arXiv subjects

J. An

Publications and source records attributed to J. An.

At least 37 records · Page 2Linked to original sources

arXiv2013

When is an axisymmetric potential separable?

An axially symmetric potential psi(R,z)=psi(r,theta) is completely separable if the ratio s:k is constant. Here r*s=d^2(r^2*psi)/dr/d(theta) and k=d^2(psi)/dR/dz. If beta=s/k, then the potential admits an integral of the form of I=(L^2+beta*v_z^2)/2+xi where xi is some function of positions determined by the potential psi. More generally, an axially symmetric potential respects the third axisymmetric integral of motion -- in addition to the classical integrals of the Hamiltonian and the axial component of the angular momentum -- if there exist three real constants a,b,c (not all simultaneously zero, a^2+b^2+c^2>0) such that a*s+b*h+c*k=0 where r*h=d^2(r*psi)/d(sigma)/d(tau) and (sigma,tau) is the parabolic coordinate in the meridional plane such that sigma^2=r+z and tau^2=r-z.

astro-ph.GA↗

arXiv2012

Fitting functions for dark matter density profiles

We present a unified parameterization of the fitting functions suitable for density profiles of dark matter haloes or elliptical galaxies. A notable feature is that the classical Einasto profile appears naturally as the continuous limiting case of the cored subfamily amongst the double power-law profiles of Zhao (1996). Based on this, we also argue that there is basically no qualitative difference between halo models well-fitted by the Einasto profile and the standard NFW model. This may even be the case quantitatively unless the resolutions of simulations and the precisions of fittings are sufficiently high to make meaningful distinction possible.

astro-ph.CO↗

arXiv2012

Phase-space consistency of stellar dynamical models determined by separable augmented densities

Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditions the distribution constructed as such is in fact non-negative everywhere in the accessible phase-space. We first generalize known necessary conditions on the augmented density using fractional calculus. The condition on the radius part R(r^2) (whose logarithmic derivative is the anisotropy parameter) is equivalent to the complete monotonicity of R(1/w)/w. The condition on the potential part on the other hand is given by its derivative up to any order not greater than (3/2-beta) being non-negative where beta is the central anisotropy parameter. We also derive a specialized inversion formula for the distribution from the separable augmented density, which leads to sufficient conditions on separable augmented densities for the non-negativity of the distribution. The last generalizes the similar condition derived earlier for the generalized Cuddeford system to arbitrary separable systems.

astro-ph.CO↗

arXiv2012

Fractional calculus, completely monotonic functions, a generalized Mittag-Leffler function and phase-space consistency of separable augmented densities

Under the separability assumption on the augmented density, a distribution function can be always constructed for a spherical population with the specified density and anisotropy profile. Then, a question arises, under what conditions the distribution constructed as such is non-negative everywhere in the entire accessible subvolume of the phase-space. We rediscover necessary conditions on the augmented density expressed with fractional calculus. The condition on the radius part R(r^2) -- whose logarithmic derivative is the anisotropy parameter -- is equivalent to R(1/w)/w being a completely monotonic function whereas the condition on the potential part is stated as its derivative up to the order not greater than 3/2-b being non-negative (where b is the central limiting value for the anisotropy parameter). We also derive the set of sufficient conditions on the separable augmented density for the non-negativity of the distribution, which generalizes the condition derived for the generalized Cuddeford system by Ciotti & Morganti to arbitrary separable systems. This is applied for the case when the anisotropy is parameterized by a monotonic function of the radius of Baes & Van Hese. The resulting criteria are found based on the complete monotonicity of generalized Mittag-Leffler functions.

math-ph↗

arXiv2011

Mass estimators in the Gaia era

Forthcoming astrometric missions such as the Gaia satellite will bring to the fore the problem of estimating the enclosed mass from a set of positions, radial velocities and proper motions of tracer stars. Here, we show how to construct the tracer mass estimator when the proper motion data are available in addition to the usual line-of-sight velocity data. Notably, the mass estimators do not require any assumption on the anisotropy, as it is naturally incorporated through the different components of proper motions. In addition, the separate treatment of the proper motions and the line-of-sight velocities is desirable because they are observationally independent and thus the propagation of the combined uncertainties is rather straightforward. The extension to projected data is also sketched, together with a possible application of measuring the masses of Galactic globular clusters.

astro-ph.GA↗

arXiv2011

OGLE-2008-BLG-513Lb: The Orbital Solution for a Microlensing Planet

A static binary star solution for OGLE-2008-BLG-513 has been found. The mass ratio and separation for this solution are q~0.28, s~0.86. This model has a chi^2 comparable to the chi^2 of the model with a planetary mass ratio and orbital motion that was presented in this paper. Because the model with a static, binary star lens is simpler than the model originally presented in this paper, Occam's Razor says it is likely to be the correct solution. Consequently, this paper has been withdrawn from ApJ.

astro-ph.EP↗

arXiv2011

Constraints on velocity anisotropy of spherical systems with separable augmented densities

If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy parameter alone, also fixes the anisotropic ratios of every higher-order velocity moment. It is inferred from this that the non-negativity of the distribution function necessarily limits the allowed behaviors of the radial function. This restriction is translated into the constraints on the behavior of the anisotropy parameter. We find that not all radial variations of the anisotropy parameter satisfy these constraints and thus that there exist anisotropy profiles that cannot be consistent with any separable augmented density.

astro-ph.CO↗

arXiv2011

MOA-2009-BLG-387Lb: A massive planet orbiting an M dwarf

We report the discovery of a planet with a high planet-to-star mass ratio in the microlensing event MOA-2009-BLG-387, which exhibited pronounced deviations over a 12-day interval, one of the longest for any planetary event. The host is an M dwarf, with a mass in the range 0.07 M_sun < M_host < 0.49M_sun at 90% confidence. The planet-star mass ratio q = 0.0132 +- 0.003 has been measured extremely well, so at the best-estimated host mass, the planet mass is m_p = 2.6 Jupiter masses for the median host mass, M = 0.19 M_sun. The host mass is determined from two "higher order" microlensing parameters. One of these, the angular Einstein radius θ_E = 0.31 +- 0.03 mas, is very well measured, but the other (the microlens parallax π_E, which is due to the Earth's orbital motion) is highly degenate with the orbital motion of the planet. We statistically resolve the degeneracy between Earth and planet orbital effects by imposing priors from a Galactic model that specifies the positions and velocities of lenses and sources and a Kepler model of orbits. The 90% confidence intervals for the distance, semi-major axis, and period of the planet are 3.5 kpc < D_L < 7.9 kpc, 1.1 AU < a < 2.7AU, and 3.8 yr < P < 7.6 yr, respectively.

astro-ph.EP↗

arXiv2011

Accurate Masses for Navarro-Frenk-White Dark Matter Haloes

We consider the problem of estimating the virial mass of a dark halo from the positions and velocities of a tracer population. Although a number of general tools are available, more progress can be made if we are able to specify the functional form of the halo potential (although not its normalization). Here, we consider the particular case of the cosmologically motivated Navarro-Frenk-White (NFW) halo and develop two simple estimators. We demonstrate their effectiveness against numerical simulations and use them to provide new mass estimates of Carina, Fornax, Sculptor, and Sextans dSphs.

astro-ph.CO↗

arXiv2010

On the augmented density of a spherical anisotropic dynamic system

This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that the partial derivatives of the Abel transformations of the augmented density must be non-negative. Applied for the separable augmented densities, this recovers the result of van Hese et al. (2011).

math-ph↗

arXiv2010

Modified Virial Formulae and the Theory of Mass Estimators

We show how to estimate the enclosed mass from the observed motions of an ensemble of test particles. Traditionally, this problem has been attacked through virial or projected mass estimators. Here, we examine and extend these systematically, and show how to construct an optimal estimator for any given assumption as to the potential. The estimators do not explicitly depend on any properties of the density of the test objects, which is desirable as in practice such information is dominated by selection effects. As particular examples, we also develop estimators tailored for the problem of estimating the mass of the Hernquist or NFW dark matter haloes from the projected positions and velocities of stars.

astro-ph.CO↗

arXiv2010

The Masses of the Milky Way and Andromeda galaxies

We present a family of robust tracer mass estimators to compute the enclosed mass of galaxy haloes from samples of discrete positional and kinematical data of tracers, such as halo stars, globular clusters and dwarf satellites. The data may be projected positions, distances, line of sight velocities or proper motions. Forms of the estimator tailored for the Milky Way galaxy and for M31 are given. Monte Carlo simulations are used to quantify the uncertainty as a function of sample size. For the Milky Way, the satellite sample consists of 26 galaxies with line-of-sight velocities. We find that the mass of the Milky Way within 300 kpc is ~ 0.9 x 10^12 solar masses assuming velocity isotropy. However, the mass estimate is sensitive to the anisotropy and could plausibly lie between 0.7 - 3.4 x 10^12 solar masses. Incorporating the proper motions of 6 Milky Way satellites into the dataset, we find ~ 1.4 x 10^12 solar masses. The range here if plausible anisotropies are used is still broader, from 1.2 - 2.7 x 10^12 solar masses. For M31, there are 23 satellite galaxies with measured line-of-sight velocities, but only M33 and IC 10 have proper motions. We use the line of sight velocities and distances of the satellite galaxies to estimate the mass of M31 within 300 kpc as ~ 1.4 x 10^12 solar masses assuming isotropy. There is only a modest dependence on anisotropy, with the mass varying between 1.3 -1.6 x 10^12 solar masses. Given the uncertainties, we conclude that the satellite data by themselves yield no reliable insights into which of the two galaxies is actually the more massive.

astro-ph.GA↗

arXiv2009

The Tilt of the Halo Velocity Ellipsoid and the Shape of the Milky Way Halo

A sample of roughly 1,800 halo subdwarf stars with radial velocities and proper motions is assembled, using the repeated multi-band Sloan Digital Sky Survey photometric measurements in Stripe 82. Our sample of halo subdwarfs is extracted via a reduced proper motion diagram and distances are obtained using photometric parallaxes, thus giving full phase space information. The tilt of the velocity ellipsoid with respect to the spherical polar coordinate system is computed and found to be consistent with zero for two of the three tilt angles, and very small for the third. We prove that if the inner halo is in a steady-state and the triaxial velocity ellipsoid is everywhere aligned in spherical polar coordinates, then the potential must be spherically symmetric. The detectable, but very mild, misalignment with spherical polars is consistent with the perturbative effects of the Galactic disk on a spherical dark halo. Banana orbits are generated at the 1:1 resonance (in horizontal and vertical frequency) by the disk. They populate Galactic potentials at the typical radii of our subdwarf sample, along with the much more dominant short-axis tubes. However, on geometric grounds alone, the tilt cannot vanish for the banana orbits and this leads to a slight, but detectable, misalignment. We argue that the tilt of the stellar halo velocity ellipsoid therefore provides a hitherto largely neglected but important line of argument that the Milky Way's dark halo, which dominates the potential, must be nearly spherical.

astro-ph.GA↗

arXiv2008

Cores and Cusps in the Dwarf Spheroidals

We consider the problem of determining the structure of the dark halo of nearby dwarf spheroidal galaxies (dSphs) from the spherical Jeans equations. Whether the dark halos are cusped or cored at the centre is an important strategic problem in modern astronomy. The observational data comprise the line-of-sight velocity dispersion of a luminous tracer population. We show that when such data are analysed to find the dark matter density with the spherical Poisson and Jeans equations, then the generic solution is a dark halo density that is cusped like an isothermal. Although milder cusps (like the Navarro-Frenk-White 1/r cusp and even cores are possible, they are not generic. Such solutions exist only if the anisotropy parameter beta and the logarithmic slope of the stellar density gamma satisfy the constraint gamma = 2 x beta at the centre or if the radial velocity dispersion falls to zero at the centre. This surprisingly strong statement is really a consequence of the assumption of spherical symmetry, and the consequent coordinate singularity at the origin. So, for example, a dSph with an exponential light profile can exist in Navarro-Frenk- White halo and have a flat velocity dispersion, but anisotropy in general drives the dark halo solution to an isothermal cusp. The identified cusp or core is therefore a consequence of the assumptions (particularly of spherical symmetry and isotropy), and not the data.

astro-ph↗

arXiv2008

Electronic Structure, Magnetism and Superconductivity of Layered Iron Compounds

The layered iron superconductors are discussed using electronic structure calculations. The four families of compounds discovered so far, including Fe(Se,Te) have closely related electronic structures. The Fermi surface consists of disconnected hole and electron cylinders and additional hole sections that depend on the specific material. This places the materials in proximity to itinerant magnetism, both due to the high density of states and due to nesting. Comparison of density functional results and experiment provides strong evidence for itinerant spin fluctuations, which are discussed in relation to superconductivity. It is proposed that the intermediate phase between the structural transition and the SDW transition in the oxy-pnictides is a nematic phase.

cond-mat.supr-con↗

arXiv2008

On Multiple Einstein Rings

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurrence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-plane lensing. Surprisingly, we show that it is possible for a single source to produce more than one Einstein ring. If two point masses (or two isothermal spheres) in different planes are aligned with observer and source on the optical axis, we show that there are up to three Einstein rings. We also discuss the image morphologies for these two models if axisymmetry is broken, and give the first instances of magnification invariants in the case of two lens planes.

astro-ph↗

arXiv2006

The Chang-Refsdal Lens Revisited

This paper provides a complete theoretical treatment of the point-mass lens perturbed by constant external shear, often called the Chang-Refsdal lens. We show that simple invariants exist for the products of the (complex) positions of the four images, as well as moment sums of their signed magnifications. The image topographies and equations of the caustics and critical curves are also studied. We derive the fully analytic expressions for precaustics, which are the loci of non-critical points that map to the caustics under the lens mapping. They constitute boundaries of the region in the image domain that maps onto the interior of the caustics. The areas under the critical curves, caustics and precaustics are all evaluated, which enables us to calculate the mean magnification of the source within the caustics. Additionally, the exact analytic expression for the magnification distribution for the source in the triangular caustics is derived, as well as a useful approximate expression. Finally, we find that the Chang-Refsdal lens with the convergence greater than unity can exhibit third-order critical behaviour, if the reduced shear is exactly equal to \sqrt{3}/2, and that the number of images for N-point masses with non-zero constant shear cannot be greater than 5N-1.

astro-ph↗

arXiv2006

A Cusp Slope -- Central Anisotropy Theorem

For a wide class of self-gravitating systems, we show that if the density is cusped like 1/r^{gamma} near the center, then the limiting value of the anisotropy parameter beta = 1 - /(2 ) at the center may not be greater than (gamma/2). Here, and are the radial and tangential velocity second moments. This follows from the non-negativity of the phase space density. We compare this theorem to other proposed relations between the cusp slope and the central anisotropy to clarify their applicabilities and underlying assumptions. The extension of this theorem to tracer populations in an externally imposed potential is also derived. In particular, for stars moving in the vicinity of a central black hole, this reduces to gamma >= beta+(1/2), indicating that an isotropic system in Keplerian potential should be cusped at least as steep as 1/r^{0.5}. Similar limits have been noticed before for specific forms of the distribution function, but here we establish this as a general result.

astro-ph↗