ON THE VARIATIONS OF FUNDAMENTAL CONSTANTS AND ACTIVE GALACTIC NUCLEUS FEEDBACK IN THE QUASI-STELLAR OBJECT HOST GALAXY RXJ0911.4+0551 at z = 2.79

The line and continuum distribution of our observations is shown in comparison to the near-infrared (NIR; archival HST-NICMOS image) in Figure 1 (left). The PdBI image shows two separate sources. The eastern source (A) is a blend of the QSO images A1, A2, and A3 (following the labeling by Burud et al. 1998), the western source is the fourth lens image of the QSO (image B) which is spatially separated from component A by ≈3''. The NIR and mm emission regions are displaced with respect to each other by about ∼025. This shift is obvious for image B but can also be established for A if one convolved the HST-NICMOS image to the PdBI beam. We interpret the offset as inaccurate astrometry (rather than an indication for differential magnification between the mm and NIR light), presumably in the HST-NICMOS image, as the coordinates in the PdBI observations are phase referenced. The PdBI position for image B is R.A.: 09^h11^m27430 (±001), decl: 05°50'547 (±015) (J2000).

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The line intensity ratio between C i and CO is comparable for both components with I_C i(2−1)/I_CO(7-6) = 0.60 ± 0.02 and 0.70 ± 0.07 for A and B, respectively. The center velocities (as measured from CO) of images A and B are in good agreement and do not show a redshift difference within the uncertainties (Δv = −4.6 ± 3.1 km s⁻¹). The intensity ratio between images B and A as measured from the integrated CO(7–6) flux density is I_B/I_A = 0.21 ± 0.01, in agreement with the flux ratio measured in the optical U-band (restframe LUV (∼100 nm); Burud et al. 1998). This suggests that the submillimeter light has a magnification similar to the optical light and in the following we adopt the lens model by Burud et al. (1998) with a magnification of μ_mag = 20.

The 3.6 GHz wide spectrum toward image A is shown at a velocity resolution of 10 km s⁻¹ in Figure 1 (right). Several other redshifted molecular transitions fall into the observed bandwidth. Some lines (indicated in the figure) might have been strong enough to be detected in RXJ0911.4+0551 based on the observed flux densities in the Orion-KL hot core (Comito et al. 2005). However, the only (but not significant) additional line feature in our spectrum is the HNC(9–8) line redshifted to 214.8 GHz.

A comparison of the CO(7–6) and C i(2–1) spectra is shown in Figure 2 (left). Both line profiles are very similar and almost perfectly described by a single Gaussian within the uncertainties of the observations. A closer inspection of the two profiles reveals that the C i spectrum is slightly narrower than the CO line. This is shown in Figure 2 (center) where we display the difference spectrum CO–C i after scaling the C i peak intensity to the peak of the CO line. The residual shows faint but significant CO excess in the |50–150| kms⁻¹ velocity intervals. From a Gaussian fit to the full line we find FWHMs of 119 ± 1.8 kms⁻¹ and 107 ± 2.4 kms⁻¹ for CO and C i, respectively (see Table 1).

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The line profiles start to deviate from a Gaussian at 10% level of the peak intensity for both lines. The line wings are best seen in the higher signal-to-noise CO(7–6) line profile at low velocity resolution (see Figure 2, right). The wings are also detected in the C i(2–1) line albeit at lower significance. The wings are visible both toward the red and the blue side of the spectrum and are detected out to ∼ ± 250 km s⁻¹. Fitting the CO(7–6) line profile with two nested Gaussian yields an improved fit to the line profile including the line wings. For the broad line component this yields a peak of ≈4.5 mJy and a line width of FWHM ≈ 290 km s⁻¹.

To determine the line centroids we fitted the line shape by models with a single Gaussian and two nested Gaussians. The line centroids for both methods agree well within the uncertainties even when all six parameters of the nested Gaussians are kept free. The fitting uncertainties, however, increase by ≈50% in the latter case. We therefore used a single component Gaussian fit for each line and omitted the line wings in the fitting process. The fitting was performed on the original resolution data as binning was found to reduce the accuracy of the results. We have compared results from different programs (CLASS, GNUPLOT) and did not find significant differences in the fitting results. We find uncertainties for the line centroids of only 500 and 600 kHz (corresponding to a velocity uncertainty of 0.7 and 0.9 km s⁻¹) for the CO and C i line, respectively. The results including the corresponding redshifts are given in Table 1.

The redshift of the CO line (z ≡ z_CO) and the redshift difference between CO and C i (Δ z ≡ z_CO − z_C i) are related to the variations of the fundamental constants via Δ z/(1 + z) = ΔF/F with F = α²/μ where α is the fine structure constant and μ is the electron-to-proton mass ratio (Levshakov et al. 2008). With the numbers in Table 1 we find Δz = (2.62 ± 1.39) × 10⁻⁵ and thus ΔF/F = (6.91 ± 3.67) × 10⁻⁶.

The line wings detected in our spectra toward RXJ0911.4+0551 are remarkably similar to those recently detected in deep CO observations toward two local galaxies hosting an AGN: Mrk 231 (Feruglio et al. 2010) and NGC 1266 (Alatalo et al. 2011). In both cases the CO wings have been interpreted as molecular outflows. While the projected outflow velocities in NGC 1266 are comparable to those detected in our spectra, the outflow signature in Mrk 231 is much more pronounced with wings detected out to ±750 km s⁻¹. Although it is tempting to interpret the line wings in RXJ0911.4+0551 as the signatures of a molecular outflow, the situation is complicated by the fact that the source is amplified by a galaxy (visible in the HST-NICMOS image shown in Figure 1) and only to a lesser degree by a nearby galaxy cluster (see Burud et al. 1998; Kneib et al. 2000). This implies that the caustic curves are very compact, unlike the smoothly varying caustics from cluster lensing. Thus, an alternative interpretation is that the lens only strongly amplifies a small part of the molecular gas distribution in the disk of RXJ0911.4+0551 (with correspondingly narrow CO line width) and that the faint, broader CO profile visible as wings is the true line width of the system with low or no lens magnification.

We can, however, use the observed line luminosity of the optically thick CO(7–6) line together with the excitation temperature of T_ex ≈ 35 K estimated from the C i line ratio (using the intensity of the lower carbon line from Walter et al. 2011) to obtain a lower limit for the size of the amplified emission region. This calculation uses Ω_s = L'_CO(7-6) (T_b CO(7-6) dv D²_A)⁻¹ μ⁻¹_mag (Solomon et al. 1997) and assumes T_b CO(7-6) ≈ T_ex Ci − T_cmb. Taking the magnification of μ_mag = 20 into account, this yields a source diameter of ∼1 kpc which is a lower limit to the true source size because (1) it assumes an area filling factor of the emission of unity, (2) a face-on geometry, and (3) the true excitation temperature of the CO(7–6) line is likely lower than our estimate from C i due to the higher critical density of the CO(7–6) transition compared to both C i lines. Thus, the true underlying source size is likely similar to what has been observed in resolved, unlensed high redshift QSO host galaxies (such as J1148+5251 with D = 2.5 kpc; Walter et al. 2004). This comparison suggests that the gravitational lens amplifies the entire molecular gas distribution of RXJ0911.4+0551 and not just a small fraction of the disk. This favors the interpretation that the narrow observed line width is due to a close to face-on orientation of the molecular disk and that the faint line wings indeed trace a molecular outflow.

We estimate the molecular gas mass in the outflow using the optically thin C i(³P₂ → ³P₁) line (see, e.g., Equation (2) in Weiß et al. 2003). We use the C i excitation temperature given above and a carbon abundance, [C i]/[H₂], of 8 × 10⁻⁵ (Walter et al. 2011) which yields a molecular gas mass (including a correction of 1.36 for Helium and correcting for the magnification) of M_outflow = 6 × 10⁸ M_☉. This mass only includes the line wings (difference between the two component and the single component fit shown in Figure 2 right, albeit for C i(2–1)) and corresponds to ≈9% of the C i(³P₂ → ³P₁) line luminosity. The total mass in the broad line component (which has been used by Feruglio et al. 2010 to estimate the outflow mass in Mrk 231) is 1.7 × 10⁹ M_☉. However, here we use the more conservative approach to estimate the outflow properties only based on the mass in the line wings (Alatalo et al. 2011). Using the HWHM = 145 km s⁻¹ from the Gaussian fit to the broad line component as a lower limit for the average outflow speed (due to the unknown outflow orientation) the kinetic energy in the outflow is E_kin > 1.2 × 10⁵⁶ erg. Thus, the outflow in RXJ0911.4+0551 is ∼3 × more massive but likely less energetic than the outflow in Mrk 231 while other key parameters (L_FIR, $M_{{{\rm H}_2}}$, M_BH) are comparable for both sources after correcting for the gravitational magnification.

For RXJ0911.4+0551 the lack of information on the size and morphology of the outflow prevents us from estimating the dynamical timescale and the outflow rate. Mapping the blue and the red line wings independently only yields an upper limit for their angular separation in the image plane of <03 (<2.4 kpc), not sufficient to obtain a meaningful limit on the outflow rate. If we assume that the outflow size is comparable to the outflows observed in Mrk 231 and NGC 1266 (r = 0.5 kpc), the outflow rate for RXJ0911.4+0551 is $\dot{M}>180$ M_☉ yr⁻¹, larger than the star formation rate (SFR = 140 M_☉ yr⁻¹; Wu et al. 2009) which would hint at AGN feedback as being the main driver for the molecular outflow (see the discussion in Alatalo et al. 2011). The corresponding gas depletion timescale would be only 40 Myr. Even if we use the observed upper limit of <2.4 kpc as the intrinsic radius for the outflow, the depletion timescale remains short (<200 Myr) which implies that a significant fraction (>50%) of molecular gas will be removed from the disk within the typical lifetime of 100 Myr for massive starbursts at high redshift (Tacconi et al. 2008).

A potential concern using mid-J CO and C i emission lines as a probe of variations of the fundamental constants is whether both lines trace the same gas on galactic scales. Observations of CO and C i in the Milky Way have shown that both lines indeed probe the same molecular material on large and small scales (Ikeda et al. 2002; Zhang et al. 2007) despite the expectations from photon dominated region models which predict that C i should only exist in small layers surrounding the CO cloud cores. As discussed in the previous section, our experiment probably probes a region of ∼1 kpc in diameter. We would therefore expect that any potential spatial differences in the CO and C i emission velocities within molecular clouds would average out to zero over these extended regions.

Given that both lines trace the same volume on large scales one would naively expect that their line profiles are identical. Our observations show that this is not the case and that the C i line profile is ∼10% narrower than the CO profile (Figure 2, left and center; Table 1). This effect, however, is expected as the opacity of CO is typically much larger than the C i opacity (for the peak of the lines in RXJ0911.4+0551 we estimate opacities of 17 and 1.0 for CO(7–6) and C i(2–1),  respectively, using large velocity gradient models). Since the gas column density and therefore the opacity decreases toward the wings of the lines and because the intensity in each velocity bin scales as (1 − e^−τ), the intensity in the wings of the C i line decreases more rapidly than in the case of CO which in turn gives rise to a narrower line profile in C i. This effect, however, is not expected to be a critical limitation for the precise determination of the line centroid (i.e., the systemic velocity or redshift of the galaxy): the line profiles of galaxy-averaged molecular emission lines are not only determined by opacity and excitation effects but also by the effective source solid angle as a function of velocity. The latter typically does not saturate (i.e., clouds do not overlap in velocity space and spatially at the same time) which prevents galaxy-averaged CO lines from saturating at their peak. As systematic instrumental effects (e.g., LSR corrections) cancel out in our simultaneous observations of both lines and local oscillator variations (defining the frequency accuracy of the spectrometer) can safely be neglected, we conclude that systematic uncertainties are small compared with the statistical uncertainties, i.e., our ability to determine variations of the fundamental constants is solely limited by the signal-to-noise ratio and line width of our spectrum.

So far, estimates on the variations of the fundamental constants using high redshift emission lines have only been published in two studies using C II and CO (in BR1202-0725 at z = 4.7 and J1148+5251 at z = 6.4, Levshakov et al. 2008) and C i and CO (in a sample of sources at z = 2.3–4.1, Curran et al. 2011) where the measurements were taken entirely from the literature. These attempts yielded 3σ limits on |ΔF/F| of <4.5 × 10⁻⁴ and <2.6 × 10⁻⁴, respectively. Our experiment improves on these limits by more than a factor of 20 (at comparable look-back time) with |ΔF/F|  <  1.1 × 10⁻⁵ (3σ). Most absorption line studies have focused on variations in Δα/α or Δμ/μ. Variations of ΔF/F are related to both these quantities via ΔF/F = 2 Δα/α−Δμ/μ (Levshakov et al. 2008). Centimeter and millimeter absorption line studies have recently used inversion lines of NH₃ in combination with rotational lines of dense gas tracers (such as HC₃N or CS) to obtain limits on Δμ/μ. This combination provides a particularly sensitive probe to Δμ/μ due to the strong coupling between their redshift difference and variations in μ (e.g., Levshakov et al. 2010). Studies using several inversion and rotational transitions toward PKS 1810−211 at z = 0.89 give a conservative limit of |Δμ/μ| < 10⁻⁶ (Murphy et al. 2008; Henkel et al. 2009). The formally most accurate application of this technique to date yields a 3σ limit of |Δμ/μ| < 3.6 × 10⁻⁷ at z = 0.68 (Kanekar 2011) albeit on a small number of spectral lines.

Limits on variations of α at high redshift do not reach such accuracy to date but some studies have reported non-zero values for Δα/α based on QSO absorption spectra (Murphy et al. 2003; Webb et al. 2011; King et al. 2012). Here we use our results to obtain an independent limit on Δα/α. If we assume Δμ/μ = 0 between z = 0 and z = 2.79 (motivated by the NH₃ results mentioned above) our observations yield Δα/α = (3.5 ± 1.8) × 10⁻⁶, consistent with zero variations of α at a look-back time of 11.3 Gyr within the uncertainties (${{|\dot{\alpha }/\alpha|}}< 4.8\times 10^{-16}\,{\rm yr}^{-1}\ (3\,\sigma)$). As such, our experiment yields comparable accuracy on a single object as work based on HIRES/Keck and UVES/VLT absorption line spectroscopy on QSO samples which give typical accuracies of 1–2 ppm (1σ; Levshakov et al. 2007; Murphy et al. 2008; Webb et al. 2011). Our source, RXJ0911.4+0551, lies nearly orthogonal to the proposed angular dipole distribution of Webb et al. (2011) and King et al. (2012) and thus does not provide a stringent test of that claim.