Monday, July 06, 2015

Astrophysical Constraints on Dark Energy v2

This is v2 of a draft we posted earlier in the year. The new version has much more detail on whether rotation curve measurements of an isolated dwarf galaxy might be able to constrain the local dark energy density. As we state in the paper (c is the local dark energy density):
In Table V, we simulate the results of measurements on v 2 (r) with corresponding error of 1%. We take ρ0 ∼ 0.2 GeV cm−3 and Rs ∼ 0.795 kpc for the dwarf galaxies. We vary the number of satellites N and their (randomly generated) orbital radii. For example, at 95% confidence level, one could bound c to be positive using 5 satellites at r ∼ 1 − 10 kpc. In order to bound c close to its cosmological value, one would need, e.g., at least 5 satellites at r ∼ 10 − 20 kpc or 10 satellites at r ∼ 5 − 15 kpc. 
... In Table VI, we simulate the results from measurements on v2(r), assuming that the corresponding error is 5%. Again, we take ρ0 ∼ 0.2 GeV cm3 and Rs ∼ 0.795 kpc for the dwarf galaxies. The table indicates that even at the sensitivity of 5%, one could rule out (at 95% confidence level) any Λ that is significantly larger than 1.58×1084 GeV2 by using, e.g., 5 satellites at r ∼ 1−10 kpc. The very existence of satellites of dwarf galaxies (even those close to the Milky Way, and hence subject to significant tidal forces that limit r) provides an upper limit on the local dark energy density, probably no more than an order of magnitude larger than the cosmological value.  
Since we are not real astronomers, it is unclear to us whether measurements of the type described above are pure science fiction or something possible, say, in the next 10-20 years. Multiple conversations with astronomers (and referees) have failed to completely resolve this issue. Note that papers in reference [11] (Swaters et al.) report velocity measurements for satellites of dwarf galaxies at radii ~ 10 kpc with existing technology.
Astrophysical Constraints on Dark Energy

Chiu Man Ho, Stephen D. H. Hsu
(Submitted on 23 Jan 2015 (v1), last revised 3 Jul 2015 (this version, v2))

Dark energy (i.e., a cosmological constant) leads, in the Newtonian approximation, to a repulsive force which grows linearly with distance and which can have astrophysical consequences. For example, the dark energy force overcomes the gravitational attraction from an isolated object (e.g., dwarf galaxy) of mass 107M⊙ at a distance of 23 kpc. Observable velocities of bound satellites (rotation curves) could be significantly affected, and therefore used to measure or constrain the dark energy density. Here, {\it isolated} means that the gravitational effect of large nearby galaxies (specifically, of their dark matter halos) is negligible; examples of isolated dwarf galaxies include Antlia or DDO 190.

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