A candidate mechanism for the heating of the solar corona in open field line regions is described. The interaction of Alfvén waves, generated in the photosphere or chromosphere, with their reflections and the subsequent driving of quasi-two-dimensional MHD turbulence is considered. A nonlinear cascade drives fluctuations toward short wavelengths which are transverse to the mean field, thereby heating at rates insensitive to restrictive Alfvén timescales. A phenomenology is presented, providing estimates of achievable heating efficiency that are most favorable.

Stars on the main sequence are expected to be completely convective if their mass lies below a certain value, Standard stellar structure codes suggest that is in the range 0.3È0.4In the present M cc .M cc M _ . paper we examine several nonstandard additions to stellar structure in order to quantify their e †ects on the value of We Ðnd that by including magnetic Ðeld e †ects, may fall to values that are signiÐ-M cc .M cc cantly smaller than the standard range. This result is of interest in understanding why coronae and chromospheres in active M dwarfs fail to exhibit detectable alterations at spectral class M3ÈM4. The structural properties of our magnetic models also explain why active M dwarfs tend to have radii that are larger than expected for their values or values that are too low for their radii. Our results T eff T eff lead us to predict that certain stars that are classiÐed as late L or T stars may actually have masses of 0.1È0.15 M _ .

Mechanisms for the deposition of heat in the lower coronal plasma are discussed, emphasizing recent attempts to reconcile the Ñuid and kinetic perspectives. Structures at magnetohydrodynamic (MHD) scales may drive a nonlinear cascade, preferentially exciting high perpendicular wavenumber Ñuctuations. Relevant dissipative kinetic processes must be identiÐed that can absorb the associated energy Ñux. The relationship between the MHD cascade and direct cyclotron absorption, including cyclotron sweep, is discussed. We conclude that for coronal and solar wind parameters the perpendicular cascade cannot be neglected and may be more rapid than cyclotron sweep. Solar wind observational evidence suggests the relevance of the ion inertial scale, which is associated with current sheet thickness during reconnection. We conclude that a signiÐcant fraction of dissipation in the corona and solar wind likely proceeds through a perpendicular cascade and small-scale reconnection, coupled to kinetic processes that act at oblique wavevectors.

The heating of the lower solar corona is examined using numerical simulations and theoretical models of magnetohydrodynamic turbulence in open magnetic regions. A turbulent energy cascade to small length scales perpendicular to the mean magnetic field can be sustained by driving with low-frequency Alfvén waves reflected from mean density and magnetic field gradients. This mechanism deposits energy efficiently in the lower corona, and we show that the spatial distribution of the heating is determined by the mean density through the Alfvén speed profile. This provides a robust heating mechanism which can explain observed high coronal temperatures and accounts for the significant heating (per unit volume) distribution below 2 solar radii needed in models of the origin of the solar wind. The obtained heating per unit mass, on the other hand, is much more extended, indicating that the heating on a per-particle basis persists throughout all the lower coronal region considered here.

We report the white light flare rates for 10 ultracool dwarfs (UCDs) using Kepler K2 short cadence data. Among our sample stars, two have spectral type M6, three are M7, three are M8 and two are L0. Most of our targets are old low mass stars. We identify a total of 283 flares in all of the stars in our sample, with Kepler energies in the range log E Kp ∼(29 -33.5) erg. Using the maximum-likelihood method of line fitting, we find that the flare frequency distribution (FFD) for each star in our sample follows a power law with slope -α in range -(1.3-2.0). We find that cooler objects tend to have shallower slopes. For some of our targets, the FFD follows either a broken power law, or a power law with an exponential cutoff. For the L0 dwarf 2MASS J12321827-0951502, we find a very shallow slope (-α = -1.3) in the Kepler energy range (0.82-130)×10 30 erg: this L0 dwarf has flare rates which are comparable to the rates of high energy flares in stars of earlier spectral types. In addition, we report photometry of two superflares: one on the L0 dwarf 2MASS J12321827-0951502 and another on the M7 dwarf 2MASS J08352366+1029318. In case of 2MASS J12321827-0951502, we report a flare brightening by a factor of ∼144 relative to the quiescent photospheric level. Likewise, for 2MASS J08352366+1029318, we report a flare brightening by a factor of ∼60 relative to the quiescent photospheric level. These two superflares have bolometric (UV/optical/infrared) energies 3.6 × 10 33 erg and 8.9 × 10 33 erg respectively, while the FWHM time scales are very short, ∼2 minutes. We find that the M8 star TRAPPIST-1 is more active than the M8.5 dwarf: 2M03264453+1919309, but less active than another M8 dwarf (2M12215066-0843197).