Engineering topics

Christodoulou, Dimitris M.

Publications and source records attributed to Christodoulou, Dimitris M..

14 records

NASA NTRS2019

Meta-Analysis of Electron Cyclotron Resonance Absorption Features Detected in High-Mass X-Ray Binaries

Using recent compilations of detailed X-ray observations and spectral models of exceptional quality, we record the electron cyclotron resonance absorption (ECRA) features that have been detected in 45 pulsating high-mass X-ray binaries (HMXBs) and ultraluminous X-ray (ULX) sources harboring neutron stars, although seven of these detections are still questionable and another 21 are single and/or not independently confirmed. From the comprehensive catalogs of Jaisawal & Naik and Staubert et al. and from several additional recent observations, we produce two lists of HMXB ECRA sources: a list of 17 sources in which multiple ECRA lines or single very low-energy lines are seen, in which we can reasonably assume that the lowest energy reveals the fundamental cyclotron level for each source; and a "contaminated" list of 38 sources including the 21 detections of single ECRA lines that may (not) be higher-level harmonics. Both lists confirm a previous result that we have obtained independently by modeling the propeller lines of Magellanic HMXB pulsars: the surface dipolar magnetic fields B * of HMXB neutron stars are segregated around five distinct values with B * = 0.28 ± 0.08, 0.55 ± 0.11, 1.3 ± 0.37, 3.0 ± 0.68 and 7.9 ± 3.1, in units of TG. However, an explanation of this phenomenon is currently lacking. We have found no correlation between these B * values and the corresponding observed spin periods, spin period derivatives, orbital periods, maximum X-ray luminosities, neutron star masses or companion star masses.

Christodoulou, Dimitris M.↗

NASA NTRS2019

Universal Expansion with Spatially Varying G

We calculate the expansion of the Universe under the assumptions that G varies in space and the radial size r of the Universe is very large (we call this the MOND regime of varying-G gravity). The inferred asymptotic behaviour turns out to be different from that found by McCrea & Milne in 1934 and our equations bear no resemblance to those of the relativistic case. In this cosmology, the scale factor R(t) increases linearly with time t, the radial velocity is driven by inertia, and gravity is incapable of hindering the expansion. Yet, Hubble’s law is borne out without any additional assumptions. When we include a repulsive acceleration a(sub de) due to dark energy, the resulting universal expansion is then driven totally by this new term and the solutions for a(sub de) → 0 do not reduce to those of the a(sub de) ≡ 0 case. This is a realization of a new Thom catastrophe: The inclusion of the new term alters the conservation of energy and the dark energy solutions are not reducible to those in the case without dark energy.

Christodoulou, Dimitris M.↗

NASA NTRS2018

Gravitational Potential and Non-relativistic Lagrangian in Modified Gravity with Varying G

We have recently shown that the baryonic Tully-Fisher (BTF) and Faber-Jackson (BFJ) relations imply that the gravitational "constant" G in the force law vary with acceleration alpha as 1/alpha . Here we derive the converse from first principles. First we obtain the gravitational potential for all accelerations and we formulate the Lagrangian for the central-force problem. Then action minimization implies the BTF/BFJ relations in the deep MOND limit as well as weak-field Weyl gravity in the Newtonian limit. The results show how we can properly formulate a nonrelativistic conformal theory of modified dynamics that reduces to MOND in its low-acceleration limit and to Weyl gravity in the opposite limit. An unavoidable conclusion is that alpha-0 , the transitional acceleration in modified dynamics, does not have a cosmological origin and it may not even be constant among galaxies and galaxy clusters.

Christodoulou, Dimitris M.↗

NASA NTRS2018

Flaring Activity from Quiescent States in Neutron-Star X-Ray Binaries

We examine systematically the observed X-ray luminosity jumps (or flares) from quiescent states in millisecond binary pulsars (MSBPs) and high-mass X-ray binary pulsars (HMXBPs). We rely on the published X-ray light curves of seven pulsars: four HMXBPs, two MSBPs and the ultraluminous X-ray pulsar M82 X-2. We discuss the physics of their flaring activities or lack thereof, paying special attention to their emission properties when they are found on the propeller line, inside the Corbet gap or near the light-cylinder barrier.We provide guiding principles for future interpretations of faint X-ray observations, as well as a method of constraining the propeller lines and the dipolar surfacemagnetic fields of pulsars using a variety of quiescent states. In the process, we clarify some disturbing inaccuracies that have made their way into the published literature.

Christodoulou, Dimitris M.↗

NASA NTRS2017

A Physical Interpretation of the Titius-Bode Rule and Its Connection to the Closed Orbits of Bertrand's Theorem

We consider the geometric Titius-Bode rule for the semimajor axes of planetary orbits. We derive an equivalent rule for the midpoints of the segments between consecutive orbits along the radial direction and we interpret it physically in terms of the work done in the gravitational field of the Sun by particles whose orbits are perturbed around each planetary orbit. On such energetic grounds, it is not surprising that some exoplanets in multiple-planet extrasolar systems obey the same relation. However, it is surprising that this simple interpretation of the Titius-Bode rule also reveals new properties of the bound closed orbits predicted by Bertrand's theorem, which has been known since 1873.

Titus-Bode rule↗

NASA NTRS2009

The Invariant Twist of Magnetic Fields in the Relativistic Jets of Active Galactic Nuclei

The origin of cosmic magnetic (B) fields remains an open question. It is generally believed that very weak primordial B fields are amplified by dynamo processes, but it appears unlikely that the amplification proceeds fast enough to account for the fields presently observed in galaxies and galaxy clusters. In an alternative scenario, cosmic B fields are generated near the inner edges of accretion disks in Active Galactic Nuclei (AGNs) by azimuthal electric currents due to the difference between the plasma electron and ion velocities that arises when the electrons are retarded by interactions with photons. While dynamo processes show no preference for the polarity of the (presumably random) seed field that they amplify, this alternative mechanism uniquely relates the polarity of the poloidal B field to the angular velocity of the accretion disk, resulting in a unique direction for the toroidal B field induced by disk rotation. Observations of the toroidal fields of 29 AGN jets revealed by parsec-scale Faraday rotation measurements show a clear asymmetry that is consistent with this model, with the probability that this asymmetry came about by chance being less than 1 %. This lends support to the hypothesis that the Universe is seeded by B fields that are generated in AGN via this mechanism

Contopoulos, Ioannis↗

NASA NTRS2002

Interchange Method in Compressible Magnetized Couette Flow: Magnetorotational and Magnetoconvective Instabilities

We obtain the general forms of the axisymmetric stability criteria in a magnetized compressible Couette flow using an energy variational principle, the so-called interchange or Chandrasekhar s met hod, which we applied successfully in the incompressible case. This formulation accounts for the simultaneous presence of gravity, rotation, a toroidal magnetic field, a weak axial magnetic field, entropy gradients, and density gradients in the initial equilibrium state. The power of the method lies in its simplicity which allows us to derive extremely compact and physically clear expressions for the relevant stability criteria despite the inclusion of so many physical effects. In the implementation of the method, all the applicable conservation laws are explicitly taken into account during the variations of a quantity with dimensions of energy which we call the free energy function. As in the incompressible case, the presence of an axial field invalidates the conservation laws of angular momentum and azimuthal magnetic flux and introduces instead isorotation and axial current conservation along field lines. Our results are therefore markedly different depending on whether an axial magnetic field is present, and generalize in two simple expressions all previously known, partial stability criteria for the appearance of magnetorotational instability. Furthermore, the coupling between magnetic tension and buoyancy and its influence to the dynamics of nonhomoentropic magnetized flows becomes quite clear from our results. In the limits of plane-parallel atmospheres and homoentropic flows, our formulation easily recovers the stability criteria for suppression of convective and Parker instabilities, as well as some related special cases studied over 40 years ago by Newcomb and Tserkovnikov via laborious variational techniques.

Christodoulou, Dimitris M.↗

NASA NTRS1995

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 1: Axisymmetric form

We analyze previous results on the stability of uniformly and differentialy rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of torodial, m = 2 intermediate or I-modes and bar modes. In the process, we demonstrate that the bar modes in stellar systems and the m = 2 I-modes in gaseous systems have many common physical characteristics and only one substantial difference: because of the anisotropy of the stress tensor, dynamical instability sets in at lower rotation in stellar systems. This difference is reflected also in the new stability criterion. The new stability parameter alpha equals (T(sub J))/(absolute value of W) is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. (T(sub J) is defined as ((L)(Omega(sub J)))/2; L is the total angular momentum; Omega(sub J) is the Jeans frequency introduced by self-gravity; and W is the total gravitational potential energy.) For stability of stellar systems alpha less than or equal to 0.254-0.258 while alpha less than or equal to 0.341-0.354 for stability of gaseous systems. For uniform rotation, one can write alpha = ((ft)/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total kinetic energy due to rotation, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. Equivalently, alpha equals t/(chi), where chi is defined as Omega/Omega(sub J) and Omega is the rotation frequency. Using these forms, alpha can be extended to and calculated for a variety of differentially rotating, gaseous and stellar, axisymmetric disk and spheroidal models whose equilibrium structures and stability characteristics are known. In this paper, we also estimate alpha for gaseous torodial models and for stellar disk systems embedded in an inert or responsive 'halo.' We find that the new stability criterion holds equally well for all these previously published axisymmetric models.

Christodoulou, Dimitris M.↗

NASA NTRS1995

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 2: Nonaxisymmetric form

We have previously introduced the parameter alpha as an indicator of stability to m = 2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous (alpha less than or approximately equal to 0.34) and stellar (alpha less than or approximately equal to 0.25) systems. This parameter can be written as alpha = (ft/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total rotational kinetic energy, W is the total gravitational potential energy, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. In this paper, we extend the stability criterion to nonaxisymmetric equilibrium systems by determining empirically the appropriate form of the function f for ellipsoids and elliptical disks and cylinders. We test the validity of this extension of the stability indicator alpha by considering its predictions for previously published, gaseous and stellar, nonaxisymmetric models. The formulation and critical values account accurately for the stability properties of m =2 modes in gaseous Riemann S-type ellipsoids (including the Jacobi and Dedekind ellipsoids) and elliptical Riemann disks as well as in stellar elliptical Freeman disks and cylinders: all these systems are dynamically stable except the stellar elliptical Freeman disks that exhibit a relatively small region of m = 2 dynamical instability. A partial disagreement in the case of stellar Freeman ellipsoids in maximum rotation may be due to the fact that the region of instability has not been previously determined with sufficient accuracy.

Christodoulou, Dimitris M.↗

NASA NTRS1995

Structural Stability and gamma-Transitions

In this work, we review some new discoveries and physical interpretations that concern the secular and dynamical instabilities and the associated structural changes in rotating, self-gravitating, incompressible fluids. For such fluids, we have been able to examine in depth and to understand physically a variety of classic results. Here we discuss the structural stability and the lambda-transitions of astrophysical fluids. We conclude with a summary of all the different types of lambda-transitions found in the course of our investigation and with a discussion of the implications of our results for superfluids, catastrophes, thermodynamical phase transitions, and the breaking of symmetry and topology.

Christodoulou, Dimitris M.↗

NASA NTRS1994

Self-gravity and dissipation in polar rings

Studies of inclined rings inside galaxy potentials have mostly considered the influence of self-gravity and viscous dissipation separately. In this study, we construct models of highly inclined ('polar') rings in an external potential including both self-gravity and dissipation due to a drag force. We do not include pressure forces and thus ignore shock heating that dominates the evolution of gaseous rings inside strongly nonspherical potentials. We adopt an oblate spheroidal scale-free logarithmic potential with axis ratio q = 0.85 and an initial inclination of 80 deg for the self-gravitating rings. We find that stellar (dissipationless) rings suffer from mass loss during their evolution. Mass loss also drives a secular change of the mean inclination toward the poles of the potential. As much as half of the ring mass escapes in the process and forms an inner and an outer shell of precessing orbits. If the remaining mass is more than approximately 0.02 of the enclosed galaxy mass, rings remain bound and do not fall apart from differential precession. The rings precess at a constant rate for more than a precession period tau(sub p) finding the configuration predicted by Sparke in 1986 which warps at larger radii toward the poles of the potential. We model shear viscosity with a velocity-dependent drag force and find that nuclear inflow dominates over self-gravity if the characteristic viscous inflow time scale tau(sub vi) is shorter than approximately 25(tau(sub p)). Rings with (tau(sub vi))/(tau(sub p)) less than or approximately equal to 25 collapse toward the nucleus of the potential within one precession period independent of the amount of self-gravity. Our results imply that stars and gas in real polar rings exhibit markedly different dynamical evolutions.

Dubinski, John↗

NASA NTRS1988

Tilted-ring models of the prolate spiral galaxies NGC 5033 and 5055

Observations of the kinematics of H I in the disks of spiral galaxies have shown that isovelocity contours often exhibit a twisted pattern. The shape of a galaxy's gravitational potential well (whether due to luminous matter or dark matter) can be determined from the direction of the twist. If this twist is a manifestation of the precession of a nonsteady-state disk, it is shown that the twists of NGC 5033 and 5055 imply an overall prolate shape, with the major axis of the potential well aligned along the rotation axis of the disk. Therefore, the luminous disks of these galaxies must be embedded in dark halos that are prolate spheroids or prolatelike triaxial figures.

Christodoulou, Dimitris M.↗

NASA NTRS1988

Star formation via the phase transition of an adiabatic gas

An analytic model based on a second-order accurate global virial analysis is used to describe two stable equilibrium states for rotating gas clouds: a pressure-supported, diffuse state and a rotationally supported, compact state. Diffuse and compact equilibrium sequences are identified along which slow, secular evolution of a gas cloud can occur. A virial analysis provides analytic expressions for the limiting masses of gas clouds at points of dynamical instability. The minimum mass below which external triggers of any amplitude cannot effectively induce star formation is identified for adiabatic gas clouds. It is suggested that fluctuations in the ISM of some galaxies may actually cause star formation to proceed primarily via a phase transition, rather than via the classical Jeans instability.

Tohline, Joel E.↗

NASA NTRS1987

The crucial role of cooling in the making of molecular clouds and stars

The role that velocity or pressure fluctuations in the H I clouds medium can play in initiating compression of sub-Jeans mass diffuse clouds is outlined. The frequently discussed idea is reviewed that substantial overpressures arising in the warm, medium and/or highly supersonic compressions of H I clouds can push sub-Jeans mass clumps to densities where gravity can take over and complete the star formation process. A nonequilibrium model is used to analyze the impact of external disturbances on gas clouds, and estimates of the required disturbance amplitudes are substantially reduced from previous estimates based on equilibrium arguments. The results reveal that a cloud which cools under compression is particularly sensitive to mild disturbances from its environment. Furthermore, the specific energy required to trigger effective compressions in a cooling medium is nearly independent of the cloud's mass. It is proposed that mildly nonlinear disturbances play a primary role in the formation of molecular cloud and stars.

Tohline, Joel E.↗