Aims: We offer a new, simpler picture of the local interstellar medium, made of a single continuous cloud enveloping the Sun. This new outlook enables the description of a diffuse cloud from within and brings to light some unexpected properties. Methods: We re-examine the kinematics and abundances of the local interstellar gas, as revealed by the published results for the ultraviolet absorption lines of MgII, FeII, and HI. Results: In contrast to previous representations, our new picture of the local interstellar medium consists of a single, monolithic cloud that surrounds the Sun in all directions and accounts for most of the matter present in the first 50 parsecs around the Sun. The cloud fills the space around us out to about 9 pc in most directions, although its boundary is very irregular with possibly a few extensions up to 20 pc. The cloud does not behave like a rigid body: gas within the cloud is being differentially decelerated in the direction of motion, and the cloud is expanding in directions perpendicular to this flow, much like a squashed balloon. Average HI volume densities inside the cloud vary between 0.03 and 0.1 cm-3 over different directions. Metals appear to be significantly depleted onto grains, and there is a steady increase in depletion from the rear of the cloud to the apex of motion. There is no evidence that changes in the ionizing radiation influence the apparent abundances. Secondary absorption components are detected in 60% of the sight lines. Almost all of them appear to be interior to the volume occupied by the main cloud. Half of the sight lines exhibit a secondary component moving at about -7.2 km/s with respect to the main component, which may be the signature of a shock propagating toward the clouds interior.
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