Three dimensional, axisymmetric cusps without chaos

We construct three dimensional axisymmetric, cuspy density distributions, whose potentials are of St\"ackel form in parabolic coordinates. As in Sridhar and Touma (1997), a black hole of arbitrary mass may be added at the centre, without destroying the St\"ackel form of the potentials. The construction uses a classic method, originally due to Kuzmin (1956), which is here extended to parabolic coordinates. The models are highly oblate, and the cusps are "weak", with the density, $\rho \propto 1/r^k$, where $0<k<1$.Comment: 5 pages, 2 figures, submitted to MNRA

Stellar Dynamics around Black Holes in Galactic Nuclei

We classify orbits of stars that are bound to central black holes in galactic nuclei. The stars move under the combined gravitational influences of the black hole and the central star cluster. Within the sphere of influence of the black hole, the orbital periods of the stars are much shorter than the periods of precession. We average over the orbital motion and end up with a simpler problem and an extra integral of motion: the product of the black hole mass and the semimajor axis of the orbit. Thus the black hole enforces some degree of regularity in its neighborhood. Well within the sphere of influence, (i) planar, as well as three dimensional, axisymmetric configurations-both of which could be lopsided-are integrable, (ii) fully three dimensional clusters with no spatial symmetry whatsover must have semi-regular dynamics with two integrals of motion. Similar considerations apply to stellar orbits when the black hole grows adiabatically. We introduce a family of planar, non-axisymmetric potential perturbations, and study the orbital structure for the harmonic case in some detail. In the centered potentials there are essentially two main families of orbits: the familiar loops and lenses, which were discussed in Sridhar and Touma (1997, MNRAS, 287, L1-L4). We study the effect of lopsidedness, and identify a family of loop orbits, whose orientation reinforces the lopsidedness, an encouraging sign for the construction of self-consistent models of eccentric, discs around black holes, such as in M31 and NGC 4486B.Comment: to appear in MNRAS, 10 pages, latex, 20 POstScript figure

A Path to Implement Precision Child Health Cardiovascular Medicine.

Congenital heart defects (CHDs) affect approximately 1% of live births and are a major source of childhood morbidity and mortality even in countries with advanced healthcare systems. Along with phenotypic heterogeneity, the underlying etiology of CHDs is multifactorial, involving genetic, epigenetic, and/or environmental contributors. Clear dissection of the underlying mechanism is a powerful step to establish individualized therapies. However, the majority of CHDs are yet to be clearly diagnosed for the underlying genetic and environmental factors, and even less with effective therapies. Although the survival rate for CHDs is steadily improving, there is still a significant unmet need for refining diagnostic precision and establishing targeted therapies to optimize life quality and to minimize future complications. In particular, proper identification of disease associated genetic variants in humans has been challenging, and this greatly impedes our ability to delineate gene-environment interactions that contribute to the pathogenesis of CHDs. Implementing a systematic multileveled approach can establish a continuum from phenotypic characterization in the clinic to molecular dissection using combined next-generation sequencing platforms and validation studies in suitable models at the bench. Key elements necessary to advance the field are: first, proper delineation of the phenotypic spectrum of CHDs; second, defining the molecular genotype/phenotype by combining whole-exome sequencing and transcriptome analysis; third, integration of phenotypic, genotypic, and molecular datasets to identify molecular network contributing to CHDs; fourth, generation of relevant disease models and multileveled experimental investigations. In order to achieve all these goals, access to high-quality biological specimens from well-defined patient cohorts is a crucial step. Therefore, establishing a CHD BioCore is an essential infrastructure and a critical step on the path toward precision child health cardiovascular medicine

Cusps without chaos

We present cuspy, non-axisymmetric, scale-free mass models of discs, whose gravitational potentials are of St\"ackel form in parabolic coordinates. A black hole may be added at the centre, without in any way affecting the St\"ackel form; the dynamics in these potentials is, of course, fully integrable. The surface density, $\Sigma_{disc}\propto 1/r^{\gamma}$, where $0 <\gamma < 1$ corresponds to steep cusps for which the central force diverges. Thus cusps, black holes, and non-axisymmetry are not a sure recipe for chaos, as is generally assumed. A new family of orbits, lens orbits, emerges to replace the box orbits of models of elliptical galaxies that have constant-density cores. Loop orbits are conspicuous by their absence. Both lenses and boxlets (the other family of orbits), can be elongated in the direction of the density distribution, a property that is favourable for the construction of non-axisymmetric, self-consistent equilibrium models of elliptical galaxies.Comment: 4 pages, 2 figures, submitted to MNRA

Polymerization on the Diamond Hierarchical Lattice: The Migdal-Kadanoff Renormalization-Group Scheme

The thermodynamics of the equilibrium polymerization model (grand-canonical ensemble of self-avoiding walks) in two dimensions is worked out by means of the Migdal-Kadanoff renormalization-group technique. This method involves renormalization-group flows in an eight-dimensional parameter space. At the critical point the number of relevant fields (positive exponents) is four. The leading exponent value differs by less than 1% from the (presumed) exact value. The results are exact for the polymerization problem defined on the diamond hierarchical lattice. Some results are peculiar to this lattice and are not expected to hold for Bravais lattices. For instance, the polymerized phase (infinite polymerization index) is dilute (zero density of chemical bonds)

Polymerization on the Diamond Hierarchical Lattice: The Migdal-Kadanoff Renormalization-Group Scheme

The thermodynamics of the equilibrium polymerization model (grand-canonical ensemble of self-avoiding walks) in two dimensions is worked out by means of the Migdal-Kadanoff renormalization-group technique. This method involves renormalization-group flows in an eight-dimensional parameter space. At the critical point the number of relevant fields (positive exponents) is four. The leading exponent value differs by less than 1% from the (presumed) exact value. The results are exact for the polymerization problem defined on the diamond hierarchical lattice. Some results are peculiar to this lattice and are not expected to hold for Bravais lattices. For instance, the polymerized phase (infinite polymerization index) is dilute (zero density of chemical bonds)

Interaction of massive black hole binaries with their stellar environment: II. Loss-cone depletion and binary orbital decay

We study the long-term evolution of massive black hole binaries (MBHBs) at the centers of galaxies using detailed scattering experiments to solve the full three-body problem. Ambient stars drawn from a isotropic Maxwellian distribution unbound to the binary are ejected by the gravitational slingshot. We construct a minimal, hybrid model for the depletion of the loss cone and the orbital decay of the binary, and show that secondary slingshots - stars returning on small impact parameter orbits to have a second super-elastic scattering with the MBHB - may considerably help the shrinking of the pair in the case of large binary mass ratios. In the absence of loss-cone refilling by two-body relaxation or other processes, the mass ejected before the stalling of a MBHB is half the binary reduced mass. About 50% of the ejected stars are expelled ejected in a "burst" lasting ~1E4 yrs M_6^1/4, where M_6 is the binary mass in units of 1E6 Msun. The loss cone is completely emptied in a few bulge crossing timescales, 1E7 yrs M_6^1/4. Even in the absence of two-body relaxation or gas dynamical processes, unequal mass and/or eccentric binaries with M_6 >0.1 can shrink to the gravitational wave emission regime in less than a Hubble time, and are therefore "safe" targets for the planned Laser Interferometer Space Antenna (LISA).Comment: Minor revision. 10 pages, 7 figures, ApJ in pres

Unstable Disk Galaxies. II. the Origin of Growing and Stationary Modes

I decompose the unstable growing modes of stellar disks to their Fourier components and present the physical mechanism of instabilities in the context of resonances. When the equilibrium distribution function is a non-uniform function of the orbital angular momentum, the capture of stars into the corotation resonance imbalances the disk angular momentum and triggers growing bar and spiral modes. The stellar disk can then recover its angular momentum balance through the response of non-resonant stars. I carry out a complete analysis of orbital structure corresponding to each Fourier component in the radial angle, and present a mathematical condition for the occurrence of van Kampen modes, which constitute a continuous family. I discuss on the discreteness and allowable pattern speeds of unstable modes and argue that the mode growth is saturated due to the resonance overlapping mechanism. An individually growing mode can also be suppressed if the corotation and inner Lindblad resonances coexist and compete to capture a group of stars. Based on this mechanism, I show that self-consistent scale-free disks with a sufficient distribution of non-circular orbits should be stable under perturbations of angular wavenumber $m>1$. I also derive a criterion for the stability of stellar disks against non-axisymmetric excitations.Comment: 15 Pages (emulateapj), 7 Figures, Accepted for Publication in The Astrophysical Journa