CO isotopolog line fluxes of viscously evolving disks: cold CO conversion insufficient to explain observed low fluxes

Protoplanetary disks are thought to evolve viscously, where the disk mass - the reservoir available for planet formation - decreases over time as material is accreted onto the central star. Observations show a correlation between dust mass and the stellar accretion rate, as expected from viscous theory. However, the gas mass inferred from 13CO and C18O line fluxes, which should be a more direct measure, shows no such correlation. Using thermochemical DALI models, we investigate how 13CO and C18O J=3-2 line fluxes change over time in a viscously evolving disk. We also investigate if the chemical conversion of CO through grain-surface chemistry combined with viscous evolution can explain the observations of disks in Lupus. The 13CO and C18O 3-2 line fluxes increase over time due to their optically thick emitting regions growing in size as the disk expands viscously. The C18O 3-2 emission is optically thin throughout the disk for only a subset of our models (Mdisk (t = 1 Myr) < 1e-3 Msun). For these disks the integrated C18O flux decreases with time, similar to the disk mass. The C18O 3-2 fluxes for the bulk of the disks in Lupus (with Mdust < 5e-5 Msun) can be reproduced to within a factor of ~2 with viscously evolving disks in which CO is converted into other species through grain-surface chemistry driven by a cosmic-ray ionization rate zeta_cr ~ 5e-17 - 1e-16 s^-1. However, explaining the stacked C18O upper limits requires a lower average abundance than our models can produce and they cannot explain the observed 13CO fluxes, which, for most disks, are more than an order of magnitude fainter than what our models predict. Reconciling the 13CO fluxes of viscously evolving disks with the observations requires either a combination of efficient vertical mixing and a high zeta_cr or low mass disks (Mdust < 3e-5 Msun) being much thinner and/or smaller than their more massive counterparts.Comment: 21 pages, 14 figures, accepted in A&

Gas Disk Sizes from CO Line Observations: A Test of Angular Momentum Evolution

The size of a disk encodes important information about its evolution. Combining new Submillimeter Array (SMA) observations with archival Atacama Large Millimeter Array (ALMA) data, we analyze mm continuum and CO emission line sizes for a sample of 44 protoplanetary disks around stars with masses of 0.15--2\,$M_{\odot}$ in several nearby star-forming regions. Sizes measured from $^{12}$CO line emission span from 50 to 1000\,au. This range could be explained by viscous evolution models with different $\alpha$ values (mostly of $10^{-4}-10^{-3}$) and/or a spread of initial conditions. The CO sizes for most disks are also consistent with MHD wind models that directly remove disk angular momentum, but very large initial disk sizes would be required to account for the very extended CO disks in the sample. As no CO size evolution is observed across stellar ages of 0.5--20\,Myr in this sample, determining the dominant mechanism of disk evolution will require a more complete sample for both younger and more evolved systems. We find that the CO emission is universally more extended than the continuum emission by an average factor of $2.9\pm1.2$. The ratio of the CO to continuum sizes does not show any trend with stellar mass, mm continuum luminosity, or the properties of substructures. The GO Tau disk has the most extended CO emission in this sample, with an extreme CO to continuum size ratio of 7.6. Seven additional disks in the sample show high size ratios ($\gtrsim4$) that we interpret as clear signs of substantial radial drift.Comment: Accepted for publication in Ap

Molecules with ALMA at Planet-forming Scales (MAPS). V. CO gas distributions

Funding: K.Z., K.R.S., J.H., J.B., J.B.B., and I.C. acknowledge the support of NASA through Hubble Fellowship grants HST-HF2-51401.001, HST-HF2-51419.001, HST-HF2-51460.001-A, HST-HF2-51427.001-A, HST-HF2-51429.001-A, and HST-HF2-51405.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. C.W. acknowledges financial support from the University of Leeds and from the Science and Technology Facilities Council (grant Nos. ST/R000549/1, ST/T000287/1, and MR/T040726/1).Here we present high-resolution (15-24 au) observations of CO isotopologue lines from the Molecules with ALMA on Planet-forming Scales (MAPS) ALMA Large Program. Our analysis employs observations of the (J = 2-1) and (1-0) lines of 13CO and C18O and the (J = 1-0) line of C17O for five protoplanetary disks. We retrieve CO gas density distributions, using three independent methods: (1) a thermochemical modeling framework based on the CO data, the broadband spectral energy distribution, and the millimeter continuum emission; (2) an empirical temperature distribution based on optically thick CO lines; and (3) a direct fit to the C17O hyperfine lines. Results from these methods generally show excellent agreement. The CO gas column density profiles of the five disks show significant variations in the absolute value and the radial shape. Assuming a gas-to-dust mass ratio of 100, all five disks have a global CO-to-H2 abundance 10-100 times lower than the interstellar medium ratio. The CO gas distributions between 150 and 400 au match well with models of viscous disks, supporting the long-standing theory. CO gas gaps appear to be correlated with continuum gap locations, but some deep continuum gaps do not have corresponding CO gaps. The relative depths of CO and dust gaps are generally consistent with predictions of planet-disk interactions, but some CO gaps are 5-10 times shallower than predictions based on dust gaps. This paper is part of the MAPS special issue of the Astrophysical Journal Supplement.Publisher PDFPeer reviewe

How Large Is a Disk—What Do Protoplanetary Disk Gas Sizes Really Mean?

It remains unclear what mechanism is driving the evolution of protoplanetary disks. Direct detection of the main candidates, either turbulence driven by magnetorotational instabilities or magnetohydrodynamical disk winds, has proven difficult, leaving the time evolution of the disk size as one of the most promising observables able to differentiate between these two mechanisms. But to do so successfully, we need to understand what the observed gas disk size actually traces. We studied the relation between R _CO,90% , the radius that encloses 90% of the ^12 CO flux, and R _c , the radius that encodes the physical disk size, in order to provide simple prescriptions for conversions between these two sizes. For an extensive grid of thermochemical models, we calculate R _CO,90% from synthetic observations and relate properties measured at this radius, such as the gas column density, to bulk disk properties, such as R _c and the disk mass M _disk . We found an empirical correlation between the gas column density at R _CO,90% and disk mass: ${N}_{\mathrm{gas}}{({R}_{\mathrm{CO},90 \% })\approx 3.73\,\times \,{10}^{21}({M}_{\mathrm{disk}}/{M}_{\odot })}^{0.34}\ {\mathrm{cm}}^{-2}$ . Using this correlation we derive an analytical prescription of R _CO,90% that only depends on R _c and M _disk . We derive R _c for disks in Lupus, Upper Sco, Taurus, and the DSHARP sample, finding that disks in the older Upper Sco region are significantly smaller (〈 R _c 〉 = 4.8 au) than disks in the younger Lupus and Taurus regions (〈 R _c 〉 = 19.8 and 20.9 au, respectively). This temporal decrease in R _c goes against predictions of both viscous and wind-driven evolution, but could be a sign of significant external photoevaporation truncating disks in Upper Sco

Effect of MHD Wind-driven Disk Evolution on the Observed Sizes of Protoplanetary Disks

Abstract It is still unclear whether the evolution of protoplanetary disks, a key ingredient in the theory of planet formation, is driven by viscous turbulence or magnetic disk winds. As viscously evolving disks expand outward over time, the evolution of disk sizes is a discriminant test for studying disk evolution. However, it is unclear how the observed disk size changes over time if disk evolution is driven by magnetic disk winds. Combining the thermo-chemical code DALI with the analytical wind-driven disk-evolution model presented in Tabone et al., we study the time evolution of the observed gas outer radius as measured from CO rotational emission (R CO,90%). The evolution of R CO,90% is driven by the evolution of the disk mass, as the physical radius stays constant over time. For a constant α DW , an extension of the α Shakura–Sunyaev parameter to wind-driven accretion, R CO,90% decreases linearly with time. Its initial size is set by the disk mass and the characteristic radius R c,0, but only R c,0 affects the evolution of R CO,90%, with a larger R c,0 resulting in a steeper decrease of R CO,90%. For a time-dependent α DW , R CO,90% stays approximately constant during most of the disk lifetime until R CO,90% rapidly shrinks as the disk dissipates. The constant α DW models are able to reproduce the observed gas disk sizes in the ∼1–3 Myr old Lupus and ∼5–11 Myr old Upper Sco star-forming regions. However, they likely overpredict the gas disk size of younger (⪅0.7 Myr) disks

On the secular evolution of the ratio between gas and dust radii in protoplanetary discs

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 time-scales, 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, RCO/Rdust. 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 RCO/Rdust evolves. Our main finding is that, for a broad range of values of disc mass, initial radius, and viscosity, RCO/Rdust 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

De onvolkomen beëindigingsregeling van artikel 7:411 BW

The termination rule of art. 7:411 of the Dutch Civil Code for service contracts builds on an incoherent understanding of termination and right to damages: this article proposes a modification to the code