Abstract
Context. Understanding convection is important in stellar physics, for example, when it is an input in stellar evolution models. Helioseismic estimates of convective flow amplitudes in deeper regions of the solar interior disagree by orders of magnitude among themselves and with simulations. Aims. We aim to assess the validity of an existing upper limit of solar convective flow amplitudes at a depth of 0.96 solar radii obtained using time-distance helioseismology and several simplifying assumptions. Methods. We generated synthetic observations for convective flow fields from a magnetohydrodynamic simulation (MURaM) using travel-time sensitivity functions and a noise model. We compared the estimates of the flow amplitude with the actual value of the flow. Results. For the scales of interest (ℓ < 100), we find that the current procedure for obtaining an upper limit gives the correct order of magnitude of the flow for the given flow fields. We also show that this estimate is not an upper limit in a strict sense because it underestimates the flow amplitude at the largest scales by a factor of about two because the scale dependence of the signal-to-noise ratio has to be taken into account. After correcting for this and after taking the dependence of the measurements on direction in Fourier space into account, we show that the obtained estimate is indeed an upper limit. Conclusions. We conclude that time-distance helioseismology is able to correctly estimate the order of magnitude (or an upper limit) of solar convective flows in the deeper interior when the vertical correlation function of the different flow components is known and the scale dependence of the signal-to-noise ratio is taken into account. We suggest that future work should include information from different target depths to better separate the effect of near-surface flows from those at greater depths. In addition, the measurements are sensitive to all three flow directions, which should be taken into account.
Highlights
Helioseismic inferences of convective motions in the solar interior yield consistent results in near-surface layers using different techniques (e.g., De Rosa et al 2000; Braun & Lindsey 2003; Hindman et al 2004; Gizon & Birch 2004; Langfellner et al 2014, 2015)
We conclude that time-distance helioseismology is able to correctly estimate the order of magnitude of solar convective flows in the deeper interior when the vertical correlation function of the different flow components is known and the scale dependence of the signal-to-noise ratio is taken into account
For MURaM-type flows, we find that the spectrum noise-correction (S/N) significantly depends on the spatial scale and is not independent of scale, as assumed by HDS2012, see the top panel in Fig. 4 and assumption (A1)
Summary
Helioseismic inferences of convective motions in the solar interior yield consistent results in near-surface layers using different techniques (e.g., De Rosa et al 2000; Braun & Lindsey 2003; Hindman et al 2004; Gizon & Birch 2004; Langfellner et al 2014, 2015). Inferences of the power spectrum of convective motions in deeper regions of the solar interior have led to conclusions that differ by more than an order of magnitude (Hanasoge et al 2012, hereafter HDS2012; Greer et al 2015) Understanding these differences and obtaining reliable estimates of the spectrum of convective motions in the Sun is important for several processes in stellar interiors, such as the maintenance of differential rotation, and for understanding the role of convection in the emergence of active regions. This is even more urgent because convective velocities from numerical simulations of solar convection exhibit largescale convective motions that are far too strong, even compared to surface observations (Gizon & Birch 2012; Lord et al 2014). This last issue is often referred to as the convective conundrum
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