Estimating the Shape of the Heliopause from IBEX Observations of Secondary Neutral Helium

The IBEX mission, as a set of imaging detectors, is able to remotely measure large-scale structures which influence the neutral component of the nearby interstellar medium. We consider the irregular cloud of inflowing interstellar neutral He as observed at IBEX. If these neutrals originate from a single distant population of He and He+, the structure of this cloud contains information on the deflection of the interstellar plasma by the obstacle of the heliopause. The combination of external forces (due to the tilted interstellar magnetic field) and internal forces (from non-spherically-symmetric solar wind and heliosheath pressures) create an obstacle in the interstellar flow which is non-axisymmetric, with different degrees of curvature along different azimuthal directions from the nose. We construct a simple model of charge-exchange emission from the deflected plasma, appropriate for comparison with the low resolution He observations at IBEX. We make two substantial simplifications in our plasma model: First, rather than dealing with a single complicated obstacle, we obtain the deflected flow field around a number of axisymmetric ellipses with different aspect ratios to the flow. The resulting flow in each case is taken to describe the plasma behavior as a function of radial position and polar angle, within different ranges of azimuthal angle about the nose. Second, since the dynamical effects of the anisotropic interstellar magnetic pressure are largely accounted for in the irregular obstacle shape itself, we represent these effects in the model flow by an isotropic effective plasma temperature. We obtain solutions for the potential flow of a compressible gas around the heliopause obstacle for a range of obstacle aspect ratios. We then calculate the corresponding line-of-sight integrated He flux that would be measured at 1 AU for each case. Comparison of the model secondary He fluxes at IBEX with the measured flux distributions in different azimuthal directions around the heliospheric nose allows us to back out an estimate of the heliopause aspect ratio in each azimuthal direction. We will present these results, giving an empirical determination of the heliopause shape in the upwind hemisphere. We will also discuss the implication of these results for the draping of the interstellar magnetic field.