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A new model of dark matter distribution in galaxies

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Abstract

In the absence of the physical understanding of the phenomenon, different empirical laws have been used as approximation for distribution of dark matter in galaxies and clusters of galaxies. We suggest a new profile which is not empirical in nature, but motivated with the physical idea that what we call dark matter is essentially the gravitational polarization of the quantum vacuum (containing virtual gravitational dipoles) by the immersed baryonic matter. It is very important to include this new profile in forthcoming studies of dark matter halos and to reveal how well it performs in comparison with empirical profiles. A good agreement of the profile with observational findings would be the first sign of unexpected gravitational properties of the quantum vacuum.

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Correspondence to Dragan Slavkov Hajdukovic.

Appendix: A constant dark matter halo surface density in galaxies

Appendix: A constant dark matter halo surface density in galaxies

Recently, using the Burkert profile (1), Donato et al. (2009) have concluded that relation ρ 0 r 0≈constant is valid over a range of 14 mag in luminosity and for all Hubble types:

$$ \rho_{0}r_{0} = 140_{ - 30}^{ + 80} \frac{M_{Sun}}{pc^{2}} $$
(15)

The work of Donato et al. confirms and extends the previous findings (Kormendy and Freeman 2004; Spano et al. 2008). In the pioneering work, Kormendy and Freeman (2004) have shown that if dark matter distribution is modeled by “pseudo-isothermal sphere” the quantity ρ 0 r 0 is just below 100M Sun /pc 2 (see Fig. 5 in their paper). It is important to note that while we have used the same notation for the free parameters ρ 0,r 0 they have different values for the Burkert profile and pseudo-isothermal sphere. Spano et al. (2008) have modeled dark matter halo with a cored isothermal sphere and have found that for 36 nearby spiral galaxies \(\rho_{0}r_{0} = 150_{-70}^{+100}M_{Sun} / pc^{2}\).

Let us rewrite Eq. (3) in the form

$$ \rho_{dm} ( r ) \cdot r = 2P_{g\max} \biggl[ \tanh \biggl( \frac{R_{c}}{r} \biggr) - \frac{R_{c}}{r}\frac{1}{2\cosh^{2} ( \frac{R_{c}}{r} )} \biggr] $$
(16)

Evidently, for r=R c , the quantity ρ dm (R c )⋅R c has the same value for all galaxies. More general, ρ dm (r)⋅r has the same value for different galaxies if r is chosen so that the ratio R c /r also has the same value for all considered galaxies. Additionally, let us note that expression in brackets in Eq. (16) changes slowly with R c /r; consequently ρ(r)⋅r≈constant if rR c or R c /r≈constant. This opens possibility to interpret relation ρ 0 r 0≈constant as a signature of the quantum vacuum.

Comparison of results (15) and (16) demands certain caution because there is a significant difference between the right-hand sides of these equations. In (16) we have o product of a distance r and dark matter density ρ dm (r) at that distance. However, in (15) the central density ρ 0 is a constant which is different from the dark matter density ρ B (r 0)=ρ 0/4 determined by Eq. (1).

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Hajdukovic, D.S. A new model of dark matter distribution in galaxies. Astrophys Space Sci 349, 1–4 (2014). https://doi.org/10.1007/s10509-013-1621-0

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