SIMBAD references

We use sensitive observations of three high-redshift sources: [C ii] ^2P_3/2 ⟶ ^2P_1/2 fine-structure 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 Δz = z_CO - z_C ii for each source where zCO and z_C 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 Δz. We derive 99 per cent confidence intervals for the marginalized posterior of Δz of (-1.9±1.3)x10^–3, (-3±8)x10^–4 and (-2±4) x 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 Δz can correspond to variations in the quantity ΔF/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)x10^–4 for a look-back time of 12.9 Gyr and of (-5±15)x10^–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.