PKS1830-211: OH and HI at z=0.89 and the first MeerKAT UHF spectrum

The Large Survey Project (LSP)"MeerKAT Absorption Line Survey"(MALS) is a blind HI 21-cm and OH 18-cm absorption line survey in the L- and UHF-bands, with the primary goal to better determine the occurrence of atomic and molecular gas in the circum-galactic and inter-galactic medium, and its redshift evolution. Here we present the first results using the UHF-band, made towards the strongly lensed radio source PKS1830-211, detecting absorption in the lens galaxy. With merely 90min of data acquired on-source for science verification and processed using the Automated Radio Telescope Imaging Pipeline (ARTIP), we detect in absorption the known HI 21-cm and OH 18-cm main lines at z=0.89 at an unprecedented signal-to-noise ratio (4000 in the continuum, with 6km/s channels). For the first time we report the detection at z=0.89 of OH satellite lines, so far not detected at z $>$ 0.25. We decompose the OH lines into a thermal and a stimulated contribution, where the 1720 and 1612 MHz lines are conjugate. The total OH 1720 MHz emission line luminosity is 6100 L_sun. This is the most luminous known 1720 MHz maser line. The absorption components of the different images of the background source, sample different light paths in the lensing galaxy, and their weight in the total absorption spectrum are expected to vary in time, on day and month time-scales. We compare the normalized spectra with those obtained more than 20 yrs ago, and find no variation. We interpret the absorption spectra with the help of a lens galaxy model, derived from an N-body hydro-dynamical simulation, with a morphology similar to its optical HST image. It is possible to reproduce the observations without invoking any central gas outflows. There are, however, distinct and faint high-velocity features, most likely high-velocity clouds. These clouds may contribute to broaden the HI and OH spectra.


Introduction
PKS 1830−211 is a highly reddened radio quasar at z=2.51 (Lidman et al. 1999), and also the brightest known radio lens in the sky. It was identified as a gravitational lens on the basis of its peculiar radio spectrum and morphology (Pramesh Rao & Subrahmanyan 1988;Jauncey et al. 1991). Its morphology (see Appendix) reveals two compact radio components, called North-East (NE) and South-West (SW), separated by one arcsecond and surrounded by a low surface-brightness Einstein ring, meaning that the background radio-source and the lens center are well aligned along the line of sight. The two compact components have a flat spectrum, with a spectral index ∼ −0.7 consistent with synchrotron emission, while the ring spectrum is steeper, such that at low frequency (< 1.7 GHz) the ring is contributing more significantly to the total flux density. Since, in projection the line of sight of PKS 1830−211 is very close to the Galactic plane (galactic latitude = −5.71 • ), and confused with stars, for a long time it was difficult to optically identify the lensing galaxy (Courbin et al. 1998). The redshift z = 0.89 of the lensing galaxy was discovered through molecular absorption (Wiklind & Combes 1996), and it was determined that most of this absorption comes from the SW image, ∼ 3 kpc from the center (Frye et al. 1997). There is also a much weaker molecular absorption at V=−150 km s −1 towards the NE image, in the opposite direction at 5 kpc from the center of the nearly face-on lensing galaxy (Wiklind & Combes 1998;Koopmans & de Bruyn 2005). Throughout this paper, the velocity scale is defined with respect to z = 0.88582 (heliocentric reference frame), which corresponds to the main molecular (e.g., CO, HCO + , and HCN) absorption components detected at mm wavelengths (Wiklind & Combes 1998).
The apparent size of the lensed images of the quasar at mm wavelengths is a fraction of a milliarcsecond (Jin et al. 2003;Guirado et al. 1999), implying that it could be possible to detect the molecular absorption of a single molecular cloud of a few pc in size. However, due to the thickness of the gaseous plane along the line of sight, the pencil beam from the quasar core travels several hundreds of pc in the galaxy, and encounters many clouds along the line of sight, covering a large velocity gradient. This broadens the absorption spectrum, since the gas actually involved in the absorption feels the velocity gradient over ∼ 1 kpc in the disk. H i 21-cm and OH 18-cm main absorption lines have also been detected at z = 0.89 (Chengalur et al. 1999;Koopmans & de Bruyn 2005).
It is worth noting that PKS 1830−211 also traces an H i 21cm absorber at z = 0.19 (Lovell et al. 1996;Allison et al. 2017), albeit with a smaller velocity width. The 90% of the total 21-cm optical depth (∆V 90 ) of the low redshift absorber is contained within 86 km s −1 (Gupta et al. 2020).
The absorber at z = 0.89 is particularly rich in molecules and also in dust. A strong absorption at rest-frame 10µm reveals amorphous or crystalline silicates (Aller et al. 2012). More than sixty molecular species associated with this absorber have been detected towards the SW component, where the inferred H 2 column density is ∼ 2 × 10 22 cm −2 (Muller et al. 2011(Muller et al. , 2014Tercero et al. 2020). In contrast, only 19 species, including atomic hydrogen and carbon, have been detected towards the NE component, where the molecular gas has a lower column density by an order of magnitude and is more diffuse. On the contrary, at cm wavelengths, it is the NE component which has the stronger absorption signal (Chengalur et al. 1999;Koopmans & de Bruyn 2005). The absorption spectrum peaks at V = −150 km s −1 , and is relatively weaker at ∼ 0 km s −1 . This suggests that, towards the center of the lensing galaxy, the gas phase is mostly molecular and the H i is depleted. Compared to the mm-absorptions, the broader linewidths of ∼ 280 km s −1 and ∼ 150 km s −1 (FWHM) for H i and OH cm-absorption, respectively, at z = 0.89 are explained by the higher thickness of the H i or OH plane, and to some extent by the more extended background radio continuum at lower frequencies.
Such a strong lens system should be useful to determine the Hubble constant, through the cosmography method or timedelay between the images. However, it is then necessary to precisely determine the mass distribution of the lens, which has been difficult, because of extinction and confusion with Milky Way stars (Courbin et al. 2002;Winn et al. 2002). Even the determination of the center of the lensing galaxy is problematic, and two models have been developed, with a bright peak at the center of the lens being a nearby star (Courbin et al. 2002) or the bulge of the lens galaxy (Winn et al. 2002). The detection of several absorption components at different velocities, towards the different images helps to determine the geometry of the lens, which is a nearly face-on spiral galaxy (Wiklind & Combes 1998). Recently, the detection of the third lensed image of PKS 1830−211 with ALMA by Muller et al. (2020) has brought more constraints leading to the refinement of the lens model.
Due to its very strong radio continuum and absorption lines, PKS 1830−211 is also one of the favorite targets for science verification at various radio telescopes. Very recently it was observed as part of the preparation for the MeerKAT Absorption Line Survey (MALS) to demonstrate the spectral line capabilities of MeerKAT. MALS has begun MeerKAT science verification observations using the L-and UHF-bands covering 900-1670 MHz and 580-1015 MHz, respectively (Gupta et al. 2017). Owing to the excellent sensitivity of MeerKAT (Jonas & MeerKAT Team 2016;Camilo et al. 2018;Mauch et al. 2020), the L-band spectrum of PKS 1830−211 presented in Gupta et al. (2020) provided a robust characterization of H i 21-cm (from z = 0.19) and OH 18cm main absorption lines from z = 0.89. Here, we present the first MeerKAT UHF-band spectrum that simultaneously covers both H i and all four OH 18-cm lines for the z = 0.89 system. This paper is structured as follows. Section 2 presents the details of the observations and data analysis with ARTIP. The results in terms of optical depths and column densities are quantified in Section 3, where we discuss the origin of the various absorption components in comparison with the molecular dense gas absorptions, and present a lens-galaxy model. Section 4 summarises our conclusions. To compute distances, we adopt a flat ΛCDM cosmology, with Ω m =0.29, Ω Λ =0.71, and the Hubble constant H 0 = 70 km s −1 Mpc −1 . At the distance of the PKS 1830−211 absorber, an arcsecond corresponds to 7.8 kpc, in physical units.

Observations and data analysis
The field centered at PKS 1830−211 was observed on July 13, 2020 using MeerKAT-64 array and 32K mode of the SKA Reconfigurable Application Board (SKARAB) correlator. For these UHF-band science verification observations, the total observable bandwidth of 544 MHz was split into 32768 frequency channels. This corresponds to a frequency resolution of 16.602 kHz, or 6.1 km s −1 at the center of the band i.e., 815.9917 MHz. The correlator dump time was 8 seconds and the data were acquired for all 4 polarization products, labelled as XX, XY, YX and YY. Of the 64 antennas, 56 participated in these observations. The baseline lengths in the dataset are in the range: 29 -7300 m. We also observed PKS 1934-638 and 3C286 for flux density and band-pass calibrations. Since PKS 1830−211 is a bonafide gain calibrator for the VLA in the C-and D-array configurations, there was no need to separately observe a complex gain calibrator. The total on-source time on PKS 1830−211 and duration of the observations are 90 and 155 mins, respectively. The full dataset in measurement set format is about 3.1 TB.
Here we are interested only in the Stokes-I properties of the target, therefore for processing we generated a measurement set consisting of only XX and YY polarization products. We also dropped the extreme 1024 frequency channels at both edges of the band. The resulting data set consisting of 30720 channels, was processed on the VROOM cluster at IUCAA using the latest version of the Automated Radio Telescope Imaging Pipeline ARTIP based on CASA 5.6.2. The details of ARTIP and data processing steps are provided in Gupta et al. (2020). In short, an initial RFI mask was applied to the data to mask the strongest radio frequency interference (RFI) in the band. Up to this stage, only ∼10.0% of the bandwidth gets flagged. After this step, the data were further flagged and calibrated using the ARTIP-CAL package. The spectral-line processing of calibrated visibilities was done using the ARTIP-CUBE package. The final continuumsubtracted spectrum of PKS 1830−211 is shown in Fig. 1. The shaded regions in the figure mark the above-mentioned initial RFI mask. For the ARTIP-CUBE processing, the frequency band was partitioned into 15 spectral windows (SPW) with an overlap of 256 frequency channels. The unique frequency ranges covered by these measurement sets are marked by vertical dashed lines in Fig. 1. For easier referencing, we refer to these as SPW-0 to -14.
For continuum imaging through the ARTIP-CONT package, a more stringent RFI mask to completely exclude band edges and RFI-afflicted regions was applied to the calibrated visibilities (see horizontal dotted lines in Fig. 1). The data were then averaged in frequency over 32 channels (∼0.531 MHz) and regridded along the frequency axis into 16 distinct spectral windows. We created a widefield broad band 6k×6k continuum image with a pixel size of 3 , spanning ∼ 5 • using tclean in CASA. The w-projection algorithm was used as the gridding algorithm in combination with Multi-scale Multi-term Multi-frequency synthesis (MTMFS) for deconvolution, with nterms = 2 and four pixel scales to model the extended emission (cf. Rau & Cornwell 2011;Bhatnagar et al. 2013;Jagannathan et al. 2017). Two rounds of phase-only selfcalibration were carried out along with a final round of amplitude and phase self-calibration. Imaging masks were appropri-ately adjusted using PyBDSF between major cycles during imaging and self-calibration (Mohan & Rafferty 2015).
The final continuum image of PKS 1830−211 constructed using robust=0 weighting has a synthesized beam of 17.4 × 13.1 with a position angle = +69.0 • . The rms noise in the continuum image is 80 µJy/beam close to the bright radio source at the center and 30 µJy/beam (dynamic range ∼380000) away from it. The total continuum flux density of the quasar is 11.40 ± 0.01 Jy at the reference frequency of 832 MHz. The quoted uncertainty on the flux density corresponds to errors from the single Gaussian component fitted to the continuum image. Note that the flux density accuracy at these low frequencies is expected to be about ∼5%. The flux density at 832 MHz is within 1.3% of the flux density of 11.25 Jy measured at 1270 MHz by Gupta et al. (2020) from the MeerKAT L-band data acquired on December 19, 2019. However, note that in general the quasar is known to be variable at radio wavelengths 1 . The in-band integrated spectral index is α = 0.

OH absorption
In the top two panels of Fig. 2, we show the main OH absorption lines with the rest frequency of 1667 and 1665 MHz. These lines were also detected in the overlapping L-band spectrum obtained with MeerKAT on December 19, 2019. The absorption obtained from the UHF spectrum presented here is in good agreement with the L-band profile (see Section 3.3 for details on variability). Combining the L-band and the UHF spectrum, we now also detect the two satellite lines at 1612 and 1720 MHz. These are presented in the bottom two panels of the figure.
This is the first time the OH satellite lines have been detected towards PKS 1830−211. This is also the highest redshift so far at which the OH satellite lines have been detected. The detection of all four OH 18-cm lines from the same spectrum allows us to investigate the nature of the absorbing gas without worrying about the line variability. Further, due to the proximity of the 18cm lines in the frequency space the structure of the background radio continuum illuminating the absorbing gas can be assumed to be the same.
The integrated optical depths of the main i.e., 1665 and 1667 MHz lines are 0.729 ± 0.012 and 1.301 ± 0.013 km s −1 , respectively. 90% of the total optical depth (∆V 90 ) of the 1667 MHz line is contained within 265 km s −1 . For an optically thin cloud, the integrated OH optical depth of the 1667 MHz line is related to the OH column density N(OH) through where T ex is the excitation temperature in Kelvin, τ 1667 (v) is the optical depth of the 1667 MHz line at velocity v, and f OH c is the covering factor (e.g., Liszt & Lucas 1996). Adopting T ex = 5.14 K i.e., coupled to the cosmic microwave background (CMB), T CMB at z = 0.89, we estimate N(OH) = (1.49 ± 0.02) × 10 15 (T ex /5.14 K)(1.0/ f OH c ) cm −2 . Note that this is a surface average, since it is likely that the filling factor is below 1.
In local thermodynamic equilibrium (LTE), the relative strengths of 18-cm lines are expected to be in the ratio, 1612:1665:1667:1720 MHz = 1:5:9:1. The total integrated optical depths of the main lines are remarkably consistent with the     LTE ratio. To explore this further, we model the two main lines using multiple Gaussian components. Assuming that these lines originate from the same gas, we tie the centers and widths of the corresponding components. The overall profiles are reasonably modeled by a three-component fit (reduced χ 2 ∼ 1.1), which is summarized in Table 1. The individual components marked as M 1 , M 2 and M 3 , and the resultant fit along with the residuals are plotted in Fig. 2 (see panels (a) and (b)). Unsurprisingly, the total absorption in components M 2 and M 3 which account for ∼98% of the total optical depth is consistent with the LTE ratio. The component M 1 is weak and it is difficult to probe its excitation character. Note that the excitation temperature of the 1.6 GHz  Table 1), respectively. The black solid line in panel (c) represents absorption under LTE due to M 1 , M 2 and M 3 . The difference between the red and black solid lines represent the maser contribution due to pumping, and is conjugate with the 1720 MHz line in (d): at V=-170km s −1 , the 1720 MHz line is in emission and 1612 MHz in absorption, while at V=-80km s −1 , the 1720 MHz is in absorption, and the 1612 MHz in emission. In all the panels, the total fit and the residuals, arbitrarily offset for clarity, are plotted as solid lines in red and magenta, respectively.
The centers and widths of corresponding components fitted to the main lines are tied.
OH transitions could be quite different from T CMB , especially in the case of far-infrared and/or collisional pumping (see below), and our assumption is conservative, although supported by the LTE ratios of the main lines.
If the OH ground state levels are indeed thermalized, the gas producing 1667 MHz absorption will have 9 times weaker opacity at the 1612 MHz line velocities. The absorption profile for 1612 MHz line based on M 1 to M 3 is represented by solid (black) lines in Fig. 2 (panel (c)). Clearly, the gas that produces absorption in the main lines can only account for 61% of the absorption in the satellite line. The remaining excess absorption can be modelled using two components S 1 and S 2 given in Table 1. It appears that the satellite lines have a large contribution due to pumping that is non-thermal, and even inverted, level population. Comparing the two satellite lines, it is clear also that the non-thermal part of the 1612 MHz line has a deficiency of absorption, due to emission (see bottom of Fig. 2).
Under certain excitation conditions, in particular pumping from far-infrared radiation, the satellite OH lines can exhibit "conjugate" behaviour i.e., as mentioned above the gas exhibiting absorption in one line produces emission in the other; this peculiar feature of the OH levels due to lambda-doubling and hyperfine structure, is a precious tool for probing the fundamental constants (Darling 2003;Chengalur & Kanekar 2003;Kanekar et al. 2018). Despite the limited SNR, the 1720 MHz profile presented in the bottom panel of Fig. 2 shows both emission and absorption features suggesting such a behavior. When the two satellite lines are perfectly conjugate, the sum of their optical depths is zero. The solid red line in the bottom panel of Fig. 2 corresponds to the sum of (i) absorption due to M 1 , M 2 and M 3 under LTE, and (ii) absorption due to S 1 and S 2 assuming perfect conjugate behavior. This simple model provides a reasonable representation of the observed 1720 MHz profile.
Note that the redshifted 1720 MHz line frequency is covered in both the L-and UHF-bands of MeerKAT. Indeed, the spectral features seen in panel (d) of Fig. 2 are also present in our L-band dataset (Gupta et al. 2020). The 1720 MHz profile presented here is already the weighted average of the spectra from the L-band data described in Gupta et al. (2020) and the present UHF-band data. Further investigation into the nature of the satellite lines and the perfection of the conjugate behavior will require a more sensitive spectrum.
But already the 1720 MHz line profile suggests that the conjugate behavior flips across at approximately -100 km s −1 , i.e., at velocities <-100 km s −1 it shows in emission and at higher velocities in absorption. Such flipping has been observed in both galactic and extragalactic systems (see e.g., cases of Centaurus A and NGC 253;van Langevelde et al. 1995;Frayer et al. 1998). The flipping crucially depends on whether the OH molecules are pumped by the rotational intra-ladder transition at 119 µm, in which case the 1720 MHz line shows in emission and 1612 MHz in absorption, or by the cross-ladder rotational transition at 79 µm, in which case the opposite happens (see Elitzur 1976, especially Fig. 1). Since, as explained in Frayer et al. (1998), the intra-ladder transition becomes optically thick much sooner (N(OH)/∆V ≈ 10 14 cm −2 km −1 s) than the cross-ladder transition (N(OH)/∆V ≈ 10 15 cm −2 km −1 s), the observed behavior for PKS 1830−211 implies that the gas exhibiting conjugate behavior at velocities > −100 km s −1 has higher OH column density than at < −100 km s −1 . Notably, we do not see any significant masing features in 1720 MHz line at velocities > −50 km s −1 i.e., closer to the center of the lensing galaxy where denser gas tracers such as high-J CO or HCO + lines towards the SW image have been detected (Muller et al. 2014).
Finally, the emission component at −170 km s −1 , which is barely detected at 3σ in the 1720 MHz line, has the total line flux density of 0.037±0.011 Jy km s −1 . At z = 0.89, this corresponds to an enormous line luminosity of ∼6100 L , which is ∼20 times more luminous than the previously brightest known 1720 MHz maser associated with PKS 1413+135 at z = 0.247 (Kanekar et al. 2004).

H i absorption
In Fig. 3, we show H i 21-cm absorption at z = 0.89. The integrated H i 21-cm optical depth is τdv= 10.050 ± 0.019 km s −1 , and the width ∆V 90 = 258 km s −1 . For an optically thin cloud the integrated 21-cm optical depth (T ≡ τdv) is related to the neutral hydrogen column density N(H i), spin temperature T s , and covering factor f H i c through, Using this we get N(H i) = (1.83 ± 0.01) × 10 21 (T s /100 K)(1.0/ f H i c ) cm −2 . The bulk of H i absorption can be identified with two components: one centered at ∼0 and the other at −150 km s −1 . These are the velocities associated with mm-wave absorption lines towards the SW and NE components, respectively. Indeed, for the earlier reported 21-cm absorption profiles, which are presented in Figs. 4 of Section 3.3, a two-component Gaussian decomposition provided a reasonable fit. However, the high signal-to-noise

Id.
Centre σ τ p (km s −1 ) (km s −1 ) (10 −3 ) A 1 -205 ± 1 15 ± 1 8.6 ± 0.6 A 2 -187 ± 40 119 ± 11 2.7 ± 1.1 A 3 -148 ± 1 24 ± 1 30.0 ± 0.9 A 4 -91 ± 2 68 ± 3 35.9 ± 1.4 A 5 22 ± 1 31 ± 1 12.2 ± 0.7 ratio of the MeerKAT spectrum requires at least five Gaussian components (A 1 to A 5 ; χ 2 ∼1.3) as presented in Table 2 and Fig. 3. The remaining structure in the residuals is at the level of τ ≤ 0.0014. It does not necessarily represent discrete physical structures. Therefore, we do not attempt to improve the fit by adding more components. Further, the Gaussian components obtained above do not necessarily represent individual physical structures. We can also retrieve the velocity components previously used to fit the OH lines. But this exercise requires more components because there is additional spectral feature present in the blue wing of H i 21cm absorption (see vertical dashed lines in Fig. 3). A rather remarkable result which can be obtained without any componentwise comparison is that the average [OH/HI] column density ratio ∼ 8 × 10 −7 is slightly higher than the typical ratio (∼ 10 −7 ) observed in the Galaxy (Li et al. 2018), and also in extra-galactic absorbers (Kanekar & Chengalur 2002;Gupta et al. 2018a). For PKS 1830−211 this may be primarily due to the fact that the absorption at ∼0 km s −1 i.e., towards the SW component originates from gas which is primarily molecular. We note that all these values are in perfect agreement with previous results, obtained more than 20 years ago (Chengalur et al. 1999;Koopmans & de Bruyn 2005).

Time variability
The continuum flux from the background blazar at z = 2.507 is significantly varying in time, by factors up to 10 in gammarays and 2 in radio (e.g., Lovell et al. 1998;Martí-Vidal et al. 2013). These variations are seen in the three lensed components (NE, SW, and ring) with time-delays. In X-rays, Oshima et al. (2001) show that the NE/SW flux ratio varies by factors as high as 7, invoking possible micro-lensing effects. While the NE and SW components are images of the blazar core, the ring is mainly due to the jet and a bright knot in the jet (e.g., Jin et al. 2003), and there is an observed jet precession period of one year (Nair et al. 2005). The delay between the two compact (NE and SW) components has been measured to be 27 days (e.g., Lovell et al. 1998;Wiklind & Combes 2001;Barnacka et al. 2011). Barnacka et al. (2015) have observed several gamma-ray flares with Fermi-LAT and derived gamma-ray time delays of 23±0.5 days and 19.7±1.2 days, which are consistent with the radio time delay; however this has been debated (see a reanalysis by Abdo et al. (2015)). With VLBA observations at 4 GHz, Garrett et al. (1997) found highly variable sub-milliarcsecond radio structures in the cores of both lensed images, during a period of 44 days. It is therefore expected that the variations of the different continuum components will be reflected in the shape of the H i and OH absorption lines through time variability.
We have compared all available H i and OH spectra from 1996 with the present MeerKAT ones. In Fig. 4, we show the comparison between all H i spectra. It is striking to see that they are all compatible, especially the last ones with high signal-tonoise ratio. No time variation is visible in the line, while the continuum varied by 40%. The MeerKAT spectrum has a 5-6 times higher signal-to-noise ratio than the old WSRT (Westerbork Synthesis Radio Telescope) data by Koopmans & de Bruyn (2005). The slight differences can therefore be completely attributed to the noise of the latter. The SNR in the WSRT spectrum is 35 at the peak of the absorption, in channels of 7.9 km s −1 . The absorption peaks at 5% of the continuum, and the SNR on the continuum is 700. The average ASKAP spectrum has an SNR∼1000 for the continuum, and 50 for the line in channels of 7.3 km s −1 , and this is the limiting factor in the comparison with MeerKAT. There is a slight difference around V=-60 km s −1 and V=-150km s −1 , of max amplitude of 1.5×10 −3 normalised to the continuum in one channel, and a lower difference in the two neighboring channels, but this leads to a difference of only 1.7σ, after averaging. Similarly, the OH spectra also show no variation. The comparison between the MeerKAT OH-main line spectra from December 19, 2019 (Gupta et al. 2020) and July 13, 2020 (this paper) sets a limit of ∆τ 3σ < 0.0008. This lack of variation at cm-wavelength contrasts with the variations detected in the mm-wave absorption spectra towards PKS 1830−211 (Muller & Guélin 2008;Muller et al. 2014). We can interpret this constancy at cm-wavelengths with several arguments: first, there are much larger absorbing regions, given the wider extent of the continuum emission, especially in the Einstein ring (while the continuum is mainly two point sources in the mm-waves); second, the absorbing medium in the H i component is more diffuse and less fragmented in dense clouds (Srianand et al. 2013;Gupta et al. 2018b), such that the motion of possible plasmons (knots) in the background jet will not produce large variations of the absorbing signal. Another factor is the height of the gas plane, which is much smaller in the dense Fig. 4. Top MeerKAT H i spectrum (black), taken on July 13, 2020, compared to the H i spectrum (red) observed on November 3, 1996 by Chengalur et al. (1999), and the one (blue) observed on 1998 October 25 by Koopmans & de Bruyn (2005), both with WSRT. All spectra have been normalized to their observed continuum. Bottom MeerKAT H i spectrum (black), taken on July 13, 2020, compared to the H i average ASKAP spectrum (red) observed in July 2014 and July-October 2015 by Allison et al. (2017). Both spectra have been normalized to their observed continuum. molecular phase than in the atomic phase. The H i plane in spiral galaxies is quite thick, up to 1 kpc or more in the flaring outer parts (Burton 1976;Olling 1996). This means that the region illuminated by a point source will range up to ∼ 1 kpc, crossing the inclined plane, as discussed in Sec. 3.4. For this reason, the H i absorption spectrum gets blurred over a size of 0.1 , the beam size of the available cm-continuum image. If the gas surface filling factor is relatively high, all sub-clumps over these regions are averaged out, washing out any spatial variation of the order of 0.2 mas. In addition, due to opacity effects, the cm and mm continuum radiation does not originate from the same volumes: the mm observations probe deeper inside the jet, and hence probably more active regions. Nair et al. (1993) proposed a detailed model for the lensing galaxy: they suggest it to be a spiral galaxy centered 0.3 NE of the SW image, of mass 10 11 M (rotational velocity ∼ 260 km s −1 ), of low eccentricity (nearly face-on), and with position angle ∼ 12 • . The discovery of molecular absorption confirmed that it should be gas rich, and the velocity difference between NE and SW images (150 km s −1 ) constrained the geometry (Wiklind & Combes 1998). Koopmans & de Bruyn (2005) made a kinematic model, taking into account more information on the lens image from Courbin et al. (2002) and Winn et al. (2002), and on the redshift of the source (Lidman et al. 1999). They concluded that the lens is inclined by i=17-32 • on the sky, with PA between −15 and 34 • . The model also depends on the velocity width of each absorbing component. Strikingly, the absorption in front of the SW image is rather broad, even relatively in the molecular gas. This could originate from non-circular motions since this region of the lensing galaxy is very close to the center (much closer than for the NE image, where the line width is smaller). Even if the background core of the blazar is a point source in the mm regime, the region involved in the lensing galaxy has an extension of h× tan(i), where h is the thickness of the plane, and i the inclination of the galaxy. The broadening of the line can therefore be essentially caused by the velocity gradient in this zone.

Kinematic model of the spectra
One of the main uncertainties in the models of Koopmans & de Bruyn (2005) is the position of the center of the lens. Now that a third image, which was postulated by Nair et al. (1993) in the cm-wave radio images, has been detected with ALMA by Muller et al. (2020), the position of the lens is a fixed parameter (very close to the third image position). Thus, it appears that the bright spot towards the center is indeed a star and not the bulge of the lens galaxy, as proposed by Courbin et al. (2002). Koopmans & de Bruyn (2005) found six best fit models, as a function of six positions of the lens center. Now we know that only one of these is close to reality, the one where their coordinates of the lens center with respect to the NE image (or AC) are (0.5 W, 0.45 S). Their result was then an inclination of i=32 • for the lens plane and PA=-15 • . In the following we fix i=26 • and PA=15 • to better fit the HST morphology of the lensing galaxy. The difference of inclination may explain why they select then a velocity dispersion of 39 km s −1 for the H i spectrum, while we need 45 km s −1 (see below).

Galaxy model and background continuum
The HST/WFPC2 F814W image published by Courbin et al. (2002) in their Fig. 2 (right) reveals the lensing object as a barred spiral galaxy, with quite a small bulge, therefore it is a relatively late-type galaxy. To model the lens, we select a snapshot from an N-body simulation, following the development of a bar and spiral arms, in a late-type object, described with stellar, gas and dark matter components, treating star formation and feedback. We chose the snapshot to have a morphology very similar to the HST image. The initial galaxy is a gSb model, described in Combes (2008) and Chilingarian et al. (2010). We project the model on the sky with an inclination of 26 • and a PA of 15 • , which are compatible with the above determinations. The resultant gas surface density and the velocity field are plotted in Fig. 5.
The 5 GHz image obtained using MERLIN (Multi-Element Radio Linked Interferometer Network) is among the best cmwavelength continuum image of the radio source (Patnaik et al. 1993). Although the redshifted H i and OH line frequencies (750-900 MHz) are much lower, we used this high-resolution map with a synthesized beam of 0.1 arcsec as the base radio continuum model. Fortunately, the spectral index is not very steep between 400 MHz and 5 GHz (see the multiple measurements with ATCA and Parkes, between 4.8 GHz and 408 MHz in NED and Section 2), at least for the main images, although it could be steeper for the Einstein ring. We will also compare the absorption spectra obtained at low frequencies with those in the millimeter domain, where the continuum image is very different due to the weaker Einstein ring component. The three compact images of the background quasar are also detected with ALMA with a beam of 0.056 arcsec (Muller et al. 2020). The adopted continuum maps for our cm-and mm-wave models are presented in the Appendix (Fig. A.1).

Computations of absorption maps and spectra
To reproduce the observations with the above continuum models, we built data cubes by projecting the models on the sky, with the fixed inclination and position angles (see above), multiplying at each spatial pixel the gas surface density with the background continuum, computing the line-of-sight velocity distribution. We select the same spatial pixel sizes as the continuum map i.e., 0.028 arcsec for the cm-wave, and 0.014 for the mm one. The adopted spectral channels are of width 6.25 km s −1 , for both.
The main parameters to vary are related to the radial distribution of the various atomic and molecular species considered in the absorption maps and the spectra. The H i distribution is well known to be depleted at the center of spiral galaxies. There are some extreme examples, such as NGC 628, IC 342, M83, M101 or NGC 7331, with a central H 2 /H i surface density ratio of ∼100 as can be seen in the THINGS H i (Walter et al. 2008) and the Heracles CO surveys (Leroy et al. 2009). Some of these radial distributions are computed in Casasola et al. (2017). We therefore selected an H i radial distribution depleted in the center, which gives more absorption weight to the NE(A) image with respect to the SW(B) image. Indeed, the distance of A from the center of the lensing galaxy is 5.3 kpc, while B is only at 2.4 kpc from the center. The contribution to the absorption spectrum from B is towards the V=0 km s −1 component while A is contributing to the V=−150 km s −1 component. The third image F. Combes et al.: PKS 1830−211: OH and H i at z = 0.89 and the first MeerKAT UHF spectrum C (and also the Einstein ring in the cm) has a continuum of the order of 1% of the A or B fluxes, which are comparable.
For the H i component, we selected a power-law radial distribution, as f = (r/r 0 ) γ , with a normalizing scale r 0 =3.89 kpc, equal to the Einstein ring radius. The gas surface density of the galaxy model was multiplied by this factor f, keeping the underlying bar/spiral structure of Fig. 5. Different radial distributions will lead to different shapes of the total absorption spectrum, in particular different ratios between the two velocity components. The best fit was obtained with γ = 2.5, very similar to the distributions selected by Koopmans & de Bruyn (2005). The velocity widths of the components is due to two factors: first the intrinsic gas dispersion, and second the averages of all gas rotational velocities in the plane of the lens, seen along the line of sight towards the continuum. The strongest continuum sources are the images of the background quasar core, and their angular sizes are quite small (∼mas), in fact smaller than the synthesized beam sizes. However, the line of sight towards these core images crosses the inclined lens galaxy plane (i = 26 • ), which has a thickness h. Regions along h× tan(i) ∼ 0.5× h are illuminated on the plane, with the corresponding velocity gradient. The width of the spectrum can therefore include velocity gradients over 0.1 arcsec, which is the resolution of the MERLIN continuum map. There is hence no need to deconvolve the continuum map for the model. Once the velocity gradients are taken into account, the simulated H i components are still too narrow, and it is necessary to add a velocity dispersion of σ v = 45 km s −1 . This might be due to extra-planar H i gas, frequently observed in nearby spiral galaxies in a few-kpc thick layer, with lagging rotational velocity, and equivalent dispersion up to 30km s −1 (Marasco et al. 2019). A similar computation has been done for the OH 18-cm main lines (and in particular the 1667 MHz main line), but with a more centrally-concentrated radial distribution, using a powerlaw index γ = 0.7. Although the OH does not suffer from the H i depletion towards the center (indeed, there is nothing like the phase change from H i to H 2 at high density), the OH radical is still distributed in a thick plane like the HI, a plane which is flaring with radius, which increases the velocity coverage of the absorption. This motivates the choice of σ v = 45 km s −1 . The latter suggests that the OH might also be sharing the extra-planar H i layer. The resulting 2D maps and the spectra are shown in Fig. 6 and 8. The 2D maps indicate in particular the relative contribution of the various regions in the absorption spectra.
Most of the absorption is coming from the core images. To test the influence of the Einstein ring, whose flux could be relatively higher at low frequency, we have artificially boosted its continuum emission by factors 3-10 with respect to the core images, but there was no significant impact on the main line components. The various contributions of the different continuum components to the total absorption spectrum are presented in Appendix (B.1). The ring is contributing a broad component. Although the ring contribution, even at low frequency, should be lower than 10%, it can however broaden the H i and OH spectra, and be responsible in part for their wide wings. Another contribution to the wings are the high velocity clouds, which will be discussed in Sec. 3.5.

Distribution of the gas absorbing the mm continuum
The continuum emission at millimeter wavelengths is much more compact than at cm, with all emission arising from the compact NE and SW images and little contribution from the ring. It is therefore interesting to compare the absorption spectra between the cm and mm domain, as this can give us constraints on the distribution of gas in the disk. For comparison, we take spectra of several species observed with ALMA, namely HCO + , H 2 O, CH + , and ArH + (see Muller et al. 2014;Müller et al. 2015;Muller et al. 2017).
The width of the various velocity components are much narrower, and this could be due both to the smaller sizes of the core images, and the smaller thickness of the dense molecular gas plane. The continuum map (cf Fig A.1 in Appendix) and the modelled datacube then have twice more spatial resolution. To reproduce the observations, the intrinsic dispersion of the gas (6 km s −1 ) in the N-body hydro simulation is sufficient, and an added convolution is not necessary. We have tried to reproduce absorption from HCO + representing generically mildly optically-thick species, the H 2 O molecule, a highly optically thick one, and ArH + , which should be a tracer of the atomic component, but with a different continuum illumination than HI. The ArH + absorption appears optically thin, but there is another species, CH + , tracing a gas with intermediate molecular fraction, which is highly optically thick. The ALMA spectra, combined to a beam encompassing all the continuum map, are represented in Fig. 9. Both HCO + and H 2 O have a highly concentrated radial distribution. We therefore selected the exponential profile, with a factor f=exp(-γ r/r 0 ), with the same r 0 =3.89 kpc, as before. For the HCO + and H 2 O distribution, the best fit was obtained with an exponential law, with γ=2.5. The main difference in their profiles is due to their different optical thickness. In addition, for H 2 O, it was necessary to deplete the central gas in front of the third image C, to avoid a too broad spectrum. Indeed, C is close to the galaxy centre, and the velocity gradient at this location reached the maximum of 220 km s −1 in projection. The resulting 2D maps and the spectra are shown in Figs. 7 and 8.
For the CH + distribution, the best fit was obtained with an exponential of γ=1.7, and for ArH + , γ=0.1. The latter is more extended, with a distribution more similar to the atomic one. In addition, the velocity components are broader, and we selected a convolution width σ v = 15 km s −1 . The latter is three times less than the H i dispersion, but still higher than the molecular gas one.
The profiles of Fig. 9 reveal small extra features with velocities lower than −200 km s −1 , or higher than 100 km s −1 . These velocities do not exist in our galaxy model, and should come either from high-velocity clouds in the halo of the galaxy, or extra tidal arms coming from a possible galaxy interaction. The line of sight of PKS 1830−211 falls at low latitude towards the Galactic center (l,b=12.2 • ,-5.7 • ), and the region is too crowded to see. It is possible that the broad H i components include these high- Fig. 7. Maps of the product (arbitrary units) between the ALMA continuum intensity and the optical depth from the galaxy model: Left for the HCO + line, very similar to the H 2 O case, both with a highly concentrated distribution and Right for the ArH + line, with a more extended distribution (see text). The axes are labelled in arcsec. velocity clouds, and are the cause of the high velocity dispersion required by the model.
In summary, there is a wide range of central concentrations for the various species, between HCO + the most concentrated and H i the most extended, a large range of optical thickness, and of gas layer height at the origin of velocity width, that can explain the various morphologies and intensities of spectral features. The spectra are normalised by the total (NE+SW) continuum level. We have assumed a flux ratio between NE and SW images of 1.5.

Conclusions
The MALS LSP project on the MeerKAT array has carried out its first science verification observations in the UHF-band, covering the 500 to 1015 MHz frequency range. The brightest known radio lens, PKS 1830−211 , has been observed and detected with high signal to noise (SNR∼ 4000 in channels of 6 km s −1 ). While the H i 21-cm and OH main lines at z = 0.89 were already known, due to the excellent sensitivity of MeerKAT we have also been successful in detecting the OH 18-cm satellite lines. We find that while the strength of the OH main lines is consistent with the LTE ratio, the satellite lines show conjugate behavior indicative of radiative pumping due to far-infrared radiation. The OH emission component in the 1720 MHz line, although at only 3σ, has the total line luminosity of 6100 L , i.e. ∼20 times more luminous than the previously brightest known 1720 MHz maser, associated with PKS 1413+135 at z = 0.247 (Kanekar et al. 2004). A detailed radiative model will be investigated further in the future, when the corresponding lines are re-observed with more SNR.
Contrary to the absorption features detected in several molecules at mm wavelengths, peaking at V = 0 km s −1 (i.e. the SW image), the main absorbing component at cm-wavelengths is at a velocity of -150 km s −1 with respect to z = 0.88582, corresponding to the NE image. We compared the obtained spectra to those previously obtained with WSRT (SNR∼ 700 with respect to the continuum and 35 at the peak of the line, in Koopmans & de Bruyn (2005)). The spectra reveal no variation, within the SNR of 35 relative to the depth of the absorption. No variation was seen either with the ASKAP spectrum of Allison et al. (2017) with SNR∼1000 with respect to the continuum and 50 at the peak of the line.
We have built a realistic lens galaxy model, from a N-body hydro simulation of an Sb-type galaxy, developing a bar and spiral arms. The galaxy is projected to obtain a similar morphology as an HST image. Combining with the best resolution cm and mm continuum images of the background quasar, we have computed data cubes to simulate the observed absorption features. The H i and OH absorption spectra are well reproduced with the main velocity field of the galaxy model. An intrinsic velocity dispersion of σ v =45 km s −1 has to be added to account for the broad widths, which can be explained by the presence of an extra-planar H i and OH gas, in addition to a thick and flaring plane. For the HCO + and H 2 O spectra, only the dispersion of 6 km s −1 yielded by the simulated dense molecular gas is sufficient to account for the observed absorption spectra. The molecular gas component is much more centrally concentrated, while the H i-component is depleted in the galaxy center. There is no need for any outflow component coming from the galaxy plane. There exist however some distinct and faint extra features, which can be interpreted as high-velocity clouds. To account for the ArH + absorption lines, observed with ALMA, a more extended distribution has to be selected, more similar to the atomic component, and a higher velocity dispersion (σ v =15 km s −1 ).