D. M. Christodoulou - University of Massachusetts Lowell

D. M. Christodoulou
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D. M. Christodoulou
University of Massachusetts Lowell
United States

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Astrophysics (13)
High Energy Astrophysical Phenomena (12)
Mathematics - Analysis of PDEs (7)
Physics - Fluid Dynamics (4)
Mathematics - Mathematical Physics (3)
Mathematical Physics (3)
General Relativity and Quantum Cosmology (2)
Astrophysics of Galaxies (2)
Cosmology and Nongalactic Astrophysics (1)
Mathematics - Differential Geometry (1)
Physics - Optics (1)
Physics - Classical Physics (1)

Publications Authored By D. M. Christodoulou

The subject of this work is the shock development problem in fluid mechanics. A shock originates from an acoustically spacelike surface in spacetime at which the 1st derivatives of the physical variables blow up. The solution requires the construction of a hypersurface in spacetime which is acoustically timelike as viewed from its future, acoustically spacelike as viewed from its past, the shock hypersurface, across which the physical variables suffer discontinuities obeying jump conditions in accordance with the integral form of the particle and energy-momentum conservation laws. Read More

We have compiled a comprehensive library of all X-ray observations of Magellanic pulsars carried out by {\it XMM-Newton}, {\it Chandra}, and {\it RXTE} in the period 1997-2014. In this work, we use the data from 53 high-mass Be/X-ray binaries in the Small Magellanic Cloud to demonstrate that the distribution of spin-period derivatives vs. spin periods of spinning-down pulsars is not at all different than that of the accreting spinning-up pulsars. Read More

The recent discoveries of pulsed X-ray emission from three ultraluminous X-ray (ULX) sources have finally enabled us to recognize a subclass within the ULX class: the great pretenders, neutron stars (NSs) that appear to emit X-ray radiation at isotropic luminosities $L_X = 7\times 10^{39}$~erg~s$^{-1}-1\times 10^{41}$~erg~s$^{-1}$ only because their emissions are strongly beamed toward our direction and our sight lines are offset by only a few degrees from their magnetic-dipole axes. The three known pretenders appear to be stronger emitters than the presumed black holes of the ULX class, such as Holmberg II \& IX X-1, IC10 X-1, and NGC300 X-1. For these three NSs, we have adopted a single reasonable assumption, that their brightest observed outbursts unfold at the Eddington rate, and we have calculated both their propeller states and their surface magnetic-field magnitudes. Read More

We have collected and analyzed the complete archive of {\itshape XMM-Newton\} (116), {\itshape Chandra\} (151), and {\itshape RXTE\} (952) observations of the Small Magellanic Cloud (SMC), spanning 1997-2014. The resulting observational library provides a comprehensive view of the physical, temporal and statistical properties of the SMC pulsar population across the luminosity range of $L_X= 10^{31.2}$--$10^{38}$~erg~s$^{-1}$. Read More

The 80 high-mass X-ray binary (HMXB) pulsars that are known to reside in the Magellanic Clouds (MCs) have been observed by the XMM-Newton and Chandra X-ray telescopes on a regular basis for 15 years, and the XMM-Newton and Chandra archives contain nearly complete information about the duty cycles of the sources with spin periods P_S < 100 s. We have rerprocessed the archival data from both observatories and we combined the output products with all the published observations of 31 MC pulsars with P_S < 100 s in an attempt to investigate the faintest X-ray emission states of these objects that occur when accretion to the polar caps proceeds at the smallest possible rates. These states determine the so-called propeller lines of the accreting pulsars and yield information about the magnitudes of their surface magnetic fields. Read More

We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical solutions of the Cauchy problem are bound to oscillate about and remain close to these intrinsic solutions. The isothermal solutions are described by power-law density profiles in the radial direction, whereas the polytropic solutions are described by radial density profiles that are powers of the zeroth-order Bessel function of the first kind. Read More

In young starburst galaxies, the X-ray population is expected to be dominated by the relics of the most massive and short-lived stars, black-hole and neutron-star high mass X-ray binaries (XRBs). In the closest such galaxy, IC 10, we have made a multi-wavelength census of these objects. Employing a novel statistical correlation technique, we have matched our list of 110 X-ray point sources, derived from a decade of Chandra observations, against published photometric data. Read More

We have monitored the Cassiopeia dwarf galaxy (IC 10) in a series of 10 Chandra ACIS-S observations to capture its variable and transient X-ray source population, which is expected to be dominated by High Mass X-ray Binaries (HMXBs). We present a sample of 21 X-ray sources that are variable between observations at the 3 sigma level, from a catalog of 110 unique point sources. We find 4 transients (flux variability ratio greater than 10) and a further 8 objects with ratio > 5. Read More

{\it NuSTAR} has detected pulsations from the ultraluminous X-ray source X-2 in M82 and archival {\it Chandra} observations have given us a good idea of its duty cycle. The newly discovered pulsar exhibited at least 4 super-Eddington outbursts in the past 15 years but, in its lowest-power state, it radiates just below the Eddington limit and its properties appear to be typical of high-mass X-ray binaries. M82 X-2 has been described as a common neutron star with a 1~TG magnetic field that occasionally accretes above the Eddington rate and as a magnetar-like pulsar with a 10-100~TG magnetic field that reaches above the quantum limit. Read More

The spins of stellar-mass black holes (BHs) and the power outputs of their jets are measurable quantities. Unfortunately, the currently employed methods do not agree and the results are controversial. Two major issues concern the measurements of BH spin and beam (jet) power. Read More

Helical magnetic fields embedded in the jets of active galactic nuclei (AGNs) are required by the broad range of theoretical models that advocate for electromagnetic launching of the jets. In most models, the direction of the magnetic field is random, but if the axial field is generated by a Cosmic Battery generated by current in the direction of rotation in the accretion disk, there is a correlation between the directions of the spin of the AGN accretion disk and of the axial field, which leads to a specific direction for the axial electric current, azimuthal magnetic field, and the resulting observed transverse Faraday-rotation (FR) gradient across the jet, due to the systematic change in the line-of-sight magnetic field. We consider new observational evidence for the presence of a nested helical magnetic-field structure such as would be brought about by the operation of the Cosmic Battery, and make predictions about the expected behavior of transverse FR gradients observed on decaparsec and kiloparsec scales. Read More

By solving analytically the various types of Lane-Emden equations with rotation, we have discovered two new coupled fundamental properties of rotating, self-gravitating, gaseous disks in equilibrium: Isothermal disks must, on average, exhibit strict power-law density profiles in radius $x$ on their equatorial planes of the form $A x^{k-1}$, where $A$ and $k-1$ are the integration constants, and "flat" rotation curves precisely such as those observed in spiral galaxy disks. Polytropic disks must, on average, exhibit strict density profiles of the form $\left[\ln(A x^k)\right]^n$, where $n$ is the polytropic index, and "flat" rotation curves described by square roots of upper incomplete gamma functions. By "on average," we mean that, irrespective of the chosen boundary conditions, the actual profiles must oscillate around and remain close to the strict mean profiles of the analytic singular equilibrium solutions. Read More

The relative phasing of the X-ray eclipse ephemeris and optical radial velocity (RV) curve for the X-ray binary IC10 X-1 suggests the He[$\lambda$4686] emission-line originates in a shadowed sector of the stellar wind that avoids ionization by X-rays from the compact object. The line attains maximum blueshift when the wind is directly toward us at mid X-ray eclipse, as is also seen in Cygnus X-3. If the RV curve is unrelated to stellar motion, evidence for a massive black hole evaporates because the mass function of the binary is unknown. Read More

An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in two variables has a global $C^2$-solution for small enough initial data. Inspired by recent work of D. Read More

The general problem of shock formation in three space dimensions was solved by D. Christodoulou in his 2007 monograph: 'The Formation of Shocks in 3-dimensional Fluids'. In this work also a complete description of the maximal development of the initial data is provided. Read More

Pulsations were recently detected from the ultraluminous X-ray source X-2 in M82. The newly discovered pulsar has been described as a common neutron star with a 1 TG magnetic field that accretes above the Eddington rate and as a magnetar-like pulsar with a 100 TG magnetic field that is above the quantum limit. We show here that this X-ray source is not exotic in any sense. Read More

In the 1990's Christodoulou introduced an idealized fluid model intended to capture some of the features of the gravitational collapse of a massive star to form a neutron star or a black hole. This was the two-phase model introduced in 'Self-gravitating relativistic fluids: a two phase model', Arch. Rational Mech. Read More

We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We then consider the static case, which describes crystalline bodies in equilibrium in free space. Read More

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the initial departure from the constant state, we establish theorems which give a complete description of the maximal development. In particular, the boundary of the domain of the maximal solution contains a singular part where the inverse density of the wave fronts vanishes and the shocks form. Read More

Affiliations: 1University of Crete, 2Academy of Athens, 3NASA/GSFC, 4University of Massachusetts Lowell

Neutron-star and black-hole X-ray binaries (XRBs) exhibit radio jets, whose properties depend on the X-ray spectral state and history of the source. In particular, black-hole XRBs emit compact, steady radio jets when they are in the so-called hard state, the jets become eruptive as the sources move toward the soft state, disappear in the soft state, and re-appear when the sources return to the hard state. On the other hand, jets from neutron-star X-ray binaries are typically weaker radio emitters than the black-hole ones at the same X-ray luminosity and in some cases radio emission is detected in the soft state. Read More

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. Read More

Five planets are presently believed to orbit the primary star of 55 Cnc, but there exists a large 5 AU gap in their distribution between the two outermost planets. This gap has attracted considerable interest because it may contain one or more lower--mass planets whose existence is not contradicted by long-term orbit stability analyses, in fact it is expected according to the "packed planetary systems" hypothesis and an empirical Titius--Bode relation recently proposed for 55 Cnc. Furthermore, the second largest planet is just the second farthest and it orbits very close to the star. Read More

The subject of this work is the formation of black holes in pure general relativity, by the focusing of incoming gravitational waves. The theorems established in this monograph constitute the first foray into the long time dynamics of general relativity in the large, that is, when the initial data are no longer confined to a suitably small neighborhood of Minkowskian data. The theorems are general, no symmetry conditions on the initial data being imposed. Read More

We have derived exact solutions of the isothermal Lane--Emden equation with and without rotation in a cylindrical geometry. The corresponding hydrostatic equilibria are most relevant to the dynamics of the protosolar nebula before and during the stages of planet and satellite formation. The nonrotating solution for the mass density is analytic, nonsingular, monotonically decreasing with radius, and it satisfies easily the usual physical boundary conditions at the center. Read More

We describe the results of numerical "2.5--dimensional" MHD simulations of an initially unmagnetized disk model orbiting a central point--mass and responding to the continual generation of poloidal magnetic field due to a secular source that emulates the Poynting--Robertson (PR) drag on electrons in the vicinity of a luminous stellar or compact accreting object. The fluid in the disk and in the surrounding hotter atmosphere has finite electrical conductivity and allows for the magnetic field to diffuse freely out of the areas where it is generated, while at the same time, the differential rotation of the disk twists the poloidal field and quickly induces a substantial toroidal--field component. Read More

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 method, 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. Read More

One of the fundamental unanswered questions in the general theory of relativity is whether ``naked'' singularities, that is singular events which are visible from infinity, may form with positive probability in the process of gravitational collapse. The conjecture that the answer to this question is in the negative has been called ``cosmic censorship.'' The present paper, which is a continuation previous work, addresses this question in the context of the spherical gravitational collapse of a scalar field. Read More

We have searched the IRAS Point Source Catalog and HIRES maps for young stellar objects (YSOs) in the direction of five \HI high-velocity clouds (HVCs). In agreement with optical searches in the halo, no evidence was found for extensive star-forming activity inside the high-latitude HVCs. Specifically, we have found no signs of star formation or YSOs in the direction of the A IV cloud or in the very-high-velocity clouds HVC~110-7-465 and HVC~114-10-440. Read More

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Landau-Ginzburg theory of phase transitions. Here we examine higher than 2nd-harmonic disturbances applied to Maclaurin spheroids, the corresponding bifurcating sequences, and their relation to nonlinear fission processes. Read More

In Papers I and II, we have used a free-energy minimization approach that stems from the Landau-Ginzburg theory of phase transitions to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Here we investigate the secular and dynamical 3rd-harmonic instabilities that appear first on the Jacobi sequence of incompressible zero- vorticity ellipsoids. Poincare found a bifurcation point on the Jacobi sequence where a 3rd-harmonic mode becomes neutral. Read More

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. Read More

We have previously introduced the parameter `alpha' as an indicator of stability to m=2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous and stellar systems. This parameter can be written as a function of the total rotational kinetic energy, the total gravitational potential energy, and as a function of the topology/connectedness and the geometric shape of a system. Here we extend the stability criterion to nonaxisymmetric equilibrium systems, such as ellipsoids and elliptical disks and cylinders. Read More

We analyze previous results on the stability of uniformly and differentially rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of toroidal, m=2 Intermediate (I) 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. Read More

A free-energy minimization approach is used to address the secular & dynamical instabilities & the bifurcations along sequences of rotating, self-gravitating fluid and stellar systems. Our approach stems from the Landau-Ginzburg theory of phase transitions. We focus on the Maclaurin sequence of oblate spheroids & on the effects of second-harmonic disturbances. Read More

We construct models of highly-inclined (``polar'') rings in an external potential including both self--gravity and dissipation due to a drag force. We adopt the oblate spheroidal scale--free logarithmic potential with axis ratio $q=0.85$ and an initial inclination of 80$^\circ$ for the self--gravitating rings. Read More