2009A&A...500..725H

Based on measurements with the Effelsberg 100-m telescope, a multi-line study of molecular species is presented toward the gravitational lens system PKS1830-211, which is by far the best known target to study dense cool gas in absorption at intermediate redshift. Determining average radial velocities and performing Large Velocity Gradient radiative transfer calculations, the aims of this study are (1) to determine the density of the gas, (2) to constrain the temperature of the cosmic microwave background (CMB), and (3) to evaluate the proton-to-electron mass ratio at redshift z∼0.89. Analyzing data from six rotational HC₃N transitions (this includes the J=7←6 line, which is likely detected for the first time in the interstellar medium) we obtain n(H₂)∼2600cm^–3 for the gas density of the south-western absorption component, assuming a background source covering factor, which is independent of frequency. With a possibly more realistic frequency dependence proportional to ν^0.5 (the maximal exponent permitted by observational boundary conditions), n(H₂)∼1700cm^–3. Again toward the south-western source, excitation temperatures of molecular species with optically thin lines and higher rotational constants are, on average, consistent with the expected temperature of the cosmic microwave background, T_CMB=5.14K. However, individually, there is a surprisingly large scatter which far surpasses expected uncertainties. A comparison of CS J=1←0 and 4←3 optical depths toward the weaker north-western absorption component results in T_ex=11K and a 1-σ error of 3K. For the main component, a comparison of velocities determined from ten optically thin NH₃ inversion lines with those from five optically thin rotational transitions of HC₃N, observed at similar frequencies, constrains potential variations of the proton-to-electron mass ratio µ to Δµ/µ<1.4x10^–6 with 3-σ confidence. Also including optically thin rotational lines from other molecular species, it is emphasized that systematic errors are ΔV<1km/s, corresponding to Δµ/µ<1.0x10^–6.