Philip J. Armitage

Dynamics of Protoplanetary Disks

Protoplanetary disks are quasi-steady structures whose evolution and dispersal determine the environment for planet formation. I review the theory of protoplanetary disk evolution and its connection to observations. Substantial progress has been made in elucidating the physics of potential angular momentum transport processes—including self-gravity, magnetorotational instability, baroclinic instabilities, and magnetic braking—and in developing testable models for disk dispersal via photoevaporation. The relative importance of these processes depends upon the initial mass, size, and magnetization of the disk, and subsequently on its opacity, ionization state, and external irradiation. Disk dynamics is therefore coupled to star formation, pre-main-sequence stellar evolution, and dust coagulation during the early stages of planet formation and may vary dramatically from star to star. The importance of validating theoretical models is emphasized, with the key observations being those that probe disk structure...

Investigating fragmentation conditions in self-gravitating accretion discs

The issue of fragmentation in self-gravitating gaseous accretion discs has implications both for the formation of stars in discs in the nuclei of active galaxies, and for the formation of gaseous planets or brown dwarfs in circumstellar discs. It is now well established that fragmentation occurs if the disc is cooled on a time-scale smaller than the local dynamical time-scale, while for longer cooling times the disc reaches a quasi-steady state in thermal equilibrium, with the cooling rate balanced by the heating due to gravitational stresses. We investigate here how the fragmentation boundary depends on the assumed equation of state. We find that the cooling time required for fragmentation increases as the specific heat ratio γ decreases, exceeding the local dynamical time-scale for γ = 7/5. This result can be easily interpreted as a consequence of there being a maximum stress (in units of the local disc pressure) that can be sustained by a self-gravitating disc in quasi-equilibrium. Fragmentation occurs if the cooling time is such that the stress required to reach thermal equilibrium exceeds this value, independent of γ . This result suggests that a quasi-steady, self-gravitating disc can never produce a stress that results in the viscous α parameter exceeding ∼0.06.

Episodic accretion in magnetically layered protoplanetary discs

We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 AU such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion onto the protostar occurs in ∼ 10 4 yr bursts with u M ∼ 10 −5 M⊙yr −1 , separated by quiescent intervals lasting ∼ 10 5 yr where u M ≈ 10 −8 M⊙yr −1 . Such bursts could lead to repeated episodes of strong mass outflow in Young Stellar Objects. The transition to this episodic mode of accretion occurs at an early epoch (t ≪ 1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼ 1 AU. The predicted rate of low mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1 – 3 AU.

Massive black hole binary mergers within subparsec scale gas discs

We study the efficiency and dynamics of supermassive black hole binary mergers driven by angular momentum loss to small-scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes very inefficient at sub-parsec distances. Gas discs may dominate binary dynamics on these scales, and promote mergers. Using numerical simulations, we investigate the evolution of the semi-major axis and eccentricity of binaries embedded within geometrically thin gas discs. Our simulations directly resolve angular momentum transport within the disc, which at the radii of interest is likely dominated by disc self-gravity. We show that the binary decays at a rate which is in good agreement with analytical estimates, while the eccentricity grows. Saturation of eccentricity growth is not observed up to values e > � 0.35. Accretion onto the black holes is variable, and is roughly modulated by the binary orbital frequency. Scaling our results, we analytically estimate the maximum rate of binary decay that is possible without fragmentation occuring within the surrounding gas disc, and compare that rate to an estimate of the stellar dynamical hardening rate. For binary masses in the range 10 5 M⊙ < � M < � 10 8 M⊙ we find that decay due to gas discs may dominate for separations below a � 10 −2 pc 0.1 pc, in the regime where the disc is optically thick. The minimum merger time scale is shorter than the Hubble time for M < � 10 7 M⊙. This implies that gas discs could commonly attend relatively low mass black hole mergers, and that a significant population of binaries might exist at separations of a few hundredths of a pc, where the combined decay rate is slowest. For more massive binaries, where this mechanism fails to act quickly enough, we suggest that scattering of stars formed within a fragmenting gas disc could act as a significant additional sink of binary angular momentum.

Dust filtration at gap edges: implications for the spectral energy distributions of discs with embedded planets

ABSTRACT The spectral energy distributions (SEDs) of some T Tauri stars display a deficit ofnear-IR flux that could be a consequence of an embedded Jupiter-mass planet partiallyclearingan inner hole in the circumstellardisc. Here, weuse two-dimensionalnumericalsimulations of the planet-disc interaction, in concert with simple models for the dustdynamics, to quantify how a planet influences the dust at different radii within thedisc. We show that pressure gradientsat the outer edge of the gap cleared by the planetact as a filter - letting particles smaller than a critical size through to the inner discwhile holding back larger particles in the outer disc. The critical particle size dependsupon the disc properties, but is typically of the order of 10 microns. This filtrationprocess will lead to discontinuous grain populations across the planet’s orbital radius,with small grains in the inner disc and an outer population of larger grains. We showthat this type of dust population is qualitatively consistent with SED modelling ofsystems that have optically thin inner holes in their circumstellar discs. This processcan also produce a very large gas-to-dust ratio in the inner disc, potentially explainingthose systems with optically thin inner cavities that still have relatively high accretionrates.Keywords: solar system: formation — planets and satellites: formation — planetarysystems: formation

Accretion during the Merger of Supermassive Black Holes

We study the evolution of disk accretion during the merger of supermassive black hole binaries in galactic nuclei. In hierarchical galaxy formation models, the most common binaries are likely to arise from minor galactic mergers and have unequal-mass black holes. Once such a binary becomes embedded in an accretion disk at a separation of a ~ 0.1 pc, the merger proceeds in two distinct phases. During the first phase, the loss of orbital angular momentum to the gaseous disk shrinks the binary on a timescale of ~107 yr. The accretion rate onto the primary black hole is not increased, and can be substantially reduced, during this disk-driven migration. At smaller separations, gravitational radiation becomes the dominant angular momentum loss process, and any gas trapped inside the orbit of the secondary is driven inward by the inspiralling black hole. The implied accretion rate just prior to coalescence exceeds the Eddington limit, so the final merger is likely to occur within a common envelope formed from the disrupted inner disk and to be accompanied by high-velocity (~104 km s-1) outflows.

Dust dynamics during protoplanetary disc clearing

We consider the dynamics of dust and gas during the clearing of protoplanetary discs. We work within the context of a photoevaporation/viscous model for the evolution of the gas disc, and use a two-fluid model to study the dynamics of dust grains as the gas disc is cleared. Small (<~10um) grains remain well-coupled to the gas, but larger (~1mm) grains are subject to inward migration from large radii (~50AU), suggesting that the time-scale for grain growth in the outer disc is ~10^4-10^5yr. We describe in detail the observable appearance of discs during clearing, and find that pressure gradients in the gas disc result in a strong enhancement of the local dust-to-gas ratio in a ring near to the inner disc edge. Lastly, we consider a simple model of the disc-planet interaction, and suggest that observations of disc masses and accretion rates provide a straightforward means of discriminating between different models of disc clearing.

Flares in Long and Short Gamma-Ray Bursts: A Common Origin in a Hyperaccreting Accretion Disk

Early-time X-ray observations of gamma-ray bursts (GRBs) with the Swift satellite have revealed a more complicated phenomenology than was known before. In particular, the presence of flaring activity on a wide range of timescales probably requires late-time energy production within the GRB engine. Since the flaring activity is observed in both long and short GRBs, its origin must be within what is in common for the two likely progenitors of the two classes of bursts: a hyperaccreting accretion disk around a black hole of a few solar masses. Here we show that some of the observational properties of the flares, such as the duration-timescale correlation, and the duration-peak luminosity anticorrelation displayed by most flares within a given burst, are qualitatively consistent with viscous disk evolution, provided that the disk at large radii either fragments or otherwise suffers large-amplitude variability. We discuss the physical conditions in the outer parts of the disk and conclude that gravitational instability, possibly followed by fragmentation, is the most likely candidate for this variability.

Accelerated planetesimal growth in self-gravitating protoplanetary discs

In this paper we consider the evolution of small planetesimals (radii ∼1‐10 m) in marginally stable, self-gravitating protoplanetary discs. The drag force between the disc gas and the embedded planetesimals generally causes the planetesimals to drift inwards through the disc at a rate that depends on the particle size. In a marginally stable, self-gravitating disc, however, the planetesimals are significantly influenced by the non-axisymmetric spiral structures resulting from the growth of the gravitational instability. The drag force now causes the planetesimals to drift towards the peaks of the spiral arms where the density and pressure are highest. For small particles that are strongly coupled to the disc gas, and for large particles that have essentially decoupled from the disc gas, the effect is not particularly significant. Intermediate-sized particles, which would generally have the largest radial drift rates, do, however, become significantly concentrated at the peaks of the spiral arms. These high-density regions may persist for, of order, an orbital period and may attain densities comparable to that of the disc gas. Although at the end of the simulation only ∼25 per cent of the planetesimal particles lie in regions of enhanced density, during the course of the simulation at least 75 per cent of the planetesimal particles have at some stage been in a such a region. We find that the concentration of particles in the spiral arms results in an increased collision rate, an effect that could significantly accelerate planetesimal growth. The density enhancements may also be sufficient for the growth of planetesimals through direct gravitational collapse. The interaction between small planetesimals and self-gravitating spiral structures may therefore play an important role in the formation of large planetesimals that will ultimately coagulate to form terrestrial planets or the cores of gas/ice giant planets.

Turbulence and Angular Momentum Transport in a Global Accretion Disk Simulation

The global development of magnetohydrodynamic turbulence in an accretion disk is studied within a simplified disk model that omits vertical stratification. Starting with a weak vertical seed field, a saturated state is obtained after a few tens of orbits in which the energy in the predominantly toroidal magnetic field is still subthermal. The efficiency of angular momentum transport, parameterized by the Shakura-Sunyaev α-parameter, is of the order of 10−1. The dominant contribution to α comes from magnetic stresses, which are enhanced by the presence of weak net vertical fields. The power spectra of the magnetic fields are flat or decline only slowly toward the largest scales accessible in the calculation, suggesting that the viscosity arising from MHD turbulence may not be a locally determined quantity. I discuss how these results compare with observationally inferred values of α and possible implications for models of jet formation.