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

¹ INAF-Osservatorio Astronomico di Trieste, via G. B. Tiepolo 11, 34131 Trieste, Italy e-mail: lev@astro.ioffe.rssi.ru
² Key Laboratory for Research in Galaxies and Cosmology, Shanghai Astronomical Observatory, CAS, 80 Nandan Road, Shanghai 200030, PR China
³ Ioffe Physical-Technical Institute, Polytekhnicheskaya Str. 26, 194021 St. Petersburg, Russia
⁴ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany

Received: 27 October 2009
Accepted: 2 April 2010

Abstract

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 = m_e/m_p 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 = (F_obs – F_lab)/F_lab can be estimated from the radial velocity offset, ΔV = V_rot – V_fs, 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 ± 0.4_stat ± 0.3_sys) × 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.