Abstract The tension between luminous matter and dynamical matter has long been an interesting and controversial topic in the investigation of galaxies. This is particularly true when we study spiral galaxies for which we have high quality observations of rotation curves. The solutions to the tension are proposed in two different approaches, one is the dark matter hypothesis and the other is MOdified Newtonian Dynamics (MOND) theory. When we test the solutions by using observational data of rotation curves, the controversy arises when we apply them to both low surface brightness (LSB) galaxies and high surface brightness (HSB) galaxies. Usually one likes to use the rotation curves of LSB galaxies, since dark matter is needed or the Newtonian acceleration falls below the characteristic acceleration \(a_0\) in most regions of such galaxies, even near their centers. But for HSB galaxies, dark matter is needed or Newtonian acceleration falls below the characteristic acceleration \(a_0\) only in their outer regions so it is helpful to single out HSB galaxies from some large sample to test the solutions. To this end, we employ a sub-sample of the rotation curves consisting of 45 non-bulgy HSB galaxies selected from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database to test two dark halo models (NFW and Burkert) and MOND. We find that, among the three models, the core-dominated Burkert halo model (\(\chi^2_v = 1.00\)) provides a better description of the observed data than the NFW model (\(\chi^2_v = 1.44\)) or MOND model (\(\chi^2_v = 1.87\)). This is not consistent with the most recent numerical simulations, which tend to favor some cuspy density profiles for HSB galaxies. For MOND, when we take \(a_0\) as a free parameter, there is no obvious correlation between \(a_0\) and disk central surface brightness at 3.6 µm of these HSB spiral galaxies, which is in line with the basic assumption of MOND that \(a_0\) should be a universal constant, but is surprisingly not consistent with the results when LSB galaxies are included. Furthermore, our fittings give \(a_0\) an average value of \((0.74 \pm 0.45) \times 10^{−8} \rm~cm~s^{−2}\), which only marginally supports the standard value of \(a_0\) (\(1.21 \times 10^{−8}\rm ~ cms~^{−2}\)). Since the standard value of \(a_0\) is strongly supported when both HSB and LSB galaxies are included in the large SPARC sample, we conclude that our slightly smaller value of \(a_0\) cannot be explained by the so called external field effect in MOND theory.

Keywords cosmology: theory — dark matter — galaxies: halos

https://doi.org/10.1088/1674-4527/21/11/271