McGaugh et al .
( 2016 ) have recently used their extensive SPARC sample of disc galaxies to update the well-known mass-discrepancy-acceleration relation ( MDAR ) : a tight correlation between the local , dynamical accelerations , g , deduced from the rotation curves at different radii , and the local baryonic , Newtonian gravitational accelerations , g _ { \scriptscriptstyle N } .
This MDAR is one of the major predicted “ MOND laws ” .
It is anything but a newly discovered relation , as it has been plotted and studied time and again ( starting with Sanders 1990 ) , with ever increasing quantity and quality of data .
The important updated analysis of McGaugh et al. , like its precedents , bears crucial ramifications for the observed dynamical anomalies in disc galaxies , and , in particular , on their resolution by the MOND paradigm .
These results , indeed , constitute a triumph for MOND .
However , unlike previous analyses of the MDAR , McGaugh et al .
have chosen to obfuscate the MOND roots of their analysis , and its connection with , and implications for , this paradigm .
For example , they find that their data are very well fit by a certain , single-parameter function , apparently picked ex machina , of the form g = g _ { \scriptscriptstyle N } \nu ( g _ { \scriptscriptstyle N } / g _ { \dagger } ) , with \nu ( y ) = ( 1 - e ^ { - \sqrt { y } } ) ^ { -1 } , and g _ { \dagger } \approx 1.2 \times 10 ^ { -8 } { cm~ { } s ^ { -2 } } .
In fact , this \nu ( y ) tightly follows the dictates of MOND : a single acceleration parameter , \nu ( y \gg 1 ) \approx 1 , and \nu ( y \ll 1 ) \approx y ^ { -1 / 2 } , from scale invariance of the deep-MOND limit .
This very same \nu ( y ) has been proposed and used repeatedly in the past in the context of MOND .
No other possible origin for such a function is known .
It was already known to reproduce rotation curves correctly , so was a priori assured success here as well .
That g _ { \dagger } plays the role , and has the well-established value , of the MOND acceleration constant , a _ { \scriptscriptstyle 0 } , is also suppressed .
The present paper corrects these oversights – bringing to light the deep connections with MOND , suppressed by McGaugh et al .
It also gives due credit to previous works , and discusses some important , but less known , aspects of this MOND relation .