Variations in the fundamental constants in the QSO host J 1148 + 5251 at z = 6 . 4 and the BR 1202 − 0725 system at z = 4 . 7

We use sensitive observations of three high-redshift sources: [C II] P3/2 → P1/2 finestructure and CO (J = 2 → 1) rotational transitions for the z = 6.4 quasar (QSO) host galaxy J1148+5251 taken with the Plateau de Bure Interferometer (PdBI) and Jansky Very Large Array, respectively, and [C II] and CO (J = 5 → 4) transitions from the QSO BR1202−0725 and its companion sub-millimetre galaxy (SMG) at z = 4.7 taken with the Atacama Large Millimeter Array and the PdBI. We use these observations to place constraints on the quantity z = zCO − zC II for each source where zCO and zC II are the observed redshifts of the CO rotational transition and [C II] fine-structure transition, respectively, using a combination of approaches: (1) modelling the emission line profiles using ‘shapelets’ – a complete orthonormal set of basis functions that allow us to recreate most physical line shapes – to compare both the emission redshifts and the line profiles themselves, in order to make inferences about the intrinsic velocity differences between the molecular and atomic gas, and (2) performing a marginalization over all model parameters in order to calculate a non-parametric estimate of z. We derive 99 per cent confidence intervals for the marginalized posterior of z of (−1.9 ± 1.3) × 10−3, (−3 ± 8) × 10−4 and (−2 ± 4) × 10−3 for J1148+5251, and the BR1202−0725 QSO and SMG, respectively. We show that the [C II] and CO (J = 2 → 1) line profiles for J1148+5251 are consistent with each other within the limits of the data, whilst the [C II] and CO (J = 5 → 4) line profiles from the BR1202−0725 QSO and SMG, respectively, have 65 and >99.9 per cent probabilities of being inconsistent, with the CO (J = 5 → 4) lines ∼30 per cent wider than the [C II] lines. Therefore, whilst the observed values of z can correspond to variations in the quantity F/F with cosmic time, where F = α2/μ, with α the fine-structure constant and μ the proton-to-electron mass ratio, of both (−3.3 ± 2.3) × 10−4 for a look-back time of 12.9 Gyr and of (−5 ± 15) × 10−5 for a look-back time of 12.4 Gyr, we propose that they are the result of the two species of gas being spatially separated as indicated by the inconsistencies in their line profiles.