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tokens: of hydrogen was switched on at s and for the first published snapshot, at s. The non-equilibrium hydrogen ionization leads to much higher electron density in the cool pockets at 0.5–2 Mm and also higher electron densities up to 3.5 Mm height. There is not much change with time of this probability density function after s. 3.6. Velocity field Spectral lines are normally observed to be broader than what the thermal broadening of the opacity profile would give. An extra free parameter, called microturbulence, is often introduced in 1D semi-empirical models to account for this broadening. The “micro” in the name comes from the fact that this parameter is introduced as an extra broadening of the opacity profile, acting in exactly the same way as thermal broadening. This would be a physically correct description in the limit of zero length-scale for the velocity field. It is also often necessary to introduce a second free parameter to account for the observed lineshape. This is called macroturbulence and is equivalent to a Gaussian convolution of the emergent intensity profile (rather than a convolution of the opacity profile as is the case for microturbulence). Realistic 3D radiation hydrodynamic simulations of the solar photosphere give line profiles that are close to the observed profiles without the addition of extra free parameters – the non-thermal broadening comes from Doppler shifts arising from the convective flows and oscillations (e.g., Asplund et al. 2000 ). Also spectral lines formed in the outer atmosphere are broader than what thermal broadening alone predicts. The nature of this non-thermal broadening in the outer atmosphere is still unclear, but the presence of strong shocks ( Carlsson Stein 1992 , 1997 ; De Pontieu et al. 2015 ), torsional motions ( De Pontieu et al. 2014a ), and Alfvén wave turbulence ( van Ballegooijen et al. 2011 ) are some of the candidates. Fig. 14 Average non-thermal velocity calculated over 1 dex in (column mass) (red, left scale) and average temperature (blue, right scale) as function of logarithmic column mass for the simulation snapshot at s. There is no simple way to characterize the macroscopic velocities in the simulation that give rise to non-thermal broadening. The effect of a given velocity field on the spectral line width depends on whether the spectral line is optically thick or optically thin, where in the atmosphere the line is formed and the width of the contribution function to intensity. One possible way of quantifying the velocity field is the standard deviation of the vertical velocity over a given height range as function of height and horizontal position. At each column of the simulation box at s we calculate the column mass scale (which is more closely related to line formation quantities like optical depth than a geometric height) and take the standard deviation of the vertical velocity over a range of 1 dex in (column mass). We multiply the standard deviation by the square root