Submillimeter continuum observations of Sagittarius B2 at subarcsecond spatial resolution

We report the first high spatial resolution submillimeter continuum observations of the Sagittarius B2 cloud complex using the Submillimeter Array (SMA). With the subarcsecond resolution provided by the SMA, the two massive star-forming clumps Sgr B2(N) and Sgr B2(M) are resolved into multiple compact sources. In total, twelve submillimeter cores are identified in the Sgr B2(M) region, while only two components are observed in the Sgr B2(N) clump. The gas mass and column density are estimated from the dust continuum emission. We find that most of the cores have gas masses in excess of 100 M$_{\odot}$ and column densities above 10$^{25}$ cm$^{-2}$. The very fragmented appearance of Sgr B2(M), in contrast to the monolithic structure of Sgr B2 (N), suggests that the former is more evolved. The density profile of the Sgr B2(N)-SMA1 core is well fitted by a Plummer density distribution. This would lead one to believe that in the evolutionary sequence of the Sgr B2 cloud complex, a massive star forms first in an homogeneous core, and the rest of the cluster forms subsequently in the then fragmenting structure.Comment: 4 pages, 2 figures, accepted by A&A letter

A scale invariance criterion for les parametrizations

Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change. The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scaleinvariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales

A scale invariance criterion for les parametrizations

Turbulent kinetic energy cascades in fluid dynamical systems are usually characterized by scale invariance. However, representations of subgrid scales in large eddy simulations do not necessarily fulfill this constraint. So far, scale invariance has been considered in the context of isotropic, incompressible, and three-dimensional turbulence. In the present paper, the theory is extended to compressible flows that obey the hydrostatic approximation, as well as to corresponding subgrid-scale parametrizations. A criterion is presented to check if the symmetries of the governing equations are correctly translated into the equations used in numerical models. By applying scaling transformations to the model equations, relations between the scaling factors are obtained by demanding that the mathematical structure of the equations does not change. The criterion is validated by recovering the breakdown of scale invariance in the classical Smagorinsky model and confirming scale invariance for the Dynamic Smagorinsky Model. The criterion also shows that the compressible continuity equation is intrinsically scale-invariant. The criterion also proves that a scaleinvariant turbulent kinetic energy equation or a scale-invariant equation of motion for a passive tracer is obtained only with a dynamic mixing length. For large-scale atmospheric flows governed by the hydrostatic balance the energy cascade is due to horizontal advection and the vertical length scale exhibits a scaling behaviour that is different from that derived for horizontal length scales

Hot HCN around young massive stars at 0.1" resolution

Massive stars form deeply embedded in dense molecular gas, which they stir and heat up and ionize. During an early phase, the ionization is confined to hypercompact HII regions, and the stellar radiation is entirely absorbed by dust, giving rise to a hot molecular core. To investigate the innermost structure of such high-mass star-forming regions, we observed vibrationally excited HCN (via the direct $\ell$-type transition of v2=1, $\Delta J$=0, J=13, which lies 1400 K above ground) toward the massive hot molecular cores G10.47+0.03, SgrB2-N, and SgrB2-M with the Very Large Array (VLA) at 7 mm, reaching a resolution of about 1000 AU (0.1"). We detect the line both in emission and in absorption against HII regions. The latter allows to derive lower limits on the column densities of hot HCN, which are several times $10^{19}$ cm$^{-2}$. We see indication of expansion motions in G10.47+0.03 and detect velocity components in SgrB2-M at 50, 60, and 70 km/s relative to the Local Standard of Rest. The emission originates in regions of less than 0.1 pc diameter around the hypercompact HII regions G10.47+0.03 B1 and SgrB2-N K2, and reaches brightness temperatures of more than 200 K. Using the three-dimensional radiative transfer code RADMC-3D, we model the sources as dense dust cores heated by stars in the HII regions, and derive masses of hot (>300 K) molecular gas of more than 100 solar masses (for an HCN fractional abundance of 10$^{-5}$), challenging current simulations of massive star formation. Heating only by the stars in the HII regions is sufficient to produce such large quantities of hot molecular gas, provided that dust is optically thick to its own radiation, leading to high temperatures through diffusion of radiation.Comment: 12 pages, 14 figures, accepted for publication in A&

Non-linear Weibel-type Soliton Modes

Discussion is given of non-linear soliton behavior including coupling between electrostatic and electromagnetic potentials for non-relativistic, weakly relativistic, and fully relativistic plasmas. For plasma distribution functions that are independent of the canonical momenta perpendicular to the soliton spatial structure direction there are, in fact, no soliton behaviors allowed because transverse currents are zero. Dependence on the transverse canonical momenta is necessary. When such is the case, it is shown that the presence or absence of a soliton is intimately connected to the functional form assumed for the particle distribution functions. Except for simple situations, the coupled non-linear equations for the electrostatic and electromagnetic potentials would seem to require numerical solution procedures. Examples are given to illustrate all of these points for non-relativistic, weakly relativistic, and fully relativistic plasmas.Comment: Accepted for publication at Journal of Physics A: Mathematical and Theoretica

Structure of evolved cluster-forming regions

Context. An approach towards understanding the formation of massive stars and star clusters is to study the structure of their hot core phase, an evolutionary stage where dust has been heated, but molecules have not yet been destroyed by ultraviolet radiation. These hot molecular cores are very line-rich, but the interpretation of line surveys is also hampered by poor knowledge of the physical and chemical structure. Aims. To constrain the radial structure of high-mass star-forming regions containing hot cores, we attempt to reproduce by radiative transfer modeling both the intensity and shape of a variety of molecular lines. Methods. We observed 12 hot cores with the Atacama Pathfinder EXperiment (APEX) in lines of HCN, HCO+, CO, and their isotopologues, including high-J lines and vibrationally excited HCN. We investigate how well the sources can be modeled as centrally heated spheres with a power-law density gradient, making use of the radiative transfer code RATRAN and the radial profile of the submm continuum emission, taken from the APEX Telescope Large Area Survey of the GALaxy (ATLASGAL). Results. Most of the observed lines have complicated shapes that incorporate self-absorption, asymmetries, and line wings. Vibrationally excited HCN is detected in all sources, and vibrationally excited H13CN in half of the sources. We are able to successfully model most features seen in the APEX data, such as the ratio of the isotopologue lines (very high optical depths), self-absorption (temperature gradient), blue asymmetries (moderate infall), vibrationally excited HCN (high inner temperatures), and H13CN (high HCN abundance under dense and hot conditions). Other features could not be reproduced, such as an occasional lack of self-absorption, the emission from high-J lines in the outer pixels of the CHAMP+ receiver (15′′−20′′ from the center), the outflow wings, and the red asymmetric profiles. Conclusions. The amount of molecular gas, in particular of HCN, at very high temperatures is larger than previously thought. A complex interplay between infall and outflow motions is present. Our basic model assumptions of pure central heating and a power-law radial density distribution can serve as approximations for most sources, but are too simple to explain all observed lines. In particular, taking into account clumpiness, multiplicity of heating sources and a more complex velocity field seems to be necessary to more closely match model calculations to observations. This would require three-dimensional radiative transfer modeling of high-resolution interferometric data

Reversal of infall in SgrB2(M) revealed by Herschel/HIFI observations of HCN lines at THz frequencies

Aims. To investigate the accretion and feedback processes in massive star formation, we analyze the shapes of emission lines from hot molecular cores, whose asymmetries trace infall and expansion motions. Methods. The high-mass star forming region SgrB2(M) was observed with Herschel/HIFI (HEXOS key project) in various lines of HCN and its isotopologues, complemented by APEX data. The observations are compared to spherically symmetric, centrally heated models with density power-law gradient and different velocity fields (infall or infall+expansion), using the radiative transfer code RATRAN. Results. The HCN line profiles are asymmetric, with the emission peak shifting from blue to red with increasing J and decreasing line opacity (HCN to H^(13)CN). This is most evident in the HCN 12–11 line at 1062 GHz. These line shapes are reproduced by a model whose velocity field changes from infall in the outer part to expansion in the inner part. Conclusions. The qualitative reproduction of the HCN lines suggests that infall dominates in the colder, outer regions, but expansion dominates in the warmer, inner regions. We are thus witnessing the onset of feedback in massive star formation, starting to reverse the infall and finally disrupting the whole molecular cloud. To obtain our result, the THz lines uniquely covered by HIFI were critically important

H2CO and CH3OH maps of the Orion Bar photodissociation region

A previous analysis of methanol and formaldehyde towards the Orion Bar concluded that the two molecular species may trace different physical components, methanol the clumpy material, and formaldehyde the interclump medium. To verify this hypothesis, we performed multi-line mapping observations of the two molecules to study their spatial distributions. The observations were performed with the IRAM-30m telescope at 218 and 241 GHz, with an angular resolution of ~11''. Additional data for H2CO from the Plateau de Bure array are also discussed. The data were analysed using an LVG approach. Both molecules are detected in our single-dish data. Our data show that CH3OH peaks towards the clumps of the Bar, but its intensity decreases below the detection threshold in the interclump material. When averaging over a large region of the interclump medium, the strongest CH3OH line is detected with a peak intensity of ~0.06K. Formaldehyde also peaks on the clumps, but it is also detected in the interclump gas. We verified that the weak intensity of CH3OH in the interclump medium is not caused by the different excitation conditions of the interclump material, but reflects a decrease in the column density of methanol. The abundance of CH3OH relative to H2CO decreases by at least one order of magnitude from the dense clumps to the interclump medium.Comment: 11 pages, accepted for publication in A&