Evaluating a proxy of the local entropy production rate on the solar photosphere

Abstract

The evaluation of the entropy production rate on the solar photosphere and its probability distribution are the key issues for studying the non-equilibrium dynamics of the solar convection. The local entropy production rate can be easily evaluated using the vertical heat flux as a proxy, which is given by a product between the line-of-sight velocity and the surface temperature. In this framework, the solar photosphere provides an incomparable laboratory to study turbulent convection in a dissipative non-equilibrium system near a steady state. In this work, we present some preliminary results on statistics of the local entropy production rate via the vertical heat flux, using line-of-sight velocity and temperature maps of the solar photosphere which are extracted from spectro-polarimetric data making use of the Center of Gravity Method and the simple black body radiation law.

Testing the Steady-State Fluctuation Relation in the Solar Photospheric Convection

“…The local vertical heat flux is evaluated from vertical velocity maps and temperature maps, as discussed in [ 55 , 56 ]. We compute the vertical velocity maps using the CoG method: where the integral is extended over the entire line profile.…”

“…Considering small perturbations of the atmospheric parameters (e.g., vertical velocity, magnetic fields, density and so on), the RFs identify the atmospheric layer where the Stokes profiles are more sensible to these perturbations; therefore, the RFs localize the atmospheric layers where the spectral line is mainly formed [ 64 ]. Using the RF for the velocity computed for the 630.15 nm spectral line (see Figure 4 ), we estimate that the atmospheric layer associated with velocity maps is km above the base of the photosphere [ 55 ]. Thus, due to the temperature fluctuations associated with the base of the photosphere (i.e., km computed from a Kurucz model [ 65 ]), we can assert that the temperature and vertical velocity signals are generated by the same atmospheric layer within the uncertainties.…”

“…Furthermore, in Equation ( 11 ) we assume and as a constant quantities, as the range of variability of those quantities lies on longer temporal scales respect to the observation duration. For further discussion, see [ 55 ]. Therefore, the heat flux in Equation ( 11 ) can be written as: where .…”

“… Response function (RF) of the vertical velocity for the Fe I 630.15 nm spectral line, averaged over the sampled spectral points of the observation. Adapted from [ 55 ]. …”