Note 1 R_☉ = 6.957*10**8 m = 0.004650 astronomical units (AUs) = 109.1 Earth equatorial radii.
This value may be a mean value: the source Wikipedia: Solar radius is a bit unclear.
where f_nHz is frequency in nanohertz and 435 nHz is a fiducial value for the internal solar rotation as the image plot itself shows.
The formula values obtained by casual inspection of the image plot are probably NOT so good. The image plot gives a 0° latitude surface sidereal period of 25.9 days, but the measured value is 24.47 days. See the solar rotation periods given the in Alien click to see image below (local link / general link: Jurgen Giesen plot) and see also Wikipedia: Solar rotation: Sidereal rotation.
The image plot gives 31.3 days for 60° latitude surface sidereal period. The measured value is more like 30.2 days (see Jurgen Giesen plot).
But maybe the image plot is NOT meant to be extrapolated to the solar photosphere.
The observed 90° latitude limit surface sidereal period is about 34 days (see Wikipedia: Solar rotation: Using sunspots to measure rotation period with a conversion from synodic period to sidereal period; Jurgen Giesen plot)
This means this region rotates nearly as if it were a rigid-rotor solid sphere even though it is a sphere of gas.
The radius 0.65 R_☉ approximately divides the inner solar radiative zone from the outer solar convective zone.
The transition between these two zones is the tachocline.
The surface ones were mostly directly observed long ago by tracking the motions of sunspots: the sunspots largely move with the solar rotation rates for solar latitudes where they appear.
Contemporaries of Galileo (1564--1642) (and Himself) used sunspots to determine early solar rotation rates (see Wikipedia: Solar rotation: Using sunspots to measure rotation: Galileo's Letters on Sunspots (1613)).
The interior solar rotation rates were learnt from helioseismology: the study of solar oscillations. The solar oscillations are observed on the surface and can then be used to infer the the interior solar rotation rates and other interior features.