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Abstract M dwarf flares observed by the Transiting Exoplanet Survey Satellite (TESS) sometimes exhibit apeak-bumplight-curve morphology, characterized by a secondary, gradual peak well after the main, impulsive peak. A similarlate phaseis frequently detected in solar flares observed in the extreme ultraviolet from longer hot coronal loops distinct from the impulsive flare structures. White-light emission has also been observed in off-limb solar flare loops. Here, we perform a suite of one-dimensional hydrodynamic loop simulations for M dwarf flares inspired by these solar examples. Our results suggest that coronal plasma condensation following impulsive flare heating can yield high electron number density in the loop, allowing it to contribute significantly to the optical light curves via free-bound and free–free emission mechanisms. Our simulation results qualitatively agree with TESS observations: the longer evolutionary timescale of coronal loops produces a distinct, secondary emission peak; its intensity increases with the injected flare energy. We argue that coronal plasma condensation is a possible mechanism for the TESS late-phase flares. 

Abstract Delta (δ) sunspots sometimes host fast photospheric flows along the central magnetic polarity inversion line (PIL). Here we study the strong Doppler shift signature in the central penumbral light bridge of solar active region NOAA 12673. Observations from the Helioseismic and Magnetic Imager (HMI) indicate highly sheared and strong magnetic fields. Large Doppler shifts up to 3.2 km s⁻¹appeared during the formation of the light bridge and persisted for about 16 hr. A new velocity estimator, called DAVE4VMwDV, reveals fast converging and shearing motion along the PIL from HMI vector magnetograms, and recovers the observed Doppler signal much better than an old version of the algorithm. The inferred velocity vectors are largely (anti-)parallel to the inclined magnetic fields, suggesting that the observed Doppler shift contains a significant contribution from the projected field-aligned flows. High-resolution observations from the Hinode/Spectro-Polarimeter further exhibit a clear correlation between the Doppler velocity and the cosine of the magnetic inclination, which is in agreement with HMI results and consistent with a field-aligned flow of about 9.6 km s⁻¹. The complex Stokes profiles suggest significant gradients of physical variables along the line of sight. We discuss the implications on theδ-spot magnetic structure and the flow-driving mechanism.