the WD (which, under the abovementioned assumptions, would be around 0.46 M⊙). Here, we explore the stability of this rapidly rotating WD using a modern equation of state (EoS) that accounts for electron–ion, electron–electron, and ion–ion interactions. For this EoS, we determine the mass density thresholds for the onset of pycnonuclear fusion reactions and study the impact of microscopic stability and rapid rotation on the structure and stability of WDs, considering them with helium, carbon, oxygen, and neon. From this analysis, we obtain a minimum mass for CTCV J2056–3014 of 0.56 M⊙ and a maximum mass of around 1.38 M⊙. If the mass of CTCV J2056–3014 is close to the lower mass limit, its equatorial radius would be on the order of 104 km due to rapid rotation. Such a radius is significantly larger than that of a nonrotating WD of average mass (0.6 M⊙), which is on the order of 7 × 103 km. The effects on the minimum mass of J2056–3014 due to changes in the temperature and composition of the stellar matter were found to be negligibly small.

The Structure and Stability of Massive Hot White Dwarfs

Abstract We investigate the structure and stability against radial oscillations, pycnonuclear reactions, and inverse β-decay of hot white dwarfs. We consider the fluid matter to be made up of nucleons and electrons confined in a Wigner–Seitz cell surrounded by free photons. It is considered that the temperature depends on the mass density considering the presence of an isothermal core. We find that the temperature produces remarkable effects on the equilibrium and radial stability of white dwarfs. The stable equilibrium configuration results are compared with those for white dwarfs estimated from the Extreme Ultraviolet Explorer survey and the Sloan Digital Sky Survey. We derive masses, radii, and central temperatures for the most massive white dwarfs according to the surface gravity and effective temperature reported by the surveys. We note that these massive stars are in the mass region where general relativity effects are important. These stars are near the threshold of instabilities due to radial oscillations, pycnonuclear reactions, and inverse β-decay. Regarding the radial stability of these stars as a function of the temperature, we find that it decreases with the increment of central temperature. We also find that the maximum-mass point and the zero eigenfrequencies of the fundamental mode are determined at the same central energy density. Regarding low-temperature stars, pycnonuclear reactions occur in similar central energy densities, and the central energy density threshold for inverse β-decay is not modified. For T c ≥ 1.0 × 108 [K], the onset of radial instability is attained before pycnonuclear reaction and inverse β-decay.

Heating in Magnetar Crusts from Electron Captures

The persistent thermal luminosity of magnetars and their outbursts suggest the existence of some internal heat sources located in their outer crust. The compression of matter accompanying the decay of the magnetic field may trigger exothermic electron captures and, possibly, pycnonuclear fusions of light elements that may have been accreted onto the surface from the fallback of supernova debris, from a disk or from the interstellar medium. This scenario bears some resemblance to deep crustal heating in accreting neutron stars, although the matter composition and the thermodynamic conditions are very different. The maximum possible amount of heat that can be released by each reaction and their locations are determined analytically taking into account the Landau–Rabi quantization of electron motion. Numerical results are also presented using experimental, as well as theoretical nuclear data. Whereas the heat deposited is mainly determined by atomic masses, the locations of the sources are found to be very sensitive to the magnetic field strength, thus providing a new way of probing the internal magnetic field of magnetars. Most sources are found to be concentrated at densities 1010–1011 g cm−3 with heat power W∞∼1035–1036 erg/s, as found empirically by comparing cooling simulations with observed thermal luminosity. The change of magnetic field required to trigger the reactions is shown to be consistent with the age of known magnetars. This suggests that electron captures and pycnonuclear fusion reactions may be a viable heating mechanism in magnetars. The present results provide consistent microscopic inputs for neutron star cooling simulations, based on the same model as that underlying the Brussels-Montreal unified equations of state.

Relevance of Dynamical Nuclear Processes in Quantum Complex Systems of Massive White Dwarfs

We revisit the properties of relativistic and quantum complex systems of massive white dwarfs (WDs) using a modern equation of state (EoS) which accounts for electron-ion interactions among lattice nuclei, and which makes use of the latest experimental atomic mass data. We estimate the mass density thresholds for the onset of nuclear reactions in the cores of massive WDs and study the impact of microscopic stability on the structure and stability of different WD constitutions. We focus on the properties of massive carbon and oxygen white dwarfs, taking into account the electron capture and pycnonuclear fusion reactions instabilities. Our results indicate that pycnonuclear reactions turn carbon WDs unstable while for oxygen WDs their instability is due to the inverse β −decay (electron capture) process. We highlight that these dynamical nuclear processes are of great relevance for assessment of stability of these quantum complex systems of massive WDs, since they constrain their maximum masses.

Nuclear and dark matter heating in massive white dwarf stars

Recently, Cheng et al. identified a number of massive white dwarfs (WD) that appear to have an additional heat source providing a luminosity near $\approx 10^{-3}L_\odot$ for multiple Gyr. In this paper we explore heating from electron capture and pycnonuclear reactions. We also explore heating from dark matter annihilation. WD stars appear to be too small to capture enough dark matter for this to be important. Finally, if dark matter condenses to very high densities inside a WD this could ignite nuclear reactions. We calculate the enhanced central density of a WD in the gravitational potential of a very dense dark matter core. While this might start a supernova, it seems unlikely to provide modest heating for a long time. We conclude that electron capture, pycnonuclear, and dark matter reactions are unlikely to provide significant heating in the massive WD that Cheng considers.

Experimental constraints on shallow heating in accreting neutron-star crusts

The observed thermal relaxation of transiently accreting neutron stars during quiescence periods in low-mass X-ray binaries suggests the existence of unknown heat sources in the shallow layers of neutron-star crust. Making use of existing experimental nuclear data, we estimate the maximum possible amount of heat that can be deposited in the outer crust of an accreting neutron star due to electron captures and pycnonuclear fusion reactions triggered by the burial of X-ray burst ashes.

Nonequilibrium Layer in the Crust of Neutron Stars and Nonequilibrium β-Processes in Astrophysics

The formation of the chemical composition of neutron star envelopes, at densities 1010–1013 g cm–3, is considered. As hot matter is compressed in the process of collapse, which leads to the explosion of a core-collapse supernova, the stage of nuclear equilibrium with free neutrino escape, kinetic equilibrium in β-processes, and, as a result, the establishment of limited nuclear equilibrium with a fixed number of nuclei takes place. Cold matter is compressed at a fixed number of nuclei whose atomic weight initially does not change and subsequently decreases. A pycnonuclear reaction of the fusion of available nuclei and a decrease in their number begin at the end. The compression of cold matter is accompanied by an increase in the mass fraction of free neutrons. In this case, the chemical composition of the envelope differs significantly from the equilibrium one and contains a considerable store of nuclear energy. Nonequilibrium β-reactions proceed at densities exceeding the upper bound for the nonequilibrium layer density, which lead to heating, nuclear energy release, and the possible attainment of a state of complete thermodynamic equilibrium. The thermodynamics of nonequilibrium β-processes, which lead to the heating of matter as neutrinos escape freely, is considered.

Nuclear physics in type I X-ray bursts

X-ray bursts (XRBs), one of the most fascinating astrophysical phenomena, are characterized by sudden 10–50 dramatic increase in luminosity by the X-ray emission of roughly 10–100 s in duration, with peak luminosities of roughly 1038 erg/s. The XRB is a recurrent phenomenon on time scales of hours to days. It is a violent nuclear process, i.e., thermonuclear runaway, occurs in a close binary system which usually consists of a neutron star (or a black hole) and a less-evolved company “donor” star (usually a red giant star). The accreted material burns stably through both the triple-α reaction and the hot, β-limited carbon-nitrogen-oxygen (HCNO) cycles, giving rise to the persistent flux. Once critical temperatures and densities are achieved in the accretion disk, breakout from this region toward higher masses can occur through α-induced reactions. Subsequently, the rapid-proton capture process (so-called rp-process) drives nucleosynthesis toward the proton drip-line. This eventually results in a rapid increase in energy generation (ultimately leading to the XRB) and nucleosynthesis up to A ~100 mass region. As the most frequent thermonuclear phenomena in the universe, the XRBs have been studied in detail in a number of space-borne X-ray satellite observatory missions, including EXOSAT (1983–1986), RXTE (1995–2012), BeppoSAX (1996–2003), Chandra (1999–2019), XMM-Newton (1999–2020) and HETE-2 (2000–2008). In the year of 2017, the Insight Hard X-ray Modulation Telescope (HXMT) had been launched, as the first X-ray astronomy satellite of China. The main scientific objectives of Insight-HXMT are: (1) To scan the Galactic Plane to find new transient sources and to monitor the known variable sources, (2) to observe X-ray binaries to study the dynamics and emission mechanism in strong gravitational or magnetic fields, and (3) to find and study γ-ray bursts with its anti-coincidence CsI detectors. Up to now, more than 90 galactic XRBs have been identified since their initial discovery in 1976. These observations have provided abundant data and opened a new era in X-ray astronomy. The surface of accreting neutron stars is characterized by a wide range of nuclear processes ranging from fragmentation at infall, over thermonuclear burning in X-ray bursts and superbursts, to electron captures and pycnonuclear fusion reactions in the neutron star crust. These processes involve the majority of the nuclei between the proton and the neutron drip line up to a maximum mass number set by the endpoint of the rp-process. In this picture, the rp-process during X-ray bursts (and maybe during stable hydrogen burning as well) plays a central role as it directly determines one of the key observables, the observed X-ray bursts. To investigate the scientific issues in XRBs, such as the observed luminosity curves, the astrophysical environment parameters in the binary system, and the isotropic abundance distributions in the burst ashes, nuclear physicists need precise nuclear-physics inputs, such as nuclear masses (or reaction Q values), half-lives, as well as thermonuclear reaction rates, and β-decay weak rates. Combined with the astrophysics models, one can understand the physics in XRBs more deeply. This paper systematically reviews the nuclear physics in type I X-ray bursts, including the scientific motivation, importance, major research topics, as well as some progress achieved, etc. Thereinto, the relevant nucleosynthesis processes and key nuclear-physics inputs required, are introduced in detail. The status and progress for the XRBs studies are introduced and prospected for the Chinese institutions. In this review, the goals of different research topics are summarized and evaluated, and the promising direction is guided for future investigations.

Theoretical exploration of S-factors for nuclear reactions of astrophysical importance

We present here a robust analytical model based on nuclear reaction theory for non-resonant fusion cross sections near Coulomb barrier. The astrophysical S-factors involving stable and neutron rich isotopes of C, O, Ne, Mg and Si for fusion reactions have been calculated in the centre of mass energy range of 2-30 MeV. The model is based on the tunneling through barrier arising out of nuclear, Coulomb and centrifugal potentials. Our formalism predicts precisely the suppression of S-factor at sub-barrier energies which are of astrophysical interest by using only five parameters for asymmetric systems and just four parameters for symmetric systems and thus providing an accurate and very compact description of S-factor. The cross sections can be convoluted with Maxwell-Boltzmann distribution of energies to obtain thermo- or pycno-nuclear reaction rates relevant to nucleosynthesis at high density environments and stellar burning at high temperatures as well as for 34Ne + 34Ne fusion occurring in the inner crust of accreting neutron stars.

Deep crustal heating by neutrinos from the surface of accreting neutron stars

We present a new mechanism for deep crustal heating in accreting neutron stars. Charged pions ($\pi^+$) are produced in nuclear collisions on the neutron star surface during active accretion and upon decay they provide a flux of neutrinos into the neutron star crust. For massive and/or compact neutron stars, neutrinos deposit $\approx 1\textrm{--} 2 \, \mathrm{MeV}$ of heat per accreted nucleon into the inner crust. The strength of neutrino heating is comparable to the previously known sources of deep crustal heating, such as from pycnonuclear fusion reactions, and is relevant for studies of cooling neutron stars. We model the thermal evolution of a transient neutron star in a low-mass X-ray binary, and in the particular case of the neutron star MXB~1659-29 we show that additional deep crustal heating requires a higher thermal conductivity for the neutron star inner crust. A better knowledge of pion production cross sections near threshold would improve the accuracy of our predictions.

Are Gravitational Waves Spinning Down PSR J1023+0038?

The pulsar J1023+0038 rotates with a frequency ν≈592 Hz and has been observed to transition between a radio state, during which it is visible as a millisecond radio pulsar, and a low-mass x-ray binary (LMXB) state, during which accretion powered x-ray pulsations are visible. Timing during the two phases reveals that during the LMXB phase the neutron star is spinning down at a rate of ν[over ˙]≈-3×10^{-15} Hz/s, which is approximately 27% faster than the rate measured during the radio phase, ν[over ˙]≈-2.4×10^{-15} Hz/s, and is at odds with the predictions of accretion models. We suggest that the increase in spin-down rate is compatible with gravitational wave emission, particularly with the creation of a "mountain" during the accretion phase. We show that asymmetries in pycnonuclear reaction rates in the crust can lead to a large enough mass quadrupole to explain the observed spin-down rate, which thus far has no other self-consistent explanation. We also suggest two observational tests of this scenario, involving radio timing at the onset of the next millisecond radio pulsar phase, when the mountain should dissipate, and accurate timing during the next LMXB phase to track the increase in torque as the mountain builds up. Another possibility is that an unstable r mode with an amplitude α≈5×10^{-8} may be present in the system.

Phase transitions, interparticle correlations, and elementary processes in dense plasmas

Astrophysical dense plasmas are those we find in the interiors, surfaces, and outer envelopes of stellar objects such as neutron stars, white dwarfs, the Sun, and giant planets. Condensed plasmas in the laboratory settings include those in ultrahigh-pressure metal-physics experiments undertaken for realization of metallic hydrogen. We review basic physics issues studied in the past 60 some years on the phase transitions, the interparticle correlations, and the elementary processes in dense plasmas, through survey on scattering of electromagnetic waves, equations of state, phase diagrams, transport processes, stellar and planetary magnetisms, and thermo- and pycnonuclear reactions.

Central Magnetic Field of a Magnetic White Dwarf Star

Abstract Observations of over-luminous Type 1a supernovae have prompted researchers to come up with various hypotheses in order to explain them. One hypothesis is based on the explosion of a progenitor super-massive magnetic white dwarf star. These stars are assumed to have very strong magnetic fields inside of them. However, there is a lack of analytic proof of the existence of such magnetic fields in the magnetic white dwarf stars. In this work, we plan to address an analytic proof of the existence of very strong magnetic fields in the center of these magnetic white dwarfs. We will see that for a one Landau-level white dwarf star, with central density , it is possible to have central magnetic fields of the order of at least. In the presence of strong magnetic fields, the threshold densities chosen for this work that correspond to instabilities due to general relativity and pycnonuclear reactions have been found to increase so that the matter does not acquire instability at such central densities.