arXiv subjects

Roman R. Rafikov

Publications and source records attributed to Roman R. Rafikov.

At least 73 records · Page 4Linked to original sources

arXiv2016

Generalized Similarity for Accretion/Decretion Disks

Decretion (or external) disks are gas disks freely expanding to large radii due to their internal stresses. They are expected to naturally arise in tidal disruption events, around Be stars, in mass-losing post main sequence binaries, as a result of supernova fallback, etc. Their evolution is theoretically understood in two regimes: when the central object does not exert torque on the disk (a standard assumption for conventional accretion disks) or when no mass inflow (or outflow) occurs at the disk center. However, many astrophysical objects - circumbinary disks, Be stars, neutron stars accreting in a propeller regime, etc. - feature non-zero torque simultaneously with the non-zero accretion (or ejection of mass) at the disk center. We provide a general description for the evolution of such disks (both linear and non-linear) in the self-similar regime, to which the disk should asymptotically converge with time. We identify a similarity parameter $λ$, which is uniquely related to the degree, to which the central mass accretion is suppressed by the non-zero central torque. The known decretion disk solutions correspond to the two discrete values of $λ$, while our new solutions cover a continuum of its physically allowed values, corresponding to either accretion or mass ejection by the central object. A direct relationship between $λ$ and central $\dot M$ and torque is also established. We describe the time evolution of the various disk characteristics for different $λ$, and show that the observable properties (spectrum and luminosity evolution) of the decretion disks are in general different from the standard accretion disks with no central torque.

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arXiv2016

Accretion and Orbital Inspiral in Gas-Assisted Supermassive Black Hole Binary Mergers

Many galaxies are expected to harbor binary supermassive black holes (SMBHs) in their centers. Their interaction with the surrounding gas results in accretion and exchange of angular momentum via tidal torques, facilitating binary inspiral. Here we explore the non-trivial coupling between these two processes and analyze how the global properties of externally supplied circumbinary disks depend on the binary accretion rate. By formulating our results in terms of the angular momentum flux driven by internal stresses, we come up with a very simple classification of the possible global disk structures, which differ from the standard constant $\dot M$ accretion disk solution. Suppression of accretion by the binary tides, leading to a significant mass accumulation in the inner disk, accelerates binary inspiral. We show that once the disk region strongly perturbed by the viscously transmitted tidal torque exceeds the binary semi-major axis, the binary can merge in less than its mass-doubling time due to accretion. Thus, unlike the inspirals driven by stellar scattering, the gas-assisted merger can occur even if the binary is embedded in a relatively low mass disk (lower than its own mass). This is important for resolving the "last parsec" problem for SMBH binaries and understanding powerful gravitational wave sources in the Universe. We argue that the enhancement of accretion by the binary found in some recent simulations cannot persist for a long time and should not affect the long-term orbital inspiral. We also review the existing simulations of the SMBH binary-disk coupling and propose a numerical setup, which is particularly well suited for verifying our theoretical predictions.

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arXiv2016

Protoplanetary Disk Heating and Evolution Driven by the Spiral Density Waves

High-resolution imaging of some protoplanetary disks in scattered light reveals presence of the global spiral arms of significant amplitude, likely excited by massive planets or stellar companions. Assuming that these arms are density waves, evolving into spiral shocks, we assess their effect on the thermodynamics, accretion, and global evolution of the disk. We derive analytical expressions for the direct (irreversible) heating, angular momentum transport, and mass accretion rate induced by the disk shocks of arbitrary strength. We find these processes to be very sensitive to the shock amplitude. Focusing on the waves of moderate strength (density jump at the shock $ΔΣ/Σ\sim 1$) we show the associated disk heating to be negligible (contributing at $\sim 1\%$ level to the energy budget) in passive, irradiated protoplanetary disks on $\sim 100$ AU scales, but becoming important within several AU from the star. At the same time, shock heating can be a significant (or even dominant) energy source in disks of cataclysmic variables, stellar X-ray binaries, and supermassive black hole binaries, heated mainly by viscous dissipation. Mass accretion induced by the global spiral shocks is comparable to (or exceeds) the mass inflow due to viscous stresses. Protoplanetary disks featuring prominent global spirals must be evolving rapidly, in $\lesssim 0.5$ Myr at $\sim 100$ AU. A direct upper limit on the disk evolution timescale can be established via the measurement of the gravitational torque due to the spiral arms from the imaging data. Our findings suggest that, regardless of their origin, global spiral waves must be important agents of the protoplanetary disk evolution. They may serve as an effective mechanism of disk dispersal and could be related to the transitional disk phenomenon.

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arXiv2015

Spreading layers in accreting objects: role of acoustic waves for angular momentum transport, mixing and thermodynamics

Disk accretion at high rate onto a white dwarf or a neutron star has been suggested to result in the formation of a spreading layer (SL) - a belt-like structure on the object's surface, in which the accreted matter steadily spreads in the poleward (meridional) direction while spinning down. To assess its basic characteristics we perform two-dimensional hydrodynamic simulations of supersonic SLs in the relevant morphology with a simple prescription for cooling. We demonstrate that supersonic shear naturally present at the base of the SL inevitably drives sonic instability that gives rise to large scale acoustic modes governing the evolution of the SL. These modes dominate the transport of momentum and energy, which is intrinsically global and cannot be characterized via some form of local effective viscosity (e.g. $α$-viscosity). The global nature of the wave-driven transport should have important implications for triggering Type I X-ray bursts in low mass X-ray binaries. The nonlinear evolution of waves into a system of shocks drives effective re-arrangement (sensitively depending on thermodynamical properties of the flow) and deceleration of the SL, which ultimately becomes transonic and susceptible to regular Kelvin-Helmholtz instability. We interpret this evolution in terms of the global structure of the SL and suggest that mixing of the SL material with the underlying stellar fluid should become effective only at intermediate latitudes on the accreting object's surface, where the flow has decelerated appreciably. In the near-equatorial regions the transport is dominated by acoustic waves and mixing is less efficient. We speculate that this latitudinal non-uniformity of mixing in accreting white dwarfs may be linked to the observed bipolar morphology of classical novae ejecta.

astro-ph.SR↗

arXiv2015

The Structure of Spiral Shocks Excited by Planetary-mass Companions

Direct imaging observations have revealed spiral structures in protoplanetary disks. Previous studies have suggested that planet-induced spiral arms cannot explain some of these spiral patterns, due to the large pitch angle and high contrast of the spiral arms in observations. We have carried out three dimensional (3-D) hydrodynamical simulations to study spiral wakes/shocks excited by young planets. We find that, in contrast with linear theory, the pitch angle of spiral arms does depend on the planet mass, which can be explained by the non-linear density wave theory. A secondary (or even a tertiary) spiral arm, especially for inner arms, is also excited by a massive planet. With a more massive planet in the disk, the excited spiral arms have larger pitch angle and the separation between the primary and secondary arms in the azimuthal direction is also larger. We also find that although the arms in the outer disk do not exhibit much vertical motion, the inner arms have significant vertical motion, which boosts the density perturbation at the disk atmosphere. Combining hydrodynamical models with Monte-Carlo radiative transfer calculations, we find that the inner spiral arms are considerably more prominent in synthetic near-IR images using full 3-D hydrodynamical models than images based on 2-D models assuming vertical hydrostatic equilibrium, indicating the need to model observations with full 3-D hydrodynamics. Overall, companion-induced spiral arms not only pinpoint the companion's position but also provide three independent ways (pitch angle, separation between two arms, and contrast of arms) to constrain the companion's mass.

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arXiv2015

Tatooine Nurseries: Structure and Evolution of Circumbinary Protoplanetary Disks

Recent discoveries of circumbinary planets by Kepler mission provide motivation for understanding their birthplaces - protoplanetary disks around stellar binaries with separations <1 AU. We explore properties and evolution of such circumbinary disks focusing on modification of their structure caused by tidal coupling to the binary. We develop a set of analytical scaling relations describing viscous evolution of the disk properties, which are verified and calibrated using 1D numerical calculations with realistic inputs. Injection of angular momentum by the central binary suppresses mass accretion onto the binary and causes radial distribution of the viscous angular momentum flux F_J to be different from that in a standard accretion disk around a single star with no torque at the center. Disks with no mass accretion at the center develop F_J profile which is flat in radius. Radial profiles of temperature and surface density are also quite different from those in disks around single stars. Damping of the density waves driven by the binary and viscous dissipation dominate heating of the inner disk (within 1-2 AU), pushing the iceline beyond 3-5 AU, depending on disk mass and age. Irradiation by the binary governs disk thermodynamics beyond ~10 AU. However, self-shadowing by the hot inner disk may render central illumination irrelevant out to ~20 AU. Spectral energy distribution of a circumbinary disk exhibits a distinctive bump around 10 micron, which may facilitate identification of such disks around unresolved binaries. Efficient tidal coupling to the disk drives orbital inspiral of the binary and may cause low-mass and compact binaries to merge into a single star within the disk lifetime. We generally find that circumbinary disks present favorable sites for planet formation (despite wider zone of volatile depletion), in agreement with the statistics of Kepler circumbinary planets.

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arXiv2015

Birth Locations of the Kepler Circumbinary Planets

The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple) secular resonances emerging in the disk. We derive analytic results for size-dependent planetesimal eccentricity, and demonstrate the key role of the disk gravity for circumbinary dynamics. We then combine these results with a simple model for collisional outcomes and find that in systems like Kepler 16, planetesimal growth starting with 10-100 m planetesimals is possible outside a few AU. The exact location exterior to which this happens is sensitive to disk eccentricity, density and precession rate, as well as to the size of the first generation of planetesimals. Strong perturbations from the binary in the inner part of the disk, combined with a secular resonance at a few AU inhibit the growth of km-sized planetesimals within 2 - 4 AU of the binary. In situ planetesimal growth in the Kepler circumbinary systems is possible only starting from large (few-km-sized) bodies in a low-mass disk with surface density less than 500 g/cm^2 at 1 AU.

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arXiv2015

Viscosity prescription for gravitationally unstable accretion disks

Gravitationally unstable accretion disks emerge in a variety of astrophysical contexts - giant planet formation, FU Orioni outbursts, feeding of AGNs, and the origin of Pop III stars. When a gravitationally unstable disk is unable to cool rapidly it settles into a quasi-stationary, fluctuating gravitoturbulent state, in which its Toomre Q remains close to a constant value Q_0~1. Here we develop an analytical formalism describing the evolution of such a disk, which is based on the assumptions of Q=Q_0 and local thermal equilibrium. Our approach works in the presence of additional sources of angular momentum transport (e.g. MRI), as well as external irradiation. Thermal balance dictates a unique value of the gravitoturbulent stress α_{gt} driving disk evolution, which is a function of the local surface density and angular frequency. We compare this approach with other commonly used gravitoturbulent viscosity prescriptions, which specify the explicit dependence of stress α_{gt} on Toomre Q in an ad hoc fashion, and identify the ones that provide consistent results. We nevertheless argue that our Q=Q_0 approach is more flexible, robust, and straightforward, and should be given preference in applications. We illustrate this with a couple of analytical calculations - locations of the snow line and of the outer edge of the dead zone in a gravitoturbulent protoplanetary disk - which clearly show the simplicity and versatility of the Q=Q_0 approach.

astro-ph.EP↗

arXiv2014

Planet formation in binaries: dynamics of planetesimals perturbed by the eccentric protoplanetary disk and the secondary

Detections of planets in eccentric, close (separations of ~20 AU) binary systems such as αCen or γCep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities resulting in destruction, rather than growth, of objects with sizes of up to several hundred km in collisions of similar-size bodies. It was recently suggested that gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disks in binaries are themselves expected to be eccentric, leading to additional planetesimal excitation. Here we develop secular theory of eccentricity evolution for planetesimals perturbed by the gravity of an elliptical protoplanetary disk (neglecting gas drag) and the companion. For the first time we derive an expression for the disturbing function due to an eccentric disk, which can be used for a variety of other astrophysical problems. We obtain explicit analytical solutions for planetesimal eccentricity evolution and delineate four different regimes of dynamical excitation. We show that in systems with massive (>10^{-2}M_Sun) disks, planetesimal eccentricity is usually determined by the gravity of the eccentric disk alone, and is comparable to the disk eccentricity. As a result, the latter imposes a lower limit on collisional velocities of solids, making their growth problematic. This fragmentation barrier can be removed if the gaseous disk rapidly precesses or if its own self-gravity is efficient at lowering disk eccentricity.

astro-ph.EP↗

arXiv2014

Planet formation in stellar binaries I: planetesimal dynamics in massive protoplanetary disks

About $20\%$ of exoplanets discovered by radial velocity surveys reside in stellar binaries. To clarify their origin one has to understand the dynamics of planetesimals in protoplanetary disks within binaries. The standard description, accounting for only gas drag and gravity of the companion star has been challenged recently, as the gravity of the protoplanetary disk was shown to play a crucial role in planetesimal dynamics. An added complication is the tendency of protoplanetary disks in binaries to become eccentric, giving rise to additional excitation of planetesimal eccentricity. Here, for the first time, we analytically explore secular dynamics of planetesimals in binaries such as $α$ Cen and $γ$ Cep under the combined action of (1) gravity of the eccentric protoplanetary disk, (2) perturbations due to the (coplanar) eccentric companion, and (3) gas drag. We derive explicit solutions for the behavior of planetesimal eccentricity ${\bf e}_p$ in non-precessing disks (and in precessing disks in certain limits). We obtain the analytical form of the distribution of relative velocities of planetesimals, which is a key input for understanding their collisional evolution. Disk gravity strongly influences relative velocities and tends to push sizes of planetesimals colliding with comparable objects at the highest speed to small values, $\sim 1$ km. We also find that planetesimals in eccentric protoplanetary disks apsidally aligned with the binary orbit collide at lower relative velocities than in mis-aligned disks. Our results highlight a decisive role that disk gravity plays in planetesimal dynamics in binaries.

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arXiv2014

Planet formation in stellar binaries II: overcoming the fragmentation barrier in alpha Centauri and gamma Cephei-like systems

Planet formation in small-separation (~20 AU) eccentric binaries such as gamma Cephei or alpha Centauri is believed to be adversely affected by the presence of the stellar companion. Strong dynamical excitation of planetesimals by the eccentric companion can result in collisional destruction (rather than growth) of 1-100 km objects, giving rise to the "fragmentation barrier" for planet formation. We revise this issue using a novel description of secular dynamics of planetesimals in binaries, which accounts for the gravity of the eccentric, coplanar protoplanetary disk, as well as gas drag. By studying planetesimal collision outcomes we show, in contrast to many previous studies, that planetesimal growth and subsequent formation of planets (including gas giants) in AU-scale orbits within ~20 AU separation binaries may be possible, provided that the protoplanetary disks are massive (>10^{-2}M_\odot) and only weakly eccentric (disk eccentricity <0.01). These requirements are compatible with both the existence of massive (several M_J) planets in gamma Cep-like systems and the results of recent simulations of gaseous disks in eccentric binaries. Terrestrial and Neptune-like planets can also form in lower-mass disks at small (sub-AU) radii. We find that fragmentation barrier is less of a problem in eccentric disks which are apsidally aligned with the binary orbit. Alignment gives rise to special locations, where (1) relative planetesimal velocities are low and (2) the timescale of their drag-induced radial drift is long. This causes planetesimal pileup at such locations in the disk and promotes their growth.

astro-ph.EP↗

arXiv2014

Scattering outcomes of close-in planets: constraints on planet migration

Many exoplanets in close-in orbits are observed to have relatively high eccentricities and large stellar obliquities. We explore the possibility that these result from planet-planet scattering by studying the dynamical outcomes from a large number of orbit integrations in systems with two and three gas-giant planets in close-in orbits (0.05 AU < a < 0.15 AU). We find that at these orbital separations, unstable systems starting with low eccentricities and mutual inclinations ($e\lesssim0.1$, $i\lesssim0.1$) generally lead to planet-planet collisions in which the collision product is a planet on a low-eccentricity, low-inclination orbit. This result is inconsistent with the observations. We conclude that eccentricity and inclination excitation from planet-planet scattering must precede migration of planets into short-period orbits. This result constrains theories of planet migration: the semi-major axis must shrink by 1-2 orders of magnitude without damping the eccentricity and inclination.

astro-ph.EP↗

arXiv2014

Secular dynamics of the triple system harbouring PSR J0337+1715 and implications for the origin of its orbital configuration

We explore secular dynamics of a recently discovered hierarchical triple system consisting of the radio pulsar PSR J0337+1715 and two white dwarfs (WDs). We show that three body interactions endow the inner binary with a large forced eccentricity and suppress its apsidal precession, to about 24% of the rate due to the general relativity. However, precession rate is still quite sensitive to the non-Newtonian effects and may be used to constrain gravity theories if measured accurately. Small value of the free eccentricity of the inner binary $e_{i}^{free}\approx 2.6\times 10^{-5}$ and vanishing forced eccentricity of the outer, relatively eccentric binary naturally result in their apsidal near-alignment. In addition, this triple system provides a unique opportunity to explore excitation of both eccentricity and inclination in neutron star-WD binaries, e.g. due to random torques caused by convective eddies in the WD progenitor. We show this process to be highly anisotropic and more effective at driving eccentricity rather than inclination. The outer binary eccentricity as well as $e_{i}^{free}$ exceed by more than an order of magnitude the predictions of the eccentricity-period relation of Phinney (1992), which is not uncommon. We also argue that the non-zero mutual inclination of the two binaries emerges at the end of the Roche lobe overflow of the outer (rather than the inner) binary.

astro-ph.SR↗

arXiv2014

Particle Concentration At Planet Induced Gap Edges and Vortices: I. Inviscid 3-D Hydro Disks

We perform a systematic study of the dynamics of dust particles in protoplanetary disks with embedded planets using global 2-D and 3-D inviscid hydrodynamic simulations. Lagrangian particles have been implemented into magnetohydrodynamic code Athena with cylindrical coordinates. We find two distinct outcomes depending on the mass of the embedded planet. In the presence of a low mass planet ($8 M_{\oplus}$), two narrow gaps start to open in the gas on each side of the planet where the density waves shock. These shallow gaps can dramatically affect particle drift speed and cause significant, roughly axisymmetric dust depletion. On the other hand, a more massive planet ($>0.1 M_{J}$) carves out a deeper gap with sharp edges, which are unstable to the vortex formation. Particles with a wide range of sizes ($0.02<Ωt_{s}<20$) are trapped and settle to the midplane in the vortex, with the strongest concentration for particles with $Ωt_{s}\sim 1$. The dust concentration is highly elongated in the $ϕ$ direction, and can be as wide as 4 disk scale heights in the radial direction. Dust surface density inside the vortex can be increased by more than a factor of 10$^2$ in a very non-axisymmetric fashion. For very big particles ($Ωt_{s}\gg 1$) we find strong eccentricity excitation, in particular around the planet and in the vicinity of the mean motion resonances, facilitating gap opening there. Our results imply that in weakly turbulent protoplanetary disk regions (e.g. the "dead zone") dust particles with a very wide range of sizes can be trapped at gap edges and inside vortices induced by planets with $M_{p}<M_{J}$, potentially accelerating planetesimal and planet formation there, and giving rise to distinctive features that can be probed by ALMA and EVLA.

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arXiv2014

Probing Oort Cloud and Local Interstellar Medium Properties via Dust Produced in Cometary Collisions

The Oort Cloud remains one of the most poorly explored regions of the Solar System. We propose that its properties can be constrained by studying a population of dust grains produced in collisions of comets in the outer Solar System. We explore the dynamics of micron-size grains outside the heliosphere (beyond ~250 AU), which are affected predominantly by the magnetic field of the interstellar medium (ISM) flow past the Sun. We derive analytic models for the production and motion of small particles as a function of their birth location in the Cloud and calculate the particle flux and velocity distribution in the inner Solar System. These models are verified by direct numerical simulations. We show that grains originating in the Oort Cloud have a unique distribution of arrival directions, which should easily distinguish them from both interplanetary and interstellar dust populations. We also demonstrate that the distribution of particle arrival velocities is uniquely determined the mass distribution and dust production rate in the Cloud. Cometary collisions within the Cloud produce a flux of micron-size grains in the inner Solar System of up to several per square meter per year. The next-generation dust detectors may be sensitive enough to detect and constrain this dust population, which will illuminate us about the Oort Cloud's properties. We also show that the recently-detected mysterious population of large (micron-size) unbound particles, which seems to arrive with the ISM flow is unlikely to be generated by collisions of comets in the Oort Cloud.

astro-ph.EP↗

arXiv2013

Search for Supermassive Black Hole Binaries in the Sloan Digital Sky Survey Spectroscopic Sample

Supermassive black hole (SMBH) binaries are expected in a Lambda CDM cosmology given that most (if not all) massive galaxies contain a massive black hole at their center. So far, however, direct evidence for such binaries has been elusive. We use cross-correlation to search for temporal velocity shifts in the MgII broad emission lines of 0.36 < z < 2 quasars with multiple observations in the Sloan Digital Sky Survey. For ~ 10^9 Msun BHs in SMBH binaries, we are sensitive to velocity drifts for binary separations of ~ 0.1 pc with orbital periods of ~100 years. We find seven candidate sub-pc--scale binaries with velocity shifts > 3.4 sigma ~ 280 km/s, where sigma is our systematic error. Comparing the detectability of SMBH binaries with the number of candidates (N < 7), we can rule out that most 10^9 Msun BHs exist in ~ 0.03-0.2 pc scale binaries, in a scenario where binaries stall at sub-pc scales for a Hubble time. We further constrain that < one-third of quasars host SMBH binaries after considering gas-assisted sub-pc evolution of SMBH binaries, although this result is very sensitive to the assumed size of the broad line region. We estimate the detectability of SMBH binaries with ongoing or next-generation surveys (e.g., BOSS, Subaru Prime Focus Spectrograph), taking into account the evolution of the sub-parsec binary in circumbinary gas disks. These future observations will provide longer time baselines for searches similar to ours and may in turn constrain the evolutionary scenarios of SMBH binaries.

astro-ph.CO↗

arXiv2013

Analysis of Spin-Orbit Misalignment in Eclipsing Binary DI Herculis

Eclipsing binary DI Herculis (DI Her) is known to exhibit anomalously slow apsidal precession, below the rate predicted by the general relativity. Recent measurements of the Rossiter-McLauglin effect indicate that stellar spins in DI Her are almost orthogonal to the orbital angular momentum, which explains the anomalous precession in agreement with the earlier theoretical suggestion by Shakura. However, these measurements yield only the projections of the spin-orbit angles onto the sky plane, leaving the spin projection onto our line of sight unconstrained. Here we describe a method of determining the full three-dimensional spin orientation of the binary components relying on the use of the gravity darkening effect, which is significant for the rapidly rotating stars in DI Her. Gravity darkening gives rise to nonuniform brightness distribution over the stellar surface, the pattern of which depends on the stellar spin orientation. Using archival photometric data obtained during multiple eclipses spread over several decades we are able to constrain the unknown spin angles in DI Her with this method, finding that spin axes of both stars lie close to the plane of the sky. Our procedure fully accounts for the precession of stellar spins over the long time span of observations.

astro-ph.SR↗

arXiv2013

Low mass planets in protoplanetary disks with net vertical magnetic fields: the Planetary Wake and Gap Opening

We study wakes and gap opening by low mass planets in gaseous protoplanetary disks threaded by net vertical magnetic fields which drive magnetohydrodynamical (MHD) turbulence through the magnetorotational instabilty (MRI), using three dimensional simulations in the unstratified local shearing box approximation. The wakes, which are excited by the planets, are damped by shocks similar to the wake damping in inviscid hydrodynamic (HD) disks. Angular momentum deposition by shock damping opens gaps in both MHD turbulent disks and inviscid HD disks even for low mass planets, in contradiction to the "thermal criterion" for gap opening. To test the "viscous criterion", we compared gap properties in MRI-turbulent disks to those in viscous HD disks having the same stress, and found that the same mass planet opens a significantly deeper and wider gap in net vertical flux MHD disks than in viscous HD disks. This difference arises due to the efficient magnetic field transport into the gap region in MRI disks, leading to a larger effective αwithin the gap. Thus, across the gap, the Maxwell stress profile is smoother than the gap density profile, and a deeper gap is needed for the Maxwell stress gradient to balance the planetary torque density. We also confirmed the large excess torque close to the planet in MHD disks, and found that long-lived density features (termed zonal flows) produced by the MRI can affect planet migration. The comparison with previous results from net toroidal flux/zero flux MHD simulations indicates that the magnetic field geometry plays an important role in the gap opening process. Overall, our results suggest that gaps can be commonly produced by low mass planets in realistic protoplanetary disks, and caution the use of a constant α-viscosity to model gaps in protoplanetary disks.

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