# Constraining the Proton-to-Electron Mass Ratio over Cosmic Time

Authors: S. P. Ellingsen, M. A. Voronkov, S. L. Breen, J. E. J. Lovell

First Author’s Institution: School of Mathematics and Physics, University of Tasmania

The idea that fundamental constants are just that — constant — underlies our entire model of the universe.  But how do we know that this is true?  One way of determining whether there have been temporal or spatial changes in these constants is to observe them in highly-redshifted objects.  This way, we can see them as emitted when the universe was significantly younger, as opposed to just measuring present-day laboratory values.  This paper attempts to determine whether the proton-to-electron mass ratio has changed over the past 7.24 Gyr, using an unexplored rotational transition in the absorption spectrum of methanol.

Fundamental Constants and Methanol Transitions

In general, changes in values such as the fine-structure constant $\alpha$, proton-to-electron mass ratio $\mu$, and nuclear g-factor $g$ can be measured through the comparison of the frequency of two transitions which have different sensitivities to variations in these constants: $\frac{\Delta \nu}{\nu} = K_{\alpha} \frac{\Delta \alpha}{\alpha} + K_{\mu} \frac{\Delta \mu}{\mu} + K_{g} \frac{\Delta g}{g}$, where the Ks represent the sensitivity of a particular transition to these changes.  Recent studies have shown that certain rotational transitions in methanol are highly sensitive to changes in the proton-to-electron mass ratio, and are therefore ideal for constraining this parameter.   By comparing the line-of-sight velocities (that is, the center frequencies) of two different methanol transitions emitted from the same region, a constraint on this ratio can be made.

An absorption spectrum of the transition, displayed as flux vs. velocity (or equivalently, observing frequency) will show a characteristic dip where the molecule absorbs radiation.  Any significant offset in the location of the dip between two rotational transitions would indicate that the proton-to-electron mass ratio was different when the object did the absorbing.  In this study, the authors observed methanol’s $2_0 \rightarrow 3_{-1}E$ transition and compared it to a previously-measured value of the $1_0 \rightarrow 2_{-1}E$ transition.

Observations

Using the Australia Telescope Compact Array (ATCA), an array of six 22-meter radio dishes, the authors observed the gravitational lens system PKS B1830-211, which consists of a quasar at redshift z = 2.507 and a primary lensing galaxy at z = 0.88582.  The lensing galaxy is nearly face-on, and previous observations have identified over 30 molecular species in it, including methanol.

The transition of interest, $2_0 \rightarrow 3_{-1}E$, has a rest frame frequency of 12.2 GHz which is redshifted to about 6.45 GHz in the lens galaxy.  The Compact Array Broadband Backend on ATCA observed the transition with 17408 spectral channels over a bandwidth of 8.5 MHz centered at 6.547 GHz, giving a spectral resolution of 488 Hz.  After taking redshift into account, the velocity resolution in the rest frame of the absorbing methanol is 2.9 km/s.  Figure 1 shows the spectrum; notice the main absorption feature close to 0 km/s.

Figure 1: The absorption from the 12.2 GHz transition of methanol at -5 km/s.

Results

To look for potential changes in the proton-to-electron mass ratio, the authors compared the above spectrum to another taken by Muller et al. (2011) of the $1_0 \rightarrow 2_{-1}E$ transition (Figure 2: rest frame frequency 60.5 GHz, redshifted to 32.1 GHz).  After applying the same redshift correction to both spectra, they fit Gaussian profiles to the lines and compared the velocities of absorption.  The difference between the lines was -0.6 + 1.6 km/s, which constrains the change in the proton-to-electron mass ratio from z = 0.89 to the present to $0.8 \pm 2.1 \times 10^{-7}$.

Figure 2: The absorption from the 60.5 GHz transition of methanol at -4 km/s.

This result is consistent with and of similar precision to other observations, and is the furthest back that this constraint has been made.  Future measurements incorporating more rotational transitions may improve the results by a factor of up to 5-10.

I am a third-year graduate student in the Astronomy Department at Harvard University, and am interested in cosmology and instrumentation for radio telescopes. I work with John Kovac on several telescopes at the South Pole designed to detect the signature of inflation in the cosmic microwave background. In 2011, I graduated from Caltech with a degree in physics. I worked with Tony Readhead to build a Ku-Band polarimeter for the 40-Meter telescope at the Owens Valley Radio Observatory, and with John Johnson on M Dwarf Metallicities.