arXiv subjects

Cathie J. Clarke

Publications and source records attributed to Cathie J. Clarke.

At least 91 records · Page 5Linked to original sources

arXiv2016

The minimum mass of detectable planets in protoplanetary discs and the derivation of planetary masses from high resolution observations

We investigate the minimum planet mass that produces observable signatures in infrared scattered light and submm continuum images and demonstrate how these images can be used to measure planet masses to within a factor of about two. To this end we perform multi-fluid gas and dust simulations of discs containing low mass planets, generating simulated observations at $1.65 μ$m, $10 μ$m and $850 μ$m. We show that the minimum planet mass that produces a detectable signature is $\sim 15 M_\oplus$: this value is strongly dependent on disc temperature and changes slightly with wavelength (favouring the submm). We also confirm previous results that there is a minimum planet mass of $\sim 20 M_\oplus$ that produces a pressure maximum in the disc: only planets above this threshold mass generate a dust trap that can eventually create a hole in the submm dust. Below this mass, planets produce annular enhancements in dust outward of the planet and a reduction in the vicinity of the planet. These features are in steady state and can be understood in terms of variations in the dust radial velocity, imposed by the perturbed gas pressure radial profile, analogous to a traffic jam. We also show how planet masses can be derived from structure in scattered light and sub-mm images. We emphasise that simulations with dust need to be run over thousands of planetary orbits so as to allow the gas profile to achieve a steady state and caution against the estimation of planet masses using gas only simulations.

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arXiv2016

Collision velocity of dust grains in self-gravitating protoplanetary discs

We have conducted the first comprehensive numerical investigation of the relative velocity distribution of dust particles in self-gravitating protoplanetary discs with a view to assessing the viability of planetesimal formation via direct collapse in such environments. The viability depends crucially on the large sizes that are preferentially collected in pressure maxima produced by transient spiral features (Stokes numbers, $St \sim 1$); growth to these size scales requires that collision velocities remain low enough that grain growth is not reversed by fragmentation. We show that, for a single sized dust population, velocity driving by the disc's gravitational perturbations is only effective for $St > 3$, while coupling to the gas velocity dominates otherwise. We develop a criterion for understanding this result in terms of the stopping distance being of order the disc scale height. Nevertheless, the relative velocities induced by differential radial drift in multi-sized dust populations are too high to allow the growth of silicate dust particles beyond $St \sim 10^{-2}$ or $10^{-1}$ ($10\,\mathrm{cm}$ to $\mathrm{m}$ sizes at $30\,\mathrm{au}$), such Stokes numbers being insufficient to allow concentration of solids in spiral features. However, for icy solids (which may survive collisions up to several $10\,\mathrm{m\,s}^{-1}$), growth to $St \sim 1$ ($10\,\mathrm{m}$ size) may be possible beyond $30\,\mathrm{au}$ from the star. Such objects would be concentrated in spiral features and could potentially produce larger icy planetesimals/comets by gravitational collapse. These planetesimals would acquire moderate eccentricities and remain unmodified over the remaining lifetime of the disc.

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arXiv2016

External photoevaporation of protoplanetary discs in sparse stellar groups: the impact of dust growth

We estimate the mass loss rates of photoevaporative winds launched from the outer edge of protoplanetary discs impinged by an ambient radiation field. We focus on mild/moderate environments (the number of stars in the group/cluster is N ~ 50), and explore disc sizes ranging between 20 and 250 AU. We evaluate the steady-state structures of the photoevaporative winds by coupling temperature estimates obtained with a PDR code with 1D radial hydrodynamical equations. We also consider the impact of dust dragging and grain growth on the final mass loss rates. We find that these winds are much more significant than have been appreciated hitherto when grain growth is included in the modelling: in particular, mass loss rates > 1e-8 M_sun/yr are predicted even for modest background field strengths ( ~ 30 G_0) in the case of discs that extend to R > 150 AU. Grain growth significantly affects the final mass loss rates by reducing the average cross section at FUV wavelengths, and thus allowing a much more vigorous flow. The radial profiles of observable quantities (in particular surface density, temperature and velocity patterns) indicate that these winds have characteristic features that are now potentially observable with ALMA. In particular, such discs should have extended gaseous emission that is dust depleted in the outer regions, characterised by a non-Keplerian rotation curve, and with a radially increasing temperature gradient.

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arXiv2016

Rapid radiative clearing of protoplanetary discs

The lack of observed transition discs with inner gas holes of radii greater than ~50AU implies that protoplanetary discs dispersed from the inside out must remove gas from the outer regions rapidly. We investigate the role of photoevaporation in the final clearing of gas from low mass discs with inner holes. In particular, we study the so-called "thermal sweeping" mechanism which results in rapid clearing of the disc. Thermal sweeping was originally thought to arise when the radial and vertical pressure scale lengths at the X-ray heated inner edge of the disc match. We demonstrate that this criterion is not fundamental. Rather, thermal sweeping occurs when the pressure maximum at the inner edge of the dust heated disc falls below the maximum possible pressure of X-ray heated gas (which depends on the local X-ray flux). We derive new critical peak volume and surface density estimates for rapid radiative clearing which, in general, result in rapid dispersal happening less readily than in previous estimates. This less efficient clearing of discs by X-ray driven thermal sweeping leaves open the issue of what mechanism can clear gas from the outer disc sufficiently quickly to explain the non-detection of cold gas around weak line T Tauri stars.

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arXiv2015

Quantification of stochastic fragmentation of self-gravitating discs

Using 2D smoothed particle hydrodynamics, we investigate the distribution of wait times between strong shocks in a turbulent, self-gravitating accretion disc. We show the resulting distributions do not depend strongly on the cooling time or resolution of the disc and that they are consistent with the predictions of earlier work (Young & Clarke 2015; Cossins et al. 2009, 2010). We use the distribution of wait times between shocks to estimate the likelihood of stochastic fragmentation by gradual contraction of shear-resistant clumps on the cooling time scale. We conclude that the stochastic fragmentation mechanism (Paardekooper 2012) cannot change the radius at which fragmentation is possible by more than ~20%, restricting direct gravitational collapse as a mechanism for giant planet formation to the outer regions of protoplanetary discs.

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arXiv2015

Binary accretion rates: dependence on temperature and mass-ratio

We perform a series of 2D smoothed particle hydrodynamics (SPH) simulations of gas accretion onto binaries via a circumbinary disc, for a range of gas temperatures and binary mass ratios ($q$). We show that increasing the gas temperature increases the accretion rate onto the primary for all values of the binary mass ratio: for example, for $q=0.1$ and a fixed binary separation, an increase of normalised sound speed by a factor of $5$ (from our "cold" to "hot" simulations) changes the fraction of the accreted gas that flows on to the primary from $ 10\%$ to $\sim40\%$. We present a simple parametrisation for the average accretion rate of each binary component accurate to within a few percent and argue that this parametrisation (rather than those in the literature based on warmer simulations) is relevant to supermassive black hole accretion and all but the widest stellar binaries. We present trajectories for the growth of $q$ during circumbinary disc accretion and argue that the period distribution of stellar "twin" binaries is strong evidence for the importance of circumbinary accretion. We also show that our parametrisation of binary accretion increases the minimum mass ratio needed for spin alignment of supermassive black holes to $q \sim 0.4$, with potentially important implications for the magnitude of velocity kicks acquired during black hole mergers.

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arXiv2015

Smoothed particle hydrodynamics simulations of gas and dust mixtures

We present a 'two-fluid' implementation of dust in smoothed particle hydrodynamics (SPH) in the test particle limit. The scheme is able to handle both short and long stopping times and reproduces the short friction time limit, which is not properly handled in other implementations. We apply novel tests to verify its accuracy and limitations, including multi-dimensional tests that have not been previously applied to the drag-coupled dust problem and which are particularly relevant to self-gravitating protoplanetary discs. Our tests demonstrate several key requirements for accurate simulations of gas-dust mixtures. Firstly, in standard SPH particle jitter can degrade the dust solution, even when the gas density is well reproduced. The use of integral gradients, a Wendland kernel and a large number of neighbours can control this, albeit at a greater computational cost. Secondly, when it is necessary to limit the artificial viscosity we recommend using the Cullen & Dehnen (2010) switch, since the alternative, using $α \sim 0.1$, can generate a large velocity noise up to ${σ_v} \lesssim 0.3 c_s$ in the dust particles. Thirdly, we find that an accurate dust density estimate requires $>400$ neighbours, since, unlike the gas, the dust particles do not feel regularization forces. This density noise applies to all particle-based two-fluid implementations of dust, irrespective of the hydro solver and could lead to numerically induced fragmentation. Although our tests show accurate dusty gas simulations are possible, care must be taken to minimize the contribution from numerical noise.

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arXiv2015

Dependence of fragmentation in self-gravitating accretion discs on small scale structure

We propose a framework for understanding the fragmentation criterion for self-gravitating discs which, in contrast to studies that emphasise the `gravoturbulent' nature of such discs, instead focuses on the properties of their quasi-regular spiral structures. Within this framework there are two evolutionary paths to fragmentation: i) collapse on the free-fall time, which requires that the ratio of cooling time to dynamical time ($β$) $< 3$ and ii) quasistatic collapse on the cooling time at a rate that is sufficiently fast that fragments are compact enough to withstand disruption when they encounter spiral features in the disc. We perform 2D grid simulations which demonstrate numerically converged fragmentation at $β< 3$ (in good agreement with Paardekooper et al. (2011) and others) and argue that this is a consequence of the fact that such simulations smooth the gravitational force on the scale $H$, the scale height of the disc. Such simulations thus only allow fragmentation via route i) above since they suppress the quasistatic contraction of fragments on scales $< H$; the inability of fragments to contract to significantly smaller scales then renders them susceptible to disruption at the next spiral arm encounter. On the other hand, 3D simulations indeed show fragmentation at higher $β$ via route ii). We derive an analytic prediction of fragmentation by route ii) when $β\lesssim 12$, based on the requirement that fragments must contract sufficiently to withstand disruption by spiral arms. We also discuss the necessary numerical requirements on both grid based and SPH codes if they are to model fragmentation via route ii).

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arXiv2015

A tidal encounter caught in the act: modelling a star-disc fly-by in the young RW Aurigae system

RW Aurigae (RW Aur) is a binary star system with a long molecular arm trailing the primary star. Cabrit et al. (2006) noted the resemblance between this extended structure and the tidal arm stripped from the primary star in the simulations of star-disc encounters by Clarke & Pringle (1993). In this paper we use new hydrodynamical models and synthetic observations to fit many of the parameters of RW Aur. Using hydrodynamic models we find that the morphological appearance of RW Aur can be indeed explained by a tidal encounter with the secondary star. We reproduce all the major morphological and kinematic features of the system. Using radiative transfer calculations, we find that synthetic CO and dust continuum observations of our hydrodynamic models agree well with observations. We reproduce all the main features of the line profiles, from emission fluxes to the optical depth of the different components of the system. The agreement between observations and simulations thus lends strong support to the hypothesis of a tidal encounter scenario. Finally, we propose a possible solution for the origin of the dimming of the primary star observed in 2010/2011 by Rodriguez et al. (2013).

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arXiv2014

The evolution of the mass ratio of accreting binaries: the role of gas temperature

We explore an unresolved controversy in the literature about the accuracy of Smoothed Particle Hydrodynamics (SPH) in modeling the accretion of gas onto a binary system, a problem with important applications to the evolution of proto-binaries as well as accreting binary super massive black holes. It has previously been suggested that SPH fails to model the flow of loosely bound material from the secondary to primary Roche lobe and that its general prediction that accretion drives mass ratios upwards is numerically flawed. Here we show with 2D SPH that this flow from secondary to primary Roche lobe is a sensitive function of gas temperature and that this largely explains the conflicting claims in the literature which have hitherto been based on either 'cold' SPH simulations or 'hot' grid based calculations. We present simulations of a specimen 'cold' and 'hot' accretion scenario which are numerically converged and evolved into a steady state. Our analysis of the conservation of the Jacobi integral of accreting particles indicates that our results are not strongly compromised by numerical dissipation. We also explore the low resolution limit and find that simulations where the ratio of SPH smoothing length to disc scale height at the edge of the circumsecondary is less than 1 accurately capture binary accretion rates.

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arXiv2014

The theory of globulettes: candidate precursors of brown dwarfs and free floating planets in H II regions

Large numbers of small opaque dust clouds - termed 'globulettes' by Gahm et al - have been observed in the H II regions surrounding young stellar clusters. With masses typically in the planetary (or low mass brown dwarf) regime, these objects are so numerous in some regions (e.g. the Rosette) that, if only a small fraction of them could ultimately collapse, then they would be a very significant source of free floating planets. Here we review the properties of globulettes and present a theoretical framework for their structure and evolution. We demonstrate that their interior structure is well described by a pressure confined isothermal Bonnor-Ebert sphere and that the observed mass-radius relation (mass approximately proportional to the radius squared) is a systematic consequence of a column density threshold below which components of the globulette are not identified. We also find that globulettes with this interior structure are very stable against collapse within H II regions. We follow Gahm et al in assuming that globulettes are detached from the tips of pillars protruding in from the swept up shell that borders the expanding H II region and produce a model for their dynamics, finding that globulettes will eventually impact the shell. We derive an expression for the time it takes to do so and show that dissipation of energy via dust cooling allows all globulettes to survive this encounter and escape into the wider ISM. Once there the ambient pressure drops and they disperse on timescales around 30-300 kyr and should be observable using ALMA out to distances of order a parsec. Since we find that globulettes are stable, the only route via which they might still form brown dwarfs or planets is during their collision with the shell or some other violent perturbative event.

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arXiv2014

Multiplicity in Early Stellar Evolution

Observations from optical to centimeter wavelengths have demonstrated that multiple systems of two or more bodies is the norm at all stellar evolutionary stages. Multiple systems are widely agreed to result from the collapse and fragmentation of cloud cores, despite the inhibiting influence of magnetic fields. Surveys of Class 0 protostars with mm interferometers have revealed a very high multiplicity frequency of about 2/3, even though there are observational difficulties in resolving close protobinaries, thus supporting the possibility that all stars could be born in multiple systems. Near-infrared adaptive optics observations of Class I protostars show a lower binary frequency relative to the Class 0 phase, a declining trend that continues through the Class II/III stages to the field population. This loss of companions is a natural consequence of dynamical interplay in small multiple systems, leading to ejection of members. We discuss observational consequences of this dynamical evolution, and its influence on circumstellar disks, and we review the evolution of circumbinary disks and their role in defining binary mass ratios. Special attention is paid to eclipsing PMS binaries, which allow for observational tests of evolutionary models of early stellar evolution. Many stars are born in clusters and small groups, and we discuss how interactions in dense stellar environments can significantly alter the distribution of binary separations through dissolution of wider binaries. The binaries and multiples we find in the field are the survivors of these internal and external destructive processes, and we provide a detailed overview of the multiplicity statistics of the field, which form a boundary condition for all models of binary evolution. Finally we discuss various formation mechanisms for massive binaries, and the properties of massive trapezia.

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arXiv2013

Characterising thermal sweeping: a rapid disc dispersal mechanism

(Abridged) We consider the properties of protoplanetary discs that are undergoing inside-out clearing by photoevaporation. In particular, we aim to characterise the conditions under which a protoplanetary disc may undergo `thermal sweeping', a rapid (< 1e4 years) disc destruction mechanism proposed to occur when a clearing disc reaches sufficiently low surface density at its inner edge and where the disc is unstable to runaway penetration by the X-rays. We use a large suite of 1D radiation-hydrodynamic simulations to probe the observable parameter space, which is unfeasible in higher dimensions. These models allow us to determine the surface density at which thermal sweeping will take over the disc's evolution and to evaluate this critical surface density as a function of X-ray luminosity, stellar mass and inner hole radius. We find that this critical surface density scales linearly with X-ray luminosity, increases with inner hole radius and decreases with stellar mass and we develop an analytic model that reproduces these results. This surface density criterion is then used to determine the evolutionary state of protoplanetary discs at the point that they become unstable to destruction by thermal sweeping. We find that transition discs created by photoevaporation will undergo thermal sweeping when their inner holes reach 20-40 AU, implying that transition discs with large holes and no accretion (which were previously a predicted outcome of the later stages of all flavours of photoevaporation model) will not form. We emphasise that the surface density criteria that we have developed apply to all situations where the disc develops an inner hole that is optically thin to X-rays. It thus applies not only to the case of holes originally created by photoevaporation but also to holes formed, for example, by the tidal influence of planets.

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arXiv2012

Do all stars in the solar neighbourhood form in clusters? A cautionary note on the use of the distribution of surface densities

Bressert et al. recently showed that the surface density distribution of low-mass, young stellar objects (YSOs) in the solar neighbourhood is approximately log-normal. The authors conclude that the star formation process is hierarchical and that only a small fraction of stars form in dense star clusters. Here, we show that the peak and the width of the density distribution are also what follow if all stars form in bound clusters which are not significantly affected by the presence of gas and expand by two-body relaxation. The peak of the surface density distribution is simply obtained from the typical ages (few Myr) and cluster membership number (few hundred) typifying nearby star-forming regions. This result depends weakly on initial cluster sizes, provided that they are sufficiently dense (initial half mass radius of <0.3 pc) for dynamical evolution to be important at an age of a few Myr. We conclude that the degeneracy of the YSO surface density distribution complicates its use as a diagnostic of the stellar formation environment.

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arXiv2012

The Periodic Spectroscopic Variability of FU Orionis

FU Orionis systems are young stars undergoing outbursts of disc accretion and where the optical spectrum contains lines associated with both the disc photosphere and a wind component. Previous observations of the prototype FU Orionis have suggested that the wind lines and the photospheric lines are modulated with periods of 14.54 and 3.54 days respectively (Herbig et al. 2003). We have re-observed the system at higher spectral resolution, by monitoring variations of optical line profiles over 21 nights in 2007 and have found periods of 13.48 and 3.6 days in the wind and disc components consistent with the above: this implies variability mechanisms that are stable over at least a decade. In addition we have found: i) that the variations in the photospheric absorption lines are confined to the blue wing of the line (around -9km/s): we tentatively ascribe this to an orbiting hotspot in the disc which is obscured by a disc warp during its receding phase. ii) The wind period is manifested not only in blue-shifted Halpha absorption, but also in red-shifted emission of Halpha and Hbeta, as well as in blue-shifted absorption of Na I D, Li I and Fe II. iii) We find that the periodic modulation of blue-shifted Halpha absorption at around -100km/s, is phase lagged with respect to variations in the other lines by ~1.8days. This is consistent with a picture in which variations at the wind base first affect chromospheric emission and then low velocity blue-shifted absorption, followed - after a lag equal to the propagation time of disturbances across the wind's acceleration region - by a response in high velocity blue-shifted absorption. Such arguments constrain the size of the acceleration region to ~10^12cm. We discuss possible mechanisms for periodic variations within the innermost 0.1AU of the disc, including the possibility that these variations indicate the presence of an embedded hot Jupiter.

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arXiv2012

Radiative Transfer in Star Formation: Testing FLD and Hybrid Methods

We perform a comparison between two radiative transfer algorithms commonly employed in hydrodynamical calculations of star formation: grey flux limited diffusion and the hybrid scheme, in addition we compare these algorithms to results from the Monte-Carlo radiative transfer code MOCASSIN. In disc like density structures the hybrid scheme performs significantly better than the FLD method in the optically thin regions, with comparable results in optically thick regions. In the case of a forming high mass star we find the FLD method significantly underestimates the radiation pressure by a factor of ~100.

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arXiv2012

Reliable estimation of the column density in Smoothed Particle Hydrodynamic simulations

We describe a simple method for estimating the vertical column density in Smoothed Particle Hydrodynamics (SPH) simulations of discs. As in the method of Stamatellos et al. (2007), the column density is estimated using pre-computed local quantities and is then used to estimate the radiative cooling rate. The cooling rate is a quantity of considerable importance, for example, in assessing the probability of disc fragmentation. Our method has three steps: (i) the column density from the particle to the mid plane is estimated using the vertical component of the gravitational acceleration, (ii) the "total surface density" from the mid plane to the surface of the disc is calculated, (iii) the column density from each particle to the surface is calculated from the difference between (i) and (ii). This method is shown to greatly improve the accuracy of column density estimates in disc geometry compared with the method of Stamatellos. On the other hand, although the accuracy of our method is still acceptable in the case of high density fragments formed within discs, we find that the Stamatellos method performs better than our method in this regime. Thus, a hybrid method (where the method is switched in regions of large over-density) may be optimal.

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arXiv2012

The rapid dispersal of low-mass virialised clusters

Infant mortality brought about by the expulsion of a star cluster's natal gas is widely invoked to explain cluster statistics at different ages. While a well studied problem, most recent studies of gas expulsion's effect on a cluster have focused on massive clusters, with stellar counts of order $10^4$. Here we argue that the evolutionary timescales associated with the compact low-mass clusters typical of the median cluster in the Solar neighborhood are short enough that significant dynamical evolution can take place over the ages usually associated with gas expulsion. To test this we perform {\it N}-body simulations of the dynamics of a very young star forming region, with initial conditions drawn from a large-scale hydrodynamic simulation of gravitational collapse and fragmentation. The subclusters we analyse, with populations of a few hundred stars, have high local star formation efficiencies and are roughly virialised even after the gas is removed. Over 10 Myr they expand to a similar degree as would be expected from gas expulsion if they were initially gas-rich, but the expansion is purely due to the internal stellar dynamics of the young clusters. The expansion is such that the stellar densities at 2 Myr match those of YSOs in the Solar neighborhood. We argue that at the low-mass end of the cluster mass spectrum, a deficit of clusters at 10s of Myr does not necessarily imply gas expulsion as a disruption mechanism.

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