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Radial Acceleration Relation between Baryons and Dark or Phantom Matter in the Super-critical 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 super-critical acceleration range $(10^{-9.5},\hspace{1ex}10^{-8})$~${\rm m}~{\rm s}^{-2}$ using a sample of nearly round pure-bulge (spheroidal, dispersion-dominated) galaxies including 24 ATLAS$^{\rm 3D}$ galaxies and 4201 SDSS galaxies covering a wide range of masses, sizes and luminosity density profiles. We consider a range of current possibilities for the stellar mass-to-light ratio ($M_\star/L$), 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 $a_{\rm X}/a_{\rm B}$ from the PDFs. Unless we ignore observed radial gradients in $M_\star/L$, or assume unreasonably strong gradients, marginalization over nuisance factors suggests $a_{\rm X}/a_{\rm B} = 10^{p} (a_{\rm B}/a_{+1})^q$ with $p = -1.00 \pm 0.03$ (stat) $^{+0.11}_{-0.06}$ (sys) and $q=-1.02 \pm 0.09$ (stat) $^{+0.16}_{-0.00}$ (sys) around a super-critical acceleration $a_{+1}\equiv 1.2\times 10^{-9}~{\rm m}~{\rm s}^{-2}$. In the context of the $Λ$CDM 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 from sub-critical acceleration data.