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Register a new userTesting viscous disc theory using the balance between stellar accretion and external photoevaporation of protoplanetary discs
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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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Many theoretical studies have shown that external photoevaporation from massive stars can severely truncate, or destroy altogether, the gaseous protoplanetary discs around young stars. In tandem, several observational studies report a correlation between the mass of a protoplanetary disc and its distance to massive ionising stars in star-forming regions, and cite external photoevaporation by the massive stars as the origin of this correlation. We present N-body simulations of the dynamical evolution of star-forming regions and determine the mass-loss in protoplanetary discs from external photoevaporation due to far ultraviolet (FUV) and extreme ultraviolet (EUV) radiation from massive stars. We find that projection effects can be significant, in that low-mass disc-hosting stars that appear close to the ionising sources may be fore- or background stars in the star-forming region. We find very little evidence in our simulations for a trend in increasing disc mass with increasing distance from the massive star(s), even when projection effects are ignored. Furthermore, the dynamical evolution of these young star-forming regions moves stars whose discs have been photoevaporated to far-flung locations, away from the ionising stars, and we suggest that any correlation between disc mass and distance the ionising star is either coincidental, or due to some process other than external photoevaporation.
Circumstellar discs are the precursors of planetary systems and develop shortly after their host star has formed. In their early stages these discs are immersed in an environment rich in gas and neighbouring stars, which can be hostile for their survival. There are several environmental processes that affect the evolution of circumstellar discs, and external photoevaporation is arguably one of the most important ones. Theoretical and observational evidence point to circumstellar discs losing mass quickly when in the vicinity of massive, bright stars. In this work we simulate circumstellar discs in clustered environments in a range of stellar densities, where the photoevaporation mass-loss process is resolved simultaneously with the stellar dynamics, stellar evolution, and the viscous evolution of the discs. Our results indicate that external photoevaporation is efficient in depleting disc masses and that the degree of its effect is related to stellar density. We find that a local stellar density lower than 100 stars pc$^{-2}$ is necessary for discs massive enough to form planets to survive for SI{2.0}{Myr}. There is an order of magnitude difference in the disc masses in regions of projected density 100 stars pc$^{-2}$ versus $10^4$ stars pc$^{-2}$. We compare our results to observations of the Lupus clouds, the Orion Nebula Cluster, the Orion Molecular Cloud-2, Taurus, and NGC 2024, and find that the trends observed between region density and disc masses are similar to those in our simulations.
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.
Many stars form in regions of enhanced stellar density, wherein the influence of stellar neighbours can have a strong influence on a protoplanetary disc (PPD) population. In particular, far ultraviolet (FUV) flux from massive stars drives thermal winds from the outer edge of PPDs, accelerating disc destruction. In this work, we present a novel technique for constraining the dynamical history of a star forming environment using PPD properties in a strongly FUV irradiated environment. Applying recent models for FUV induced mass loss rates to the PPD population of Cygnus OB2, we constrain how long ago primordial gas was expelled from the region; $ 0.5$ Myr ago if the Shakura & Sunyaev $alpha$-viscosity parameter is $alpha = 10^{-2}$ (corresponding to a viscous timescale of $tau_mathrm{visc} approx 0.5$ Myr for a disc of scale radius $40$ au around a $1, M_odot$ star). This value of $alpha$ is effectively an upper limit, since it assumes efficient extinction of FUV photons throughout the embedded phase. With this gas expulsion timescale we are able to produce a full dynamical model that fits kinematic and morphological data as well as disc fractions. We suggest Cygnus OB2 was originally composed of distinct massive clumps or filaments, each with a stellar mass $sim 10^4 , M_odot$. Finally we predict that in regions of efficient FUV induced mass loss, disc mass $M_mathrm{disc}$ as a function of stellar host mass $m_mathrm{star}$ follows a power law with $M_mathrm{disc} propto m_mathrm{star}^beta$, where $beta gtrsim 2.7$ (depending on disc initial conditions and FUV exposure). This is steeper than observed correlations in regions of moderate FUV flux ($1 < beta <1.9$), and offers a promising diagnostic to establish the influence of external photoevaporation in a given region.
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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