arXiv subjects

Roman R. Rafikov

Publications and source records attributed to Roman R. Rafikov.

At least 19 recordsLinked to original sources

arXiv2026

Debris Disc Substructures Induced by Secular Planetary Perturbations

Observations of debris discs have the potential to provide us with valuable information about massive planets perturbing them gravitationally. In this work, we explore the evolution of the azimuthally-averaged (or axisymmetric) surface density (ASD) -- a characteristic routinely derived from observations -- in a disc secularly perturbed by an inner planet. We develop detailed analytical understanding of ASD evolution and verify it using a novel numerical framework DebrisPy, which we make publicly available. With these tools we show that in a secularly evolving disc ASD develops a set of sharp features -- weakly discontinuous peaks at eccentricity nulls and sharp discontinuities at caustic points where particle periastra or apoastra pile up -- marching out through the disc as it ages. We probe the dependence of these features on planetary eccentricity, ratio of the free to forced particle eccentricity, and underlying radial mass distribution, showing in particular that more eccentric planets produce more prominent ASD features. Convolution with the PSF of realistic observations (as well as the non-zero random free eccentricity of debris) smooths out these features, but they can still be detectable in high-resolution observations. Radial locations of secular ASD peaks follow a particular, well-defined pattern, which should unambiguously point to their secular nature in observations. We illustrate how both detection and non-detection of such secular features in observed discs can be used (in combination with other constraints) to measure or constrain key parameters of perturbing planets (even those not yet detected) -- mass, semi-major axis and eccentricity.

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arXiv2026

$αβq_\mathrm{th}$-mapping of planet-induced density wave damping in protoplanetary discs

Planets embedded in protoplanetary discs are capable of creating a wide variety of substructures through gravitational interactions. This process is mediated through the excitation and damping of density waves which carry angular momentum across the disc. Therefore, to interpret observations of substructures, it is critical to understand the physical processes which lead to deposition of wave angular momentum to the disc fluid. In this study, we explore the relative efficiency of viscosity ($α$), cooling ($β$), and non-linear wave evolution ($q_\mathrm{th}$) in damping planet-generated density waves. We run a large suite of hydrodynamic simulations varying viscosity, cooling timescale, and planetary mass, from which we extract radial profiles of wave angular momentum deposition. We quantify the efficiency of different wave damping mechanisms as a joint function of planetary mass, viscosity and cooling time. We find that nonlinear wave evolution leading to shock formation is typically the most important cause of angular momentum deposition, but that cooling on timescales comparable to local orbital time reaches similar levels of importance for low mass planets (sub-thermal, $q_\mathrm{th}<1$). On the contrary, linear wave damping due to viscosity is rather inefficient, requiring $α\gtrsim 10^{-1.5}$ to noticeably affect damping of waves launched by thermal mass planets. Even for lowest mass planets considered ($q_\mathrm{th}=0.025$), viscosity affects wave damping only if $α\gtrsim 10^{-2.9}$. Our findings could be applied to interpret observations of protoplanetary discs; they are also important for understanding wave propagation in other types of astrophysical discs.

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arXiv2026

Conservation laws in non-inertial frames and non-conservation of energy of relative motion in two-body problem

The dynamics of systems of multiple gravitationally interacting bodies is often studied in a frame attached to one of the objects (e.g. a central star in a planetary system). As this frame is generally non-inertial, indirect forces appear in the equations describing the motion of bodies relative to the reference object. According to the convention adopted in celestial mechanics, the associated indirect acceleration is defined to be different for every object under consideration, whereas the gravitational coupling between each body and the reference object is described via the effective two-body potential, which does not obey the equivalence principle. Here we point out that a slightly different and more physically motivated definition of the indirect acceleration provides significant benefits when interpreting relative motion in a non-inertial frame. First, the indirect acceleration ends up being the same for all objects in the system. Second, the non-conservation of momentum, angular momentum, and energy of the whole system in a non-inertial frame naturally follow from the action of the indirect acceleration on the system as an external force. We also argue that the vis viva integral of the classical two-body problem should not be interpreted as a statement of energy conservation in a non-inertial frame attached to one of the bodies. The energy of relative motion is not conserved in this frame due to the work done on the two-body system by the indirect force. These results can be useful for interpreting dynamics in various astrophysical contexts, in particular the physics of disc-planet coupling.

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arXiv2026

Indirect forces in disc-planet interaction

Gravitational coupling between a protoplanetary disc and an embedded planet is often studied in a frame attached to a central star. This frame is non-inertial because of the stellar reflex motion, leading to indirect forces arising in the star-planet-disc system. Here we examine the impact produced by these forces on several aspects of disc-planet coupling using analytical and numerical means. We explore how neglecting indirect forces changes (1) the spatial pattern of the surface density perturbation in the disc, (2) the calculation of the torque exerted on the disc by the planet, and (3) the torque on the planet exerted by the disc. For low-mass planets, in the linear regime, the differences in the perturbation pattern are only in its $m=1$ azimuthal harmonic, with an amplitude increasing with the distance from the star. In this regime both the torque on the planet and the deposition torque density in the disc are only weakly affected by non-inclusion of indirect forces, corroborating some results of studies neglecting indirect forces altogether. For higher mass planets, a broader range of azimuthal harmonics of the perturbation are affected. Also, indirect forces have a stronger effect on the planetary torque and on planet migration in the Type II regime. We highlight the importance of including the planetary indirect force in the calculation of the torque on the disc (if disc evolution accounts for indirect force) to ensure conservation of angular momentum carried by the planet-driven density waves. The corresponding indirect torque has an oscillatory, radially-diverging character.

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arXiv2025

How two-dimensional are planet-disc interactions? II. Radiation hydrodynamics and suitable cooling prescriptions

The ring and gap structures found in observed protoplanetary disks are often attributed to embedded gap-opening planets and typically modeled with simplified thermodynamics in the 2D, thin disk approximation. However, it has been shown that radiative cooling and meridional processes play key roles in planet-disk interaction, though their computational cost has limited their exploration. We investigate the differences between 2D and 3D models of gap-opening planets while also comparing thermodynamical frameworks ranging from locally isothermal to fully radiative. We also compare simplified cooling recipes to fully radiative models in an effort to motivate the inclusion of radiative effects in future modeling even in a parametrized manner. We perform hydrodynamical simulations in both 2D and 3D, and then compare the angular momentum deposition by planetary spirals to assess gap opening efficiency. We repeat comparisons with different thermodynamical treatments: locally isothermal, adiabatic, local beta cooling, and fully radiative including radiative diffusion. We find that 2D models are able to capture the essential physics of gap opening with remarkable accuracy, even when including full radiation transport in both cases. Simple cooling prescriptions can capture the trends found in fully radiative models, albeit slightly overestimating gap opening efficiency near the planet. Inherently 3D effects such as vertical flows that cannot be captured in 2D can explain the differences between the two approaches, but do not impact gap opening significantly. Our findings encourage the use of models that include radiative processes in the study of planet-disk interaction, even with simplified yet physically motivated cooling prescriptions in lieu of full radiation transport. This is particularly important in the context of substructure-inducing planets in the ALMA-sensitive disk regions (>10 au).

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arXiv2025

Wave-Mediated Boundary Layers of Accretion Discs: Role of Internal Structure of the Accretor

Disc accretion onto astrophysical objects with a material surface proceeds through the boundary layer (BL) -- a radially narrow region in the inner disc where the incoming gas must slow down its rotation before settling onto the surface of the accretor. Here we numerically study a BL in which the angular momentum transport in the layer is accomplished via the excitation of global acoustic waves. While the earlier studies of such wave-mediated BLs typically modeled the internal structure of the central object as a globally isothermal sphere with sharply rising density profile, here we explore the effect of other internal density and temperature profiles on the mode operation. We model the inner structure of an accretor as a polytropic sphere, allowing a shallower increase of density and a non-trivial temperature profile inside the object. While the mix of acoustic modes observed in our long-duration (1000 inner orbits long) 2D hydrodynamic simulations is a weak function of the polytropic index $n$ of the accretor's structure, the mass accretion rate and the angular momentum flux across the BL show a clear dependence on $n$, both decreasing in amplitude as $n$ is lowered. Interestingly, in 2D these transport metrics are better correlated not with $n$ but with a total mass inside the central object contained within the simulation domain. These results improve our understanding of the wave-mediated BL accretion by quantifying the effect of the inner structure of the accretor on the excitation and propagation of acoustic modes mediating the BL transport.

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arXiv2025

How two-dimensional are planet--disc interactions? I. Locally isothermal discs

Planet--disc interactions, despite being fundamentally three-dimensional, are often studied in the two-dimensional `thin-disk' approximation. The overall morphology of planet--disc interactions has ben shown to be similar in both 2D and 3D simulations, however, the ability of a 2D simulation to quantitatively match 3D results depends strongly on how the potential of the planet is handled. Typically, the 2D planetary potential is smoothed out using some `smoothing length', a free parameter, for which different values have been proposed, depending on the particular aspect of the interaction focused on. In this paper, we re-derive 2D Navier--Stokes in detail for planet--disc interactions to find better ways to represent the 2D gravitational force. We perform a large suite of 2D and 3D simulations to test these force prescriptions. We identify the parts of the interaction that are fundamentally 3D, and test how well our new force prescriptions, as well as traditional smoothed potentials, are able to match 3D simulations. Overall, we find that the optimal way to represent the planetary potential is the `Bessel-type potential', but that even in this case 2D simulations are unable to reproduce the correct scaling of the total torque with background gradients, and are at best able match the one-sided Lindblad torque and gap widths to level of 10 per cent. We find that analysis of observed gap structures based on standard 2D simulations may systematically underestimate planetary masses by a factor of two, and discuss the impacts of 3D effects on observations of velocity kinks.

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arXiv2025

Activity in White Dwarf Debris Disks I: Spitzer Legacy Reveals Variability Incompatible with the Canonical Model

This study presents all available, multi-epoch 3.6 and 4.5 $μ$m photometry from Spitzer Space Telescope observations of white dwarf debris disks, including weekly cadence observations of 16 relatively bright systems, and 5 h staring-mode observations for five of these. Significant variability is detected in 85 per cent of disks and across all timescales probed, from minutes to weeks to years, where the largest flux changes correlate with the longest time baselines, and the infrared excesses persist utterly. While each source is idiosyncratic, the overall results indicate the most variable disks correlate with those that are the brightest (dustiest), and also among those with detected gas, demonstrating both dust and gas are produced via ongoing collisions. There is a correlation between flux and colour changes, where disks tend to appear redder when dimmer and bluer when brighter, consistent with an excess of small dust grains produced in collisions, followed by a gradual return to equilibrium. The overall results are a drastic departure from the predictions of the canonical - geometrically thin, optically thick - disk in both flux and colour, but are broadly consistent with collisional evolution based on a simple model. The data presented herein constitute a legacy resource that can inform time-series studies of polluted and dusty white dwarfs, and importantly serve as a basis for future disk modelling, beyond the pioneering canonical framework.

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arXiv2024

Early stages of gap opening by planets in protoplanetary discs

Annular substructures in protoplanetary discs, ubiquitous in sub-mm observations, can be caused by gravitational coupling between a disc and its embedded planets. Planetary density waves inject angular momentum into the disc leading to gap opening only after travelling some distance and steepening into shocks (in the absence of linear damping); no angular momentum is deposited in the planetary coorbital region, where the wave has not shocked yet. Despite that, simulations show mass evacuation from the coorbital region even in inviscid discs, leading to smooth, double-trough gap profiles. Here we consider the early, time-dependent stages of planetary gap opening in inviscid discs. We find that an often-overlooked contribution to the angular momentum balance caused by the time-variability of the specific angular momentum of the disc fluid (caused, in turn, by the time-variability of the radial pressure support) plays a key role in gap opening. Focusing on the regime of shallow gaps with depths of $\lesssim 20\%$, we demonstrate analytically that early gap opening is a self-similar process, with the amplitude of the planet-driven perturbation growing linearly in time and the radial gap profile that can be computed semi-analytically. We show that mass indeed gets evacuated from the coorbital region even in inviscid discs. This evolution pattern holds even in viscous discs over a limited period of time. These results are found to be in excellent agreement with 2D numerical simulations. Our simple gap evolution solutions can be used in studies of dust dynamics near planets and for interpreting protoplanetary disc observations.

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arXiv2024

Eccentric planet-disc interactions: orbital migration and eccentricity evolution

Gravitational coupling between a protoplanetary disc and an embedded eccentric planet is an important, long-standing problem, which has been not yet been conclusively explored. Here we study the torque and associated orbital evolution of an eccentric planet in a two-dimensional disc via the semi-analytical, fully global linear approach. Our methodology has the advantage that the spatial structure of the density waves launched by the planet is solved for fully. This allows us to account for the possibility of torque excitation over an extended radial interval for each Fourier harmonic of the perturbation, as opposed to earlier approximate treatments localized around Lindblad and corotation resonances. We systematically explore the torque behaviour across the space of disc properties (assuming power law profiles for the disc surface density and temperature), including the aspect ratio. Crucially, we examine the torque variation as the orbital eccentricity becomes supersonic relative to the gas motion (when planetary eccentricity is of order the disc aspect ratio), finding that the torque robustly reverses its sign near this transition. We also find that for shallow surface density gradients planetary migration may become outwards beyond this transition, although the rapid eccentricity damping (which is typically $\sim 10^2$ times faster than the orbital migration rate) would quickly restore inwards migration as the planet circularizes. Our self-consistently computed torques are in qualitative agreement with past numerical studies of eccentric planet-disc coupling. We provide our torque data for different disc parameters to the community for future testing and implementation in population synthesis studies.

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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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arXiv2023

Orbital evolution of LIGO/Virgo binaries in stellar clusters driven by cluster tides, stellar encounters and general relativity

Origin of LIGO/Virgo gravitational wave events may involve production of binaries with relativistic components in dense stellar systems - globular or nuclear star clusters - and their subsequent evolution towards merger. Orbital parameters of these binaries (the inner orbit) and their motion inside the cluster (the outer orbit) evolve due to both external agents - random encounters with cluster stars and cluster tides due to the smooth cluster potential - and the internal ones - various sources of dissipation and precession within the binary. We present a numerical framework - Binary Evolution in Stellar Clusters (BESC) - that follows the evolution of the binary inner and outer orbits accounting for all these effects simultaneously, enabling efficient Monte Carlo studies. The secular effect of cluster tides is computed in the singly-averaged approximation, without averaging over the outer binary orbit. As to stellar encounters, we include the effects of both close and distant flybys on the inner and outer orbits of the binary, respectively. In particular, this allows us to explicitly account for the dynamical friction sinking the binary towards the cluster centre. Also, given our focus on the LIGO/Virgo sources, we include the general relativistic precession (which suppresses cluster tides at high eccentricities) and the gravitational wave emission (shrinking the binary orbit). We use BESC to illustrate a number of characteristic binary evolutionary outcomes and discuss relative contributions of different physical processes. BESC can also be used to study other objects in clusters, e.g. blue stragglers, hot Jupiters, X-ray binaries, etc.

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arXiv2023

Gravitational torque in circumbinary discs: global radial oscillations

Circumbinary discs (CBDs) arise in many astrophysical settings, including young stellar binaries and supermassive black hole binaries. Their structure is mediated by gravitational torques exerted on the disc by the central binary. The spatial distribution of the binary torque density (so-called excitation torque density) in CBDs is known to feature global large-amplitude, quasi-periodic oscillations, which are often interpreted in terms of the local resonant Lindblad torques. Here we investigate the nature of these torque oscillations using 2D, inviscid hydrodynamic simulations and theoretical calculations. We show that torque oscillations arise due to the gravitational coupling of the binary potential to the density waves launched near the inner cavity and freely propagating out in the disc. We provide analytical predictions for the radial periodicity of the torque density oscillations and verify them with simulations, showing that disc sound speed and the multiplicity of the density wave spiral arms are the key factors setting the radial structure of the oscillations. Resonant Lindblad torques play no direct role in determining the radial structure and periodicity of the torque oscillations and manifest themselves only by driving the density waves in the disc. We also find that vortices forming at the inner edge of the disc can provide a non-trivial contribution to the angular momentum transport in the CBD. Our results can be applied to understanding torque behaviour in other settings, e.g. discs in cataclysmic variables and X-ray binaries.

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arXiv2023

Formation of Gaps in Self-gravitating Debris Disks by Secular Resonance in a Single-planet System. II. Towards a Self-consistent Model

High-resolution observations of several debris disks reveal structures such as gaps and spirals, suggestive of gravitational perturbations induced by underlying planets. Most existing studies of planet--debris disk interactions ignore the gravity of the disk, treating it as a reservoir of massless planetesimals. In this paper, we continue our investigation into the long-term interaction between a single eccentric planet and an external, massive debris disk. Building upon our previous work, here we consider not only the axisymmetric component of the disk's gravitational potential, but also the non-axisymmetric torque that the disk exerts on the planet (ignoring for now only the non-axisymmetric component of the disk self-gravity). To this goal, we develop and test a semi-analytic `$N$-ring' framework that is based on a generalized (softened) version of the classical Laplace--Lagrange secular theory. Using this tool, we demonstrate that even when the disk is less massive than the planet, not only can a secular resonance be established within the disk that leads to the formation of a wide gap, but that the very same resonance also damps the planetary eccentricity $e_p$ via a process known as resonant friction. The resulting gap is initially non-axisymmetric (akin to those observed in HD 92945 and HD 206893), but evolves to become more axisymmetric (similar to that in HD 107146) as $e_p(t)\rightarrow0$ with time. We also develop analytic understanding of these findings, finding good quantitative agreement with the outcomes of the $N$-ring calculations. Our results may be used to infer both the dynamical masses of (gapped) debris disks and the dynamical history of the planets interior to them, as we exemplify for HD 206893.

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arXiv2023

Torque wiggles -- a robust feature of the global disc-planet interaction

Gravitational coupling between planets and protoplanetary discs is responsible for many important phenomena such as planet migration and gap formation. The key quantitative characteristics of this coupling is the excitation torque density -- the torque (per unit radius) imparted on the disc by planetary gravity. Recent global simulations and linear calculations found an intricate pattern of low-amplitude, quasi-periodic oscillations in the global radial distribution of torque density in the outer disc, which we call torque wiggles. Here we show that torque wiggles are a robust outcome of global disc-planet interaction and exist despite the variation of disc parameters and thermodynamic assumptions (including $β$-cooling). They result from coupling of the planetary potential to the planet-driven density wave freely propagating in the disc. We developed analytical theory of this phenomenon based on approximate self-similarity of the planet-driven density waves in the outer disc. We used it, together with linear calculations and simulations, to show that (a) the radial periodicity of the wiggles is determined by the global shape of the planet-driven density wave (its wrapping in the disc) and (b) the sharp features in the torque density distribution result from constructive interference of different azimuthal (Fourier) torque contributions at radii where the planetary wake crosses the star-planet line. In the linear regime the torque wiggles represent a weak effect, affecting the total (integrated) torque by only a few per cent. However, their significance should increase in the non-linear regime, when a gap (or a cavity) forms around the perturber's orbit.

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arXiv2023

Modeling planet-induced gaps and rings in ALMA disks: the role of in-plane radiative diffusion

ALMA observations of protoplanetary disks in dust continuum emission reveal a variety of annular structures. Attributing the existence of such features to embedded planets is a popular scenario, supported by studies using hydrodynamical models. Recent work has shown that radiative cooling greatly influences the capability of planet-driven spiral density waves to transport angular momentum, ultimately deciding the number, position, and depth of rings and gaps that a planet can carve in a disk. However, radiation transport has only been treated via local thermal relaxation, not taking into account radiative diffusion along the disk plane. We compare the previous state-of-the-art models of planet-disk interaction with local cooling prescriptions to our new models that include cooling in the vertical direction and radiative diffusion in the plane of the disk, and show that the response of the disk to the induced spiral waves can differ significantly when comparing these two treatments of the disk thermodynamics. We follow up with synthetic emission maps of ALMA systems, and show that our new models reproduce the observations found in the literature better than models with local cooling. We conclude that appropriate treatment of radiation transport is key to constraining the parameter space when interpreting ALMA observations using the planet-disk interaction scenario.

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arXiv2023

Vortex weighing and dating of planets in protoplanetary discs

High-resolution sub-mm observations of some protoplanetary discs reveal non-asixymmetric features, which can often be interpreted as dust concentrations in vortices that form at the edges of gaps carved out by the embedded planets. We use recent results on the timescale for the planet-driven vortex development in low-viscosity discs to set constraints on the mass and age of a planet producing the vortex. Knowledge of the age of the central star in a vortex-bearing protoplanetary disc system allows one to set a lower limit on the planetary mass at the level of several tens of $M_\oplus$. Also, an independent upper limit on the planetary mass would constrain the planetary age, although given the current direct imaging detection limits this constraint is not yet very stringent (it is also sensitively dependent on the disc scale height). These results can be extended to account for the history of planetary mass accretion if it is known. We apply our calculations to several protoplanetary discs harbouring vortex-like features as revealed by ALMA and set limits of $(30-50)M_\oplus$ (for disc aspect ratio of $0.1$) on the minimum masses of putative planets that could be responsible for these vortices. Our vortex-based method provides an independent way of constraining the properties of embedded planets, complementary to other approaches.

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arXiv2022

Emergence of vortices at the edges of planet-driven gaps in protoplanetary discs

Young planets embedded in protoplanetary discs (PPDs) excite spiral density waves, which propagate, shock and deposit angular momentum in the disc. This results in gap opening around the planetary orbit, even for low (sub-thermal) mass planets, provided that the effective viscosity in the disc is low. The edges of these planet-induced gaps are known to be prone to emergence of observable vortices via the Rossby Wave Instability (RWI). We study timescales for the development of vortices driven by low mass planets in inviscid discs. We employ a recently developed semi-analytical theory of vortensity production by the planet-driven shock to predict vortensity evolution near the planet, from which we derive the radial profile of the planet-induced gap as a function of time (this procedure can have multiple other uses, e.g. to study dust trapping, suppression of pebble accretion, etc.). We then analyze the linear stability of the gap edges against the RWI, obtaining the timescales for the first appearance of unstable modes and (later) fully developed vortices at gap edges. We present useful formulae for these timescales as functions of planetary and disc parameters and provide their physical justification. We also thoroughly test our semi-analytical framework against high resolution 2D hydrodynamic simulations, confirming the accuracy of our theoretical predictions. We discuss ways in which our semi-analytical framework can be extended to incorporate additional physics, e.g. planetary accretion, migration, and non-zero disc viscosity. Our results can be used to interpret observations of PPDs and to predict emergence of vortices in simulations.

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