Astrophysics

   

Two New Non Baryonic Dark Matter Density Profiles for Milky Way Halo

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 [17] 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, [8] 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 [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 [ 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 [17] Bhattacharjee, P.2014 and Direct DM got from rotation curve [5] 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. [5] 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 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. Parameters A&B are recalculated in order to be coherent with regression analysis and dimensional analysis. Namely, power of E become 5/3 instead to be decimal number coming from regression analysis and formulas acquire a new elegant aspect. In tenth chapter is got and solved the differential equation for gravitational field E, inside solar system, accepting the same new values A& B recalculated for M31 galaxy. It is got a formula for E, which tend to Newtonian formula if it is neglected the dark matter term. This fact is a strong back to power B=5/3 found by dimensional analysis. Also it is calculated dark matter contained inside spherical corona definite by perihelion and aphelion radius of Mercury. It has been got 3.2 times MEARTH which is a considerable amount of dark matter. By qualitative reasoning it is defended that this excessive amount of dark matter suggest that cannot be accepted the coefficient A got for M31 when is calculated dark matter inside Solar system because both gravitational systems have a tremendous different sizes.

Comments: 27 Pages. It is a bit clear than the previous one.

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Submission history

[v1] 2017-01-28 10:24:55
[v2] 2017-08-23 10:55:55 (removed)
[v3] 2017-08-24 08:41:06
[v4] 2017-08-25 09:04:21
[v5] 2017-09-18 16:06:01
[v6] 2017-10-08 16:45:00
[v7] 2019-09-10 16:01:20
[v8] 2019-09-17 17:00:50

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