arXiv subjects

Scott Tremaine

Publications and source records attributed to Scott Tremaine.

At least 19 recordsLinked to original sources

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 $σ_R \propto t^{1/2}$ for initially cold orbits at early times, and $σ_R \propto t^{1/5}$ for warmer orbits at late times, contrary to the classic $σ_R \propto t^{1/3}$ 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 $\mathrm{rms}\,δJ_R\,/\,\mathrm{rms}\,δJ_φ\approx 0.055$, where $J_R$ and $J_φ$ 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 $λ_* \sim 600\,$pc and correlation timescales of $τ_* \sim 70\,$Myr. We provide simple fitting formulae for the corresponding diffusion coefficients. In Paper II, we study the ISM's role in vertical disk heating.

astro-ph.GA↗

arXiv2026

Measuring Apsidal Clustering

The decade-long debate over the existence of apsidal clustering in the outer solar system is poised for reignition given the plethora of distant trans-Neptunian object (TNO) discoveries expected from the forthcoming Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). Here, we present a new conditional-likelihood method to measure apsidal clustering that is insensitive to uneven survey footprints. We calculate the long-term orbital stability of distant TNOs, which allows us to expand the known sample of relevant objects from 21 to 25. We apply our new method to this up-to-date sample, showing that the significance of the apsidal clustering in the outer solar system has fallen from $2.7σ$ to $1.9σ$, and that the direction of clustering is not well constrained. This new method is suitable for application to the growing sample of known TNOs, and the results will reveal whether the evidence for a hypothetical Planet X from apsidal clustering is real or spurious.

astro-ph.EP↗

arXiv2026

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.

astro-ph.GA↗

arXiv2025

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.

astro-ph.GA↗

arXiv2025

The Inner Kernel of the Classical Kuiper Belt

The `kernel' of the classical Kuiper belt was discovered by Petit et al. (2011) as a visual overdensity of objects with low ecliptic inclinations and eccentricities at semimajor axes near 44 AU. This raises the question - are there other structures present in the classical Kuiper belt? If there are, clustering algorithms applied to orbits transformed into free elements may yield the best chance of discovery. Here, we derive barycentric free orbital elements for objects in the classical Kuiper belt, and use the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm to identify a new structure, which we dub the inner kernel, located at $a \sim 43 \mathrm{\; AU}$ just inward of the kernel ($a \sim 44 \mathrm{\; AU}$), which we also recover. It is yet unclear whether the inner kernel is an extension of the kernel or a distinct structure. Forthcoming observations, including those by the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) may provide further evidence for the existence of this structure, and perhaps resolve the question of whether there are two distinct structures.

astro-ph.EP↗

arXiv2025

Dynamical evolution of stellar binaries in galactic centers

Stellar binaries in galactic centers are relevant to several observable phenomena, including hypervelocity stars, X-ray binaries, and mergers of stars and compact objects; however, we know little about the properties of these binaries. Past works have suggested that a small fraction of them should contract to a few stellar radii or collide, due to the co-operation of stellar tides and the eccentricity oscillations induced by the strong tidal field of the central massive black hole. We revisit this model with several updates. We first argue that when a binary's pericenter separation is driven down to a few stellar radii, diffusive excitation of stellar tides should quickly contract the orbit, saving the stars from collision. Instead, the stars should end up as a very tight binary. We then show that vector resonant relaxation and perturbations from passing stars -- effects not included in past models -- dramatically increase the prevalence of such encounters. In numerical experiments, we find that 1 in 5 binaries around 1 pc from Sgr A* should tidally contract in this way while still on the main sequence. This rate climbs to 3 in 5 around 0.01 pc, inward of which it plateaus. We briefly discuss observable implications of these results, with particular attention to young stellar binaries in the Galactic Center.

astro-ph.GA↗

arXiv2025

Limits on Stellar Flybys in the Solar Birth Cluster

The orbits of small bodies in the outer solar system are particularly sensitive to gravitational perturbations, including stellar flybys. Stellar clusters, with low velocity dispersions and high number densities, can be the source of strong and frequent flybys. As a result, we can infer what properties of the solar birth environment would be incompatible with the structure of the outer solar system observed today. Here, we explore with $n-$body simulations the implications of the low inclinations ($i < 20^{\circ}$) of the distant sednoids (objects with perihelia $q > 40 \mathrm{\; AU}$ and semimajor axes $a > 400 \mathrm{\; AU}$) for the properties of the solar birth cluster. We find that the existence of these orbits, if they were in place in the Sun's birth cluster phase, would limit the product of the stellar number density and the Sun's residence time in the birth cluster to $\lesssim 5 \times 10^3 \mathrm{\; Myr \; pc^{-3}}$, as compared to the weaker limit $\lesssim 5 \times 10^4 \mathrm{\; Myr \; pc^{-3}}$ implied by the low inclinations of the cold classical Kuiper belt.

astro-ph.EP↗

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.

astro-ph.GA↗

arXiv2025

Measuring the Mean Plane of the Distant Kuiper Belt

In the absence of any unseen planetary-mass bodies in the outer solar system, the mean plane of the distant Kuiper belt should be the same as the plane orthogonal to the angular momentum vector of the solar system -- the invariable plane. Here, we measure the mean plane of the non-resonant Kuiper belt across semimajor axes 50 - 400 AU. We introduce a new method to measure the mean plane that we demonstrate to be independent of observational bias. In particular, our results are not biased by surveys that look only at limited areas on the celestial sphere. We find a warp relative to the invariable plane at semimajor axes of 80 - 400 AU (98% confidence) and 80 - 200 AU (96% confidence), but not at 50 - 80 AU or 200 - 400 AU. If it is not spurious, a possible explanation for this warp is an unseen planet in the outer solar system. With $n$-body simulations, we find that a planet with mass between that of Mercury and the Earth, semimajor axis in the range 100 - 200 AU, and inclination $\gtrsim 10^{\circ}$ to be the most likely cause of the warp; however, parameters outside of these ranges are still possible. Such a body is distinct in both mass and semimajor axis from the various versions of an unseen planet invoked to explain apsidal clustering in the outer solar system. The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) is expected to confirm or deny the existence of the warp reported here, and might detect the planet that may produce it.

astro-ph.EP↗

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.

astro-ph.GA↗

arXiv2024

Orbit of a Possible Planet X

The plausibility of an unseen planet in the outer solar system, and the expected orbit and mass of such a planet, have long been a topic of inquiry and debate. We calculate the long-term orbital stability of distant TNOs, which allows us to expand the sample of objects that would carry dynamical information about a hypothetical unseen planet in the solar system. Using this expanded sample, we find statistically significant clustering at the $\sim 3 σ$ level for TNOs with semimajor axes $>170$ AU, in longitude of perihelion ($\varpi$), but not in inclination ($i$), argument of perihelion ($ω$) or longitude of node ($Ω$). Since a natural explanation for clustering in $\varpi$ is an unseen planet, we run 300 $n$-body simulations with the giant planets, a disk of test particles representing Kuiper belt objects, and an additional planet with varied initial conditions for its mass, semimajor axis, eccentricity, and inclination. Based on the distribution of test particles after $1-2$ Gyr, we compute relative likelihoods given the actual distribution of $\varpi$ as a function of semimajor axis for distant TNOs on stable orbits using a significantly larger sample than previous work. We find the best-fit unseen planet parameters to be: mass $m_p = 4.4\pm1.1\mathrm{\;M_{\oplus}}$, semimajor axis $a_p=290\pm30\mathrm{\;AU}$, eccentricity $e_p=0.29\pm0.13$, and inclination $i_p=6.8\pm5.0^{\circ}$. Only $0.06\%$ of the Brown & Batygin (2021) Planet Nine reference population produce probabilities within $1σ$ of the maximum within our quadrivariate model, indicating that our work identifies a distinct preferred region of parameter space for an unseen planet in the solar system.

astro-ph.EP↗

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.

astro-ph.GA↗

arXiv2024

The Black Hole Mass and Photometric Components of NGC 4826

We present IR photometry and HST imaging and spectroscopy of Sab galaxy NGC 4826. Schwarzschild dynamical modeling is used to measure its central black hole mass $M$. Photometric decomposition is used to enable a comparison of $M$ to published scaling relations between black hole masses and properties of host bulges. This decomposition implies that NGC 4826 contains classical and pseudo bulges of approximately equal mass. The classical bulge has best-fit Sérsic index $n=3.27$. The pseudobulge is made up of three parts, an inner lens ($n=0.18$ at $r\lesssim4^{\prime\prime}$), an outer lens ($n=0.17$ at $r \lesssim 45^{\prime\prime}$), and a $n=0.58$ component required to match the surface brightness between the lens components. The total $V$-band luminosity of the galaxy is $M_{VT}=-21.07$, the ratio of classical bulge to total light is $B/T\simeq0.12$, and the ratio of pseudobulge to total light is $PB/T\simeq0.13$. The outer disk is exponential ($n=1.07$) and makes up $D/T=0.75$ of the light of the galaxy. Our best-fit Schwarzschild model has a black hole mass with $1σ$ uncertainties of $M=8.4^{+1.7}_{-0.6}\times10^6\ M_\odot$ and a stellar $K$-band mass-to-light ratio of $Υ_K=0.46\pm0.03\ M_{\odot}\ \mathrm{L}_{\odot}^{-1}$ at the assumed distance of 7.27 Mpc. Our modeling is marginally consistent with $M=0$ at the $3σ$ limit. These best-fit parameters were calculated assuming the black hole is located where the velocity dispersion is largest; this is offset from the maximum surface brightness, probably because of dust absorption. The black hole mass -- one of the smallest measured by modeling stellar dynamics -- satisfies the well known correlations of $M$ with the $K$-band luminosity, stellar mass, and velocity dispersion of the classical bulge only in contrast to total (classical plus pseudo) bulge luminosity.

astro-ph.GA↗

arXiv2024

Iron Snails: non-equilibrium dynamics and spiral abundance patterns

Galaxies are not in a dynamical steady state. They continually undergo perturbations, e.g., from infalling dwarf galaxies and dark-matter substructure. After a dynamical perturbation, stars phase mix towards a new steady state; in so doing they generally form spiral structures, such as spiral density waves in galaxy disks and the Gaia Snail observed in the vertical phase-space density in the solar neighborhood. Structures in phase-space density can be hard to measure accurately, because spatially varying selection effects imprint their own patterns on the density. However, stellar labels such as metallicity, or other element abundances, or stellar masses and ages, can be measured even in the face of complex or unknown spatial selection functions. We show that if the equilibrium galaxy has phase-space gradients in these labels, any perturbation that could raise a spiral wave in the phase-space density will raise a spiral wave in the distribution of labels as well. We work out the relationship between the spiral patterns in the density and in the labels. As an example, we analyze the Gaia Snail and show that its amplitude and dynamical age as derived from elemental abundances (mainly [Mg/Fe]) follow similar patterns to those derived from the phase-space density. Our best model dates the Snail's perturbation to about 400 Myr ago although we find significant variations with angular momentum in the best-fit age. Conceptually, the ideas presented here are related to Orbital Torus Imaging, chemical tagging, and other methods that use stellar labels to trace dynamics.

astro-ph.GA↗

arXiv2024

Studying Binary Formation under Dynamical Friction Using Hill's Problem

Using the equations of motion from Hill's problem, with added accelerations for different forms of dynamical friction, we provide the (to-date) broadest scale-free study of friction-driven binary formation in gaseous disks and stellar clusters. We focus mainly on binary formation between stellar-mass black holes in active galactic nuclei (AGNi), considering both gas dynamical friction from AGN disks and stellar dynamical friction from the nuclear star cluster. We first find simple, dimensionless friction coefficients that approximate the effects of standard models for gas and stellar dynamical friction. We perform extensive simulations of Hill's problem under such friction, and we present a picture of binary formation through encounters between single stars on nearby orbits, as a function of friction parameter, eccentricity, and inclination. Notably, we find that the local binary formation rate is a linear function of the friction coefficient so long as the friction is weak. Due to the dimensionless nature of our model problem, our findings are generalizable to binary formation at all scales (e.g., intermediate-mass black holes in a star cluster, planetesimals in a gaseous disk).

astro-ph.GA↗

arXiv2024

Testing MOND on small bodies in the remote solar system

Modified Newtonian dynamics (MOND), which postulates a breakdown of Newton's laws of gravity/dynamics below some critical acceleration threshold, can explain many otherwise puzzling observational phenomena on galactic scales. MOND competes with the hypothesis of dark matter, which successfully explains the cosmic microwave background and large-scale structure. Here we provide the first solar-system test of MOND that probes the sub-critical acceleration regime. Using the Bekenstein-Milgrom AQUAL formulation, we simulate the evolution of myriads of test particles (planetesimals or comets) born in the trans-Neptunian region and scattered by the giant planets over the lifetime of the Sun to heliocentric distances of $10^2$-$10^5$ au. We include the effects of the Galactic tidal field and passing stars. While Newtonian simulations reproduce the distribution of binding energies of long-period and Oort-cloud comets detectable from Earth, MOND-based simulations do not. This conclusion is robust to plausible changes in the migration history of the planets, the migration history of the Sun, the MOND transition function, effects of the Sun's birth cluster, and the fading properties of long-period comets. For the most popular version of AQUAL, characterized by a gradual transition between the Newtonian and MOND regimes, our MOND-based simulations also fail to reproduce the orbital distribution of trans-Neptunian objects in the detached disk (perihelion > 38 au). Our results do not rule out some MOND theories more elaborate than AQUAL, in which non-Newtonian effects are screened on small spatial scales, at small masses, or in external gravitational fields comparable in strength to the critical acceleration.

astro-ph.CO↗

arXiv2023

Scattered Disk Dynamics: The Mapping Approach

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map shows excellent agreement with direct numerical integrations and elucidates how the dynamics depends on perturber mass and pericenter distance. We also use the map to explore the onset of chaos, statistical descriptions of chaotic transport, and sticking in mean-motion resonances. We discuss implications of our mapping model for the dynamical evolution of the solar system's scattered disk and other highly eccentric trans-Neptunian objects.

astro-ph.EP↗

arXiv2023

The Hamiltonian for von Zeipel-Lidov-Kozai oscillations

The Hamiltonian used in classical analyses of von Zeipel-Lidov-Kozai or ZLK oscillations in hierarchical triple systems is based on the quadrupole potential from a distant body on a fixed orbit, averaged over the orbits of both the inner and the outer bodies ("double-averaging"). This approximation can be misleading, because the corresponding Hamiltonian conserves the component of angular momentum of the inner binary normal to the orbit of the outer binary, thereby restricting the volume of phase space that the system can access. This defect is usually remedied by including the effects of the octopole potential, or by allowing the outer orbit to respond to variations in the inner orbit. However, in a wide variety of astrophysical systems nonlinear perturbations are comparable to or greater than these effects. The long-term effects of nonlinear perturbations are described by an additional Hamiltonian, which we call Brown's Hamiltonian. At least three different forms of Brown's Hamiltonian are found in the literature; we show that all three are related by a gauge freedom, although one is much simpler than the others. We argue that investigations of ZLK oscillations in triple systems should include Brown's Hamiltonian.

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