Massive Iron Cores Research Articles

Characterizing the possible interior structures of the nearby Exoplanets Proxima Centauri b and Ross-128 b

ABSTRACT We developed a new numerical model to constrain the interior structure of rocky Exoplanets, and applied it to the nearby planets Proxima Centauri b and Ross-128 b. The recently measured elemental abundances of red dwarfs and Alpha Centauri were utilized to infer the bulk composition of each planet, and to measure their core mass fractions (CMFs). The results of our model predicted that the radius of Proxima b at its minimum mass may be 1.036 ± 0.040 R⊕, and if its mass is as high as 2 M⊕, 1.170 ± 0.040 R⊕. The radius of Ross-128 b at minimum mass may be 1.034 ± 0.040 R⊕, with its radius at an upper bound mass of 2 M⊕ being 1.150 ± 0.040 R⊕. Both planets may have thin mantles with similar conditions to Earth, but not convecting as vigorously. The CMFs might lie in the ranges of 20–59 per cent and 34–59 per cent for Proxima b and Ross-128 b, respectively, making it very likely they have massive iron cores. Their central temperatures may be high enough to partially melt the cores, and possibly generate magnetic fields. If they have magnetic fields at present, they are most likely to be multipolar in nature due to slow rotation speeds resulting from stellar tidal effects. The field strengths were predicted to have values of 0.06–0.23 G for Proxima b, and 0.07–0.14 G for Ross-128 b. If either planet contains more than 10 per cent of their mass in volatiles, magnetic fields would either be non-existent or very weak. The conditions of both planets may be hostile for habitability.

On the minimum mass of neutron stars

We investigate remnant neutron star masses (in particular, the minimum allowed mass) by performing advanced stellar evolution calculations and neutrino-radiation hydrodynamics simulations for core-collapse supernova explosions. We find that, based on standard astrophysical scenarios, low-mass carbon-oxygen cores can have sufficiently massive iron cores that eventually collapse, explode as supernovae, and give rise to remnant neutron stars that have a minimum mass of 1.17 M⊙ – compatible with the lowest mass of the neutron star precisely measured in a binary system of PSR J0453+1559.

Sound isolation of large transformers mounted on raised floors

Transformers for substation service mounted on elevated floors often cause spurious sound to be transmitted to the spaces below it. Magnetostriction vibration of the massive iron core at 120 Hz and its harmonics drives the supporting floor to emit sound into the spaces below. Contemporary vibration isolation design fails to prescribe the proper isolation method since the mass of that transformer considerably exceeds that of the participating mass of the concrete floor. A vibration isolation paradigm is proposed of a two-body system in inertial space; the participating mass of the concrete floor being the second active body; the virtual mass of the pair along with the spring stiffness determines the resonance frequency. The ratio of that resonant frequency to that to be isolated is a measure of the expected isolation. For good isolation, the resonant frequency should be 1/10th that of the vibration to be isolated. The floor participating mass is approximated as a square one-half wavelength of the thin conc...

Shrinking wrinkling Mercury

As Mercury's interior cools and its massive iron core freezes, its surface feels the squeeze. A comprehensive global census of compressional deformation features indicates that Mercury has shrunk by at least 5 km in radius over the past 4 billion years.

Extension and optimization of the load range of DRT test systems for testing extra-long HV and UHV cables

In the last few years, the demand for testing extra-long cables, such as submarine cables has grown rapidly. The existing testing methods have been complemented by a new testing technology called DRT (Differential Resonance Technology). This testing method enables testing of extra-long cables by comparably small and light-weight equipment using a low frequency for the test voltage, e.g. 0.1 Hz up to 5 Hz. This leads to a significant decrease of the required power of the test source (P. Mohaupt and A. Bergman in CIGRE 2010). In a resonant circuit only the losses of the generator’s individual components, specifically the high voltage reactor, have to be covered by the mains. The testing power itself remains fully compensated. Typical ratios between the testing power and the input power of resonant test systems start at 50 and go up to 100, depending on the load. Unfortunately, voltage generation based on inductive generation principles such as resonant circuits cannot economically be used for frequencies below 10 Hz due to the massive iron cores needed for such a low frequency. The DRT method for the generation of low frequency high voltage is based on a high frequency voltage whose amplitude is modulated by the desired low frequency. Using a resonator, which is tuned to the high frequency, and a demodulator, the desired low frequency high voltage can be generated (P. Mohaupt and A. Bergman in CIGRE 2010; P. Mohaupt and T. Mehl in Jicable 2011). The input power required—and in direct relation to this the size and weight of the equipment—is significantly smaller than for other existing methods. In order to optimize the operation performance of the DRT system, this paper describes mathematical methods and algorithms, which have already been implemented and tested in a DRT test set. The basis for these algorithms is a mathematical description of the system based on an envelope model. Using this mathematical description of the nonlinear system behavior, a systematic analysis of the performance and the limits of the system can be given. The theoretical approach was experimentally proven by measuring the output voltage and the input power of a prototype unit ultimately designed to produce 200 kV rms. A first test was performed at SP Technical Research Institute of Sweden, using their reference measurement system for very low frequency (VLF) S. Bergman and A. Bergman (Proc. CPEM Conf. Dig., pp. 682–683, 2010; IEEE Trans. Instrum. Meas. 60:2422–2426, 2011) to measure the high VLF voltage. The reference measurement system provides a traceable uncertainty of down to 0.04 % over a voltage range up to 200 kV rms. The frequency range of the reference system is from 0.1 Hz up to 50 Hz. This system permits acquisition of complete wave-forms that can be analysed for harmonic content and/or THD (Total Harmonic Distortion). Further tests are planned, where the connected load will be increased to the specified maximum 1 μF at 200 kV, and the characteristics will be explored both as regards to output voltage quality, input power requirements and distortion on the input current.

The Most Massive Core‐Collapse Supernova Progenitors

The discovery of the extremely luminous supernova SN 2006gy, possibly interpreted as a pair instability supernova, renewed the interest in very massive stars. We explore the evolution of these objects, which end their life as pair instability supernovae or as core collapse supernovae with relatively massive iron cores, up to about $3 M_\odot$.

Around the Pair Instability Valley – Massive SN Progenitors

AbstractThe discovery of the extremely luminous supernova SN 2006gy, possibly interpreted as a pair instability supernova, renewed the interest in very massive stars. We explore the evolution of these objects, which end their life as pair instability supernovae or as core collapse supernovae with relatively massive iron cores, up to about 3 M⊙.

Numerical Study of Stellar Core Collapse and Neutrino Emission: Probing the Spherically Symmetric Black Hole Progenitors with 3–30M⊙Iron Cores

The existence of various anomalous stars, such as the first stars in the universe or stars produced by stellar mergers, has been recently proposed. Some of these stars will result in black hole formation. In this study, we investigate iron core collapse and black hole formation systematically for the iron-core mass range of 3 - 30Msun, which has not been studied well so far. Models used here are mostly isentropic iron cores that may be produced in merged stars in the present universe but we also employ a model that is meant for a Population III star and is obtained by evolutionary calculation. We solve numerically the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail under spherical symmetry. As a result, we find that massive iron cores with ~10Msun unexpectedly produce a bounce owing to the thermal pressure of nucleons before black hole formation. The features of neutrino signals emitted from such massive iron cores differ in time evolution and spectrum from those of ordinary supernovae. Firstly, the neutronization burst is less remarkable or disappears completely for more massive models because the density is lower at the bounce. Secondly, the spectra of neutrinos, except the electron type, are softer owing to the electron-positron pair creation before the bounce. We also study the effects of the initial density profile, finding that the larger the initial density gradient is, the more steeply the neutronization burst declines. Further more, we suggest a way to probe into the black hole progenitors from the neutrino emission and estimate the event number for the currently operating neutrino detectors.

Axisymmetric collapse simulations of rotating massive stellar cores in full general relativity: Numerical study for prompt black hole formation

We perform axisymmetric simulations for gravitational collapse of a massive iron core to a black hole in full general relativity. The iron cores are modeled by $\ensuremath{\Gamma}=4/3$ equilibrium polytrope for simplicity. The hydrodynamic equations are solved using a high-resolution shock-capturing scheme with a parametric equation of state. The Cartoon method is adopted for solving the Einstein equations. Simulations are performed for a wide variety of initial conditions changing the mass ($\ensuremath{\approx}2.0--3.0{M}_{\ensuremath{\bigodot}}$), the angular momentum, the rotational velocity profile of the core, and the parameters of the equations of state which are chosen so that the maximum mass of the cold spherical polytrope is $\ensuremath{\approx}1.6{M}_{\ensuremath{\bigodot}}$. Then, the criterion for the prompt black hole formation is clarified in terms of the mass and the angular momentum for several rotational velocity profile of the core and equations of state. It is found that (i) with the increase of the thermal energy generated by shocks, the threshold mass for the prompt black hole formation is increased by 20--40%, (ii) the rotational centrifugal force increases the threshold mass by $\ensuremath{\lesssim}25%$, (iii) with the increase of the degree of differential rotation, the threshold mass is also increased, and (iv) the amplification factors shown in the results (i)--(iii) depend sensitively on the equation of state. We also find that the collapse dynamics and the structure of the shock formed at the bounce depend strongly on the stiffness of the adopted equation of state. In particular, as a new feature, a strong bipolar explosion is observed for the collapse of rapidly rotating iron cores with an equation of state which is stiff in subnuclear density and soft in supranuclear density. Gravitational waves are computed in terms of a quadrupole formula. It is also found that the waveform depends sensitively on the equations of state.

Dynamic model of an electromagnetic massive core brake actuator

A dynamic model has been developed for the simulation of transient behavior of the disk axial motion in a cylindrical massive iron core electromagnetic brake comprising dc excitation. The model is based on magnetic and electric equivalent circuits of iron core. The flux and the eddy current distribution in the massive iron core are described by coaxial shells. Within each shell, uniform current and flux distribution are assumed. Lumped parameters are used for the evaluation of reluctances. The transient problem is solved in two steps. First, two sets of steady-state solutions are solved by iteration-one following a rising, and the other a falling magnetization curve. In the second step, the equivalent coil, the magnetic and eddy current circuits, and the mechanical system are expressed in a state variable form and analyzed with a general-purpose simulation program. Simulated transients during magnetization and demagnetization are compared to experimental results. The model is suitable for educational and commercial purposes.

The electromagnetic levitation and guidance technology of the 'transrapid' test facility Emsland

A large scale test facility for the high speed ground transportation system TRANSRAPID has been built in Emsland. In the near future this test facility will show the economic feasibility of such a system. An essential component of this system is the magnetic levitation and guidance system of the vehicle. The requirements on this suspension system are: good ride comfort, high reliability and low operating costs. The elements of the suspension system are controlled cross field electromagnets with massive iron cores and rails for guidance and controlled longitudinal field magnets with a laminated iron core and rail for levitation. The reason for lamination is the combination of three operating tasks in the levitation magnets. These are: levitation, propulsion, and inductive power transfer to the vehicle. These magnets generate the exciting field of the synchronous linear motor. Due to these tasks the theoretical model for a levitation magnet has to be expanded in order to be able to describe these effects in dynamic simulations. The mechanical and the electrical structure of the suspension system must have several redundancies in order to get a high overall safety.

Calculation of frequency responses of electro-magnetic levitation magnets

As all EMS-vehicle magnets of the Transrapid family have heretofore been equipped with massive iron cores acting on massive armature rails eddy currents due to varying coil currents and air gaps must be taken into account if force (F) and current (J) have to be calculated correctly. A method is presented which allows their calculation for infinitely small harmonic voltage (dV) and gap variations (dG). In this case we have a linear problem to solve. We establish a two dimensional model of the magnet which contains the essential data of the magnet (air gap, pole width, amp.turns, average length of force lines) and which can be solved by simple fourier series expansion. In order to fit the results for frequency zero to experimental or theoretical force characteristics, we define the two relative permeabilities <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu_{r}= B/(H cdot \mu_{o})</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu_{a} = dB/(dH \cdot \mu_{o})</tex> which are calculated by fitting F(J,G) and dF/dJ at the operating point. Although these frequency responses are only the basis for a parameter identification method for a given electro-mechanical structure of a magnet, we get good results for force variation and power consumption of the magnet if the amplitudes of voltage and gap variations are not too large.