The density, the cosmic microwave background, and the proton-to-electron mass ratio in a cloud at redshift 0.9

Based on measurements with the Effelsberg 100-m telescope, a multi-line study of molecular species is presented toward the gravitational lens system PKS 1830-211, 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 similar to 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(H-2) similar to 2600 cm(-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 nu(0.5) (the maximal exponent permitted by observational boundary conditions), n(H-2) similar to 1700 cm(-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 = 5.14 K. 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 = 11 K and a 1-sigma error of 3 K. 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 mu to Delta mu/mu < 1.4 x 10(-6) with 3-sigma confidence. Also including optically thin rotational lines from other molecular species, it is emphasized that systematic errors are Delta V < 1 km s(-1), corresponding to Delta mu/mu < 1.0 x 10(-6).