Estimation of acoustic travel-time systematic variations due to observational height difference across the solar disk. Shukur Kholikov 1 and Aleksander Serebryanskiy 2 National Solar Observatory (1), Tucson, AZ Astronomical Institute (2), Uzbekistan

Introduction Recently Zhao et al. (2012) addressed a new systematic signal in time-distance measurements, which may be a key point to deep meridional flow measurements. The main idea in this approach is to remove observed systematic travel-time shifts from travel-time differences. The source of these systematics is not completely understood, but is most-likely related to existing observational limitations such as changing of height of the line formation across the solar disk, which produces extra acoustic travel-time shift in cross-correlation measurements between different locations on the disk. Later, Baldner & Schou (2012) showed that the effect of the vertical flows from convection in the outer convective zone can also affect travel-time measurements. This additional travel-time shift is a function of disk location and introduces center-to-limb variations in typical time-distance measurements. In this paper we use more than 600 daily GONG velocity images. In order to decrease possible projection effects we have selected dates with duty cycle more than 85% and time periods when solar tilt angle B 0 ≤4 These requirements set narrow range and substantially decreases amount of data can be used.

Assuming that above mentioned center-to-limb variations are the same in any direction on solar disk, we compute them using only equatorial part of the observations. In this configuration, travel-time differences for a particular travel distance are the sum of center-to-limb variation and residual time-shift due to internal solar rotation (surface rotation is removed by tracking of daily velocities). Fortunately the part related to the solar rotation is a constant for a fixed travel distance and can be easily subtracted. We exploit this opportunity to remove center-to- limb variations from our meridional travel-time measurements before doing helioseismic inversions to extract flow speed as a function of depth. Another approach to obtain center-to-limb systematic variations is to measure travel time differences at different locations of the solar disk. In Figure1 schematic configuration of signal locations to compute cross-correlations is presented. Acoustic travel times between green/black central points and arcs should be nearly same, since both locations are located at approximately same center-to-limb distance. In case of central (red) and annuli (blue) two locations are located at different center-to-limb distance.

Varying the radius of the circle relation between separation distance between locations and travel time difference can be estimated. Travel-time difference as a function of travel distance is shown in Figure 2. Figure 1 Ingoing and outgoing travel times between central (red) point and annuli (blue) are different due to observational line formation height difference. For signals located nearly same relative to center (green/black points and arcs) acoustic travel time in both directions is the same. Figure 2 Travel-time differences between opposite propagating acoustic waves. Time difference between center to annuli is significant and linearly increases by travel distance (red). The case when endpoints of cross- correlations where located at the same position on the disk (relative to center) is plotted in blue.

Figure 3 Meridional travel-time differences and center-to-limb corrections as a function of travel distance (propagation depth) and latitude. There is a tendency of increasing of time differences in typical North-South travel times (right). East-West (bottom top) and observational line formation height based (bottom right) center-to-limb systematic travel- time differences. Corrected meridional travel-time differences using these two techniques (bottom right). In both cases decrease of the time-differences with depth can be seen. For deeper convection zone there is clear sign change in travel-times, compelling evidence that travel times may change sign (thus signaling a flow reversal).

Figure 4 Inversion results of center-to-limb corrected (EW) meridional travel-times. In top panel flow speed is presented as a function of latitude (horizontal) and depth. The color convention in this map is : red poleward and magenta Equatorward flow. Limitation of measurements in small travel-distances do not allow recovering flow at the surface. Average profile of the flow for latitude range degree is showed is bottom panel. Changing the flow direction at ~50-60 Mm is obviously seen.

Summary ● Center-to-limb variations of travel-time measurements show similar pattern as meridional travel-time differences and can be removed using East-West systematic time differences ● Observational line formation height may be one possible source of extra time-shifts ● Meridional flow turns back to the Equator at depth Mm and extends down to tachocline region ● More data to be involved to increase statistical significance and look at temporal variations of the return flow