Astrophysics

   

Dark Matter Density Function Depending on Intensity of Gravitational Field as Universal Law

Authors: Manuel Abarca Hernandez

Dark Matter Density Function Depending on Gravitational Field as Universal Law The purpose this work is to study density function of Dark Matter (D.M.) depending on E, total intensity of gravitational field, in a group of six big spiral galaxies and try to explore a possible Universal law between both magnitudes. Galaxies selected are the following ones: Milky Way, M31, NGC 3031, NGC 3992, NGC 7331, NGC 2841 The reason why it has been made this work is to check the model of DM proposed by the author in his previous paper [5] Abarca,M.2014 viXra. Dark Matter model by quantum vacuum. Briefly, in that work was exposed a original theory of DM. This new theory defends that DM is generated by the own gravitational field according an unknown quantum gravitational mechanism. In other words, Density of Dark Matter in a point P of space, depend on E, according a Universal law. Therefore if two different points P and Q belonging different galaxies had the same E, intensity of gravitational field, then they should have the same density of DM. In short, If E(P) = E(Q) then Density DM(P) = Density DM (Q). In the present paper, for each galaxy it will be calculated E, total intensity of gravitational field, depending on R. This calculus is carry out through the Rotational Curve and the Virial Theorem. In addition, for each galaxy it is considered a Dark matter density function, which is tabulated depending on R. After, it is plotted DM density depending on E. Data of eight galactic set are studied statistically and it is concluded that its coefficient correlation is enough high to fit a potential function to DM density depending on E. Statistical process has been carefully detailed through the paper, so I have found plausible to postulate this function as Universal for big galaxies. I have considered a big galaxy if its velocity inside its flat region of rotation curve is up to 200 Km/s. Dark matter function Density as Universal law for big galaxies Density DM = 1,26 • 10^ - 6 • E^ B where B = 1,74 inside a dominion 100 < E < 6500 Where Unit for Density D.M. is 10^ -3 MSUN /pc^3 or m MSUN /pc^3 and Unit for E is Km^ 2 / s^ 2 / Kpc The same function with other suitable system of units is Density DM = 3,7323 • 10^ 17 • E^ B being B = 1,74 Where Unit for Density D.M. is mMSUN /pc^3 and Unit for E is m/s^2. In chapter 12 it is calculated Local DM density (Sun region). Recent measures of Sun are Radius = and Sun Velocity = With such values, intensity of gravitational field in Sun Region ESUN = Km^2/s^2/ Kpc and Density DM in Sun region = 6,45 mMSUN / pc^3 = 0,245 GeV/cm^3 . This value agrees with direct measures of Local DM density. In chapter 14, DM density potential function has been checked with NFW profile in Milky Way and it has been found that agreement between both curves are mainly under 10 % inside the whole dominion up to 375 Kpc which is an excellent agreement in astrophysics¡. In chapter 15, DM density potential function has been checked with NFW profile in M31.Although the agreement between both functions is not so good as in Milky Way case, relative error is enough small to accept that M31 supports DM density potential function. In chapter 16, density potential function is written depending on radius x, and it is clearly showed that this function is equivalent to NFW, relative error inside the whole dominion are enough small that they could be considered come from error in astronomical measures. Finally in chapter 17 has been got a Bernoulli differential equation for gravitational field which allows to calculate potential density function depending on radius. In addition potential function has been compared with NFW density function through halo region and it has been found that relative differences are below 13% in Milky Way and below 16% in M31 galaxy. This is a superb result as can understand any astrophysicist ¡ In my opinion, it has been justified properly that results could confirm DM density as universal law, especially if it is considered experimental error in rotation curves and error in calculus of DM density functions. The author think that it may be worth to study a bigger number of galaxies in order to check or reject results got in this paper because Dark matter nature is one of the most important challenges for astrophysics science nowadays.

Comments: 76 Pages. In this version it has been got a Bernouilli differential equation for gravitational field which allows to calculate DM density depending on radius.

Download: PDF

Submission history

[v1] 2015-10-18 16:35:46
[v2] 2015-10-20 14:34:31
[v3] 2015-10-24 17:31:34
[v4] 2015-10-28 15:11:06
[v5] 2015-11-02 07:55:13
[v6] 2015-11-03 10:15:08
[v7] 2015-11-09 13:46:33
[v8] 2015-11-29 17:53:30

Unique-IP document downloads: 346 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus