Thermonuclear Burning Research Articles

Influence of plasma self-radiation model on thermonuclear burning simulation results

The one-dimensional problem on two-sided irradiation by proton beams of the plane layer of condensed DT mixture with density ρ0 = 100ρs, where ρs is the fuel solid-state density at atmospheric pressure, is considered. The effect of the plasma self-radiation on the thermonuclear burn-up factor as well as the role of the inverse Compton effect are studied. It is shown that the inverse Compton effect decreases the burn-up factor down to about 3% while the plasma self-radiation in whole decreases it down to about 9%.

FAILURE OF A NEUTRINO-DRIVEN EXPLOSION AFTER CORE-COLLAPSE MAY LEAD TO A THERMONUCLEAR SUPERNOVA

We demonstrate that $\sim10\,\textrm{s}$ after the core-collapse of a massive star, a thermonuclear explosion of the outer shells is possible for some (tuned) initial density and composition profiles, assuming that the neutrinos failed to explode the star. The explosion may lead to a successful supernova, as first suggested by Burbidge et al. We perform a series of one-dimensional (1D) calculations of collapsing massive stars with simplified initial density profiles (similar to the results of stellar evolution calculations) and various compositions (not similar to 1D stellar evolution calculations). We assume that the neutrinos escaped with a negligible effect on the outer layers, which inevitably collapse. As the shells collapse, they compress and heat up adiabatically, enhancing the rate of thermonuclear burning. In some cases, where significant shells of mixed helium and oxygen are present with pre-collapsed burning times of $\lesssim100\,\textrm{s}$ ($\approx10$ times the free-fall time), a thermonuclear detonation wave is ignited, which unbinds the outer layers of the star, leading to a supernova. The energy released is small, $\lesssim10^{50}\,\textrm{erg}$, and negligible amounts of synthesized material (including $^{56}$Ni) are ejected, implying that these 1D simulations are unlikely to represent typical core-collapse supernovae. However, they do serve as a proof of concept that the core-collapse-induced thermonuclear explosions are possible, and more realistic two-dimensional and three-dimensional simulations are within current computational capabilities.

Modeling type Ia supernovae and quark novae

Compact astrophysical objects can change their structure and composition in combustion-like processes. In the case of white dwarfs, thermonuclear burning can even lead to an explosion as a Type la supernova. We give a brief account of the physical concepts of combustion and of methods to model this phenomenon in large-scale numerical simulations. As examples for application we discuss thermonuclear explosions of white dwarfs and to hypothetical “quark novae” transforming neutron stars into strange quark stars.

PHOTOIONIZATION HEATING OF NOVA EJECTA BY THE POST-OUTBURST SUPERSOFT SOURCE

The expanding ejecta from a classical nova remains hot enough ($\sim10^{4}\, {\rm K}$) to be detected in thermal radio emission for up to years after the cessation of mass loss triggered by a thermonuclear instability on the underlying white dwarf (WD). Nebular spectroscopy of nova remnants confirms the hot temperatures observed in radio observations. During this same period, the unstable thermonuclear burning transitions to a prolonged period of stable burning of the remnant hydrogen-rich envelope, causing the WD to become, temporarily, a super-soft X-ray source. We show that photoionization heating of the expanding ejecta by the hot WD maintains the observed nearly constant temperature of $(1-4)\times10^4\mathrm{~K}$ for up to a year before an eventual decline in temperature due to either the cessation of the supersoft phase or the onset of a predominantly adiabatic expansion. We simulate the expanding ejecta using a one-zone model as well as the Cloudy spectral synthesis code, both incorporating the time-dependent WD effective temperatures for a range of masses from $0.60\ M_{\odot}$ to $1.10\ M_{\odot}$. We show that the duration of the nearly isothermal phase depends most strongly on the velocity and mass of the ejecta and that the ejecta temperature depends on the WD's effective temperature, and hence its mass.

X-Ray Observations of VY Scl-Type Nova-Like Binaries in the High and Low State

Four VY Scl-type nova-like systems were observed in X-rays both during the low and the high optical states. They are BZ Cam, MV Lyr, TT Ari, and V794 Aql. Using archival ROSAT, <em>Swift</em> and <em>SUZAKU</em> observations we found that the X-ray flux for BZ Cam is higher during the low state, but there is no supersoft X-ray source (SSS) that would indicate the thermonuclear burning predicted in a previous article. The X-ray flux is lower by a factor 2–10 in the low than the high state in other systems, and does not reflect the drop in <em>˙M</em> inferred from optical and UV data. The best fit model for the X-ray spectra is a collisionally ionized plasma model. The X-ray flux may originate in a shocked wind or in accretion onto polar caps in intermediate polar systems that continues even during the low state.

Analytical Dependence of the Ignition Dynamics Parameters on the Low-Z Impurity Concentration

Abstract In this paper, thermonuclear burning of the deuterium-tritium (D/T) plasma of an inertial confinement fusion (ICF) target is studied in the presence of low-Z impurities (lithium, beryllium, and carbon) with arbitrary concentrations. The effect of impurities produced due to the mixing of the thermonuclear fuel with the material of the structural elements of the target during its compression on the process of target burning is studied. Also, the effect of impurity concentration on the plasma ignition parameters such as ignition temperature, confinement parameter ρR, and ignition energy are discussed. The models are constructed for an isobaric and an isochoric plasma for the case in which the burning is initiated in the central heated region of the target and then propagated into the surrounding relatively cold fuel. In ICF spherical implosions of the D/T fuel, the ignition parameters as ignition temperature and parameter ρR in the hot spot are approximately 7 - 10 keV and 0.2 - 0.4 g cm-2 respectively, and these values are increased by the presence of impurities.

ON THE EFFECT OF EXPLOSIVE THERMONUCLEAR BURNING ON THE ACCRETED ENVELOPES OF WHITE DWARFS IN CATACLYSMIC VARIABLES

The detection of heavy elements at suprasolar abundances in the atmospheres of some accreting white dwarfs in cataclysmic variables, coupled with the high temperatures needed to produce these elements requires explosive thermonuclear burning. The central temperatures of any formerly more massive secondary stars in CVs undergoing hydrostatic CNO burning are far too low to produce these elements. Evidence is presented that at least some cataclysmic variables contain donor secondaries that have been contaminated by repeated novae ejecta and are transferring this material back to the white dwarf. This scenario does not exclude the channel in which formerly more massive donor stars underwent CNO processing in ystems that underwent thermal timescale mass transfer. Implications for the progenitors of CVs are discussed.

The thermal stability of helium burning on accreting neutron stars

Thermonuclear burning on the surface of accreting neutron stars is observed to stabilize at accretion rates almost an order of magnitude lower than theoretical models predict. One way to resolve this discrepancy is by including a base heating flux that can stabilize the layer. We focus our attention on pure helium accretion, for which we calculate the effect of a base heating flux on the critical accretion rate at which thermonuclear burning stabilizes. We use the mesa stellar evolution code to calculate |$\dot{m}_{\rm crit}$| as a function of the base flux, and derive analytic fitting formulae for |$\dot{m}_{\rm crit}$| and the burning temperature at that critical accretion rate, based on a one-zone model. We also investigate whether the critical accretion rate can be determined by examining steady-state models only, without time-dependent simulations. We examine the argument that the stability boundary coincides with the turning point |${\rm d}y_{\rm burn}/{\rm d}\dot{m}=0$| in the steady-state models, and find that it does not hold outside of the one zone, zero base flux case. A linear stability analysis of a large suite of steady-state models is also carried out, which yields critical accretion rates a factor of ∼3 larger than the mesa result, but with a similar dependence on base flux. Lastly, we discuss the implications of our results for the ultracompact X-ray binary 4U 1820-30.

THE CLASSIFICATION OF MAGNETOHYDRODYNAMIC REGIMES OF THERMONUCLEAR COMBUSTION

Physical properties of magnetohydrodynamic (MHD) reaction fronts are studied as functions of the thermodynamic conditions, and the strength and orientation of the magnetic field in the unburned matter through which the fronts propagate. We determine the conditions for the existence of the various types of MHD reaction fronts and the character of the changes in physical quantities across these reaction fronts. The analysis is carried out in general for a perfect gas equation of state and a constant energy release, and then extended to thermonuclear reaction fronts in degenerate carbon-oxygen mixtures and degenerate helium in conditions typical of Type Ia supernova explosions. We find that as unburned matter enters perpendicular to a reaction front, the release of energy through burning generates shear velocity in the reacting gas that, depending on the type of reaction front, strengthens or weakens the magnetic field. In addition, we find that the steady-state propagation of a reaction front is impossible for certain ranges of magnetic field direction. Our results provide insight into the phenomena of MHD thermonuclear combustion that is relevant to the interpretation of future simulations of SN Ia explosions that have magnetic fields systematically incorporated.

Numerical Experiments for Nuclear Flashes toward Superbursts in an Accreting Neutron Star

We show that the superburst would be originated from thermonuclear burning ignited by accumulated fuels in the deep layers compared to normal X-ray bursts. Two cases are investigated for models related to superbursts by following thermal evolution of a realistic neutron star: helium flash and carbon flash accompanied with many normal bursts. For a helium flash, the burst shows the long duration when the accretion rate is low compared with the observation. The flash could become a superburst if the burning develops to the deflagration and/or detonation. For a carbon flash accompanied with many normal bursts, after successive 2786 normal bursts during 1.81 × 109 s, the temperature reaches the deflagration temperature. This is due to the produced carbon which amount reaches to ≈0.1 in the mass fraction. The flash will develop to dynamical phenomena of the deflagration and/or detonation, which may lead to a superburst.

Special Issue on the 13th International Workshop on the Physics of Compressible Turbulent Mixing

The study of compressible turbulent mixing associated with Richtmyer-Meshkov (RM), Rayleigh-Taylor (RT), and Kelvin-Helmholtz (KH) instabilities is motivated by diverse applications in science and engineering, including supersonic combustion, detonation, instability of collapsing gas bubbles, stratified flows in geophysical applications, chemical engineering, inertial confinement fusion (ICF), supernovae, and molecular clouds. Further, the interaction of shock waves with materials is also of interest in biomedical applications, such as fragmentation of cancer cells during shockwave chemotherapy and cavitation damage to human tissues during lithotripsy. In many of these applications, the Reynolds number is very high and the instabilities rapidly lead to turbulent mixing. In the case of ICF, which is regarded as a promising approach to controlled thermonuclear fusion: (1) these instabilities lead to the growth of perturbations on the interfaces within the capsules; (2) perturbations grow into the nonlinear regime by mode coupling and eventually cause mixing of materials; and (3) material mixing inhibits thermonuclear burning of the fuel.There are ongoing research efforts at centers in the USA, UK, France, Russia, and China to design improved shock tube experiments in order to further elucidate RM instability and better understand turbulent mixing across material interfaces. Novel experiments are also being performed to further investigate RT and KH instabilities, as well as combinations of these instabilities. There are, however, a number of difficulties associated with experiments, including separating the initial gas regions, the interpretation of visualization images and challenges with diagnostics, and the inability to measure certain quantities of interest either because of their intrinsic nature (e.g., vorticity) or because of practical limitations in the experimental configurations. Computational, theoretical, and modeling studies have been widely conducted in parallel with experiments to complement the data obtained from the experiments, help design and interpret results from experiments, develop reduced model descriptions (such as Reynolds-averaged and buoyancy-drag models), and validate numerical methods and codes by comparisons to experimental data. Numerical simulation techniques applied to these instability and mixing problems include direct numerical simulation (DNS), large eddy simulation (LES), and monotone or implicit LES (ILES).The 13th International Workshop on the Physics of Compressible Turbulent Mixing (IWPCTM13) was organized in the UK by Cranfield University at Woburn Abbey (July 15–20). The conference was cohosted by the Atomic Weapons Establishment, with additional sponsorship from the Commissariat à l’Énergie Atomique et aux Énergies Alternatives, Los Alamos National Laboratory, and Lawrence Livermore National Laboratory. The conference was attended by more than 70 scientists from the UK, USA, Russia, France, China, India, and Spain. Experimental, theoretical, and computational studies of mixing processes applied to a range of problems were discussed at the workshop. The IWPCTM13 offered an excellent opportunity to an international group of delegates from national laboratories, institutes, and universities to review the state-of-the-art research on compressible turbulent mixing and to stimulate the discussion of future research in this field (for more information on this series of workshops and for proceedings from previous workshops, see http://www.iwpctm.org). This special issue of the Journal of Fluids Engineering publishes peer-reviewed papers originally presented at the IWPCTM13.Both experimental and computational papers are included. Experimental studies concern laser-driven hydrodynamic experiments; comparisons of tilted rocket rig experiments with DNS, ILES, and turbulence model predictions; and shock tube experiments. The computational studies focus on LES and Reynolds-averaged turbulence modeling of RT and RM mixing in fluids and solids. The results showed that significant progress has been made with regard to simulation and modeling techniques for turbulent mixing. However, further research is required to assess the accuracy and efficiency of different turbulence models against numerical simulation and experimental data in order to reduce the modeling uncertainty in applications such as ICF. A review of phase separation, microchannel devices is also presented. Finally, the papers discussed at the conference included applications of advanced computational methods and models in astrophysics.The guest editors of this special issue would like to thank all of the authors for their efforts in preparing their contributions as well as all of the reviewers for their assistance in reviewing these papers. Finally, we would like to thank the Journal of Fluids Engineering Editor, Malcolm Andrews, the Editorial Office, Amber Grady-Fuller, and the Production Coordinator at the American Society of Mechanical Engineers for their encouragement and assistance during the course of this special issue publication.

CHARACTERIZING THE EVOLVING X-RAY SPECTRAL FEATURES DURING A SUPERBURST FROM 4U 1636-536

Recent studies have shown that runaway thermonuclear burning of material accreted onto neutron stars, i.e. Type I X-ray bursts, may affect the accretion disk. We investigate this by performing a detailed time-resolved spectral analysis of the superburst from 4U 1636-536 observed in 2001 with the Rossi X-ray Timing Explorer. Superbursts are attributed to the thermonuclear burning of carbon, and are approximately 1000 times more energetic than the regular short Type I bursts. This allows us to study detailed spectra for over 11 ks, compared to at most 100 s for regular bursts. A feature is present in the superburst spectra around 6.4 keV that is well fit with an emission line and an absorption edge, suggestive of reflection of the superburst off the accretion disk. The line and edge parameters evolve over time: the edge energy decreases from 9.4 keV at the peak to 8.1 keV in the tail, and both features become weaker in the tail. This is only the second superburst for which this has been detected, and shows that this behavior is present even without strong radius expansion. Furthermore, we find the persistent flux to almost double during the superburst, and return to the pre-superburst level in the tail. The combination of reflection features and increased persistent emission indicates that the superburst had a strong impact on the inner accretion disk, and it emphasizes that X-ray bursts provide a unique probe of accretion physics.

REACTION RATE AND COMPOSITION DEPENDENCE OF THE STABILITY OF THERMONUCLEAR BURNING ON ACCRETING NEUTRON STARS

The stability of thermonuclear burning of hydrogen and helium accreted onto neutron stars is strongly dependent on the mass accretion rate. The burning behavior is observed to change from Type I X-ray bursts to stable burning, with oscillatory burning occurring at the transition. Simulations predict the transition at a ten times higher mass accretion rate than observed. Using numerical models we investigate how the transition depends on the hydrogen, helium, and CNO mass fractions of the accreted material, as well as on the nuclear reaction rates of triple alpha and the hot-CNO breakout reactions 15O(a,g)19Ne and 18Ne(a,p)21Na. For a lower hydrogen content the transition is at higher accretion rates. Furthermore, most experimentally allowed reaction rate variations change the transition accretion rate by at most 10%. A factor ten decrease of the 15O(a,g)19Ne rate, however, produces an increase of the transition accretion rate of 35%. None of our models reproduce the transition at the observed rate, and depending on the true 15O(a,g)19Ne reaction rate, the actual discrepancy may be substantially larger. We find that the width of the interval of accretion rates with marginally stable burning depends strongly on both composition and reaction rates. Furthermore, close to the stability transition, our models predict that X-ray bursts have extended tails where freshly accreted fuel prolongs nuclear burning.

Theoretical rates of pulsation period change in the Galactic Cepheids

Theoretical estimates of the rates of radial pulsation period change in Galactic Cepheids with initial masses 5.5 M ⊙ ≤ M ZAMS ≤ 13 M ⊙, chemical composition X = 0.7, Z = 0.02 and periods 1.5 day ≤ Π ≤ 100 day are obtained from consistent stellar evolution and nonlinear stellar pulsation computations. Pulsational instability was investigated for three crossings of the instability strip by the evolutionary track in the HR diagram. The first crossing occurs at the post-main sequence helium core gravitational contraction stage which proceeds in the Kelvin-Helmholtz timescale whereas the second and the third crossings take place at the evolutionary stage of thermonuclear core helium burning. During each crossing of the instability strip the period of radial pulsations is a quadratic function of the stellar evolution time. Theoretical rates of the pulsation period change agree with observations but the scatter of observational estimates of $$\dot \Pi$$ noticeably exceeds the width of the band $$\left( {\delta \log \left| {\dot \Pi } \right| \leqslant 0.6} \right)$$ confining evolutionary tracks in the period-period change rate diagram. One of the causes of the large scatter with very high values of $$\dot \Pi$$ in Cepheids with increasing periods might be the stars that cross the instability strip for the first time. Their fraction ranges from 2% for M ZAMS = 5.5 M ⊙ to 9% for M ZAMS = 13 M ⊙ and variables α UMi and IX Cas seem to belong to such objects.

FINDING THE FIRST COSMIC EXPLOSIONS. III. PULSATIONAL PAIR-INSTABILITY SUPERNOVAE

Population III supernovae have been the focus of growing attention because of their potential to directly probe the properties of the first stars, particularly the most energetic events that can be seen at the edge of the observable universe. But until now pair-pulsation supernovae, in which explosive thermonuclear burning in massive stars fails to unbind them but can eject their outer layers into space, have been overlooked as cosmic beacons at the earliest redshifts. These shells can later collide and, like Type IIn supernovae, produce superluminous events in the UV at high redshifts that could be detected in the near infrared today. We present numerical simulations of a 110 M$_{\odot}$ pair-pulsation explosion done with the Los Alamos radiation hydrodynamics code RAGE. We find that collisions between consecutive pair pulsations are visible in the near infrared out to z $\sim$ 15 - 20 and can probe the earliest stellar populations at cosmic dawn.

Evolution and pulsation period change in the Large Magellanic Cloud Cepheids

Theoretical estimates of the pulsation period change rates in LMC Cepheids are obtained from consistent calculation of stellar evolution and nonlinear stellar pulsation for stars with initial chemical composition X = 0.7, Z = 0.008, initial masses 5M ⊙ ≤ M ZAMS ≤ 9M ⊙ and pulsation periods ranged from 2.2 to 29 day. The Cepheid hydrodynamical models correspond to the evolutionary stage of thermonuclear core helium burning. During evolution across the instability strip in the HR diagram the pulsation period Π of Cepheids is the quadratic function of the evolution time for the both fundamental mode and first overtone. Cepheids with initial masses M ZAMS ≥ 7M ⊙ pulsate in the fundamental mode and the period change rate \(\dot \Pi\) varies nearly by a factor of two for both crossings of the instability strip. In the period-period change rate diagram the values of Π and \(\dot \Pi\) concentrate within the strips, their slope and half-width depending on both the direction of the movement in the HR-diagram and the pulsation mode. For oscillations in the fundamental mode the half-widths of the strip are \(\delta log\dot \Pi = 0.35\) and \(\delta log\dot \Pi = 0.2\) for the first and the secon crossings of the instability strip, respectively. Results of computations are comparedwith observations of nearly 700 LMC Cepheids. Within existing observational uncertainties of \(\dot \Pi\) the theoretical dependences of the period change rate on the pulsation period are in a good agreement with observations.

Solar abundance of manganese: a case for near Chandrasekhar-mass Type Ia supernova progenitors

Context: Manganese is predominantly synthesised in Type Ia supernova (SN Ia) explosions. Owing to the entropy dependence of the Mn yield in explosive thermonuclear burning, SNe Ia involving near Chandrasekhar-mass white dwarfs (WDs) are predicted to produce Mn to Fe ratios significantly exceeding those of SN Ia explosions involving sub-Chandrasekhar mass primary WDs. Of all current supernova explosion models, only SN Ia models involving near-Chandrasekhar mass WDs produce [Mn/Fe] > 0.0. Aims: Using the specific yields for competing SN Ia scenarios, we aim to constrain the relative fractions of exploding near-Chandrasekhar mass to sub-Chandrasekhar mass primary WDs in the Galaxy. Methods: We extract the Mn yields from three-dimensional thermonuclear supernova simulations referring to different initial setups and progenitor channels. We then compute the chemical evolution of Mn in the Solar neighborhood, assuming SNe Ia are made up of different relative fractions of the considered explosion models. Results: We find that due to the entropy dependence of freeze-out yields from nuclear statistical equilibrium, [Mn/Fe] strongly depends on the mass of the exploding WD, with near-Chandraskher mass WDs producing substantially higher [Mn/Fe] than sub-Chandrasekhar mass WDs. Of all nucleosynthetic sources potentially influencing the chemical evolution of Mn, only explosion models involving the thermonuclear incineration of near-Chandrasekhar mass WDs predict solar or super-solar [Mn/Fe]. Consequently, we find in our chemical evolution calculations that the observed [Mn/Fe] in the Solar neighborhood at [Fe/H] > 0.0 cannot be reproduced without near-Chandrasekhar mass SN Ia primaries. Assuming that 50 per cent of all SNe Ia stem from explosive thermonuclear burning in near-Chandrasekhar mass WDs results in a good match to data.

Thermonuclear burning ignition and propagation in surface layers of neutron stars. 1. General study and one-zone model without mass-flow

We develop and study a general model describing ignition and propagation of burning. It is applied to explosive thermonuclear burning in surface layers of neutron stars. For this purpose an one-zone model of a thin surface layer is developed. We study thermonuclear burning ignition and propagation along the layer with its help.

Investigation of burning in type Ia supernovae

Type Ia supernovae are important cosmological objects that have played a major role in determining the composition of the Universe. Despite four decades of studies, there is no complete understanding of the explosion mechanism. One of the main problems consists in describing the burning wave propagation through the presupernova, a white dwarf. It is well known from observations that an initially slow flame accelerates and transforms into detonation as it moves. The acceleration mechanism realized in supernovae is not yet known, but it is believed to occur through various instabilities. The Landau-Darrieus instability of a thin deflagration thermonuclear burning front propagating through the presupernova is investigated. Direct numerical simulations of burning by the level-set method are presented. Small perturbations at the front are shown to merge into one large cusp after some time. As a flame with limited sizes moves, this leads only to a slight increase in the velocity, which does not allow it to accelerate to the speed of sound.

An overview of white dwarf stars

We present a brief summary of what is currently known about white dwarf stars, with an emphasis on their evolutionary and internal properties. As is well known, white dwarfs represent the end products of stellar evolution for the vast majority of stars and, as such, bear the signatures of past events (such as mass loss, mixing phases, loss and redistribution of angular momentum, and thermonuclear burning) that are of essential importance in the evolution of stars in general. In addition, white dwarf stars represent ideal testbeds for our understanding of matter under extreme conditions, and work on their constitutive physics (neutrino production rates, conductive and radiative opacities, interior liquid/solid equations of state, partially ionized and partially degenerate envelope equations of state, diffusion coefficients, line broadening mechanisms) is still being actively pursued. Given a set of constitutive physics, cooling white dwarfs can be used advantageously as cosmochronometers. Moreover, the field has been blessed by the existence of four distinct families of pulsating white dwarfs, each mapping a different evolutionary phase, and this allows the application of the asteroseismological method to probe and test their internal structure and evolutionary state. We set the stage for the reviews that follow on cooling white dwarfs as cosmochronometers and physics laboratories, as well as on the properties of pulsating white dwarfs and the asteroseismological results that can be inferred. 1. BASIC FACTS ABOUT WHITE DWARFS • White dwarfs are the end products of stellar evolution for the vast (95%) majority of stars. They have run out of thermonuclear fuel, and most of them have burned H and He in their interiors. • Most observable white dwarfs are isolated or part of non-interacting binaries. They are believed to have C-O cores and to descend from main sequence stars with masses in the range from slightly less than 1Mto ∼8M� . This maps into a narrow range offinal masses centered around ∼0.6M� . This implies important mass loss in previous evolutionary (red giant) phases. • White dwarfs have a stratified structure (see Fig. 1). Most have a C-O core (containing ∼99% of the total mass M) surrounded by a thin He mantle (∼1% M at most), itself surrounded by a thinner but opaque H envelope (∼0.01% M at most). • White dwarfs are compact cooling bodies in hydrostatic equilibrium; gravity is balanced by degenerate electron pressure. This implies an evolution at almost constant radius. From a pulsation point of view, white dwarfs have a mechanical structure radically different from those of non- degenerate stars (see Fig. 2).