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Table 1.

Measured characteristics of solar sectoral r modes.

This work Löptien et al. (2018)
1996–2017 (MDI & HMI) 2010–2016 (HMI)


Period in e-folding
m νstart ωm/2π Γm/2π A B Ωeq frame lifetime δτrms vrms ωm/2π
(nHz) (nHz) (nHz) (days) (days) (s) (m s−1) (nHz)
3 −330 −253 ± 2 18 ± 1 −46 505 0.07 1.0 −259
4 −350 −198 ± 5 −58 109 0.08 1.3
5 −330 −156 ± 2 15 ± 1 −74 445 0.06 1.0 −157 ± 4
6 −310 −86 181 0.06 1.1 −129 ± 8
7 −280 −110 ± 4 11 ± 1 −105 92 0.11 2.2 −112 ± 4
8 −240 −91 ± 3 −128 198 0.09 1.9 −90 ± 3
9 −236 −82 ± 5 12 ± 1 −142 112 0.08 1.7 −86 ± 6
10 −225 9 ± 1 −193 68 0.09 2.2 −75 ± 5
11 −225 −48 ± 7 5 ± 1 −239 44 0.08 2.2 −75 ± 7
12 −209 −36 ± 8 5 ± 1 −323 49 0.06 1.7 −59 ± 6
13 −190 −26 ± 7 3 ± 1 −449 45 0.06 2.0 −40 ± 10
14 −206 −35 ± 5 4 ± 0.4 −326 135 0.03 1.2
15 −197 4 ± 0.3 −519 345 0.03 1.1

Notes. Parameters ωm (mode frequency), Γm (full width at half maximum), A (maximum height of the Lorentzian function), and B (background power) that give the best fit to the power spectrum for each m in the range 3 ≤ m ≤ 15. The frequency νstart defines the frequency range [νstart, νstart + 300 nHz] for the Lorentzian fit. The 68% confidence interval on each parameter is indicated by the upper and lower bounds estimated from Monte Carlo simulations. The modes with m <  10 have a quality factor ωmm >  1 in the corotating frame (the frame for Rossby waves). However, the modes with m ≥ 10 have a quality factor less than or comparable to one. The e-folding lifetime, 2/Γm, is given for each mode, as well as the oscillation period measured in the Sun’s corotating frame (rotating at Ωeq/2π = 453.1 nHz). Negative oscillation periods indicates retrograde propagation. The rms south-north travel-time shift δτrms for each m is obtained from the fitted Lorentzian Fm(ω)−B using Parseval’s theorem with the window function taken into account. The rms horizontal flow speed of the r modes along the equator in the near-surface layers, vrms, is converted from the δτrms using conversion constants estimated from forward modeling (see text). A typical error in the vrms is about 0.5 m s−1 based on the error propagation. The maximum flow speed along the equator for each mode is related to the rms flow speed by . Also listed are the mode frequencies from Löptien et al. (2018) for comparison.

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