No Arabic abstract
New high resolution spectroscopic and medium resolution spectropolarimetric data, complemented with optical broad and narrow band imaging, of the B[e] star HD 87643 are presented. The spectrum of HD 87643 exhibits the hybrid characteristics well known to be representative of the group of B[e] stars; a fast wind with an expansion velocity in excess of 1000 km/s is measured in the hydrogen and helium lines, while a slower component is traced by lower excitation lines and forbidden lines. Clues to the geometry of the rapidly expanding circumstellar shell are provided by the startling polarization changes across Halpha. Comparison with published schematic calculations indicates that the polarizing material is located in a slowly rotating, expanding disk structure. A hydrodynamical model is then presented whose results are consistent with the original two-wind concept for B[e] stars and exhibits kinematic properties that may well explain the observed spectral features in HD 87643. The model calculations use as input a B star undergoing mass loss, surrounded by an optically thick disk. The resulting configuration consists of a fast polar wind from the star and a slowly expanding disk wind. The model also predicts that the stellar wind at intermediate latitudes is slower and denser than in the polar region.
HD 50138 is a B[e] star surrounded by a large amount of circumstellar gas and dust. Its spectrum shows characteristics which may indicate either a pre- or a post-main-sequence system. Mapping the kinematics of the gas in the inner few au of the system contributes to a better understanding of its physical nature. We present the first high spatial and spectral resolution interferometric observations of the Br-gamma line of HD~50138, obtained with VLTI/AMBER. The line emission originates from a region more compact (up to 3 au) than the continuum-emitting region. Blue- and red-shifted emission originates from the two different hemispheres of an elongated structure perpendicular to the polarization angle. The velocity of the emitting medium decreases radially. An overall offset along the NW direction between the line- and continuum-emitting regions is observed. We compare the data with a geometric model of a thin Keplerian disk and a spherical halo on top of a Gaussian continuum. Most of the data are well reproduced by this model, except for the variability, the global offset and the visibility at the systemic velocity. The evolutionary state of the system is discussed; most diagnostics are ambiguous and may point either to a post-main-sequence or a pre-main-sequence nature.
We investigate the possible role of line-driven winds in the circumstellar envelope in B[e] stars, mainly the role of the $Omega$-slow wind solution, which is characterized by a slower terminal velocity and higher mass-loss rate, in comparison with the standard (m-CAK) wind solution. In this work, we assume two scenarios: 1) a spherically symmetric star and 2) a scenario that considers the oblate shape, considering only the oblate correction factor. For certain values of the line force parameters (according to previous works), we obtain in both scenarios a density contrast $gtrsim10^{2}$ between equatorial and polar densities, characterized for a fast polar wind and a slow and denser wind when the $Omega$-slow wind solution is obtained. All this properties are enhanced when the oblate correction factor is included in our calculations.
A search for the decays $B^0_sto e^+e^-$ and $B^0to e^+e^-$ is performed using data collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$, $8$ and $13,text{TeV}$, corresponding to integrated luminosities of $1$, $2$ and $2,text{fb}^{-1}$, respectively. No signal is observed. Assuming no contribution from $B^0to e^+e^-$ decays, an upper limit of $mathcal{B}(B^0_sto e^+e^-)<9.4,(11.2)times10^{-9}$ is obtained at $90,(95),%$ confidence level. If no $B^0_sto e^+e^-$ contribution is assumed, a limit of $mathcal{B}(B^0to e^+e^-)<2.5,(3.0)times10^{-9}$ is determined at $90,(95),%$ confidence level. These upper limits are more than one order of magnitude lower than the previous values.
We present interferometric observations with the Atacama Large Millimeter Array (ALMA) of the free-free continuum and recombination line emission at 1 and 3mm of the Red Square Nebula surrounding the B[e]-type star MWC922. The unknown distance to the source is usually taken to be d=1.7-3 kpc. The unprecedented angular resolution (up to ~0.02arcsec) and exquisite sensitivity of these data unveil, for the first time, the structure and kinematics of the emerging, compact ionized region at its center. We imaged the line emission of H30a and H39a, previously detected with single-dish observations, as well as of H51epsilon, H55gamma, and H63delta, detected for the first time in this work. The line emission is seen over a full velocity range of ~180 km/s arising in a region of diameter <0.14arcsec (less than a few hundred au) in the maser line H30a, which is the most intense transition reported here. We resolve the spatio-kinematic structure of a nearly edge-on disk rotating around a central mass of ~10Msun (d=1.7 kpc) or ~18Msun (d=3 kpc), assuming Keplerian rotation. Our data also unveil a fast (~100 km/s) bipolar ejection (a jet?) orthogonal to the disk. In addition, a slow (<15km/s) wind may be lifting off the disk. Both, the slow and the fast winds are found to be rotating in a similar manner to the ionized layers of the disk. This represents the first empirical proof of rotation in a bipolar wind expanding at high velocity (~100 km/s). (abridged)
The aim of this short note is to provide three geometric visualizations of a fascinating inequality $b^{e}<e^{b}$ when $e<b$.