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 PKS1830-211. Obtaining 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, and (3) to evaluate the proton-to-electron mass ratio at redshift 0.9. 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 about 2000 cm-3 for the gas density of the south-western absorption component. 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 an excitation temperature of 11 K and a 1-sigma error of 3 K. For the south-eastern 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, with respect to its present value, to <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 smaller than 1 km/s, corresponding to an uncertainty of 10-6.