Can high frequency acoustic waves heat the quiet sun chromosphere?

We use Hinode/SOT Ca II H-line and blue continuum broadband observations to study the presence and power of high frequency acoustic waves at high spatial resolution. We find that there is no dominant power at small spatial scales; the integrated power using the full resolution of Hinode (0.″05 pixels, 0.″16 resolution) is larger than the power in the data degraded to 0"5 pixels (TRACE pixel size) by only a factor of 1.2. At 20mHz the ratio is 1.6. Combining this result with the estimates of the acoustic flux based on TRACE data of Fossum and Carlsson (2006, ApJ, 646, 579), we conclude that the total energy flux in acoustic waves of frequency 5-40 mHz entering the internetwork chromosphere of the quiet Sun is less than 800 W m^-2, inadequate to balance the radiative losses in a static chromosphere by a factor of five.