Robust Constraint on a Drifting Proton-to-Electron Mass Ratio at $z\mathbf{=}0.89$ from Methanol Observation at Three Radio Telescopes

A limit on a possible cosmological variation of the proton-to-electron mass ratio $\mu$ is derived from methanol (${\mathrm{CH}}_3\mathrm{OH}$) absorption lines in the benchmark PKS1830–211 lensing galaxy at redshift $z=0.89$ observed with the Effelsberg 100-m radio telescope, the Institute de Radio Astronomie Millimétrique 30-m telescope, and the Atacama Large Millimeter/submillimeter Array. Ten different absorption lines of ${\mathrm{CH}}_3\mathrm{OH}$ covering a wide range of sensitivity coefficients $K_{\mu }$ are used to derive a purely statistical $1\sigma$ constraint of $\Delta \mu /\mu =(1.5\pm 1.5)\times {10}^{-7}$ for a lookback time of 7.5 billion years. Systematic effects of chemical segregation, excitation temperature, frequency dependence, and time variability of the background source are quantified. A multidimensional linear regression analysis leads to a robust constraint of $\Delta \mu /\mu =(-1.0\pm {0.8}_{\mathrm{stat}}\pm {1.0}_{\mathrm{sys}})\times {10}^{-7}$.

Figure 1

Some of the observed methanol transitions toward PKS1830–211 with their approximate observed frequencies ${\nu }_{\mathrm{obs}}$, observation epoch, sensitivity coefficients $K_{\mu }$, and channel spacings $dv$ indicated in each panel for recordings at (a) the Effelsberg radio telescope, (b) the IRAM 30-m telescope, and (c) the ALMA array. The intensity is normalized to the total continuum flux, except for (c), where the SW image could be observed exclusively. Gaussian fits to the absorption profiles are displayed in light green with residuals shown at the top of each panel.

Figure 2

The positions of the ten observed methanol lines (represented by $V_{\mathrm{LSR}}/c$ with respect to $z=0.88582$) are plotted versus their sensitivity coefficients $K_{\mu }$. Note that some transitions were observed multiple times; hence, 17 data points are displayed. The slope of a straight line fitted to the data set represents $-\Delta \mu /\mu$. The $A$ transitions observed at Effelsberg are offset from $K_{\mu }=-1$ to 0 for clarity.

Figure 3

The positions of 16 observed methanol absorptions (leaving out the data point measured in 2009) as a function of various parameters: (a) symmetry, (b) excitation temperature of the lower level, (c) epoch of observation, and (d) observed frequency. The color coding is the same as in Fig. 2. The solid lines show a fit using a linear or quadratic function of form $y=a_0+a_{1}x+a_2{x}^2$.