Evidence of ubiquitous Alfvén pulses transporting energy from the photosphere to the upper chromosphere

The multi-million degree temperature increase from the middle to the upper solar atmosphere is one of the most fascinating puzzles in plasma-astrophysics. Although magnetic waves might transport enough energy from the photosphere to heat up the local chromosphere and corona, observationally validating their ubiquity has proved challenging. Here, we show observational evidence that ubiquitous Alfvén pulses are excited by prevalent intensity swirls in the solar photosphere. Correlation analysis between swirls detected at different heights in the solar atmosphere, together with realistic numerical simulations, show that these Alfvén pulses propagate upwards and reach chromospheric layers. We found that Alfvén pulses carry sufficient energy flux (1.9 to 7.7 kW m−2) to balance the local upper chromospheric energy losses (~0.1 kW m−2) in quiet regions. Whether this wave energy flux is actually dissipated in the chromosphere and can lead to heating that balances the losses is still an open question.

Frame Blind Deconvolution (MOMFBD) 1 method. The standard CRISPRED pipeline 2 , including 23 additional steps to account for differential stretching 3 , was also used. After applying the above The numerical simulation used in this work has been performed employing SAC 4 , which solves 29 the full ideal, compressible MHD equations for a perturbation within a gravitationally stratified 30 background atmosphere. The governing equations are given by: Here, ρ, v, e, B, p k and p t are the perturbed density, perturbed velocity vector, perturbed energy 32 density per unit volume, perturbed magnetic field vector, perturbed kinetic pressure and perturbed 33 total pressure, respectively. γ is the gas adiabatic index, set to be 5/3 in the simulation. g is 34 the gravitational field vector, set to be -274 m s −2 along the z-direction. Subscript b denotes 35 background parameters. Sub-grid numerical diffusion and resistivity are applied to the equations 36 as the terms D. Details of these hyperdiffusive and hyperresistive terms could be found in Equation

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The self-similar expanding open magnetic flux tube embedded into the background atmo-39 sphere, similar to flux tubes constructed and studied in previous work 5, 6 , has been constructed 40 analytically from the following equations: (2) Here, B x , B y and B z are the x−, y− and z−component of the magnetic field of the flux tube.
where, B 0z (0) is the magnetic field strength of the flux tube at its bottom (800 G), and z 3 is the 48 chomospheric scale height (0.45 Mm). The corresponding pressure and density deviations from 49 the non-magnetic equilibrium of the background atmosphere are then calculated based on the total 50 pressure balance 6, 7 . More details could be found in Appendix B of the reference 6 .  pulse introduces an azimuthal magnetic field perturbation defined as: Here, again, r is the distance to the axis of the flux tube. ϑ is the azimuthal angle. All the above 80 values are set for the best appearance of the visualization. in/out-flows that may happen, would the passing pulse not be Alfvén. 87 We shall notice that the above scenario is based on two basic conditions: plasma is frozen-in and there is a local density inhomogeneity. Under the small-amplitude, short-wavelength assumption, the energy flux carried into the upper 98 chromosphere by a single Alfvén pulse could be expressed as: where, ρ ≈ 4 × 10 −8 kg m −3 is the mass density at the bottom of the upper chromosphere in the where, F A = 1.9 -7.7 kW m −2 is the energy flux carried by a single Alfvén pulse estimated above.

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Having considered the above effects, we demonstrate that the average energy flux contributed 129 by Alfvén pulses estimated above (33 -131 W m −2 ) should be the lower limit. We shall also 130 note that, possible reflection and dissipation may also affect the local energy budget. However, 131 we do not see any evidence of reflection or dissipation of these Alfvén pulses in the data. This 132 may be an interesting future direction to investigate, but is beyond the scope of the current study.  been found to correspond to strong HMI magnetic field regions. As a comparison, we further did a result. Unsurprisingly, again, 3.3% swirls have been found to correspond to strong HMI magnetic 184 field regions. All the above results indicate that, HMI observations are too coarse to be used.

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To conclude, we are not able to see any reliable solution for this particular problem using 186 solar observations at the current stage. As far as we are aware, there are possibly two ways to 187 study this particular problem: 1) applying swirl detection and MBP detection algorithms to realistic 188 simulation data (for example Bifrost). This will be one of our future avenues of work, however,  HMI LOS magnetogram at 08:07:26 UT in the FOV of the studied SST observations in the paper, with a scale of the absolute LOS magnetic field strength from 0 G (white) to 50 G (black). Red and blue contours: clockwise and counter-clockwise photospheric intensity swirls detected from SST Fe I 6302Å wideband observations at almost the same time. Any swirl with even one point having absolute magnetic field strength above 30 G is contoured out with solid lines. All others are contoured out with dashed lines. Source data are provided in the Source Data file.