Global, three-dimensional, ideal MHD simulations of Earth's bow shock
are reported for low Alfven Mach numbers M(A) and quasi-perpendicular
magnetic field orientations. The simulations use a hard, infinitely co
nducting magnetopause obstacle, with axisymmetric three-dimensional lo
cation given by a scaled standard model, to directly address previous
gasdynamic (GD) and field-aligned MHD (FA-MHD) work. Tests of the simu
lated shocks' density jumps X for 1.4 less than or similar to M(A) les
s than or similar to 10 and the high M(A) shock location, and reproduc
tion of the GD relation between magnetosheath thickness and X for quas
i-gasdynamic MHD runs with M(A) his, confirm that the MHD code is work
ing correctly. The MHD simulations show the standoff distance a(s) inc
reasing monotonically with decreasing M(A). Significantly larger a, ar
e found at low MA than predicted by GD and phenomenological MHD models
and FA-MHD simulations, as required qualitatively by observations. Th
e GD and FA-MHD predictions err qualitatively, predicting either const
ant or decreasing a(s) with decreasing M(A). This qualitative differen
ce between quasiperpendicular MHD and FA-MHD simulations is direct evi
dence for a(s) depending on the magnetic field orientation theta. The
enhancement factor over the phenomenological MHD predictions at M(A) s
imilar to 2.4 agrees quantitatively with one observational estimate. A
linear relationship is found between the magnetosheath thickness and
X, modified both quantitatively and intrinsically by MHD effects from
the GD result. The MHD and GD results agree in the high M(A) limit. An
MHD theory is developed for a(s), restricted to sufficiently perpendi
cular theta and high sonic Mach numbers M(S). It explains the simulati
on results with excellent accuracy. Observational and further simulati
on testing of this MHD theory, and of its predicted M(A), theta, and M
(S) effects, is desirable.