Bubbles in planetary nebulae and clusters of galaxies: Jet properties

I derive constraints on jet properties for inflating pairs of bubbles in planetary nebulae and clusters of galaxies. This work is motivated by the similarity in morphology and some non-dimensional quantities between X-ray-deficient bubbles in clusters of galaxies and the optical-deficient bubbles in planetary nebulae, which were pointed out in an earlier work. In the present Paper I find that for inflating fat bubbles, the opening angle of the jets must be large, i.e., the half opening angle measured from the symmetry axis of the jets should typically be alpha greater than or similar to 40degrees. For such wide-opening angle jets, a collimated fast wind (CFW) is a more appropriate term. Narrow jets will form elongated lobes rather than fat bubbles. I emphasize the need to include jets with large opening angle, i.e., alpha similar or equal to 30-70degrees, in simulating bubble inflation in both planetary nebulae and (cooling flow) clusters of galaxies.