3.4 Quasar absorption spectra

3.4.1 Generalities

Quasar (QSO) absorption lines provide a powerful probe of the variation of fundamental constants. Absorption lines in intervening clouds along the line of sight of the QSO give access to the spectra of the atoms present in the cloud, that it is to paleo-spectra. The method was first used by Savedoff [447] who constrained the time variation of the fine-structure constraint from the doublet separations seen in galaxy emission spectra. For general introduction to these observations, we refer to [412Jump To The Next Citation Point, 474, 271].

Indeed, one cannot use a single transition compared to its laboratory value since the expansion of the universe induces a global redshifting of all spectra. In order to tackle down a variation of the fundamental constants, one should resort on various transitions and look for chromatic effects that can indeed not be reproduce by the expansion of the universe, which acts chromatically on all wavelengths.

To achieve such a test, one needs to understand the dependencies of different types of transitions, in a similar way as for atomic clock experiments. [175Jump To The Next Citation Point, 169] suggested to use the convenient formulation

⌊ ⌋ ⌊ ⌋ ( )2 ( )4 ω = ω0 + q⌈ αEM-- − 1⌉ + q2⌈ αEM-- − 1⌉ , (70 ) α(E0M) α(E0M)
in order to take into account the dependence of the spectra on the fine-structure constant. ω is the energy in the rest-frame of the cloud, that is at a redshift z, ω0 is the energy measured today in the laboratory. q and q2 are two coefficients that determine the frequency dependence on a variation of αEM and that arise from the relativistic corrections for the transition under consideration. The coefficient q is typically an order of magnitude larger than q 2 so that the possibility to constrain a variation of the fine-structure constant is mainly determined by q. These coefficients were computed for a large set of transitions, first using a relativistic Hartree–Fock method and then using many-body perturbation theory. We refer to [175, 45, 14Jump To The Next Citation Point] for an extensive discussion of the computational methods and a list of the q-coefficients for various transitions relevant for both quasar spectra and atomic clock experiments. Figure 3View Image summarizes some of these results. The uncertainty in q are typically smaller than 30 cm–1 for Mg, Si, Al and Zn, but much larger for Cr, Fe and Ni due to their more complicated electronic configurations. The accuracy for ω0 from dedicated laboratory measurements now reach 0.004 cm −1. It is important to stress that the form (70View Equation) ensures that errors in the q-coefficients cannot lead to a non zero detection of Δ αEM.
View Image

Figure 3: Summary of the values of some coefficients entering the parameterization (70View Equation) and necessary to interpret the QSO absorption spectra data. From [367Jump To The Next Citation Point]

The shift between two lines is easier to measure when the difference between the q-coefficients of the two lines is large, which occurs, e.g., for two levels with large q of opposite sign. Many methods were developed to take this into account. The alkali doublet method (AD) focuses on the fine-structure doublet of alkali atoms. It was then generalized to the many-multiplet method (MM), which uses correlations between various transitions in different atoms. As can be seen on Figure 3View Image, some transitions are almost insensitive to a variation of αEM. This is the case of Mg ii, which can be used as an anchor, i.e., a reference point. To obtain strong constraints one can either compare transitions of light atoms with those of heavy atoms (because the αEM dependence of the ground state scales as 2 Z) or compare s − p and d − p transitions in heavy elements (in that case, the relativistic correction will be of opposite signs). This latter effect increases the sensitivity and strengthens the method against systematic errors. However, the results of this method rely on two assumptions: (i) ionization and chemical homogeneity and (ii) isotopic abundance of Mg ii close to the terrestrial value. Even though these are reasonable assumptions, one cannot completely rule out systematic biases that they could induce. The AD method completely avoids the assumption of homogeneity because, by construction, the two lines of the doublet must have the same profile. Indeed the AD method avoids the implicit assumption of the MM method that chemical and ionization inhomogeneities are negligible. Another way to avoid the influence of small spectral shift due to ionization inhomogeneities within the absorber and due to possible non-zero offset between different exposures was to rely on different transitions of a single ion in individual exposure. This method has been called the Single ion differential alpha measurement method (SIDAM).

Most studies are based on optical techniques due to the profusion of strong UV transitions that are redshifted into the optical band (this includes AD, MM, SIDAM and it implies that they can be applied only above a given redshift, e.g., Si iv at z > 1.3, Fe iiλ1608 at z > 1) or on radio techniques since radio transitions arise from many different physical effects (hyperfine splitting and in particular H i 21 cm hyperfine transition, molecular rotation, Lambda-doubling, etc). In the latter case, the line frequencies and their comparisons yield constraints on different sets of fundamental constants including αEM, gp and μ. Thus, these techniques are complementary since systematic effects are different in optical and radio regimes. Also the radio techniques offer some advantages: (1) to reach high spectral resolution (< 1 km ∕s), alleviating in particular problems with line blending and the use of, e.g., masers allow to reach a frequency calibration better than roughly 10 m/s; (2) in general, the sensitivity of the line position to a variation of a constant is higher; (3) the isotopic lines are observed separately, while in optical there is a blend with possible differential saturations (see, e.g., [109] for a discussion).

Let us first emphasize that the shifts in the absorption lines to be detected are extremely small. For instance a change of αEM of order 10–5 corresponds a shift of at most 20 mÅ for a redshift of z ∼ 2, which would corresponds to a shift of order ∼ 0.5 km ∕s, or to about a third of a pixel at a spectral resolution of R ∼ 40000, as achieved with Keck/HIRES or VLT/UVES. As we shall discuss later, there are several sources of uncertainty that hamper the measurement. In particular, the absorption lines have complex profiles (because they result from the propagation of photons through a highly inhomogeneous medium) that are fitted using a combination of Voigt profiles. Each of these components depends on several parameters including the redshift, the column density and the width of the line (Doppler parameter) to which one now needs to add the constants that are assumed to be varying. These parameters are constrained assuming that the profiles are the same for all transitions, which is indeed a non-trivial assumption for transitions from different species (this was one of the driving motivations to use the transition from a single species and of the SIDAM method). More important, the fit is usually not unique. This is not a problem when the lines are not saturated but it can increase the error on αEM by a factor 2 in the case of strongly saturated lines [91Jump To The Next Citation Point].

3.4.2 Alkali doublet method (AD)

The first method used to set constraint on the time variation of the fine-structure constant relies on fine-structure doublets splitting for which

2 4 Δ ν ∝ α-EMZ--R-∞-. 2n3
It follows that the relative separation is proportional α EM, Δ ν∕¯ν ∝ α2 EM so that the variation of the fine structure constant at a redshift z can be obtained as
( Δ αEM ) cr [( Δλ ) (Δ λ ) ] ------ (z) = -- -¯-- ∕ -¯-- − 1 , αEM 2 λ z λ 0
where cr ∼ 1 is a number taking into account the relativistic corrections. This expression is indeed a simple approach of the alkali doublet since one should, as for atomic clocks, take into account the relativistic corrections more precisely. Using the formulation (70View Equation), one can deduce that
δq + δq cr = --------2, δq + 2δq2
where the δq are the differences between the q-coefficients for the doublet transitions.

Several authors have applied the AD method to doublets of several species such as, e.g., C iv, N v, O vi, Mg ii, Al iii, Si ii, Si iv. We refer to Section III.3 of FVC [500Jump To The Next Citation Point] for a summary of their results (see also [318]) and focus on the three most recent analysis, based on the Si iv doublet. In this particular case, q = 766 (resp. 362) cm–1 and q2 = 48 (resp. –8) cm–1 for Si iv λ1393 (resp. λ1402) so that cr = 0.8914. The method is based on a χ2 minimization of multiple component Voigt profile fits to the absorption features in the QSO spectra. In general such a profile depends on three parameters, the column density N, the Doppler width (b) and the redshift. It is now extended to include Δ αEM ∕αEM. The fit is carried out by simultaneously varying these parameters for each component.

One limitation may arise from the isotopic composition of silicium. Silicium has three naturally occurring isotopes with terrestrial abundances 28Si:29Si:30Si = 92.23:4.68:3.09 so that each absorption line is a composite of absorption lines from the three isotopes. However, it was shown that this effect of isotopic shifts [377Jump To The Next Citation Point] is negligible in the case of Si iv.

3.4.3 Many multiplet method (MM)

A generalization of the AD method, known as the many-mulptiplet was proposed in [176]. It relies on the combination of transitions from different species. In particular, as can be seen on Figure 3View Image, some transitions are fairly unsensitive to a change of the fine-structure constant (e.g., Mg ii or Mg i, hence providing good anchors) while others such as Fe ii are more sensitive. The first implementation [522Jump To The Next Citation Point] of the method was based on a measurement of the shift of the Fe ii (the rest wavelengths of which are very sensitive to αEM) spectrum with respect to the one of Mg ii. This comparison increases the sensitivity compared with methods using only alkali doublets. Two series of analyses were performed during the past ten years and lead to contradictory conclusions. The accuracy of the measurements depends on how well the absorption line profiles are modeled.

Keck/HIRES data.
The MM-method was first applied in [522] who analyzed one transition of the Mg ii doublet and five Fe ii transitions from three multiplets. Using 30 absorption systems toward 17 quasars, they obtained

Δ αEM ∕αEM = (− 0.17 ± 0.39) × 10− 5, 0.6 < z < 1 − 5 Δ αEM ∕αEM = (− 1.88 ± 0.53) × 10 , 1 < z < 1.6.
This was the first claim that a constant may have varied during the evolution of the universe. It was later confirmed in a re-analysis [376Jump To The Next Citation Point, 524Jump To The Next Citation Point] of the initial sample and by including new optical QSO data to reach 28 absorption systems with redshift z = 0.5– 1.8 plus 18 damped Lyman-α absorption systems towards 13 QSO plus 21 Si iv absorption systems toward 13 QSO. The analysis used mainly the multiplets of Ni ii, Cr ii and Zn ii and Mg i, Mg i, Al ii, Al iii and Fe ii was also included. The most recent analysis [369] relies on 128 absorption spectra, later updated [367Jump To The Next Citation Point] to include 143 absorption systems. The more robust estimates is the weighted mean
−5 Δ αEM ∕αEM = (− 0.57 ± 0.11) × 10 , 0.2 < z < 4.2. (74 )
The resolution for most spectra was R ∼ 45000 and the S/N per pixel ranges from 4 to 240, with most spectral regions with S/N∼ 30. The wavelength scale was calibrated by mean of a thorium-argon emission lamp. This calibration is crucial and its quality is discussed in [368Jump To The Next Citation Point, 374Jump To The Next Citation Point] for the Keck/HIRES (see also [236Jump To The Next Citation Point]) as well as [534Jump To The Next Citation Point] for the VLT/UVES measurements. The low-z (z < 1.8) and high-z rely on different ions and transitions with very different αEM-dependencies. At low-z, the Mg transitions are used as anchors against which the large positive shifts in the Fe ii can be measured. At high-z, different transitions are fitted (Fe ii, S ii, Cr ii, Ni ii, Zn ii, Al ii, Al iii). The two sub-samples respond differently to simple systematic errors due to their different arrangement of q-coefficients in wavelength space. The analysis for each sample give the weighted mean
Δα ∕ α = (− 0.54 ± 0.12) × 10−5, 0.2 < z < 1.8 EM EM −5 ΔαEM ∕ αEM = (− 0.74 ± 0.17) × 10 , 1.8 < z < 4.2, (75 )
with respectively 77 and 66 systems.

Hunting systematics.
While performing this kind of observations a number of problems and systematic effects have to be taken into account and controlled. (1) Errors in the determination of laboratory wavelengths to which the observations are compared. (2) While comparing wavelengths from different atoms one has to take into account that they may be located in different regions of the cloud with different velocities and hence with different Doppler shifts. (3) One has to ensure that there is no transition not blended by transitions of another system. (4) The differential isotopic saturation has to be controlled. Usually quasar absorption systems are expected to have lower heavy element abundances. The spatial inhomogeneity of these abundances may also play a role. (5) Hyperfine splitting can induce a saturation similar to isotopic abundances. (6) The variation of the velocity of the Earth during the integration of a quasar spectrum can also induce differential Doppler shift. (7) Atmospheric dispersion across the spectral direction of the spectrograph slit can stretch the spectrum. It was shown that, on average, this can, for low redshift observations, mimic a negative Δ αEM ∕αEM, while this is no more the case for high redshift observations (hence emphasizing the complementarity of these observations). (8) The presence of a magnetic field will shift the energy levels by Zeeman effect. (9) Temperature variations during the observation will change the air refractive index in the spectrograph. In particular, flexures in the instrument are dealt with by recording a calibration lamp spectrum before and after the science exposure and the signal-to-noise and stability of the lamp is crucial (10) Instrumental effects such as variations of the intrinsic instrument profile have to be controlled. All these effects have been discussed in detail in [374, 376] to argue that none of them can explain the current detection. This was recently complemented by a study on the calibration since adistortion of the wavelength scale could lead to a non-zero value of Δ αEM. The quality of the calibration is discussed in [368] and shown to have a negligible effect on the measurements (a similar result has been obtained for the VLT/UVES data [534Jump To The Next Citation Point]).

As we pointed out earlier, one assumption of the method concerns the isotopic abundances of Mg ii that can affect the low-z sample since any changes in the isotopic composition will alter the value of effective rest-wavelengths. This isotopic composition is assumed to be close to terrestrial 24Mg:25Mg:26Mg = 79:10:11. No direct measurement of 26 25 24 rMg = ( Mg + Mg )∕ Mg in QSO absorber is currently feasible due to the small separation of the isotopic absorption lines. However, it was shown [231], on the basis of molecular absorption lines of MgH that rMg generally decreases with decreasing metallicity. In standard models it should be near 0 at zero metallicity since type II supernovae are primarily producers of 24Mg. It was also argued that 13C is a tracer of 25Mg and was shown to be low in the case of HE 0515-4414 [321]. However, contrary to this trend, it was found [552] that rMg can reach high values for some giant stars in the globular cluster NGC 6752 with metallicity [Fe/H]∼ − 1.6. This led Ashenfelter et al. [18Jump To The Next Citation Point] to propose a chemical evolution model with strongly enhanced population of intermediate (2– 8M ⊙) stars, which in their asymptotic giant branch phase are the dominant factories for heavy Mg at low metallicities typical of QSO absorption systems, as a possible explanation of the low-z Keck/HIRES observations without any variation of αEM. It would require that rMg reaches 0.62, compared to 0.27 (but then the UVES/VLT constraints would be converted to a detection). Care needs to be taken since the star formation history can be different ine each region, even in each absorber, so that one cannot a priori use the best-fit obtained from the Keck data to the UVES/VLT data. However, such modified nucleosynthetic history will lead to an overproduction of elements such as P, Si, Al, P above current constraints [192], but this later model is not the same as the one of Ref. [18] that was tuned to avoid these problems.

In conclusion, no compelling evidence for a systematic effect has been raised at the moment.

VLT/UVES data.
The previous results, and their importance for fundamental physics, led another team to check this detection using observations from UVES spectrograph operating on the VLT. In order to avoid as much systematics as possible, and based on numerical simulations, they apply a series of selection criteria [90Jump To The Next Citation Point] on the systems used to constrain the time variation of the fine-structure constant: (1) consider only lines with similar ionization potentials (Mg ii, Fe ii, Si ii and Al ii) as they are most likely to originate from similar regions in the cloud; (2) avoid absorption lines contaminated by atmospheric lines; (3) consider only systems with hight enough column density to ensure that all the mutiplets are detected at more than 5σ; (4) demand than at least one of the anchor lines is not saturated to have a robust measurement of the redshift; (5) reject strongly saturated systems with large velocity spread; (6) keep only systems for which the majority of the components are separated from the neighboring by more than the Doppler shift parameter. The advantage of this choice is to reject most complex or degenerate systems, which could result in uncontrolled systematics effects. The drawback is indeed that the analysis will be based on less systems.

Refs. [90Jump To The Next Citation Point, 470Jump To The Next Citation Point] analyzed the observations of 23 absorption systems, fulfilling the above criteria, in direction of 18 QSO with a S/N ranging between 50 and 80 per pixel and a resolution R > 44000. They concluded that

−5 Δ αEM ∕αEM = (− 0.06 ± 0.06) × 10 , 0.4 < z < 2.3,
hence giving a 3σ constraint on a variation of αEM.

This analysis was challenged by Murphy, Webb and Flambaum [372Jump To The Next Citation Point, 371Jump To The Next Citation Point, 370Jump To The Next Citation Point]. Using (quoting them) the same reduced data, using the same fits to the absorption profiles, they claim to find different individual measurements of Δ αEM ∕αEM and a weighted mean,

−5 Δ αEM ∕αEM = (− 0.44 ± 0.16) × 10 , 0.4 < z < 2.3,
which differs from the above cited value. The main points that were raised are (1) the fact that some of the uncertainties on ΔαEM ∕αEM are smaller than a minimum uncertainty that they estimated and (2) the quality of the statistical analysis (in particular on the basis of the χ2 curves). These arguments were responded in [471Jump To The Next Citation Point] The revision [471Jump To The Next Citation Point] of the VLT/UVES constraint rejects two more than 4σ deviant systems that were claimed to dominate the re-analysis [371Jump To The Next Citation Point, 370Jump To The Next Citation Point] and concludes that
Δ αEM ∕αEM = (0.01 ± 0.15) × 10−5, 0.4 < z < 2.3, (76 )
emphasizing that the errors are probably larger.

On the basis of the articles [372, 371, 370] and the answer [471Jump To The Next Citation Point], it is indeed difficult (without having played with the data) to engage one of the parties. This exchange has enlightened some differences in the statistical analysis.

To finish, let us mention that [361Jump To The Next Citation Point] reanalyzed some systems of [90Jump To The Next Citation Point, 470] by means of the SIDAM method (see below) and disagree with some of them, claiming for a problem of calibration. They also claim that the errors quoted in [367Jump To The Next Citation Point] are underestimated by a factor 1.5.

Regressional MM (RMM).
The MM method was adapted to use a linear regression method [427Jump To The Next Citation Point]. The idea is to measure the redshift zi deduced from the transition i and plot zi as a function of the sensitivity coefficient. If ΔαEM ⁄= 0 then there should exist a linear relation with a slope proportional to Δ αEM ∕αEM. On a single absorption system (VLT/UVES), on the basis of Fe ii transition, they concluded that

−6 Δ αEM ∕αEM = (− 0.4 ± 1.9 ± 2.7syst) × 10 , z = 1.15, (77 )
compared to Δ α ∕α = (0.1 ± 1.7) × 10 −6 EM EM that is obtained with the standard MM technique on the same data. This is also consistent with the constraint (79View Equation) obtained on the same system with the HARPS spectrograph.

Open controversy.
At the moment, we have to face a situation in which two teams have performed two independent analyses based on data sets obtained by two instruments on two telescopes. Their conclusions do not agree, since only one of them is claiming for a detection of a variation of the fine-structure constant. This discrepancy between VLT/UVES and Keck/Hires results is yet to be resolved. In particular, they use data from a different telescopes observing a different (Southern/Northern) hemisphere. Ref. [236Jump To The Next Citation Point] provides an analysis of the wavelength accuracy of the Keck/HIRES spectrograph. An absolute uncertainty of Δz ∼ 10 −5, corresponding to Δ λ ∼ 0.02 ˚A with daily drift of Δz ∼ 5 × 10− 6 and multiday drift of Δz ∼ 2 × 10 −5. While the cause of this drift remains unknown, it is argued [236] that this level of systematic uncertainty makes it difficult to use the Keck/HIRES to constrain the time variation of αEM (at least for a single system or a small sample since the distortion pattern pertains to the echelle orders as they are recorded on the CDD, that is it is similar from exposure to exposure, the effect on Δ αEM ∕αEM for an ensemble of absorbers at different redshifts would be random since the transitions fall in different places with respect to the pattern of the disortion). This needs to be confirmed and investigated in more detail. We refer to [373] for a discussion on the Keck wavelength calibration error and [534] for the VLT/UVES as well as [86] for a discussion on the ThAr calibration.

On the one hand, it is appropriate that one team has reanalyzed the data of the other and challenged its analysis. This would indeed lead to an improvement in the robustness of these results. Indeed a similar reverse analysis would also be appropriate. On the other hand both teams have achieved an amazing work in order to understand and quantify all sources of systematics. Both developments, as well as the new techniques, which are appearing, should hopefully set this observational issue. Today, it is unfortunately premature to choose one data set compared to the other.

A recent data [523Jump To The Next Citation Point] set of 60 quasar spectra (yielding 153 absorption systems) for the VLT was used and split at z = 1.8 to get

(ΔαEM ∕ αEM ) = (− 0.06 ± 0.16) × 10−5, VLT;z<1.8
in agreement with the former study [471], while at higher redshift
(Δ αEM ∕αEM ) = (+0.61 ± 0.20 ) × 10 −5. VLTz>1.8
This higher component exhibits a positive variation of αEM, that is of opposite sign with respect to the previous Keck/HIRES detection [367Jump To The Next Citation Point]
−5 − 5 (Δ αEM ∕αEM )Keck;z<1.8 = (− 0.54 ± 0.12 ) × 10 , (Δ αEM ∕αEM )Keck;z>1.8 = (− 0.74 ± 0.17) × 10 .
It was pointed out that the Keck/HIRES and VLT/UVES observations can be made consistent in the case the fine structure constant is spatially varying [523Jump To The Next Citation Point]. Indeed, one can note that they do not correspond to the same hemisphere and invoke a spatial variation. [523Jump To The Next Citation Point] concludes that the distribution of αEM is well represented by a spatial dipole, significant at 4.1σ, in the direction right ascension 17.3 ± 0.6 hours and declination − 61 ± 9 deg (see also [50Jump To The Next Citation Point, 48]). This emphasizes the difficulty in comparing different data sets and shows that the constraints can easily be combined as long as they are compatible with no variation but one must care about a possible spatial variation otherwise.

3.4.4 Single ion differential measurement (SIDAM)

This method [320] is an adaptation of the MM method in order to avoid the influence of small spectral shifts due to ionization inhomogeneities within the absorbers as well as to non-zero offsets between different exposures. It was mainly used with Fe ii, which provides transitions with positive and negative q-coefficients (see Figure 3View Image). Since it relies on a single ion, it is less sensitive to isotopic abundances, and in particular not sensitive to the one of Mg.

The first analysis relies on the QSO HE 0515-4414 that was used in [427] to get the constraint (77View Equation). An independent analysis [361Jump To The Next Citation Point] of the same system gave a weighted mean

− 6 Δ αEM ∕αEM = (− 0.12 ± 1.79) × 10 , z = 1.15, (78 )
at 1σ. The same system was studied independently, using the HARPS spectrograph mounted on the 3.6 m telescope at La Silla observatory [92]. The HARPS spectrograph has a higher resolution that UVES; R ∼ 112000. Observations based on Fe ii with a S/N of about 30 – 40 per pixel set the constraint
−6 Δ αEM ∕αEM = (0.5 ± 2.4) × 10 , z = 1.15. (79 )
The second constraint [325, 361Jump To The Next Citation Point] is obtained from an absorption system toward Q 1101-264,
Δ αEM ∕αEM = (5.66 ± 2.67 ) × 10− 6, z = 1.84, (80 )
These constraints do not seem to be compatible with the results of the Keck/HIRES based on the MM method. A potential systematic uncertainty, which can affect these constraints is the relative shift of the wavelength calibration in the blue and the red arms of UVES where the distant Fe lines are recorded simultaneously (see, e.g., [359] for a discussion of the systematics of this analysis).

3.4.5 H i-21 cm vs. UV: x = α2EMgp ∕ μ

The comparison of UV heavy element transitions with the hyperfine H i transition allows to extract [496]

2 x ≡ α EMgp∕μ,
since the hyperfine transition is proportional to 2 −1 αEMgp μ R ∞ while optical transitions are simply proportional to R ∞. It follows that constraints on the time variation of x can be obtained from high resolution 21 cm spectra compared to UV lines, e.g., of Si ii, Fe ii and/or Mg ii, as first performed in [548] in z ∼ 0.524 absorber.

Using 9 absorption systems, there was no evidence for any variation of x [494Jump To The Next Citation Point],

Δx ∕x = (− 0.63 ± 0.99) × 10−5, 0.23 < z < 2.35, (81 )
This constraint was criticised in [275] on the basis that the systems have multiple components and that it is not necessary that the strongest absorption arises in the same component in both type of lines. However, the error analysis of [494Jump To The Next Citation Point] tries to estimate the effect of the assumption that the strongest absorption arises in the same component.

Following [147Jump To The Next Citation Point], we note that the systems lie in two widely-separated ranges and that the two samples have completely different scatter. Therefore it can be split into two samples of respectively 5 and 4 systems to get

− 5 Δx ∕x = (1.02 ± 1.68 ) × 10 , 0.23 < z < 0.53, (82 ) Δx ∕x = (0.58 ± 1.94 ) × 10− 5, 1.7 < z < 2.35. (83 )

In such an approach two main difficulties arise: (1) the radio and optical source must coincide (in the optical QSO can be considered pointlike and it must be checked that this is also the case for the radio source), (2) the clouds responsible for the 21 cm and UV absorptions must be localized in the same place. Therefore, the systems must be selected with care and today the number of such systems is small and are actively looked for [411Jump To The Next Citation Point].

The recent detection of 21 cm and molecular hydrogen absorption lines in the same damped Lyman-α system at zabs = 3.174 towards SDSS J1337+3152 constrains [472Jump To The Next Citation Point] the variation x to

Δx ∕x = − (1.7 ± 1.7) × 10−6, z = 3.174. (84 )
This system is unique since it allows for 21 cm, H2 and UV observation so that in principle one can measure αEM, x and μ independently. However, as the H2 column density was low, only Werner band absorption lines are seen so that the range of sensitivity coefficients is too narrow to provide a stringent constraint, Δ μ∕μ < 4 × 10 −4. It was also shown that the H 2 and 21 cm are shifted because of the inhomogeneity of the gas, hence emphasizing this limitation. [411Jump To The Next Citation Point] also mentioned that 4 systems at z = 1.3 sets −6 Δx ∕x = (0.0 ± 1.5) × 10 and that another system at z = 3.1 gives Δx ∕x = (0.2 ± 0.5) × 10 −6. Note also that the comparison [274] with C i at z ∼ 1.4 –1.6 towards Q0458-020 and Q2337-011, yields Δx ∕x = (6.8 ± 1.0) × 10−6 over the band o redshift 0 < ⟨z⟩ ≤ 1.46, but this analysis ignores an important wavelength calibration estimated to be of the order of −6 6.7 × 10. It was argued that, using the existing constraints on Δ μ∕ μ, this measurement is inconsistent with claims of a smaller value of αEM from the many-multiplet method, unless fractional changes in gp are larger than those in αEM and μ.

3.4.6 H i vs. molecular transitions: 2 y ≡ gp α EM

The H i 21 cm hyperfine transition frequency is proportional to gpμ− 1α2EMR ∞ (see Section 3.1.1). On the other hand, the rotational transition frequencies of diatomic are inversely proportional to their reduced mass M. As on the example of Equation (35View Equation) where we compared an electronic transition to a vibro-rotational transition, the comparison of the hyperfine and rotational frequencies is proportional to

νhf- 2 M-- 2 ν ∝ gpα EM m ≃ gpαEM ≡ y, rot p
where the variation of M ∕mp is usually suppressed by a large factor of the order of the ratio between the proton mass and nucleon binding energy in nuclei, so that we can safely neglect it.

The constraint on the variation of y is directly determined by comparing the redshift as determined from H i and molecular absorption lines,

Δy-- zmol −-zH y = 1 + z . mol

This method was first applied [513] to the CO molecular absorption lines [536Jump To The Next Citation Point] towards PKS 1413+135 to get

Δy ∕y = (− 4 ± 6) × 10− 5 z = 0.247.
The most recent constraint [375Jump To The Next Citation Point] relies on the comparison of the published redshifts of two absorption systems determined both from H i and molecular absorption. The first is a system at z = 0.6847 in the direction of TXS 0218+357 for which the spectra of CO(1-2), 13CO(1-2), C18O(1-2), CO(2-3), HCO+(1-2) and HCN(1-2) are available. They concluded that
−5 Δy ∕y = (− 0.16 ± 0.54) × 10 z = 0.6847. (85 )
The second system is an absorption system in direction of PKS 1413+135 for which the molecular lines of CO(1-2), HCO+(1-2) and HCO+(2-3) have been detected. The analysis led to
−5 Δy ∕y = (− 0.2 ± 0.44 ) × 10 , z = 0.247. (86 )
[78] obtains the constraints |Δy ∕y | < 3.4 × 10−5 at z ∼ 0.25 and z ∼ 0.685.

The radio domain has the advantage of heterodyne techniques, with a spectral resolution of 106 or more, and dealing with cold gas and narrow lines. The main systematics is the kinematical bias, i.e., that the different lines do not come exactly from the same material along the line of sight, with the same velocity. To improve this method one needs to find more sources, which may be possible with the radio telescope ALMA 3.

3.4.7 OH - 18 cm: 2 1.57 F = gp(α EM μ )

Using transitions originating from a single species, like with SIDAM, allows to reduce the systematic effects. The 18 cm lines of the OH radical offers such a possibility [95Jump To The Next Citation Point, 272].

The ground state, 2 Π3∕2J = 3 ∕2, of OH is split into two levels by Λ-doubling and each of these doubled level is further split into two hyperfine-structure states. Thus, it has two “main” lines (ΔF = 0) and two “satellite” lines (ΔF = 1). Since these four lines arise from two different physical processes (Λ-doubling and hyperfine splitting), they enjoy the same Rydberg dependence but different gp and αEM dependencies. By comparing the four transitions to the H i hyperfine line, one can have access to

F ≡ gp(α2EMμ )1.57 (87 )
and it was also proposed to combine them with HCO+ transitions to lift the degeneracy.

Using the four 18 cm OH lines from the gravitational lens at z ∼ 0.765 toward PMN J0134-0931 and comparing the H i 21 cm and OH absorption redshifts of the different components allowed to set the constraint [276Jump To The Next Citation Point]

−5 ΔF ∕F = (− 0.44 ± 0.36 ± 1.0syst) × 10 , z = 0.765, (88 )
where the second error is due to velocity offsets between OH and H i assuming a velocity dispersion of 3 km/s. A similar analysis [138Jump To The Next Citation Point] in a system in the direction of PKS 1413+135 gave
−5 ΔF ∕F = (0.51 ± 1.26) × 10 , z = 0.2467. (89 )

3.4.8 Far infrared fine-structure lines: ′ 2 F = α EM μ

Another combination [300] of constants can be obtained from the comparison of far infrared fine-structure spectra with rotational transitions, which respectively behaves as R∞ α2 EM and R ∞ ¯μ = R ∞ ∕μ so that they give access to

F ′ = α2EMμ.
A good candidate for the rotational lines is CO since it is the second most abundant molecule in the Universe after H2.

Using the C ii fine-structure and CO rotational emission lines from the quasars J1148+5251 and BR 1202-0725, it was concluded that

′ ′ −4 ΔF ∕F = (0.1 ± 1.0) × 10 , z = 6.42, (90 ) ΔF ′∕F ′ = (1.4 ± 1.5) × 10−5, z = 4.69, (91 )
which represents the best constraints at high redshift. As usual, when comparing the frequencies of two different species, one must account for random Doppler shifts caused by non-identical spatial distributions of the two species. Several other candidates for microwave and FIR lines with good sensitivities are discussed in [299].

3.4.9 “Conjugate” satellite OH lines: 1.85 G = gp(αEM μ )

The satellite OH 18 cm lines are conjugate so that the two lines have the same shape, but with one line in emission and the other in absorption. This arises due to an inversion of the level of populations within the ground state of the OH molecule. This behavior has recently been discovered at cosmological distances and it was shown [95Jump To The Next Citation Point] that a comparison between the sum and difference of satellite line redshifts probes 1.85 G = gp(αEM μ).

From the analysis of the two conjugate satellite OH systems at z ∼ 0.247 towards PKS 1413+135 and at z ∼ 0.765 towards PMN J0134-0931, it was concluded [95Jump To The Next Citation Point] that

|ΔG ∕G| < 7.6 × 10−5. (92 )
It was also applied to a nearby system, Centaurus A, to give − 5 |ΔG ∕G | < 1.6 × 10 at z ∼ 0.0018. A more recent analysis [273Jump To The Next Citation Point] claims for a tentative evidence (with 2.6σ significance, or at 99.1% confidence) for a smaller value of G
ΔG ∕G = (− 1.18 ± 0.46) × 10− 5 (93 )
for the system at z ∼ 0.247 towards PKS 1413+135.

One strength of this method is that it guarantees that the satellite lines arise from the same gas, preventing from velocity offset between the lines. Also, the shape of the two lines must agree if they arise from the same gas.

3.4.10 Molecular spectra and the electron-to-proton mass ratio

As was pointed out in Section 3.1, molecular lines can provide a test of the variation4 [488] of μ since rotational and vibrational transitions are respectively inversely proportional to their reduce mass and its square-root [see Equation (35View Equation)].

Constraints with H2

H2 is the most abundant molecule in the universe and there were many attempts to use its absorption spectra to put constraints on the time variation of μ despite the fact that H2 is very difficult to detect [387Jump To The Next Citation Point].

As proposed in [512], the sensitivity of a vibro-rotational wavelength to a variation of μ can be parameterized as

( ) λi = λ0i(1 + zabs) 1 + Ki Δ-μ- , μ
where 0 λi is the laboratory wavelength (in the vacuum) and λi is the wavelength of the transition i in the rest-frame of the cloud, that is at a redshift zabs so that the observed wavelength is λi∕(1 + zabs). Ki is a sensitivity coefficient analogous to the q-coefficient introduced in Equation (70View Equation), but with different normalization since in the parameterization we would have q = ω0K ∕2 i i i,
dlnλi- Ki ≡ dln μ
corresponding to the Lyman and Werner bands of molecular hydrogen. From this expression, one can deduce that the observed redshift measured from the transition i is simply
Δ-μ- zi = zabs + bKi, b ≡ − (1 + zabs) μ ,
which implies in particular that zabs is not the mean of the zi if Δ μ ⁄= 0 . Indeed zi is measured with some uncertainty of the astronomical measurements λi and by errors of the laboratory measurements λ0i. But if Δ μ ⁄= 0 there must exist a correlation between zi and Ki so that a linear regression of zi (measurement) as a function of Ki (computed) allows to extract (zabs,b) and their statistical significance.

We refer to Section V.C of FVC [500Jump To The Next Citation Point] for earlier studies and we focus on the latest results. The recent constraints are mainly based on the molecular hydrogen of two damped Lyman-α absorption systems at z = 2.3377 and 3.0249 in the direction of two quasars (Q 1232+082 and Q 0347-382) for which a first analysis of VLT/UVES data showed [262] a slight indication of a variation,

Δμ ∕μ = (5.7 ± 3.8) × 10 −5
at 1.5σ for the combined analysis. The lines were selected so that they are isolated, unsaturated and unblended. It follows that the analysis relies on 12 lines (over 50 detected) for the first quasar and 18 (over 80) for second but the two selected spectra had no transition in common. The authors performed their analysis with two laboratory catalogs and got different results. They point out that the errors on the laboratory wavelengths are comparable to those of the astronomical measurements.

It was further improved with an analysis of two absorption systems at z = 2.5947 and z = 3.0249 in the directions of Q 0405-443 and Q 0347-383 observed with the VLT/UVES spectrograph. The data have a resolution R = 53000 and a S/N ratio ranging between 30 and 70. The same selection criteria where applied, letting respectively 39 (out of 40) and 37 (out of 42) lines for each spectrum and only 7 transitions in common. The combined analysis of the two systems led [261]

−5 −5 Δ μ ∕μ = (1.65 ± 0.74) × 10 or Δ μ∕μ = (3.05 ± 0.75) × 10 ,
according to the laboratory measurements that were used. The same data were reanalyzed with new and highly accurate measurements of the Lyman bands of H2, which implied a reevaluation of the sensitivity coefficient Ki. It leads to the two constraints [431Jump To The Next Citation Point]
Δ μ∕μ = (2.78 ± 0.88) × 10−5, z = 2.59, (94 ) Δ μ∕μ = (2.06 ± 0.79) × 10−5, z = 3.02, (95 )
leading to a 3.5σ detection for the weighted mean Δ μ∕μ = (2.4 ± 0.66) × 10−5. The authors of [431Jump To The Next Citation Point] do not claim for a detection and are cautious enough to state that systematics dominate the measurements. The data of the z = 3.02 absorption system were re-analyzed in [529], which claim that they lead to the bound − 5 |Δ μ∕ μ| < 4.9 × 10 at a 2σ level, instead of Equation (95View Equation). Adding a new set of 6 spectra, it was concluded that −6 Δ μ∕μ = (15 ± 14 ) × 10 for the weighted fit [530].

These two systems were reanalyzed [289Jump To The Next Citation Point], adding a new system in direction of Q 0528-250,

Δ μ∕μ = (1.01 ± 0.62) × 10−5, z = 2.59, (96 ) −5 Δ μ∕μ = (0.82 ± 0.74) × 10 , z = 2.8, (97 ) Δ μ∕μ = (0.26 ± 0.30) × 10−5, z = 3.02, (98 )
respectively with 52, 68 and 64 lines. This gives a weighted mean of − 6 (2.6 ± 3.0) × 10 at z ∼ 2.81. To compare with the previous data, the analysis of the two quasars in common was performed by using the same lines (this implies adding 3 and removing 16 for Q 0405-443 and adding 4 and removing 35 for Q 0347-383) to get respectively (− 1.02 ± 0.89 ) × 10− 5 (z = 2.59) and (− 1.2 ± 1.4) × 10−5 (z = 3.02). Both analyses disagree and this latter analysis indicates a systematic shift of Δ μ∕ μ toward 0. A second re-analysis of the same data was performed in [490Jump To The Next Citation Point, 489] using a different analysis method to get
Δ μ ∕μ = (− 7 ± 8) × 10−6. (99 )
Recently discovered molecular transitions at z = 2.059 toward the quasar J2123-0050 observed by the Keck telescope allow to obtain 86 H2 transitions and 7 HD transitions to conclude [342Jump To The Next Citation Point]
Δμ ∕μ = (5.6 ± 5.5 ± 2.7 ) × 10−6, z = 2.059. (100 ) stat syst

This method is subject to important systematic errors among which (1) the sensitivity to the laboratory wavelengths (since the use of two different catalogs yield different results [431Jump To The Next Citation Point]), (2) the molecular lines are located in the Lyman-α forest where they can be strongly blended with intervening H i Lyman-α absorption lines, which requires a careful fitting of the lines [289Jump To The Next Citation Point] since it is hard to find lines that are not contaminated. From an observational point of view, very few damped Lyman-α systems have a measurable amount of H2 so that only a dozen systems is actually known even though more systems will be obtained soon [411]. To finish, the sensitivity coefficients are usually low, typically of the order of 10–2. Some advantages of using H2 arise from the fact there are several hundred available H2 lines so that many lines from the same ground state can be used to eliminate different kinematics between regions of different excitation temperatures. The overlap between Lyman and Werner bands also allow to reduce the errors of calibration.

To conclude, the combination of all the existing observations indicate that μ is constant at the 10–5 level during the past 11 Gigayrs while an improvement of a factor 10 can be expected in the five coming years.

Other constraints

It was recently proposed [201Jump To The Next Citation Point, 202] that the inversion spectrum of ammonia allows for a better sensitivity to μ. The inversion vibro-rotational mode is described by a double well with the first two levels below the barrier. The tunneling implies that these two levels are split in inversion doublets. It was concluded that the inversion transitions scale as νinv ∼ ¯μ4.46, compared with a rotational transition, which scales as νrot ∼ ¯μ. This implies that the redshifts determined by the two types of transitions are modified according to δzinv = 4.46(1 + zabs)Δμ ∕μ and δzrot ∼ (1 + zabs)Δ μ∕μ so that

zinv −-zrot- Δμ ∕μ = 0.289 1 + zabs .
Only one quasar absorption system, at z = 0.68466 in the direction of B 0218+357, displaying NH3 is currently known and allows for this test. A first analysis [201] estimated from the published redshift uncertainties that a precision of ∼ 2 × 10− 6 on Δ μ ∕μ can be achieved. A detailed measurement [366Jump To The Next Citation Point] of the ammonia inversion transitions by comparison to HCN and HCO+ rotational transitions concluded that
|Δ μ∕μ| < 1.8 × 10−6, z = 0.685, (101 )
at a 2σ level. Recently the analysis of the comparison of NH3 to HC3N spectra was performed toward the gravitational lens system PKS 1830-211 (z ≃ 0.89), which is a much more suitable system, with 10 detected NH3 inversion lines and a forest of rotational transitions. It reached the conclusion that
−6 |Δ μ ∕μ| < 1.4 × 10 , z = 0.89, (102 )
at a 3σ level [250Jump To The Next Citation Point]. From a comparison of the ammonia inversion lines with the NH3 rotational transitions, it was concluded [353Jump To The Next Citation Point]
−6 |Δ μ ∕μ| < 3.8 × 10 , z = 0.89, (103 )
at 95% C.L. One strength of this analysis is to focus on lines arising from only one molecular species but it was mentioned that the frequencies of the inversion lines are about 25 times lower than the rotational ones, which might cause differences in the absorbed background radio continuum.

This method was also applied [323Jump To The Next Citation Point] in the Milky Way, in order to constrain the spatial variation of μ in the galaxy (see Section 6.1.3). Using ammonia emission lines from interstellar molecular clouds (Perseus molecular core, the Pipe nebula and the infrared dark clouds) it was concluded that − 8 Δ μ = (4 − 14) × 10. This indicates a positive velocity offset between the ammonia inversion transition and rotational transitions of other molecules. Two systems being located toward the galactic center while one is in the direction of the anti-center, this may indicate a spatial variation of μ on galactic scales.

New possibilities

The detection of several deuterated molecular hydrogen HD transitions makes it possible to test the variation of μ in the same way as with H2 but in a completely independent way, even though today it has been detected only in 2 places in the universe. The sensitivity coefficients have been published in [263] and HD was first detected by [387].

HD was recently detected [473] together with CO and H2 in a DLA cloud at a redshift of 2.418 toward SDSS1439+11 with 5 lines of HD in 3 components together with several H2 lines in 7 components. It allowed to set the 3σ limit of |Δ μ∕ μ| < 9 × 10−5 [412Jump To The Next Citation Point].

Even though the small number of lines does not allow to reach the level of accuracy of H2 it is a very promising system in particular to obtain independent measurements.

3.4.11 Emission spectra

Similar analysis to constrain the time variation of the fundamental constants were also performed with emission spectra. Very few such estimates have been performed, since it is less sensitive and harder to extend to sources with high redshift. In particular, emission lines are usually broad as compared to absorption lines and the larger individual errors need to be beaten by large statistics.

The O iii doublet analysis [24] from a sample of 165 quasars from SDSS gave the constraint

Δ α ∕α = (12 ± 7 ) × 10− 5, 0.16 < z < 0.8. (104 ) EM EM
The method was then extended straightforwardly along the lines of the MM method and applied [238] to the fine-structure transitions in Ne iii, Ne v, O iii, O i and S ii multiplets from a sample of 14 Seyfert 1.5 galaxies to derive the constraint
−5 ΔαEM ∕ αEM = (150 ± 70) × 10 , 0.035 < z < 0.281. (105 )

3.4.12 Conclusion and prospects

This subsection illustrates the diversity of methods and the progresses that have been achieved to set robust constraints on the variation of fundamental constants. Many systems are now used, giving access to different combinations of the constants. It exploits a large part of the electromagnetic spectrum from far infrared to ultra violet and radio bands and optical and radio techniques have played complementary roles. The most recent and accurate constraints are summarized in Table 10 and Figure 4View Image.

Table 10: Summary of the latest constraints on the variation of fundamental constants obtained from the analysis of quasar absorption spectra. We recall that y ≡ g α2 p EM, F ≡ g (α2 μ)1.57 p EM, 2 x ≡ αEMgp ∕μ, ′ 2 F ≡ α EMμ and μ ≡ mp ∕me, 1.85 G = gp(α μ).


Method System Constraint (× 10–5) Redshift Ref.

α EM

AD 21 (–0.5 ± 1.3) 2.33 – 3.08 [377Jump To The Next Citation Point]

AD 15 (–0.15 ± 0.43) 1.59 – 2.92 [91]

AD 9 (–3.09 ± 8.46) 1.19 – 1.84 [349]

MM 143 (–0.57 ± 0.11) 0.2 – 4.2 [367]

MM 21 (0.01 ± 0.15) 0.4 – 2.3 [90]

SIDAM 1 (–0.012 ± 0.179) 1.15 [361Jump To The Next Citation Point]

SIDAM 1 (0.566 ± 0.267) 1.84 [361]


H i - mol 1 (–0.16 ± 0.54) 0.6847 [375Jump To The Next Citation Point]

H i - mol 1 (–0.2 ± 0.44) 0.247 [375]

CO, CHO+ (–4 ± 6) 0.247 [536]


OH - H i 1 (–0.44 ± 0.36 ± 1.0syst) 0.765 [276]

OH - H i 1 (0.51 ± 1.26) 0.2467 [138]


H i - UV 9 (–0.63 ± 0.99) 0.23 – 2.35 [494]

H i - UV 2 (–0.17 ± 0.17) 3.174 [472]

F ′

C ii - CO 1 (1 ± 10) 4.69 [327Jump To The Next Citation Point]

C ii - CO 1 (14 ± 15) 6.42 [327]


OH 1 < 1.1 0.247, 0.765 [95Jump To The Next Citation Point]

OH 1 < 1.16 0.0018 [95]

OH 1 (–1.18 ± 0.46) 0.247 [273]


H2 1 (2.78 ± 0.88) 2.59 [431Jump To The Next Citation Point]

H2 1 (2.06 ± 0.79) 3.02 [431]

H2 1 (1.01 ± 0.62) 2.59 [289Jump To The Next Citation Point]

H2 1 (0.82 ± 0.74) 2.8 [289Jump To The Next Citation Point]

H2 1 (0.26 ± 0.30) 3.02 [289]

H2 1 (0.7 ± 0.8) 3.02, 2.59 [490]

NH3 1 < 0.18 0.685 [366]

NH3 1 < 0.38 0.685 [353]

HC3N 1 < 0.14 0.89 [250]

HD 1 < 9 2.418 [412]

HD 1 (0.56 ± 0.55stat ± 0.27syst) 2.059 [342]

View Image

Figure 4: Summary of the direct constraints on αEM obtained from the AD (blue), MM (red) and AD (green) methods (left) and on μ (right) that are summarized in Table 10.

At the moment, only one analysis claims to have detected a variation of the fine structure constant (Keck/HIRES) while the VLT/UVES points toward no variation of the fine structure constant. It has led to the proposition that αEM may be space dependent and exhibit a dipole, the origin of which is not explained. Needless to say that such a controversy and hypotheses are sane since it will help improve the analysis of this data, but it is premature to conclude on the issue of this debate and the jury is still out. Most of the systematics have been investigated in detail and now seem under control.

Let us what we can learn on the physics from these measurement. As an example, consider the constraints obtained on μ, y and F in the redshift band 0.6 – 0.8 (see Table 10). They can be used to extract independent constraints on gp, αEM and μ

Δ μ∕μ = (0 ± 0.18) × 10−5, Δ αEM ∕ αEM = (− 0.27 ± 2.09)× 10−5, Δgp ∕gp = (0.38 ± 4.73)× 10 −5.
This shows that one can test the compatibility of the constraints obtained from different kind of systems. Independently of these constraints, we have seen in Section 6.3 that in grand unification theory the variation of the constants are correlated. The former constraints show that if Δ lnμ = RΔ ln α EM then the constraint (101View Equation) imposes that −6 |R Δ ln αEM | < 1.8 × 10. In general R is expected to be of the order of 30 − 50. Even if its value its time-dependent, that would mean that −7 Δ ln αEM ∼ (1 − 5) × 10, which is highly incompatible with the constraint (74View Equation) obtained by the same team on αEM, but also on the constraints (71View Equation) and (72View Equation) obtained from the AD method and on which both teams agree. This illustrates how important the whole set of data is since one will probably be able to constrain the order of magnitude of R in a near future, which would be a very important piece of information for the theoretical investigations.

We mention in the course of this paragraph many possibilities to improve these constraints.

Since the AD method is free of the two main assumptions of the MM method, it seems important to increase the precision of this method as well as any method relying only on one species. This can be achieved by increasing the S/N ratio and spectral resolution of the data used or by increasing the sample size and including new transitions (e.g., cobalt [172, 187]).

The search for a better resolution is being investigated in many direction. With the current resolution of R ∼ 40000, the observed line positions can be determined with an accuracy of ˚ σ λ ∼ 1 m A. This implies that the accuracy on Δ αEM ∕αEM is of the order of 10–5 for lines with typical q-coefficients. As we have seen this limit can be improved to 10–6 when more transitions or systems are used together. Any improvement is related to the possibility to measure line positions more accurately. This can be done by increasing R up to the point at which the narrowest lines in the absorption systems are resolved. The Bohlin formula [62] gives the estimates

( ) ( ) Δ λpix 1 M 3∕2 σλ ∼ Δ λpix W----- √---- √---- , obs Ne 12
where Δ λpix is the pixel size, Wobs is the observed equivalent width, Ne is the mean number of photoelectron at the continuum level and M is the number of pixel covering the line profile. The metal lines have intrinsic width of a few km/s. Thus, one can expect improvements from higher spectral resolution. Progresses concerning the calibration are also expected, using, e.g., laser comb [478]. Let us just mention, the EXPRESSO (Echelle Spectrograph for PREcision Super Stable Observation) project [115] on 4 VLT units or the CODEX (COsmic Dynamics EXplorer) on E-ELT projects [360, 357, 507]. They shall provide a resolving power of R = 150000 to be compared to the HARPS5 (High Accuracy Radial velocity planet Searcher) spectrograph (R ∼ 112000) has been used but it is operating on a 3.6 m telescope.

The limitation may then lie in the statistics and the calibration and it would be useful to use more than two QSO with overlapping spectra to cross-calibrate the line positions. This means that one needs to discover more absorption systems suited for these analyses. Much progress is expected. For instance, the FIR lines are expected to be observed by a new generation of telescopes such as HERSCHEL6. While the size of the radio sample is still small, surveys are being carried out so that the number of known redshift OH, HI and HCO+ absorption systems will increase. For instance the future Square Kilometer Array (SKA) will be able to detect relative changes of the order of 10–7 in αEM.

In conclusion, it is clear that these constraints and the understanding of the absorption systems will increase in the coming years.

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