Mechanical Energy Deposition in Cool Star Atmospheres: Resonant Coupling to Coronal Loops in M Dwarfs

The efficiency of coronal heating epsilon(cor) in a star can be quantified by L-X/L-bol, i.e., the ratio of X-ray luminosity to bolometric luminosity. The efficiency of chromospheric heating in the same star epsilon(chr) is typically assumed to be proportional to L(H alpha)/L-bol or L(Ca K)/L-bol where the lines H alpha and Ca K are often the two strongest emission lines in the visible spectrum: the constant of proportionality (eta = epsilon(chr)/[L(H alpha)/L-bol] > 1) includes contributions from many other lines emitted by the chromosphere. In the case of the quiet Sun, it has been known for decades that, in the Sun, the efficiency of chromospheric heating is larger by a factor of epsilon(chr)/epsilon(cor) > 10 than the efficiency of coronal heating. Over the intervening years, data pertaining to epsilon(cor) and epsilon(chr) have been estimated for an increasingly large sample of main-sequence stars with spectral types later than the Sun. These data suggest that among M dwarfs, the efficiency ratio epsilon(chr)/epsilon(cor) may in some stars become smaller than in the solar case. The effect of this is such that the value of epsilon(cor) may become comparable to the value of epsilon(chr). Here, we seek to understand why coronal heating may be >10 times more efficient (relative to chromospheric heating) in certain M dwarfs than in the Sun. Using data on coronal loop properties in flaring stars, we examine the hypothesis that in M dwarfs, the enhanced efficiency of coronal heating may be related to resonant coupling between coronal loops and the source of mechanical energy in the convection zone.