tokens: is injected from a planar boundary of a lateral extent large enough to contain the spread of cloud debris but small compared with the wind radius, and collides with a uniform heavy cloud initially embedded in a uniform, dilute ambient gas representing the galactic medium. We denote the velocity and density of that flow by β ws and n as , respectively, but note that this flow may represent either the shocked ambient flow, if cloud crashing and cloudlets acceleration occur in that region, or the wind itself if the shock crossing time of the cloud is considerably longer than the wind expansion time t f given in equation ( 4 ). The planar approximation of the initial flow is justified by the small ratio between the cloud radius to the putative cloud’s distance from the wind’s source, as explained in the previous section. Cooling of the gas is also included in the simulations in a manner specified next. Each simulation has been run for long enough time to allow complete destruction of the cloud and subsequent acceleration of the cloudlets to high velocities. The output data of the simulation gives the spatial distribution of cloud fragments at any given time, their velocities, densities, and temperatures. These data are used to produce column density histograms in velocity space along different lines of sight, which serve us later (equation 9 ) in creating synthetic spectra that can be compared with observed BAL spectra. It also enables us to get a grasp on the general dynamical and thermal evolution of the cloud fragments, and to understand which of the following processes happen faster in different stages of the system: further fragmentation accompanied by shock heating versus cooling. 3.1 Set-up We use the pluto code (Mignone et al. 2007 ) version 4.0 in 2D Cartesian coordinates in the non-relativistic HD module on an ideal gas with an adiabatic index γ = 5/3. We performed several experiments differing in the size of the simulation box, the implementation of cooling and the ratio of densities, κ, between the cloud and the wind. In each of these experiments, the ranges of the Cartesian coordinates are of the form 0 x x max and | y | y max , the unit length is equal to 1 pc and the resolution along each Cartesian direction is 0.01 pc. The initial condition of the simulation is a static circular cloud of uniform density n c with a radius R c = 1, surrounded by a static ambient medium of uniform density n a . The cloud centre is located initially at y = 0 and x = x c > 0, as close as possible to the wind source at x = 0, but far enough to allow the bow shock created by the cloud–wind collision to remain in the simulation box at all times. The boundary condition at x = 0 is a planar flow of uniform density n ws moving at a speed of ws along the x- direction towards the cloud. On the remaining boundaries we use open boundary conditions. It is worth noting that in the absence of cooling the evolution of the system depends only on the density ratio κ =
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula