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Register a new userProtoplanetary Disc Response to Distant Tidal Encounters in Stellar Clusters
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The majority of stars form in a clustered environment. This has an impact on the evolution of surrounding protoplanetary discs (PPDs) due to either photoevaporation or tidal truncation. Consequently, the development of planets depends on formation environment. Here we present the first thorough investigation of tidally induced angular momentum loss in PPDs in the distant regime, partly motivated by claims in the literature for the importance of distant encounters in disc evolution. We employ both theoretical predictions and dynamical/hydrodynamical simulations in 2D and 3D. Our theoretical analysis is based on that of Ostriker (1994) and leads us to conclude that in the limit that the closest approach distance $x_{min} gg r$, the radius of a particle ring, the fractional change in angular momentum scales as $(x_{min}/r)^{-5}$. This asymptotic limit ensures that the cumulative effect of distant encounters is minor in terms of its influence on disc evolution. The angular momentum transfer is dominated by the $m=2$ Lindblad resonance for closer encounters and by the $m=1$, $omega = 0$ Lindblad resonance at large $x_{min}/r$. We contextualise these results by comparing expected angular momentum loss for the outer edge of a PPD due to distant and close encounters. Contrary to the suggestions of previous works we do not find that distant encounters contribute significantly to angular momentum loss in PPDs. We define an upper limit for closest approach distance where interactions are significant as a function of arbitrary host to perturber mass ratio $M_2/M_1$.
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Most stars form and spend their early life in regions of enhanced stellar density. Therefore the evolution of protoplanetary discs (PPDs) hosted by such stars are subject to the influence of other members of the cluster. Physically, PPDs might be truncated either by photoevaporation due to ultraviolet flux from massive stars, or tidal truncation due to close stellar encounters. Here we aim to compare the two effects in real cluster environments. In this vein we first review the properties of well studied stellar clusters with a focus on stellar number density, which largely dictates the degree of tidal truncation, and far ultraviolet (FUV) flux, which is indicative of the rate of external photoevaporation. We then review the theoretical PPD truncation radius due to an arbitrary encounter, additionally taking into account the role of eccentric encounters that play a role in hot clusters with a 1D velocity dispersion $sigma_v > 2$ km/s. Our treatment is then applied statistically to varying local environments to establish a canonical threshold for the local stellar density ($n_{c} > 10^4$ pc$^{-3}$) for which encounters can play a significant role in shaping the distribution of PPD radii over a timescale $sim 3$ Myr. By combining theoretical mass loss rates due to FUV flux with viscous spreading in a PPD we establish a similar threshold for which a massive disc is completely destroyed by external photoevaporation. Comparing these thresholds in local clusters we find that if either mechanism has a significant impact on the PPD population then photoevaporation is always the dominating influence.
The discovery of planetary systems outside of the solar system has challenged some of the tenets of planetary formation. Among the difficult-to-explain observations, are systems with a giant planet orbiting a very-low mass star, such as the recently discovered GJ~3512b planetary system, where a Jupiter-like planet orbits an $M$-star in a tight and eccentric orbit. Systems such as this one are not predicted by the core accretion theory of planet formation. Here we suggest a novel mechanism, in which the giant planet is born around a more typical Sun-like star ($M_{*,1}$), but is subsequently exchanged during a dynamical interaction with a flyby low-mass star ($M_{*,2}$). We perform state-of-the-art $N$-body simulations with $M_{*,1}=1M_odot$ and $M_{*,2}=0.1M_odot$ to study the statistical outcomes of this interaction, and show that exchanges result in high eccentricities for the new orbit around the low-mass star, while about half of the outcomes result in tighter orbits than the planet had around its birth star. We numerically compute the cross section for planet exchange, and show that an upper limit for the probability per planetary system to have undergone such an event is $Gammasim 4.4(M_{rm c}/100M_odot)^{-2}(a_{rm p}/{rm AU}) (sigma/1,{rm km},{rm s}^{-1})^{5}$Gyr$^{-1}$, where $a_{rm p}$ is the planet semi-major axis around the birth star, $sigma$ the velocity dispersion of the star cluster, and $M_{rm c}$ the total mass of the star cluster. Hence these planet exchanges could be relatively common for stars born in open clusters and groups, should already be observed in the exoplanet database, and provide new avenues to create unexpected planetary architectures.
The nature and rate of (viscous) angular momentum transport in protoplanetary discs (PPDs) has important consequences for the formation process of planetary systems. While accretion rates onto the central star yield constraints on such transport in the inner regions of a PPD, empirical constraints on viscous spreading in the outer regions remain challenging to obtain. Here we demonstrate a novel method to probe the angular momentum transport at the outer edge of the disc. This method applies to PPDs that have lost a significant fraction of their mass due to thermal winds driven by UV irradiation from a neighbouring OB star. We demonstrate that this external photoevaporation can explain the observed depletion of discs in the 3-5 Myr old $sigma$ Orionis region, and use our model to make predictions motivating future empirical investigations of disc winds. For populations of intermediate-age PPDs, in viscous models we show that the mass flux outwards due to angular momentum redistribution is balanced by the mass-loss in the photoevaporative wind. A comparison between wind mass-loss and stellar accretion rates therefore offers an independent constraint on viscous models in the outer regions of PPDs.
Observations indicate that the dispersal of protoplanetary discs in star clusters occurs on time scales of about 5 Myr. Several processes are thought to be responsible for this disc dispersal. Here we compare two of these processes: dynamical encounters and interaction with the interstellar medium, which includes face-on accretion and ram pressure stripping. We perform simulations of embedded star clusters with parameterisations for both processes to determine the environment in which either of these processes is dominant. We find that face-on accretion, including ram pressure stripping, is the dominant disc truncation process if the fraction of the total cluster mass in stars is $lesssim 30,%$ regardless of the cluster mass and radius. Dynamical encounters require stellar densities $gtrsim 10^4$ pc$^{-3}$ combined with a mass fraction in stars of $approx 90,%$ to become the dominant process. Our results show that during the embedded phase of the cluster, the truncation of the discs is dominated by face-on accretion and dynamical encounters become dominant when the intra-cluster gas has been expelled. As a result of face-on accretion the protoplanetary discs become compact and their surface density increases. In contrast, dynamical encounters lead to discs that are less massive and remain larger.
Proto-planetary disc surveys conducted with ALMA are measuring disc radii in multiple star forming regions. The disc radius is a fundamental quantity to diagnose whether discs undergo viscous spreading, discriminating between viscosity or angular momentum removal by winds as drivers of disc evolution. Observationally, however, the sub-mm continuum emission is dominated by the dust, which also drifts inwards, complicating the picture. In this paper we investigate, using theoretical models of dust grain growth and radial drift, how the radii of dusty viscous proto-planetary discs evolve with time. Despite the existence of a sharp outer edge in the dust distribution, we find that the radius enclosing most of the dust $textit{mass}$ increases with time, closely following the evolution of the gas radius. This behaviour arises because, although dust initially grows and drifts rapidly onto the star, the residual dust retained on Myr timescales is relatively well coupled to the gas. Observing the expansion of the dust disc requires using definitions based on high fractions of the disc $textit{flux}$ (e.g. 95 per cent) and very long integrations with ALMA, because the dust grains in the outer part of the disc are small and have a low sub-mm opacity. We show that existing surveys lack the sensitivity to detect viscous spreading. The disc radii they measure do not trace the mass radius or the sharp outer edge in the dust distribution, but the outer limit of where the grains have significant sub-mm opacity. We predict that these observed radii should shrink with time.
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