Inverse biquadrate force might be proved with inverse square attenuation of light intensity.

## Attenuation by the spaceEdit

Unit time areal density of momentum is normally dependent on Inverse square of distance for perfect vacuum without any absorption, scattering and reflection by dark matter. Optical attenuation by Solid is described by the factor of exp(-kr). Although 1/rr factor is abnormal for opotics. density variation of dark matter from the astronomic object isn't negligible and is proportianl to -ln(rr)/r which is primitive.

Function -2lnr/r has a minimum about -0.74 at r=2.73 and asymtotically approaches to 0.

Density function inbetween the astronomical objects may be rewritten.

$ D(r)/D_0 = C_l - 2 lnr/r $

where $ C_l > $ 0.74 and r is also normalized value of distance r=d/$ r_0 $

To find $ r_0 $ & $ D_0 $; out is very necessary to proceed. Temperature and mass density against altitude from the NRLMSISE-00 standard atmosphere model shows that local minimum is between 100km and 160km.

## Rigorous approachEdit

Above equation is not rigorous.

$ A = \Pi exp(-k_x (r) \Delta r) =exp(- \int k_x(r) dr ) $

where $ k_x (r) $ is extinction coefficients.

Inverse square attenuation is given by the following equations.

$ \int k_x(r) dr = 2ln(r) $

$ k_x(r) = 2/r $

Which is assumed to be propotional to the density of the space.

## Rotation curves as evidence of a dark matter haloEdit

The presence of dark matter in the halo is demonstrated by its gravitational effect on a spiral galaxy's rotation curve. Without large amounts of mass in the extended halo, the rotational velocity of the galaxy should decrease at large distance from the galactic core. However, observations of spiral galaxies, particularly radio observations of line emission from neutral atomic hydrogen (known, in astronomical parlance, as HI), show that the rotation curve of most spiral galaxies remains flat far beyond the visible matter. The absence of any visible matter to account for these observations implies the presence of unobserved (i.e. dark) matter. Asserting that this dark matter does not exist would mean that the accepted theory of gravitation (General Relativity) is wrong, and while that could be possible, most scientists would require extensive amounts of compelling evidence before considering it.

The Navarro-Frenk-White profile:^{[5]}

$ \rho(r)=\frac{\rm constant}{(r/a)(1+r/a)^2} $

is often used to model the distribution of mass in dark matter halos. Theoretical dark matter halos produced in computer simulations are best described by the Einasto profile:^{[6]}

$ \rho(r) = \rho_0 e^{-\alpha r^n}. $

## See alsoEdit

## ReferencesEdit

- ↑ Peter Schneider (2006).
*Extragalactic Astronomy and Cosmology*, Springer. p. 4, Figure 1.4. ISBN 3540331743, http://books.google.com/books?id=uP1Hz-6sHaMC&pg=PA100&dq=rotation+Milky+way&lr=&as_brr=0&as_pt=ALLTYPES#PPA5,M1. - ↑ Theo Koupelis, Karl F Kuhn (2007).
*In Quest of the Universe*, Jones & Bartlett Publishers. p. 492; Figure 16-13. ISBN 0763743879, http://books.google.com/books?id=6rTttN4ZdyoC&pg=PA491&dq=Milky+Way+%22rotation+curve%22&lr=&as_brr=0&as_pt=ALLTYPES#PPA492,M1. - ↑ Mark H. Jones, Robert J. Lambourne, David John Adams (2004).
*An Introduction to Galaxies and Cosmology*, Cambridge University Press. p. 21; Figure 1.13. ISBN 0521546230, http://books.google.com/books?id=36K1PfetZegC&pg=PA20&dq=Milky+Way+%22rotation+curve%22&lr=&as_brr=0&as_pt=ALLTYPES#PPA21,M1. - ↑ After Peratt, A. L., "Advances in Numerical Modeling of Astrophysical and Space Plasmas" (1966)
*Astrophysics and Space Science*, v. 242, Issue 1/2, p. 93-163. - ↑ Navarro, J. et al. (1997), A Universal Density Profile from Hierarchical Clustering
- ↑ Merritt, D.
*et al.*(2006), Empirical Models for Dark Matter Halos. I. Nonparametric Construction of Density Profiles and Comparison with Parametric Models