Coulomb corrections to the equation of state of nuclear statistical equilibrium matter: implications for SNIa nucleosynthesis and the accretion-induced collapse of white dwarfs

Coulomb corrections to the equation of state of degenerate matter are usually neglected in high-temperature regimes, owing to the inverse dependence of the plasma coupling constant, Γ, on temperature. However, nuclear statistical equilibrium matter is characterized by a large abundance by mass of large- Z (iron group) nuclei. It is found that Coulomb corrections to the ion ideal gas equation of state of matter in nuclear statistical equilibrium are important at temperatures T ≲5–10×10⁹ K and densities ρ ≳10⁸ g cm⁻³. At a temperature T =8.5×10⁹ K and a density ρ =8×10⁹ g cm⁻³, the neutronization rate is larger by ≳28 per cent when Coulomb corrections are included. However, the conductive velocity of a thermonuclear deflagration wave in C–O drops by ∼16 per cent when Coulomb corrections to the heat capacity are taken into account. The implications for SNIa models and nucleosynthesis, and also for the accretion-induced collapse of white dwarfs, are discussed. Particularly relevant is the result that the minimum density for collapse of a white dwarf to a neutron star is shifted down to 5.5–6×10⁹ g cm⁻³, a value substantially lower than previously thought.     

Star formation triggered by supernova explosions in young galaxies

We study the evolution of supernova remnants in a low-metallicity medium   Z /Z_⊙= 10⁻⁴ to 10⁻²  in the early universe, using one-dimensional hydrodynamics with non-equilibrium chemistry. Once a post-shock layer is able to cool radiatively, a dense shell forms behind the shock. If this shell becomes gravitationally unstable and fragments into pieces, next-generation stars are expected to form from these fragments. To explore the possibility of this triggered star formation, we apply a linear perturbation analysis of an expanding shell to our results and constrain the parameter range of ambient density, explosion energy and metallicity where fragmentation of the shell occurs. For the explosion energy of  10⁵¹ erg (10⁵² erg)  , the shell fragmentation occurs for ambient densities higher than  ≳10² cm⁻³ (10 cm⁻³  ), respectively. This condition depends little on the metallicity in the ranges we examined. We find that the mode of star formation triggered occurs only in massive  (≳10⁸ M_⊙)  haloes.     

Secular instability of g-modes in rotating neutron stars

Gravitational radiation tends to drive gravity modes in rotating neutron stars to become unstable. For an inviscid star, the instability sets in when the rotation frequency is about 0.7 times the corresponding mode frequency of the non-rotating star. Neutron stars with spin frequencies ≳100 Hz are susceptible to this instability, with a growth time of the order of years. However, it is likely that viscous dissipation suppresses the instability except for a narrow range of temperatures around 10⁹ K. We also show that the viscosity-driven instability of g-modes is absent.     

Investigation of the single neutron exposure model for the s-process: the primary nature of the neutron source

The primary nature of the ¹³C neutron source is very significant for the studies of the s -process nucleosynthesis. In this paper we present an attempt to fit the element abundances observed in 16 s -rich stars using parametric model of the single neutron exposure. The calculated results indicate that almost all s -elements were made in a single neutron exposure for nine sample stars. Although a large spread of neutron exposure is obtained, the maximum value of the neutron exposure will reach about 7.0 mbarn⁻¹, which is close to the theoretical predictions by the asymptotic giant branch (AGB) model. The calculated result is a significant evidence for the primary nature of the neutron source. Combining the result obtained in this work and the neutron exposure–initial mass relations, a large spread of neutron exposure can be explained by the different initial stellar mass and their time evolution. The possibility that the rotationally induced mixing process can lead to a spread of the neutron exposure in AGB stars is also existent.     

Self-enrichment by asymptotic giant branch stars in globular clusters: comparison between intermediate and high metallicities

We present theoretical evolutionary sequences of intermediate-mass stars  ( M = 3 − 6.5 M_⊙)  with metallicity   Z = 0.004  . Our goal is to test whether the self-enrichment scenario by massive asymptotic giant branch stars may work for the high-metallicity globular clusters, after previous works by the same group showed that the theoretical yields by this class of objects can reproduce the observed trends among the abundances of some elements, namely the O–Al and O–Na anticorrelations, at intermediate metallicities, i.e.  [Fe/H]=−1.3  . We find that the increase in the metallicity favours only a modest decrease of the luminosity and the temperature at the bottom of the envelope for the same core mass, and also the efficiency of the third dredge-up is scarcely altered. On the contrary, differences are found in the yields, due to the different impact that processes with the same efficiency have on the overall abundance of envelopes with different metallicities. We expect the same qualitative patterns as in the intermediate-metallicity case, but the slopes of some of the relationships among the abundances of some elements are different. We compare the sodium–oxygen anticorrelation for clusters of intermediate metallicity ( Z ≈ 10⁻³) and clusters of metallicity large as in these new models. Although the observational data are still too scarce, the models are consistent with the observed trends, provided that only stars of   M ≳ 5 M_⊙  contribute to self-enrichment.     

Time-variable emission from transiently accreting neutron stars in quiescence due to deep crustal heating

Transiently accreting neutron stars in quiescence ( L _X ≲10³⁴ erg s⁻¹) have been observed to vary in intensity by factors of few, over time-scales of days to years. If the quiescent luminosity is powered by a hot neutron star core, the core cooling time-scale is much longer than the recurrence time, and cannot explain the observed, more rapid variability. However, the non-equilibrium reactions which occur in the crust during outbursts deposit energy in isodensity shells, from which the thermal diffusion time-scale to the photosphere is days to years. The predicted magnitude of variability is too low to explain the observed variability unless – as is widely believed – the neutrons beyond the neutron-drip density are superfluid. Even then, the variability due to this mechanism in models with standard core neutrino cooling processes is less than 50 per cent – still too low to explain the reported variability. However, models with rapid core neutrino cooling can produce a variability by a factor as great as 20, on time-scales of days to years following an outburst. Thus, the factors of ∼ few intensity variability observed from transiently accreting neutron stars can be accounted for by this mechanism only if rapid core cooling processes are active.     

Emergence of magnetic field due to spin-polarized baryon matter in neutron stars

A model of the ferromagnetic origin of magnetic fields of neutron stars is considered. In this model, the magnetic phase transition occurs inside the core of neutron stars soon after formation. However, owing to the high electrical conductivity the core magnetic field is initially fully screened. We study how this magnetic field emerges for an outside observer. After some time, the induced field that screens the ferromagnetic field decays enough to uncover a detectable fraction of the ferromagnetic field. We calculate the time-scale of decay of the screening field and study how it depends on the size of the ferromagnetic core. We find that the same fractional decay of the screening field occurs earlier for larger cores. We conjecture that weak fields of millisecond pulsars, B ∼10⁸–10⁹ G, could be identified with ferromagnetic fields of unshielded fraction ε ∼10⁻⁴–10⁻³ resulting from the decay of screening fields by a factor 1− ε in ∼10⁸ yr since their birth.     

Surface abundances of light elements for a large sample of early B-type stars – IV. The magnesium abundance in 52 stars – a test of metallicity

From high-resolution spectra a non-local thermodynamic equilibrium analysis of the Mg  ii 4481.2-Å  feature is implemented for 52 early and medium local B stars on the main sequence (MS). The influence of the neighbouring line Al  iii 4479.9-Å  is considered. The magnesium abundance is determined; it is found that  log ɛ(Mg) = 7.67 ± 0.21  on average. It is shown that uncertainties in the microturbulent parameter V_t are the main source of errors in  log ɛ(Mg)  . When using 36 stars with the most reliable V_t values derived from O  ii and N  ii lines, we obtain the mean abundance  log ɛ(Mg) = 7.59 ± 0.15  . The latter value is precisely confirmed for several hot B stars from an analysis of the Mg  ii 7877-Å  weak line. The derived abundance  log ɛ(Mg) = 7.59 ± 0.15  is in excellent agreement with the solar magnesium abundance  log ɛ_⊙ (Mg) = 7.55 ± 0.02  , as well as with the proto-Sun abundance  log ɛ _ps (Mg) = 7.62 ± 0.02  . Thus, it is confirmed that the Sun and the B-type MS stars in our neighbourhood have the same metallicity.     

Neon abundances in normal late-B and mercury–manganese stars

We make new non-local thermodynamic equilibrium calculations to deduce the abundances of neon from visible-region echelle spectra of selected Ne  i lines in seven normal stars and 20 HgMn stars. We find that the best strong blend-free Ne line that can be used at the lower end of the effective temperature T _eff range is λ 6402, although several other potentially useful Ne  i lines are found in the red region of the spectra of these stars. The mean neon abundance in the normal stars (log  A =8.10) is in excellent agreement with the standard abundance of neon (8.08). However, in HgMn stars neon is almost universally underabundant, ranging from marginal deficits of 0.1–0.3 dex to underabundances of an order of magnitude or more. In many cases, the lines are so weak that only upper limits can be established. The most extreme example found is υ Her with an underabundance of at least 1.5 dex. These underabundances are qualitatively expected from radiative acceleration calculations, which show that Ne has a very small radiative acceleration in the photosphere, and that it is expected to undergo gravitational settling if the mixing processes are sufficiently weak and there is no strong stellar wind. According to theoretical predictions , the low Ne abundances place an important constraint on the intensity of such stellar winds, which must be less than 10⁻¹⁴ M_⊙ yr⁻¹ if they are non-turbulent.     

The origin of the lead-rich stars in the Galactic halo: investigation of model parameters for the s-process

Several stars at the low-metallicity extreme of the Galactic halo show large spreads of lead and associated 'heavy' s-process elements ([Pb/hs]). Theoretically, an s-process pattern should be obtained from an AGB star with a fixed metallicity and initial mass. For the third dredge-up and the s-process model, several important properties depend primarily on the core mass of AGB stars. Zijlstra reported that the initial-to-final mass relation steepens at low metallicity, due to low mass-loss efficiency. This might affect the model parameters of the AGB stars, e.g. the overlap factor and the neutron irradiation time, in particular at low metallicity. The calculated results do indeed show that the overlap factor and the neutron irradiation time are significantly small at low metallicities, especially for  3.0 M_⊙ AGB  stars. The scatter of [Pb/hs] found in low metallicities can therefore be explained naturally when varying the initial mass of the low-mass AGB stars.     

Cosmological origin of the lowest metallicity halo stars

We explore the predictions of the standard hierarchical clustering scenario of galaxy formation, regarding the numbers and metallicities of PopIII stars that are likely to be found within our Galaxy today. By PopIII we refer to stars formed at large redshift ( z >4), with low metallicities ([ Z /Z_⊙]<−2.5) and in small systems (total mass ≲ 2×10⁸ M_⊙) that are extremely sensitive to stellar feedback, and which through a prescribed merging history end up becoming part of the Milky Way today. An analytic, extended Press–Schechter formalism is used to obtain the mass functions of haloes which will host PopIII stars at a given redshift, and which will end up in Milky Way sized systems today. Each of these is modelled as a mini-galaxy, with a detailed treatment of the dark halo structure, angular momentum distribution, final gas temperature and disc instabilities, all of which determine the fraction of the baryons that are subject to star formation. The use of new primordial metallicity stellar evolutionary models allows us to trace the history of the stars formed, and give accurate estimates of their expected numbers today and their location in L /L_⊙ versus T /K Hertzsprung–Russell (HR) diagrams. A first comparison with observational data suggests that the initial mass function (IMF) of the first stars was increasingly high-mass weighted towards high redshifts, levelling off at z ≳9 at a characteristic stellar mass scale m _s=10–15 M_⊙.     

Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as E_p / E , it is found that the stability condition is a ( E / U ) < E_p / E ≲ 0.8 where E /U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 10³ in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the toroidal field can be very much stronger than the poloidal–given that in realistic stars we expect E / U < 10⁻⁶. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession and a 'hidden' energy source for magnetars.     

Calculated spectra for HeH+ and its effect on the opacity of cool metal-poor stars

The wavelength and Einstein A coefficient are calculated for all rotation–vibration transitions of  ⁴He¹H⁺, ³He¹H⁺, ⁴He²H⁺  and  ³ He²H⁺  , giving a complete line list and the partition function for  ⁴HeH⁺  and its isotopologues. This opacity is included in the calculation of the total opacity of low-metallicity stars and its effect is analysed for different conditions of temperature, density and hydrogen number fraction. For a low helium number fraction (as in the Sun), it is found that HeH⁺ has a visible but small effect for very low densities  (ρ≤ 10⁻¹⁰ g cm⁻³)  , at temperatures around 3500 K. However, for high helium number fraction, the effect of HeH⁺ becomes important for higher densities  (ρ≤ 10⁻⁶ g cm⁻³)  , its effect being most important for a temperature around 3500 K. Synthetic spectra for a variety of different conditions are presented.     

Two populations of metal-free stars in the early Universe

We construct star formation histories at redshifts z ≳ 5 for two physically distinct populations of primordial, metal-free stars, motivated by theoretical and observational arguments that have hinted towards the existence of an intermediate stellar generation between Population III and Population I/II. Taking into account the cosmological parameters as recently revised by the Wilkinson Microwave Anisotropy Probe after three years of operation, we determine self-consistent reionization histories and discuss the resulting chemical enrichment from these early stellar generations. We find that the bulk of ionizing photons and heavy elements produced at high redshifts must have originated in Population II.5 stars, which formed out of primordial gas in haloes with virial temperatures ≳10⁴ K, and had typical masses ≳10 M_⊙. Classical Population III stars, formed in minihaloes and having masses ≳100 M_⊙, on the other hand, had only a minor impact on reionization and early metal enrichment. Specifically, we conclude that only ≃10 per cent by mass of metal-free star formation went into Population III.     

Magnetic hydrogen atmosphere models and the neutron star RX J1856.5–3754

RX J1856.5−3754 is one of the brightest nearby isolated neutron stars (INSs), and considerable observational resources have been devoted to it. However, current models are unable to satisfactorily explain the data. We show that our latest models of a thin, magnetic, partially ionized hydrogen atmosphere on top of a condensed surface can fit the entire spectrum, from X-rays to optical, of RX J1856.5−3754, within the uncertainties. In our simplest model, the best-fitting parameters are an interstellar column density   N _H≈ 1 × 10²⁰ cm⁻²  and an emitting area with   R ^∞≈ 17 km  (assuming a distance to RX J1856.5−3754 of 140 pc), temperature   T ^∞≈ 4.3 × 10⁵ K  , gravitational redshift   z _g ∼ 0.22  , atmospheric hydrogen column   y _H≈ 1 g cm⁻²  , and magnetic field   B ≈ (3–4) × 10¹² G  ; the values for the temperature and magnetic field indicate an effective average over the surface. We also calculate a more realistic model, which accounts for magnetic field and temperature variations over the NS surface as well as general relativistic effects, to determine pulsations; we find that there exist viewing geometries that produce pulsations near the currently observed limits. The origin of the thin atmospheres required to fit the data is an important question, and we briefly discuss mechanisms for producing these atmospheres. Our model thus represents the most self-consistent picture to date for explaining all the observations of RX J1856.5−3754.     

Almost analytic models of ultramagnetized neutron star envelopes

Recent ROSAT measurements show that the X-ray emission from isolated neutron stars is modulated at the stellar rotation period. To interpret these measurements, one needs precise calculations of the heat transfer through the thin insulating envelopes of neutron stars. We present nearly analytic models of the thermal structure of the envelopes of ultramagnetized neutron stars. Specifically, we examine the limit in which only the ground Landau level is filled. We use the models to estimate the amplitude of modulation expected from non-uniformities in the surface temperatures of strongly magnetized neutron stars. In addition, we estimate cooling rates for stars with fields B  ∼ 10¹⁵ − 10¹⁶ G, which are relevant to models that invoke 'magnetars' to account for soft γ-ray emission from some repeating sources.     

Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.     

The effect of the 19F(α, p)22Ne reaction rate uncertainty on the yield of fluorine from Wolf–Rayet stars

In the light of recent recalculations of the  ¹⁹F(α, p)²²Ne  reaction rate, we present results of the expected yield of ¹⁹F from Wolf–Rayet (WR) stars. In addition to using the recommended rate, we have computed models using the upper and lower limits for the rate, and hence we constrain the uncertainty in the yield with respect to this reaction. We find a yield of  3.1 × 10⁻⁴ M_⊙  of ¹⁹F with our recommended rate, and a difference of a factor of 2 between the yields computed with the upper and lower limits. In comparison with previous work we find a difference in the yield of a factor of approximately 4, connected with a different choice of mass loss. Model uncertainties must be carefully evaluated in order to obtain a reliable estimate of the yield, together with its uncertainties, of fluorine from WR stars.     

Collapse and fragmentation of rotating magnetized clouds – I. Magnetic flux–spin relation

We discuss the evolution of the magnetic flux density and angular velocity in a molecular cloud core, on the basis of three-dimensional numerical simulations, in which a rotating magnetized cloud fragments and collapses to form a very dense optically thick core of  >5 × 10¹⁰ cm⁻³  . As the density increases towards the formation of the optically thick core, the magnetic flux density and angular velocity converge towards a single relationship between the two quantities. If the core is magnetically dominated its magnetic flux density approaches  1.5( n /5 × 10¹⁰ cm⁻³)^1/2 mG  , while if the core is rotationally dominated the angular velocity approaches  2.57 × 10⁻³ ( n /5 × 10¹⁰ cm⁻³)^1/2 yr⁻¹  , where n is the density of the gas. We also find that the ratio of the angular velocity to the magnetic flux density remains nearly constant until the density exceeds  5 × 10¹⁰ cm⁻³  . Fragmentation of the very dense core and emergence of outflows from fragments will be shown in the subsequent paper.     

Pycnonuclear burning of 34Ne in accreting neutron stars

We study the pycnonuclear burning of ³⁴Ne in the inner crust of an accreting neutron star. We show that the associated energy production rate can be calculated analytically for any arbitrary temporal variability of the mass accretion rate. We argue that the theoretical time-scale for ³⁴Ne burning is currently very uncertain and ranges from a fraction of a millisecond to a few years. The fastest allowable burning may change the composition of the accreted crust while the slowest burning leads to a time-independent nuclear energy generation rate for a variable accretion. The results are important for constructing self-consistent models of the accreted crust and deep crustal heating in neutron stars which enter soft X-ray transients.