Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.

We present the results of an interferometric study of the N2H + (1–0) emission from nine nearby, isolated, low-mass protostellar cores, using the OVRO millimeter array. The main goal of this study is the kinematic characterization of the cores in terms of rotation, turbulence, and fragmentation. Eight of the nine objects have compact N2H + cores with FWHM radii of 1200 − 3500 AU, spatially coin...

The MHD virial theorem may be used to estimate the magnetic energy of active regions based on vector magnetic fields measured at the photosphere or chromosphere. However, the virial estimate depends on the measured vector magnetic field being forcefree. Departure from force-freeness leads to an unknown systematic error in the virial energy estimate, and an origin dependence of the result. We pr...

We identify Local Group (LG) analogs in the IllustrisTNG cosmological simulation, and use these to study two mass estimators for LG: one based on timing argument (TA) virial theorem (VT). Including updated measurements of Milky Way-M31 tangential velocity constant, we show that TA estimator slightly overestimates true median LG-mass, though ratio is consistent at approximate 90\% c.l. These are...