**Authors:** Manuel Abarca Hernandez

In this work has been calculated two new DM density profiles inside halo region of Milky Way, MW hereafter, and it has been demonstrated that both ones are mathematically equivalents. The first 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. In fact this function got by power regression has a correlation coefficient of 0,85. The second one, DM density as power of E, E is gravitational field, has been introduced by author in previous papers, [8] Abarca,M.2016, where it has been used to study 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 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 [1] Abarca,M.2014. Dark matter model by quantum vacuum. [8] 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 [5] Sofue,Y.2015. In addition it is got a power regression for rotation curve points in halo region whose function is v = a•r^b getting a correlation coefficient bigger than 0,85. 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 function got in chapter three. In fifth chapter it has been demonstrated that a power regression function for rotation curve is mathematically equivalent that DM density depend 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 rotation curve). In sixth chapter it has been got that for radius bigger than 44 kpc ratio baryonic density versus DM density is under 2% so it is reasonable to consider negligible baryonic density in order to develop theory introduced in this work. The seventh is a short chapter where is compared direct DM density got with NFW density profile fitted by Sofue in his paper. [5] Sofue, Y.2015. Relative differences between both density profiles are under 25% inside main part of halo dominion. In addition it is explained why NFW profile is bigger than direct DM throughout dominion. Eighth chapter, called Masses in Milky Way, is dedicated to calculate masses through dynamical method and NFW profile. In addition both methods are compared at different radius. Results show that relative differences of masses are under 20% inside main part of radius dominion. In ninth 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 tenth chapter, it is introduced a new definition for halo radius. According theory DM generated by gravitational field, it is right to definite halo as region where gravitational field dominate over gravitational field of galactic neighbour. So it is calculated that halo radius for MW is 292 kpc and halo radius for M31 is 478 kpc. Also are calculated total masses which belong these new radius and it is calculated new ratio baryonic mass vs total mass. Such ratio is 18% for MW and 8 % for M31.

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[v1] 2016-09-07 03:42:13

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