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 ($\phi_{rec}$) that quantifies the strength of the released magnetic free energy during 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 SXR to radio waveband, we derive a scaling law between two novel power metrics for the flare and CME-associated processes. The metrics of 'flare power' ($P_{flare}=\sqrt{L_X\phi_{rec}}$) and 'CME power' ($P_{CME}= \sqrt{L_R {V_{CME}}^2}$), where $V_{CME}$ is the CME speed, scale as $P_{flare}\propto P_{CME}^{0.76 \pm 0.04}$. Besides, $L_X$ and $\phi_{rec}$ show power-law trends with $P_{CME}$ with indices of 1.12$\pm$0.05 and 0.61$\pm$0.05 respectively. These power-laws help infer the spatially resolved physical parameters, $V_{CME}$ and $\phi_{rec}$, from disk-averaged observables, $L_X$ and $L_R$ during solar-stellar 'flare- CME- type-II' events.