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

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany e-mail: chenkel@mpifr-bonn.mpg.de
² Centre for Astrophysics and Supercomputing, Swinburne University, PO Box 218, Victoria 3122, Australia
³ National Institute of Standards and Technology, M.S. 817.03, 325 Broadway, 80305 Boulder, USA
⁴ School of Physics, University of New South Wales, Sydney, N.S.W. 2052, Australia
⁵ National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
⁶ Academia Sinica Institute of Astronomy and Astrophysics, PO Box 23–141, Taipei, 106, Taiwan
⁷ Onsala Space Observatory, 439–92 Onsala, Sweden
⁸ CalTech, 1200 E. California Blvd., Caltech Astronomy, 105–24, Pasadena, CA 91125–2400, USA
⁹ Purple Mountain Observatory, Chinese Academy of Sciences, 210008 Nanjing, PR China

Received: 4 December 2008
Accepted: 26 March 2009

Abstract

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 . Analyzing data from six rotational HC₃N transitions (this includes the line, which is likely detected for the first time in the interstellar medium) we obtain n(H₂) ~ 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 (the maximal exponent permitted by observational boundary conditions), n(H₂) ~ 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,  K. However, individually, there is a surprisingly large scatter which far surpasses expected uncertainties. A comparison of CS and optical depths toward the weaker north-western absorption component results in  K and a 1-σ 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 μ to with 3-σ confidence. Also including optically thin rotational lines from other molecular species, it is emphasized that systematic errors are  km s^-1, corresponding to .