Modelling the asymmetries of the Sun’s radial p-mode line profiles

Abstract

Context. The advent of space-borne missions has substantially increased the number and quality of the measured power spectrum of solar-like oscillators. It now allows for the p-mode line profiles to be resolved and facilitates an estimation of their asymmetry. The fact that this asymmetry can be measured for a variety of stars other than the Sun calls for a revisiting of acoustic mode asymmetry modelling. This asymmetry has been shown to be related to a highly localised source of stochastic driving in layers just beneath the surface. However, existing models assume a very simplified, point-like source of excitation. Furthermore, mode asymmetry could also be impacted by a correlation between the acoustic noise and the oscillating mode. Prior studies have modelled this impact, but only in a parametrised fashion, which deprives them of their predictive power. Aims. In this paper, we aim to develop a predictive model for solar radial p-mode line profiles in the velocity spectrum. Unlike the approach favoured by prior studies, this model is not described by free parameters and we do not use fitting procedures to match the observations. Instead, we use an analytical turbulence model coupled with constraints extracted from a 3D hydrodynamic simulation of the solar atmosphere. We then compare the resulting asymmetries with their observationally derived counterpart. Methods. We model the velocity power spectral density by convolving a realistic stochastic source term with the Green's function associated with the radial homogeneous wave equation. We compute the Green's function by numerically integrating the wave equation and we use theoretical considerations to model the source term. We reconstruct the velocity power spectral density and extract the line profile of radial p-modes as well as their asymmetry. Results. We find that stochastic excitation localised beneath the mode upper turning point generates negative asymmetry for ν < ν max and positive asymmetry for ν > ν max . On the other hand, stochastic excitation localised above this limit generates negative asymmetry throughout the p-mode spectrum. As a result of the spatial extent of the source of excitation, both cases play a role in the total observed asymmetries. By taking this spatial extent into account and using a realistic description of the spectrum of turbulent kinetic energy, both a qualitative and quantitative agreement can be found with solar observations performed by the GONG network. We also find that the impact of the correlation between acoustic noise and oscillation is negligible for mode asymmetry in the velocity spectrum.

Velocity-intensity asymmetry reversal of solar radial p-modes

“…In order to adapt our p-mode stochastic excitation model to intensity observations, it is first necessary to model the intensity Green's function associated to radial p-modes. Indeed, in Philidet et al (2020), the wave equation was written in terms of a wave variable Ψ ω , related to the velocity fluctuations through…”

“…where V(r) is the acoustic potential, Γ ω is the frequencydependent damping rate of the oscillations, and S (r) is a source term proportional to the divergence of the fluctuating Reynolds stresses. The damping rates Γ ω are inferred from observations; we use the same values as those presented in Table 1 of Philidet et al (2020). For a given value of ω, convolving the Green's function of Eq.…”

“…The remainder of the procedure is identical to the one detailed in Philidet et al (2020). More precisely, to derive Ψ ω , we convolve the Green's function G ω and the source term S associated to the inhomogeneous wave equation (Eq.…”

“…These prior studies used parameterised models, and aimed to find best-fit values for their free parameters by applying fitting procedures to individual peaks in the observed spectrum. Philidet et al (2020) followed a different approach, which consisted in modelling mode asymmetry without fitting any free parameters to the available observational data. Instead, they developed an analytical model of stochastic excitation, coupled with a 3D hydrodynamical simulation of the stellar atmosphere.…”

“…In this context, our objective is to question this assumption, and to show that the radiative flux reacts more complexly to temperature variations, which has a crucial impact on line profile asymmetry in the intensity spectra. To that end, we extend the model of Philidet et al (2020) for intensity observations. We show that, unlike what was previously thought, source localisation impacts velocity and intensity observations differently, so that an additional physical mechanism is not necessary to account for asymmetry reversal, except maybe at high frequency.…”