arXiv subjects

Roman R. Rafikov

Publications and source records attributed to Roman R. Rafikov.

At least 109 records · Page 6Linked to original sources

arXiv2009

Properties of gravitoturbulent accretion disks

We explore the properties of cold gravitoturbulent accretion disks - non-fragmenting disks hovering on the verge of gravitational instability - using a realistic prescription for the effective viscosity caused by gravitational torques. This prescription is based on a direct relationship between the angular momentum transport in a thin accretion disk and the disk cooling in a steady state. Assuming that opacity is dominated by dust we are able to self-consistently derive disk properties for a given $\dot M$ assuming marginal gravitational stability. We also allow external irradiation of the disk and account for a non-zero background viscosity which can be due to the MRI. Spatial transitions between different co-existing disk states (e.g. between irradiated and self-luminous or between gravitoturbulent and viscous) are described and the location of the boundary at which disk must fragment is determined in a variety of situations. We demonstrate in particular that at low enough $\dot M$ external irradiation stabilizes gravitoturbulent disk against fragmentation all the way to infinity thus providing means of steady mass transport to the central object. Implications of our results for the possibility of planet formation by gravitational instability in protoplanetary disks and star formation in the Galactic Center and for the problem of feeding supermassive black holes in galactic nuclei are discussed.

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arXiv2008

Stellar proper motion and the timing of planetary transits

Duration and period of transits in extrasolar planetary systems can exhibit long-term variations for a variety of reasons. Here we investigate how systemic proper motion, which steadily re-orients planetary orbit with respect to our line of sight, affects the timing of transits. We find that in a typical system with a period of several days proper motion at the level of 100 mas/yr makes transit duration vary at a rate ~10-100 ms/yr. In some isolated systems this variation is at the measurable level (can be as high as 0.6 s/yr for GJ436) and may exceed all other transit timing contributions (due to the general relativity, stellar quadrupole, etc.). In addition, proper motion causes evolution of the observed orbital period via the Shklovskii effect at a rate $\gtrsim 10$ $μ$s/yr for the nearby transiting systems (0.26 ms/yr in GJ436), which in some cases exceeds all other contributions to $\dot P$. Earth's motion around the Sun gives rise to additional periodic timing signal (even for systems with zero intrinsic proper motion) allowing a full determination of the spatial orientation of the planetary orbit. Unlike most other timing effects the proper motion signatures persist even in systems with zero eccentricity and get stronger as the planetary period increases. They should be the dominant cause of transit timing variations in isolated wide separation (periods of months) systems that will be sought by Kepler.

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arXiv2007

Stellar growth by disk accretion: the effect of disk irradiation on the protostellar evolution

Young stars are expected to gain most of their mass by accretion from a disk that forms around them as a result of angular momentum conservation in the collapsing protostellar cloud. Accretion initially proceeds at high rates of 10^{-6}-10^{-5} M_Sun/yr resulting in strong irradiation of the stellar surface by the hot inner portion of the disk and leading to the suppression of the intrinsic stellar luminosity. Here we investigate how this luminosity suppression affects evolution of the protostellar properties. Using simple model based on the energy balance of accreting star we demonstrate that disk irradiation causes only a slight increase of the protostellar radius, at the level of several per cent. Such a weak effect is explained by a minor role played by the intrinsic stellar luminosity (at the time when it is significantly altered by irradiation) in the protostellar energy budget compared to the stellar deuterium burning luminosity and the inflow of the gravitational potential energy brought in by the freshly accreted material. Our results justify the neglect of irradiation effects in previous studies of the protostellar growth via disk accretion. Evolution of some other actively accreting objects such as young brown dwarfs and planets should also be only weakly sensitive to the effects of disk irradiation.

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arXiv2006

The Effects of Finite Emission Height in Precision Pulsar Timing

Precision timing is the key ingredient of ongoing pulsar-based gravitational wave searches and tests of general relativity using binary pulsars. The conventional approach to timing explicitly assumes that the radio emitting region is located at the center of the pulsar, while polarimetric observations suggest that radio emission is in fact produced at altitudes ranging from tens to thousands of kilometers above the neutron star surface. Here we present a calculation of the effects of finite emission height on the timing of binary pulsars using a simple model for the emitting region geometry. Finite height of emission changes the propagation path of radio photons through the binary and gives rise to a large spin velocity of the emission region co-rotating with the neutron star. Under favorable conditions these two effects introduce corrections to the conventional time delays at the microsecond level (for a millisecond pulsar in a double neutron star binary with a period of several hours and assuming the emission height of 100 km). Exploiting the dependence of the emission height on frequency (radius-to-frequency mapping) and using multi-frequency observations one should be able to detect these timing corrections even though they are formally degenerate with conventional time delays. Although even in the most accurately timed systems the magnitude of the finite emission height effects is currently somewhat below timing precision, longer-term observations and future facilities like SKA will make measurement of these effects possible, providing an independent check of existing emission height estimates.

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arXiv2006

Convective cooling and fragmentation of gravitationally unstable disks

Gravitationally unstable disks can fragment and form bound objects provided that their cooling time is short. In protoplanetary disks radiative cooling is likely to be too slow to permit formation of planets by fragmentation within several tens of AU from the star. Recently, convection has been suggested as a faster means of heat loss from the disk but here we demonstrate that it is only marginally more efficient than the radiative cooling. The crucial factor is the rate at which energy can be radiated from the disk photosphere, which is robustly limited from above in the convective case by the adiabatic temperature gradient (given a certain midplane temperature). Thus, although vigorous convection is definitely possible in disks, the inefficiency of radiative loss from the photosphere may create a bottleneck limiting the ability of the disk to form self-gravitating objects. Based on this argument we derive a set of analytical constraints which diagnose the susceptibility of an unstable disk to fragmentation and show that the formation of giant planets by fragmentation of protoplanetary disks is unlikely to occur at distances of tens of AU. At the same time these constraints do not preclude the possibility of fragmentation and star formation in accretion disks around supermassive black holes.

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arXiv2006

Effects of Pulsar Rotation on Timing Measurements of the Double Pulsar System J0737-3039

We study the effect of pulsar rotation on timing of binary pulsars, with particular emphasis on the double pulsar system J0737-3039. Special relativistic aberration due to the orbital motion of pulsar changes both the longitude and colatitude of the emission direction with respect to the pulsar spin axis. The former gives rise to a shift of the arrival time of the pulse centroid (this is the conventional ``longitudinal'' aberration delay), the latter results in a distortion (contraction or dilation) of the pulse profile on the orbital timescale. The amplitude of pulse distortion depends inversely on the variation of polarization position angle across the pulse. For small angle between the pulsar magnetic and spin axes, as inferred for PSR J0737-3039A from polarimetric observations, the pulse distortion is significant (\sim 1%) and the associated ``latitudinal'' aberration delay is much larger than the longitudinal one. By monitoring the arrival time of separate pulse components as a function of pulsar orbital phase, the latitudinal aberration delay may be easily measured with the current timing precision, thus constraining the spin geometry of the system. The latitudinal delay can also be detected by monitoring system's orbital parameters on the geodetic precession timescale. Because of the near edge-on orbital orientation of the PSR J0737-3039 system, general relativistic bending of pulsar A's radio beam near its superior conjunction also introduces spin-dependent time delays of similar order of magnitude as the aberration delays. In addition, light bending splits the pulse profile into two variable components, corresponding to two gravitationally lensed images of the source. Detection of lensing effects is challenging, but may be possible with existing technology.

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arXiv2006

Effects of Gravitational Lensing and Companion Motion on the Binary Pulsar Timing

The measurement of the Shapiro time delay in binary pulsar systems with highly inclined orbit can be affected both by the motion of the pulsar's companion because of the finite time it takes a photon to cross the binary, and by the gravitational light bending if the orbit is sufficiently edge-on relative to the line of sight. Here we calculate the effect of retardation due to the companion's motion on various time delays in pulsar binaries, including the Shaipro delay, the geometric lensing delay, and the lens-induced delays associated with the pulsar rotation. Our results can be applied to systems so highly inclined that near conjunction gravitational lensing of the pulsar radiation by the companion becomes important (the recently discovered double pulsar system J0737-3039 may exemplify such a system). To the leading order, the effect of retardation is to shift all the delay curves backward in time around the orbit conjunction, without affecting the shape and amplitude of the curves. The time shift is of order the photon orbit crossing time, and ranges from a second to a few minutes for the observed binary pulsar systems. In the double pulsar system J0737-3039, the motion of the companion may also affect the interpretation of the recent correlated interstellar scintillation measurements. Finally, we show that lensing sets an upper limit on the magnitude of the frame-dragging time delay caused by the companion's spin, and makes this delay unobservable in stellar-mass binary pulsar systems.

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arXiv2006

Microwave emission from spinning dust in circumstellar disks

In the high density environments of circumstellar disks dust grains are expected to grow to large sizes by coagulation. Somewhat unexpectedly, recent near-IR observations of PAH features from disks around Herbig Ae/Be stars demonstrate that substantial amount of dust mass in these disks (up to several tens of per cent of the total carbon content) can be locked up in particles with sizes ranging from several to tens of nanometers. We investigate the possibility of detecting the electric dipole emission produced by these nanoparticles as they spin at thermal rates (tens of GHz) in cold gas. We show that such emission peaks in the microwave range and dominates over the thermal disk emission at ν< 50 GHz typically by a factor of several if > 5 % of the total carbon abundance is locked up in nanoparticles. We test the sensitivity of this prediction to various stellar and disk parameters and show that if the potential contamination of the spinning dust component by the free-free and/or synchrotron emission can be removed, then the best chances of detecting this emission would be in disks with small opacity, having SEDs with steep sub-mm slopes (which minimizes thermal disk emission at GHz frequencies). Detection of the spinning dust emission would provide important evidence for the existence, properties, and origin of the population of small dust particles in protoplanetary disks, with possible ramifications for planet formation.

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arXiv2006

Structure of Passive Circumstellar Disks: Beyond the Two-Temperature Approximation

Structure and spectral energy distributions (SEDs) of externally irradiated circumstellar disks are often computed on the basis of the two-temperature model of Chiang & Goldreich. We refine these calculations by using a more realistic temperature profile which is continuous at all optical depths and thus goes beyond the two-temperature model. It is based on the approximate solution of the radiation transfer in the disk obtained from the frequency-integrated moment equations in the Eddington approximation. We come up with a simple procedure (``constant g_z approximation'') for treating the vertical structure of the disk in regions where its optical depth to stellar radiation is high. This allows us to obtain expressions for the vertical profiles of density and pressure at every point in the disk and to determine the shape of its surface. Armed with these analytical results we calculate the full radial structure of the disk and demonstrate that it favorably agrees with the results of direct numerical calculations. We also describe a simple and efficient way of the SED calculation based on our adopted temperature profile. Resulting spectra provide very good match (especially at short wavelengths) to the results of more detailed (but also more time-consuming) SED calculations solving the full frequency- and angle-dependent radiation transfer within the disk.

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arXiv2005

Magnetospheric eclipses in the double pulsar system J0737-3039

We argue that eclipses of radio emission from the millisecond pulsar A in the double pulsar system J0737-3039 are due to synchrotron absorption by plasma in the closed field line region of the magnetosphere of its normal pulsar companion B. A's radio beam only illuminates B's magnetosphere for about 10 minutes surrounding the time of eclipse. During this time it heats particles at r\gtrsim 10^9 cm to relativistic energies and enables extra plasma to be trapped by magnetic mirroring. An enhancement of the plasma density by a factor \sim 10^2 is required to match the duration and optical depth of the observed eclipses. The extra plasma might be supplied by a source near B through Bγpair creation by energetic photons produced in B's outer gap. Excitation of pairs' gyrational motions by cyclotron absorption of A's radio beam can result in their becoming trapped between conjugate mirror points in B's magnetosphere. Because the trapping efficiency decreases with increasing optical depth, the plasma density enhancement saturates even under steady state illumination. The result is an eclipse with finite, frequency dependent, optical depth. After illumination by A's radio beam ceases, the trapped particles cool and are lost. The entire cycle repeats every orbital period. We speculate that the asymmetries between eclipse ingress and egress result in part from the magnetosphere's evolution toward a steady state when illuminated by A's radio beam. We predict that A's linear polarization will vary with both eclipse phase and B's rotational phase.

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arXiv2005

Effects of Gravitational Lensing in the Double Pulsar System J0737-3039

We investigate the effects of gravitational lensing in the binary pulsar system J0737-3039. Current measurement of the orbital inclination allows the millisecond pulsar (A) to pass very close (at R_{min}=4000 km) in projection to the companion pulsar (B), with R_{min} comparable to the Einstein radius (2600 km). For this separation at the conjunction, lensing causes small (about 10%) magnification of the pulsar A signal on a timescale of several seconds, and displaces the pulsar image on the sky plane by about 1200 km. More importantly, lensing introduces a correction (of several microsec) to the conventional Shapiro delay formula used in pulsar timing analysis, and gives rise to a geometric time delay together with the delays associated with the pulsar spin period. These lensing effects can influence the determination of the system parameters by both timing and scintillation studies. Given the current uncertainty in the orbital inclination, more extreme manifestations of lensing (e.g. magnification by a factor of several) are possible. We compare our predictions with the existing observations and discuss the possibility of detecting gravitational lensing signatures in the system. The anomalously high point in A's lightcurve close to superior conjunction might be caused by gravitational lensing.

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arXiv2004

Fast accretion of small planetesimals by protoplanetary cores

We explore the dynamics of small planetesimals coexisting with massive protoplanetary cores in a gaseous nebula. Gas drag strongly affects the motion of small bodies leading to the decay of their eccentricities and inclinations, which are excited by the gravity of protoplanetary cores. Drag acting on larger ($\gtrsim 1$ km), high velocity planetesimals causes a mere reduction of their average random velocity. By contrast, drag qualitatively changes the dynamics of smaller ($\lesssim 0.1-1$ km), low velocity objects: (1) small planetesimals sediment towards the midplane of the nebula forming vertically thin subdisk; (2) their random velocities rapidly decay between successive passages of the cores and, as a result, encounters with cores typically occur at the minimum relative velocity allowed by the shear in the disk. This leads to a drastic increase in the accretion rate of small planetesimals by the protoplanetary cores, allowing cores to grow faster than expected in the simple oligarchic picture, provided that the population of small planetesimals contains more than roughly 1% of the solid mass in the nebula. Fragmentation of larger planetesimals ($\gtrsim 1$ km) in energetic collisions triggered by the gravitational scattering by cores can easily channel this amount of material into small bodies on reasonable timescales ($< 1$ Myr in the outer Solar System), providing a means for the rapid growth (within several Myr at 30 AU) of rather massive protoplanetary cores. Effects of inelastic collisions between planetesimals and presence of multiple protoplanetary cores are discussed.

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arXiv2003

Effects of Planetesimal Dynamics on the Formation of Terrestrial Planets

Formation of terrestrial planets by agglomeration of planetesimals in protoplanetary disks sensitively depends on the velocity evolution of planetesimals. We describe a novel semi-analytical approach to the treatment of planetesimal dynamics incorporating the gravitational scattering by massive protoplanetary bodies. Using this method we confirm that planets grow very slowly in the outer Solar System if gravitational scattering is the only process determining planetesimal velocities, making it hard for giant planets to acquire their massive gaseous envelopes within less than 10 Myr. We put forward several possibilities for alleviating this problem.

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arXiv2003

Dynamical evolution of planetesimals in protoplanetary disks

The current picture of terrestrial planet formation relies heavily on our understanding of the dynamical evolution of planetesimals -- asteroid-like bodies thought to be planetary building blocks. In this study we investigate the growth of eccentricities and inclinations of planetesimals in spatially homogeneous protoplanetary disks using methods of kinetic theory. We explore disks with a realistic mass spectrum of planetesimals evolving in time, similar to that obtained in self-consistent simulations of planetesimal coagulation. We calculate the behavior of planetesimal random velocities as a function of the planetesimal mass spectrum both analytically and numerically; results obtained by the two approaches agree quite well. Scaling of random velocity with mass can always be represented as a combination of power laws corresponding to different velocity regimes (shear- or dispersion-dominated) of planetesimal gravitational interactions. For different mass spectra we calculate analytically the exponents and time dependent normalizations of these power laws, as well as the positions of the transition regions between different regimes. It is shown that random energy equipartition between different planetesimals can only be achieved in disks with very steep mass distributions (differential surface number density of planetesimals falling off steeper than m^{-4}), or in the runaway tails. In systems with shallow mass spectra (shallower than m^{-3}) random velocities of small planetesimals turn out to be independent of their masses. We also discuss the damping effects of inelastic collisions between planetesimals and of gas drag, and their importance in modifying planetesimal random velocities.

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arXiv2002

Planetesimal disk evolution driven by planetesimal-planetesimal gravitational scattering

We investigate the process of an inhomogeneous planetesimal disk evolution caused by the planetesimal-planetesimal gravitational scattering. We develop a rather general approach based on the kinetic theory which self-consistently describes the evolution in time and space of both the disk surface density and its kinematic properties -- dispersions of eccentricity and inclination. The gravitational scattering of planetesimals is assumed to be in the dispersion-dominated regime which considerably simplifies analytical treatment. The resultant equations are of advection-diffusion type. Distance dependent scattering coefficients entering these equations are calculated analytically under the assumption of two-body scattering in the leading order in Coulomb logarithm. They are essentially nonlocal in nature. Our approach allows one to explore the dynamics of nonuniform planetesimal disks with arbitrary mass and random velocity distributions. It can also naturally include other physical mechanisms which are important for the evolution of such disks -- gas drag, migration, and so on.

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arXiv2002

Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering

The process of gravitational scattering of planetesimals by a massive protoplanetary embryo is explored theoretically. We propose a method to describe the evolution of the disk surface density, eccentricity, and inclination caused by the embryo-planetesimal interaction. It relies on the analytical treatment of the scattering in two extreme regimes of the planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and dispersion-dominated (dynamically ``hot''). In the former, planetesimal scattering can be treated as a deterministic process. In the latter, scattering is mostly weak because of the large relative velocities of interacting bodies. This allows one to use the Fokker-Planck approximation and the two-body approximation to explore the disk evolution. We compare the results obtained by this method with the outcomes of the direct numerical integrations of planetesimal orbits and they agree quite well. In the intermediate velocity regime an approximate treatment of the disk evolution is proposed based on interpolation between the two extreme regimes. We also calculate the rate of embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that it is in agreement with both the simulations and earlier calculations. Finally we discuss the question of the direction of the embryo-planetesimal interaction in the dispersion-dominated regime and demonstrate that it is repulsive. This means that the embryo always forms a gap in the disk around it, which is in contrast with the results of other authors. The machinery developed here will be applied to realistic protoplanetary systems in future papers.

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arXiv2002

The growth of planetary embryos: orderly, runaway, or oligarchic?

We consider the growth of a protoplanetary embryo embedded in a planetesimal disk. We take into account the dynamical evolution of the disk caused by (1) planetesimal-planetesimal interactions, which increase random motions and smooth gradients in the disk, and (2) gravitational scattering of planetesimals by the embryo, which tends to heat up the disk locally and repels planetesimals away. The embryo's growth is self-consistently coupled to the planetesimal disk dynamics. We demonstrate that details of the evolution depend on only two dimensionless parameters incorporating all the physical characteristics of the problem: the ratio of the physical radius to the Hill radius of any solid body in the disk and the number of planetesimals inside the annulus of the disk with width equal to the planetesimal Hill radius. The results of exploration in the framework of our model of several situations typical for protosolar nebula can be summarized as follows: initially, the planetesimal disk dynamics is not affected by the presence of the embryo and the growth of the embryo's mass proceeds very rapidly in the runaway regime. Later on, when the embryo starts being dynamically important, its accretion slows down similar to the ``oligarchic'' growth picture. The scenario of orderly growth suggested by Safronov (1972) is never realized in our calculations; scenario of runaway growth suggested by Wetherill & Stewart (1989) is only realized for a limited range in mass. Slow character of the planetesimal accretion on the oligarchic stage of the embryo's accumulation leads to a considerable increase of the protoplanetary formation timescale compared to that following from a simple runaway accretion picture valid in the homogeneous planetesimal disks.

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arXiv2001

Termination of planetary accretion due to gap formation

The process of gap formation by a growing planetary embryo embedded in a planetesimal disk is considered. It is shown that there exists a single parameter characterizing this process, which represents the competition between the gravitational influence of the embryo and planetesimal-planetesimal scattering. For realistic assumptions about the properties of the planetesimal disk and the planetary embryo, a gap is opened long before the embryo can accrete all the bodies within its region of influence. The implication of this result is that the embryo stops growing and, thus, large bodies formed during the coagulation stage should be less massive than is usually assumed. For conditions expected at 1 AU in the solar protoplanetary disk, gap formation is expected to occur around bodies of mass < 10^24 g. The effect of protoplanetary radial migration is also discussed.

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