Several aspects of the 4d imprint of the 5d bulk Weyl radiation are investigated within a recently proposed model solution. It is shown that the solution has a number of physically interesting properties. The constraints on the model imposed by combined measurements of rotation curve and lensing are discussed. A brief comparison with a well-known scalar field model is also given.Key words: gravitation -galaxies: general -galaxies: structure -dark matter.
I N T RO D U C T I O NEarly observations led to the hypothesis that there could be large amounts of non-luminous matter hidden in the galactic haloes (Oort 1930;Zwicky 1933Zwicky , 1937. Later observations of flat rotation curves of spiral galaxies confirmed the hypothesis (Freeman 1970;Roberts & Rots 1973;Ostriker, Peebles & Yahill 1974;Einasto, Kaasik & Saar 1974;Rubin, Thonnard & Ford 1978;Rubin, Roberts & Ford 1979;Sofue & Rubin 2001;Kochanek et al. 2005). Doppler emissions from stable circular orbits of neutral hydrogen clouds in the halo allow the measurement of tangential velocity v tg (r) of the clouds treated as probe particles. According to Newton's laws, centrifugal acceleration v 2 tg /r should balance the gravitational attraction GM(r)/r 2 , which immediately gives v 2 tg = GM(r)/r. That is, one would expect a fall-off of v 2 tg (r) with r. However, observations indicate that this is not the case: v tg approximately levels off with r in the halo region. The only way to reconcile this result of observation is to hypothesize that the mass M(r) increases linearly with distance r. Luminous mass distribution in the galaxy does not follow this behaviour. Hence, we conclude that there must be huge amounts of non-luminous matter hidden in the halo. This unseen matter is given a technical name, dark matter.
We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko et al. (2014). It turns out that stability depends more strongly on the dark matter central density ρ 0 than on other parameters of the solution. This property then yields an upper limit on ρ 0 for each individual galaxy, which we call here ρ upper 0 , such that stable circular orbits are possible only when the constraint ρ 0 ≤ ρ upper 0 is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius R DM ∼ 180 kpc and find that ρ upper 0 ∼ 2.37 × 10 11 M kpc −3 . This limit turns out to be about four orders of magnitude larger than the latest data on central density ρ 0 arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the EiBI solution could qualify as yet another viable alternative model for dark matter.
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