Overturn Time Research Articles

Effect of porous layer and initial salt gradient on improving SGSP stability: Transient numerical simulation and theoretical analysis

The salt gradient solar pond (SGSP) is a low-cost and large-scale solar energy capture and storage device. The stability of the non-convective zone (NCZ) is critical for the well-functioning and efficiency of SGSP. To understand when and how SGSP lost its effectiveness, the turbulent double-diffusive convection in solar ponds was first solved numerically with a Large Eddy Simulations (LES) model. The simulations show that attaching a porous layer or increasing the initial salt concentration effectively delays the destruction of NCZ. By increasing the initial salt concentration from 5.2% to 20.8%, the destruction time increases from 7 to 22 h. By attaching a porous layer, the overturn time can increase by about 8 h, resulting in a temperature rise from 46 °C to 73 °C in the storage layer. The flow field analysis shows that both interface erosion and turbulent mixing in NCZ cause the destruction of NCZ. The stability analysis shows that the turbulent mixing decreases the salinity gradient in NCZ, making it more susceptible to erosion. By inhibiting the turbulent mixing, the porous layer at the bottom can effectively delay the arrival of NCZ destruction. Thus, the heat storage capacity and stability of solar ponds are enhanced.

Constraints on Magnetic Braking from the G8 Dwarf Stars 61 UMa and τ Cet

During the first half of their main-sequence lifetimes, stars rapidly lose angular momentum to their magnetized winds, a process known as magnetic braking. Recent observations suggest a substantial decrease in the magnetic braking efficiency when stars reach a critical value of the Rossby number, the stellar rotation period normalized by the convective overturn timescale. Cooler stars have deeper convection zones with longer overturn times, reaching this critical Rossby number at slower rotation rates. The nature and timing of the transition to weakened magnetic braking have previously been constrained by several solar analogs and two slightly hotter stars. In this Letter, we derive the first direct constraints from stars cooler than the Sun. We present new spectropolarimetry of the old G8 dwarf τ Cet from the Large Binocular Telescope, and we reanalyze a published Zeeman Doppler image of the younger G8 star 61 UMa, yielding the large-scale magnetic field strengths and morphologies. We estimate mass-loss rates using archival X-ray observations and inferences from Lyα measurements, and we adopt other stellar properties from asteroseismology and spectral energy distribution fitting. The resulting calculations of the wind braking torque demonstrate that the rate of angular momentum loss drops by a factor of 300 between the ages of these two stars (1.4–9 Gyr), well above theoretical expectations. We summarize the available data to help constrain the value of the critical Rossby number, and we identify a new signature of the long-period detection edge in recent measurements from the Kepler mission.

Stellar Convective Penetration: Parameterized Theory and Dynamical Simulations

Abstract Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well-understood. Here, we present 3D numerical simulations that exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the “penetration parameter”  , which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh and Zahn, we construct an energy-based theoretical model in which  controls the extent of penetration. We test this theory using 3D numerical simulations that employ a simplified Boussinesq model of stellar convection. The convection is driven by internal heating, and we use a height-dependent radiative conductivity. This allows us to separately specify  and the stiffness  of the radiative–convective boundary. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stars, we expect  ≈ 1 , and in this regime, our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to ∼20%–30% of a mixing length. We present a MESA stellar model of the Sun that employs our parameterization of convective penetration as a proof of concept. Finally, we discuss prospects for extending these results to more realistic stellar contexts.

Tracing water column euxinia in Eastern Mediterranean Sapropels S5 and S7

Sapropels S5 and S7 formed in the semi-enclosed Eastern Mediterranean Sea (EMS) during peak interglacial periods MIS5e and MIS7a, respectively, are considered among the most strongly developed Quaternary sapropels. This study investigates the redox dynamics of the water column during their formation, via Fe isotope and Fe speciation studies of cores taken at 2550 m depth at site ODP-967. Both sapropels show an inverse correlation between δ56Fe and FeT/Al, with slopes mostly matching that found for the Black Sea, pointing to a benthic shelf to basin shuttle of Fe and subsequent precipitation of Fe sulphides in euxinic bottom waters. An exception to these Black Sea-type trends occurs during the later, peak, stages of S7, where the negative δ56Fe - FeT/Al slope shallows. Fe speciation studies reveal that the dominant highly reactive Fe phase (FeHR) in the sapropels is pyrite, with Fe (oxyhydr)oxides forming the second major mineral component. Correspondingly, FeHR/FeT plots show increased strengthening of anoxic water conditions during the passage from pre-sapropel sediment into the sapropel. Nevertheless, despite the evidence for euxinic conditions from both Fe isotopes and high Mo concentrations in the sapropel, Fepy/FeHR ratios remain below values commonly used to identify water column euxinia. This apparent contradiction is ascribed to the sedimentary preservation of a high flux of crystalline Fe (oxyhydr)oxide minerals to the basin, which resulted in a relatively low degree of sulphidation, despite the presence of euxinic bottom waters. Thus, the operationally defined ferruginous/euxinic boundary for EMS sapropels is better placed at Fepy/FeHR = 0.6, which is somewhat below the usually ascribed lower limit of 0.7. Consistent with the significant presence of crystalline Fe (oxyhydr)oxides, the change in the δ56Fe - FeT/Al slope during peak S7 is ascribed to an enhanced monsoon-driven flux of detrital Fe(III) oxides from the River Nile into the EMS basin and comcomitant diagenetic sulphidation. Euxinic water column conditions in sapropel S5 and S7 are interpreted here to reflect the positive balance between dissolved sulphide formation and rates of reductive dissolution of Fe (oxyhydr)oxide minerals. Both of these parameters in turn depend on the extent to which water overturn times are reduced and export productivity increased during sapropel formation.

Approaching Earth’s core conditions in high-resolution geodynamo simulations

SUMMARY The geodynamo features a broad separation between the large scale at which Earth’s magnetic field is sustained against ohmic dissipation and the small scales of the turbulent and electrically conducting underlying fluid flow in the outer core. Here, the properties of this scale separation are analysed using high-resolution numerical simulations that approach closer to Earth’s core conditions than earlier models. The new simulations are obtained by increasing the resolution and gradually relaxing the hyperdiffusive approximation of previously published low-resolution cases. This upsizing process does not perturb the previously obtained large-scale, leading-order quasi-geostrophic (QG) and first-order magneto-Archimedes-Coriolis (MAC) force balances. As a result, upsizing causes only weak transients typically lasting a fraction of a convective overturn time, thereby demonstrating the efficiency of this approach to reach extreme conditions at reduced computational cost. As Earth’s core conditions are approached in the upsized simulations, Ohmic losses dissipate up to 97 per cent of the injected convective power. Kinetic energy spectra feature a gradually broadening self-similar, power-law spectral range extending over more than a decade in length scale. In this range, the spectral energy density profile of vorticity is shown to be approximately flat between the large scale at which the magnetic field draws its energy from convection through the QG-MAC force balance and the small scale at which this energy is dissipated. The resulting velocity and density anomaly planforms in the physical space consist in large-scale columnar sheets and plumes, respectively, co-existing with small-scale vorticity filaments and density anomaly ramifications. In contrast, magnetic field planforms keep their large-scale structure after upsizing. The small-scale vorticity filaments are aligned with the large-scale magnetic field lines, thereby minimizing the dynamical influence of the Lorentz force. The diagnostic outputs of the upsized simulations are more consistent with the asymptotic QG-MAC theory than those of the low-resolution cases that they originate from, but still feature small residual deviations that may call for further theoretical refinements to account for the structuring constraints of the magnetic field on the flow.

Spherical convective dynamos in the rapidly rotating asymptotic regime

Self-sustained convective dynamos in planetary systems operate in an asymptotic regime of rapid rotation, where a balance is thought to hold between the Coriolis, pressure, buoyancy and Lorentz forces (the MAC balance). Classical numerical solutions have previously been obtained in a regime of moderate rotation where viscous and inertial forces are still significant. We define a uni-dimensional path in parameter space between classical models and asymptotic conditions from the requirements to enforce a MAC balance and to preserve the ratio between the magnetic diffusion and convective overturn times (the magnetic Reynolds number). Direct numerical simulations performed along this path show that the spatial structure of the solution at scales larger than the magnetic dissipation length is largely invariant. This enables the definition of large-eddy simulations resting on the assumption that small-scale details of the hydrodynamic turbulence are irrelevant to the determination of the large-scale asymptotic state. These simulations are shown to be in good agreement with direct simulations in the range where both are feasible, and can be computed for control parameter values far beyond the current state of the art, such as an Ekman number $E=10^{-8}$. We obtain strong-field convective dynamos approaching the MAC balance and a Taylor state to an unprecedented degree of accuracy. The physical connection between classical models and asymptotic conditions is shown to be devoid of abrupt transitions, demonstrating the asymptotic relevance of classical numerical dynamo mechanisms. The fields of the system are confirmed to follow diffusivity-free, power-based scaling laws along the path.

地球型惑星内部物理学の最近の進展

Great advances on observational studies of terrestrial planets including our own Earth since the 1990s suggest that we should fundamentally revise our view on the evolution of planetary interiors. It has been implicitly assumed that the mantle of a terrestrial planet evolves quasi-statically due to heat extraction by mantle convection. Tomographic studies on the Earth's mantle together with geologic studies, however, show that the overturn time of mantle convection is on the order of a billion years, which is comparable to the age of the Earth. So the evolution of the Earth's mantle is a dynamic process and the quasi-static model of mantle evolution is no longer tenable. Images of terrestrial planets recently sent from spacecraft suggest that the evolution of terrestrial planets depends systematically on their size, and that the evolution of the Earth should be understood in the context of this systematic relationship. The finding of super-Earths implies that we must figure a way to infer the evolution of these planets from limited information, such as the planetary mass, radius, and the composition of the atmosphere, on the basis of studies on terrestrial planets in our solar system. Geologic studies on Archean continents older than 2.5 billion years show that the tectonic regime of early Earth is qualitatively different from that of modern Earth, so the magmatism-mantle convection system in the Earth must have experienced a regime-transition at some point in its history. More dynamically oriented models of mantle evolution would be useful for predicting how the Earth's mantle evolved at its earliest stages on the basis of observations of other celestial bodies such as the Moon, where the old surface is still preserved. Further refinement of seismic studies on the Earth's interior combined with studies on the properties of mantle materials under high pressures are crucial to improve our understanding of the history of the Earth's interior.

A power spectrum for the geomagnetic dipole moment

We use stochastic models for fluctuations in the dipole moment to derive a geomagnetic power spectrum. The theoretical spectrum is represented as a function of frequency f in the general form Af−n with smooth transitions between changes in the exponent n. A flat spectrum (n=0) at low frequencies changes to n=2 at intermediate frequencies. We attribute the transition frequency to the decay time of dipole fluctuations. Accounting for correlated noise in the stochastic model introduces another transition from n=2 to 4, where the transition frequency is set by the correlation time of the noise. Numerical geodynamo models suggest that the correlation time is less than the convective overturn time and may be related to the lifetime of helical eddies. Applying these results to paleomagnetic estimates of the power spectrum yields a correlation time of 100 to 200 yrs. Evidence for a transition between n=0 and n=2 in paleomagnetic power spectra is interpreted as a constraint on the electrical conductivity of the core. Additional correlation times in the noise model are expected to produce a transition to n=6, possibly associated with diffusion of the dipole field through a magnetic boundary layer at the top of the core.

GENERALIZED INVESTIGATION OF THE ROTATION-ACTIVITY RELATION: FAVORING ROTATION PERIOD INSTEAD OF ROSSBY NUMBER

Magnetic activity in Sun-like and low-mass stars causes X-ray coronal emission, which is stronger for more rapidly rotating stars. This relation is often interpreted in terms of the Rossby number, i.e., the ratio of rotation period to convective overturn time. We reconsider this interpretation on the basis of the observed X-ray emission and rotation periods of 821 stars with masses below 1.4 Msun. A generalized analysis of the relation between X-ray luminosity normalized by bolometric luminosity, L_X/L_bol, and combinations of rotational period, P, and stellar radius, R, shows that the Rossby formulation does not provide the solution with minimal scatter. Instead, we find that the relation L_X/L_bol ~ P^{-2}R^{-4} optimally describes the non-saturated fraction of the stars. This relation is equivalent to L_X ~ P^{-2}, indicating that the rotation period alone determines the total X-ray emission. Since L_X is directly related to the magnetic flux at the stellar surface, this means that the surface flux is determined solely by the star's rotation and is independent of other stellar parameters. While a formulation in terms of a Rossby number would be consistent with these results if the convective overturn time scales exactly as L_bol^{-1/2}, our generalized approach emphasizes the need to test a broader range of mechanisms for dynamo action in cool stars.

Two‐stage evolution of the Earth's mantle inferred from numerical simulation of coupled magmatism‐mantle convection system with tectonic plates

AbstractSelf‐consistent numerical models are developed for a coupled magmatism‐mantle convection system with tectonic plates in a two‐dimensional rectangular box to understand the Earth's mantle evolution. The mantle evolves in two stages owing to decaying internal and basal heating, provided that the lithosphere is mechanically strong enough to inhibit spontaneous formation of new subduction zones by ridge push force. On the earlier stage that continues for the first 1–2 Gyr, the deep mantle is strongly heated, and hot materials there frequently ascend to the surface as bursts. The mantle bursts cause vigorous magmatism and make the lithosphere move chaotically. The thermostat effect of the vigorous magmatism keeps the average temperature in the upper mantle below about 1800 K no matter how strongly the mantle is heated. As the heating rate of the mantle declines, however, the mantle evolves into the later stage where mantle bursts subside, rigid tectonic plates emerge to move rather steadily, and subducted basaltic crusts accumulate on the core‐mantle boundary to form compositionally dense piles. Hot plumes occasionally ascend from the basaltic piles to cause magmatism. It takes time on the order of one billion years for the slabs that sink into the lower mantle to return back to the upper mantle, and the long overturn time makes the thermal history of the upper mantle, which has been petrologically constrained for the Earth, distinct from that of the whole mantle. The long overturn time also makes water injected into the mantle by slabs distribute heterogeneously.

E2D-ROPS: Development and tests of an automatically deployable, in height and width, front-mounted ROPS for narrow-track tractors

The main cause of death in agriculture has been the overturning of tractors lacking ROPS. Front mounted rollbars are usually foldable to be used in low clearance situations. Most fatal accidents involving tractors with foldable ROPS have occurred because, at the moment of the overturn, the ROPS was at the lower position. In this research, an automatically deployable front-mounted ROPS for narrow tractors, using airbag inflators able to increase simultaneously the height and the upper width of the ROPS, was designed, constructed and tested. The double change of the ROPS geometry reduces the continuous rolling risk, increases the safety zone in a lateral direction, and allows the ROPS height, the bending moments at critical sections and the ROPS beams sections to be reduced. This ROPS has been named ‘Ejectable in Two Dimensions ROPS’ (E2D-ROPS). Using an FE computer program, the necessary sections for E2D-ROPS to be mounted in two tractor models, ensuring a positive result for Code 6 tests, were calculated using different reference masses. An E2D-ROPS prototype was designed, constructed and mounted on a John Deere 60 C tractor. The tractor was tilted and when its lateral inclination reached 60°, an inclinometer activated two airbag inflators, located into its inclined beams, which deployed and locked the E2D-ROPS at its operative position in 102 ms. The E2D-ROPS was tested, using only one airbag inflator located into its transverse beam and was deployed and locked in 312 ms. The system works correctly because these times are lower than the overturn time.

On the possibility of a folded crustal layer stored in the hydrous mantle transition zone

Previous numerical studies of mantle convection focusing on subduction dynamics have indicated that viscosity (rheological) heterogeneity in the subducting plates and the surrounding mantle may have a primary effect on the behavior of subducting plates. Meanwhile, the existence of a low-viscosity layer (LVL) beneath the mantle transition zone (MTZ) has been suggested by several geodynamic studies. We investigated the effects of a rheologically weaker crustal layer in a hydrous (wet) MTZ with an underlying LVL on the behavior of subducting plates and determined the trace of crustal material using a numerical simulation model of subduction dynamics in three-dimensional regional spherical geometry. The combined effect of a rheologically weaker crustal layer and an LVL beneath the MTZ produces characteristic transient behavior of the crustal layer, whose trace shows a folded, loop-like feature in the wet MTZ along with a folded subducting slab in the LVL. This phenomenon is caused by mechanical interaction of the crustal layer with an upward positive bending force due to the main body of the subducting slab folding in the LVL and an enhanced downward negative buoyancy force due to an increase in density from the garnet to the post-garnet phase of crustal material. The transiently folded crustal layer behind the root of the stagnant slab is also observed. This result is consistent with seismological evidence suggesting a piece of subducted oceanic crust in the uppermost lower mantle beneath the subducting slab in the Mariana trench. Over half of the subducted crust is temporarily stored in the MTZ. However, this stored crustal material begins to penetrate into the lower mantle within 10Myr, a relatively short timeframe relative to the overturn time of mantle convection. Eventually, most of the crustal material is entrained into the lower mantle, but a non-negligible portion remains stored in the MTZ for >50Myr after the beginning of the accumulation of subducted crust in the MTZ.

Steady and fluctuating inner core rotation in numerical geodynamo models

We present a systematic survey of numerical geodynamo simulations where the inner core is allowed to differentially rotate in the longitudinal direction with respect to the mantle. We focus on the long-term behaviour of inner core rotation, on timescales much longer than the overturn time of the fluid outer core, including the steady component of rotation. The inner core is subject to viscous and magnetic torques exerted by the fluid outer core, and a gravitational restoring torque exerted by the mantle. We show that the rate of steady inner core rotation is limited by the differential rotation between spherical surfaces that the convective dynamics can sustain across the fluid outer core. We further show that this differential rotation is determined by a torque balance between the resistive Lorentz force and the Coriolis force on spherical surfaces within the fluid core. We derive a scaling law on the basis of this equilibrium suggesting that the ratio of the steady inner core rotation to typical angular velocity within the fluid core should be proportional to the square root of the Ekman number, in agreement with our numerical results. The addition of gravitational coupling does not alter this scaling, though it further reduces the amplitude of inner core rotation. In contrast, the long-term fluctuations in inner core rotation remain proportional to the fluid core angular velocity, with no apparent dependency on the Ekman number. If the same torque balance pertains to the Earth's core conditions, the inner core rotation then consists in a very slow super rotation of a few degrees per million years, superimposed over large fluctuations (at about a tenth of a degree per year). This suggests that the present-day seismically inferred inner core rotation is a fragment of a time-varying signal, rather than a steady super rotation. For the inner core rotation fluctuations not to cause excessive variations in the length-of-day, the strength of the gravitational coupling between the inner core and the mantle must be smaller than previously published values. We finally explore how the torque balance which we observe in our models could be altered in planetary cores, yielding possibly larger values of the steady rotation.

Observations and Models of the Long-Term Evolution of Earth’s Magnetic Field

The geomagnetic signal contains an enormous temporal range—from geomag- netic jerks on time scales of less than a year to the evolution of Earth's dipole moment over billions of years. This review compares observations and numerical models of the long-term range of that signal, for periods much larger than the typical overturn time of Earth's core. On time scales of 10 5 -10 9 years, the geomagnetic field reveals the control of mantle ther- modynamic conditions on core dynamics. We first briefly describe the general formalism of numerical dynamo simulations and available paleomagnetic data sets that provide insight into paleofield behavior. Models for the morphology of the time-averaged geomagnetic field over the last 5 million years are presented, with emphasis on the possible departures from the geocentric axial dipole hypothesis and interpretations in terms of core dynamics. We discuss the power spectrum of the dipole moment, as it is a well-constrained aspect of the geomagnetic field on the million year time scale. We then summarize paleosecular varia- tion and intensity over the past 200 million years, with emphasis on the possible dynamical causes for the occurrence of superchrons. Finally, we highlight the geological evolution of the geodynamo in light of the oldest paleomagnetic records available. A summary is given in the form of a tentative classification of well-constrained observations and robust numerical modeling results.

THE INTERIOR DYNAMICS OF WATER PLANETS

The ever-expanding catalog of detected super-Earths calls for theoretical studies of their properties in the case of a substantial water layer. This work considers such water planets with a range of masses and water mass fractions (2 to 5 M_Earth, 0.02% to 50% H2 O). First, we model the thermal and dynamical structure of the near-surface for icy and oceanic surfaces, finding separate regimes where the planet is expected to maintain a subsurface liquid ocean and where it is expected to exhibit ice tectonics. Newly discovered exoplanets may be placed into one of these regimes given estimates of surface temperature, heat flux, and gravity. Second, we construct a parameterized convection model for the underlying ice mantle of higher ice phases, finding that materials released from the silicate iron core should traverse the ice mantle on the timescale of 0.1 to 100 megayears. We present the dependence of the overturn times of the ice mantle and the planetary radius on total mass and water mass fraction. Finally, we discuss the implications of these internal processes on atmospheric observables.

EVIDENCE FOR MAGNETIC FLUX SATURATION IN RAPIDLY ROTATING M STARS

We present magnetic flux measurements in seven rapidly rotating M dwarfs. Our sample stars have X-ray and H-alpha emission indicative of saturated emission, i.e., emission at a high level independent of rotation rate. Our measurements are made using near-infrared FeH molecular spectra observed with HIRES at Keck. Because of their large convective overturn times, the rotation velocity of M stars with small Rossby numbers is relatively slow and does not hamper the measurement of Zeeman splitting. The Rossby numbers of our sample stars are as small as 0.01. All our sample stars exhibit magnetic flux of kilo-Gauss strength. We find that the magnetic flux saturates in the same regime as saturation of coronal and chromospheric emission, at a critical Rossby number of around 0.1. The filling factors of both field and emission are near unity by then. We conclude that the strength of surface magnetic fields remains independent of rotation rate below that; making the Rossby number yet smaller by a factor of ten has little effect. These saturated M-star dynamos generate an integrated magnetic flux of roughly 3 kG, with a scatter of about 1 kG. The relation between emission and flux also has substantial scatter.

The narrowest M-dwarf line profiles and the rotation-activity connection at very slow rotation

Context. The rotation-activity connection explains stellar activity in terms of rotation and convective overturn time. It is well established in stars of spectral types F–K as well as in M-type stars of young clusters, in which rotation is still very rapid even among M-dwarfs. The rotation-activity connection is not established in field M-dwarfs, because they rotate very slowly, and detecting rotation periods or rotational line broadening is a challenge. In field M-dwarfs, saturation sets in below vrot = 5k m s −1 , hence they are expected to populate the non-saturated part of the rotation-activity connection. Aims. This work for the first time shows intrinsically resolved spectral lines of slowly rotating M-dwarfs and makes a first comparison to estimates of convective velocities. By measuring rotation velocities in a sample of mostly inactive M-dwarfs, the unsaturated part of the rotation-activity connection is followed into the regime of very low activity. Methods. Spectra of ten M-dwarfs are taken at a resolving power of R = 200 000 at the CES in the near infrared region where molecular FeH has strong absorption bands. The intrinsically very narrow lines are compared to model calculations of convective flows, and rotational broadening is measured. Results. In one star, an upper limit of v sini = 1k m s −1 was found, significant rotation was detected in the other nine objects. All inactive stars show rotation below or equal to 2 km s −1 . In the two active stars AD Leo and YZ CMi, rotation velocities are found to be 40–50% below the results from earlier studies. Conclusions. The rotation activity connection holds in field early-M stars, too. Activity and rotation velocities of the sample stars are well in agreement with the relation found in earlier and younger stars. The intrinsic absorption profiles of molecular FeH lines are consistent with calculations from atomic Fe lines. Investigation of FeH line profiles is a very promising tool to measure convection patterns at the surfaces of M-stars.

Closed-form expressions for particle relative velocities induced by turbulence

In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times comparable to, or much longer than, the large eddy overturn time). We note that some previous studies may have adopted previous simple expressions, which we find to be in error regarding the size dependence in the large particle regime.

Supernova remnant energetics and magnetars: no evidence in favour of millisecond proto-neutron stars

Abstract It is generally accepted that anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are magnetars, i.e. neutron stars with extremely high surface magnetic fields (B > 1014 G). The origin of these high magnetic fields is uncertain, but a popular hypothesis is that magnetars are born with an initial spin period not much exceeding the convective overturn time (∼3 ms), which results in a powerful dynamo action, amplifying the seed magnetic field to ≳1015 G. Part of this rotation energy is then expected to power the supernova through rapid magnetic braking. It is therefore possible that magnetar creation is accompanied by supernovae that are an order of magnitude more energetic than normal supernovae, provided their initial spin period is ∼1 ms. However, we list here evidence that the explosion energies of these supernova remnants associated with AXPs and SGRs - Kes 73 (AXP 1E 1841-045), CTB 109 (AXP 1E2259+586) and N49 (SGR 0526-66) - are close to the canonical supernova explosion energy of 1051 erg, suggesting an initial spin period of P0≳ 5 ms. We therefore do not find evidence that magnetars are formed from rapidly rotating proto-neutron stars, allowing for the possibility that they descend from stellar progenitors with high magnetic field cores, and discuss the merits of both formation scenarios. In an appendix we describe the analysis of XMM-Newton observations of Kes 73 and N49 used to derive the explosion energies for these remnants.

The dependence of the Rossby number and XUV—Lyα emission flux with age for solar-like G-type stars

Abstract Stellar parameters of 11 G-type stars with ages ranging from 0.1 to 8.5 Gyr, from the Sun in Time programme, were used to compute the Rossby number, ℜ, for each star. The Rossby number for each star was calculated from the rotation period and the convective overturn time derived from spectral type (B−V). It was found to vary essentially as t0.5, where t is the stellar age in Gyr. The Rossby number is used as an index of X-ray—ultraviolet (XUV) (1–1200 Å) and Lyα activity, defined as the ratio of the total emission flux in these spectral regions to the total bolometric emission. Expressions for the ratio of the stellar surface XUV and Lyα emission flux relative to present mean solar surface flux values are given in terms of ℜ. It is shown that the observed activity in these stars varies as ℜ−β, where β takes values of 2.5 and 1.5 for XUV and Lyα, respectively. Expressions for deriving the Rossby number from B−V and age are also given. Thus, one can use the stellar B−V and effective temperature variation with age to calculate the XUV and Lyα emission flux relative to present solar values. As an example, the evolution of the solar XUV and Lyα with age from 0.1 to 8.5 Gyr is given. The variation of the stellar ultraviolet flux with age can be used in photochemical models to study the evolution of planetary atmospheres orbiting such stars.