TITLE:
Equivalence between Direct Mass and NFW-Total Mass Formula in MW and M31 Galaxies
AUTHORS:
Manuel Abarca
KEYWORDS:
Dark Matter, Dark Matter by Quantum Gravitation, NFW DM Density Profile, Milky Way, M31 Galaxy
JOURNAL NAME:
Journal of High Energy Physics, Gravitation and Cosmology,
Vol.11 No.3,
July
30,
2025
ABSTRACT: In the framework of Dark Matter by Quantum Gravitation (DMbQG) theory hereafter, the Direct mass gives the total mass into the halo region, growing with the square root of radius. This formula has only one specific parameter for each galaxy. The NFW profile is a universal method that gives the DM mass function depending on radius at the bulge, the disk and the galactic halo. This function is defined by two parameters. The DMbQG theory claims that DM is generated by the own gravitational field and consequently the DM halo is unbounded. In the paper [1] (Abarca, M. 2024) was proved that it is the Dark energy the mechanism able to counterbalance the DM but at cluster scale. As the direct mass is linked to the total mass (baryonic plus DM), in the paper has been developed a method to integrate the baryonic matter into the NFW DM function in order to be able to compare both functions connected to the total mass. Thanks this method has been possible to define the R200-TOTAL and the M200-TOTAL both referred to a sphere whose total mass has a mean density equal to 200 times the critic density of the Universe. The main achievement of this paper is to demonstrate that the Direct mass function and the NFW-total mass function are equivalents into the halo region of MW and the M31. The equivalence of the two formulas for masses is based on four tests, all of them tested successfully for the both galaxies. Test I. Comparison the R200-TOTAL and the M200-TOTAL calculated by the two different formulas, for MW and M31. Both the Direct mass and the NFW mass formula gives similar values to R200-TOTAL and the M200-TOTAL, compatibles with the equality if it is considered the error measures. Test II. Using the M200-TOTAL, given by the NFW method, is calculated the parameter
a
2
which is compared with the one got in the framework of DMbQG theory. This process is made in MW and M31 and the comparison is compatible with the equality if it is considered the error measures. Test III. Is similar to test II but using the R200-TOTAL and the M200-TOTAL and the result is successful as well. Test IV. The direct mass function and the NFW-total mass function are compared into the halo region up to R200-TOTAL. It is proved that its relative differences are below 10% into a wide region of the galactic halo up to R200-TOTAL and beyond. Although the thesis of this paper is for any galaxies, the calculus has been made with MW and M31, because they are the best well studied galaxies and his data have the maximum of accuracy. The prove reach in this paper is valuable because the NFW is a trustable profile for DM, tested in thousands of galaxies, and although the DMbQG theory claims that DM has an unbounded halo region, it gives similar results in the halo region common for both theories i.e. up to the virial radius.