  Energetic neutral atoms (ENA) are an important tool for investigating the
structure of the heliosphere. Recently, it was observed that fluxes of ENAs
(with energy $\le$ 55 keV) coming from the upwind and downwind regions of the
heliosphere are similar in strength. This led the authors of these observations
to hypothesize that the heliosphere is bubble-like rather than comet-like,
meaning that it has no extended tail. We investigate the directional
distribution of the ENA flux for a wide energy range (3--88 keV) including the
observations from IBEX (Interstellar Boundary Explorer), INCA (Ion and Neutral
Camera, on board Cassini), and HSTOF (High energy Suprathermal Time Of Flight
sensor, on board SOHO, Solar and Heliospheric Observatory). An essential
element is the model of pickup ion acceleration at the termination shock (TS)
proposed by Zank. We use state of the art models of the global heliosphere,
interstellar neutral gas density, and pickup ion distributions. The results,
based on the "comet-like" model of the heliosphere, are close in flux magnitude
to ENA observations by IBEX, HSTOF and partly by INCA (except for the 5.2-13.5
keV energy channel). We find that the ENA flux from the tail dominates at high
energy (in agreement with HSTOF, but not INCA). At low energy, our comet-like
model produces the similar strengths of the ENA fluxes from the upwind and
downwind directions, which, therefore, removes this as a compelling argument
for a bubble-like heliosphere.
