The photospheric Poynting flux and coronal heating

Some models of coronal heating suppose that convective motions at the photosphere shuffle the footpoints of coronal magnetic fields and thereby inject sufficient magnetic energy upward to account for observed coronal and chromospheric energy losses in active regions. Using high-resolution observations of plage magnetic fields made with the Solar Optical Telescope aboard the Hinode satellite, we investigate this idea by estimating the upward transport of magnetic energy-the vertical Poynting flux, Sz-across the photosphere in a plage region. To do so, we combine the following: (i) estimates of photospheric horizontal velocities, v(h), determined by local correlation tracking applied to a sequence of line-of-sight magnetic field maps from the Narrowband Filter Imager, with (ii) a vector magnetic field measurement from the SpectroPolarimeter. Plage fields are ideal observational targets for estimating energy injection by convection, because they are (i) strong enough to be measured with relatively small uncertainties, (ii) not so strong that convection is heavily suppressed (as within umbrae), and (iii) unipolar, so S-z in plage is not influenced by mixed-polarity processes (e.g., flux emergence) unrelated to heating in stable, active-region fields. In this plage region, we found that the average Sz varied in space, but was positive (upward) and sufficient to explain coronal heating, with values near (5 +/- 1) x 10(7) erg cm(-2) s(-1). We find the energy input per unit magnetic flux to be on the order of 10(5) erg s(-1) Mx(-1). A comparison of intensity in a Ca II image co-registered with one plage magnetogram shows stronger spatial correlations with both total field strength and unsigned vertical field, vertical bar B-z vertical bar, than either S-z or horizontal flux density, B-h. The observed Ca II brightness enhancement, however, probably contains a strong contribution from a near-photosphere hot-wall effect, which is unrelated to heating in the solar atmosphere.