Interaction of CO2 with small rutile crystallites-an EHMO study

Several possible adsorption sites and adsorption geometries of CO2 on small rutile fragments were studied by Extended Hückel Molecular Orbital (EHMO) calculations. The parameters for the rutile part were optimised to reproduce the experimental rutile bulk structure and were tested in several small clusters up to [(TiO2)31(OH)32]32−•6H2O, a 175 atoms cluster. It was found that the average experimental bond legth can be reproduced with good accuracy. However the slight distortion of the TiO6 octahedra is calculated with the wrong sign (four long and two short Ti−O bonds). The agreement for the angle αO-Ti-O is less satisfactory. The study shows that CO2 can adsorb on fivefold coordinated surface titanium sites as well as surface oxygen sites. This means that CO2 can act as either Lewis base or acid. In the case of binding as a Lewis base, CO2 can adsorb linearly forming a single Ti−OCO bond, or interact with two neighboring Ti4+ sites. A chelating structure forming two Ti−O bonds was found to be weakly stable at the most. When CO2 behaves as a Lewis acid, a carbonate-like structure is formed by interaction with either terminal oxygen ions or bridging oxygen center

Unlocking CO Depletion in Protoplanetary Disks II. Primordial C/H Predictions Inside the CO Snowline

CO is thought to be the main reservoir of volatile carbon in protoplanetary disks, and thus the primary initial source of carbon in the atmospheres of forming giant planets. However, recent observations of protoplanetary disks point towards low volatile carbon abundances in many systems, including at radii interior to the CO snowline. One potential explanation is that gas phase carbon is chemically reprocessed into less volatile species, which are frozen on dust grain surfaces as ice. This mechanism has the potential to change the primordial C/H ratio in the gas. However, current observations primarily probe the upper layers of the disk. It is not clear if the low volatile carbon abundances extend to the midplane, where planets form. We have run a grid of 198 chemical models, exploring how the chemical reprocessing of CO depends on disk mass, dust grain size distribution, temperature, cosmic ray and X-ray ionization rate, and initial water abundance. Building on our previous work focusing on the warm molecular layer, here we analyze the results for our grid of models in the disk midplane at 12 au. We find that either an ISM level cosmic ray ionization rate or the presence of UV photons due to a low dust surface density are needed to chemically reduce the midplane CO gas abundance by at least an order of magnitude within 1 Myr. In the majority of our models CO does not undergo substantial reprocessing by in situ chemistry and there is little change in the gas phase C/H and C/O ratios over the lifetime of the typical disk. However, in the small sub-set of disks where the disk midplane is subject to a source of ionization or photolysis, the gas phase C/O ratio increases by up to nearly 9 orders of magnitude due to conversion of CO into volatile hydrocarbons.Comment: Accepted for publication in ApJ, 15 pages, 10 figures, 3 table

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.Comment: 20 pages, references added, minor corrections mad

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

An ALMA Survey of H₂CO in Protoplanetary Disks

H₂CO is one of the most abundant organic molecules in protoplanetary disks and can serve as a precursor to more complex organic chemistry. We present an Atacama Large Millimeter/submillimeter Array survey of H₂CO toward 15 disks covering a range of stellar spectral types, stellar ages, and dust continuum morphologies. H₂CO is detected toward 13 disks and tentatively detected toward a fourteenth. We find both centrally peaked and centrally depressed emission morphologies, and half of the disks show ring-like structures at or beyond expected CO snowline locations. Together these morphologies suggest that H₂CO in disks is commonly produced through both gas-phase and CO-ice-regulated grain-surface chemistry. We extract disk-averaged and azimuthally-averaged H₂CO excitation temperatures and column densities for four disks with multiple H₂CO line detections. The temperatures are between 20–50 K, with the exception of colder temperatures in the DM Tau disk. These temperatures suggest that H₂CO emission in disks generally emerges from the warm molecular layer, with some contributions from the colder midplane. Applying the same H₂CO excitation temperatures to all disks in the survey, we find that H₂CO column densities span almost three orders of magnitude (~5 × 10¹¹–5 × 10¹⁴ cm⁻²). The column densities appear uncorrelated with disk size and stellar age, but Herbig Ae disks may have less H₂CO compared to T Tauri disks, possibly because of less CO freeze-out. More H₂CO observations toward Herbig Ae disks are needed to confirm this tentative trend, and to better constrain under which disk conditions H₂CO and other oxygen-bearing organics efficiently form during planet formation

Probing the Gas Content of Late-stage Protoplanetary Disks with N_2H^+

The lifetime of gas in circumstellar disks is a fundamental quantity that informs our understanding of planet formation. Studying disk gas evolution requires measurements of disk masses around stars of various ages. Because H_2 gas is unobservable under most disk conditions, total disk masses are based on indirect tracers such as sub-mm dust and CO emission. The uncertainty in the relation between these tracers and the disk mass increases as the disk evolves. In a few well-studied disks, CO exhibits depletions of up to 100× below the assumed interstellar value. Thus, additional tracers are required to accurately determine the total gas mass. The relative lack of nitrogen found in solid solar system bodies may indicate that it persists in volatile form, making nitrogen-bearing species more robust tracers of gas in more evolved disks. Here we present Atacama Large Millimeter/submillimeter Array detections of N_2H^+ in two mature, ~5–11 Myr old disks in the Upper Scorpius OB Association. Such detections imply the presence of H_2-rich gas and sources of ionization, both required for N_2H^+ formation. The Upper Sco disks also show elevated N_2H^+/CO flux ratios when compared to previously observed disks with ≳10× higher CO fluxes. Based on line ratio predictions from a grid of thermochemical disk models, a significantly reduced CO/H_2 abundance of <10^(−6) for a gas-to-dust ratio of ≳100 is required to produce the observed N_2H^+ fluxes. These systems appear to maintain H_2 gas reservoirs and indicate that carbon- and nitrogen-bearing species follow distinct physical or chemical pathways as disks evolve

The Radial Distribution of H_2 and CO in TW Hya as Revealed by Resolved ALMA Observations of CO Isotopologues

CO is widely used as a tracer of molecular gas. However, there is now mounting evidence that gas phase carbon is depleted in the disk around TW Hya. Previous efforts to quantify this depletion have been hampered by uncertainties regarding the radial thermal structure in the disk. Here we present resolved ALMA observations of ^(13)CO 3-2, C^(18)O 3-2, ^(13)CO 6-5, and C^(18)O 6-5 emission in TW Hya, which allow us to derive radial gas temperature and gas surface density profiles, as well as map the CO abundance as a function of radius. These observations provide a measurement of the surface CO snowline at ~30 AU and show evidence for an outer ring of CO emission centered at 53 AU, a feature previously seen only in less abundant species. Further, the derived CO gas temperature profile constrains the freeze out temperature of CO in the warm molecular layer to <21K. Combined with the previous detection of HD 1-0, these data constrain the surface density of the warm H_2 gas in the inner ~30 AU such that Σwarm gas = 4.7^(+3.0)_(-2.9) g cm^(-2)(R/10 au)^(-1/2). We find that CO is depleted by two orders of magnitude from R = 10-60 AU, with the small amount of CO returning to the gas phase inside the surface CO snowline insufficient to explain the overall depletion. Finally, this new data is used in conjunction with previous modeling of the TW Hya disk to constrain the midplane CO snowline to 17–23 AU

Loop Groups, Kaluza-Klein Reduction and M-Theory

We show that the data of a principal G-bundle over a principal circle bundle is equivalent to that of a \hat{LG} = U(1) |x LG bundle over the base of the circle bundle. We apply this to the Kaluza-Klein reduction of M-theory to IIA and show that certain generalized characteristic classes of the loop group bundle encode the Bianchi identities of the antisymmetric tensor fields of IIA supergravity. We further show that the low dimensional characteristic classes of the central extension of the loop group encode the Bianchi identities of massive IIA, thereby adding support to the conjectures of hep-th/0203218.Comment: 26 pages, LaTeX, utarticle.cls, v2:clarifications and refs adde