Radial Acceleration Relation between Baryons and Dark or Phantom Matter in the Supercritical Acceleration Regime of Nearly Spherical Galaxies

The central regions of nearby elliptical galaxies are dominated by baryons (stars) and provide interesting laboratories for studying the radial acceleration relation (RAR). We carry out exploratory analyses and discuss the possibility of constraining the RAR in the supercritical acceleration range (10(-9.5), 10(-8)) m s(-2) by using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies. This sample includes 24 ATLAS(3D) galaxies and 4201 SDSS galaxies, and covers a wide range of masses, sizes, and luminosity density profiles. We consider a range of current possibilities for the stellar mass-to-light ratio (M-*/L), its gradient, and dark or phantom matter (DM/PM) halo profiles. We obtain the probability density functions (PDFs) of the parameters of the considered models via Bayesian inference based on spherical Jeans Monte Carlo modeling of the observed velocity dispersions. We then constrain the DM/PM-to-baryon acceleration ratio a(X)/a(B) from the PDFs. Unless we ignore observed radial gradients in M-*/L, or assume unreasonably strong gradients, marginalization over nuisance factors suggests a(X)/a(B) = 10(P)(a(B)/a+1)(q) with p = -1.00 +/- 0.03 (stat)(-0.06)(+0.11) it (sys) and q = -1.02 +/- 0.09 (stat)(-0.00)(+0.016)(sys) around a supercritical acceleration a(+1) 1.2 x 10(-9) m s(-2 ). In the context of the ACDM paradigm, this RAR suggests that the NFW DM halo profile is a reasonable description of galactic halos even after the processes of galaxy formation and evolution. In the context of the MOND paradigm, this RAR favors the "Simple" interpolating function but is inconsistent with the vast majority of other theoretical proposals and fitting functions motivated mainly by subcritical acceleration data.