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Andreas Burkert - One of the best experts on this subject based on the ideXlab platform.
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quantifying the interplay between gravity and magnetic field in molecular clouds a possible multiscale Energy equipartition in ngc 6334
Monthly Notices of the Royal Astronomical Society, 2018Co-Authors: Andreas BurkertAbstract:The interplay between gravity, turbulence and the magnetic field determines the evolution of the molecular interstellar medium (ISM) and the formation of the stars. In spite of growing interests, there remains a lack of understanding of the importance of magnetic field over multiple scales. We derive the magnetic Energy spectrum - a measure that constraints the multiscale distribution of the magnetic Energy, and compare it with the Gravitational Energy spectrum derived in Li & Burkert. In our formalism, the Gravitational Energy spectrum is purely determined by the surface density probability density distribution (PDF), and the magnetic Energy spectrum is determined by both the surface density PDF and the magnetic field-density relation. If regions have density PDFs close to P(Sigma) similar to Sigma(-2) and a universal magnetic field-density relation B similar to rho(1/2), we expect a multiscale near equipartition between gravity and the magnetic fields. This equipartition is found to be true in NGC 6334, where estimates of magnetic fields over multiple scales (from 0.1 pc to a few parsec) are available. However, the current observations are still limited in sample size. In the future, it is necessary to obtain multiscale measurements of magnetic fields from different clouds with different surface density PDFs and apply our formalism to further study the gravity-magnetic field interplay.
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probing the multiscale interplay between gravity and turbulence power law like Gravitational Energy spectra of the orion complex
Monthly Notices of the Royal Astronomical Society, 2017Co-Authors: Andreas BurkertAbstract:Gravity plays a determining role in the evolution of the molecular ISM. In 2016, we proposed a measure called Gravitational Energy spectrum to quantify the importance of gravity on multiple physical scales. In this paper, using a wavelet-based decomposition technique, we derive the Gravitational Energy spectra of the Orion A and the Orion B molecular cloud from observational data. The Gravitational Energy spectra exhibit power-law-like behaviours. From a few parsec down to similar to 0.1 pc scale, the Orion A and Orion B molecular cloud have E-p(k) similar to k(-1.88) and E-p(k) similar to k(-2.09), respectively. These scaling exponents are close to the scaling exponents of the kinetic Energy power spectrum of compressible turbulence (where E similar to k(-2)), with a near-equipartition of turbulent versus Gravitational Energy on multiple scales. This provides a clear evidence that gravity is able to counteract effectively against turbulent motion for these length-scales. The results confirm our earlier analytical estimates. For the Orion A molecular cloud, gravity inevitably dominates turbulence inside the cloud. Our results provide a clear observational proof that gravity is playing a determining role in the evolution these molecular clouds from the cloud scale down to similar to 0.1 pc. However, turbulence is likely to dominate in clouds such as California. The method is general and should be applicable to all the astrophysical problems where gravity plays a role.
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constructing multiscale Gravitational Energy spectra from molecular cloud surface density pdf interplay between turbulence and gravity
Monthly Notices of the Royal Astronomical Society, 2016Co-Authors: Andreas BurkertAbstract:Gravity is believed to be important on multiple physical scales in molecular clouds. However, quantitative constraints on gravity are still lacking. We derive an analytical formula which provides estimates on multiscale Gravitational Energy distribution using the observed surface density probability distribution function (PDF). Our analytical formalism also enables one to convert the observed column density PDF into an estimated volume density PDF, and to obtain average radial density profile rho(r). For a region with N-col similar to N-gamma N, the Gravitational Energy spectra is E-p(k) similar to k(-4(1-1/gamma N)). We apply the formula to observations of molecular clouds, and find that a scaling index of -2 of the surface density PDF implies that rho similar to r(-2) and E-p(k) similar to k(-2). The results are valid from the cloud scale (a few parsec) to around similar to 0.1 pc. Because of the resemblance the scaling index of the Gravitational Energy spectrum and the that of the kinetic Energy power spectrum of the Burgers turbulence (where E similar to k(-2)), our result indicates that gravity can act effectively against turbulence over a multitude of physical scales. This is the critical scaling index which divides molecular clouds into two categories: clouds like Orion and Ophiuchus have shallower power laws, and the amount of Gravitational Energy is too large for turbulence to be effective inside the cloud. Because gravity dominates, we call this type of cloud g-type clouds. On the other hand, clouds like the California molecular cloud and the Pipe nebula have steeper power laws, and turbulence can overcome gravity if it can cascade effectively from the large scale. We call this type of cloud t-type clouds. The analytical formula can be used to determine if gravity is dominating cloud evolution when the column density PDF can be reliably determined.
Robert B Mann - One of the best experts on this subject based on the ideXlab platform.
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momentum in general relativity local versus quasilocal conservation laws
Classical and Quantum Gravity, 2013Co-Authors: Richard J Epp, Paul L Mcgrath, Robert B MannAbstract:We construct a general relativistic conservation law for linear and angular momentum for matter and Gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic Energy conservation law with the same features (McGrath et al 2012 Class. Quantum Grav. 29 215012). Our approach uses the Brown and York (1993 Phys. Rev. D 47 1407–19) quasilocal stress–Energy–momentum tensor for matter and Gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in (Epp et al 2009 Class. Quantum Grav. 26 035015; 2012 Classical and Quantum Gravity: Theory, Analysis, and Applications (Nova Science)). The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and Gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of Gravitational Energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of Gravitational Energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes' law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner–Nordstrom black hole.
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momentum in general relativity local versus quasilocal conservation laws
arXiv: General Relativity and Quantum Cosmology, 2013Co-Authors: Richard J Epp, Paul L Mcgrath, Robert B MannAbstract:We construct a general relativistic conservation law for linear and angular momentum for matter and Gravitational fields in a finite volume of space that does not rely on any spacetime symmetries. This work builds on our previous construction of a general relativistic Energy conservation law with the same features. Our approach uses the Brown and York quasilocal stress-Energy-momentum tensor for matter and Gravitational fields, plus the concept of a rigid quasilocal frame (RQF) introduced in previous work. The RQF approach allows us to construct, in a generic spacetime, frames of reference whose boundaries are rigid (their shape and size do not change with time), and that have precisely the same six arbitrary time-dependent degrees of freedom as the accelerating and tumbling rigid frames we are familiar with in Newtonian mechanics. These RQFs, in turn, give rise to a completely general conservation law for the six components of momentum (three linear and three angular) of a finite system of matter and Gravitational fields. We compare in detail this quasilocal RQF approach to constructing conservation laws with the usual local one based on spacetime symmetries, and discuss the shortcomings of the latter. These RQF conservation laws lead to a deeper understanding of physics in the form of simple, exact, operational definitions of Gravitational Energy and momentum fluxes, which in turn reveal, for the first time, the exact, detailed mechanisms of Gravitational Energy and momentum transfer taking place in a wide variety of physical phenomena, including a simple falling apple. As a concrete example, we derive a general relativistic version of Archimedes' law that we apply to understand electrostatic weight and buoyant force in the context of a Reissner-Nordstrom black hole.
J E Pringle - One of the best experts on this subject based on the ideXlab platform.
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the accretion disc dynamo in the solar nebula
Monthly Notices of the Royal Astronomical Society, 2010Co-Authors: A R King, J E PringleAbstract:The nearest accretion disc to us in space if not time was the protosolar nebula. Remnants of this nebula thus potentially offer unique insight into how discs work. In particular the existence of chondrules, which must have formed in the disc as small molten droplets, requires strong and intermittent heating of disc material. We argue that this places important constraints on the way Gravitational Energy is released in accretion discs, which are not met by current shearing-box simulations of magnetorotational instability (MRI)-driven dynamos. A deeper understanding of accretion Energy release in discs may require a better model for these dynamos.
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the accretion disc dynamo in the solar nebula
arXiv: Solar and Stellar Astrophysics, 2010Co-Authors: A R King, J E PringleAbstract:The nearest accretion disc to us in space if not time was the protosolar nebula. Remnants of this nebula thus potentially offer unique insight into how discs work. In particular the existence of chondrules, which must have formed in the disc as small molten droplets, requires strong and intermittent heating of disc material. We argue that this places important constraints on the way Gravitational Energy is released in accretion discs, which are not met by current shearing--box simulations of MRI--driven dynamos. A deeper understanding of accretion Energy release in discs may require a better model for these dynamos.
Raffaella Schneider - One of the best experts on this subject based on the ideXlab platform.
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stochastic background of Gravitational waves generated by a cosmological population of young rapidly rotating neutron stars
Monthly Notices of the Royal Astronomical Society, 1999Co-Authors: Valeria Ferrari, S Matarrese, Raffaella SchneiderAbstract:We estimate the spectral properties of the stochastic background of Gravitational radiation emitted by a cosmological population of hot, young, rapidly rotating neutron stars. Their formation rate as a function of redshift is deduced from an observation-based determination of the star formation history in the Universe, and the Gravitational Energy is assumed to be radiated during the spin-down phase associated with the newly discovered r-mode instability. We calculate the overall signal produced by the ensemble of such neutron stars, assuming various cosmological backgrounds. We find that the spectral strain amplitude has a maximum ≈ (2-4)× 10-26Hz-1/2 , at frequencies ≈ (30-60) Hz, while the corresponding closure density, h2ΟGW, has a maximum amplitude plateau of ≈ (2.2-3.3) × 10-8 in the frequency range (500-1700) Hz. We compare our results with a preliminary analysis done by Owen et al., and discuss the detectability of this background.
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stochastic background of Gravitational waves generated by a cosmological population of young rapidly rotating neutron stars
arXiv: Astrophysics, 1998Co-Authors: Valeria Ferrari, S Matarrese, Raffaella SchneiderAbstract:We estimate the spectral properties of the stochastic background of Gravitational radiation emitted by a cosmological population of hot, young, rapidly rotating neutron stars. Their formation rate as a function of redshift is deduced from an observation-based determination of the star formation history in the Universe, and the Gravitational Energy is assumed to be radiated during the spin-down phase associated to the newly discovered r-mode instability. We calculate the overall signal produced by the ensemble of such neutron stars, assuming various cosmological backgrounds. We find that the spectral strain amplitude has a maximum $\approx (2-4)\times 10^{-26} {Hz}^{-1/2}$, at frequencies $\approx (30-60)$ Hz, while the corresponding closure density, $h^2 \Omega_{GW}$, has a maximum amplitude plateau of $\approx (2.2-3.3) \times 10^{-8}$ in the frequency range $(500-1700)$ Hz. We compare our results with a preliminary analysis done by Owen et al. (1998), and discuss the detectability of this background.
Gamal G L Nashed - One of the best experts on this subject based on the ideXlab platform.
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spherically symmetric solution in higher dimensional teleparallel equivalent of general relativity
Chinese Physics B, 2013Co-Authors: Gamal G L NashedAbstract:A theory of (N+1)-dimensional gravity is developed on the basis of the teleparallel equivalent of general relativity (TEGR). The fundamental Gravitational field variables are the (N+1)-dimensional vector fields, defined globally on a manifold M, and the Gravitational field is attributed to the torsion. The form of Lagrangian density is quadratic in torsion tensor. We then give an exact five-dimensional spherically symmetric solution (Schwarzschild (4+1)-dimensions). Finally, we calculate Energy and spatial momentum using Gravitational Energy—momentum tensor and superpotential 2-form.
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charged axially symmetric solution and Energy in teleparallel theory equivalent to general relativity
arXiv: General Relativity and Quantum Cosmology, 2007Co-Authors: Gamal G L NashedAbstract:An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity (TEGR). The associated metric has the structure function $G(\xi)=1-{\xi}^2-2mA{\xi}^3-q^2A^2{\xi}^4$. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorisable form $(1-{\xi}^2)(1+r_{+}A\xi)(1+r_{-}A\xi)$ with $r_{\pm}$ as the horizons of Reissner-Nordstr$\ddot{o}$m space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner-Nordstr$\ddot{o}$m black hole. In Calculating the Energy content of this tetrad field using the Gravitational Energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the Gravitational Energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the Energy.
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charged axially symmetric solution and Energy in teleparallel theory equivalent to general relativity
European Physical Journal C, 2007Co-Authors: Gamal G L NashedAbstract:An exact charged solution with axial symmetry is obtained in the teleparallel equivalent of general relativity. The associated metric has the structure function G(ξ)=1-ξ2-2mAξ3-q2A2ξ4. The fourth order nature of the structure function can make calculations cumbersome. Using a coordinate transformation we get a tetrad whose metric has the structure function in a factorizable form (1-ξ2)(1+r+Aξ)(1+r-Aξ) with r± as the horizons of Reissner–Nordstrom space-time. This new form has the advantage that its roots are now trivial to write down. Then, we study the singularities of this space-time. Using another coordinate transformation, we obtain a tetrad field. Its associated metric yields the Reissner–Nordstrom black hole. In calculating the Energy content of this tetrad field using the Gravitational Energy-momentum, we find that the resulting form depends on the radial coordinate! Using the regularized expression of the Gravitational Energy-momentum in the teleparallel equivalent of general relativity we get a consistent value for the Energy.
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kerr newman solution and Energy in teleparallel equivalent of einstein theory
arXiv: General Relativity and Quantum Cosmology, 2006Co-Authors: Gamal G L NashedAbstract:An exact charged axially symmetric solution of the coupled Gravitational and electromagnetic fields in the teleparallel equivalent of Einstein theory is derived. It is characterized by three parameters ``$ $the Gravitational mass $M$, the charge parameter $Q$ and the rotation parameter $a$" and its associated metric gives Kerr-Newman spacetime. The parallel vector field and the electromagnetic vector potential are axially symmetric. We then, calculate the total Energy using the Gravitational Energy-momentum. The Energy is found to be shared by its interior as well as exterior. Switching off the charge parameter we find that no Energy is shared by the exterior of the Kerr-Newman black hole.
