The Angular Momentum Problem during Star Formation - Magnetically Linked Aligned Rotators - Part Two - Results
Solutions of the three-fragment problem are presented graphically for different values of σ, the ratio of half the moment of inertia of a fragment to that of the medium between consecutive fragments, namely, for σ= 0.1, 1.0, and 5.0. The values 0.1 and 5.0 already represent the behavior in the low-σ and high-σ limits respectively. Smaller values of σ represent later stages of contraction of a fragment. The central fragment's angular momentum decreases exponentially in time with an e-folding time &tau ∥ = στ0, where τ0 is the Alfven crossing time between consecutive fragments (typically, τ0 = 106 yr). Resolution of the problem can be achieved in a fraction of the Alfven crossing time in the low-σ cases, whereas it takes many bounces of the torsional Alfven waves between fragments before the angular momentum problem can be resolved for an individual fragment in the high-σ cases. Even in the low-σ cases, however, the problem is regenerated by returning torsional Alfven waves. For star formation to take place in magnetically linked fragments, the magnetic field should decouple from the matter during the low-spin phase not only a likely, but perhaps an inevitable possibility because gravity is unopposed by centrifugal forces at that stage. The net angular momentum of the system of fragments plus interfragment medium can decrease very rapidly the smaller the σ, the more rapid the decrease. Even so, considerable rotational kinetic energy (and therefore rms angular momentum) and potential energy in twists of the field lines remain trapped in the system for many Alfven crossing times. This sharing and trapping of energy in a system of magnetically linked fragments has important consequences for star formation and for interpretation of observations of rotating fragments or clouds (e.g., it can cause a fragment to rotate near or even above breakup).