The appearance of a radio-pulsar magnetosphere from a vacuum with a strong magnetic field. Motion of charged particles

The motion of electrons and positrons in the vacuum magnetosphere of a neutron star with a surface magnetic field of B ≈ 10¹² G is considered. Particles created in the magnetosphere or falling into it from outside are virtually instantaneously accelerated to Lorentz factors γ ≈ 10⁸. After crossing the force-free surface, where the projection of the electric field onto the magnetic field vanishes, a particle begins to undergo ultra-relativistic oscillations. The particle experiences a regular drift along the force-free surface simultaneous with this oscillatory motion.     

Dissipative collapse of a magnetic flux rope with a force-free internal field

We have obtained new exact solutions describing the self-similar, uniform compression of twisted magnetic flux tubes (a magnetic flux rope) with a linear, force-free internal field with α = const in a resistive medium during the course of their dissipative evolution. Formally, the radius of the rope a decreases to zero over a finite time. This time turns out to be relatively short (several hours) for a rope with a radius of several hundred kilometers, if the helicity of the magnetic field in the rope is high: αa ≫ 1.     

The magnetic field of the pulsating subdwarf Balloon 090100001

We have analyzed polarization observations of the subdwarf Bal 09, which is one of a group of hybrid sdB stars that display simultaneously both short- and long-period pulsations. Certain properties previously unknown for subdwarfs have been established for Bal 09, such as variations of the pulsation amplitude of the main oscillation mode, rotational splitting of multiplets, and variations of this splitting. Information about the stellar magnetic field must be considered if we wish to explain these properties. New observational data enabling estimation of the longitudinal magnetic field of Bal 09 have been obtained on the main stellar spectrograph of the 6-m telescope of the Special Astrophysical Observatory. Studies of the longitudinal component of the magnetic field 〈B _z 〉 were carried out using a regression analysis. This method simultaneously yields estimates of the uncertainty in 〈B _z 〉. Test measurements of 〈B _z 〉 were carried out using the same method. For the star HD 158974, which has zero total magnetic field, the estimated longitudinal magnetic field is 〈B _z 〉 = −4 ± 5 G. The standard magnetic field for the Ap star α ²CVn was measured to be −363 ± 17 G, in very good agreement with measurements in the literature. The estimated longitudinal magnetic field for Bal 09 is 34 ± 63G—appreciably lower than values established earlier for six subdwarfs, ≈1.5 kG. The results of the regression analysis for both individual spectral subranges and for intervals containing characteristic spectral features did not indicate reliable detections of a magnetic field exceeding the uncertainties in 〈B _z 〉. The uncertainty in 〈B _z 〉, which was 60–80 G for the entire spectral range and 140–200 G for selected spectral intervals, leads to an estimated upper limit on the longitudinal magnetic field 〈B _z 〉 for Bal 09. This estimate for 〈B _z 〉 can place observational constraints on theoretical explanations for the amplitude variations of the pulsations, rotational splitting of multiplets, and possible variations of the internal structure of the star.     

Formation and destruction of periclase by fluid flow in two contact aureoles

Periclase formed in steeply dipping marbles from the Beinn an Dubhaich aureole, Scotland, and the Silver Star aureole, Montana, by the reaction dolomite = periclase + calcite + CO₂. Equilibrium between rock and fluids with X _{CO 2} < 1 requires that reaction was infiltration-driven. Brucite pseudomorphs after periclase occur in the Beinn an Dubhaich aureole either as bed-by-bed replacement of dolomite or in a lens along the contact between dolomite and a pre-metamorphic dike. Transport theory predicts that infiltration drove both periclase reaction and ¹⁸O-depletion fronts which moved at significantly different velocities along the flow path. The distributions of brucite and ¹⁸O-depleted rocks are identical in surface exposures, thus indicating upward flow. Time-integrated flux (q) was <500 mol/cm² and the fluid source was magmatic. Because periclase and its hydrated equivalent brucite are unaltered to dolomite by retrograde reactions, the exposure of brucite marbles accurately images the flow paths of peak metamorphic fluids. In the Silver Star aureole brucite pseudomorphs after periclase exclusively occur in tabular bodies that are beds with elevated Mg/Ca. The spatial pattern of ¹⁸O-depletion requires upward vertical fluid flow. Estimated prograde q ≈ 10³–10⁴ mol/cm² and the fluid source was magmatic. Low Mg/Ca, ¹⁸O-depleted, brucite-free rocks pose a dilemma because the periclase reaction front should have traveled ≈18 times further through them than the isotope alteration front. The dilemma is resolved by reaction textures that indicate periclase and brucite were destroyed in low Mg/Ca rocks by infiltration-driven retrograde carbonation reactions. Values of retrograde q were ≈10³–10⁴ mol/cm². Brucite (after periclase) was preserved only in high Mg/Ca layers where periclase developed in greater abundance. The geometry of brucite marbles at Silver Star thus reflects the location of high Mg/Ca beds rather than the geometry of fluid flow. Retrograde reactions must be considered before the mineralogical record of prograde fluid flow can correctly be interpreted. In both aureoles fluid flow, mineral reaction, and isotope depletion were structurally controlled by bedding and lithologic contacts. Received: 30 July 1996 / Accepted: 21 March 1997     

Determining the Inclination of the Kiloparsec-Scale Jet of the Quasar 3C 273 Based on Competition of Mechanisms for the Knot X-ray Emission

Based on the idea that the X-ray emission of the knots in the kiloparsec-scale jet of 3C 273 located closest to the active nucleus is due to inverse Compton scattering on the quasar radiation, while the X-ray emission of knots further from the nucleus is due to inverse Compton scattering on the cosmic microwave background, we find that the angle of the jet to the line of sight is θ ≈ 30°. The magnetic field and electron density in the knots are estimated. It is concluded that there is a break in the electron-energy spectrum at a Lorentz factor of г ∼ 10⁶. It is shown that the energy density of the relativistic electrons in the knots appreciably exceeds the energy density in the magnetic field.     

Gamma-ray bursts as a result of the interaction of a shock from a supernova and a neutron-star companion

A supernova explosion in a close binary system in which one of the components is a compact magnetized object (neutron star or white dwarf) can form a narrow “tail” with length l _t ～10⁹ cm, width h _t ～10⁸ cm, and magnetic field B _t ～10⁶, due to the resulting shock wave flowing around the magnetosphere of the compact object. The energy released by the reconnection of magnetic field lines in this tail can accelerate electrons to relativistic speeds (γ≈10⁴), creating the conditions required for powerful synchrotron radiation at energies from hundreds of keV to several MeV, i.e., for a gamma-ray burst (GRB). The duration of this radiation will depend on the power of the shock that forms during the supernova. If the shock is not sufficiently powerful to tear off the magnetosphere tail from the compact object, the duration of the GRB will not exceed l _t /V _A ≤1 s, and the conditions necessary for an “afterglow” at softer energies will not arise. If the shock is more powerful, the tail can be torn from the magnetosphere, forming a narrow ejection, which is perceived in its relativistic motion toward the observer(Γ～10⁴) as an afterglow whose duration grows from tens of seconds at gamma-ray energies to tens of days in the optical. This may explain why afterglows are observed only in association with long GRBs (T ₉₀>10 s). Very short GRBs (T ₉₀<0.1 s) may be local, i.e., low-power, phenomena occurring in close pairs containing compact, magnetized objects, in which there is again an interaction between the magnetosphere of the compact object and a shock wave, but the shock is initiated by a flare on the companion, which is a red-dwarf cataclysmic variable, rather than by a supernova.     

An experimental study of Ostwald ripening of olivine and plagioclase in silicate melts: implications for the growth and size of crystals in magmas

We carried out an experimental study to characterize the kinetics of Ostwald ripening in the forsterite-basalt system and in the plagioclase (An₆₅)-andesite system. Eight experiments were done in each system to monitor the evolution of mean grain size and crystal size distribution (CSD) with time t; the experiments were performed in a 1-atmosphere quench furnace, at 1,250°C for plagioclase and 1,300°C for olivine. Very contrasted coarsening kinetics were observed in the two series. In the plagioclase series, the mean grain size increased as log(t), from ≈3 μm to only 8.7 μm in 336 h. The kinetic law in log(t) means that Ostwald ripening was rate-limited by surface nucleation at plagioclase-liquid interfaces. In the olivine series, the mean grain size increased as t ^1/3, from ≈3 μm to 23.2 μm in 496 h. A kinetic law in t ^1/3 is expected when Ostwald ripening is rate-limited either by diffusion in the liquid or by grain growth/dissolution controlled by a screw dislocation mechanism. The shape of olivine CSDs, in particular their positive skewness, indicates that grain coarsening in the olivine experiments was controlled by a screw dislocation mechanism, not by diffusion. As the degrees of undercooling ΔT (or supersaturation) involved in Ostwald ripening are essentially <1°C, the mechanisms of crystal growth identified in our experiments are expected to be those prevailing during the slow crystallisation of large magma chambers. We extrapolated our experimental data to geological time scales to estimate the effect of Ostwald ripening on the size of crystals in magmas. In the case of plagioclase, Ostwald ripening is only efficient for mean grain sizes of a few microns to 20 μm, even for a time scale of 10⁵ years. It can, however, result in a significant decrease of the number of small crystals per unit volume, and contribute to the development of convex upwards CSDs. For olivine, the mean grain size increases from 2–3 μm to ≈70 μm in 1 year and 700 μm in 10³ years; a mean grain size of 3 mm is reached in 10⁵ years. Accordingly, the rate of grain size-dependent processes, such as compaction of olivine-rich cumulates or melt extraction from partially molten peridotites, may significantly be enhanced by textural coarsening.     

Gamma-ray bursts as a result of an interaction of a supernova shock with the star-companion in a binary system

Interaction of a fast shock wave generated during a supernova explosion with a magnetized star-companion of the supernova precursor produces a current sheet. We consider an evolution of this current sheet and show that a singularity (shock) is formed in finite time within the ideal magnetohydrodynamics framework. Charged particles (electrons) are accelerated in the vicinity of the singularity, and their distribution function has a plateau up to the energies of the order of 10⁴ mc ². These fast particles radiate in the γ-range in the strong magnetic field of the current sheet (B ≃ 10⁶ G). Radiation is concentrated within a narrow angle around the current sheet, Δθ ≃ 3 × 10⁻⁴, and its spectrum has the maximum at several hundreds of keV. Presented calculations confirm the model of cosmological GRBs proposed earlier by Istomin & Komberg.     

Temperature dependence on the electron paramagnetic resonance spectra of natural jasper from Taroko Gorge (Taiwan)

Structural properties of natural jasper from Taroko Gorge (Taiwan) have been investigated by means of powder X-ray diffraction, electron paramagnetic resonance (EPR) and Fourier transform infrared spectroscopic techniques. The EPR spectrum at room temperature exhibits a sharp resonance signal at g = 2.007 and two more resonance signals centered at g ≈ 4.3 and 14.0. The resonance signal at g = 2.007 has been attributed to the E′ center and is related to a natural radiation-induced paramagnetic defect. Two more resonance signals centered at g ≈ 4.3 and 14.0 are characteristic of Fe³⁺ ions. The EPR spectra recorded at room temperature of jasper samples, heat-treated at temperatures ranging from 473 to 1,473 K exhibit marked temperature dependence. The resonance signal corresponding to E′ center disappears at elevated temperatures. A broad, intense resonance signal centered at g ≈ 2.0 appears at elevated temperatures. This resonance signal is a characteristic of Fe³⁺ ions, which are present as hematite in the jasper sample. The intensity of the resonance signal becomes dominant at elevated temperatures at ≥873 K, masking g ≈ 4.3 and g ≈ 14.0 resonance signals. The EPR spectra of jasper heat-treated at 673 K have been recorded at temperatures between 123 and 296 K. The population of spin levels (N) has been calculated for the broad g ≈ 2.0 resonance signal. It is found that N decreases with decreasing temperature. The linewidth (ΔH) of g ≈ 2.0 resonance signal of the heat-treated jasper is found to increase with decreasing temperature. This has been attributed to spin–spin interaction of the Fe³⁺ ions present in the form of hematite in the studied jasper sample.     

Magnetohydrostatic model for a coronal hole

A model treating a solar coronal hole as an axially symmetrical magnetic formation that is in equilibrium with the surrounding medium is proposed. The model is applicable in the lower corona (to heights of the order of several hundreds of Mm), where the influence of the solar-wind outflow on the state of the system can still be neglected. The magnetic field of the coronal hole is comprised of a relatively weak open flux that varies with height, which extends into interplanetary space, and a closed field, whose flux closes at the chromosphere near the coronal hole. Simple analytical formulas are obtained, which demonstrate for a given equilibrium configuration of the plasma and field the main effect of interest—the lowering of the temperature and density of the gas in the coronal hole compared to their values in the corona at the same geometric height. In particular, it is shown that, at heights of several tens of Mm, the temperature and density of the plasma in the coronal hole are roughly half the corresponding values at the same height in the corona, if the cross-sectional radius of the hole exceeds the scale height in the corona by roughly a factor of 1.5: R _h ≈ 1.5H(T ₀). In the special case when R _h ≈ H(T ₀), the plasma temperature in the hole is equal to the coronal temperature, and the darkening of the coronal hole is due only to an appreciable reduction of the plasma density in the hole, compared to the coronal density. An analogy of the properties of coronal holes and sunspots is discussed, based on the similarity of the magnetic structures of these formations. In spite of the fundamental difference in the mechanisms for energy transport in coronal holes and sunspots, the equilibrium distributions of the plasma parameters in these formations are determined only by the magnetic and gravitational forces, giving rise to a number of common properties, due to their similar magnetic structures.     

Study of the electrical charge transport in ilvaite using impedance spectroscopy and thermopower data

The electrical conduction in the mineral ilvaite was studied between ≈170 and 450 K. A natural ilvaite from Elba (Italy) was found to be semiconducting with a DC conductivity 1.8×10^–3 (Ωcm)^–1 at 300 K, measured parallel (∥) to the [001] direction; perpendicular (⊥) to [001] it was 1.4×10^–5 (Ωcm)^–1, i.e. the conductivity is highly anisotropic. The conduction is effected by a hopping charge transport between localized levels in the energy gap associated with activation energies E _A =0.3–0.5 eV. It is concluded that impurities (Mg,Al,Mn) may play a decisive role in the charge hopping transport ∥ [001] that is basically governed by Fe²⁺-Fe³⁺ pairs on A-sites of the lattice as the source of electrons. Although the E_A-values were similar for both measured directions, the sign of thermopower is different which points to different charge transfer mechanisms. The bulk DC conductivity σ_DC ^AC for measurements ∥ [001], obtained by extrapolation of AC data using impedance spectroscopy, could only be determined at T<300 K owing to sample–electrode interfacial effects. In contrast, the bulk σ_DC ^AC⊥ [001] showed a slight break at ≈380 K that may reflect the structural phase transition monoclinic→orthorhombic at ≈345 K. From AC conductivity measurements in the frequency range 20 Hz–1 MHz at T<300 K, a dispersive character of electronic relaxation was found, resembling that of amorphous semiconductors and of impurity conduction in crystalline semiconductors where it was ascribed to charge hopping processes of electrons between localized levels of cation pairs or clusters of limited lengths. Received: 4 August 1997 / Revised, accepted: 12 January 1998     

Magnetic fabric development in a highly anisotropic magnetite-bearing ductile shear zone (Seve Nappe Complex,Scandinavian Caledonides)

Magnetite-bearing mylonitic garnet–micaschists close to the major suture between the Baltica and Iapetus terranes (Seve Nappe Complex, Scandinavian Caledonides) show very high anisotropy of magnetic susceptibility (AMS) with corrected degree of anisotropy (P′) up to 4.8. Three different magnetic fabric types can be distinguished. They correspond to protomylonite (type I, P′ < 2), mylonite (type II, 2 < P′ < 3), and ultramylonite (type III, P′ > 3), respectively. The orientation of the ellipsoid axes from all applied magnetic fabric methods in this study is similar with shallow dips of the metamorphic foliation toward WSW and subhorizontal, mostly NW–SE trending mineral lineation. Differences between subfabrics were minimized under high shear strain as all markers tend to align parallel with the shear plane. The very high anisotropies and mostly oblate ellipsoid shapes of type III correlate with high magnetic susceptibility (k _mean up to 55 × 10⁻³ SI units) and are related to the concentration of magnetite aggregates with shape-preferred orientation. They show a distinct field dependence of magnetic susceptibility of up to 10% in the k _max-direction. We attribute this field dependence to a “memory” of high strains in the domain walls of the crystals acquired during synkinematic magnetite growth during shear zone fabric development at temperatures of 550–570°C.     

Gamma-ray bursts from a close pulsar binary system?

The close neutron-star binary system comprised of the radio pulsars PSR J0737-3039 A,B is discussed. An analysis of the observational data indicates that the wind from pulsar A, which is more powerful than the wind from pulsar B, strongly distorts the magnetosphere of pulsar B. A shock separating the relativistic wind from pulsar A and the corotating magnetosphere of pulsar B should form inside the light cylinder of pulsar B. A weakly diverging “tail” of magnetic field is also formed, which stores a magnetic energy on the order of 10³⁰ erg. This energy could be liberated over a short time on the order of 0.1 s as a result of reconnection of the magnetic-force lines in this “tail,” leading to an outburst of electromagnetic radiation with energies near 100 keV, with an observed flux at the Earth of 4 × 10^?11 erg cm^?2 s^?2. Such outbursts would occur sporadically, as in the case of magnetic substorms in the Earth’s magnetosphere.     

Ion acoustic instability of HPT particles,FAC density,anomalous resistivity and parallel electric field in the auroral region

During the magnetic storm of 21st March 1990, the DE-1 spacecraft encountered the auroral region at high invariant latitude at altitudes ranging from a few thousand kilometers in the ionosphere to many earth radii in the magnetosphere. The magnetic field perturbations interpretable as field aligned current (FAC) layers and the electrostatic turbulence possibly due to electrostatic ion acoustic instability driven by these currents are shown. The critical drift velocity of Hot Plasma Torus (HPT) electrons and the growth rate of ion acoustic wave as a function of electron to ion temperature ratio (T _e/T_i) for low and high current densities and energy of HPT electrons are found out. The intense FAC destabilizes the ion acoustic wave and the resultant electrostatic turbulence creates an anomalous resistivity. The current driven resistivity produces parallel electric field and high power dissipation. The anomalous resistivityη, potential difference along the auroral field lines V_t|, intensity of electric field turbulenceE _t| and power produced per unit volumeP are computed. It is found that the change in westward magnetic perturbation increasesJ _t|, η, V_t|, E_t| andP. Hence HPT electrons are heated and accelerated due to power dissipation during magnetically active periods in the auroral region. Concerning, applications, such HPT electrons can be used in particle accelerators like electron ring accelerator, smokatron etc.     

Environmental magnetic and geochemical characteristics of Chennai coastal sediments,Bay of Bengal,India

In this study, environmental magnetic, heavy metal and statistical analyses were conducted on 21 surface sediments collected from Chennai coast, India, to examine the feasibility of heavy metal pollution using magnetic susceptibility. The Chennai coastal sediment samples are dominated by ferrimagnetic minerals corresponding to magnetite-like minerals. The percentage of frequency dependent magnetic susceptibility reflects the presence of super-paramagnetic/single domain magnetic minerals in Chennai harbour, Cooum and Adayar rivers sediments. High pollution load index in sample E1, E2, CH7, C11, C12 and A16 is mainly due to anthropogenic activities such as, harbour activities, Cooum and Adayar rivers input and industrial effluent. Factor analysis shows that the magnetic concentration dependent parameters (χ, χ _ARM and SIRM) covary with the heavy metal concentrations, suggesting that the input of magnetic minerals and heavy metals in Chennai coastal sediments are derived from the same anthropogenic sources. Strong correlation obtained between pollution load index (PLI) and concentration dependent parameters (χ, χ _ARM and SIRM) for the polluted samples with magnetic susceptibility excess of 50×10^− 8 m³kg^− 1. Significant correlations between heavy metals and magnetic susceptibility point out the potential of magnetic screening/monitoring for simple and rapid proxy indicator of heavy metal pollution in marine sediments.     

Theory for preliminary negative impulse in storm sudden commencement inH at equatorial stations

It is shown that the storm sudden commencement (SSC) inH field at low latitude station consists of only a positive excursion when the interplanetary shock due to the solar plasma impinging on the magnetosphere is associated with a southward excursion of the interplanetary magnetic field (IMF). When the signature of SSC at low latitude station consists of a preliminary negative excursion preceding the main positive excursion of theH field, the solar plasma causing the compression is associated with a northward excursion of the IMF. It is suggested that the signature of SSC(H) at equatorial stations is the result of combined effect of the compression of magnetosphere by the solar plasma as well as due to the electric field effects associated with the velocity of the solar plasma (v) interacting with the northward component (Bz) of the interplanetary field (i.e.,E =−v _x Bz).     

Himalayan inverted metamorphism constrained by oxygen isotope thermometry

Inverted metamorphic field gradients are preserved in two amphibolite facies metapelitic sequences forming the crystalline core zone of the Himalayan orogen in the Sutlej valley (NW India). In the High Himalayan Crystalline Sequence (HHCS), metamorphic conditions increase upwards from the staurolite zone at the base, through the kyanite-in and sillimanite-in isograds, finally to reach partial melting conditions at the top. The structurally lower Lesser Himalayan Crystalline Sequence (LHCS) shows a gradual superposition of garnet-in, staurolite-in and kyanite + sillimanite-in isograds. Although phase equilibria constraints imply inverted temperature field gradients in both units, garnet-biotite (GARB) rim thermometry indicates final equilibration at a nearly uniform temperature around T ≈ 600 °C across these sequences. The P-T path and garnet zoning data show that this apparent lack of thermal field gradient is mainly the consequence of a resetting of the GARB equilibria during cooling. In order to constrain peak temperature conditions, 20 samples along the studied section have been analysed for oxygen isotope thermometry. The isotopic fractionations recorded by quartz-garnet and quartz-aluminosilicate mineral pairs indicate temperatures consistent with phase equilibria and P-T path constraints for metamorphic peak conditions. Together with barometry results, based on net transfer continuous reactions, the oxygen isotope thermometry indicates peak conditions characterized by: (1) a temperature increase from T ≈ 570 to 750 °C at a nearly constant pressure around P ≈ 800 MPa, from the base to the top of the HHCS unit; (2) a temperature increase from T ≈ 610 to 700 °C and a pressure decrease from P ≈ 900 to 700 MPa, from the base to the top of the LHCS metapelites. Oxygen isotope thermometry thus provides the first quantitative data demonstrating that the Himalayan inverted metamorphism can be associated with a complete inversion of the thermal field gradient across the crystalline core zone of this orogen. Received: 1 April 1999 / Accepted: 12 July 1999     

Formation of the disk structure and jets in the symbiotic system Z and during periods of activity in 2006–2010

We present an analysis of spectrophotometric observations of the latest cycle of activity of the symbiotic binary Z And from 2006 to 2010. We estimate the temperature of the hot component of Z And to be ≈150 000−170 000 K at minimum brightness, decreasing to ≈90 000 K at the brightness maximum. Our estimate of the electron density in the gaseous nebula is N _e = 10¹⁰−10¹² cm⁻³ in the region of formation of lines of neutral helium and N _e = 10⁶−10⁷ cm⁻³ in the region of formation of the [OIII] and [NeIII] nebular lines. A trend for the gas density derived from helium lines to increase and the gas density derived from [OIII] and [NeIII] lines to simultaneously decrease with increasing brightness of the system was observed. Our estimates show that the ratios of the theoretical and observed fluxes in the [OIII] and [NeIII] lines agree best when the O/Ne ratio is similar to its value for planetary nebulae. The model spectral energy distribution showed that, in addition to a cool component and gaseous nebula, a relatively cool pseudophotosphere (5250–11 500 K) is present in the system. The simultaneous presence of a relatively cool pseudophotosphere and high-ionization spectral lines is probably related to a disk-like structure of the pseudophotosphere. The pseudophotosphere formed very rapidly—over several weeks—during a period of increasing brightness of Z And. We infer that in 2009, as in 2006, the activity of the system was accompanied by a collimated bipolar ejection of matter (jets). In contrast to the situation in 2006, the jets were detected even before the system reached its maximum brightness. Moreover, components with velocities close to 1200 km/s disappeared at the maximum, while those with velocities close to 1800 km/s appeared.     

Mode of formation of hibonite (CaAl12O19) within the U-Th skarns from the granulites of S-E Madagascar

 In Madagascar, hibonite occurs as a rather frequent mineral within thorianite-bearing skarns which are widespread in the Pan African granulitic formations constituting the S-E part of the Island (Tranomaro area). In these skarns, leucocratic segregations made up of CO₃-scapolite to meionite (An_equivalent=89–95% which implies T≥850° C), spinel and corundum were formed at stage 1 of metasomatism in a titanite-bearing matrix consisting of scapolite (An_eq=77–88) and aluminous diopside. During stage 2 of metasomatism, scapolite from the lenses were altered to anorthite+calcite while the less calcic scapolite remained stable which indicates T≈800° C. Hibonite crystallized at the expense of corundum and spinel. Expressed as mol% of the CaAl₁₂O₁₉/Ca(Al₁₀TiR²⁺)O₁₉/REE(Al₁₁R²⁺)O₁₉ [+Th (Al₁₀R²⁺ ₂)O₁₉] end-members (R ²⁺=Mg, Fe²⁺, Zn²⁺; Al=Al, Fe³⁺; Ti=Ti, Si), its composition varies from 26/72/2 to 50/23/27. The ideal activity of the CaAl₁₂O₁₉ component is about 0.25. Fluid inclusions in corundum, hibonite and anorthite are composed of nearly pure CO₂. In corundum, the isochores for primary inclusions are in agreement with the P-T estimates for regional metamorphism and stage 1 metasomatism (T≈850° C, P≈5 kbar). Inclusions with the highest density in hibonite and anorthite constrain P to about 3–3.5 kbar for T=800° C. Thermodynamic calculations indicate that, in addition to a low activity of CaAl₁₂O₁₉, stability of hibonite in equilibrium with anorthite and calcite implies an extremely low activity of silica (below the zircon-baddeleyite buffer). By contrast the activity of CO₂ may be high, in agreement with the observed fluid compositions. These results are corroborated by a short comparison with the other granulite occurrences of hibonite in Tanzania and South India. Received: 18 August 1994 / Accepted: 12 October 1995