arXiv subjects

Roman R. Rafikov

Publications and source records attributed to Roman R. Rafikov.

At least 37 records · Page 2Linked to original sources

arXiv2022

Density waves in protoplanetary discs excited by eccentric planets: linear theory

Spiral density waves observed in protoplanetary discs have often been used to infer the presence of embedded planets. This inference relies both on simulations as well as the linear theory of planet-disc interaction developed for planets on circular orbits to predict the morphology of the density wake. In this work we develop and implement a linear framework for calculating the structure of the density wave in a gaseous disc driven by an eccentric planet. Our approach takes into account both the essential azimuthal and temporal periodicities of the problem, allowing us to treat any periodic perturbing potential (i.e. not only that of an eccentric planet). We test our framework by calculating the morphology of the density waves excited by an eccentric, low-mass planet embedded in a globally isothermal disc and compare our results to the recent direct numerical simulations (and heuristic wavelet analysis) of the same problem by Zhu and Zhang. We find excellent agreement with the numerical simulations, capturing all the complex eccentric features including spiral bifurcations, wave crossings and planet-wave detachments, with improved accuracy and detail compared with the wavelet method. This illustrates the power of our linear framework in reproducing the morphology of complicated time-dependent density wakes, presenting it as a valuable tool for future studies of eccentric planet-disc interactions.

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arXiv2022

Radial Profiles of Surface Density in Debris Discs

Resolved observations of debris discs can be used to derive radial profiles of Azimuthally-averaged Surface Density (ASD), which carries important information about the disc structure even in presence of non-axisymmetric features and has improved signal-to-noise characteristics. We develop a (semi-)analytical formalism allowing one to relate ASD to the underlying semi-major axis and eccentricity distributions of the debris particles in a straightforward manner. This approach does not involve the distribution of particle apsidal angles, thus simplifying calculations. It is a much faster, more flexible and effective way of calculating ASD than the Monte Carlo sampling of orbital parameters of debris particles. We present explicit analytical results based on this technique for a number of particle eccentricity distributions, including two cases of particular practical importance: a prescribed radial profile of eccentricity, and the Rayleigh distribution of eccentricities. We then show how our framework can be applied to observations of debris discs and rings for retrieving either the semi-major axis distribution or (in some cases) the eccentricity distribution of debris, thus providing direct information about the architecture and dynamical processes operating in debris discs. Our approach also provides a fast and efficient way of forward modeling observations. Applications of this technique to other astrophysical systems, e.g. the nuclear stellar disc in M31 or tenuous planetary rings, are also discussed.

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arXiv2022

Anatomy of a slow merger: dissecting secularly-driven inspirals of LIGO/Virgo gravitational wave sources

The dozens of compact object mergers detected by LIGO/Virgo raise a key theoretical question: how do initially wide binaries shrink sufficiently quickly that they are able to merge via gravitational wave (GW) radiation within a Hubble time? One promising class of answers involves secular driving of binary eccentricity by some external tidal perturbation. This perturbation can arise due to the presence of a tertiary point mass, in which case the system exhibits Lidov-Kozai (LK) dynamics, or it can stem from the tidal field of the stellar cluster in which the binary orbits. While these secular tide-driven mechanisms have been studied exhaustively in the case of no GW emission, when GWs are included the dynamical behavior is still incompletely understood. In this paper we consider compact object binaries driven to merger via high eccentricity excitation by (doubly-averaged, test-particle quadrupole level) cluster tides - which includes LK-driven mergers as a special case - and include the effects of both general relativistic precession and GW emission. We provide for the first time an analytical understanding of the different evolutionary stages of the binary's semimajor axis, secular oscillation timescale, and phase space structure all the way to merger. Our results will inform future population synthesis calculations of compact object binary mergers from hierarchical triples and stellar clusters.

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arXiv2022

Boundary Layers of Accretion Disks: Wave-Driven Transport and Disk Evolution

Astrophysical objects possessing a material surface (white dwarfs, young stars, etc.) may accrete gas from the disc through the so-called surface boundary layer (BL), in which the angular velocity of the accreting gas experiences a sharp drop. Acoustic waves excited by the supersonic shear in the BL play an important role in mediating the angular momentum and mass transport through that region. Here we examine the characteristics of the angular momentum transport produced by the different types of wave modes emerging in the inner disc, using the results of a large suite of hydrodynamic simulations of the BLs. We provide a comparative analysis of the transport properties of different modes across the range of relevant disc parameters. In particular, we identify the types of modes which are responsible for the mass accretion onto the central object. We find the correlated perturbations of surface density and radial velocity to provide an important contribution to the mass accretion rate. Although the wave-driven transport is intrinsically non-local, we do observe a clear correlation between the angular momentum flux injected into the disc by the waves and the mass accretion rate through the BL. We find the efficiency of angular momentum transport (normalized by thermal pressure) to be a weak function of the flow Mach number. We also quantify the wave-driven evolution of the inner disc, in particular the modification of the angular frequency profile in the disc. Our results pave the way for understanding wave-mediated transport in future three-dimensional, magnetohydrodynamic studies of the BLs.

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arXiv2021

Eclipse timing the Milky Way's gravitational potential

We show that a small, but \textit{measurable} shift in the eclipse mid-point time of eclipsing binary (EBs) stars of $\sim$ 0.1 seconds over a decade baseline can be used to directly measure the Galactic acceleration of stars in the Milky Way at $\sim$ kpc distances from the Sun. We consider contributions to the period drift rate from dynamical mechanisms other than the Galaxy's gravitational field, and show that the Galactic acceleration can be reliably measured using a sample of $\textit{Kepler}$ EBs with orbital and stellar parameters from the literature. Given the uncertainties on the formulation of tidal decay, our approach here is necessarily approximate, and the contribution from tidal decay is an upper limit assuming the stars are not tidally synchronized. We also use simple analytic relations to search for well-timed sources in the \textit{Kepler} field, and find $\sim$ 70 additional detached EBs with low eccentricities that have estimated timing precision better than 1 second. We illustrate the method with a prototypical, precisely timed EB using an archival \textit{Kepler} light curve and a modern synthetic \textit{HST} light curve (which provides a decade baseline). This novel method establishes a realistic possibility for obtaining fundamental Galactic parameters using eclipse timing to measure Galactic accelerations, along with other emerging new methods, including pulsar timing and extreme precision radial velocity observations. This acceleration signal grows quadratically with time. Therefore, given baselines established in the near-future for distant EBs, we can expect to measure the period drift in the future with space missions like \textit{JWST} and the \textit{Roman Space Telescope}.

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arXiv2021

Boundary Layers of Accretion Disks: Discovery of Vortex-Driven Modes and Other Waves

Disk accretion onto weakly magnetized objects possessing a material surface must proceed via the so-called boundary layer (BL) - a region at the inner edge of the disk, in which the velocity of accreting material abruptly decreases from its Keplerian value. Supersonic shear arising in the BL is known to be conducive to excitation of acoustic waves that propagate into both the accretor and the disk, enabling angular momentum and mass transport across the BL. We carry out a numerical exploration of different wave modes that operate near the BL, focusing on their morphological characteristics in the innermost parts of accretion disk. Using a large suite of simulations covering a broad range of Mach numbers (of the supersonic shear flow in the BL), we provide accurate characterization of the different types of modes, verifying their properties against analytical results, when available. We discover new types of modes, in particular, global spiral density waves launched by vortices forming in the disk near the BL as a result of the Rossby wave instability; this instability is triggered by the vortensity production in that region caused by the nonlinear damping of acoustic waves. Azimuthal wavenumbers of the dominant modes that we observe appear to increase monotonically with the Mach number of the runs, but a particular mix of modes found in a simulation is mildly stochastic. Our results provide a basis for better understanding of the angular momentum and mass transport across the BL as well as the emission variability in accreting objects.

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arXiv2021

Planet-driven density waves in protoplanetary discs: numerical verification of nonlinear evolution theory

Gravitational coupling between protoplanetary discs and planets embedded in them leads to the emergence of spiral density waves, which evolve into shocks as they propagate through the disc. We explore the performance of a semi-analytical framework for describing the nonlinear evolution of the global planet-driven density waves, focusing on the low planet mass regime (below the so-called thermal mass). We show that this framework accurately captures the (quasi-)self-similar evolution of the wave properties expressed in terms of properly rescaled variables, provided that certain theoretical inputs are calibrated using numerical simulations (an approximate, first principles calculation of the wave evolution based on the inviscid Burgers equation is in qualitative agreement with simulations but overpredicts wave damping at the quantitative level). We provide fitting formulae for such inputs, in particular, the strength and global shape of the planet-driven shock accounting for nonlinear effects. We use this nonlinear framework to theoretically compute vortensity production in the disc by the global spiral shock and numerically verify the accuracy of this calculation. Our results can be used for interpreting observations of spiral features in discs, kinematic signatures of embedded planets in CO line emission ("kinks"), and for understanding the emergence of planet-driven vortices in protoplanetary discs.

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arXiv2021

Planet formation in stellar binaries: Global simulations of planetesimal growth

Planet formation around one component of a tight, eccentric binary system such as $γ$ Cephei (with semimajor axis around 20 AU) is theoretically challenging because of destructive high-velocity collisions between planetesimals. Despite this fragmentation barrier, planets are known to exist in such orbital configurations. Here we present a novel numerical framework for carrying out multi-annulus coagulation-fragmentation calculations of planetesimal growth, which fully accounts for the specifics of planetesimal dynamics in binaries, details of planetesimal collision outcomes, and the radial transport of solids in the disk due to the gas drag-driven inspiral. Our dynamical inputs properly incorporate the gravitational effects of both the eccentric stellar companion and the massive non-axisymmetric protoplanetary disk in which planetesimals reside, as well as gas drag. We identify a set of disk parameters that lead to successful planetesimal growth in systems such as $γ$ Cephei or $α$ Centauri starting from $1-10$ km size objects. We identify the apsidal alignment of a protoplanetary disk with the binary orbit as one of the critical conditions for successful planetesimal growth: It naturally leads to the emergence of a dynamically quiet location in the disk (as long as the disk eccentricity is of order several percent), where favorable conditions for planetesimal growth exist. Accounting for the gravitational effect of a protoplanetary disk plays a key role in arriving at this conclusion, in agreement with our previous results. These findings lend support to the streaming instability as the mechanism of planetesimal formation. They provide important insights for theories of planet formation around both binary and single stars, as well as for the hydrodynamic simulations of protoplanetary disks in binaries (for which we identify a set of key diagnostics to verify).

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arXiv2021

Secular dynamics of binaries in stellar clusters -- III. Doubly-averaged dynamics in the presence of general relativistic precession

Secular evolution of binaries driven by an external (tidal) potential is a classic astrophysical problem. Tidal perturbations can arise due to an external point mass, as in the Lidov-Kozai (LK) theory of hierarchical triples, or due to an extended stellar system (e.g. galaxy or globular cluster) in which the binary resides. For many applications, general-relativistic (GR) apsidal precession is important, and has been accounted for in some LK calculations. Here we generalise and extend these studies by exploring in detail the effect of GR precession on (quadrupole-level) tidal evolution of binaries orbiting in arbitrary axisymmetric potentials (which includes LK theory as a special case). We study the (doubly-averaged) orbital dynamics for arbitrary strengths of GR and binary initial conditions and uncover entirely new phase space morphologies with important implications for the binary orbital evolution. We also explore how GR precession affects secular evolution of binary orbital elements when the binary reaches high eccentricity ($e\to 1$) and delineate several different dynamical regimes. Our results are applicable to a variety of astrophysical systems. In particular, they can be used to understand the high-eccentricity behaviour of (cluster) tide-driven compact object mergers -- i.e. LIGO/Virgo gravitational wave sources -- for which GR effects are crucial.

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arXiv2021

Doppler Boosting of the S-stars in the Galactic Center

Astrometry and spectroscopy of the S-stars in the Galactic Center provide a unique way to probe the properties of the central supermassive black hole, as well as the post-Newtonian effects caused by its gravity, e.g. gravitational redshift and general relativistic precession. It has also been suggested that the photometry of S-stars can be used for studying the properties of gaseous environment of Sgr A$^*$. Due to the high velocities of the S-stars, sometimes approaching $~0.1c$, their photometric signal should be considerably affected by the Doppler boosting. We calculate this relativistic effect for several S-stars closely approaching the central black hole (most of them recently announced) and show that the amplitude of the photometric variability due to the Doppler boosting for some of them (S62 and S4714) exceeds $6\%$; for the well studied star S2 it is about $2\%$. Measurement of the Doppler boosting can confirm the existence and help refine orbital parameters of the S-stars with noisy spectroscopy and astrometry. This effect should be explicitly accounted for when the photometry of S-stars is used for probing the medium around the Sgr A$^*$. We discuss the observability of the Doppler boosting given the complications typical for the Galactic Center and conclude, in particular, that the purely photometric detection of the higher order relativistic corrections to the Doppler boosting signal (due to the gravitational redshift and transverse Doppler shift, which we also calculate) is hardly possible for the S-stars.

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arXiv2021

Formation of Gaps in Self-Gravitating Debris Disks by Secular Resonance in a Single-planet System I: A Simplified Model

Spatially resolved images of debris disks frequently reveal complex morphologies such as gaps, spirals, and warps. Most existing models for explaining such morphologies focus on the role of massive perturbers (i.e. planets, stellar companions), ignoring the gravitational effects of the disk itself. Here we investigate the secular interaction between an eccentric planet and a massive, external debris disk using a simple analytical model. Our framework accounts for both the gravitational coupling between the disk and the planet, as well as the disk self-gravity -- with the limitation that it ignores the non-axisymmetric component of the disk (self-)gravity. We find generally that even when the disk is less massive than the planet, the system may feature secular resonances within the disk (contrary to what may be naively expected), where planetesimal eccentricities get significantly excited. Given this outcome we propose that double-ringed debris disks, such as those around HD 107146 and HD 92945, could be the result of secular resonances with a yet-undetected planet interior to the disk. We characterize the dependence of the properties of the secular resonances (i.e. locations, timescales, and widths) on the planet and disk parameters, finding that the mechanism is robust provided the disk is massive enough. As an example, we apply our results to HD 107146 and find that this mechanism readily produces $\sim 20$ au wide non-axisymmetric gaps. Our results may be used to set constraints on the total mass of double-ringed debris disks. We demonstrate this for HD 206893, for which we infer a disk mass of $\approx 170$ Earth masses by considering perturbations from the known brown dwarf companion.

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arXiv2020

Gaps and Rings in Protoplanetary Disks with Realistic Thermodynamics: The Critical Role of In-Plane Radiation Transport

Many protoplanetary disks exhibit annular gaps in dust emission, which may be produced by planets. Simulations of planet-disk interaction aimed at interpreting these observations often treat the disk thermodynamics in an overly simplified manner, which does not properly capture the dynamics of planet-driven density waves driving gap formation. Here we explore substructure formation in disks using analytical calculations and hydrodynamical simulations that include a physically-motivated prescription for radiative effects associated with the planet-induced density waves. For the first time, our treatment accounts not only for cooling from the disk surface, but also for radiation transport along the disk midplane. We show that this in-plane cooling, with a characteristic timescale typically an order of magnitude shorter than the one due to surface cooling, plays a critical role in density wave propagation and dissipation (we provide a simple estimate of this timescale). We also show that viscosity, at the levels expected in protoplanetary disks ($α\lesssim 10^{-3}$), has a negligible effect on density wave dynamics. Using synthetic maps of dust continuum emission, we find that the multiplicity and shape of the gaps produced by planets are sensitive to the physical parameters---disk temperature, mass, and opacity---that determine the damping of density waves. Planets orbiting at $\lesssim 20$ au produce the most diverse variety of gap/ring structures, although significant variation is also found for planets at $\gtrsim 50$ au. By improving the treatment of physics governing planet-disk coupling, our results present new ways of probing the planetary interpretation of annular substructures in disks.

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arXiv2020

Planet-disk interaction in disks with cooling: basic theory

Gravitational coupling between young planets and their parent disks is often explored using numerical simulations, which typically treat the disk thermodynamics in a highly simplified manner. In particular, many studies adopt the locally isothermal approximation, in which the disk temperature is a fixed function of the stellocentric distance. We explore the dynamics of planet-driven density waves in disks with more general thermodynamics, in which the temperature is relaxed towards an equilibrium profile on a finite cooling timescale $t_{\rm c}$. We use both linear perturbation theory and direct numerical simulations to examine the global structure of density waves launched by planets in such disks. A key diagnostic used in this study is the behavior of the wave angular momentum flux (AMF), which directly determines the evolution of the underlying disk. The AMF of free waves is constant for slowly cooling (adiabatic) disks, but scales with the disk temperature for rapidly cooling (and locally isothermal) disks. However, cooling must be extremely fast, with $β= Ωt_{\rm c} \lesssim 10^{-3}$ for the locally isothermal approximation to provide a good description of density wave dynamics in the linear regime (relaxing to $β\lesssim 10^{-2}$ when nonlinear effects are important). For intermediate cooling timescales, density waves are subject to a strong linear damping. This modifies the appearance of planet-driven spiral arms and the characteristics of axisymmetric structures produced by massive planets: in disks with $β\approx 0.1$ -- $1$, a near-thermal mass planet opens only a single wide gap around its orbit, in contrast to the several narrow gaps produced when cooling is either faster or slower.

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arXiv2019

O(N^2) fragmentation algorithm

Collisional fragmentation is a ubiquitous phenomenon arising in a variety of astrophysical systems, from asteroid belts to debris and protoplanetary disks. Numerical studies of fragmentation typically rely on discretizing the size distribution of colliding objects into a large number N of bins in mass space, usually logarithmically spaced. A standard approach for redistributing the debris produced in collisions into the corresponding mass bins results in O(N^3) calculation, which leads to significant computational overhead when N is large. Here we formulate a more efficient explicit O(N^2) fragmentation algorithm, which works when the size spectrum of fragments produced in an individual collision has a self-similar shape with only a single characteristic mass scale (which can have arbitrary dependence on the energy and masses of colliding objects). Fragment size spectra used in existing fragmentation codes typically possess this property. We also show that our O(N^2) approach can be easily extended to work with non-self-similar fragment size distributions, for which we provide a worked example. This algorithm offers a substantial speedup of fragmentation calculations for large N> 100, even over the implicit methods, making it an attractive tool for studying collisionally evolving systems.

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arXiv2019

Potential softening and eccentricity dynamics in razor-thin, nearly-Keplerian discs

In many astrophysical problems involving discs (gaseous or particulate) orbiting a dominant central mass, gravitational potential of the disc plays an important dynamical role. Its impact on the motion of external objects, as well as on the dynamics of the disc itself, can usually be studied using secular approximation. This is often done using softened gravity to avoid singularities arising in calculation of the orbit-averaged potential --- disturbing function --- of a razor-thin disc using classical Laplace-Lagrange theory. We explore the performance of several softening formalisms proposed in the literature in reproducing the correct eccentricity dynamics in the disc potential. We identify softening models that, in the limit of zero softening, give results converging to the expected behavior exactly, approximately or not converging at all. We also develop a general framework for computing secular disturbing function given an arbitrary softening prescription for a rather general form of the interaction potential. Our results demonstrate that numerical treatments of the secular disc dynamics, representing the disc as a collection of $N$ gravitationally interacting annuli, are rather demanding: for a given value of the (dimensionless) softening parameter, $ς\ll 1$, accurate representation of eccentricity dynamics requires $N \sim Cς^{-χ}\gg 1$, with $C\sim O(10)$, $1.5\lesssim χ\lesssim 2$. In discs with sharp edges a very small value of the softening parameter $ς$ ($\lesssim 10^{-3}$) is required to correctly reproduce eccentricity dynamics near the disc boundaries; this finding is relevant for modelling planetary rings.

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arXiv2019

Secular dynamics of binaries in stellar clusters I: general formulation and dependence on cluster potential

Orbital evolution of binary systems in dense stellar clusters is important in a variety of contexts: origin of blue stragglers, progenitors of compact object mergers, millisecond pulsars, and so on. Here we consider the general problem of secular evolution of the orbital elements of a binary system driven by the smooth tidal field of an axisymmetric stellar cluster (globular, nuclear, etc.) in which the binary orbits. We derive a secular Hamiltonian (averaged over both the inner Keplerian orbit of the binary and its outer orbit within the cluster) valid to quadrupole order for an arbitrary cluster potential and explore its characteristics. This doubly-averaged 'tidal' Hamiltonian depends on just two parameters, which fully absorb the information about the background cluster potential and the binary's orbit within it: a dimensional parameter $A$ setting the secular timescale, and a dimensionless parameter $Γ$ which determines the phase portrait of the binary's inner orbital evolution. We examine the dependence of $A$ and $Γ$ on cluster potential (both spherical and axisymmetric) and on the binary orbit within the cluster. Our theory reproduces known secular results - such as Lidov-Kozai evolution and the effect of the Galactic tide on Oort Cloud comets - in appropriate limits, but is more general. It provides a universal framework for understanding dynamical evolution of various types of binaries driven by the smooth tidal field of any axisymmetric potential. In a companion paper (Hamilton & Rafikov 2019b) we provide a detailed exploration of the resulting orbital dynamics.

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arXiv2019

Secular dynamics of binaries in stellar clusters II: dynamical evolution

Dense stellar clusters are natural sites for the origin and evolution of exotic objects such as relativistic binaries (potential gravitational wave sources), blue stragglers, etc. We investigate the secular dynamics of a binary system driven by the global tidal field of an axisymmetric stellar cluster in which the binary orbits. In a companion paper (Hamilton & Rafikov 2019a) we developed a general Hamiltonian framework describing such systems. The effective (doubly-averaged) Hamiltonian derived there encapsulates all information about the tidal potential experienced by the binary in its orbit around the cluster in a single parameter $Γ$. Here we provide a thorough exploration of the phase-space of the corresponding secular problem as $Γ$ is varied. We find that for $Γ> 1/5$ the phase-space structure and the evolution of binary orbital element are qualitatively similar to the Lidov-Kozai problem. However, this is only one of four possible regimes, because the dynamics are qualitatively changed by bifurcations at $Γ= 1/5,0,-1/5$. We show how the dynamics are altered in each regime and calculate characteristics such as secular evolution timescale, maximum possible eccentricity, etc. We verify the predictions of our doubly-averaged formalism numerically and find it to be very accurate when its underlying assumptions are fulfilled, typically meaning that the secular timescale should exceed the period of the binary around the cluster by $\gtrsim 10-10^2$ (depending on the cluster potential and binary orbit). Our results may be relevant for understanding the nature of a variety of exotic systems harboured by stellar clusters.

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arXiv2019

Compact object binary mergers driven by cluster tides: a new channel for LIGO/Virgo gravitational wave events

The detections of gravitational waves produced in mergers of binary black holes (BH) and neutron stars (NS) by LIGO/Virgo have stimulated interest in the origin of the progenitor binaries. Dense stellar systems - globular and nuclear star clusters - are natural sites of compact object binary formation and evolution towards merger. Here we explore a new channel for the production of binary mergers in clusters, in which the tidal field of the cluster secularly drives the binary to high eccentricity (even in the absence of a central massive black hole) until gravitational wave emission becomes important. We employ the recently developed secular theory of cluster tide-driven binary evolution to compute present day merger rates for BH-BH, NS-BH and NS-NS binaries, varying cluster potential and central concentration of the binary population (but ignoring cluster evolution and stellar flybys for now). Unlike other mechanisms, this new dynamical channel can produce a significant number of mergers out to cluster-centric distances of several pc. For NS-NS binaries we find merger rates in the range $0.01-0.07$ Gpc$^{-3}$ yr$^{-1}$ from globular clusters and $0.1-0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear clusters. For NS-BH and BH-BH binaries we find small merger rates from globular clusters, but a rate of $0.1 - 0.2$ Gpc$^{-3}$ yr$^{-1}$ from cusped nuclear clusters, contributing to the observed LIGO/Virgo rate at the level of several per cent. Therefore, cluster tide-driven mergers constitute a new channel that can be further explored with current and future gravitational wave detectors.

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