Novel scaling laws to derive spatially resolved flare and CME parameters from sun-as-a-star observables

Coronal mass ejections (CMEs) are often associated with X-ray (SXR) flares powered by magnetic reconnection in the low corona, while the CME shocks in the upper corona and interplanetary (IP) space accelerate electrons often producing the type II radio bursts. The CME and the reconnection event are part of the same energy release process as highlighted by the correlation between reconnection flux ( ϕ rec ) that quantifies the strength of the released magnetic free energy during the SXR flare, and the CME kinetic energy that drives the IP shocks leading to type II bursts. Unlike the Sun, these physical parameters cannot be directly inferred in stellar observations. Hence, scaling laws between unresolved sun-as-a-star observables, namely SXR luminosity ( L X ) and type II luminosity ( L R ), and the physical properties of the associated dynamical events are crucial. Such scaling laws also provide insights into the interconnections between the particle acceleration processes across low-corona to IP space during solar-stellar “flare-CME-type II” events. Using long-term solar data in the SXR to radio waveband, we derived a scaling law between two novel power metrics for the flare and CME-associated processes. The metrics of “flare power” ( P flare = √( L X ϕ rec )) and “CME power” ( P CME = √( L R V CME 2 )), where V CME is the CME speed, scale as P flare ∝ P CME 0.76 ± 0.04 . In addition, L X and ϕ rec show power-law trends with P CME with indices of 1.12 ± 0.05 and 0.61 ± 0.05, respectively. These power laws help infer the spatially resolved physical parameters, V CME and ϕ rec , from disk-averaged observables, L X and L R during solar-stellar flare-CME-type II events.