Asymmetry Reversal in Solar Acoustic Modes Dali Georgobiani (1), Robert F. Stein (1), Aake Nordlund (2) 1. Physics & Astronomy Department, Michigan State University, Biomedical & Physical Sciences Bldg., East Lansing, MI Teoretisk Astrofysik Center, Denmark Grundforskningsfond,Juliane Maries Vej 30, DK-2100 København Ø, Denmark

Abstract The solar acoustic mode profiles are asymmetric. Peaks of velocity power spectra have more power on the low frequency sides, whereas intensity profiles show the opposite sense of asymmetry. This asymmetry reversal is believed to be caused by the presence of correlated background noise. We study solar oscillations using numerical simulations of the upper convection zone. The modes in our simulation have the same asymmetries and asymmetry reversal as the observed modes. The temperature and velocity power spectra at optical depth   1 have the opposite asymmetry as is observed for the intensity and velocity spectra. At a fixed geometrical depth, corresponding to  1, however, the temperature and velocity spectra have the same asymmetry.

We believe the asymmetry reversal in the emergent intensity is due to opacity effects on the radiation transfer. The opacity in the photosphere is very temperature sensitive. The larger temperature fluctuations (at fixed geometrical height) on the low frequency side of the mode produces larger opacity fluctuations there, which in turn leads to larger variations in the height of unit optical depth. When the temperature is high, the opacity is large, so unit optical depth occurs higher in the atmosphere where the temperature (which decreases outward) is smaller. When the temperature is low, the opacity is small, so unit optical depth occurs deeper in the atmosphere where the temperature is higher. This reduces the magnitude of the observed fluctuations in the radiation temperature, which in accordance with the Eddington-Barbier relations, is equal to the gas temperature at unit optical depth. The larger temperature fluctuations on the low frequency side of the mode peak leads to a larger reduction in the radiation temperature on that side and reverses the asymmetry of the mode intensity spectral peak.

Numerical Model Stein – Nordlund 3D code –Complete system of HD equations –Radiative Transfer

Oscillations: P-modes Simulations vs Observations: Mode profiles and asymmetries demonstrate similar behavior Similar asymmetry reversal Similar phase relations

Intensity Asymmetry Spectrum of intensity. The solid curve is boxcar smoothed over  65  Hz Spectrum of temperature at  = 1. Its asymmetry is similar to the intensity asymmetry

Velocity Asymmetry Spectrum of velocity at  1. Its spectrum is same at fixed geometrical depth corresponding to = 1 Spectrum of temperature at = 1. The temperature spectrum has the same asymmetry as the velocity

Closer Look: Fundamental Mode The velocity (green) and temperature (purple) spectra for the first non-radial f-mode at = 1. The velocity and temperature profiles look similar to each other. Curves are smoothed over 32  Hz The velocity (green) and temperature (purple) spectra for the first non-radial f-mode at  = 1. The amplitude of the temperature fluctuations is non - uniformly reduced across the mode peak

Radiation role in the asymmetry reversal The temperature (purple) and opacity (green) spectrum for the first non - radial f-mode at = 1. The larger temperature fluctuations on the low frequency side of the mode produce larger opacity variations The spectrum of the height of  = 1 (green) and temperature (purple) measured at local  = 1. This height varies more on the low frequency side of the mode, where the opacity variation is larger, which in turn reduces temperature fluctuations

Conclusion We have found that the emergent intensity and the temperature spectra at local instantaneous optical depth unity have the opposite asymmetry to the velocity as is observed, while the temperature at fixed geometric depth corresponding to average optical depth unity has the same asymmetry as the velocity. This indicates that radiation transfer plays a crucial role in the asymmetry reversal observed between the intensity and Doppler velocity, and that this reversal is not due solely to effects of correlated noise. The mode asymmetry has been shown to depend on the separation of observation location and source location. T (  ) and T (  are observed at different heights. Oscillation induced opacity changes vary the location of radiation emission (   1) in a way that reduces the magnitude of the temperature fluctuations and reverses their asymmetry