LOW MACH NUMBER PREDICTIONS IN AN EXTENDED AXIALLY-SYMMETRICAL MHD THEORY OF THE MAGNETOSHEATH

A recent axisymmetric magnetohydrodynamic (MHD) model for the Earth's magnetosheath near the Sun-Earth line, with boundary conditions given by Rankine-Hugoniot (RH) equations at the bow shock and the Chapman-Fe rraro (CF) condition at the magnetopause, is extended by including sma ller terms in the CF condition that become important at low Mach numbe rs. Three conclusions are predicted for the magnetosheath. (1) The mag netosheath thickness Delta(ms) decreases with decreasing Alfven Mach n umber M-A for M-A > M (in which only the ''gasdynamic'' root of the R H equations for the bow shock boundary is physical), where M similar to 2 is the root-transition value for the RH equations at which all 3 roots coalesce. When M-A < M switch-on shock roots (purely MHD) are a lso physical, and Delta(ms) associated with those roots shows a rapid increase to a large value, followed by a rapid decrease back to a very small value as the decreasing M-A approaches 1. Thus Delta(ms) associ ated with these switch-on roots may give more distant bow shocks, and may rapidly vary with small M-A changes. (2) Delta(ms) is very sensiti ve to the value for the CF constant k(CF) at the magnetopause. For lar ger M-A and sonic Mach numbers M-s the ratio of Delta(ms) to the geoce ntric radial distance a(mp) of the magnetopause varies from 0.44 for 9 0% coupling efficiency of the solar wind momentum density to the magne topause down to 0.18 for 60% coupling efficiency. This suggests a bala nce between the solar wind coupling efficiency to the magnetopause and the thickness of the magnetosheath, in which an increase (decrease) i n the coupling efficiency increases (decreases) the thickness of the m agnetosheath to counter that efficiency by moving the bow shock furthe r upstream (downstream), hence minimizing the variation in time of tha t coupling efficiency. (3) The linear relation between Delta(ms) and t he density ratio rho(sw)/rho(bs) observed in simulations breaks down f or M-A or M-s less than or similar to 2. The slope steadily drops as M -s --> 1, but increases as M-A --> 1.