Searching for spatial variations of α2/μ in the Milky Way

Aims. We probe the dependence of alpha(2)/mu 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 = alpha(2)/mu, where mu = m(e)/m(p) is the electron-to-proton mass ratio, and alpha = e(2)/((h) over barc) 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 Delta F/F = (F-obs - F-lab)/F-lab can be estimated from the radial velocity offset, Delta V = V-rot - V-fs, between the low-laying rotational transitions in carbon monoxide (CO)-C-13 and the fine-structure transitions in atomic carbon [C I]. A model-dependent constraint on Delta alpha/alpha can be obtained from Delta F/F using Delta mu/mu independently measured from the ammonia method. Results. Currently available radio astronomical datasets provide an upper limit on vertical bar Delta V vertical bar < 110 m s(-1) (1 sigma). When interpreted in terms of the spatial variation of F, this gives vertical bar Delta F/F vertical bar < 3.7 x 10(-7). An order of magnitude improvement in this limit will allow us to independently test a non-zero value of Delta mu/mu = (2.2 +/- 0.4(stat) +/- 0.3(sys)) x 10(-8), recently found with the ammonia method. Considering that the ammonia method restricts the spatial variation of mu at the level of vertical bar Delta mu/mu vertical bar <= 3x10(-8) and assuming that Delta F/F is the same in the entire interstellar medium, one obtains that the spatial variation of a does not exceed the value vertical bar Delta alpha/alpha vertical bar < 2 x 10(-7). Since extragalactic gas clouds have similar densities to those in the interstellar medium, the bound on Delta alpha/alpha is also expected to be less than 2 x 10(-7) at high redshift if no significant temporal dependence of alpha is present.