Accounting for the Solar Acoustic and Luminosity Variations from the Deep Convection Zone

Recent helioseismic observations (Duvall et al.) have demonstrated how new data analysis techniques can determine local changes in the acoustic properties beneath the photosphere. The recent results provide compelling evidence of a latitudinal sound speed variation. Using results from numerical simulations, we show here how this acoustic variation has the correct form and amplitude needed to account for the previously observed solar photometric changes. In this picture, both the acoustic and irradiance changes may be caused by magnetically induced entropy fluctuations near the base of the solar convection zone. Subject headings: Sun: activity — Sun: magnetic fields— Sun: oscillations Three distinct global solar observables have been observationally linked to the solar magnetic cycle: the solar irradiance (the average flux at the mean Earth-Sun distance in the ecliptic plane) (Willson & Hudson 1991), the solar luminosity (the implied flux integrated over all directions away from the Sun) (Kuhn, Libbrecht, & Dicke 1988), and the acoustic p-mode frequencies and frequency splittings of individual spherical harmonic multiplets (Woodard & Noyes 1985; Kuhn 1988). While all of the observations seem secure, obtaining an understanding of how the magnetic, luminosity, and acoustic solar cycles are causally related has been difficult. Several attempts to explain the acoustic solar variations in terms of near-photospheric magnetic fields (cf. Gough & Thomson 1988; Goldreich et al. 1991; Jain & Roberts 1993) suffer because the required field strengths are larger than what is observed near the photosphere (Lin 1995). These models also leave the luminosity cycle unexplained. Attempts to relate the solar acoustic and photometric asphericity to a magnetically induced radiative instability (Kuhn 1993, 1994, 1996) at the base of the convection zone have also been criticized as incomplete (Gough 1994), although the new local helioseismic data may now clarify these questions. Duvall et al. (1996) report the detection of a global-scale effective sound speed asphericity using a ‘‘time-distance’’ analysis technique. While the observation of symmetric latitude bands is not surprising (global p-mode splitting analyses have measured this pattern; Kuhn 1988), to detect these effects in an 8.5 hr time series is remarkable. Similarly, as has been observed in global frequency data (Kuhn 1990), Duvall et al. (1996) found that the perturbation is largest near the photosphere. Their analysis has an important advantage over spectral techniques because it more directly provides spatially (and temporally) localized sound speed information. A direct comparison of the local acoustic and photometric solar data is now possible, and it is likely that the new time-distance results will be important for distinguishing between magnetic and thermal origins to the solar cycle asphericity changes. The last photometric brightness observations from the Princeton Solar Oblateness telescope were obtained during the summer of 1990 (Kuhn & Libbrecht 1991)—about 6 months before the Duvall et al. (1996) helioseismic data were collected. Figure 1 plots the photospheric brightness obtained from the two-color photometry of 1990, expressed as a brightness temperature deviation from the average. The vertical scale gives the effective temperature asphericity in kelvins as a function of solar latitude (as it was measured from within a few arcseconds of the limb). The dotted line in this figure shows the acoustic propagation time from Duvall et al. (1996), scaled by the numerical factor of20.5 K s (and offset by about 35 minutes). Although the acoustic variation at high latitudes is weaker than the photometric change, the latitude dependence of both data sets is similar. For example, bright latitude bands at H208 north and south latitude are clearly associated with faster acoustic propagation times. There are many subtleties to the two data sets, but we can speculate that the high-latitude difference between the two is related to disk-projection effects. Despite these differences, it is evident that a 1 s propagation time decrease corresponds to an average brightness temperature excess of about 0.5 K. Can this correlation be explained as a result of a perturbed thermal model? Duvall et al. (1996) suggested that a 200 K photospheric temperature excess would be needed to explain the acoustic bands. In fact, magnetized fluid near the base of the convection zone in the midlatitude activity bands may transport excess entropy to the photosphere (Kuhn 1994, 1996). Vertically coherent updrafts may also deposit entropy from deep in the convection zone to the surface (Parker 1995). Numerical convection experiments do not have the spatial dynamic range to model the entire convection zone but have been successful at describing the complicated superadiabatic region near the photosphere (Nordlund & Stein 1990). In this discussion, we have used numerical experiments to explore the energy transport properties of the upper convection zone. Adapting the code developed by Nordlund & Stein (1990), we simulated the boundary between latitude regions with different upward entropy at their lower boundaries. The THE ASTROPHYSICAL JOURNAL, 463 :L117–L119, 1996 June 1 q 1996. 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