Abstract
Microturbulence (\(\xi \)) is a key parameter introduced in stellar spectroscopy to explain the strength of saturated lines by formally incorporating an additional thermal broadening term in the line opacity profile. Although our Sun can serve as an important testing bench to check the usual assumption of constant \(\xi \), the detailed behavior of how \(\xi \) varies from the disk center through the limb seems to have never been investigated so far. In order to fill this gap, local \(\xi \) values on the solar disk were determined from the equivalent widths of 46 Fe i lines at 32 points from the center to the limb by requiring the consistency between the abundances derived from lines of various strengths. The run of \(\xi \) with \(\theta \) (angle between the line of sight and the surface normal) was found to be only gradual from ≈ 1.0 km s−1 (at \(\sin \theta = 0\): disk center) to ≈ 1.3 km s−1 (at \(\sin \theta \approx 0.7\): two-thirds of radial distance); but thereafter increasing more steeply up to ≈ 2 km s−1 (at \(\sin \theta = 0.97\): limb). This result further suggests that the microturbulence derived from the flux spectrum of the disk-integrated Sun is \(\approx 20\)% larger than that of the disk-center value, which is almost consistent with the prediction from 3D hydrodynamical model atmospheres.
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Notes
Complete data of \(W_{ii}\) (\(ii = 00, \ldots , 31\)) at 32 points between the center and the limb for these 46 lines are available in the supplementary material of TU19 (“all_clvdata”).
This parameter is indicative of the \(T\)-sensitivity of \(W_{00}\) at the disk center and defined as \(K_{00} \equiv (d\log W/d\log T)_{00}\), which was numerically evaluated for each line (cf. Equation 6 in TU19).
Note that \(\sigma '\) should be divided by \(\sqrt{2}\) in order to avoid duplication because the original abundance set already has an intrinsic dispersion of \(\sigma _{0}\).
In Takeda (2019), an analytical formula of \(\xi = 1 + 0.6\sin \theta \) (km s−1) was applied as the \(\theta \)-dependent solar microturbulence, which was tentatively devised in analogy with the \(\theta \)-dependence of the macroturbulence. That relation was not appropriate as viewed from the present knowledge since it does not correctly reproduce the characteristic trend in terms of the increasing rate of \(\xi \) (becoming steeper towards the limb).
Meaningful information can also be read in Figure 7c. First, \(q_{1}\) is only marginally influenced (i.e., slightly shifting to higher frequencies) by the inclusion of macroturbulence and rotation as seen from the results of Cases 1 – 3. Second, the first zero of the rotational broadening function (so-called Carroll’s zero) is not observed at all in the transform for Case 3, which means that the rotational effect on the profile is no more expressed by a convolution of the broadening function for the case of slow rotators (cf. Takeda, 2019).
It should not be misunderstood that \(\xi \approx \)1.1 – 1.2 km s−1 is actually derived for the Sun from the line flux profile analysis. As briefly remarked in Section 1, \(\xi \)(profile) tends to be lower than \(\xi \)(EW); for example, Gray (1977) derived \(\xi = 0.5\) km s−1 from the profile analysis of Fe i 6252.554 line. See, e.g., Section 4.3 in Takeda et al. (1996) for consideration on this discrepancy.
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Takeda, Y. Center–Limb Variation of Solar Photospheric Microturbulence. Sol Phys 297, 4 (2022). https://doi.org/10.1007/s11207-021-01931-0
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DOI: https://doi.org/10.1007/s11207-021-01931-0