tokens: peak shows up in the sum of the correlation at 900 nHz Instruments: no confirmed detection in other instruments (GONG, BiSON) measuring solar radial velocities. Although the detection claimed in F17 is not always reproducible, we must point out that it is quite remarkable to have obtained 2 peaks above the 10% threshold in Fig. 1 , which was not obtained in F17. It clearly shows that the levels of these 2 peaks are very sensitive to the details of the procedure. 3. Reproducing the analysis of FS18 3.1. g-mode asymptotic model In FS18, the analysis done in F17 was pushed further by correlating an asymptotic model of g -mode periods with the power spectrum of the time series of round-trip travel time. The asymptotic model of g -mode period P n , l can be found in Provost Berthomieu (1986) as: where n is the order of the mode, l is the degree of the mode, and P 0 , V 1 , V 2 and θ are all related to the solar model. Equation ( 2 ) can be solved for P n , l and can then be rewritten as: where is a quantity of order . Assuming that n ≫ 1, we can then rewrite P n , l as: where is the asymptotic periodicity of the modes of degree l , n 0 is an arbitrary value of g -mode order and α is given by: Finally, we can rewrite Eq. ( 3 ) as: This equation is the same as Eq. (14) in F17 except that α in our formula is directly related to P l while in F17 it is taken as a free parameter α l . In F17, the model of the g -mode frequency is then given by: where ν l is the rotational mode splitting for modes of degree l assumed to be independent of n and m . In addition, each mode of tesseral order m ≠ 0 of a given l is assumed to be observed with a weight w l , m less than 1. In summary, for l = 1 there are five independent parameters defining the model: P 1 , P min, 1 , α 1 , ν 1 and w 1, 1 ; while for l = 2, there are six independent parameters defining the model: P 2 , P min, 2 , α 2 , ν 2 , w 2, 1 and w 2, 2 . Here we note that F17 assumed that the parameters so defined are independent of each other, while as shown by Eq. ( 5 ) the P l and α depend upon P 0 . Here in order to reproduce, the findings of FS18 we followed the prescription of F17 for the independence of the parameters. 3.2. Optimisation of the correlation The model given by Eqs. ( 6 ) and ( 7 ) is then correlated with the smoothed power spectrum of time series of round-trip travel time. Here we note that the power spectrum is smoothed over 2 bins in FS18 rather than the 6 bins of F17. The computed correlation is made symmetrical by adding a flipped version of the correlation to itself. Then in FS18, the correlation value at 0 and at the splitting lag are optimised or fine tuned by adjusting all 5 parameters for l = 1 and all 6 parameters for l = 2. The optimisation procedure in FS18 is not detailed but done by hand (Fossat, priv. comm., 2018). In the course of the investigation, it appeared that the finding of a maximum could not be made possible by any simple optimisation routine mainly because
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