ALBERT

Description: We employ the -variance analysis and study the turbulent gas dynamics of simulated molecular clouds (MCs). Our models account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas. We investigate simulations using three different initial mean number densities of n 0  = 30, 100 and 300 cm –3 that span the range of values typical for MCs in the solar neighbourhood. Furthermore, we model the CO line emission in a post-processing step using a radiative transfer code. We evaluate -variance spectra for centroid velocity (CV) maps as well as for integrated intensity and column density maps for various chemical components: the total, H 2 and 12 CO number density and the integrated intensity of both the 12 CO and 13 CO ( J  = 1 -〉 0) lines. The spectral slopes of the -variance computed on the CV maps for the total and H 2 number density are significantly steeper compared to the different CO tracers. We find slopes for the linewidth–size relation ranging from 0.4 to 0.7 for the total and H 2 density models, while the slopes for the various CO tracers range from 0.2 to 0.4 and underestimate the values for the total and H 2 density by a factor of 1.5–3.0. We demonstrate that optical depth effects can significantly alter the -variance spectra. Furthermore, we report a critical density threshold of ~100 cm –3 at which the -variance slopes of the various CO tracers change sign. We thus conclude that carbon monoxide traces the total cloud structure well only if the average cloud density lies above this limit.

Description: We employ the -variance analysis and study the turbulent gas dynamics of simulated molecular clouds (MCs). Our models account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas. We investigate simulations using three different initial mean number densities of n 0  = 30, 100 and 300 cm –3 that span the range of values typical for MCs in the solar neighbourhood. Furthermore, we model the CO line emission in a post-processing step using a radiative transfer code. We evaluate -variance spectra for centroid velocity (CV) maps as well as for integrated intensity and column density maps for various chemical components: the total, H 2 and 12 CO number density and the integrated intensity of both the 12 CO and 13 CO ( J  = 1 -〉 0) lines. The spectral slopes of the -variance computed on the CV maps for the total and H 2 number density are significantly steeper compared to the different CO tracers. We find slopes for the linewidth–size relation ranging from 0.4 to 0.7 for the total and H 2 density models, while the slopes for the various CO tracers range from 0.2 to 0.4 and underestimate the values for the total and H 2 density by a factor of 1.5–3.0. We demonstrate that optical depth effects can significantly alter the -variance spectra. Furthermore, we report a critical density threshold of ~100 cm –3 at which the -variance slopes of the various CO tracers change sign. We thus conclude that carbon monoxide traces the total cloud structure well only if the average cloud density lies above this limit.

Description: We run numerical simulations of molecular clouds, adopting properties similar to those found in the central molecular zone (CMZ) of the Milky Way. For this, we employ the moving mesh code arepo and perform simulations which account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of gas and dust. We perform simulations using an initial density of n 0 = 10 3 cm –3 and a mass of 1.3 x 10 5 M . Furthermore, we vary the virial parameter, defined as the ratio of kinetic and potential energy, α = E kin /| E pot |, by adjusting the velocity dispersion. We set it to α = 0.5, 2.0 and 8.0, in order to analyse the impact of the kinetic energy on our results. We account for the extreme conditions in the CMZ and increase both the interstellar radiation field (ISRF) and the cosmic ray flux (CRF) by a factor of 1000 compared to the values found in the solar neighbourhood. We use the radiative transfer code radmc -3 d to compute synthetic images in various diagnostic lines. These are [C ii ] at 158 μm, [O i ] (145 μm), [O i ] (63 μm), 12 CO ( J = 1 -〉 0) and 13 CO ( J = 1 -〉 0) at 2600 and 2720 μm, respectively. When α is large, the turbulence disperses much of the gas in the cloud, reducing its mean density and allowing the ISRF to penetrate more deeply into the cloud's interior. This significantly alters the chemical composition of the cloud, leading to the dissociation of a significant amount of the molecular gas. On the other hand, when α is small, the cloud remains compact, allowing more of the molecular gas to survive. We show that in each case the atomic tracers accurately reflect most of the physical properties of both the H 2 and the total gas of the cloud and that they provide a useful alternative to molecular lines when studying the interstellar medium in the CMZ.

Description: We use principal component analysis (PCA) to study the gas dynamics in numerical simulations of typical molecular clouds (MCs). Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry. We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n 0  = 30, 100, 300 cm –3 that span the range of values typical for MCs in the solar neighbourhood and investigate the slope α PCA of the pseudo-structure function computed by PCA for several components: the total density, H 2 density, 12 CO density, 12 CO J = 1 -〉 0 intensity and 13 CO J = 1 -〉 0 intensity. We estimate power-law indices α PCA for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ±0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

Description: We compute structure functions and Fourier spectra of 2D centroid velocity maps in order to study the gas dynamics of typical molecular clouds in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n 0  = 30, 100 and 300 cm –3 to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H 2 number density, 12 CO number density as well as the integrated intensity of 12 CO ( J  = 1 -〉 0) and 13 CO ( J  = 1 -〉 0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H 2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H 2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.

Description: We use the arepo moving mesh code to simulate the evolution of molecular clouds exposed to a harsh environment similar to that found in the galactic centre (GC), in an effort to understand why the star formation efficiency (SFE) of clouds in this environment is so small. Our simulations include a simplified treatment of time-dependent chemistry and account for the highly non-isothermal nature of the gas and the dust. We model clouds with a total mass of 1.3  x 10 5 M and explore the effects of varying the mean cloud density and the virial parameter, α = E kin /| E pot |. We vary the latter from α = 0.5 to 8.0, and so many of the clouds that we simulate are gravitationally unbound. We expose our model clouds to an interstellar radiation field (ISRF) and cosmic ray flux (CRF) that are both a factor of 1000 higher than the values found in the solar neighbourhood. As a reference, we also run simulations with local solar neighbourhood values of the ISRF and the CRF in order to better constrain the effects of the extreme conditions in the GC on the SFE. Despite the harsh environment and the large turbulent velocity dispersions adopted, we find that all of the simulated clouds form stars within less than a gravitational free-fall time. Increasing the virial parameter from α = 0.5 to 8.0 decreases the SFE by a factor of ~4–10, while increasing the ISRF/CRF by a factor of 1000 decreases the SFE again by a factor of ~2–6. However, even in our most unbound clouds, the SFE remains higher than that inferred for real GC clouds. We therefore conclude that high levels of turbulence and strong external heating are not enough by themselves to lead to a persistently low SFE at the centre of the Galaxy.

Description: Some systems of close-in ‘super-Earths’ contain five or more planets on non-resonant but compact and nearly coplanar orbits. The Kepler-11 system is an iconic representative of this class of system. It is challenging to explain their origins given that planet–disc interactions are thought to be essential to maintain such a high degree of coplanarity, yet these same interactions invariably cause planets to migrate into chains of mean motion resonances. Here, we mine a large data set of dynamical simulations of super-Earth formation by migration. These simulations match the observed period ratio distribution as long as the vast majority of planet pairs in resonance become dynamically unstable. When instabilities take place resonances are broken during a late phase of giant impacts, and typical surviving systems have planet pairs with significant mutual orbital inclinations. However, a subset of our unstable simulations matches the Kepler-11 system in terms of coplanarity, compactness, planet-multiplicity, and non-resonant state. This subset has dynamical instability phases typically much shorter than ordinary systems. Unstable systems may keep a high degree of coplanarity post-instability if planets collide at very low orbital inclinations (≲1○) or if collisions promote efficient damping of orbital inclinations. If planetary scattering during the instability takes place at low orbital inclinations (i ≲ 1○), orbital inclinations are barely increased by encounters before planets collide. When planetary scattering pumps orbital inclinations to higher values (≳1○) planets tend to collide at higher mutual orbital inclinations, but depending on the geometry of collisions mergers’ orbital inclinations may be efficiently damped. Each of these formation pathways can produce analogues to the Kepler-11 system.