True versus apparent shapes of bow shocks
  Astrophysical bow shocks are a common result of the interaction between two
supersonic plasma flows, such as winds or jets from stars or active galaxies,
or streams due to the relative motion between a star and the interstellar
medium. For cylindrically symmetric bow shocks, we develop a general theory for
the effects of inclination angle on the apparent shape. We propose a new
two-dimensional classification scheme for bow shapes, which is based on
dimensionless geometric ratios that can be estimated from observational images.
The two ratios are related to the flatness of the bow's apex, which we term
planitude and the openness of its wings, which we term alatude. We calculate
the expected distribution in the planitude-alatude plane for a variety of
simple geometrical and physical models: quadrics of revolution, wilkinoids,
cantoids, and ancantoids. We further test our methods against numerical
magnetohydrodynamical simulations of stellar bow shocks and find that the
apparent planitude and alatude measured from infrared dust continuum maps serve
as accurate diagnostics of the shape of the contact discontinuity, which can be
used to discriminate between different physical models. We present an algorithm
that can determine the planitude and alatude from observed bow shock emission
maps with a precision of 10 to 20%.
