Free Access
Volume 561, January 2014
Article Number A84
Number of page(s) 17
Section Astrophysical processes
Published online 06 January 2014

Online material

Appendix A: Background and first-order contributions to the momentum influx

Here we evaluate 2 and 1, the first two coefficients on the right-hand side of Eq. (55). We will show that both coefficients are zero. The first is (A.1)Substituting f2 = β   sin   θ/2 , this becomes The background flow, while it certainly carries z-momentum, makes no net contribution to the influx.

The integral expression for the second coefficient is lengthier, and we write it as (A.2)where and It is convenient to split up the integral in Eq. (A.2) by region. For the downstream part, which we denote as , we use Eqs. (15) and (16) for f1 and g-1. We find, after algebraic simplification, that (A.3)We now use the identity

to conclude that (A.4)Similarly, the upstream part is (A.5)so that (A.6)For the intermediate piece, to be denoted , we use Eqs. (21) and (22) for f1 and g-1. Although we have established that C =  +1 , we will see that is independent of this parameter, so we retain the original notation. After algebraic manipulation, we find (A.7)Using the identity we infer that (A.8)In summary, we have (A.9)

© ESO, 2014

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.