Magnetohydrostatic equilibrium in starspots: dependences on color (T_(eff)) and surface gravity (g)

Temperature contrasts and magnetic field strengths of sunspot umbrae broadly follow the thermal-magnetic relationship obtained from magnetohydrostatic equilibrium. Using a compilation of recent observations, especially in molecular bands, of temperature contrasts of starspots in cool stars, and a grid of Kurucz stellar model atmospheres constructed to cover layers of sub-surface convection zone, we examine how the above relationship scales with effective temperature T_{eff}, surface gravity g and the associated changes in opacity of stellar photospheric gas. We calculate expected field strengths in starpots and find that a given relative reduction in temperatures (or the same darkness contrasts) yield increasing field strengths against decreasing T_{eff} due to a combination of pressure and opacity variations against T_{eff}.