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Register a new userProtoplanetary disc truncation mechanisms in stellar clusters: comparing external photoevaporation and tidal encounters
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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.
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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 $M_2/M_1$.
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.
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.
High resolution spectra of typical wind diagnostics ([OI] 6300 r{A} and other forbidden emission lines) can often be decomposed into multiple components: high-velocity components with blueshifts up to several 100 km/s are usually attributed to fast jets, while narrow (NLVC) and broad (BLVC) low-velocity components are believed to trace slower disc winds. Under the assumption that the line-broadening is dominated by Keplerian rotation, several studies have found that the BLVCs should trace gas launched between 0.05 and 0.5 au and correlations between the properties of BLVCs and NLVCs have been interpreted as evidence for the emission tracing an extended MHD wind and not a photoevaporative wind. We calculated synthetic line profiles obtained from detailed photoionisation calculations of an X-ray photoevaporation model and a simple MHD wind model and analyzed the emission regions of different diagnostic lines and the resulting spectral profiles. The photoevaporation model reproduces most of the observed NLVCs but not the BLVCs or HVCs. The MHD model is able to reproduce all components but produces Keplerian double peaks at average inclinations that are rarely observed. The combination of MHD and photoevaporative winds could solve this problem. Our results suggest that the Gaussian decomposition does not allow for a clear distinction of flux from different wind regions and that the line broadening is often dominated by the velocity gradient in the outflow rather than by Keplerian rotation. We show that observed correlations between BLVC and NLVC do not necessarily imply a common origin in an extended MHD wind.
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.
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