TY - JOUR
T1 - X-WINDS IN ACTION
AU - CAI, Mike J.
AU - SHANG, Hsien
AU - LIN, Hsiao-Hsuan
AU - SHU, Frank H.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - The interaction of accretion disks with the magnetospheres of young stars can produce X-winds and funnel flows. With the assumption of axial symmetry and steady state flow, the problem can be formulated in terms of quantities that are conserved along streamlines, such as the Bernoulli integral (BI), plus a partial differential equation (PDE), called the Grad-Shafranov equation (GSE), that governs the distribution of streamlines in the meridional plane. The GSE plus BI yields a PDE of mixed type, elliptic before critical surfaces where the flow speed equals certain characteristic wave speeds are crossed and hyperbolic afterward. The computational difficulties are exacerbated by the locations of the critical surfaces not being known in advance. To overcome diese obstacles, we consider a variational principle by which the GSE can be attacked by extremizing an action integral, with all other conserved quantities of the problem explicitly included as part of the overall formulation. To simplify actual applications we adopt die cold limit of a negligibly small ratio of the sound speed to the speed of Keplerian rotation in the disk where the X-wind is launched. We also ignore the obstructing effects of any magnetic fields that might thread a disk approximated to be infinitesimally thin. We then introduce trial functions with adjustable coefficients to minimize the variations that give the GSE. We tabulate the resulting coefficients so that other workers can have analytic forms to reconstruct X-wind solutions for various astronomical, cosmochemical, and meteoritical applications.
AB - The interaction of accretion disks with the magnetospheres of young stars can produce X-winds and funnel flows. With the assumption of axial symmetry and steady state flow, the problem can be formulated in terms of quantities that are conserved along streamlines, such as the Bernoulli integral (BI), plus a partial differential equation (PDE), called the Grad-Shafranov equation (GSE), that governs the distribution of streamlines in the meridional plane. The GSE plus BI yields a PDE of mixed type, elliptic before critical surfaces where the flow speed equals certain characteristic wave speeds are crossed and hyperbolic afterward. The computational difficulties are exacerbated by the locations of the critical surfaces not being known in advance. To overcome diese obstacles, we consider a variational principle by which the GSE can be attacked by extremizing an action integral, with all other conserved quantities of the problem explicitly included as part of the overall formulation. To simplify actual applications we adopt die cold limit of a negligibly small ratio of the sound speed to the speed of Keplerian rotation in the disk where the X-wind is launched. We also ignore the obstructing effects of any magnetic fields that might thread a disk approximated to be infinitesimally thin. We then introduce trial functions with adjustable coefficients to minimize the variations that give the GSE. We tabulate the resulting coefficients so that other workers can have analytic forms to reconstruct X-wind solutions for various astronomical, cosmochemical, and meteoritical applications.
KW - Accretion, accretion disks
KW - ISM: jets and outflows
KW - MHD
KW - Stars: pre-main-sequence
KW - Stars: winds, outflows
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U2 - 10.1086/523788
DO - 10.1086/523788
M3 - 21_Publication in refereed journal
VL - 672
SP - 489
EP - 503
JO - Astrophysical Journal
JF - Astrophysical Journal
SN - 0004-637X
IS - 1
ER -