# Field line distribution of mass density at geostationary orbit

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The distribution of mass density along the field lines affects the ratios of toroidal (azimuthally oscillating) Alfven frequencies, and given the ratios of these frequencies, we can get information about that distribution. Here we assume the commonly used power law form for the field line distribution, 𝜌m=𝜌m,eq(LRE∕R)𝛼, where 𝜌m,eq is the value of the mass density (m) at the magnetic equator, L is the L shell, R-E is the Earth's radius, R is the geocentric distance to a point on the field line, and is the power law coefficient. Positive values of indicate that (m) increases away from the magnetic equator, zero value indicates that (m) is constant along the magnetic field line, and negative indicates that there is a local peak in (m) at the magnetic equator. Using 12years of observations of toroidal Alfven frequencies by the Geostationary Operational Environmental Satellites, we study the typical dependence of inferred values of on the magnetic local time (MLT), the phase of the solar cycle as specified by the F-10.7 extreme ultraviolet solar flux, and geomagnetic activity as specified by the auroral electrojet (AE) index. Over the mostly dayside range of the observations, we find that decreases with respect to increasing MLT and F-10.7, but increases with respect to increasing AE. We develop a formula that depends on all three parameters, 3Dmodel=2.2+1.3.cos(MLT15 degrees)+0.0026AEcos(MLT-0.8)15 degrees)+2.110-5AEF10.7-0.010F10.7, that models the binned values of within a standard deviation of 0.3. While we do not yet have a complete theoretical understanding of why should depend on these parameters in such a way, we do make some observations and speculations about the causes. At least part of the dependence is related to that of (m,eq); higher , corresponding to steeper variation with respect to magnetic latitude, occurs when (m,eq) is lower.