We present low spectral resolution molecular interferometric observations at 1.2 mm obtained with the Combined Array for Research in Millimetre-wave Astronomy (CARMA) towards the C-rich AGB star IRC+10216. We have mapped the emission of several lines
of SiS, H13CN, SiO, and SiC2 in the ground and first excited vibrational states with a high angular resolution of 0.25 arcsec. These observations have allowed us to partially resolve the emission of the envelope at distances from the star <50 stellar radii (R*), where the stellar wind is mainly accelerated. The structure of the molecular emission has been modelled with a 3D radiation transfer code. The emission of line SiS(v=0,J=14-13) is best reproduced with a set of maser emitting arcs arranged between 5 and 20 R*. The abundance of H13CN with respect to H2 decreases from 8e-7 at 1-5 R* to 3e-7 at 20 R*. The SiO observations are explained with an abundance <2e-8 in the shell-like region between 1 and 5 R*. At this point, the SiO abundance sharply increases up to (2-3)e-7. The vibrational temperature of SiO increases by a factor of 2 due North-East between 20 and 50 R*. SiC2 is formed at the stellar surface with an abundance of 8e-7 decreasing down to 8e-8 at 20 R* probably due to depletion on to dust grains. Several asymmetries are found in the abundance distributions of H13CN, SiO, and SiC2 which define three remarkable directions (North-East, South-Southwest, and South-East) in the explored region of the envelope. There are some differences between the red- and blue-shifted emissions of these molecules suggesting the existence of additional asymmetries in their abundance distributions along the line-of-sight.
We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which are all sa
tisfied if the manifold is curvature homogeneous. This leads to a complete description of four- and six-dimensional Kaehler gradient Ricci solitons with constant scalar curvature.
We present (sub)millimeter line and continuum observations in a mosaicing mode of the massive star forming region Cepheus A East made with the Submillimeter Array (SMA). Our mosaic covers a total area of about 3$$ $times$ 12$$ centered in the HW 2/3
region. For the first time, this observational study encloses a high angular resolution ($sim$ 3$$) together with a large scale mapping of Cepheus A East. We report compact and high velocity $^{12}$CO(2-1) emission associated with the multiple east-west bright H$_2$ condensations present in the region. Blueshifted and redshifted gas emission is found towards the east as well as west of HW 2/3. The observations suggest the presence of multiple large-scale east-west outflows that seems to be powered at smaller scales by radio sources associated with the young stars HW2, HW3c and HW3d. A kinematical study of part of the data suggests that the molecular outflow powered by HW2 is precesing with time as recently reported. Our data reveal five periodic ejections of material separated approximately every 10$^circ$ as projected in the plane of the sky. The most recent ejections appear to move toward the plane of the sky. An energetic explosive event as the one that occurred in Orion BN/KL or DR21 does not explain the kinematics, and the dynamical times of the multiple ejections found here. The continuum observations only revealed a strong millimeter source associated with the HW 2/3 region. High angular resolution observations allow us to resolve this extended dusty object in only two compact sources (with spatial sizes of approximately 300 AU) associated with HW2 and HW3c. Finally, the bright optical/X-Ray HH 168 -- GDD37 object might be produced by strong shocks related with the outflow from HW3c.
We present several molecular line emission arcsec and subarcsec observations obtained with the Submillimeter Array (SMA) in the direction of the massive protostar IRAS 18162-2048, the exciting source of HH 80-81. The data clearly indicates the pres
ence of a compact (radius~425-850 AU) SO2 structure, enveloping the more compact (radius~150 AU) 1.4 millimeter dust emission (reported in a previous paper). The emission spatially coincides with the position of the prominent thermal radio jet which terminates at the HH 80-81 and HH 80N Herbig-Haro objects. Furthermore, the molecular emission is elongated in the direction perpendicular to the axis of the thermal radio jet, suggesting a disk-like structure. We derive a total dynamic mass (disk-like structure and protostar) of 11-15 msun. The SO2 spectral line data also allow us to constrain the structure temperature between 120-160 K and the volume density > 2x10^9 cm-3. We also find that such a rotating flattened system could be unstable due to gravitational disturbances. The data from C17O line emission show a dense core within this star-forming region. Additionally, the H2CO and the SO emissions appear clumpy and trace the disk-like structure, a possible interaction between a molecular core and the outflows, and in part, the cavity walls excavated by the thermal radio jet.
We show that the scalar curvature of a steady gradient Ricci soliton satisfying that the ratio between the square norm of the Ricci tensor and the square of the scalar curvature is bounded by one half, is boundend from below by the hyperbolic secant
of one half the distance function from a fixed point.
