Unified Scaling Relation for Coronal Temperature Anomaly and Solar Wind Acceleration

Abstract. The solar atmosphere exhibits two long-standing observational puzzles: the coronal temperature anomaly, in which the million-degree corona lies far hotter than the 5500 K photosphere beneath it, and the high-speed solar-wind outflow, whose measured 300–800 km s⁻¹ velocities cannot be fully reproduced by classical thermal-expansion models. Standard interpretations rely on two separate ad-hoc physical mechanisms: nanoflare magnetic reconnection and Alfvén-wave dissipation, without a unified quantitative scaling law connecting the two phenomena. This work introduces a density-damped perturbation framework and derives a scaling relation designated the Local Perturbation Energy Equipartition Law: T_corona/T_phot ∝ η(n_phot/n_corona). Outward-propagating perturbation flux originating inside the star experiences strong collisional damping within the dense photosphere, limiting the photospheric equilibrium temperature. Above the photosphere, plasma density drops sharply, collisional damping weakens drastically, and high-amplitude perturbation energy is retained within the tenuous coronal plasma, naturally producing million-degree coronal temperatures.

The same perturbation flux continuously transfers momentum to charged particles, accelerating solar-wind plasma to observed outflow velocities. The dimensionless factor η represents solid-angle and magnetic-topology coupling efficiency rather than a free fitting parameter. Order-of-magnitude calculations using in-situ measurements from the Parker Solar Probe yield temperature and speed ranges consistent with observations. Several falsifiable observational predictions for stellar coronae and stellar outflows, including expectations for M-type red-dwarf stars, are provided. This mechanism avoids invoking separate heating and acceleration patches and may be applicable to other main-sequence stars.