© ESO, 2013

1. Introduction

Metal lines of absorption systems due to intervening galaxies along the line of sight towards distant quasars provide insight into the atomic structure at the cosmic time and location of the intervening object. All atomic transitions depend on the fine-structure constant, offering a way to probe possible variations in its value in space and time. The seminal papers of Savedoff (1956) and Bahcall et al. (1967) took advantage of the dependence of the relative separation of fine-structure doublet transitions on α and used the alkali doublets observed in the first extragalactic sources to limit Δα/α at the level of a few percent. More recently, the many-multiplet (MM) method has been introduced, which allows all observed transitions to be compared, thereby gaining access to the typically much larger dependence of the ground-state energy levels on α (Dzuba et al. 1999). Overall, the MM method improves the sensitivity to the measurement of a variation in α by more than an order of magnitude over the alkali-doublet method. Moreover, the individual dependence on α of different atoms and transitions allows better control of instrumental and astrophysical systematic errors.

A first analysis using the MM method on quasar absorption spectra obtained at the Keck telescope revealed hints that in the early universe the fine structure constant was smaller than today by ~6 parts per million (ppm; Webb et al. 1999; Murphy et al. 2001, 2003). However, the analysis of smaller data sets obtained from the Very Large Telescope (VLT) in Chile by other groups did not confirm the variation of α (Quast et al. 2004; Chand et al. 2004; Levshakov et al. 2005, 2006), though in some cases these analyses and uncertainty estimates have been challenged (Murphy et al. 2007b, 2008) (but see Srianand et al. 2007). A recent analysis has been performed on a new sample built up by merging 141 measurements from Keck with 154 measurements from VLT (Webb et al. 2011; King et al. 2012). The merged sample indicates a spatial variation in α across the sky at the 4.1σ level with amplitude ~10 ppm. Since the Keck telescope in Hawaii is at a latitude of 20° N, and the VLT in Chile is at latitude of 25° S, the two subsamples survey relatively different hemispheres, and the study of the merged sample provides a much more complete sky coverage. Remarkably, the two sets of measurements are consistent along the region of the sky covered by the two telescopes. So far, this spatial variation has been formally consistent with the null results obtained by other groups since the lines-of-sight fall into a region with minimal reported variation.

It has to be noted that a large-scale spatial variation of this magnitude is not expected. It cannot be obtained easily in the simplest theoretical models where varying fundamental couplings are due to dynamical scalar fields. One can nevertheless reproduce it by constructing toy models, for example, as the result of domains formed at the spontaneous breaking of a discrete symmetry for a dilaton-like scalar field coupled to electromagnetism (Olive et al. 2011). In any case, if such a result is confirmed, it will highlight the presence of currently unknown mechanisms that cause nature’s physical couplings to have different values in different regions of the universe. Observational and experimental confirmation or refutation of these results is therefore important. In addition to their intrinsic interest, these measurements (either detections or null results) can shed light on the enigma of dark energy (Amendola et al. 2012).

One possible weakness in the evidence for variations in α is that it derives mostly from archival Keck and VLT spectra. In particular, the majority of the spectra analysed by King et al. (2012) were obtained in service observing mode at the VLT. While spectroscopic quasar observations are generally straightforward, the service calibration plan for most VLT/UVES observations only include wavelength calibration exposures of a thorium-argon (ThAr) lamp many hours after the relevant quasar exposures. This introduces the possibility of systematic miscalibrations of the quasar wavelength scales. With this possibility in mind, and motivated by the need to confirm or refute current evidence for variations in α, we are conducting ESO Large Program 185.A-0745, “The UVES Large Program for testing Fundamental Physics”. The aim is to obtain high signal-to-noise ratio (S/N ~ 100 per pixel) spectra of ~12 bright quasars, carefully selected to contain a total of ~25 absorbers along their sight lines in which Δα/α can be determined with precision better than ~10 ppm. In each quasar line-of-sight there is at least one absorber in which we expect a precision approaching ~2 ppm based on the variety of metal-line transitions available and the shape/structure of their absorption profiles.

In the present work we focus on the first line-of-sight from the programme: the bright quasar HE 2217−2818. This sight line shows five separate absorption systems at redshifts 0.9−1.7 in which α-sensitive transitions can be observed at high resolution with unusually high S/N. This line of sight subtends an angle of Θ ≈ 58° with respect to the pole of the simplest model of dipolar variation in α across the sky in King et al. (2012). The expected signal at this position on the sky is therefore Δα/α ≈ +5.4 ppm. Achieving a statistical precision in Δα/α of ≲2 ppm as we aim to do in the z_abs = 1.6919 absorber towards HE 2217−2818 in this paper using our new, high-S/N observations therefore contains the possibility of evidence for or against the dipolar model of spatial variation in α. However, another major goal of studying this first quasar from the Large Program is to reveal systematic errors that may not randomize over the larger sample we will present in future papers. In particular, for the absorption system at z_abs = 1.6919, we present the results of two separate analyses to assist in the assessment of systematic effects.

2. Data analysis

2.1. Observations

HE 2217−2818 is a relatively bright quasar with V ≈ 16.0 and with z_em = 2.46. Its spectrum shows several intervening systems at z_abs = 0.600, 0.7866, 0.9424, 1.054, 1.083, 1.200, 1.5558, 1.6279, 1.6919 , and 2.181. However, only some of them, i.e. those detected in multiple transitions of the low-ionization ions Fe ii, Si ii, and Mg ii at z_abs= 0.7866, 0.9424, 1.5558, 1.6279, and 1.6919, are suitable for probing the fine-structure constant. The other systems have metal lines that are either too weak or which fall in the Lyman forest shortwards of ≈420 nm.

The observations of HE 2217−2818 were performed with UVES on VLT on the nights of 13, 15, 16, and 17 June 2010, during the first visitor-mode run of observations for our Large Program. The journal of observations and relevant additional information are given in Table 1. The observations comprised 16 separate UVES exposures of ≈4000 s duration taken on five successive nights for a total of ≈64 000 s of integration. Half of the observations were taken with dichroic N. 2 with central wavelengths of the blue and red arms at 437 and 760 nm (setting 437 + 760). The other half were taken with the dichroic N. 1 in the 390 + 580 nm setting. These two wavelength settings overlap somewhat, and as a whole they provide almost complete spectral coverage from 350 up to 947 nm. The CCDs were set with no on-chip binning, and the pixel size ranged between 0.013−0.015 Å pixel^-1, or 1.12 km s^-1pixel^-1at 400 nm, along the dispersion direction. For all observations the slit width was set to 0.8′′, providing an instrumental line-spread function with a full width at half maximum (FWHM) of ≈3.57 pixel in the 390 nm frames and ≈4.38 pixel in the 580 nm frame, with a variation of about 20% along the individual echelle orders. This corresponds to a resolving power of R ≈ 55 000. During the observations the seeing varied in the range between 0.5′′ and 1′′ as measured by the Differential Image Motion Monitor telescopes at Paranal Observatory. However, at the slightly higher and more protected location of VLT Unit Telescope 2 (on which UVES is mounted), the seeing was generally 10−30% better, as measured on the telescope guiding instrumentation.

2.2. Data reduction

We followed two independent approaches to the data reduction. Both analyses utilized the common pipeline language (CPL) version of the various tools constituting the UVES data reduction pipeline¹. The pipeline first bias-corrects and flat-fields the quasar exposures. The Echelle orders are curved and somewhat tilted with respect to the CCD rows/columns, so the pipeline locates them using an exposure of a quartz lamp observed through a pinhole instead of a standard slit. The quasar flux is then extracted with an optimal extraction method over the several pixels in the cross dispersion direction where the source flux is distributed. The wavelength calibration was performed using ThAr lamp exposures and it is a particularly important step for our purposes − see detailed discussion in Sect. 2.3 below. While the CPL code redisperses the spectra on to a linear wavelength scale by default, we used only the original, un-redispersed flux and error array for each Echelle order in subsequent reduction steps. After wavelength calibration, the air wavelength scale of each quasar exposure was corrected from air to vacuum using the Edlén (1966) formula, and placed in the solar system’s barycentric reference frame using the date and time of the mid-point of the exposure’s integration.

In the first analysis approach, the extracted flux from individual exposures was redispersed to a common linear wavelength grid and co-added with standard routines within the ESO MIDAS package using the S/N at the Echelle-order centres as weights. The quasar continuum was fitted in local regions around absorption lines with low-order polynomials. In the second analysis approach, a custom code, uves_popler² was used to redisperse the flux from individual exposures onto a common log-linear wavelength scale with dispersion 1.3 km s^-1 pixel^-1. The flux from all exposures was scaled to match that of overlapping orders and then co-added with inverse-variance weighting and cosmic ray rejection. uves_popler was also used to automatically fit a continuum to the final spectrum. This continuum was generally acceptable, though some local adjustments were made using low-order polynomial fits in the vicinity of some metal absorption lines.

2.3. Wavelength calibration

A variation in α should manifest itself as small radial velocity shifts between transitions. These transitions may fall many Echelle orders apart in the quasar spectrum. Since the signal for a non-zero Δα/α comes from the relative wavelength spacing of these transitions, having an accurate wavelength scale is crucial. The standard method used to calibrate the wavelength scale for a given science exposure with UVES is to take a hollow cathode ThAr arc lamp exposure with the same echelle and cross-disperser settings as the science exposure. Since December 2001, ESO has implemented an automatic resetting of the Cross Disperser encoder positions of UVES at the start of every image acquisition³. This policy was introduced to allow the use of day-time ThAr calibration frames to save on night-time calibration overheads. A negative aspect of this choice is that it implies that calibrations are taken under different conditions (e.g. ambient temperature, pressure, telescope pointing, telescope−instrument orientation differences etc.) from those prevailing during the quasar observations. It also implies that a ThAr exposure taken immediately before or after a quasar exposure may not accurately reflect the wavelength scale of the latter: the grating encoders are reset at each new acquisition sequence, so each time the quasar or ThAr arc is acquired for a subsequent exposure, the grating encoders, are, in principle, moved.

One of the principal aims of our new observations is to avoid possible systematic effects introduced by this service calibration plan. Therefore, ThAr exposures were taken before and after each quasar observation during the entire observing run, though only the ThAr frame taken after the quasar exposure was attached to the quasar exposure: this special mode allows us to avoid the automatic resets of grating positions between the quasar and calibration exposures. For this reason, the wavelength calibration of each quasar exposure studied in this paper was performed with its corresponding attached ThAr exposure. This procedure ensures that no mechanical movements occur between the quasar and ThAr frames and provides the best possible calibration for UVES.

The minimum and maximum temperatures during exposures within the spectrograph in correspondence to the blue arm’s CCD camera are monitored. During science exposures, typical changes are ΔT ≤ 0.1 K, with two cases showing changes of 0.2 K. Ambient air pressure values are surveyed at the beginning and end of the exposures and reveal pressure changes of ΔP = 0.2 to 0.8 mbar. The impact of the temperature and pressure variations on UVES radial velocity stability are of 50 m s^-1 for ΔT = 0.3 K or ΔP = 1 mbar⁴. The measured values assure radial velocity stability within ≈50 m s^-1. Of course, if such a spurious velocity shift were equally imparted to all transitions in a given spectrum, this would not result in a spurious shift in Δα/α, because only velocity shifts between transitions should affect a measured value of Δα/α. According to the Edlén (1966) formula for the refractive index of air, pressure, and temperature changes of 0.1 K and 1 mbar would cause differential velocity shifts of ≲15 m s^-1 across the wavelength range of the spectrum studied here, implying a negligible effect on Δα/α.

The use of attached ThAr lamps, together with the use of no on-chip pixel binning, and a narrower spectrograph slit are the main differences with respect to most of the previous observations dealing with the search for the variability of fundamental physical constants using UVES.

In the first analysis approach, the wavelength calibration was established with the CPL pipeline’s standard method, i.e. extraction of the ThAr flux along the centre of each Echelle order. In the second analysis approach, the ThAr flux was extracted using the object profile weights from its corresponding quasar exposure. The procedure for the selection of ThAr lines and the analysis leading to a wavelength solution follows the one outlined in Murphy et al. (2007a). Specifically, in the 390 nm or 437 nm frames about 400 ThAr lines were identified, and more than 55% of them were used to calibrate the lamp exposures. A polynomial of the fifth order was adopted to match the selected lines. Residuals of the wavelength calibrations were typically ≈0.34 mÅ, or ≈24 m s^-1 at 400 nm and symmetrically distributed at all wavelengths. We note that uncertainties of the laboratory wavelengths in individual thorium lines vary from about 15 m s^-1 up to more than 100 m s^-1 for the poorly known lines (Lovis & Pepe 2007; Murphy et al. 2007a).

2.4. Slit effects

The optical paths of the ThAr and quasar light beams through the spectrograph are not identical, so there may be effects that cannot be traced by the ThAr calibrations. The most important one is the difference in the slit illumination between a point-like source, such as a quasar, and the calibration lamp, which provides a relatively uniform illumination of the slit. Even when the point-like source is well centred on the slit, the precise position could vary slightly from one exposure to the next, depending also on telescope guiding and tracking. In UVES, a 1$\stackrel{\mathrm{″}}{.}$0 slit-width corresponds to ≈7.5 km s^-1 when projected onto the CCD. Therefore even a small shift of 0$\stackrel{\mathrm{″}}{.}$01 in the centroid of the light is sufficient to induce a shift of ~100 m s^-1 in the entire spectrum relative to its corresponding ThAr calibration exposure. Exposures taken at different times will in general show different radial velocity shifts due to this effect. Indeed, this effect has been measured by Wendt & Molaro (2012) by cross-correlating 15 UVES spectra of quasar Q0347−383. These spectra showed peak-to-peak excursions of up to ≈800 m s^-1 with an average deviation of 170 m s^-1.

Such a slit shift of all metal absorption lines by the same velocity in a single spectrum does not affect Δα/α. However, this effect becomes relevant when co-adding different exposures and when comparing, as for our observations, spectra obtained with different UVES settings: the mean slit shift will vary as a function of wavelength because of the different contributions from different settings at different wavelengths. This can produce a systematic effect on Δα/α if absorption lines from quite different wavelength regions are used. Also, small radial velocity shifts between exposures will produce a slight degradation of the S/N and of the effective instrumental line shape in the final co-added spectrum. The desire to obtain co-added quasar spectra with high S/N precludes the use of individual quasar exposures for analysis because they usually have S/N that are too low. One exception was the very bright quasar HE 0515−4414, which provided one of the highest statistical precisions on Δα/α from an individual absorption system so far (Levshakov et al. 2005).

In our first analysis approach we measured the relative slit shifts of the individual quasar exposures by cross-correlating them with the mean spectrum. After selecting regions without telluric lines or cosmic-ray features, we applied the XCSAO code from IRAF to cross-correlating the strongest absorption features. The two settings are summarized in Fig. 1. Despite the fact that relatively few features can be used for the purpose, global radial velocity shifts between different exposures were detected with high confidence. These slit shifts are typically a few hundred m s^-1 with a maximum amplitude of ≈700 m s^-1, in agreement with Wendt & Molaro (2012).

Fig. 1 Radial velocity “slit shifts” between absorption lines in individual exposures and the same lines in the mean spectrum. Left panel: shifts for the 390 nm (crosses) and 580 nm (triangles) settings. Right panel: shifts for the 437 nm (crosses) and bluer chip of the 760 nm (triangles) settings. In both panels, blue points correspond to the first analysis approach and the red points correspond to the second analysis approach. Representative error bars for each analysis approach are shown in each panel.

The second analysis approach used a custom χ² minimization technique to compare each individual exposure with the mean spectrum (rather than a cross-correlation method). This method is described in detail by Evans & Murphy (2013). Its principle advantage for this application is that it does not require prior identification of strong absorption features, instead utilizing all absorption features that contain enough spectral information to provide a reliable shift measurement for each exposure. The slit shifts measured via this second approach are also shown in Fig. 1. In general there is very good agreement between the measurements from the two approaches, broadly consistent with the typical uncertainty of ~30−80 m s^-1.

In Fig. 1 it is interesting to note that, in general, the shifts of the two different UVES arms of a given setting are comparable in amplitude and sign. This is expected in the case of good optical alignment of the two separate slits of the two UVES arms (blue and red). This is not obvious a priori because the two arms of the spectrograph have two different entrance slits, and any optical misalignment will produce radial velocity differences between the two arms’ spectra. Molaro et al. (2008a) compared the radial velocity measured in the two arms using the sunlight reflected by an asteroid, and came to a similar conclusion. We note that with UVES, no telescope or instrument control is provided to control the relative slit alignment with the desirable accuracy, and the optical alignment can, in principle, change from one observing run to another.

In both analysis approaches, each exposure was corrected for the slit shifts discussed above. The eight exposures were then combined in each setting separately to allow overlapping regions of neighbouring settings to be compared using the same two approaches as are discussed above (cross-correlation and χ² minimization). This revealed residual velocity shifts, referred to as “setting shifts” hereafter, between the 390 and 437-nm co-added spectra of −60 ± 52 and −93 ± 38 m s^-1 in the first and second analysis approaches, respectively. The settings shifts between the overlapping portions of the 580 and 760-nm co-added spectra were −7 ± 48 (first approach) and −155 ± 43 m s^-1(second approach). Unfortunately, there are too few strong, particularly narrow absorption features in the small overlapping wavelength range (~4800−4950 Å) between the 437 and 580-nm settings, so we cannot check the setting shifts between them with adequate precision. However, the previous results for the slit shifts between the two UVES arms discussed above provide evidence that the shift between the 437 and 580-nm settings should be consistent with zero within ~30 m s^-1. That is, we should expect the 390-vs-437-nm and 580-vs-760-nm setting shifts to be consistent with each other within each analysis approach, which we do observe. Indeed, for the second analysis approach, we adopted a single setting shift of −124 ± 41 m s^-1 as representative of the 390-vs-437 and 580-vs-760-nm estimates. We should not expect large differences between the setting shifts of the two different approaches, and this also seems to be observed.

In both analysis approaches, the final spectrum (in which Δα/α is to be measured) was formed by co-adding the eight exposures in all settings after removing the “slit shifts” and “setting shifts” from the individual exposures. These final spectra have a high S/N, with values up to ≈100 in the continuum in most of the spectral regions of interest. In Sect. 4.1.1 we consider the effect of not correcting for the slit and setting shifts.

2.5. Known systematic effects in the wavelength calibration

The possible presence of distortions in wavelength scales of Keck/HIRES spectra was investigated by Griest et al. (2010) by comparing the ThAr wavelength scale with the one established from I2-cell observations. In the wavelength range ~5000−6200 Å covered by the iodine cell absorptions, they found a sawtooth distortion pattern with an amplitude of typically 300 m s^-1 along each echelle order. The distortions are such that transitions at the order edges appear at different velocities with respect to transitions at the order centres when the two calibrations are compared. Whitmore et al. (2010) repeated the same test for UVES and found similar effects, though the sawtooth distortion shows reduced peak-to-peak velocity variations of ~200 m s^-1.

The origin of these distortion is not clear. Wilken et al. (2010) detected very small differences in the size of physical pixels due to CCD manufacturing on spectra obtained with the HARPS spectrograph at the 3.6m ESO telescope on La Silla, and calibrated by means of a Laser Frequency Comb. In general, an individual CCD sensor is built up by means of several unit cells or blocks that are connected to each other during the design or layout phase of the development cycle of the sensor. The block stitching process could produce misalignments between different CCD blocks of the order of ~10^-2 of the pixel size. The calibration polynomial cannot cope with these sudden changes in the dispersion solution and oscillates to accommodate it. This overcompensation will produce local calibration distortions. Since blocks have typical sizes of 512 pixels, or ≈13 Å in UVES, shifts could occur even for neighbouring absorption lines, such as the Mg ii doublet, or even within a single absorption profile where the components span several hundred km s^-1 and may fall over two different CCD manufacturing blocks. We test for systematic errors of this kind in Sect. 4.1.1.

We note that Molaro et al. (2011) compared solar features observed both with HARPS and UVES and found such intra-order distortions in the UVES spectrum on a typical scale of ≈10 Å. In HARPS the offsets were measured up to 50 m s^-1within one order and in UVES, where the pixel size is a factor 3 bigger, the offsets could be a factor 3 larger. We note also that the ±40 m s^-1 inaccuracies of the HARPS wavelength scale revealed by the Laser Frequency Comb test contribute to the linelist constructed for use with UVES (Lovis & Pepe 2007; Murphy et al. 2007a).

3. Many-multiplet method and fitting

3.1. Many-multiplet method

The change in the rest-frame frequencies between the laboratory, ω_i(0), and in an absorber at redshift z, ω_i(z), due to a small variation in α, i.e. Δα/α≪ 1, is proportional to a q-coefficient for that transition: ${\mathit{\omega }}_{\mathit{i}}\mathrm{\left(}\mathit{z}\mathrm{\right)}\mathrm{\equiv }{\mathit{\omega }}_{\mathit{i}}\mathrm{\left(}\mathrm{0}\mathrm{\right)}\mathrm{+}{\mathit{q}}_{\mathit{i}}\mathrm{[}{\left({\mathit{\alpha }}_{\mathit{z}}\mathit{/}{\mathit{\alpha }}_{\mathrm{0}}\right)}^{\mathrm{2}}\mathrm{-}{\mathrm{1}}^{\mathrm{]}}\hspace{0.17em}\mathit{,}$(1)where α₀ and α_z are the laboratory and absorber values of α, respectively (Dzuba et al. 1999). The q-coefficients for the transitions of interest are given in the last column of Table 2. The change in frequency is observable as a velocity shift, Δv_i, of transition i: $\frac{\mathrm{\Delta }{\mathit{v}}_{\mathit{i}}}{\mathit{c}}\mathrm{\approx }\mathrm{-}\mathrm{2}\frac{\mathrm{\Delta }\mathit{\alpha }}{\mathit{\alpha }}\frac{{\mathit{q}}_{\mathit{i}}}{{\mathit{\omega }}_{\mathit{i}}\mathrm{\left(}\mathrm{0}\mathrm{\right)}}\mathrm{·}$(2)The MM method is based on the comparison of measured velocity shifts from several transitions having different q-coefficients to compute the best-fitting Δα/α.

When applied across a variety of different ionic species (i.e. different atoms or ionization stages of the same atom), the MM method assumes that the different species trace the same material, or at least that there are no substantial intrinsic velocity shifts between the absorption lines of different species. Therefore, to reduce the number of free parameters in a fit to all transitions of all species, we impose the requirement that corresponding fitted velocity components in different species share the same overall redshifts (i.e. cosmological redshift and peculiar velocity combined). Unless there is evidence that lines are thermally broadened, we also assume that the lines are broadened by macro-turbulence motions. That is, we assume that corresponding velocity components in different species have the same fitted Doppler broadening parameter.

The laboratory atomic parameters used in our analyses – rest-frame frequencies, oscillatory strengths, etc. – were taken from a new compilation (Murphy & Berengut, in prep.), the important details of which are not significantly different from what is used by King et al. (2012). These are reported in Table 2. In particular, the laboratory wavelength for the Fe ii λ1608 transition was taken from Nave & Sansonetti (2011). The isotopic structures of most transitions are also reported, together with the composite laboratory wavelength expected for a solar isotope composition.

3.2. Selection of transitions

To build the best model of the velocity structure of an absorption system, we try to include as many different transitions as possible. However, the presence of contaminating absorption lines could strongly skew the analysis, so we did not include transitions that were blended with absorption features of other systems at other redshifts. For the two different analysis approaches, we took two approaches to deal with sky (telluric) lines. The first approach was to remove the regions affected by the telluric lines if their presence could be established based on the spectrum itself, or through comparison with a standard star spectrum taken during our observations. The second approach was more conservative, completely rejecting transitions that had any possible telluric line contamination, even if only in a small part of the velocity structure of the transition. Finally, in neither approach did we consider any transitions that fall in the Lyα forest portion of the spectrum for the analysis of Δα/α, even if part of their velocity structure presented no evidence of contamination by broad Lyα lines.

3.3. Absorption-line fitting

The model fitting of the absorption profile is performed by means of the non-linear least squares Voigt profile fitting programme VPFIT by Bob Carswell and John Webb⁵. This code has been widely used for the absorption line analysis and has been modified to incorporate α as a free parameter in the fit (Murphy et al. 2003). For a given transition to be fitted, the model is specified by defining the number of components, the spectral region on which the fitting is performed and the instrumental profile. The analysis in both approaches proceeds in two basic steps. The first one consists in obtaining a fiducial model for the absorption while keeping Δα/α fixed at zero. That is, the number of velocity components and their distribution across the absorption complex is refined without any influence on or from a varying Δα/α parameter. Once the model for the absorption has been derived, giving a satisfactory fit of the data with all residuals consistent with the error arrays, Δα/α is introduced as a new free parameter to provide a better fit to the data.

The statistical uncertainty in Δα/α is determined from the relevant diagonal term of the covariance matrix of the best-fitting solution. This is multiplied by $\sqrt{{\mathit{\chi }}_{\mathit{\nu }}^{\mathrm{2}}}$, where ${\mathit{\chi }}_{\mathit{\nu }}^{\mathrm{2}}$ is the χ² between the model and data per degree of freedom, ν, to yield more reliable uncertainties (Press et al. 1992). The accuracy and reliability of these statistical uncertainties has been confirmed with detailed Monte Carlo and also Monte-Carlo Markov-chain simulations (King et al. 2009; Murphy 2002). This approach is successful because the covariance between the Δα/α parameter and other parameters in the fit is minimal. However, this is not always true for parameters of individual components in the fit. In particular, the column density and Doppler broadening parameters of an individual component are covariant, and strongly covariant with those parameters of close-blended neighbouring components. In the final absorption profile models presented in Tables 4−8, and described in the following sections, we present only statistical uncertainties derived from the diagonal terms of the covariance matrix for the parameters of individual components.

Finally, during the fitting process, we set a lower limit on the Doppler parameter for individual components of b = 0.5 km s^-1, which is well below the FWHM resolution of the spectra (~5.5 km s^-1). These unresolved components generally have formal uncertainties (quoted in Tables 4−8) exceeding 0.5 km s^-1. In these cases, and for other components with b-parameters uncertainties exceeding their best-fitted value, it should be recognized that, while b is formally consistent with zero, this does not indicate that the component is redundant in the fit.

3.4. Instrument profile

The FWHM of the instrumental profile of UVES varies by ≈20% along every echelle order due to the spectrograph anamorphosis. Therefore, the FWHM was computed by averaging the width of unblended thorium emission lines in the wavelength region around the metal absorption lines used to derive Δα/α. That is, the FWHM was calculated separately for each transition. Moreover, it is known that the FWHM of ThAr lines produced by a fully-illuminated slit is slightly broader than what is produced by a point source that under-fills the slit. Simple models suggest that, even with FWHM seeing equivalent to the slit width, the reduction in the FWHM resolution is ≈10%. The values used in the present analysis are those given in Table 3 reduced by 10%.

4. Analysis of absorption systems

We present below the analysis of the five absorption systems towards HE 2217−2818 in which we can measure Δα/α. We focus first on the highest redshift absorber, the one at z_abs = 1.6919, because this provides by-far the highest statistical precision on Δα/α and, therefore, requires the most comprehensive analysis and consideration of underlying systematic errors. We therefore describe our two different analysis approaches in detail for this system. For the other absorbers, we do not present all details of systematic error checks because the statistical uncertainly dominates the total error budget. We present only the results one analysis approach (the second) for simplicity.

4.1. Absorption system at z_abs = 1.6919

The system at redshift z_abs = 1.6919 shows a quite complex velocity structure with many separate strong, narrow features spread over ~250 km s^-1. The transitions observed redwards of the Lyα forest in our spectral range are potentially useful for measuring Δα/α are Al ii λλ1670, Al ii λλ1854, 1862, Mg ii λλ2796 and Fe ii λλ1608, 2344, 2374, 2382, 2586, 2600. Unfortunately, the detected Mg ii λ2796 transition cannot be used because it is partially contaminated by a strong sky emission at ≈7526.8 Å. The Mg ii λ2803 and Mg i λ2852 transitions were not detected because they fall into the gap between the two red-arm CCDs in the 760-nm setting. The subset of these transitions used to constrain Δα/α in the second analysis approach is shown in Fig. 2.

Figure 2 shows that the velocity structure and relative strength of the different features is very similar in all the low-ionization transitions. The Al iii λλ1854/1862 doublet is not observed with high S/N and is not particularly strong. Since a higher ionization species than the other transitions, including it in the analysis may introduce a stronger sensitivity to possible ionization differences between species. However, no evidence of any differences in velocity structure is evident in Fig. 2, even though the relative strength of some features differs from the lower ionization transitions. In general, some features are quite weak even in the stronger transitions and so they are not detectable in the weaker transitions. Even by cursory visual inspection, it is clear that the stronger features are not symmetric and particularly narrow (unresolved); instead, their breadth and asymmetries reveal unresolved complex velocity structure.

Fig. 2 Transitions in absorption system at zabs = 1.6919 used to derive Δα/α in our second analysis approach. The Voigt profile model (green line) is plotted over the data (blue histogram). The velocity of each fitted component is marked with a vertical line, and the residuals between the data and model, normalized by the error spectrum, are shown above each transition. The top panel shows the composite residual spectrum − the mean spectrum of the normalized residuals for all transitions shown − in units of σ.

Careful inspection of the spectrum of a fast-rotating star allowed us to precisely identify the position of telluric features. The Fe iiλ2344, Fe iiλ2586, and Fe iiλ2600 all fall in a spectral region affected by telluric lines. Removing telluric absorption features is quite a difficult task because they vary with the physical conditions of the Earth’s atmosphere, thereby introducing time and line-of-sight dependencies. We did not attempt a correction, but instead we adopted two different approaches to deal with this.

In the first analysis approach we excluded the spectral portions around the telluric lines in these transitions but included the remaining portions in the Δα/α analysis. For Fe iiλ2344 we considered only the intervals 6310.5−6311.5 and 6312.25−6312.7 Å. For Fe iiλ2586 we considered only the intervals 6959.6−6961.5 and 6964.4−6965.75 Å  and for Fe iiλ2600 the intervals 6996.7−7000.5 and 7001.55−7002.79 Å. Our second analysis approach only considers the transitions that are not affected by telluric or any other contaminating lines. These are the three Fe ii transitions λλ1608, 2374, 2382, the Al iiλ1670 transition, and the Al iii λλ1854/1862 doublet, as shown in Fig. 2.

The models of the absorption profiles were built up, step-by-step, by adding components at different velocities in all fitted species simultaneously and minimizing χ² at each step with Δα/α fixed at zero. The absorber’s velocity structure is quite complex, and our first and second analysis approaches used 30 and 32 velocity components, respectively, to obtain statistically acceptable fits with χ² per degree of freedom, ${\mathit{\chi }}_{\mathit{\nu }}^{\mathrm{2}}\mathrm{\approx }\mathrm{1}$. This large number of velocity components is consistent the aforementioned characteristics of the profile: the five main features all show asymmetries and require at least two or three components each to adequately fit them. Additional components are needed to account for weak absorption between these main features and the need for these components is clear from inspecting the line profiles of the optically thick transitions. We note that these weak components do not influence the value of Δα/α significantly. The first analysis approach excluded two of these components; i.e., the first approach represents a “minimally complex” model. Conversely, the second approach required that the chosen model was the one that minimized ${\mathit{\chi }}_{\mathit{\nu }}^{\mathrm{2}}$. The 32-component model is provided in Table 4, with the final ${\mathit{\chi }}_{\mathit{\nu }}^{\mathrm{2}}\mathrm{=}\mathrm{1.20}$.

After the number and nominal relative velocities of the fitted components are finalized, Δα/α is introduced as an additional free parameter and determined in the χ² process along with all other free parameters. The two analysis approaches give the following best-fit values and 1σ statistical uncertainties for Δα/α: $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\{\begin{array}{c}\\ \mathrm{-}\mathrm{3.8}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{2.1}}_{\mathrm{stat}}\mathrm{ppm}& \mathrm{\left(}\mathrm{firstapproach}\mathrm{\right)}\mathit{,}\\ \mathrm{+}\mathrm{1.3}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{2.4}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{ppm}& \mathrm{\left(}\mathrm{secondapproach}\mathrm{\right)}\mathrm{.}\end{array}$(3)The main constraints on Δα/α are contributed by the combination of the high S/N transitions with diverse q-coefficients, i.e. those of Al ii and Fe ii, particularly the Fe ii λ1608 transition, that has a q-coefficient with an opposite sign to the others. The results from the two analysis approaches in Eq. (3) appear at first to be rather inconsistent. This may indicate that important systematic errors are present in the calibration and analysis steps, since these constitute the main difference between the two approaches. We explore possible systematic errors in more detail in Sect. 4.1.1 below.

One notable difference between the two analysis approaches is that the first includes six Fe ii transitions, or parts thereof (after masking telluric features), thereby making an analysis that uses just those transitions feasible. Using just one ionic species alleviates the possibility that ionization effects may systematically affect Δα/α (e.g. Levshakov et al. 2005). Of course, in the case of Fe ii, the precision and accuracy of the result depend heavily on the Fe ii λ1608 transition, and any possible systematic errors applying to the data or wavelength calibration relevant to it. To conduct this Fe-only test, we restricted the region analysed in each transition to the velocity range −35 to +250 km s^-1 in Fig. 2. This effectively removed the two velocity components in the model for the first approach that corresponds to the weak features at the blue and red flanks of the absorber. A further two velocity components from that model were discarded as unnecessary by vpfit because the high S/N Al ii λ1670 transition had been removed. This left the model with 26 components. Furthermore, we derived Δα/α on a different reduction of the spectrum, with a slightly different binning and exposure combination approach to those presented above. The result based on this Fe-only analysis is Δα/α = +1.14 ± 2.58_stat ppm. The difference between this result and the one from the first approach in Eq. (3) demonstrates that systematic effects may play an important role in the total uncertainty in Δα/α. We turn to quantifying the systematic error budget for this absorber below.

4.1.1. Systematic error tests

We ran a number of tests on the second analysis approach to uncover the sensitivity of the result to various systematic effects. For each of these tests, we find the maximum deviation between the second approach’s Δα/α value in Eq. (3) and the one given by the test, adding the results in quadrature to estimate the total systematic error budget.

Firstly, to test the convergence of the fitting procedure, we restarted the χ² minimization from its final solution but with starting values of Δα/α set to +1σ and −1σ away from its fiducial value. Both these test fits converged to Δα/α values very close to those in Eq. (3). The largest difference was 0.03 ppm, which we added in quadrature to the total systematic error budget.

The second test investigated the effect that co-adding the individual exposures into a final spectrum has on the absorption line centroids and, therefore, Δα/α. The software used to combine the spectra in the second analysis approach, uves_popler, first redisperses all Echelle orders, from all exposures, onto a common wavelength scale with a constant pixel size in velocity space. A dispersion of 1.30 km s^-1 pixel^-1 was used for the final spectrum. To test the effect of redispersing and co-adding the individual exposures, we produced four new co-added spectra with slightly different dispersion values − 1.28, 1.29, 1.3, and 1.32 km s^-1 pixel^-1 , which ensures that the pixel grids will be very different for each transition from spectrum to spectrum. The values of Δα/α for these four different spectra varied by at most 0.54 ppm, and this was added in quadrature to the total systematic error budget.

The third test quantified the possible effect the intra-order distortions of the UVES wavelength scale found by Whitmore et al. (2010) may have on Δα/α. For each Echelle order, of each exposure, we applied a sawtooth distortion to the existing wavelength scale and then co-added them in the usual way. The distortion applied had a peak-to-peak amplitude of 200 m s^-1, varying from −100 m s^-1 at the order edges to +100 m s^-1 and the order centres. We also produced a second distorted spectrum where this sawtooth pattern was reversed. Of course, we cannot be sure that the effect identified by Whitmore et al. (2010) is present in our spectra or that it has the same pattern or magnitude in our spectra, but the two distorted spectra produced in this way allow us to gauge the size of the effect on Δα/α. Refitting for Δα/α on these distorted spectra gives a maximum deviation between the distorted and fiducial results of 0.56 ppm.

The final test was aimed at understanding the effect that the slit shifts and setting shifts discussed in Sect. 2.4 have on Δα/α. The most straightforward test is to determine Δα/α using spectra in which these corrections have not been applied in the second analysis approach. Unsurprisingly, not applying the setting shift (−124 ± 41 m s^-1) produces the largest difference in Δα/α, 1.2 ppm, thus demonstrating that, were these effects not corrected, they would have caused a significant systematic error, or about 50% of the statistical error. However, while we have corrected for these effects, we can not have done so perfectly, and errors in our corrections will propagate as systematic errors in Δα/α. The relative uncertainty on the setting shift is 33%, so we expect that the residual systematic error in this case is of the order of 0.4 ppm.

After adding the above estimates of the systematic error in quadrature, the total systematic error budget is 0.96 ppm. That is, the final result from the second analysis approach is $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\hspace{0.17em}\mathrm{+}\mathrm{1.3}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{2.4}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{1.0}}_{\mathrm{sys}}\hspace{0.17em}\mathrm{ppm}\hspace{0.17em}\mathit{.}$(4)

4.2. Absorption system at z_abs = 1.6279

The transitions used to constrain Δα/α in the second analysis approach for the absorption system at z_abs = 1.6279 are shown in Fig. 3. The absorption profile model parameters from this approach are provided in Table 5. The absorption spans ~100 km s^-1 with three main features that are rather broad and very asymmetric, revealing quite a complex underlying velocity structure. Detected transitions not used to constrain Δα/α include strong Si ii λ1526 absorption, which falls in the Lyα forest.

Fig. 3 Absorption profile for system at zabs = 1.6279 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 5.

The broad and multi-component nature of the three main absorption features translates to large statistical uncertainties on the redshifts of the velocity components and, therefore, to Δα/α. The systematic error budget was determined by conducting the same systematic error tests as conducted on the z_abs = 1.6919 absorber in Sect. 4.1.1. The final result for this z_abs = 1.6279 absorber is then $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\hspace{0.17em}\mathrm{+}\mathrm{37.2}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{20.6}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{39.4}}_{\mathrm{sys}}\hspace{0.17em}\mathrm{ppm}\mathit{.}$(5)

4.3. Absorption system at z_abs = 1.5558

The transitions used to constrain Δα/α in the second analysis approach for the absorption system at z_abs = 1.5558 are shown in Fig. 4. The absorption profile model parameters from this approach are provided in Table 6. The absorption spans ~100 km s^-1 with three main features that appear at first to be rather symmetric and narrower than the three features in the z_abs = 1.6279 absorber. Indeed, the underlying velocity structure of these three features appears to be dominated by a single strong component in each case. However, our detailed approach to fitting all the statistically required velocity components reveals that several weaker components are required for an adequate fit. These are required for the higher optical depth transitions of Mg ii λ2796 and Al ii λ1670. There are three telluric features that contaminate the Mg ii λ2803, so this is excluded from the analysis.

Fig. 4 Absorption profile for system at zabs = 1.5558 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 6.

The χ² minimization analysis of the z_abs = 1.5558 profiles shown in Fig. 4 and the systematic error tests conducted in Sect. 4.1.1 provide a final result of $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\mathrm{-}\mathrm{0.2}\mathrm{\pm }{\mathrm{24.9}}_{\mathrm{stat}}\mathrm{\pm }{\mathrm{3.6}}_{\mathrm{sys}}\hspace{0.17em}\mathrm{ppm}\mathit{.}$(6) Given the relatively large statistical uncertainty on Δα/α in this absorber, we neglect here the systematic error budget because it will be much smaller.

4.4. Absorption systems at z_abs = 0.9407 and 0.9424

The absorption around z_abs = 0.941 comprises two absorption complexes, one with the main absorption at z_abs = 0.9407 and the second with the strongest absorption at z_abs = 0.9424. They are separated by ~300 km s^-1 without any hint of absorption in any of the strongest detected transitions. We therefore fit them separately. The transitions used to constrain Δα/α in the second analysis approach for these systems are shown in Figs. 5 and 6. The absorption profile model parameters from this approach are provided in Table 7.

Fig. 5 Absorption profile for system at zabs = 0.9407 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 7.

Fig. 6 Absorption profile for system at zabs = 0.9424 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 7.

The absorption at z_abs = 0.9407 spans ~100 km s^-1  and at z_abs = 0.9407 it spans ~180 km s^-1 in the strongest transition, Mg ii λ2796. The first system comprises two well-separated features, while the second comprises four closely separated strong features, but in both systems the strong features are broad and smooth with strong asymmetries. Thus, fairly complex absorption models were fitted to these systems, with the strong features comprising several velocity components of similar strength each.

The χ² minimization analysis of the profiles shown in Figs. 5 and 6, and the systematic error tests in Sect. 4.1.1, provide the following results: $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\{\begin{array}{c}\\ \mathrm{+}\mathrm{21.4}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{24.2}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{20.9}}_{\mathrm{sys}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{ppm}& \hspace{0.17em}\hspace{0.17em}\mathrm{at}{\mathit{z}}_{\mathrm{abs}}\mathrm{=}\mathrm{0.9407}\mathit{,}\\ \mathrm{+}\mathrm{9.3}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{12.7}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{9.8}}_{\mathrm{sys}}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\mathrm{ppm}& \hspace{0.17em}\hspace{0.17em}\mathrm{at}{\mathit{z}}_{\mathrm{abs}}\mathrm{=}\mathrm{0.9424.}\end{array}$(7)Given the relatively large statistical uncertainties on Δα/α in these absorbers, we neglect the systematic error budgets because they will be much smaller.

4.5. Absorption system at z_abs = 0.7866

The transitions used to constrain Δα/α in the second analysis approach for the absorption system at z_abs = 0.7866 are shown in Fig. 7. The absorption profile model parameters from this approach are provided in Table 8. The absorption spans ~90 km s^-1 in one broad complex of several highly blended features, each of which shows visual evidence of asymmetries, and none of which are particularly narrow. Thus, like all the other absorbers studied here, the main absorption features require several velocity components for an adequate fit. Detected transitions not used to constrain Δα/α include strong Si ii λ1526 absorption that falls in the Lyα forest.

Fig. 7 Absorption profile for system at zabs = 0.7866 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 8.

The χ² minimization analysis of the z_abs = 0.7866 profiles shown in Fig. 7 and the systematic error tests in Sect. 4.1.1 provide a final result of $\mathrm{\Delta }\mathit{\alpha }\mathit{/}\mathit{\alpha }\mathrm{=}\mathrm{+}\mathrm{7.3}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{35.9}}_{\mathrm{stat}}\hspace{0.17em}\mathrm{\pm }\hspace{0.17em}{\mathrm{21.4}}_{\mathrm{sys}}\hspace{0.17em}\mathrm{ppm}\hspace{0.17em}\mathit{.}$(8)Given the relatively large statistical uncertainty on Δα/α in this absorber, we neglect here the systematic error budget because it will be much smaller.

5. Discussion

Current searches for cosmological variations in the fine-structure constant are based on the analysis of large samples of absorption systems observed at different redshifts and directions in the sky. Thanks to the large size of these samples, it is possible to reach an ensemble sensitivity of a few ppm in Δα/α. On the other hand, deep observations of a few selected lines of sight are capable of producing measurements with similar statistical errors. The two approaches have both intrinsic merits: the former is more effective in detecting possible changes as a function of redshift or across different regions of space, and possibly for averaging down systematic effects; the last allows more detailed analysis, potentially facilitating the identification of possible systematic errors that may go undetected in a large number of systems.

Fig. 8 Summary of Δα/α measurements towards HE 2217−2818. Each absorption system’s Δα/α value from the second analysis approach is plotted with its 1σ statistical uncertainty, plus the total uncertainty formed by quadrature addition of the statistical and systematic errors in Table 9.

The line of sight towards the relatively bright quasar HE 2217−2818 is rich with absorption systems. Our MM analysis of the five systems observed at z_abs = 0.7866, 0.9407, 0.9424, 1.5558, 1.6279  and 1.6919 provides no evidence of a change of the fine-structure constant. In particular, the system at z_abs = 1.6919 provides a very precise bound on variations in α: Δα/α = +1.3 ± 2.4_stat ± 1.0_sys ppm. This result, stemming from our second analysis approach in which we conducted several tests to constrain the systematic error budget, differs somewhat from the first approach, conducted separately with different details of the data reduction, calibration, and analysis:  ppm. This may indicate that systematic errors are greater than expected from the range of tests we conducted. However, it is interesting to note that restricting the first approach to the six Fe ii transitions and using a modified absorption model yields a similar result to the second approach, Δα/α = +1.1 ± 2.6_stat ppm. Clearly, it is important to continue to refine the analysis techniques to minimize differences in the results obtained by different approaches. Our future papers on this and other quasars in our Large Program of new VLT/UVES observations will aim at that goal.

The main reasons for the small statistical uncertainty in Δα/α from the z_abs = 1.6919 absorber are the several narrow absorption features across its absorption profile including the Fe iiλ1608 transition that, compared to the other Fe ii transitions in particular, provide a wide range of q-coefficients among the fitted transitions, and the high S/N of the spectra. Unfortunately, the absorption features that characterize the four other absorbers tended to be somewhat broader. And with a narrower range of q coefficients available from the fitted transitions, the statistical uncertainties in those absorbers exceeded 10 ppm.

The bound on Δα/α obtained from the z_abs = 1.6919 system is one of the most precise measurements available from an individual absorber. Three other studies of individual absorbers have claimed measurements with comparably small uncertainties. These are Δα/α = −0.07 ± 1.8 ppm obtained from absorption at z_abs = 1.15 towards the extremely bright quasar HE 0515−4414 (Molaro et al. 2008b), Δα/α = 5.4 ± 2.5 ppm from the system at z_abs = 1.84 towards quasar Q 1101−264 (Levshakov et al. 2006), and Δα/α = −1.5 ± 2.6 ppm from the system at z_abs = 1.58 towards HE 0001−2340 (Agafonova et al. 2011). The first two were both obtained by comparing only Fe ii lines with each other, while the last was derived through a comparison of Fe ii and Si ii transitions. The result at z_abs = 1.6919 presented here was obtained by comparing Al ii λ1670 and several Fe ii transitions, including Fe ii λ1608. Broad agreement is found when using only the Fe ii lines, particularly when considering the total systematic error budget of 2.4 ppm and the strong dependence on Fe ii λ1608 in that case. Therefore, we find no strong evidence of any influence from differential ionization effects that may be present when comparing different ions.

Recently, King et al. (2012) have analysed a new sample of 153 measurements obtained from observations taken with UVES at the ESO VLT, adding to the previous sample of 143 absorption systems obtained from the analysis of Keck/HIRES spectra (Murphy et al. 2003). The two samples generally probe different directions in the universe, and rather surprisingly they show a different dependence on redshift; that is, α has appeared on average to be smaller in the past in the northern hemisphere but larger in the past in the southern hemisphere. This is particularly the case for the combined dataset at redshift ≥1.8. Overall, the variation across the sky can be simply and consistently represented by a monopole (i.e. a constant offset in α from the current laboratory value) plus a spatial dipole in the direction with right ascension 17.3 ± 1.0 h and declination −61 ± 10 degrees (King et al. 2012). The spatial dependence is fitted with Δα/α = m + AcosΘ, where A is the dipole amplitude A = 9.7 ± 2.1 ppm, Θ is the angle on the sky between a quasar sight-line and the best-fit dipole position, and m = −1.78 ± 0.84 ppm is the monopole term. A simpler model, without the monopole term, gives A = 10.2 ± 2.1 ppm with a pole towards right ascension 17.4 ± 0.9 h and declination −58 ± 9 degrees (King et al. 2012).

The dipole amplitude of ≈10 ppm could in principle be revealed by precise measurements along individual lines of sight. The pole and anti-pole directions are observationally difficult regions to study, particularly the pole that is very close to the Galactic centre and virtually devoid of bright quasars. Towards the directions for which precise individual absorbers have been studied, the variation in α expected by the dipole model is small and cannot be revealed by current accuracies⁶. However, the line of sight towards HE 2217−2818 subtends an angle Θ = 58.8° with respect to the simple dipole-only model above which it is small enough to produce a signal that may be detectable along this single line of sight: the predicted signal is Δα/α = +5.4 ± 1.7 ppm. For a simple comparison with our main result here (Δα/α = +1.3 ± 2.4_stat ± 1.0_sys ppm), we combined its statistical and systematic error terms in quadrature, which reveals that it differs from this simple dipole prediction (including its uncertainty) by 1.3σ. The prediction from the monopole+dipole model at the sky position of HE 2217−2818 is Δα/α = +3.2 ± 1.7 ppm⁷. Thus, our most precise result towards HE 2217−2818 does not directly support evidence of a dipolar variation in α across the sky, though it does not provide compelling evidence against it either.

6. Conclusions

The line of sight towards the relatively bright quasar HE 2217−2818 is rich with absorption systems and is located in the sky at a favourable position for probing the recently proposed presence of spatial variation of the fine structure constant, α. It is the first quasar from our ongoing VLT/UVES Large Program to measure Δα/α in ~25 absorbers towards ~12 bright quasars, from which we expect to make ~20 measurements of Δα/α with precision ≲10 ppm. Approximately ten of these − the absorbers that are the main targets of the Large Programme − will provide very high statistical precisions of ~2 ppm each and systematic uncertainties ≲2 ppm. This will yield a final ensemble precision of better than 1 ppm with the additional aim of better understanding possible systematic uncertainties at this accuracy level. Our MM analysis here of the five absorption systems observed at z_abs = 0.7866, 0.9407, 0.9424, 1.5558, 1.6279  and 1.6919 is in keeping with these goals: the highest-redshift absorber provides a very precise and robust measurement at the ~2 ppm level while the four others provide weaker constraints ≳10 ppm.

The high S/N, sharp absorption features, and diversity of sensitivity to α in the transitions of the z_abs = 1.6919 absorber provides the most stringent measurement of Δα/α for this line of sight. Two separate approaches to the data reduction, calibration, and absorption-line fitting yielded slightly different results −  −3.8 ppm and Δα/α = +1.3 ± 2.4_stat , though both are consistent with no variation in α. We also investigated a number of sources of systematic errors in this system and the effect that they might have on the final measurement. Our final result for this absorber, including both statistical and systematic error terms, is Δα/α = +1.3 ± 2.4_stat ± 1.0_sys. The results for all the absorption systems are summarized in Table 9.

If the evidence for a spatial variation of α across the sky presented by Webb et al. (2011) and King et al. (2012) represents reality, then the simplest model of those results − a dipolar variation in α − predicts Δα/α = 5.4 ± 1.7 ppm in the direction of the line of sight of HE 2217−2818. Our constraint on Δα/α from the z_abs = 1.6919 absorber neither strongly supports nor conflicts with that prediction.

Online material

Acknowledgments

An anonymous referee is acknowledged for several pieces of advice. P.M. and C.J.M. acknowledge support from grants PTDC/FIS/111725/2009 and PTDC/CTE-AST/098604/2008 from the FCT, Portugal. The work of P.M. was partially funded by grant CAUP-06/2010-BCC. The work of C.J.M. is funded by a Ciência 2007 Research Contract, funded by FCT/MCTES (Portugal) and POPH/FSE (EC). M.T.M. thanks the Australian Research Council for funding under the Discovery Projects scheme (DP110100866). P.P.J. is supported in part by Agence Nationale pour la Recherche under contract ANR-10-Blan-0510-01. R.S. and P.P.J. gratefully acknowledge support from the Indo-French Centre for the Promotion of Advanced Research (Centre Franco-Indien pour la promotion de la recherche avancée) under Project N.4304-2. S.L. has been supported by FONDECYT grant number 1100214. The work of I.I.A. and S.A.L. is supported by DFG Sonderforschungsbereich SFB 676 Teilprojekt C4 and, in part, by the State Programme Leading Scientific Schools of Russian Federation (grant NSh 4035.2012.2).

References

All Tables

All Figures

Fig. 1 Radial velocity “slit shifts” between absorption lines in individual exposures and the same lines in the mean spectrum. Left panel: shifts for the 390 nm (crosses) and 580 nm (triangles) settings. Right panel: shifts for the 437 nm (crosses) and bluer chip of the 760 nm (triangles) settings. In both panels, blue points correspond to the first analysis approach and the red points correspond to the second analysis approach. Representative error bars for each analysis approach are shown in each panel.

In the text

Fig. 2 Transitions in absorption system at zabs = 1.6919 used to derive Δα/α in our second analysis approach. The Voigt profile model (green line) is plotted over the data (blue histogram). The velocity of each fitted component is marked with a vertical line, and the residuals between the data and model, normalized by the error spectrum, are shown above each transition. The top panel shows the composite residual spectrum − the mean spectrum of the normalized residuals for all transitions shown − in units of σ.

In the text

	Fig. 3 Absorption profile for system at zabs = 1.6279 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 5.
In the text

	Fig. 4 Absorption profile for system at zabs = 1.5558 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 6.
In the text

	Fig. 5 Absorption profile for system at zabs = 0.9407 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 7.
In the text

	Fig. 6 Absorption profile for system at zabs = 0.9424 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 7.
In the text

	Fig. 7 Absorption profile for system at zabs = 0.7866 with transitions used in the second analysis approach for determining Δα/α. The figure is structured as in Fig. 2. Details of the absorption profile fit are given in Table 8.
In the text

	Fig. 8 Summary of Δα/α measurements towards HE 2217−2818. Each absorption system’s Δα/α value from the second analysis approach is plotted with its 1σ statistical uncertainty, plus the total uncertainty formed by quadrature addition of the statistical and systematic errors in Table 9.
In the text