A latitude-dependent wind model for Mira's cometary head

We present a 3D numerical simulation of the recently discovered cometary structure produced as Mira travels through the galactic ISM. In our simulation, we consider that Mira ejects a steady, latitude-dependent wind, which interacts with a homogeneous, streaming environment. The axisymmetry of the problem is broken by the lack of alignment between the direction of the relative motion of the environment and the polar axis of the latitude-dependent wind. With this model, we are able to produce a cometary head with a ``double bow shock'' which agrees well with the structure of the head of Mira's comet. We therefore conclude that a time-dependence in the ejected wind is not required for reproducing the observed double bow shock.Comment: 4 pages, 4 figures, accepted for publication in ApJ

3D numerical model of the Omega Nebula (M17): simulated thermal X-ray emission

We present 3D hydrodynamical simulations of the superbubble M17, also known as the Omega nebula, carried out with the adaptive grid code yguazu'-a, which includes radiative cooling. The superbubble is modelled considering the winds of 11 individual stars from the open cluster inside the nebula (NGC 6618), for which there are estimates of the mass loss rates and terminal velocities based on their spectral types. These stars are located inside a dense interstellar medium, and they are bounded by two dense molecular clouds. We carried out three numerical models of this scenario, considering different line of sight positions of the stars (the position in the plane of the sky is known, thus fixed). Synthetic thermal X-ray emission maps are calculated from the numerical models and compared with ROSAT observations of this astrophysical object. Our models reproduce successfully both the observed X-ray morphology and the total X-ray luminosity, without taking into account thermal conduction effects.Comment: 8 pages, 6 figures, accepted for publication in MNRA

Alliance free and alliance cover sets

A \emph{defensive} (\emph{offensive}) $k$-\emph{alliance} in $\Gamma=(V,E)$ is a set $S\subseteq V$ such that every $v$ in $S$ (in the boundary of $S$) has at least $k$ more neighbors in $S$ than it has in $V\setminus S$. A set $X\subseteq V$ is \emph{defensive} (\emph{offensive}) $k$-\emph{alliance free,} if for all defensive (offensive) $k$-alliance $S$, $S\setminus X\neq\emptyset$, i.e., $X$ does not contain any defensive (offensive) $k$-alliance as a subset. A set $Y \subseteq V$ is a \emph{defensive} (\emph{offensive}) $k$-\emph{alliance cover}, if for all defensive (offensive) $k$-alliance $S$, $S\cap Y\neq\emptyset$, i.e., $Y$ contains at least one vertex from each defensive (offensive) $k$-alliance of $\Gamma$. In this paper we show several mathematical properties of defensive (offensive) $k$-alliance free sets and defensive (offensive) $k$-alliance cover sets, including tight bounds on the cardinality of defensive (offensive) $k$-alliance free (cover) sets

A model of Mira's cometary head/tail entering the Local Bubble

We model the cometary structure around Mira as the interaction of an AGB wind from Mira A, and a streaming environment. Our simulations introduce the following new element: we assume that after 200 kyr of evolution in a dense environment Mira entered the Local Bubble (low density coronal gas). As Mira enters the bubble, the head of the comet expands quite rapidly, while the tail remains well collimated for a 100 kyr timescale. The result is a broad-head/narrow-tail structure that resembles the observed morphology of Mira's comet. The simulations were carried out with our new adaptive grid code WALICXE, which is described in detail.Comment: 12 pages, 8 figures (4 in color). Accepted for publication in The Astrophysical Journa