arXiv subjects

James Binney

Publications and source records attributed to James Binney.

At least 19 recordsLinked to original sources

arXiv2026

Distribution functions for spheroids

Galaxy models comprising several components (including dark matter) that are bound by the self-consistently generated gravitational field are readily constructed from distribution functions (DFs) that are analytic functions of the action integrals J. We explain why such models have unphysical velocity distributions unless the DFs of hot components satisfy certain conditions as J_\phi -> 0. We show how DFs for both isotropic and radially biased spherical systems can be constructed with specified f(J). We show how to construct DFs for flattened systems with significant velocity anisotropy. Construction of self-consistent models rather than populations that are confined by an external potential leads to the conclusion that radially-biased spherical systems are generically unstable to quadrupolar perturbations. Chaos is likely key to maintenance of these constraints during adiabatic disc growth.

astro-ph.GA↗

arXiv2025

A New Torus Generator for AGAMA

Code is presented that computes and exploits orbital tori for any axisymmetric gravitational potential. The code is a development of the AGAMA software package for action-based galaxy modelling and can be downloaded as the AGAMAb code library. Although coded in C++, most of its functions can be accessed from Python. We add to the package functions that facilitate confronting models with data, which involve sky coordinates, lines of sight, distances, extinction, etc. The new torus generator can produce tori for both highly eccentric and nearly circular orbits that lie beyond the range of the earlier torus-mapping code. Tori can be created by interpolation between tori at very low cost. Tori are fundamentally devices for computing ordinary phase-space coordinates from angle-action coordinates, but AGAMAb includes an action finder that returns angle-action coordinates from any given phase-space location. This action finder yields the torus through the given point, so it includes the functionality of an orbit integrator. The action finder is more accurate and reliable but computationally more costly than the widely used Staeckel Fudge. We show how AGAMAb can be used to generate sophisticated but cheap models of tidal streams and use it to analyse data for the GD1 stream. With the most recently published distances to the stream, energy and angular momentum imply that the end that must be leading is trailing, but extremely small changes to the distances rectify the problem.

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arXiv2025

Actions of highly eccentric orbits

The challenge presented by computing actions for eccentric orbits in axisymmetric potentials is discussed. In the limit of vanishing angular momentum about the potential's symmetry axis, there is a clean distinction between box and loop orbits. We show that this distinction persists into the regime of non-zero angular momentum. In the case of a Staeckel potential, there is a critical value I_{3crit}(E) of the third integral I_3 below which I_3 does not contribute to the centrifugal barrier. An orbit is of box or loop type according as its value of I_3 is smaller or greater than I_{3crit}. We give algorithms for determining I_{3crit}(E) and the critical action Jzcrit below which orbits in any given potential are boxes. It is hard to compute the actions and especially the frequencies of orbits that have Jz ~ Jzcrit using the Staeckel Fudge. A modification of the Fudge that alleviates the problem is described.

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arXiv2024

Disc distortion revisited

We revisit the dynamics of razor-thin, stone-cold, self-gravitating discs. By recasting the equations into standard cylindrical coordinates, the linearised vertical dynamics of an exponential disc can be followed for several gigayears on a laptop in a few minutes. An initially warped disc rapidly evolves into a flat inner region and an outward-propagating spiral corrugation wave that rapidly winds up and would quickly thicken a disc with non-zero radial velocity dispersion. The Sgr dwarf galaxy generates a similar warp in the Galactic disc as it passes through pericentre, and the warp generated by the dwarf's last pericentre ~ 35 Myr ago is remarkably similar to the warp traced by the Galaxy's HI disc. The resemblance to the observed warp is fleeting but its timing is perfect. For the adopted parameters the amplitude of the model warp is a factor 3 too small, but there are several reasons for this being so. The marked flaring of our Galaxy's low-alpha disc just outside the solar circle can be explained as a legacy of earlier pericentres.

astro-ph.GA↗

arXiv2023

Chemodynamical models of our Galaxy

A chemodynamical model of our galaxy is fitted to data from DR17 of the APOGEE survey supplemented with data from the StarHorse catalogue and gaia DR3. Dynamically, the model is defined by action-based distribution functions for dark matter and six stellar components plus a gas disc. The gravitational potential jointly generated by the model's components is used to examine the galaxy's chemical composition within action space. The observational data probably cover all parts of action space that are populated by stars. The overwhelming majority of stars have angular momentum J_ϕ>0 implying that they were born in the Galactic disc. High-alpha stars dominate in a region that is sharply bounded by J_ϕ\la J_ϕ(solar). Chemically the model is defined by giving each stellar component a Gaussian distribution in ([Fe/H],[Mg/Fe]) space about a mean that is a linear function of the actions. The model's 47 dynamical parameters are chosen to maximise the likelihood of the data given the model in 72 three-dimensional velocity spaces while its 70 chemical parameters are similarly chosen in five-dimensional chemo-dynamical space. The circular speed falls steadily from 237\kms at R=4\kpc to 218\kms at R=20\kpc. Dark matter contributes half the radial force on the Sun and has local density 0.011\msun\pc^{-3}, there being 24.5\msun\pc^{-2} in dark matter and 26.5\msun\pc^{-2} in stars within 1.1\kpc of the plane.

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arXiv2022

Our Galaxy's youngest disc

We investigate the structure of our Galaxy's young stellar disc by fitting the distribution functions (DFs) of a new family to five-dimensional Gaia data for a sample of $47\,000$ OB stars. Tests of the fitting procedure show that the young disc's DF would be strongly constrained by Gaia data if the distribution of Galactic dust were accurately known. The DF that best fits the real data accurately predicts the kinematics of stars at their observed locations, but it predicts the spatial distribution of stars poorly, almost certainly on account of errors in the best-available dust map. We argue that dust models could be greatly improved by modifying the dust model until the spatial distribution of stars predicted by a DF agreed with the data. The surface density of OB stars is predicted to peak at $R\simeq5.5\mbox{kpc}$, slightly outside the reported peak in the surface density of molecular gas; we suggest that the latter radius may have been under-estimated through the use of poor kinematic distances. The velocity distributions predicted by the best-fit DF for stars with measured line-of-sight velocities $v_\parallel$ reveal that the outer disc is disturbed at the level of 10 $\mbox{km}~\mbox{s}^{-1}$ in agreement with earlier studies, and that the measured values of $v_\parallel$ have significant contributions from the orbital velocities of binaries. Hence the outer disc is colder than it is sometimes reported to be.

astro-ph.GA↗

arXiv2022

Self-consistent models of our Galaxy

A new class of models of stellar discs is introduced and used to build a self-consistent model of our Galaxy. The model is defined by the parameters that specify the action-based distribution functions (DFs) f(J) of four stellar discs (three thin-disc age cohorts and a thick disc), spheroidal bulge and spheroidal stellar and dark haloes. From these DFs plus a specified distribution of gas, we solve for the densities of stars and dark matter and the potential they generate. The principal observational constraints are the kinematics of stars with Gaia RVS data and the density of stars in the column above the Sun. The model predicts the density and kinematics of stars and dark matter throughout the Galaxy. We determine the structure of the dark halo prior to the infall of baryons. A simple extension of the DFs of stellar components to include chemistry allows the model to reproduce the way the Galaxy's chemistry is observed to vary in the (R,z) plane. Surprisingly, the data indicate that high-alpha stars are confined to orbits with J_z >~ 50 kpc km/s. The code used to create the model is available on Github.

astro-ph.GA↗

arXiv2021

Modelling the stellar halo with RR-Lyrae stars

A seven-parameter distribution function (DF) is fitted to $20\,000$ RR-Lyrae stars for which only astrometric data are available. The observational data are predicted by the DF in conjunction with the gravitational potential of a self-consistent model Galaxy defined by DFs for the dark halo, the bulge and a four-component disc. Tests of the technique developed to deal with missing line-of-sight velocities show that adding such velocities tightens constraints on the DF only slightly. The recovered model of the RR-Lyrae population confirms that the population is flattened and has a strongly radially biased velocity distribution. At large radii its density profile tends to $ρ\sim r^{-4.5}$ but no power law provides a good fit inside the solar sphere. The model is shown to provide an excellent fit to the data for stars brighter than $r=16.5$ but at certain longitudes it predicts too few faint stars at Galactocentric radii $\sim20\mbox{kpc}$, possibly signalling that the halo is not axisymmetric. The DF is used to predict the velocity distribution of BHB stars for which space velocities are available. The $z$ components are predicted successfully but too much anisotropy in the $v_Rv_ϕ$ plane is expected.

astro-ph.GA↗

arXiv2021

Modes of a stellar system II: non-ergodic systems

An equation is derived for the energy of a small disturbance in a system that is generated by a distribution function (DF) of the form $f(\vJ)$ -- most galaxies and star clusters can be closely approximated by such a DF. The theory of van Kampen modes is extended to such general systems. An inner product on the space of DFs is defined such that the energy of a disturbance is its norm under this product. It is shown that van Kampen modes that differ in frequency are then orthogonal, with the consequence that the energies of van Kampen modes are additive. Consequently, most of the insight into the dynamics of ergodic systems that was gained in a recent paper on the van Kampen modes of ergodic systems applies to real clusters and galaxies.

astro-ph.GA↗

arXiv2021

Probabilistic distribution functions

Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is identified so DFs can be weighted in a consistent way.

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arXiv2021

Modes of a stellar system I: ergodic systems

The excursions of star clusters and galaxies around statistical equilibria are studied. For a stable ergodic model Antonov's Hermitian operator on six-dimensional phase space has the normal modes as its eigenfunctions. The excitation energy of the system is just the sum of the (positive) energies associated with each normal mode. Formulae are given for the DFs of modes, which are of the type first described by van Kampen rather than Landau, and Landau `modes' can be expressed as sums of van Kampen modes. Each van Kampen mode comprises the response of non-resonant stars to driving by the gravitational field of stars on a group of resonant tori, so its structure is sensitive to the degree of self gravity. The emergence of global distortions in N-body models when particles are started from an analytical equilibrium is explained in terms of the interplay of normal modes. The positivity of modal energies opens the way to modelling the thermal properties of clusters in close analogy with those of crystals.

astro-ph.GA↗

arXiv2020

The Sixth Data Release of the Radial Velocity Experiment (RAVE) -- II: Stellar Atmospheric Parameters, Chemical Abundances and Distances

We present part 2 of the 6th and final Data Release (DR6 or FDR) of the Radial Velocity Experiment (RAVE), a magnitude-limited (9<I<12) spectroscopic survey of Galactic stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra (R~7500) cover the Ca-triplet region (8410-8795A) and span the complete time frame from the start of RAVE observations on 12 April 2003 to their completion on 4 April 2013. In the second of two publications, we present the data products derived from 518387 observations of 451783 unique stars using a suite of advanced reduction pipelines focussing on stellar atmospheric parameters, in particular purely spectroscopically derived stellar atmospheric parameters (Teff, log(g), and the overall metallicity), enhanced stellar atmospheric parameters inferred via a Bayesian pipeline using Gaia DR2 astrometric priors, and asteroseismically calibrated stellar atmospheric parameters for giant stars based on asteroseismic observations for 699 K2 stars. In addition, we provide abundances of the elements Fe, Al, and Ni, as well as an overall [alpha/Fe] ratio obtained using a new pipeline based on the GAUGUIN optimization method that is able to deal with variable signal-to-noise ratios. The RAVE DR6 catalogs are cross matched with relevant astrometric and photometric catalogs, and are complemented by orbital parameters and effective temperatures based on the infrared flux method. The data can be accessed via the RAVE Web site (http://rave-survey.org) or the Vizier database.

astro-ph.SR↗

arXiv2020

The Sixth Data Release of the Radial Velocity Experiment (RAVE) -- I: Survey Description, Spectra and Radial Velocities

The Radial Velocity Experiment (RAVE) is a magnitude-limited (9<I<12) spectroscopic survey of Galactic stars randomly selected in the southern hemisphere. The RAVE medium-resolution spectra (R~7500) cover the Ca-triplet region (8410-8795A). The 6th and final data release (DR6 or FDR) is based on 518387 observations of 451783 unique stars. RAVE observations were taken between 12 April 2003 and 4 April 2013. Here we present the genesis, setup and data reduction of RAVE as well as wavelength-calibrated and flux-normalized spectra and error spectra for all observations in RAVE DR6. Furthermore, we present derived spectral classification and radial velocities for the RAVE targets, complemented by cross matches with Gaia DR2 and other relevant catalogs. A comparison between internal error estimates, variances derived from stars with more than one observing epoch and a comparison with radial velocities of Gaia DR2 reveals consistently that 68% of the objects have a velocity accuracy better than 1.4 km/s, while 95% of the objects have radial velocities better than 4.0 km/s. Stellar atmospheric parameters, abundances and distances are presented in subsequent publication. The data can be accessed via the RAVE Web (http://rave-survey.org) or the Vizier database.

astro-ph.SR↗

arXiv2019

Angle-action variables for orbits trapped at a Lindblad resonance

The conventional approach to orbit trapping at Lindblad resonances via a pendulum equation fails when the parent of the trapped orbits is too circular. The problem is explained and resolved in the context of the Torus Mapper and a realistic Galaxy model. Tori are computed for orbits trapped at both the inner and outer Lindblad resonances of our Galaxy. At the outer Lindblad resonance, orbits are quasiperiodic and can be accurately fitted by torus mapping. At the inner Lindblad resonance, orbits are significantly chaotic although far from ergodic, and each orbit explores a small range of tori obtained by torus mapping.

astro-ph.GA↗

arXiv2019

Trapped orbits and solar-neighbourhood kinematics

Torus mapping yields constants of motion for stars trapped at a resonance. Each such constant of motion yields a system of contours in velocity space at the Sun and neighbouring points. If Jeans' theorem applied to resonantly trapped orbits, the density of stars in velocity space would be equal at all intersections of any two contours. A quantitative measure of the violation of this principal is defined and used to assess various pattern speeds for a model of the bar recently fitted to observations of interstellar gas. Trapping at corotation of a bar with pattern speed in the range 33-36 /Gyr is favoured and trapping at the outer Lindblad resonance is disfavoured. As one moves around the Sun the structure of velocity space varies quite rapidly, both as regards the observed star density and the zones of trapped orbits. The data seem consistent with trapping at corotation.

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arXiv2019

Modelling our Galaxy

Dynamical models will be key to exploitation of the incoming flood data for our Galaxy. Modelling techniques are reviewed with an emphasis on f(J) modelling.

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arXiv2019

Flattened stellar systems based on distribution functions depending on actions

We address an issue that arises when self-consistently flattened dynamical stellar systems are constructed by adopting a distribution function (DF) that depends on the action integrals. The velocity distribution at points on the symmetry axis is controlled by the the dependence of the DF on just one action, while at points off the symmetry axis two actions are involved. Consequently, the physical requirement that the velocity distribution evolves continuously in the neighbourhood of the symmetry axis restricts the functional forms of acceptable DFs. An algorithm for conforming to this restriction is presented and used to construct a variety of flattened models.

astro-ph.GA↗

arXiv2019

The shearing sheet and swing amplification revisited

The principal results of the classic analysis of the shearing sheet and swing amplification by Julian & Toomre (1966) are re-derived in a more accessible way and then used to gain a better quantitative understanding of the dynamics of stellar discs. The axisymmetric limit of the shearing sheet is derived and used to re-derive Kalnajs' 1965 dispersion relation and Toomre's 1964 stability criterion for axisymmetric disturbances. Using the shearing sheet to revisit Toomre's important 1969 paper on the group velocity implied by Lin-Shu-Kalnajs dispersion relation, we discover that two rather than one wavepackets emerges inside corotation: one each side of the inner Lindblad resonance. Although LSK dispersion relation provides useful interpretations of both wavepackets, the shearing sheet highlights the limitations of the LSK approach to disc dynamics. Disturbances by no means avoid an annulus around corotation, as the LSK dispersion relation implies. While disturbances of the shearing sheet have a limited life in real space, they live on much longer in velocity space, which Gaia allows us to probe extensively. C++ code is provided to facilitate applications of winding spiral waves.

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