Formation and evolution of low-mass Algols

We discuss the origin, evolution and fate of low-mass Algols (LMA) that have components with initial masses less than 2.5 M₀. The semi-major axes of orbits of pre-LMA do not exceed 20–25 R₀. The rate of formation of Algol-type stars is 0.01/year. Magnetic stellar winds may be the factor that determines the evolution of LMA. Most LMA end their lives as double helium degenerate dwarfs with M₁/M₂ 0.88 (like L870-2). Some of them even merge through angular momentum loss caused by gravitational waves.     

Who is who in Algol-land ?- Part I -

We computed the evolution through case A mass transfer for 8 systems with mass of the primary equal to 3 and 5 M₀, mass ratios 0.7 and 0.9, and different periods. To this we added similar results from Packet (1988) for M_i = 9 M₀, q_i = 0.6, P_i = 1.62 d.During the mass transfer two competing mechanisms in the gainer decide on the evolution of the system: the rejuvenation of this star as the increasing convective core mixes fresh hydrogen into the inner regions, and the acceleration of nuclear burning, responding to the increasing mass.In all the cases the net result is a faster decrease of the central hydrogen content compared to the mass losing star. The secondary fills its own critical Roche lobe and reversed mass transfer starts.From our results and those of Nakamura and Nakamura (1984), we find that reversed mass transfer occurs after core hydrogen burning of the secondary (case A₁B₂) approximately for periods larger than 1 d (M_1i = 3 M₀) to 2 d (M_1i = 13.4 M₀). For smaller periods this happens before the gainer ends its core hydrogen burning (case A₁A₂).     

The evolution of massive stars

The evolution of stars with masses between 15 M ₀ and 100M ₀ is considered. Stars in this mass range lose a considerable fraction of their matter during their evolution.The treatment of convection, semi-convection and the influence of mass loss by stellar winds at different evolutionary phases are analysed as well as the adopted opacities.Evolutionary sequences computed by various groups are examined and compared with observations, and the advanced evolution of a 15M ₀ and a 25M ₀ star from zero-age main sequence (ZAMS) through iron collapse is discussed.The effect of centrifugal forces on stellar wind mass loss and the influence of rotation on evolutionary models is examined. As a consequence of the outflow of matter deeper layers show up and when the mass loss rates are large enough layers with changed composition, due to interior nuclear reactions, appear on the surface.The evolution of massive close binaries as well during the phase of mass loss by stellar wind as during the mass exchange and mass loss phase due to Roche lobe overflow is treated in detail, and the value of the parameters governing mass and angular momentum losses are discussed.The problem of the Wolf-Rayet stars, their origin and the possibilities of their production either as single stars or as massive binaries is examined.Finally, the origin of X-ray binaries is discussed and the scenario for the formation of these objects (starting from massive ZAMS close binaries, through Wolf-Rayet binaries leading to OB-stars with a compact companion after a supernova explosion) is reviewed and completed, including stellar wind mass loss.     

The evolution of massive stars to explosion

We review the possible evolutionary paths from massive stars to explosive endpoints as various types of supernovae associated with Population I and hence with massive stars: Type II-P, Type II-L, Type Ib, Type Ic, and the hybrid events SN 1987K and SN 1993J. We identify SN 1954A as another hybrid event from the evidence for both H and He in its spectrum with velocities nearly the same as SN 1983J. Evidence for ejected⁵⁶Ni mass of 0.07 M suggests that SN II-P underwent standard iron core collapse, not collapse of an O–Ne–Mg core nor thermonuclear explosion of a C–O core. Most SN II-P presumably arise in single stars or wide binaries of 10–20 M. There may be indirect evidence for duplicity in some cases in the form of strong Ba II lines, such as characterized SN 1987A. SN II-L are recognizably distinct from typical SN II-P and must undergo a significantly different evolution. Despite indications that SN II-L have small envelopes that may be helium enriched, they are also distinct from events like SN 1993J that must have yet again a different evolution. The SN II-L that share a common Luminosity seem to have ejected a small nickel mass and hence may come from stars with O–Ne–Mg cores. The amount of nickel ejected by the exceptionally bright events, SN 1980K and SN 1979C, remains controversial. SN Ib require the complete loss of the H envelope, either to a binary companion or to a wind. The few identified have relatively large ejecta masses. It is not clear what evolutionary processes distinguish SN Ib's evolving in binary systems from hybrid events that retain some H in the envelope. SN Ic events are both H and He deficient. Binary models that can account for transfer of an extended helium envelope from low mass helium cores, 2 to 4 M, imply C–O core masses that are roughly consistent with that deduced from the ejecta mass plus a neutron star, 2 to 3 M. It is possible that the hybrid events are the result of Roche lobe overflow and that the pure events, SN Ib or SN Ic, result from common envelope evolution.     

The Milky Way 3-Helium Abundance

We are making precise determinations of the abundance of the light isotope of helium, ³He. The ³He abundance in Milky Way sources impacts stellar evolution, chemical evolution, and cosmology. The abundance of ³He is derived from measurements of the hyperfine transition of ³He⁺ which has a rest wavelength of 3.46 cm (8.665 GHz). As with all the light elements, the present interstellar ³He abundance results from a combination of Big Bang Nucleosynthesis (BBNS) and stellar nucleosynthesis. We are measuring the ³He abundance in Milky Way H ii regions and planetary nebulae (PNe). The source sample is currently comprised of 60 H ii regions and 12 PNe. H ii regions are examples of zero-age objects that are young relative to the age of the Galaxy. Therefore their abundances chronicle the results of billions of years of Galactic chemical evolution. PNe probe material that has been ejected from low-mass (M≤ 2M _⊙) to intermediate-mass (M∼2–5M _⊙) stars to be further processed by future stellar generations. Because the Milky Way ISM is optically thin at centimeter wavelengths, our source sample probes a larger volume of the Galactic disk than does any other light element tracer of Galactic chemical evolution. The sources in our sample possess a wide range of physical properties (including object type, size, temperature, excitation, etc.). The ³He abundances we derive have led to what has been called “The ³He Problem”.     

Ages and Geologic Histories of Martian Meteorites

We review the radiometric ages of the 16 currently known Martian meteorites, classified as 11 shergottites (8 basaltic and 3 lherzolitic), 3 nakhlites (clinopyroxenites), Chassigny (a dunite), and the orthopyroxenite ALH84001. The basaltic shergottites represent surface lava flows, the others magmas that solidified at depth. Shock effects correlate with these compositional types, and, in each case, they can be attributed to a single shock event, most likely the meteorite's ejection from Mars. Peak pressures in the range 15 – 45 GPa appear to be a "launch window": shergottites experienced ～30 – 45 GPa, nakhlites ～20 ± 5 GPa, Chassigny ～35 GPa, and ALH84001 ～35 – 40 GPa. Two meteorites, lherzolitic shergottite Y-793605 and orthopyroxenite ALH84001, are monomict breccias, indicating a two-phase shock history in toto: monomict brecciation at depth in a first impact and later shock metamorphism in a second impact, probably the ejection event. Crystallization ages of shergottites show only two pronounced groups designated S₁ (～175 Myr), including 4 of 6 dated basalts and all 3 lherzolites, and S₂ (330 – 475 Myr), including two basaltic shergottites and probably a third according to preliminary data. Ejection ages of shergottites, defined as the sum of their cosmic ray exposure ages and their terrestrial residence ages, range from the oldest (～20 Myr) to the youngest (～0.7 Myr) values for Martian meteorites. Five groups are distinguished and designated S_Dho (one basalt, ～20 Myr), S_L (two lherzolites of overlapping ejection ages, 3.94 ± 0.40 Myr and 4.70 ± 0.50 Myr), S (four basalts and one lherzolite, ～2.7 – 3.1 Myr), S_DaG (two basalts, ～1.25 Myr), and S_E (the youngest basalt, 0.73 ± 0.15 Myr). Consequently, crystallization age group S₁ includes ejection age groups S_L, S_E and 4 of the 5 members of S, whereas S₂ includes the remaining member of S and one of the two members of S_DaG. Shock effects are different for basalts and lherzolites in group S/S₁. Similarities to the dated meteorite DaG476 suggest that the two shergottites that are not dated yet belong to group S₂. Whether or not S₂ is a single group is unclear at present. If crystallization age group S₁ represents a single ejection event, pre-exposure on the Martian surface is required to account for ejection ages of S_L that are greater than ejection ages of S, whereas secondary breakup in space is required to account for ejection ages of S_E less than those of S. Because one member of crystallization age group S₂ belongs to ejection group S, the maximum number of shergottite ejection events is 6, whereas the minimum number is 2. Crystallization ages of nakhlites and Chassigny are concordant at ～1.3 Gyr. These meteorites also have concordant ejection ages, i.e., they were ejected together in a single event (NC). Shock effects vary within group NC between the nakhlites and Chassigny. The orthopyroxenite ALH84001 is characterized by the oldest crystallization age of ～4.5 Gyr. Its secondary carbonates are ～3.9 Gyr old, an age corresponding to the time of Ar-outgassing from silicates. Carbonate formation appears to have coincided with impact metamorphism, either directly, or indirectly, perhaps via precipitation from a transient impact crater lake. The crystallization age and the ejection age of ALH84001, the second oldest ejection age at 15.0 ± 0.8 Myr, give evidence for another ejection event (O). Consequently, the total number of ejection events for the 16 Martian meteorites lies in the range 4 – 8. The Martian meteorites indicate that Martian magmatism has been active over most of Martian geologic history, in agreement with the inferred very young ages of flood basalt flows observed in Elysium and Amazonis Planitia with the Mars Orbital Camera (MOC) on the Mars Global Surveyor (MGS). The provenance of the youngest meteorites must be found among the youngest volcanic surfaces on Mars, i.e., in the Tharsis, Amazonis, and Elysium regions.     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

Structure of reconnection layers in the magnetosphere

Magnetic reconnection can lead to the formation of observed boundary layers at the dayside magnetopause and in the nightside plasma sheet of the earth's magnetosphere. In this paper, the structure of these reconnection layers is studied by solving the one-dimensional Riemann problem for the evolution of a current sheet. Analytical method, resistive MHD simulations, and hybrid simulations are used. Based on the ideal MHD formulation, rotational discontinuities, slow shocks, slow expansion waves, and contact discontinuity are present in the dayside reconnection layer. Fast expansion waves are also present in the solution of the Riemann problem, but they quickly propagate out of the reconnection layer. Our study provides a coherent picture for the transition from the reconnection layer with two slow shocks in Petschek's model to the reconnection layer with a rotational discontinuity and a slow expansion wave in Levy et al's model. In the resistive MHD simulations, the rotational discontinuities are replaced by intermediate shocks or time-dependent intermediate shocks. In the hybrid simulations, the time-dependent intermediate shock quickly evolves to a steady rotational discontinuity, and the contact discontinuity does not exist. The magnetotail reconnection layer consists of two slow shocks. Hybrid simulations of slow shocks indicate that there exists a critical number,M _c, such that for slow shocks with an intermediate Mach numberM _IM _c, a large-amplitude rotational wavetrain is present in the downstream region. For slow shocks withM _I<M _c, the downstream wavetrain does not exist. Chaotic ion orbits in the downstream wave provide an efficient mechanism for ion heating and wave damping and explain the existence of the critical numberM _c in slow shocks.     

Characteristics and interpretation of the photometric variability of eta carinae and its nebula

A short review is given on the history of the peculiar variable object Car and on a number of relevant references describing and discussing its physical characteristics and behaviour, based on different types of observational techniques. The star is known to be variable since the 17th century. The excessive mass loss to which it was subject during the 19th century is now visible as an ellipsoidal reflection nebula of 15 diameter: the so-called homunculus. The remainder of the paper is spent on different kinds of problems partly based on the results of a decade of photometric monitoring in the VBLUW photometric system of Walraven. Foreground reddening and reddening by dust in the homunculus are determined and amount to E(B - V) _J = 0 50 and < 6, respectively. Scanning of the homunculus revealed an estimate for the photometric characteristics of the central object, which presumably consists of a massive hot star surrounded by a cooler gas envelope. The total luminosity is derived using fluxes of various sources in the wavelength region 0.15 < < 175 n resulting in M _bol = - 12 3 ± 0 2. The total observed flux corrected for foreground extinction corresponds to a star with R 96 R if T _eff 30 000 K. The mass may be near 150 M . The excess luminosity in 1843, when the star was presumably bolometrically at least 2 5 brighter than at present, may have been caused by envelope-energized pulsations when the star's luminosity was close to its Eddington limit. The temperature should then have been 50 000 K. The mass loss rate, during the excess luminosity phase lasting 30 yr, is estimated to amount to M 4 × 10^-3 M yr^-1. At present the mass loss may be M 10^-4M yr^-1. Since the homunculus is mainly built up from material expelled in the 30 yr interval (from 1830 to 1860), its total mass amounts to M _hom 0.15 M . The historical observations of the colours of Car and a comparison with the characteristics of S Dor type stars, suggest that Car was subject to a number of S Dor type phases similar to those of P Cyg (in the 17th century), S Dor and others. A satisfactory explanation is found for the complete historical light curve. The decrease in light after the 1843 maximum by 9 ^m , presumably consists of a fading of the luminosity excess and the S Dor effect by 2 5 and 3^m, respectively, and a 3 5 extinction by circumstellar dust. The small amplitude light variations which Car showed during the last decade, were studied with the aid of the variations of the Balmer jump. They are presumably caused by temperature variations of the central star.Percy and Welch (1983) (Publ. Astron. Soc. Pacific 95, 491) have observed P Cyg on a number of nights in 1982 and found for the photometric variations a time scale of 30 to 50 days and an amplitude of 0 _. ^m 15.Based partly on observations collected at the ESO, La Silla, Chile.     

CCD spectroscopy of the W Serpentis binaries KX And and RX Cas

Initial results are presented from a study of H profiles in the two interacting binaries KX And and RX Cas of W Serpentis type. The used CCD spectra with a resolution of 0.13Å/px were obtained with the 2.2m telescope and the Coudé spectrograph at the German-Spanish Astronomical Center at Calar Alto/Spain.KX And. This star is probably a non-eclipsing member of the W Serpentis type interactive binaries and has a period of P = 38.908 days. Our seven spectra of KX And were obtained at phase 0.54 – 0.75. The P Cyg profiles of the H line during our observations indicate an expanding shell. The asymetry becomes blue-sided at phase 0.67 and increases thereafter. This points toward a strong outflow of matter in the vicinity of the L3 point.RX Cas. According to the model of Andersen et al. (1988) the primary is a mid-B type star with M = 5.8M and R = 2.5R . The star is completely obscured by a geometrically and optically thick disk, which is supplied by mass transfer from the other component. The secondary is a K1 giant with M = 1.8M and R = 23.5R and fills out his critical Roche lobe. Radiative and geometrical properties of the disk are variable and its structure is probably not homogenous.Five spectra of RX Cas were obtained during the primary eclipse (phase 0.95 – 0.19). The observed double-peak emission is seen only after the eclipse with a separation of 250 km/s peak-to-peak, while during the eclipse an asymetric line profile can be observed with a red-shifted emission always presented. Also, a central emission at = 0.94 should be noticed, probably originating in the vicinity of L1.The observations of both systems indicate that we are dealing with strongly interacting binaries. Further observations are planned for better covering of phase.Visiting Astronomer, German-Spanish Astronomical Center, Calar Alto, operated by the Max-Planck-Institut für Astronomie Heidelberg jointly with the Spanish National Commision for Astronomy.     

A gentle process for the formation of Algols

This work is concerned with binary systems that we call moderately close. These are systems in which the primary (by which we mean the initially more massive star) fills its Roche lobe when it is on the giant branch with a deep convective envelope but before helium ignition (late case B). We find that if the mass ratio q(= M ₁/M ₂) < q _crit = 0.7 when the primary fills its Roche lobe positive feedback will lead to a rapid hydrodynamic phase of mass transfer which will probably lead to common envelope evolution and thence to either coalescence or possibly to a close binary in a planetary nebula. Although most Algols have probably filled their Roche lobes before evolving off the main-sequence we find that some could not have and are therefore moderately close. Since rapid overflow is unlikely to lead to an Algol-like system there must be some way of avoiding it. The most likely possibility is that the primary can lose sufficient mass to reduce q below q _crit before overflow begins. Ordinary mass loss rates are insufficient but evidence that enhanced mass loss does take place is provided by RS CVn systems that have inverted mass ratios but have not yet begun mass transfer. We postulate that the cause of enhanced mass loss lies in the heating of the corona by by magnetic fields maintained by an — dynamo which is enhanced by tidal effects associated with corotation. In order to model the the effects of enhanced mass loss we ignore the details and adopt an empirical approach calibrating a simple formula with the RS CVn system Z Her. Using further empirical relations (deduced from detailed stellar models) that describe the evolution of red giants we have investigated the effect on a large number of systems of various initial mass ratios and periods. These are notable in that some systems can now enter a much gentler Algol-like overflow phase and others are prevented from transferring mass altogether. We have also investigated the effects of enhanced angular momentum loss induced by corotation of the wind in the strong magnetic fields and consider this in relation to observed period changes. We find that a typical moderately close Algol-like system evolves through an RS CVn like system and then possibly a symbiotic state before becoming an Algol and then goes on through a red giant-white dwarf state which may become symbiotic before ending up as a double white dwarf system in either a close or wide orbit depending on how much mass is lost before the secondary fills its Roche lobe.     

The Supermassive Black Hole—Galaxy Connection

The observed scaling relations imply that supermassive black holes (SMBH) and their host galaxies evolve together. Near-Eddington winds from the SMBH accretion discs explain many aspects of this connection. The wind Eddington factor \(\dot{m}\) should be in the range ～1–30. A factor \(\dot{m}\sim 1\) give black hole winds with velocities v～0.1c, observable in X-rays, just as seen in the most extreme ultrafast outflows (UFOs). Higher Eddington factors predict slower and less ionized winds, observable in the UV, as in BAL QSOs. In all cases the wind must shock against the host interstellar gas and it is plausible that these shocks should cool efficiently. There is detailed observational evidence for this in some UFOs. The wind sweeps up the interstellar gas into a thin shell and propels it outwards. For SMBH masses below a certain critical (M–σ) value, all these outflows eventually stall and fall back, as the Eddington thrust of the wind is too weak to drive the gas to large radii. But once the SMBH mass reaches the critical M–σ value the global character of the outflow changes completely. The wind shock is no longer efficiently cooled, and the resulting thermal expansion drives the interstellar gas far from the black hole, which is unlikely to grow significantly further. Simple estimates of the maximum stellar bulge mass M _b allowed by self-limited star formation show that the SMBH mass is typically about 10^?3 M _b at this point, in line with observation. The expansion-driven outflow reaches speeds v _out?1200 km?s^?1 and drives rates \(\dot{M}_{\mathrm{out}}\sim 4000~\mathrm {M}_{\odot }\,\mathrm{yr}^{-1}\) in cool (molecular) gas, giving a typical outflow mechanical energy L _mech?0.05L _Edd, where L _Edd is the Eddington luminosity of the central SMBH. This is again in line with observation. These massive outflows may be what makes galaxies become red and dead, and can have several other potentially observable effects. In particular they have the right properties to enrich the intergalactic gas with metals. Our current picture of SMBH-galaxy coevolution is still incomplete, as there is no predictive theory of how the hole accretes gas from its surroundings. Recent progress in understanding how large-scale discs of gas can partially cancel angular momentum and promote dynamical infall offers a possible way forward.     

CCD spectroscopy of the W Serpentis binaries KX And and RX Cas

Initial results are presented from a study of H _γ profiles in the two interacting binaries KX And and RX Cas of W Serpentis type. The used CCD spectra with a resolution of 0.13Å/px were obtained with the 2.2m telescope and the Coudé spectrograph at the German-Spanish Astronomical Center at Calar Alto/Spain. KX And. This star is probably a non-eclipsing member of the W Serpentis type interactive binaries and has a period of P = 38.908 days. Our seven spectra of KX And were obtained at phase 0.54 – 0.75. The P Cyg profiles of the H _γ line during our observations indicate an expanding shell. The asymetry becomes blue-sided at phase 0.67 and increases thereafter. This points toward a strong outflow of matter in the vicinity of the L3 point. RX Cas. According to the model of Andersen et al. (1988) the primary is a mid-B type star with M = 5.8M _⊙ and R = 2.5R _⊙. The star is completely obscured by a geometrically and optically thick disk, which is supplied by mass transfer from the other component. The secondary is a K1 giant with M = 1.8M _⊙ and R = 23.5R _⊙ and fills out his critical Roche lobe. Radiative and geometrical properties of the disk are variable and its structure is probably not homogenous. Five spectra of RX Cas were obtained during the primary eclipse (phase 0.95 – 0.19). The observed double-peak emission is seen only after the eclipse with a separation of ≈ 250 km/s peak-to-peak, while during the eclipse an asymetric line profile can be observed with a red-shifted emission always presented. Also, a central emission at φ = 0.94 should be noticed, probably originating in the vicinity of L1. The observations of both systems indicate that we are dealing with strongly interacting binaries. Further observations are planned for better covering of phase.     

Presupernova models and supernovae

Present status of the theories for presupernova evolution and triggering mechanisms of supernova explosions are summarized and discussed from the standpoint of the theory of stellar structure and evolution. It is not intended to collect every detail of numerical results thus far obtained, but to extract physically clear-cut understanding from complexities of the numerical stellar models. For this purpose the evolution of stellar cores is discussed in a generalized fashion. The following types of the supernova explosions are discussed. The carbon deflagration supernova of intermediate mass star which results in the total disruption of the star. Massive star evolves into a supernova triggered by photo-dissociation of iron nuclei which results in a formation of a neutron star or a black hole depending on its mass. These two are typical types of the sueprnovae. Between them there remains a range of mass for which collapse of the stellar core is triggered by electron captures, which has been recently shown to leave a neutron star despite oxygen deflagration competing with the electron captures. Also discussed are combustion and detonation of helium or carbon which take place in accreting white dwarfs, and the collapse which is triggered by electron-pair creation in very massive stars.Appendix: Notations A mass number of atomic nucleus - B _v(a, b) incomplete beta function - c _p specific heat at constant pressure - c _p sound velocity - c(sub) center of the star - E _e mean energy of an electron captured by nucleus - E _n nuclear energy release from unit mass of the nuclear fuel specified by n - E _thr threshold energy (9.3) - E _thr,0 energy difference between the ground states of daughter nucleus and parent nucleus (9.1) - E energy of gamma ray emitted from daughter nucleus (9.1) - E _v mean energy of a neutrino emitted by electron capture (9.1) - f flatness parameter (2.17) - g local gravitational acceleration (2.16) - H atomic mass unit - H _p scale height of pressure (2.22) - H (sub) hydrogen-burning shell - k Boltzmann constant - l mixing length of convection - L _cr(M _r ) local Eddington's critical luminosity (4.3) - L _n integrated nuclear energy generation rate by nuclear fuel specified by n - L _v neutrino luminosity - L _{v, cr}(M _r ) local Eddington's critical neutrino luminosity (11.2) - M (current) mass of a star - m _M core mass contained interior to the carbon-burning shell - M _Ch Chandrasekhar's limiting mass (9.6) - M _H core mass contained interior to the hydrogen-burning shell - M _He core mass contained interior to the helium-burning shell - M _ms mass of a star at its zero-age min-sequence - M _O core mass contained interior to the oxygen-burning shell - M _r mass contained interior to a shell at r - M _Si core mass contained interior to the silicon-burning shell - M _WD mass of white dwarf (7.1) - M ₀ normalization factor to the non-dimensional mass (3.3) - M ₁ core mass (3.6) - N polytropic index between pressure and density (2.3) - n polytropic index between pressure and temperature (10.1) - N _A Avogadro number - N _ad adiabatic polytropic index - N _e number of electrons in unit mass of matter - NSE nuclear statistical equilibrium - P pressure - ph (sub) photosphere - Q _e mass fraction of the envelope exterior of the shell e (2.14) - R stellar radius - r radial distance of a shell - r ₀ normalization factor to the non-dimensional radius (3.2) - s specific entropy - S _i specific entropy of ions - T temperature - U homology invariant defined by (2.1) - u _gas specific internal energy of gas - u _rad energy of the radiation field per volume in which unit mass of gas is contained (6.4) - V homology invariant defined by (2.2) - _def velocity of deflagration front (6.10) - X concentration by weight of hydrogen - Y concentration by weight of helium - Y _e mole number of electrons in one gram of matter (9.7) - Y _v mole number of neutrinos in one gram of matter - Z concentration by weight of the elements other than hydrogen and helium - z shock strength (6.6) - 1 (sub) usually denotes the core edge (2.13) - ratio of the mixing length to the scale height of pressure (l/H _p ) - ratio of gas pressure to the total pressure - ratio of the specific heats - gD locus of singularity in U-V plane (2.5) - M(H _p ) mass contained within unit scale height of pressure (4.4) - _ec energy rate by electron captures (9.5) - _n nuclear energy generation rate by the nuclear fuel specified by n - _v neutrino loss rate - L _v ^(D) neutrino loss rate excluding the neutrinos from the electron captures (9.4) - non-dimensional density (3.1) - P/, not the non-dimensional temperature (2.7) - _W Weinberg's angle (5.8) - opacity - _v neutrino opacity (11.2) - describes the effect of electron degeneracy in equation of state (2.19) - _ec rate of electron capture - mean molecular weight - _e mean molecular weight of electrons - _e chemical potential of an electron excluding the rest mass (8.1) - _i mean molecular weight of ions - non-dimensional radius (3.1) - non-dimensional pressure (3.1) - matter density - _cr ^GR critical density above which the general relativistic instability sets in - _cr critical density for reimplosion of the core by beta processes (Section 5) - _ign density at the ignition - _nse density above which the deflagrated matter results in NSE composition - _e non-dimensional entropy of electron-per one electron in units of k(9.2) - _ff timescale of free fall (6.2) - _h (H _p ) timescale of heat transport over unit scale height of pressure (4.4) - _n nuclear timescale for a change in temperature (6.1) - non-dimensional mass (3.1) - _e chemical potential of an electron in units of kT (8.1)     

The synthesis of helium and CNO isotopes in massive stars

We present helium and CNO isotopic yields for massive mass-losing stars in the initial mass range 15M M _i 50M . We investigate their dependence on assumptions about mass loss rates, internal mixing processes, and metallicity, and specify the contributions from stellar winds and from supernova ejecta.     

SN 1987A and SN 1993J: Testing stellar evolution theory?

Nearby supernovae like SN 1987A and SN 1993J provide valuable constraints on the late evolution of massive stars. For this purpose, we review evolutionary models for the progenitor of SN 1987A and confront them with five observational/theoretical tests we devised. We show that single-star models (with the possible exception of rapid-rotation models) fail at least two of these tests, while two binary models (accretion and merger models) are consistent with all available constraints. We conclude that it is most likely that the progenitor of SN 1987A had a binary companion, either at the time of the explosion or at least in the not-too-distant past, and that SN 1987A should therefore not be used to calibrate single stellar evolution theory. For SN 1993J, we infer from the presupernova photometry and the early light curve that its progenitor was a 15M star that lost almost all of its hydrogen-rich envelope prior to the supernova. This seems to require that the progenitor underwent stable case C mass transfer. We discuss future observational tests of binary models for both supernovae.     

Parametric study on the flutter sensitivity of a wide-chord hollow fan blade

In recent years, the hollow fan blades have been widely used to meet the demand for light weight and good performance of the aero-engine. However, the relationship between the hollow structure and the aeroelastic stability has not been studied yet in the open literature. In this paper, it has been investigated for an H-shaped hollow fan blade. Before studying the flutter behavior, the methods of parametric modeling and auto-generation of Finite Element Model (FEM) are presented. The influence of the feature parameters on the vibration frequency and mode shape (as the input of flutter calculation) of the first three modes are analyzed by the Orthogonal Experimental Design (OED) method. The results show that the parameters have a more remarkable impact on the first torsional mode and thus it is concerned in the flutter sensitivity analysis. Compared with the solid blade, the minimum aerodynamic damping of the hollow blade decreases, indicating that the hollow structure makes the aeroelastic stability worse. For the parameters describing the hollow section, the rib number N has the greatest influence on the minimum aerodynamic damping, followed by the wall thickness W₅. For the parameters in the height of hollow segment, the aerodynamic damping increases with the increase of parameters M₁ and M₂. This means that reducing the height of the hollow segment is helpful to improve the aeroelastic stability. Compared with the impact of parameters in hollow section, the variation of aerodynamic damping caused by the height of the hollow segment is small.     

Bump masses and radii of BL Herculis variables

Bump masses and radii are derived for 18 BL Her stars from the observed bump phase and the accurately known fundamental period. The mean mass M/M = 0.60 ± 0.09 agrees precisely with predictions from standard stellar evolution theory and gives a new test of the theoretical models. The derived radius of V553 Centauri is in good agreement with the radius recently determined by an independent modified Baade-Wesselink method by Balona. Finally, a preliminary discussion of possible continuations of the BL Her bump progression is given.     

Starburst galaxies

Bursts of massive star formation can temporarily dominate the luminosity of galaxies spanning a wide range of morphological types. This review is concerned primarily with such events in the central 1 kpc region of spiral galaxies which result from bar driven inflows of gas triggered by interactions or mergers. Most of the stellar radiant luminosity of such bursts is absorbed by dust and re-emitted in the far-infrared and is accompanied by radio and X-ray emission from supernova remnants which can also act collectively to drive galaxy scale outflows. Both evolutionary stellar models and estimates of the gas depletion times are consistent with typical burst durations of 10^7–8 yr. Spatially-resolved studies of nearby starburst galaxies reveal that the activity is distributed over many individual star forming complexes within rings and other structures organized by interactions between bars and the disc over a range of scales. More distant and extreme examples associated with mergers of massive spirals have luminosities > 10¹³ L and molecular gas masses > 10¹⁰ M implying star formation rates > 1000 M yr^–1 which can only be sustained for 10⁷ yr. In the most luminous merging systems, however, the relative importance of starburst and AGN activity and their possible evolutionary connection is still a hotly debated issue. Also controversial are suggestions that starbursts in addition to a black hole are required to account for the properties of AGNs or that starbursts alone may be sufficient under certain conditions. In a wider context, starbursts must clearly have played an important role in galaxy formation and evolution at earlier times. Recent detections of high redshift galaxies show that star formation was underway at z 4 but do not support a continuing increase of the strong evolution in the co-moving star formation density seen out to z l. Primeval starburst pre-cursors of spheroidal systems also remain elusive. The most distant candidates are radio galaxies and quasars at z = 4–5 and a possible population of objects responsible for an isotropic sub-mm wave background tentatively claimed to have been detected by the COBE satellite.