Erratum: Remarks on the spherical scalar field halo in galaxies [Phys. Rev. D80, 047301 (2009)]

Abstract

Matos, Guzmán and Nuñez proposed a model for the galactic halo within the framework of scalar field theory. We argue that an analysis involving the full metric can reveal the true physical nature of the halo only when a certain condition is maintained. We fix that condition and also calculate its impact on observable parameters of the model.One of the outstanding problems in modern astrophysics is the problem of dark matter which is invoked as an explanation for the observed flat rotation curves in the galactic halo. 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 interpret this result of observation is to accept that the mass M (r) increases linearly with distance r. Luminous mass distribution in the galaxy does not follow this behavior. Hence the hypothesis that there must be huge amounts of nonluminous matter hidden in the halo. This unseen matter is given a technical name dark matter.Despite the fact that the exact nature of dark matter is as yet unknown, several analytic halo models exist in the literature including those provided by scalar-tensor theories (see for instance [1]). In particular, the scalar field model first proposed by Matos, Guzmán and Nuñez [2] has received considerable attention. It is important to note that the authors primarily constructed an exact solution of Einstein's field equations sourced by a scalar field that provides a density profile of 1/r 2 together with other appealing features of the metric 1

Chromomagnetic and chromoelectric dipole moments of the top quark in the fourth-generation THDM

“…Since D R,4i and U R,4i parametrize the mixings between the quarks of the fourth-generation and those of the first three generations, Σ d ij and Σ u ij (i, j = 1, 2, 3) are expected to be very small. This fact becomes evident in the parametrization introduced in [70] in terms of one complex…”

“…Thus, |U tb | and ρ tb will be the only free parameters involved in the CMDM and CEDM. From the experimental data on Z, K, and B decays as well as B-meson mixing, the upper bound |U tb | < 0.12 was extracted [70]. We will then use |U tb | 10 −1 and ρ tb ∈ [−π, π].…”

“…(7) in terms of the complex parameters t and b , which means that η u 43 ≡ δ t and η d 43 ≡ δ b . However, there are no experimental bounds on these parameters, though the authors of [70]…”

Two diverse models of embedding class one

“…On the other hand, we also made use of Eq. (27), e λ(r) = (1 − b(r)/r + Q 2 /r 2 ) −1 , which gives us the effective shape function used in Ref. [23]:…”

“…To that end, let us return to Refs. [27]- [29], which deal with typical galaxies, including our own. Suppose we assume for now that B 0 = 1 in Eq.…”