Authors: Manuel Abarca Hernandez
In this work has been calculated two new non baryonic DM density profiles inside halo region of Milky Way, MW hereafter, and it has been demonstrated that both ones are mathematically equivalents. Data have been got from rotation curve published in  Bhattacharjee, P.2014. The first profile is called Direct DM density because it is got directly from velocity as power regression of radius in halo rotation curve. In other words velocity of rotation curve depend on radius as a power function. The second one, DM density as power of E, E is gravitational field, has been introduced by author in previous papers,  Abarca,M.2016, where it has been used to study non baryonic DM in several galaxies. It is called “as power of E” because DM density depend on E as a power function. Hypothesis which is the basis of theory is that non baryonic DM is generated locally by the own gravitational field according a power law. DM density = A• E^B where A& B are coefficients and E is gravitational intensity of field. To find reasons that author has to do so daring statement, reader can consult  Abarca,M.2014. Dark matter model by quantum vacuum.  Abarca,M.2016. Dark matter density on big galaxies depend on gravitational field as Universal law and other papers quoted in bibliography. Briefly will be explained method followed to develop this paper. Firstly are presented rotation curve and table with data points inside MW halo. These data come from [ 17] Bhattacharjee, P. Chaudary, S. Kundu, S.2014. In addition it is fitted a power regression of rotation curve points in halo region whose function is v = a•r^b . In fourth chapter it is developed a mathematical method to get a new DM density depending on radius called direct DM density because it is got directly from power regression of velocity depending on radius. Also it is compared Direct DM got from rotation curve  Bhattacharjee, P.2014 and Direct DM got from rotation curve  Sofue, Y.2015. It is shown that relative difference oscillates between 2.6% at 40 kpc and 3.8 % at 190 kpc which is a very exiguous difference. It is a very good news that two prominent teams of researchers got so similar results. In fifth chapter it has been demonstrated that Direct DM profile is mathematically equivalent to DM density depending on gravitational field, as a power function i.e. DM density = A• E^B, where A& B are cleared up depending on a & b (parameters of power regression of velocity). In sixth chapter it has been got that for radius bigger than 40 kpc ratio baryonic density versus DM density is under 4% so it is reasonable to consider negligible baryonic density in order to develop theory introduced in this work. In seventh chapter is compared Direct DM density got in this paper with NFW density profile fitted by Sofue in his paper.  Sofue, Y.2015. Throughout dominion NFW profile is bigger than Direct DM profile. Its relative difference oscillate between 25% at 40 kpc and 22% at 190 kpc. In my opinion this remarkable fact could be explained because NFW profile is fitted with total DM enclosed inside galactic disc and as it is known inside bulge and disc there is an unknown amount of baryonic DM such as dwarf browns and cold gas clouds. However Direct DM profile is fitted with data which radius are bigger than 40 kpc where baryonic matter is negligible. It is clear that extra DM density data inside disc have influence over the whole NFW profile so it is right to conclude that relative difference between Direct DM and NFW profile might be explained by baryonic DM inside bulge and disc. In eight chapter is compared DM density as power E in MW with DM density as power E in M31, which was published in [ 11] Abarca,M.2016. Results show that at a specific E, both DM densities are very similar. Relative differences are under 15 % inside main part of dominion. This fact support strongly author hypothesis about DM as power of E as Universal law. In ninth chapter it is made dimensional analysis for DM density formula through Buckingham theorem with one pi monomial (G and h as universal constant), and two pi monomials with G, h and c as universal constant. Through a mathematical analysis it is it is rejected density formula with only one pi monomial so it is needed to consider density formula with two pi monomials. Physically it is right because according my theory DM density it is generated by a quantum gravitational phenomena which include virtual particles whose speed is c.
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