Unmixing Model Research Articles

Theoretical light curve of a Type 2p supernova

The light curve and other observable diagnostics are presented for what should be a typical Type II 'plateau' supernova, the explosion of a 15 solar mass red supergiant. The calculations are carried out using a multi-frequency radiation transport code that includes opacity from all important mechanisms-bound-bound, bound-free, free-free, and electron scattering. It is found that the inclusion of opacity sources besides electron scattering increases the computed lenght of the plateau in the 15 solar mass model by approximately 30 days. Especially important is the ultraviolet cutoff caused by a thick forest of lines. Deposition and escape of gamma-rays from radioactive decay are also accurately simulated. We find that the presence of 0.06 solar mass of ejected Ni-56 extends the length of the plateau from approximately 100 days to approximately 140 dys. Because of the large hydrogen envleope and radius in this model, mixing does not appreciably alter the bolometric light curve, although it does change the gamma-ray light curve significantly. With 0.06 solar mass of ejected Ni-56, the unmixed (mixed) model peaks in escaping gamma-rays at 576 (466) days with gamma-ray luminosity of 3 x 10(exp 38) ergs/s. Except for the local group, the gamma-rays from an extragalactic 15 solar mass SNe IIp will be too faint to detect with any exsiting detectors. However, a Galactic SNe IIp would be quite bright and easily detectable.

The eta -baryon octet.

The recent tantalizing experimental support for an $\ensuremath{\eta}$-baryon ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ unmixed octet challenges conventional model wisdom. The establishment of the $\ensuremath{\Xi}(1868)$ member of the $\ensuremath{\eta}$ octet will give strong affirmation that the negative-parity baryon mass spectrum could be mixing-free.

The Atnarpa Igneous Complex, southeast Arunta Inlier, central Australia: implications for subduction at an Early-Mid Proterozoic continental margin

Three distinctive igneous suites have been identified from the Atnarpa Igneous Complex, southeast margin of the Arunta Inlier, central Australia. The 1879 +11, −10 Ma gabbro-diorite-tonalite-trondhjemite suite (SiO 2=49–78%) shows both calc-alkaline and trondhjemitic affinities. The overall depletion of Nb, Ti, Y, K and Rb in this suite indicates that its parental magma must have been depleted in these elements. It is the oldest zircon age so far obtained in the Arunta Inlier. The 1873 +11 −10 Ma low-Al tonalite-trondhjemite-granodiorite suite is also depleted in K and Rb. However, unlike either the 1879 Ma or the 1751 Ma suites, it has lower Al 2O 3 and Sr at comparable SiO 2 levels and display flat HREEs and negative Eu anomalies. The 1751±12 Ma younger tonalite suite is high in Sr, Sr/Y and Al 2O 3, and low in Zr, Ti, Nb, Y, Th and U, and displays a strongly fractionated REE pattern with HREE depletion, typical of Archaean high-Al tonalite-trondhjemite-granodiorite suites. Such geochemical features contrast with the 1850–1880 Ma old K, Rb, REE, Th-enriched, Na, Sr-depleted Barramundi Igneous Association, widespread in Proterozoic terrains of northern Australia. The parental magma of the 1879±11 Ma suite is considered to be derived by subduction-related partial melting of a metasomatised-hybridised mantle wedge with phlogopite retained in the residue, the parental magma of the 1873±11 Ma low-Al suite, by relatively low-pressure partial melting of a mafic source with residual plagioclase left in the residue, and the 1751±12 Ma younger tonalite suite, by partial melting of a subducted oceanic crust at mantle depth with residual garnet±amphibole. These processes contrast with models of restite unmixing of a geochemically uniform, but fractionated, preexisting mantle-derived underplate previously proposed for the K-rich Barramundi Igneous Association. Combining geochemical features of the Atnarpa Igneous Complex with reported data from the Harts Range and the Alice Springs areas, we propose that the southeast margin of the Arunta Inlier represents a convergent continental margin during the Early to Middle Proterozoic which has undergone at least two episodes of subduction-related magmatism (1860–1880 Ma and 1730–1770 Ma). Such continental margin subduction could provide additional driving force for crust-mantle delamination and ensialic A-subduction within the preexisting continental crust further north. Both within-plate vertical underplating and marginal lateral accretion could be important processes for Proterozoic crustal evolution.

The Layos Granite, Hercynian Complex of Toledo (Spain): an example of parautochthonous restite-rich granite in a granulitic area

ABSTRACTThe Layos Granite forms elongated massifs within the Toledo Complex of central Spain. It is late-tectonic with respect to the F2 regional phase and simultaneous with the metamorphic peak of the region, which reached a maximum temperature of 800–850°C and pressures of 400–600 MPa. Field studies indicate that this intrusion belongs to the “regional migmatite terrane granite” type. This granite is typically interlayered with sill-like veins and elongated bodies of cordierite/garnet-bearing leucogranites. Enclaves are widespread and comprise restitic types (quartz lumps, biotite, cordierite and sillimanite-rich enclaves) and refractory metamorphic country-rocks including orthogneisses, amphibolites, quartzites, conglomerates and calc-silicate rocks.These granites vary from quartz-rich tonalites to melamonzogranites and define a S-type trend on a QAP plot. Cordierite and biotite are the mafic phases of the rocks. The particularly high percentage of cordierite (10%–30%) varies inversely with the silica content. Sillimanite is a common accessory mineral, always included in cordierite, suggesting a restitic origin. The mineral chemistry of the Layos Granite is similar to that of the leucogranites and country-rock peraluminous granulites (kinzigites), indicating a close approach to equilibrium. The uniform composition of plagioclase (An25), the high albitic content of the K-feldspar, the continuous variation in the Fe/Mg ratios of the mafic minerals, and the high Ti content of the biotites (2.5–6.5%) suggest a genetic relationship.Geochemically, the Layos Granite is strongly peraluminous. Normative corundum lies between 4% and 10% and varies inversely with increase in SiO2. The CaO content is typically low (<1.25%) and shows little variation; similarly the LILE show a limited range. On many variation diagrams, linear trends from peraluminous granulites to the Layos Granite and associated leucogranite can be observed. The chemical characteristics argue against an igneous fractionation or fusion mechanism for the diversification of the Layos Granite. A restite unmixing model between a granulitic pole (represented by the granulites of the Toledo Complex) and a minimum melt (leucogranites) could explain the main chemical variation of the Layos Granite. Melting of a pelitic protolith under anhydrous conditions (biotite dehydration melting) could lead to minimum-temperature melt compositions and a strongly peraluminous residuum.For the most mafic granites (61–63% SiO2), it is estimated that the trapped restite component must have been around 65%. This high proportion of restite is close to the estimated rheological critical melt fraction, but field evidence suggests that this critical value has been exceeded. This high restite component implies high viscosity of the melt which, together with the anhydrous assemblage of the Layos Granite and the associated leucogranites, indicates H2O-undersaturated melting conditions. Under such conditions, the high viscosity magma (crystal-liquid mush) had a restricted movement capacity, leading to the development of parautochthonous plutonic bodies.

Genesis of Peraluminous Granites II. Mineralogy and Chemistry of the Tourem Complex (North Portugal). Sequential Melting vs. Restite Unmixing

The Tourem granitic complex (North Portugal) consists of quartz- and alkali-feldspar-rich felsic granites, biotite- and plagioclase-rich heterogeneous granites, and cordierite-biotite granites, containing numerous enclaves of orthogneisses and metapelitic schists. Mineralogical, chemical, and experimental data suggest that all the granites and the orthogneiss enclaves are genetically related. The felsic granites are characterized by normally zoned plagioclase, absence of cordierite, high SiO2 and K2O (72–74 wt.% and 5·4–6·4 wt.%, respectively), moderate P2O5 and REE (0·22–0·24% and 85·0–95·7 ppm), and low Fe2O3* and Zr contents (1·3–1·5% and 80–90 ppm). These features are consistent with those of restite-free melts formed by low extents of melting. Melting experiments show that these felsic granites are likely to be derived by melting of a source material similar to the orthogneiss enclaves under low water activities (∼0·5), at relatively high temperature (∼ 800°C) and <30% melting. The heterogeneous and cordierite-biotite granites display high cordierite contents (up to 30%) in addition to biotite (5–25%), complexly zoned plagioclase, and high Fe2O3 (2·72–6·99%), CaO (0·56–1·95%), Zr (101–213 ppm), and Ce (39·8–98·1 ppm) contents, suggesting that the melts contained significant proportions of residual biotite, cordierite, plagioclase, and accessories. Experimental data indicate that the melts were generated under water-undersaturated conditions but by higher extents of melting (30–60% melting) with probably a larger amount of available water compared with the felsic granites. The major and trace element chemical trends of the granites, which do not define single arrays on two-element variation diagrams, and experimental data show that the generation of the Tourem anatectic complex cannot be explained by the restite unmixing model but could have resulted from sequential low extents of melting with efficient melt segregation followed by higher extents of melting with restite retention.

Anomalous small-angle-X-ray scattering on Al–Zn and Al–Zn–Ag alloys

Anomalous small-angle scattering (ASAXS) spectra from Al–Zn and Al–Zn–Ag alloys have been recorded at the Stanford Synchrotron Radiation Laboratory (SSRL). The data were obtained at different energies close to the Zn absorption edge. For the binary alloy, the ASAXS intensities follow quantitatively the variation in the atomic scattering factor of zinc. For the ternary alloys, the anomalous effect decreases when the Zn content decreases. Although only weighted sums of the partial structure functions could be determined, it is shown that the results are consistent with the `two-phase' unmixing model and the direction of tie lines of the metastable miscibility gap has been determined. A new method for analyzing ASAXS data for two absorption edges is proposed.

The evolution of mixed long-lived stars

We have computed evolutionary models of partially mixed stars by treating the extent of mixing and the degree of nonthermal pressure support as parameters. Unmixed and mixed models are compared to the distribution of blue stragglers in the old open cluster NGC 7789. Standard models fail to account for the apparent frequency of occurrence of blue stragglers redward of the normal main-sequence band. Theoretial time-constant loci for mixed models indicate that the distribution of blue stragglers can be understood in this way. A distribution of values of the mass fraction mixed 0.3< or approx. =q/sub mix/< or approx. =0.9 is required; a single value is insufficient. The mass distribution is strongly concentrated in the range 1.7-2.2 M/sub sun/. No straggler in this cluster demands a finite nonthermal pressure. Models with q/sub mix/ = 0.8 and 0.4 were followed through helium burning which occurs at a point midway between the main sequence and the standard giant branch for q/sub mix/ = 0.8 and on the red giant branch for q/sub mix/ = 0.4. The outer surface convection zone never pentrates the region of ad hoc mixing because of the presence of a vigorous, hydrogen-burning shell. We conclude that extensive internal mixingmore » remains a viable hypothesis to account for the existence of blue stragglers.« less

Effects of Sudden Mixing in the Solar Core on Solar Neutrinos and Ice Ages

A CONTINUOUS mixing throughout much of the solar interior might maintain a large abundance of hydrogen at the centre of the Sun, thus lowering the temperature relative to an unmixed model and lowering the 8B neutrino flux by a factor 4 or so. Although this suggestion is unconventional and some aspects of it are not very appealing in terms of present stellar evolution theory4,5, once again the solar neutrino problem is facing a crisis. Davis and his co-workers reported at the Solar Neutrino Conference in San Clemente and Irvine, California, in February 1972, a new upper limit of the solar neutrino fluxes equivalent to 1 s.n.u. (10−36 interactions per second per 37Cl target atom). Solar model calculations, allowing for the recent reduction of the proton-proton reaction rate due to meson exchange effects (M. Gari and A. M. Huffman, unpublished), predict a neutrino flux equivalent to 7 s.n.u. (refs. 6,7). Our previous mixing hypothesis would be inadequate to resolve the present discrepancy, partly because the flux reduction factor is not large enough and partly because the neutrino fluxes from s solar sources other than 8B should produce a counting rate equivalent to slightly more than 1 s.n.u. and the reduction in these fluxes due to mixing would be smaller due to the lower temperature sensitivity of the sources.

Climatic change in cosmic perspective

A summary of the writer's interpretation of long-range climatic change is presented. A gradual rise in solar radiation and terrestrial temperatures over billions of years must take place, as a necessary consequence of stellar evolution with constant mass. It will be culminating in a steep heat peak 1–6 billion years from now. The hypothesis of a decrease of the gravitational constant in inverse proportion to the “expansion age” of the universe cannot be reconciled with palaeoclimatic data except when the time scale is assumed to be unacceptably long. The “astronomical” chronology of the Quaternary, or that based on the variation of the orbital elements of the Earth, is without sufficient foundation. Apparent synchronization of two unrelated sets of fluctuating data can be achieved by slight adjustments in the relative time intervals of one of them; the apparently perfect coincidence so obtained may be completely spurious, when only the succession of events is given, without a knowledge of the actual intervals of time. The climatic heat balance of the Earth as a whole, including convective transport and storage, has been analyzed and the results applied to the correlation of glaciation with global insolation. Extreme variations of the Earth's orbital elements are unable to account for the amplitude of the glacial-interglacial fluctuations. The “ astronomical” theory of Quaternary climatic change is thus inadequate quantitatively, as well as unconvincing chronologically. Variations in global cloudiness can account quantitatively for the palaeoclimatic fluctuations, but the ad hoc character of the hypothesis, and the difficulty of accounting for the recurrence of the glacial epochs, make it rather unattractive. Volcanic dust as a cause must be excluded de facto, as it is not present now in sufficient quantities to explain the low global temperature, as compared with the Tertiary. The interplay of nuclear reactions (hydrogen burning to helium) and gas diffusion in the Sun's interior necessarily leads to disturbances which can account for the recurrent deterioration of the global climate after intervals of a few hundred million years, if the Kramers source of opacity is significant, or if the content of elements heavier than helium in and around the Sun's core is not less than 1–2%. This yields a plausible model to account for the long-range major palaeoclimatic fluctuations, as being caused by the variation in the Sun's radiative output. The fluctuations during one ice age, or the successive advances and retreats of the glaciers on Earth, could be a kind of “flickering” of solar radiation as conditioned by the peripheral convective region of the Sun, but a unique theory of it cannot yet be offered. Much of what follows depends on the consideration of the evolution of unmixed gaseous stellar models with nuclear energy generation. With the advent of electronic computers, much solid work has been done in this direction, especially the brilliant achievements of Martin Schwarzschild and his school. The start was made by the writer's pioneering work (Öpik, 1938 a,b). Yet the best electronic results are no better than their basic assumptions; the admissible span in the results is so wide that the former handmade calculations are still within the probable or plausible limits of assumptions. A revision of the climatic theory on the basis of the new models would not lead to significantly new results. Also, only in the author's work has gas diffusion in the central regions of the Sun been allowed for, and found to be of decisive importance. Therefore, as well as for the sake of uniformity, the climatic problems as analyzed here are viewed against the background of the writer's own work on stellar models.