Numerical determination of the cutoff frequency in solar models

Abstract

Context. In stratified atmospheres, acoustic waves can only propagate if their frequency is above the cutoff value. The determination of the cutoff frequency is fundamental for several topics in solar physics, such as evaluating the contribution of those waves to the chromospheric heating or the application of seismic techniques. However, different theories provide different cutoff values. Aims. We developed an alternative method to derive the cutoff frequency in several standard solar models, including various quiet-Sun and umbral atmospheres. The effects of magnetic field and radiative losses on the cutoff are examined. Methods. We performed numerical simulations of wave propagation in the solar atmosphere using the code MANCHA. The cutoff frequency is determined from the inspection of phase difference spectra computed between the velocity signal at two atmospheric heights. The process is performed by choosing pairs of heights across all the layers between the photosphere and the chromosphere, to derive the vertical stratification of the cutoff in the solar models.Results. The cutoff frequency predicted by the theoretical calculations departs significantly from the measurements obtained from the numerical simulations. In quiet-Sun atmospheres, the cutoff shows a strong dependence on the magnetic field for adiabatic wave propagation. When radiative losses are taken into account, the cutoff frequency is greatly reduced and the variation of the cutoff with the strength of the magnetic field is lower. The effect of the radiative losses in the cutoff is necessary to understand recent quiet-Sun and sunspot observations. In the presence of inclined magnetic fields, our numerical calculations confirm the reduction of the cutoff frequency due to the reduced gravity experienced by waves propagating along field lines. An additional reduction is also found in regions with significant changes in the temperature, due to the lower temperature gradient along the path of field-guided waves. Conclusions. Our results show solid evidences of the stratification of the cutoff frequency in the solar atmosphere. The cutoff values are not correctly captured by theoretical estimates. In addition, most of the widely-used analytical cutoff formulae neglect the impact of magnetic fields and radiative losses, whose role is critical to determine the evanescent or propagating nature of the waves.

Oscillations observed in Umbra, Plage, Quiet-Sun and the Polarity Inversion Line of Active Region 11158 using HMI/SDO Data

“…The most extensive work on MHD waves using HMI data, in coordination with AIA data, has been carried out by Rajaguru et al (2019Rajaguru et al ( , 2013, with the important findings that small scale magnetic elements channel significantly more acoustic wave energy into the chromosphere than originally expected. These waves have frequencies between 2-5 mHz and the findings support Centeno et al (2009); Khomenko et al (2008); Felipe & Sangeetha (2020) in the argument that radiative losses, not magnetic inclinations, are responsible for lowering the cutoff frequencies for the thin magnetic structures and enable a large amount of wave flux to move upwards.…”

“…The cutoff frequency can be further reduced either by the inclination of the magnetic field with respect to the solar surface, by a factor of cosθ where θ is the inclination (Bel & Leroy 1977), or by radiative losses in thin vertical flux tubes such as faculae (Centeno et al 2009;Khomenko et al 2008). Cutoff frequencies in umbra and pores are on the order of ∼4 mHz and those in smaller magnetic structures that suffer significant radiative losses can be as low as 2 mHz, although recent numerical simulations (Felipe & Sangeetha 2020) show that the cutoff frequencies in thin structures do not get quite that low. The exact reduction of cutoff frequencies due to radiative losses in magnetic structures is still an open question.…”

Slow magneto-acoustic waves in simulations of a solar plage region carry enough energy to heat the chromosphere

“…The shift of the dominant wave period from 5-minute in the photospheric oscillations to 3-minute in the chromospheric oscillations is often attributed to the cut-off period of the temperature minimum (Michalitsanos 1973;Bel & Leroy 1977;Fleck & Schmitz 1991;Verth & Jess 2016;McIntosh & Jefferies 2006;Khomenko & Collados 2015;Chae et al 2017). The effective cut-off period may, however, increase due to inclination of the magnetic field relative to the vertical (Schwartz & Bel 1984;De Pontieu et al 2004 or due to departure from adiabaticity (Khomenko et al 2008;Felipe & Sangeetha 2020), resulting in the propagation of waves with periods of more than 3-minutes. de Wijn et al (2009) showed that waves with three-minute periods propagate in the central facular chromosphere where magnetic field is more vertical while five-minute waves propagate at the peripheral regions where the magnetic field is both inclined and expanding.…”