Limits on a Gravitational Field Dependence of the Proton--Electron Mass Ratio from H$_2$ in White Dwarf Stars

Spectra of molecular hydrogen (H$_2$) are employed to search for a possible proton-to-electron mass ratio ($mu$) dependence on gravity. The Lyman transitions of H$_2$, observed with the Hubble Space Telescope towards white dwarf stars that underwent a gravitational collapse, are compared to accurate laboratory spectra taking into account the high temperature conditions ($T sim 13,000$ K) of their photospheres. We derive sensitivity coefficients $K_i$ which define how the individual H$_2$ transitions shift due to $mu$-dependence. The spectrum of white dwarf star GD133 yields a $Deltamu/mu$ constraint of $(-2.7pm4.7_{rm stat}pm 0.2_{rm sys})times10^{-5}$ for a local environment of a gravitational potential $phisim10^4 phi_textrm{Earth}$, while that of G29$-$38 yields $Deltamu/mu=(-5.8pm3.8_{rm stat}pm 0.3_{rm sys})times10^{-5}$ for a potential of $2 times 10^4$ $phi_textrm{Earth}$.

Robust Constraint on a Drifting Proton-to-Electron Mass Ratio at z=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 (CH$_3$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 Millim{e}trique 30-m telescope, and the Atacama Large Millimeter/submillimeter Array. Ten different absorption lines of CH$_3$OH covering a wide range of sensitivity coefficients $K_{mu}$ are used to derive a purely statistical 1-$sigma$ constraint of $Deltamu/mu = (1.5 pm 1.5) times 10^{-7}$ 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 multi-dimensional linear regression analysis leads to a robust constraint of $Deltamu/mu = (-1.0 pm 0.8_{rm stat} pm 1.0_{rm sys}) times 10^{-7}$.

Analysis of Molecular Hydrogen Absorption toward QSO B0642-5038 for a Varying Proton-to-Electron Mass Ratio

Rovibronic molecular hydrogen (H$_2$) transitions at redshift $z_{rm abs} simeq 2.659$ towards the background quasar B0642$-$5038 are examined for a possible cosmological variation in the proton-to-electron mass ratio, $mu$. We utilise an archival spectrum from the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of $sim$35 per 2.5-km$,$s$^{-1}$ pixel at the observed H$_2$ wavelengths (335--410 nm). Some 111 H$_2$ transitions in the Lyman and Werner bands have been identified in the damped Lyman $alpha$ system for which a kinetic gas temperature of $sim$84 K and a molecular fraction $log f = -2.18pm0.08$ is determined. The H$_2$ absorption lines are included in a comprehensive fitting method, which allows us to extract a constraint on a variation of the proton-electron mass ratio, $Deltamu/mu$, from all transitions at once. We obtain $Deltamu/mu = (17.1 pm 4.5_{rm stat} pm3.7_{rm sys})times10^{-6}$. However, we find evidence that this measurement has been affected by wavelength miscalibration errors recently identified in UVES. A correction based on observations of objects with solar-like spectra gives a smaller $Deltamu/mu$ value and contributes to a larger systematic uncertainty: $Deltamu/mu = (12.7 pm 4.5_{rm stat} pm4.2_{rm sys})times10^{-6}$.

Constraint on a variation of the proton-to-electron mass ratio from H2 absorption towards quasar Q2348-011

Molecular hydrogen (H2) absorption features observed in the line-of-sight to Q2348-011 at redshift zabs = 2.426 are analysed for the purpose of detecting a possible variation of the proton-to-electron mass ratio mu=mp/me. By its structure Q2348-011 is the most complex analysed H2 absorption system at high redshift so far, featuring at least seven distinctly visible molecular velocity components. The multiple velocity components associated with each transition of H2 were modeled simultaneously by means of a comprehensive fitting method. The fiducial model resulted in dmu/mu = (-0.68 +/- 2.78) x 10^-5, showing no sign that mu in this particular absorber is different from its current laboratory value. Although not as tight a constraint as other absorbers have recently provided, this result is consistent with the results from all previously analysed H2-bearing sight-lines. Combining all such measurements yields a constraint of dmu/mu < 10^-5 for the redshift range z = (2--3).

Search for cosmological mu variation from high redshift H2 absorption; a status report

Observations of H2 spectra in the line-of-sight of distant quasars may reveal a variation of the proton-electron mass ratio mu=m_p/m_e at high redshift, typically for z>2. Currently four high-quality systems (Q0347-383, Q0405-443, Q0528-250 and J2123-005) have been analyzed returning a constraint Dmu/mu < 1 x 10^{-5}. We present data and a mu-variation analysis of another system, Q2348-011 at redshift z_{abs}=2.42, delivering dmu/mu = (-1.5 pm 1.6) x 10^{-5}. In addition to observational data the status of the laboratory measurements is reviewed. The future possibilities of deriving a competitive constraint on Dmu/mu from the known high-redshift H2 absorbers is investigated, resulting in the identification of a number of potentially useful systems for detecting mu-variation.