Several nearby individual low column density interstellar cloudlets have been identified previously based on kinematical features evident in high-resolution Ca + observations near the Sun. One of these cloudlets, the ‘Apex Cloud ” (AC), is within 5 pc of the Sun in the solar apex direction. The question of which interstellar cloud will constitute the next galactic environment of the Sun in principle can be determined from cloudlet velocities. The interstellar absorption lines towards α Cen (the nearest star) are consistent within measurement uncertainties with the projected G-cloud (GC) and AC velocities, and also with the velocity of the cloud inside of the solar system (the Local Interstellar Cloud, LIC) providing a small velocity gradient is present in the LIC. The high GC column density towards α Oph compared to α Aql suggests that α Aql may be embedded in the GC so that the AC would be closer to the Sun than the GC. This scenario favors the AC as the next cloud to be encountered by the Sun, and the AC would have a supersonic velocity with respect to the LIC. The weak feature at the AC velocity towards 36 Oph suggests that the AC cloud is either patchy or does not extend to this direction. Alternatively, if the GC is the cloud which is foreground to α Cen, the similar values for N(H o) in the GC components towards α Cen and 36 Oph indicates this cloud is entirely contained within the nearest ∼1.3 pc, and the Ca + GC data towards α Oph would then imply a cloud volume density of ∼5 cm −3, with dramatic consequences for the heliosphere in the near future. Subject headings: ISM: clouds, structure 1
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