3D model of bow shocks

Context. Shocks produced by outflows from young stars are often observed as bow-shaped structures in which the H2 line strength and morphology are characteristic of the physical and chemical environments and the velocity of the impact. Aims. We present a 3D model of interstellar bow shocks propagating in a homogeneous molecular medium with a uniform magnetic field. The model enables us to estimate the shock conditions in observed flows. As an example, we show how the model can reproduce rovibrational H2 observations of a bow shock in OMC1. Methods. The 3D model is constructed by associating a planar shock with every point on a 3D bow skeleton. The planar shocks are modelled with a highly sophisticated chemical reaction network that is essential for predicting accurate shock widths and line emissions. The shock conditions vary along the bow surface and determine the shock type, the local thickness, and brightness of the bow shell. The motion of the cooling gas parallel to the bow surface is also considered. The bow shock can move at an arbitrary inclination to the magnetic field and to the observer, and we model the projected morphology and radial velocity distribution in the plane-of-sky. Results. The morphology of a bow shock is highly dependent on the orientation of the magnetic field and the inclination of the flow. Bow shocks can appear in many different guises and do not necessarily show a characteristic bow shape. The ratio of the H2 v = 2-1 S(1) line to the v = 1-0 S(1) line is variable across the flow and the spatial offset between the peaks of the lines may be used to estimate the inclination of the flow. The radial velocity comes to a maximum behind the apparent apex of the bow shock when the flow is seen at an inclination different from face-on. Under certain circumstances the radial velocity of an expanding bow shock can show the same signatures as a rotating flow. In this case a velocity gradient perpendicular to the outflow direction is a projection effect of an expanding bow shock lighting up asymmetrically because of the orientation of the magnetic field. With the 3D model we reproduce the brightness levels in three H2 lines as well as the shape and size of a chosen bow shock in OMC1. The inferred bow inclination and the orientation and strength of the magnetic field fit into the pattern suggested by independent observations