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Register a new userThe time evolution of dusty protoplanetary disc radii: observed and physical radii differ
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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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A key problem in protoplanetary disc evolution is understanding the efficiency of dust radial drift. This process makes the observed dust disc sizes shrink on relatively short timescales, implying that discs started much larger than what we see now. In this paper we use an independent constraint, the gas radius (as probed by CO rotational emission), to test disc evolution models. In particular, we consider the ratio between the dust and gas radius, $R_{rm CO}/R_{rm dust}$. We model the time evolution of protoplanetary discs under the influence of viscous evolution, grain growth, and radial drift. Then, using the radiative transfer code RADMC with approximate chemistry, we compute the dust and gas radii of the models and investigate how $R_{rm CO}/R_{rm dust}$ evolves. Our main finding is that, for a broad range of values of disc mass, initial radius, and viscosity, $R_{rm CO}/R_{rm dust}$ becomes large (>5) after only a short time (<1 Myr) due to radial drift. This is at odds with measurements in young star forming regions such as Lupus, which find much smaller values, implying that dust radial drift is too efficient in these models. Substructures, commonly invoked to stop radial drift in large, bright discs, must then be present, although currently unresolved, in most discs.
The formation of planets strongly depends on the total amount as well as on the spatial distribution of solids in protoplanetary disks. Thanks to the improvements in resolution and sensitivity provided by ALMA, measurements of the surface density of mm-sized grains are now possible on large samples of disks. Such measurements provide statistical constraints that can be used to inform our understanding of the initial conditions of planet formation. We analyze spatially resolved observations of 36 protoplanetary disks in the Lupus star forming complex from our ALMA survey at 890 micron, aiming to determine physical properties such as the dust surface density, the disk mass and size and to provide a constraint on the temperature profile. We fit the observations directly in the uv-plane using a two-layer disk model that computes the 890 micron emission by solving the energy balance at each disk radius. For 22 out of 36 protoplanetary disks we derive robust estimates of their physical properties. The sample covers stellar masses between ~0.1 and ~2 Solar masses, and we find no trend between the average disk temperatures and the stellar parameters. We find, instead, a correlation between the integrated sub-mm flux (a proxy for the disk mass) and the exponential cut-off radii (a proxy of the disk size) of the Lupus disks. Comparing these results with observations at similar angular resolution of Taurus-Auriga/Ophiuchus disks found in literature and scaling them to the same distance, we observe that the Lupus disks are generally fainter and larger at a high level of statistical significance. Considering the 1-2 Myr age difference between these regions, it is possible to tentatively explain the offset in the disk mass/disk size relation with viscous spreading, however with the current measurements other mechanisms cannot be ruled out.
We perform a comprehensive demographic study of the CO extent relative to dust of the disk population in the Lupus clouds, in order to find indications of dust evolution and possible correlations with other properties. We increase up to 42 the number of disks of the region with measured CO and dust sizes ($R_{mathrm{CO}}$, $R_{mathrm{dust}}$) from observations with the Atacama Large Millimeter/submillimeter Array (ALMA). The sizes are obtained from modeling the ${^{12}}$CO $J = 2-1$ line emission and continuum emission at $sim 0.89$ mm with an empirical function (Nuker profile or Gaussian function). The CO emission is more extended than the dust continuum, with a $R_{68%}^{mathrm{CO}}$/$R_{68%}^{mathrm{dust}}$ median value of 2.5, for the entire population and for a sub-sample with high completeness. 6 disks, around $15%$ of the Lupus disk population have a size ratio above 4. Based on thermo-chemical modeling, this value can only be explained if the disk has undergone grain growth and radial drift. These disks do not have unusual properties in terms of stellar mass ($M_{star}$), disk mass ($M_{mathrm{disk}}$), CO and dust sizes ($R_{mathrm{CO}}$, $R_{mathrm{dust}}$), and mass accretion. We search for correlations between the size ratio and $M_{star}$, $M_{mathrm{disk}}$, $R_{mathrm{CO}}$ and $R_{mathrm{dust}}$: only a weak monotonic anti-correlation with the $R_{mathrm{dust}}$ is found. The lack of strong correlations is remarkable and suggests that the bulk of the population may be in a similar evolutionary stage, independent of the stellar and disk properties. These results should be further investigated, since the optical depth difference between CO and dust continuum may play a role in the inferred size ratios. Lastly, the CO emission for the majority of the disks is consistent with optically thick emission and an average CO temperature of around 30 K.
The stellar birth environment can significantly shorten protoplanetary disc (PPD) lifetimes due to the influence of stellar feedback mechanisms. The degree to which these mechanisms suppress the time and mass available for planet formation is dependent on the local far-ultraviolet (FUV) field strength, stellar density, and ISM properties. In this work, we present the first theoretical framework quantifying the distribution of PPD dispersal time-scales as a function of parameters that describe the galactic environment. We calculate the probability density function for FUV flux and stellar density in the solar neighbourhood. In agreement with previous studies, we find that external photoevaporation is the dominant environment-related factor influencing local stellar populations after the embedded phase. Applying our general prescription to the Central Molecular Zone of the Milky Way (i.e. the central ~250 pc), we predict that 90% of PPDs in the region are destroyed within 1 Myr of the dispersal of the parent molecular cloud. Even in such dense environments, we find that external photoevaporation is the dominant disc depletion mechanism over dynamical encounters between stars. PPDs around low-mass stars are particularly sensitive to FUV-induced mass loss, due to a shallower gravitational potential. For stars of mass ~1 $M_odot$, the solar neighbourhood lies at approximately the highest gas surface density for which PPD dispersal is still relatively unaffected by external FUV photons, with a median PPD dispersal timescale of ~4 Myr. We highlight the key questions to be addressed to further contextualise the significance of the local galactic environment for planet formation.
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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