Self-gravity in thin discs and edge effects: an extension of Paczynski's approximation

As hydrostatic equilibrium of gaseous discs is partly governed by the gravity field, we have estimated the component caused by a vertically homogeneous disc, with a special attention for the outer regions where self-gravity classically appears. The accuracy of the integral formula is better than 1%, whatever the disc thickness, radial extension and radial density profile. At order zero, the field is even algebraic for thin discs and writes $- 4 \pi G \Sigma(R) f_{edge} (R)$ at disc surface, thereby correcting Paczynski's formula by a multiplying factor $f_{edge} \gtrsim 1/2$, which depends on the relative distance to the edges and the local disc thickness. For very centrally condensed discs however, this local contribution can be surpassed by action of mass stored in the inner regions, possibly resulting in $f_{edge} \gg 1$. A criterion setting the limit between these two regimes is derived. These result are robust in the sense that the details of vertical stratification are not critical. We briefly discuss how hydrostatic equilibrium is impacted. In particular, the disc flaring should not reverse in the self-gravitating region, which contradicts what is usually obtained from Paczynski's formula. This suggests that i) these outer regions are probably not fully shadowed by the inner ones (important when illuminated by a central star), and ii) the flared shape of discs does not firmly prove the absence or weakness of self-gravity.Comment: Accepted for publication in A&

Constraints on the Formation Regions of Comets from their D:H Ratios

Studies of the D:H ratio in H2O within the Solar nebula provide a relationship between the degree of enrichment of deuterium and the distance from the young Sun. In the context of cometary formation, such models suggest that comets which formed in different regions of the Solar nebula should have measurably different D:H ratios. We aim to illustrate how the observed comets can give information about the formation regions of the reservoirs in which they originated. After a discussion of the current understanding of the regions in which comets formed, simple models of plausible formation regions for two different cometary reservoirs (the Edgeworth-Kuiper belt and the Oort Cloud) are convolved with a deuterium-enrichment profile for the pre-solar nebula. This allows us to illustrate how different formation regions for these objects can lead to great variations in the deuterium enrichment distributions that we would observe in comets today. We also provide an illustrative example of how variations in the population within a source region can modify the resulting observational profile. The convolution of a deuterium-enrichment profile with examples of proto-cometary populations gives a feel for how observations could be used to draw conclusions on the formation region of comets which are currently fed into the inner Solar system from at least two reservoirs. Such observations have, to date, been carried out on only three comets, but future work with instruments such as ALMA and Herschel should vastly improve the dataset, leading to a clearer consensus on the formation of the Oort cloud and Edgeworth-Kuiper bel

From Prestellar to Protostellar Cores II. Time Dependence and Deuterium Fractionation

We investigate the molecular evolution and D/H abundance ratios that develop as star formation proceeds from a dense-cloud core to a protostellar core, by solving a gas-grain reaction network applied to a 1-D radiative hydrodynamic model with infalling fluid parcels. Spatial distributions of gas and ice-mantle species are calculated at the first-core stage, and at times after the birth of a protostar. Gas-phase methanol and methane are more abundant than CO at radii $r\lesssim 100$ AU in the first-core stage, but gradually decrease with time, while abundances of larger organic species increase. The warm-up phase, when complex organic molecules are efficiently formed, is longer-lived for those fluid parcels in-falling at later stages. The formation of unsaturated carbon chains (warm carbon-chain chemistry) is also more effective in later stages; C$^+$, which reacts with CH$_4$ to form carbon chains, increases in abundance as the envelope density decreases. The large organic molecules and carbon chains are strongly deuterated, mainly due to high D/H ratios in the parent molecules, determined in the cold phase. We also extend our model to simulate simply the chemistry in circumstellar disks, by suspending the 1-D infall of a fluid parcel at constant disk radii. The species CH$_3$OCH$_3$ and HCOOCH$_3$ increase in abundance in $10^4-10^5$ yr at the fixed warm temperature; both also have high D/H ratios.Comment: accepted to ApJ. 55 pages, 7 figures, 3 table

Evidence for DCO+ as a probe of ionization in the warm disk surface

In this Letter we model the chemistry of DCO$^{+}$ in protoplanetary disks. We find that the overall distribution of the DCO$^{+}$ abundance is qualitatively similar to that of CO but is dominated by thin layer located at the inner disk surface. To understand its distribution, we investigate the different key gas-phase deuteration pathways that can lead to the formation of DCO$^{+}$. Our analysis shows that the recent update in the exothermicity of the reaction involving CH$_2$D$^{+}$ as a parent molecule of DCO$^{+}$ favors deuterium fractionation in warmer conditions. As a result the formation of DCO$^{+}$ is enhanced in the inner warm surface layers of the disk where X-ray ionization occurs. Our analysis points out that DCO$^{+}$ is not a reliable tracer of the CO snow line as previously suggested. We thus predict that DCO$^{+}$ is a tracer of active deuterium and in particular X-ray ionization of the inner disk.Comment: Accepted for publication in the Astrophysical Journal Letters (ApJL). 11 pages, 5 figure

Mercury-T: a new code to study tidally evolving multi-planet systems: applications to Kepler-62

A large proportion of observed planetary systems contain several planets in a compact orbital configuration, and often harbor at least one close-in object. These systems are then most likely tidally evolving. We investigate how the effects of planet-planet interactions influence the tidal evolution of planets. We introduce for that purpose a new open-source addition to the Mercury N-body code, Mercury-T, which takes into account tides, general relativity and the effect of rotation-induced flattening in order to simulate the dynamical and tidal evolution of multi-planet systems. It uses a standard equilibrium tidal model, the constant time lag model. Besides, the evolution of the radius of several host bodies has been implemented (brown dwarfs, M-dwarfs of mass 0.1 M-circle dot, Sun-like stars, Jupiter). We validate the new code by comparing its output for one-planet systems to the secular equations results. We find that this code does respect the conservation of total angular momentum. We applied this new tool to the planetary system Kepler-62. We find that tides influence the stability of the system in some cases. We also show that while the four inner planets of the systems are likely to have slow rotation rates and small obliquities, the fifth planet could have a fast rotation rate and a high obliquity. This means that the two habitable zone planets of this system, Kepler-62e ad f are likely to have very different climate features, and this of course would influence their potential at hosting surface liquid water

Formation and Composition of Planetesimals

International audienceThe composition of planetesimals depends upon the epoch and the location of their formation in the solar nebula. Meteorites produced in the hot inner nebula contain refractory compounds. Volatiles were present in icy planetesimals and cometesimals produced in the cold outer nebula. However, the mechanism responsible for their trapping is still controversial. We argue for a general scenario valid in all regions of the turbulent nebula where water condensed as a crystalline ice (Hersant et al., 2004). Volatiles were trapped in the form of clathrate hydrates in the continuously cooling nebula. The epoch of clathration of a given species depends upon the temperature and the pressure required for the stability of the clathrate hydrate. The efficiency of the mechanism depends upon the local amount of ice available. This scenario is the only one so far which proposes a quantitative interpretation of the non detection of N2 in several comets of the Oort cloud (Iro et al., 2003). It may explain the large variation of the CO abundance observed in comets and predicts an Ar/O ratio much less than the upper limit of 0.1 times the solar ratio estimated on C/2001 A2 (Weaver et al., 2002). Under the assumption that the amount of water ice present at 5 AU was higher than the value corresponding to the solar O/H ratio by a factor 2.2 at least, the clathration scenario reproduces the quasi uniform enrichment with respect to solar of the Ar, Kr, Xe, C, N and S elements measured in Jupiter by the Galileo probe. The interpretation of the non-uniform enrichment in C, N and S in Saturn requires that ice was less abundant at 10 AU than at 5 AU so that CO and N2 were not clathrated in the feeding zone of the planet while CH4, NH3 and H2S were. As a result, the 14N/15N ratio in Saturn should be intermediate between that in Jupiter and the terrestrial ratio. Ar and Kr should be solar while Xe should be enriched by a factor 17. The enrichments in C, N and S in Uranus and Neptune suggest that available ice was able to form clathrates of CH4, CO and the NH3 hydrate, but not the clathrate of N2. The enrichment of oxygen by a factor 440 in Neptune inferred by Lodders and Fegley (1994) from the detection of CO in the troposphere of the planet is higher by at least a factor 2.5 than the lower limit of O/H required for the clathration of CO and CH4 and for the hydration of NH3. If CO detected by Encrenaz et al. (2004) in Uranus originates from the interior of the planet, the O/H ratio in the envelope must be around of order of 260 times the solar ratio, then also consistent with the trapping of detected volatiles by clathration. It is predicted that Ar and Kr are solar in the two planets while Xe would be enriched by a factor 30 to 70. Observational tests of the validity of the clathration scenario are proposed

Turbulence dans la nébulence solaire primitive et formation du système solaire externe

PARIS7-Bibliothèque centrale (751132105) / SudocMEUDON-Observatoire (920482302) / SudocSudocFranceF

Condensation-inhibited convection in hydrogen-rich atmospheres

In an atmosphere, a cloud condensation region is characterized by a strong vertical gradient in the abundance of the related condensing species. On Earth, the ensuing gradient of mean molecular weight has relatively few dynamical consequences because N2 is heavier than water vapor, so that only the release of latent heat significantly impacts convection. On the contrary, in a hydrogen dominated atmosphere (e.g., giant planets), all condensing species are significantly heavier than the background gas. This can stabilize the atmosphere against convection near a cloud deck if the enrichment in the given species exceeds a critical threshold. This raises two questions. What is transporting energy in such a stabilized layer, and how affected can the thermal profile of giant planets be? To answer these questions, we first carry out a linear analysis of the convective and double-diffusive instabilities in a condensable medium showing that an efficient condensation can suppress double-diffusive convection. This suggests that a stable radiative layer can form near a cloud condensation level, leading to an increase in the temperature of the deep adiabat. Then, we investigate the impact of the condensation of the most abundant species (water) with a steady-state atmosphere model. Compared to standard models, the temperature increase can reach several hundred degrees at the quenching depth of key chemical tracers. Overall, this effect could have many implications for our understanding of the dynamical and chemical state of the atmosphere of giant planets, for their future observations (with Juno for example), and for their internal evolution

# Constraints on the Formation Regions of Comets from their D:H Ratios

International audienceStudies of the D:H ratio in H2O within the Solar nebula provide a relationship between the degree of enrichment of deuterium and the distance from the young Sun. In the context of cometary formation, such models suggest that comets which formed in different regions of the Solar nebula should have measurably different D:H ratios. We aim to illustrate how the observed comets can give information about the formation regions of the reservoirs in which they originated. After a discussion of the current understanding of the regions in which comets formed, simple models of plausible formation regions for two different cometary reservoirs (the Edgeworth Kuiper belt and the Oort Cloud) are convolved with a deuterium-enrichment profile for the pre-solar nebula. This allows us to illustrate how different formation regions for these objects can lead to great variations in the deuterium enrichment distributions that we would observe in comets today. We also provide an illustrative example of how variations in the population within a source region can modify the resulting observational profile. The convolution of a deuterium-enrichment profile with examples of proto-cometary populations gives a feel for how observations could be used to draw conclusions on the formation region of comets which are currently fed into the inner Solar system from at least two reservoirs. Such observations have, to date, been carried out on only three comets, but future work with instruments such as ALMA and Herschel should vastly improve the dataset, leading to a clearer consensus on the formation of the Oort cloud and Edgeworth Kuiper belt

Constraints on the Formation Regions of Comets from their D:H Ratios

International audienceStudies of the D:H ratio in H2O within the Solar nebula provide a relationship between the degree of enrichment of deuterium and the distance from the young Sun. In the context of cometary formation, such models suggest that comets which formed in different regions of the Solar nebula should have measurably different D:H ratios. We aim to illustrate how the observed comets can give information about the formation regions of the reservoirs in which they originated. After a discussion of the current understanding of the regions in which comets formed, simple models of plausible formation regions for two different cometary reservoirs (the Edgeworth Kuiper belt and the Oort Cloud) are convolved with a deuterium-enrichment profile for the pre-solar nebula. This allows us to illustrate how different formation regions for these objects can lead to great variations in the deuterium enrichment distributions that we would observe in comets today. We also provide an illustrative example of how variations in the population within a source region can modify the resulting observational profile. The convolution of a deuterium-enrichment profile with examples of proto-cometary populations gives a feel for how observations could be used to draw conclusions on the formation region of comets which are currently fed into the inner Solar system from at least two reservoirs. Such observations have, to date, been carried out on only three comets, but future work with instruments such as ALMA and Herschel should vastly improve the dataset, leading to a clearer consensus on the formation of the Oort cloud and Edgeworth Kuiper belt