arXiv subjects

Re'em Sari

Publications and source records attributed to Re'em Sari.

At least 127 records · Page 7Linked to original sources

arXiv2006

The effect of Semi-Collisional Accretion on Planetary Spins

Planetesimal accretion during planet formation is usually treated as collisionless. Such accretion from a uniform and dynamically cold disk predicts protoplanets with slow retrograde rotation. However, if the building blocks of protoplanets, planetesimals, are small, of order of a meter in size, then they are likely to collide within the protoplanet's sphere of gravitational influence, creating a prograde accretion disk around the protoplanet. The accretion of such a disk results in the formation of protoplanets spinning in the prograde sense with the maximal spin rate allowed before centrifugal forces break them apart. As a result of semi-collisional accretion, the final spin of a planet after giant impacts is not completely random but is biased toward prograde rotation. The eventual accretion of the remaining planetesimals in the post giant-impact phase might again be in the semi-collisional regime and delivers a significant amount of additional prograde angular momentum to the terrestrial planets. We suggest that in our Solar System, semi-collisional accretion gave rise to the preference for prograde rotation observed in the terrestrial planets and perhaps the largest asteroids.

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arXiv2006

The Self-Similarity of Shear-Dominated Viscous Stirring

We examine the growth of eccentricities of a population of particles with initially circular orbits around a central massive body. Successive encounters between pairs of particles increase the eccentricities in the disk on average. As long as the epicyclic motions of the particles are small compared to the shearing motion between Keplerian orbits, there is no preferred scale for the eccentricities. The simplification due to this self-similarity allows us to find an analytic form for the distribution function; full numerical integrations of a disk with 200 planetesimals verify our analytical self-similar distribution. The shape of this non-equilibrium profile is identical to the equilibrium profile of a shear-dominated population whose mutual excitations are balanced by dynamical friction or Epstein gas drag.

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arXiv2006

Pure and loaded fireballs in SGR giant flares

On December 27, 2004, a giant flare from SGR 1806$-$20 was detected on earth. Its thermal spectrum and temperature suggest that the flare resulted from an energy release of about $10^{47}$ erg/sec close to the surface of a neutron star in the form of radiation and/or pairs. This plasma expanded under its own pressure producing a fireball and the observed gamma-rays escaped once the fireball became optically thin. The giant flare was followed by a bright radio afterglow, with an observable extended size, implying an energetic relativistic outflow. We revisit here the evolution of relativistic fireballs and we calculate the Lorentz factor and energy remaining in relativistic outflow once the radiation escapes. We show that pairs that arise naturally in a pure pairs-radiation fireball do not carry enough energy to account for the observed afterglow. We consider various alternatives and we show that if the relativistic outflow that causes the afterglow is related directly to the prompt flare, then the initial fireball must be loaded by baryons or Poynting flux. While we focus on parameters applicable to the giant flare and the radio afterglow of SGR 1806$-$20 the calculations presented here might be also applicable to GRBs.

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arXiv2006

Protoplanet Dynamics in a Shear-Dominated Disk

The velocity dispersion, or eccentricity distribution, of protoplanets interacting with planetesimals is set by a balance between dynamical friction and viscous stirring. We calculate analytically the eccentricity distribution function of protoplanets embedded in a cold, shear-dominated planetesimal swarm. We find a distinctly non-Rayleigh distribution with a simple analytical form. The peak of the distribution lies much lower than the root-mean-squared value, indicating that while most of the bodies have similarly small eccentricities, a small subset of the population contains most of the thermal energy. We also measure the shear-dominated eccentricity distribution using numerical simulations. The numerical code treats each protoplanet explicitly and adds an additional force term to each body to represent the dynamical friction of the planetesimals. Without fitting any parameters, the eccentricity distribution of protoplanets in the N-body simulation agrees with the analytical results. This distribution function provides a useful tool for testing hybrid numerical simulations of late-stage planet formation.

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arXiv2006

Spherical Accretion

We compare different examples of spherical accretion onto a gravitating mass. Limiting cases include the accretion of a collisionally dominated fluid and the accretion of collisionless particles. We derive expressions for the accretion rate and density profile for semi-collisional accretion which bridges the gap between these limiting cases. Particle crossing of the Hill sphere during the formation of the outer planets is likely to have taken place in the semi-collisional regime.

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arXiv2005

Self-similar solutions for relativistic shocks emerging from stars with polytropic envelopes

We consider a strong ultrarelativistic shock moving through a star whose envelope has a polytrope-like density profile. When the shock is close to the star's outer boundary, its behavior follows the self-similar solution given by Sari (2005) for implosions in planar geometry. Here we outline this solution and find the asymptotic solution as the shock reaches the star's edge. We then show that the motion after the shock breaks out of the star is described by a self-similar solution remarkably like the solution for the motion inside the star. In particular, the characteristic Lorentz factor, pressure, and density vary with time according to the same power laws both before and after the shock breaks out of the star. After emergence from the star, however, the self-similar solution's characteristic position corresponds to a point behind the leading edge of the flow rather than at the shock front, and the relevant range of values for the similarity variable changes. Our numerical integrations agree well with the analytic results both before and after the shock reaches the star's edge.

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arXiv2005

First and second-type self-similar solutions of implosions and explosions containing ultra-relativistic shocks

We derive self similar solutions for ultra-relativistic shock waves propagating into cold material of powerlaw density profile in radius rho ~ r^-k. We treat both implosions and explosions in three geometries: planar, cylindrical and spherical. For spherical explosions these are the first type solutions of Blandford and McKee for k<4 and the second type solutions found by Best and Sari for k>5-sqrt(3/4). In addition we find new, hollow (with evacuated interior), first type solutions that may be applicable for 4<k<17/4. This ``sequence'' with increasing k of first type solutions, hollow first type solutions, and then second type solutions is reminiscent of the non-relativistic sequence. However, while in the non relativistic case there is a range of k which corresponds to a ``gap'' - a range in $k$ with neither first nor second type solutions which separates the hollow first type solutions and the second type solutions, here there is an ``overlap'': a range of k for which current considerations allow for both hollow first and second type solutions. Further understanding is needed to determine which of the two solutions apply in this overlap regime. We provide similar exploration for the other geometries and for imploding configurations. Interestingly, we find a gap for imploding spherical shocks and exploding planar shocks and an overlap for imploding planar solutions. Cylindrical configurations have no hollow solutions and exhibit direct transition from first type to second type solutions, without a gap or an overlap region.

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arXiv2004

Planet Formation by Coagulation: A Focus on Uranus and Neptune

Planets form in the circumstellar disks of young stars. We review the basic physical processes by which solid bodies accrete each other and alter each others' random velocities, and we provide order-of-magnitude derivations for the rates of these processes. We discuss and exercise the two-groups approximation, a simple yet powerful technique for solving the evolution equations for protoplanet growth. We describe orderly, runaway, neutral, and oligarchic growth. We also delineate the conditions under which each occurs. We refute a popular misconception by showing that the outer planets formed quickly by accreting small bodies. Then we address the final stages of planet formation. Oligarchy ends when the surface density of the oligarchs becomes comparable to that of the small bodies. Dynamical friction is no longer able to balance viscous stirring and the oligarchs' random velocities increase. In the inner-planet system, oligarchs collide and coalesce. In the outer-planet system, some of the oligarchs are ejected. In both the inner- and outer-planet systems, this stage ends once the number of big bodies has been reduced to the point that their mutual interactions no longer produce large-scale chaos. Subsequently, dynamical friction by the residual small bodies circularizes and flattens their orbits. The final stage of planet formation involves the clean up of the residual small bodies. Clean up has been poorly explored.

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arXiv2004

Final Stages of Planet Formation

We address three questions regarding solar system planets. What determined their number? Why are their orbits nearly circular and coplanar? How long did they take to form? Runaway accretion in a disk of small bodies resulted in a tiny fraction of the bodies growing much larger than all the others. This was followed by oligarchic growth during which the big bodies maintained similar masses and uniformly spaced semi-major axes. We depart from standard treatments of planet formation by assuming that as the big bodies got bigger, the small ones got smaller as the result of undergoing a collisional fragmentation cascade. It follows that oligarchy was a brief stage in solar system evolution. When the oligarchs' surface mass density matched that of the small bodies, dynamical friction was no longer able to balance viscous stirring, so their velocity dispersion increased to the extent that their orbits crossed. This marked the end of oligarchy. What happened next differed in the inner and outer parts of the planetary system. In the inner part, where the ratios of the escape velocities from the surfaces of the planets to the escape velocities from their orbits are smaller than unity, big bodies collided and coalesced after their random velocities became comparable to their escape velocities. In the outer part, where these ratios are larger than unity, the random velocities of some of the big bodies continued to rise until they were ejected. In both parts, the number density of the big bodies eventually decreased to the extent that gravitational interactions among them no longer produced large scale chaos. After that their orbital eccentricities and inclinations were damped by dynamical friction from the remaining small bodies. The last and longest stage in planet formation was the clean up of small bodies.

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arXiv2004

Shaping the Kuiper belt size spectrum by shattering large but strengthless bodies

The observed size distribution of Kuiper belt objects (KBOs)--small icy and rocky solar system bodies orbiting beyond Neptune--is well described by a power law at large KBO sizes. However, recent work by Bernstein et al. (2003) indicates that the size spectrum breaks and becomes shallower for KBOs smaller than about 70 km in size. Here we show that we expect such a break at KBO radius ~40 km since destructive collisions are frequent for smaller KBOs. Specifically, we assume that KBOs are rubble piles with low material strength rather than solid monoliths. This gives a power-law slope q~3 where the number N(r) of KBOs larger than a size r is given by $N(r) \propto r^{1-q}$; the break location follows from this slope through a self-consistent calculation. The existence of this break, the break's location, and the power-law slope we expect below the break are consistent with the findings of Bernstein et al. (2003). The agreement with observations indicates that KBOs are effectively strengthless rubble piles.

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arXiv2003

Planet - Disk Symbiosis

Planets form in disks around young stars. Interactions with these disks cause them to migrate and thus affect their final orbital periods. We suggest that the connection between planets and disks may be deeper and involve a symbiotic evolution. By contributing to the outward transport of angular momentum, planets promote disk accretion. Here we demonstrate that planets sufficiently massive to open gaps could be the primary agents driving disk accretion. Those having masses below the gap opening threshold drift inward more rapidly than the disk material and can only play a minor role in its accretion. Eccentricity growth during gap formation may involve an even more intimate symbiosis. Given a small initial eccentricity, just a fraction of a percent, the orbital eccentricity of a massive planet may grow rapidly once a mass in excess of the planet's mass has been repelled to form a gap around the planet's orbit. Then, as the planet's radial excursions approach the gap's width, subsequent eccentricity growth slows so that the planet's orbit continues to be confined within the gap.

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arXiv2003

Jets in GRBs: Tests and Predictions for the Structured Jet Model

The two leading interpretations of achromatic breaks that are observed in the light curves of GRBs afterglow are (i) the manifestation of the edge of a jet, which has a roughly uniform energy profile and a sharp edge and (ii) a line of sight effect in jets with a variable energy profile. The first scenario requires the inner engine to produce a jet with a different opening angle each explosion, while the latter requires a standard engine. The physical structure of the jet is a crucial factor in understanding GRB progenitors, and therefore discriminating the two jet scenarios is particularly relevant. In the structured jet case, specific predictions can be made for the distribution of observed break angles $θ_{\rm break}$, while that distribution is arbitrary in the first scenario. We derive the theoretical distribution for the structured jet model. Specifically, we predict the most common angle to be about 0.12 rad, in rough agreement with the sample. If this agreement would hold as the sample size increases, it would strengthen the case for the standard jet hypothesis. We show that a prediction of this model is that the average viewing angle is an increasing function of the survey sensitivity, and in particular that a mission like {\em Swift} will find the typical viewing angle to be about 0.3 rad. The local event rate predicted by this model is $R_{\rm GRB}(z=0)\sim 0.5 $ Gpc$^{-3}$ yr$^{-1}$.

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arXiv2003

A generalization of the Lagrangian points: studies of resonance for highly eccentric orbits

We develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass ratio mu << 1. We use this framework to explore mean-motion resonances between the test particle and the secondary mass. This approach leads to (i) a redefinition of resonance orders to reflect the importance of interactions at periapse; (ii) a pendulum-like equation describing the librations of resonance orbits; (iii) an analogy between these new fixed points and the Lagrangian points as well as between librations around the fixed points and the well known tadpole and horseshoe orbits; (iv) a condition a ~ mu^(-2/5) for the onset of chaos at large semimajor axis a; (v) the existence of a range mu < ~5 x 10^(-6) in secondary mass for which a test particle initially close to the secondary cannot escape from the system, at least in the planar problem; (vi) a simple explanation for the presence of asymmetric librations in exterior 1:N resonances.

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arXiv2002

Formation of Kuiper Belt Binaries

It appears that at least several percent of large Kuiper belt objects are members of wide binaries. Physical collisions are too infrequent to account for their formation. Collisionless gravitational interactions are more promising. These provide two channels for binary formation. In each, the initial step is the formation of a transient binary when two large bodies penetrate each other's Hill spheres. Stabilization of a transient binary requires that it lose energy. Either dynamical friction due to small bodies or the scattering of a third large body can be responsible. Our estimates favor the former, albeit by a small margin. We predict that most objects of size comparable to those currently observed in the Kuiper belt are members of multiple systems. More specifically, we derive the probability that a large body is a member of a binary with semi-major axis of order a. The probability depends upon sigma, the total surface density, Sigma, the surface density of large bodies having radius R, and theta=10^-4, the angle subtended by the solar radius as seen from the Kuiper belt. For (sigma/Sigma)R<a< R/theta, the probability is just (Sigma/rho R)theta^-2, the optical depth of the large bodies divided by the solid angle subtended by the Sun. For R<a<r_u=(sigma/Sigma)R, it varies inversely with semimajor axis and reaches (sigma/rho R)theta^-2 at a=R. Based on current surveys of the Kuiper belt, we estimate Sigma/rho=3 10^-4cm and R=100km. We obtain sigma/rho=0.3cm by extrapolating the surface density deduced for the minimum mass solar nebula. Rough predictions are: outside of the critical separation r_u/a_odot=3'', the binary probability is 0.3%; at separations of 0.2'', comparable to current resolving capabilities, it reaches 5%, in agreement with results from the HST binary survey by Brown.

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arXiv2002

Eccentricity Evolution for Planets in Gaseous Disks

We investigate the hypothesis that interactions between a giant planet and the disk from which it forms promote eccentricity growth. These interactions are concentrated at discrete Lindblad and corotation resonances. Interactions at principal Lindblad resonances cause the planet's orbit to migrate and open a gap in the disk if the planet is sufficiently massive. Those at first order Lindblad and corotation resonances change the planet's orbital eccentricity. Eccentricity is excited by interactions at external Lindblad resonances which are located on the opposite side of corotation from the planet, and damped by co-orbital Lindblad resonances which overlap the planet's orbit. If the planet clears a gap in the disk, the rate of eccentricity damping by co-orbital Lindblad resonances is reduced. Density gradients associated with the gap activate eccentricity damping by corotation resonances at a rate which initially marginally exceeds that of eccentricity excitation by external Lindblad resonances. But the corotation torque drives a mass flux which reduces the density gradient near the resonance. Sufficient partial saturation of corotation resonances can tip the balance in favor of eccentricity excitation. A minimal initial eccentricity of a few percent is required to overcome viscous diffusion which acts to unsaturate corotation resonances by reestablishing the large scale density gradient. Thus eccentricity growth is a finite amplitude instability. Formally, interactions at the apsidal resonance, which is a special kind of co-orbital Lindblad resonance, appears to damp eccentricity faster than external Lindblad resonances can excite it. However, apsidal waves have such long wavelengths that they do not propagate in protoplanetary disks. This reduces eccentricity damping by the apsidal resonance to a modest level.

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arXiv2001

The Shape of Spectral Breaks in GRB Afterglows

Gamma-Ray Burst (GRB) afterglows are well described by synchrotron emission from relativistic blast waves expanding into an external medium. The blast wave is believed to amplify the magnetic field and accelerate the electrons into a power law distribution of energies promptly behind the shock. These electrons then cool both adiabatically and by emitting synchrotron and inverse Compton radiation. The resulting spectra is known to consist several power law segments, which smoothly join at certain break frequencies. Here, we give a complete description of all possible spectra under those assumptions, and find that there are 5 possible regimes, depending on the ordering of the break frequencies. The flux density is calculated by integrating over the contributions from all the shocked region, using the Blandford McKee solution. This allows us to calculate more accurate expressions for the value of these break frequencies, and describe the shape of the spectral breaks around them. This also provides the shape of breaks in the light curves caused by the passage of a break frequency through the observed band. These new, more exact, estimates are different from more simple calculations by up to a factor of about 70, and describe some new regimes which where previously ignored.

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arXiv2001

Physical Constraints From Broadband Afterglow Fits:GRB000926 as an Example

We develop a model to fit the broadband afterglows of GRBs from the intrinsic parameters of the fireball's synchrotron emission, and apply it to a few well-studied events, with the goal of constraining the intrinsic variability of GRB parameters. We give an example here of fitting to the recent bright event GRB000926.

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arXiv2001

Lower Limits on Lorentz Factors in Gamma Ray Bursts

As is well-known, the requirement that gamma ray bursts (GRB's) be optically thin to high energy photons yields a lower limit on the Lorentz factor (γ) of the expansion. In this paper, we provide a simple derivation of the lower limit on γdue to the annihilation of photon pairs, and correct the errors in some of the previous calculations of this limit. We also derive a second limit on γdue to scattering of photons by pair-created electrons and positrons. For some bursts, this limit is the more stringent. In addition, we show that a third limit on γ, which is obtained by considering the scattering of photons by electrons which accompany baryons, is nearly always less important than the second limit. Finally, we evaluate these limits for a number of bursts.

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