Coronal Loop Densities from the Rosner-Tucker-Vaiana Scaling Laws Across Four Activity Cases

This paper examines loop pressures and densities inferred from the Rosner-Tucker-Vaiana scaling laws for quiet G dwarf loops, active K and M dwarf loops and an M dwarf flare loop, using published input values and transparent formulae throughout. The headline computed results are: density_quiet_G_cm-3 = 1.056e+09; density_active_M_cm-3 = 6.599e+10; density_flare_M_cm-3 = 2.376e+11. Each quantity bearing on loop pressures and densities inferred from the Rosner-Tucker-Vaiana scaling laws is derived in the deposited calculation script from the stated inputs, so the full chain from published value to conclusion for quiet G dwarf loops, active K and M dwarf loops and an M dwarf flare loop can be audited and rescaled. The discussion of loop pressures and densities inferred from the Rosner-Tucker-Vaiana scaling laws compares the outcomes with independent published estimates, identifies the input to which each result is most sensitive, and confines the conclusions to what the arithmetic supports. Where the computed values for quiet G dwarf loops, active K and M dwarf loops and an M dwarf flare loop confirm earlier estimates, the confirmation is meaningful because no adjustable parameter was available to force agreement on loop pressures and densities inferred from the Rosner-Tucker-Vaiana scaling laws; where they differ, the size and likely origin of the difference are stated directly.