arXiv subjects

Chris Hamilton

Publications and source records attributed to Chris Hamilton.

At least 19 recordsLinked to original sources

arXiv2026

Turbulent gas-rich discs at high redshift: the origin of early massive stellar bars

Recent observations combining the power of ALMA and JWST have revealed large ($3-7$ kpc), massive ($3-10\times10^{10}\,\mathrm{M}_\odot$) stellar bars at $z=4-5$ when the Universe was only 1.2-1.6 Gyr old. At this early epoch, the host galaxy was baryon-dominated (typically 75\% gas, 25\% stars) within the observed extent of the disc ($8-15$ kpc). Using NEXUS $N$-body/hydrodynamic simulations, we show that such bars can form promptly (400$-$800 Myr), provided the disc mass fraction is high ($f_{\rm disc}\gtrsim 70\%$) and the bar is gas-dominated at the time of its formation, consistent with the observations. In this limit, gas-free bars are unstable to vertical bending modes, but a dominant gas component suppresses this instability. Unlike massive bars in the local Universe, these early bars were sites of vigorous star formation, as we show. Remarkably, for gas-rich models with $f_{\rm gas}\lesssim60\%$, the bars develop X-shaped boxy bulges; at higher gas fractions ($f_{\rm gas}> 60\%$), diffusion suppresses resonant orbit trapping and the emerging bar collapses within 1 Gyr to form a classical bulge. The bar formation time, length, mass, and $m=2$ Fourier amplitude are all inversely related to $f_{\rm gas}$. We present a simple analytic model for how stochastic forcing shifts the bar onset time, defined as the time at which the growing bar amplitude reaches a specified threshold.

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arXiv2026

Swing amplification in star-gas disks

Recent JWST and ALMA observations have revealed stellar bars and spirals in gas-rich galactic disks at redshifts as high as $z \simeq 4$. The simplest theoretical paradigm we have for understanding such non-axisymmetric features is the linear theory of swing amplification (SA) in the 2D shearing sheet. However, while the SA mechanism in a gaseous shearing sheet was first studied in 1965, and that in a collisionless stellar sheet in 1966, the coupled star-gas linear SA equations have never been solved explicitly. Here we write down these equations and use them to study the evolution of non-axisymmetric swinging waves in stable disks. We find that waves are often amplified temporarily by factors of $10-100$ or more, and that the maximum \textit{non-axisymmetric} amplification factor is tightly correlated with the system's distance from the \textit{axisymmetric} stability boundary in the $(1/Q_\mathrm{s}, 1/Q_\mathrm{g})$ plane. The true star-gas behavior differs significantly from the `two-fluid' idealizations used in the past, because phase mixing of the collisionless stellar component acts as a sink of perturbation energy. Closely analogous results hold for finite-thickness disks except for the shifting of the stability boundary. We provide a \texttt{python} code that calculates the SA factors and maximally-amplified wavelength given the background disk parameters.

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arXiv2026

Evolution of Binaries Under Stochastic Perturbations

We develop a general Fokker-Planck framework describing the dynamical evolution of Keplerian binaries subjected to stochastic perturbations. The formalism provides an algorithmic way to obtain the Fokker-Planck drift and diffusion coefficients of any set of orbital variables given the statistics of the perturbations. We apply the method to three physically distinct regimes: adiabatic tidal perturbations, white-noise tidal perturbations, and impulsive encounters with a third body of arbitrary density profile. In each regime we provide explicit drift and diffusion coefficients for all six orbital elements, derive the associated evolution timescale, and obtain analytic steady-state distribution functions. Our results extend previous treatments by including the evolution of the binary's orientation, retaining the complete tensor structure of tidal correlators, treating non-pointlike perturbers, and resolving the exact geometry of impulsive encounters. The latter correction leads to a steady-state eccentricity distribution that is slightly sub-thermal. We also show how these equations can be applied directly in several astrophysical scenarios, including binaries perturbed by dark matter subhaloes, ultralight dark matter, and the interstellar medium. This work delivers both a complete mathematical framework and a practical toolkit for stochastic binary evolution, providing ready-to-evaluate equations to be applied directly to binary population data.

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arXiv2026

Short-Range Forces Can Catalyze Extreme Orbital Evolution in Hierarchical Triples

Hierarchical triples are promising environments for producing exotica such as black hole mergers and hot Jupiters, because of the von Zeipel-Lidov-Kozai (ZLK) effect, whereby a distant tertiary can torque an inner binary to high eccentricity over secular timescales. In the double-averaged (DA) approximation to ZLK, this eccentricity excitation is suppressed by apsidal precession due to "short-range forces" (SRFs) like relativity and tidal/rotational bulges. Here we show that, when the DA approximation breaks down, SRFs often catalyze, rather than suppress, extreme eccentricity behavior. This occurs because SRFs can drive large, discrete jumps in the binary's effective "adiabatic invariants" during high-eccentricity episodes. These nonadiabatic jumps can dramatically alter the maximum/minimum eccentricity and secular period of astrophysically relevant triples, including some for which SRFs were previously thought irrelevant. Even the angular momentum component j_z evolves secularly -- to our knowledge, this is the first time such evolution has been demonstrated from a test-particle quadrupole-order, three-body mechanism. In short, binaries may explore much more of phase space than is implied by any (semi-)analytic ZLK theory of which we are aware. We demonstrate this at the test-particle quadrupole level; in a companion work we show how even more-extreme behavior occurs when the jumps are combined with octupolar ZLK evolution.

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arXiv2026

Interstellar Medium-Driven Orbital Transport -- I. Radial Heating and Migration

Interstellar medium (ISM) structures gravitationally perturb stellar orbits in galactic disks, driving orbital heating and migration. However, studies of these transport processes tend to model the ISM very crudely, e.g., as a collection of compact, spherical ``clouds'' moving in the disk plane. Here, we revisit this problem with more realistic models of ISM density fluctuations drawn from the TIGRESS-NCR magnetohydrodynamic simulations, which follow the physics governing the ISM in Milky-Way-like conditions at high resolution. By integrating test-particle trajectories through time-dependent TIGRESS-NCR structures, we uncover transport behavior that contrasts sharply with conventional theoretical expectations. Notably, radial heating scales as $\sigma_R \propto t^{1/2}$ for initially cold orbits at early times, and $\sigma_R \propto t^{1/5}$ for warmer orbits at late times, contrary to the classic $\sigma_R \propto t^{1/3}$ prediction. The ISM drives substantial radial migration, accounting for $\gtrsim 30\%$ of that observed in the solar neighborhood (even without stellar spiral structure), and leads to a very low heating-to-migration ratio of $\mathrm{rms}\,\delta J_R\,/\,\mathrm{rms}\,\delta J_\varphi \approx 0.055$, where $J_R$ and $J_\varphi$ are the radial and azimuthal actions respectively. Vertical motion suppresses the amplitude of radial transport, but does not change the basic scalings. All our simulation results can be explained using quasilinear diffusion theory, accounting for the fact that the dominant ISM fluctuations have wavelengths of $\lambda_* \sim 600\,$pc and correlation timescales of $\tau_* \sim 70\,$Myr. We provide simple fitting formulae for the corresponding diffusion coefficients. In Paper II, we study the ISM's role in vertical disk heating.

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arXiv2026

Phase spirals across galactic disks I: Exploring dynamical influences on winding

The vertical phase-space spirals in the Milky Way are clear evidence of disequilibrium. However, they are challenging to study because phase mixing signals evolve under the influence of many different dynamical processes and can be driven by many sources of disequilibrium. We characterize phase spirals in two simulations -- one test particle and one N-body -- with basis function expansions, using these to derive winding times ($T_{\rm fit}$). We find that phase spirals in the test particle simulation wind up as expected from pure phase mixing theory while those in the self-consistent simulation do not. Specifically, in the N-body simulation we find that (i) the onset of winding is delayed, (ii) the winding rate is slowed, and (iii) the rate of winding oscillates with time. The extent of these effects depends on the azimuthal action $J_\phi$ of the phase spiral region. We build some physical intuition for these effects through 1-D toy models which follow a group of co-moving stars traveling through several different evolving potentials. We find that phase spiral winding can be delayed until the group no longer moves coherently with the midplane of the (perturbed) potential and oscillates with time as the group experiences (e.g.) a breathing mode traveling through the disk. Rates of winding change as the vertical structure of the disk evolves. The modifications to winding are strongest in the inner galaxy where the disk potential dominates. We conclude that in the Milky Way, all calculations of the winding time should be interpreted as lower limits and that the most trustworthy winding times are likely in the outer disk.

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arXiv2026

On the radial velocity wave in the Galactic disk

Stars in the Galactic disk have mean radial velocities $\overline{v}_R$ that oscillate as a function of angular momentum $J_\varphi$. This `$J_\varphi$-${\overline{v}}_R$ wave' signal also exhibits a systematic phase shift when stars are binned by their dynamical temperatures. However, the origin of the wave is unknown. Here we use linear perturbation theory to derive a simple analytic formula for the $J_\varphi$-$\overline{v}_R$ signal that depends on the equilibrium properties of the Galaxy and the history of recent perturbations to it. The formula naturally explains the phase shift, but also predicts that different classes of perturbation should drive $J_\varphi$-$\overline{v}_R$ signals with very different morphologies. Ignoring the self-gravity of disk fluctuations, it suggests that neither a distant tidal kick (e.g., from the Sgr dwarf) nor a rigidly-rotating Galactic bar can produce a qualitatively correct $J_\varphi$-$\overline{v}_R$ wave signal. However, short-lived spiral arms can, and by performing an MCMC fit we identify a spiral perturbation that drives a $J_\varphi$-${\overline{v}}_R$ signal in reasonable agreement with the data. We verify the analytic formula with test particle simulations, finding it to be highly accurate when applied to dynamically cold stellar populations. More work is needed to deal with hotter orbits, and to incorporate the fluctuations' self-gravity and the role of interstellar gas.

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arXiv2025

Galactokinetics II: Spiral structure

We present a unified theory of linear spiral structure in stellar disks. We begin by identifying the characteristic scales involved in the spiral structure problem and listing some quantitative requirements of a successful theory. We then write down the general linear response theory for thin disks, making clear the equivalence between different representations (e.g., Volterra, Landau, van Kampen) of the theory. Next, using the asymptotic expansions developed in our previous galactokinetics paper, we consider spiral structure on different spatial scales and thereby show how several classic results - including Lindblad-Kalnajs density waves, swing amplification, Lin-Shu-Kalnajs modes, and groove instabilities - emerge as limiting cases. In addition, many of our asymptotic results connect smoothly when extrapolated to intermediate regimes, rendering the analytic theory valid over a larger range of scales than naively expected. Finally, we identify situations in which nonlinear physics is unavoidable. Though many nonlinear questions remain unanswered, we hope that the theoretical synthesis developed here will allow us to both connect and distinguish the plethora of ideas that have accumulated over the last six decades of spiral structure studies, and will provide a foundation upon which a comprehensive theory might ultimately be built.

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arXiv2025

Characterizing Density and Gravitational Potential Fluctuations of the Interstellar Medium

Substructure in the interstellar medium (ISM) is crucial for establishing the correlation between star formation and feedback and has the capacity to significantly perturb stellar orbits, thus playing a central role in galaxy dynamics and evolution. Contemporary surveys of gas and dust emission in nearby galaxies resolve structure down to $\sim 10\,$pc scales, demanding theoretical models of ISM substructure with matching fidelity. In this work, we address this need by quantitatively characterizing the gas density in state-of-the-art MHD simulations of disk galaxies that resolve pc to kpc scales. The TIGRESS-NCR framework we employ includes sheared galactic rotation, self-consistent star formation and feedback, and nonequilibrium chemistry and cooling. We fit simple analytic models to the one-point spatial, two-point spatial, and two-point spatio-temporal statistics of the surface density fluctuation field. We find that for both solar neighborhood and inner-galaxy conditions, (i) the surface density fluctuations follow a log-normal distribution, (ii) the linear and logarithmic fluctuation power spectra are well-approximated as power laws with indices of $\approx -2.2$ and $\approx -2.8$ respectively, and (iii) lifetimes of structures at different scales are set by a combination of feedback and effective pressure terms. Additionally, we find that the vertical structure of the gas is well-modeled by a mixture of exponential and sech$^2$ profiles, allowing us to link the surface density statistics to those of the volume density and gravitational potential. We provide convenient parameterizations for incorporating realistic ISM effects into stellar-dynamical studies and for comparison with multi-wavelength observations.

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arXiv2025

Galactic echoes

Gaia has revealed a variety of substructures in the phase space of stars in the Solar neighborhood, including the vertical `Snail' in $(z,v_z)$ space. Such substructures are often interpreted as the incompletely phase-mixed response of the disc stars to a single perturbation, such as an impulsive encounter with a satellite galaxy. In this paper we consider the possibility that such structures contain manifestations of phase space echoes. First established in plasma physics in the 1960s, echoes arise when a collisionless system is perturbed twice: the macroscopic responses to both perturbations mix to small scales in phase space, whereupon they couple nonlinearly, producing a third macroscopic `echo' response without the need for a third perturbation. We derive the galactic analogue of the plasma echo theory using angle-action variables and apply it to a one-dimensional model of vertical motion in the Milky Way. We verify the predicted echo behavior using idealized test particle simulations, both with and without the inclusion of diffusion through orbital scattering off molecular clouds. While we conclude that the Gaia Snail itself is unlikely a (pure) echo effect, the basic physics we uncover is sufficiently generic that we expect phase-space echoes to be common in disc galaxies.

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arXiv2025

Origin of the two-armed vertical phase-spiral in the inner Galactic disk

Gaia recently revealed a two-armed spiral pattern in the vertical phase-space distribution of the inner Galactic disk (guiding radius $R_\textrm{g} \sim 6.2$ kpc), indicating that some non-adiabatic perturbation symmetric about the mid-plane is driving the inner disk out of equilibrium. The non-axisymmetric structures in the disk (e.g., the bar or spiral arms) have been suspected to be the major source for such a perturbation. However, both the lifetime and the period of these internal perturbations are typically longer than the period at which stars oscillate vertically, implying that the perturbation is generally adiabatic. This issue is particularly pronounced in the inner Galaxy, where the vertical oscillation period is shorter and therefore adiabatically shielded more than the outer disk. We show that two-armed phase spirals can naturally form in the inner disk if there is a vertical resonance that breaks the adiabaticity; otherwise, their formation requires a perturber with an unrealistically short lifetime. We predict analytically and confirm with simulations that a steadily rotating (non-winding) two-armed phase spiral forms near the resonance when stars are subject to both periodic perturbations (e.g., by spiral arms) and stochastic perturbations (e.g., by giant molecular clouds). Due to the presence of multiple resonances, the vertical phase-space exhibits several local phase spirals that rotate steadily at distinct frequencies, together forming a global phase spiral that evolves over time. Our results demonstrate that, contrary to earlier predictions, the formation of the two-armed phase spiral does not require transient perturbations with lifetimes shorter than the vertical oscillation period.

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arXiv2024

On the maximum disk heating attributable to fuzzy dark matter

Fuzzy dark matter (FDM) granulations would drive orbital transport of stars in galactic disks, and in particular would produce roughly equal amounts of radial heating and radial migration. However, observations suggest that heating has been much less efficient than migration in our Galaxy. We argue that this decreases the amount of radial heating, $\mathcal{H}_\mathrm{FDM}$, that can safely be attributed to FDM. Consequently, lower bounds on the FDM particle mass $m$ derived through Galactic disk kinematics should be revised upwards; a rough estimate is $m \gtrsim 1.3\times 10^{-22} \mathrm{eV} \times [(\mathcal{H}_\mathrm{FDM}/\mathcal{H})/0.1]^{-1/2}$, where $\mathcal{H}$ is the total observed radial heating.

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arXiv2024

Why is the Galactic disk so cool?

The bulk of old stars in the Galactic disk have migrated radially by up to several kpc in their lifetimes, yet the disk has remained relatively cool, i.e., the ratio of radial heating to migration has been small. Here, we demonstrate that this small ratio places very strong constraints on which mechanisms could have been responsible for orbital transport in our Galaxy. For instance, Sellwood & Binney's mechanism of nonlinear horseshoe transport by spirals tends to produce too high a ratio of heating to migration, unless the spirals' amplitudes are heavily suppressed away from their corotation resonances, or their pitch angles are significantly larger than is observed. This problem is only made worse if one includes the effect of the Galactic bar, diffusion due to disk or halo substructure, etc. Resonant (but non-horseshoe) scattering by spirals can drive transport consistent with the data, but even this requires some fine-tuning. In short, reproducing both the observed radial migration and the small ratio of heating to migration is a highly nontrivial requirement, and poses a significant challenge to models of the Milky Way's dynamical history, theories of spiral structure, and the identification of 'Milky Way analogues' in cosmological simulations.

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arXiv2024

Galactokinetics

Galactic disks lie at the heart of many of the most pressing astrophysical puzzles. There are sophisticated kinetic theories that describe some aspects of galaxy disk dynamics, but extracting quantitative predictions from those theories has proven very difficult, meaning they have shed little light on observations/simulations of galaxies. Here, we begin to address this issue by developing a tractable theory describing fluctuations and transport in thin galactic disks. Our main conceptual advance is to split potential fluctuations into asymptotic wavelength regimes relative to orbital guiding radius and epicyclic amplitude (similar to plasma gyrokinetics), and then to treat separately the dynamics in each regime. As an illustration, we apply our results to quasilinear theory, calculating the angular-momentum transport due to a transient spiral. At each stage we verify our formulae with numerical examples. Our approach should simplify many important calculations in galactic disk dynamics. In a follow-up paper, we apply these ideas to the theory of linear spiral structure in stellar disks.

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arXiv2024

Kinetic Theory of Stellar Systems: A Tutorial

Stellar systems - star clusters, galaxies, dark matter haloes, and so on - are ubiquitous characters in the evolutionary tale of our Universe. This tutorial article is an introduction to the collective dynamical evolution of the very large numbers of stars and/or other self-gravitating objects that comprise such systems, i.e. their kinetic theory. We begin by introducing the basic phenomenology of stellar systems, and explaining why and when we must develop a kinetic theory that transcends the traditional two-body relaxation picture of Chandrasekhar. We study the orbits that comprise stellar systems, how those orbits are modified by perturbations, how a system responds self-consistently to fluctuations in its gravitational potential, and how one can predict the long term fate of a stellar system in various dynamical regimes. Though our treatment is necessarily mathematical, we develop the formalism only to the extent that it facilitates real calculations. We give many examples throughout the text of the equations being applied to topics of major astrophysical importance. Furthermore, in the 1960s and 1970s the kinetic theory of stellar systems was a fledgling subject which developed in tandem with the kinetic theory of plasmas. However, the two fields have long since diverged. Yet once one has become fluent in both Plasmaish and Galacticese, and has a dictionary relating the two, one can pull ideas directly from one field to solve a problem in the other. Therefore, another aim of this tutorial article is to provide our plasma colleagues with a jargon-light understanding of the key properties of stellar systems, to point out the many direct analogies between stellar- and plasma-kinetic calculations, and ultimately to convince them that stellar dynamics and plasma kinetics are, in a deep and beautiful and useful sense, the same thing.

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arXiv2023

Binary mergers in the centers of galaxies: synergy between stellar flybys and tidal fields

Galactic centers are very dynamically active environments, often harbouring a nuclear star cluster and supermassive black hole at their cores. Binaries in these environments are subject to strong tidal fields that can efficiently torque its orbit, exciting near unity eccentricities that ultimately lead to their merger. In turn, frequent close interactions with passing stars impulsively perturb the orbit of the binary, generally softening their orbit until their evaporation, potentially hindering the role of tides to drive these mergers. In this work, we study the evolution of compact object binaries in the galactic center and their merger rates, focusing for the first time on the combined effect of the cluster's tidal field and flyby interactions. We find a significant synergy between both processes, where merger rates increase by a factor of ~10-30 compared to models in which only flybys or tides are taken into account. This synergy is a consequence of the persistent tides-driven eccentricity excitation that is enhanced by the gradual diffusion of $j_z$ driven by flybys. The merger efficiency peaks when the diffusion rate is ~10-100 slower than the tides-driven torquing. Added to this synergy, we also find that the gradual softening of the binary can lift the relativistic quenching of initially tight binaries, otherwise unable to reach extreme eccentricities, and thus expanding the available phase-space for mergers. Cumulatively, we conclude that despite the gradual softening of binaries due to flybys, these greatly enhance their merger rates in galaxy centers by promoting the tidal field-driven eccentricity excitation.

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arXiv2023

Eccentricity dynamics of wide binaries -- II. The effect of stellar encounters and constraints on formation channels

GAIA wide stellar binaries (separations $\sim 10^3-10^{4.5}$ AU) are observed to have a superthermal eccentricity distribution function (DF), well-fit by $P(e) \propto e^\alpha$ with $\alpha \sim 1.2$. In Modak \& Hamilton (2023), we proved that this DF cannot have been produced by Galactic tidal torques starting from any realistic DF that was not already superthermal. Here, we consider the other major dynamical effect on wide binaries: encounters with passing stars. We derive and solve the Fokker-Planck equation governing the evolution of binaries in semimajor axis and eccentricity under many weak, impulsive, penetrative stellar encounters. We show analytically that these encounters drive the eccentricity DF towards thermal on the same timescale as they drive the semimajor axes $a$ towards disruption, $t_\mathrm{ion} \sim 4\,\mathrm{Gyr}\,(a/10^4\,\mathrm{AU})^{-1}$. We conclude that the observed superthermal DF must derive from an even more superthermal (i.e. higher $\alpha$) birth distribution. This requirement places strong constraints on the dominant binary formation channels. A testable prediction of our theory is that $\alpha$ should be a monotonically decreasing function of binary age.

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arXiv2023

Relativistic phase space diffusion of compact object binaries in stellar clusters and hierarchical triples

The LIGO/Virgo detections of compact object mergers have posed a challenge for theories of binary evolution and coalescence. One promising avenue for producing mergers dynamically is through secular eccentricity oscillations driven by an external perturber, be it a tertiary companion (as in the Lidov-Kozai (LK) mechanism) or the tidal field of the stellar cluster in which the binary orbits. The simplest theoretical models of these oscillations use a 'doubly-averaged' (DA) approximation, averaging both over the binary's internal Keplerian orbit and its 'outer' barycentric orbit relative to the perturber. However, DA theories do not account for fluctuations of the perturbing torque on the outer orbital timescale, which are known to increase a binary's eccentricity beyond the maximum DA value, potentially accelerating mergers. Here we reconsider the impact of these short-timescale fluctuations in the test-particle quadrupolar limit for binaries perturbed by arbitrary spherical cluster potentials (including LK as a special case), {in particular including 1pN} general relativistic (GR) apsidal precession of the internal orbit. Focusing on the behavior of the binary orbital elements around peak eccentricity, we discover a new effect, relativistic phase space diffusion (RPSD), in which a binary can jump to a completely new dynamical trajectory on an outer orbital timescale, violating the approximate conservation of DA integrals of motion. RPSD arises from an interplay between secular behavior at extremely high eccentricity, short-timescale fluctuations, and rapid GR precession, and can change the subsequent secular evolution dramatically. This effect occurs even in hierarchical triples, but has not been uncovered until now.

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