Searching for spatial variations ofα²/μin the Milky Way

Aims. We probe the dependence of α2/μ on the ambient matter density by means of spectral observations in submm- and mm-wave bands. Methods. A procedure is suggested for exploring the value of F = α2/μ, where μ = me/mp is the electron-to-proton mass ratio, and α = e2/ is the fine-structure constant. The fundamental physical constants, which are measured in different physical environments of high (terrestrial) and low (interstellar) densities of baryonic matter are supposed to vary in chameleon-like scalar field models, which predict that both masses and coupling constant may depend on the local matter density. The parameter ΔF/F = (Fobs – Flab)/Flab can be estimated from the radial velocity offset, ΔV = Vrot – Vfs, between the low-laying rotational transitions in carbon monoxide 13CO and the fine-structure transitions in atomic carbon [C i]. A model-dependent constraint on Δα/α can be obtained from ΔF/F using Δμ/μ independently measured from the ammonia method. Results. Currently available radio astronomical datasets provide an upper limit on |ΔV| < 110 m s-1 (1σ). When interpreted in terms of the spatial variation of F, this gives |ΔF/F| < 3.7 × 10-7. An order of magnitude improvement in this limit will allow us to independently test a non-zero value of Δμ/μ = (2.2 ± 0.4stat ± 0.3sys) × 10-8, recently found with the ammonia method. Considering that the ammonia method restricts the spatial variation of μ at the level of |Δμ/μ| ≤ 3 × 10-8 and assuming that ΔF/F is the same in the entire interstellar medium, one obtains that the spatial variation of α does not exceed the value |Δα/α| < 2 × 10-7. Since extragalactic gas clouds have similar densities to those in the interstellar medium, the bound on Δα/α is also expected to be less than 2 × 10-7 at high redshift if no significant temporal dependence of α is present.