On acoustic and gravity waves in the solar photosphere and their energy transport

Abstract

Aims. We study acoustic and atmospheric gravity waves in the quiet Sun to estimate their energy transport to the chromosphere. Methods. A two-dimensional time sequence from quiet Sun disc centre was analysed with simultaneous spectroscopic observations in Fe i 5576 Å and Fe i 5434 Å (both with Landé factor g = 0). We calculated response functions of the velocities for the line minimum shifts and atmospheric transmissions of waves for the two lines. For this, NLTE line formation in granular and intergranular model atmospheres from numerical simulations were performed. For the interpretation of the observed waves and for the estimates of energy fluxes, we assumed adiabatic propagation of plane waves in an isothermal model atmosphere. Fourier analyses of intensity and velocity fluctuations were carried out. They yield power, phase, and coherence as functions of frequency ν (from temporal Fourier transforms) and in the k h −ν plane (from three-dimensional transforms). The power spectra, together with the mass densities at velocity formation heights, give then the energy fluxes. Results. The rms velocities found here in the acoustic and gravity wave domains are lower by a factor ∼1.5 as in earlier work. We therefore admit a factor of 2 for an upward correction of the estimated fluxes. For acoustic waves we find: 1) upward propagating waves are present on the Sun with frequencies up to 14−15 mHz (periods U ≈ 70 s); 2) the approximation of plane adiabatic waves in an isothermal atmosphere appears adequate for estimating the energy fluxes; 3) the acoustic energy fluxes are in the same range as found in our earlier work from ground-based, two-dimensional spectroscopy, 1500−3100 W m −2 at an atmospheric height of ∼380 km and 1300−2700 W m −2 at 570 km. The energy flux carried by gravity waves is difficult to determine. We find: 1) phase and coherence spectra between continuum and velocity fluctuations show that convective overshoot and gravity waves are superimposed. We account for the convective flows using these coherence spectra. 2) At low frequencies, the vertical wavelength Λ z can be short ( 300 km), yielding large corrections for atmospheric transmissions (factors >100). We thus exclude from the flux estimates waves with |k z | > 20 Mm −1 and with vertical group velocities υ gr,z < 0.3 km s −1 . They are likely to be strongly reduced in amplitude by radiative damping. 3) With these caveats, the energy fluxes carried by gravity waves are found in the range of 4000−8200 W m −2 at 380 km and 700−1400 W m −2 at 570 km. Gravity waves thus also contribute to the energy transport into the chromosphere.

Internal Gravity Waves in the Magnetized Solar Atmosphere. II. Energy Transport

“…Convective overshooting at the location of a convective/stable interface (Hurlburt et al 1986;Goldreich & Kumar 1990;Rogers & Glatzmaier 2005;Lecoanet & Quataert 2013;Ansong & Sutherland 2010;Alvan et al 2014Alvan et al , 2015Pinçon et al 2016Pinçon et al , 2017 is thought to be how IGWs are generated in the solar atmosphere. This has been confirmed by reported observations of IGWs in the solar atmosphere by several authors (Komm et al 1991;Rutten & Krijger 2003;Straus et al 2008;Stodilka 2008;Straus et al 2009;Kneer & Bello González 2011;Nagashima et al 2014). Vigeesh et al (2017, hereafter Paper I) looked at IGWs generated in model solar atmospheres and investigated the effect of magnetic fields on their propagation.…”

“…which can be written in terms of the vertical phase velocity (v ph,z ) as (Kneer & Bello González 2011), v g,z = −v ph,z sin 2 (ω/N ).…”

Synthetic observations of internal gravity waves in the solar atmosphere

“…Vigeesh & Roth: Synthetic observations of internal gravity waves in the solar atmosphere sults with those of Kneer & Bello González (2011). They looked at the Fe i λλ 5576 Å and 5434 Å lines, which were scanned quasi-simultaneously.…”

“…Several observations have provided strong evidence for the presence of internal gravity waves (IGWs) in the solar atmosphere (Straus et al 2008;Kneer & Bello González 2011;Nagashima et al 2014). These waves owe their existence to the proximity of an unstable layer adjacent to a stable environment.…”

The quiet-Sun photosphere and chromosphere

“…[149][150][151]). Recent estimates combining Fourier observations with simulations, but applying linear theory, suggest that the gravity-wave energy flux into the upper chromosphere is comparable to the acoustic flux [152,153]. These waves remain understudied.…”