11institutetext: Observatoire de Paris, LERMA, Collège de France, CNRS, PSL
University, Sorbonne University, 75014, Paris — 11email:
<EMAIL_ADDRESS>22institutetext: Inter-University Centre for
Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007, India

# Cold molecules in H i 21-cm absorbers across redshifts $\sim$ 0.1 - 4
††thanks: Based on observations carried out with the IRAM-30m telescope and
NOEMA, the NOrthern Extended Millimeter Array – IRAM (Institute of
RAdioastronomy in Millimeter).

F. Combes Cold molecules in H i 21-cm absorbers across redshifts $\sim$ 0.1 -
4 ††thanks: Based on observations carried out with the IRAM-30m telescope and
NOEMA, the NOrthern Extended Millimeter Array – IRAM (Institute of
RAdioastronomy in Millimeter). Cold molecules in H i 21-cm absorbers across
redshifts $\sim$ 0.1 - 4 ††thanks: Based on observations carried out with the
IRAM-30m telescope and NOEMA, the NOrthern Extended Millimeter Array – IRAM
(Institute of RAdioastronomy in Millimeter).  N. Gupta Cold molecules in H i
21-cm absorbers across redshifts $\sim$ 0.1 - 4 ††thanks: Based on
observations carried out with the IRAM-30m telescope and NOEMA, the NOrthern
Extended Millimeter Array – IRAM (Institute of RAdioastronomy in Millimeter).
Cold molecules in H i 21-cm absorbers across redshifts $\sim$ 0.1 - 4
††thanks: Based on observations carried out with the IRAM-30m telescope and
NOEMA, the NOrthern Extended Millimeter Array – IRAM (Institute of
RAdioastronomy in Millimeter).

(Received: October 2023; accepted: December 2023)

Absorption lines at high redshift in front of quasars are quite rare in the
millimeter domain. Only five associated and five intervening systems are
known. However, these bring very useful information complementary to emission
lines, for instance, to distinguish between inflows and outflows. They are
also good candidates to study the variations of the fundamental constants of
physics. We report here the search for CO and other molecules in emission and
absorption in front of a sample of 30 targets, comprising 16 associated and 14
intervening H i 21-cm absorbers. The observations have been done with the
IRAM-30m telescope, simultaneously at 3mm and 2mm, exploring several lines of
the CO ladder and HCO+, according to the redshift. Eight targets have been
detected in emission, of which five are new. The derived molecular gas masses
range from 109 to 7$\times$ 1011 M⊙ and the highest redshift detection ($z$ =
3.387) corresponds to a low metallicity damped Lyman-$\alpha$ absorber. We
also report four new detections in absorption. Two of the associated CO
absorption line detections at high redshift ($z$=1.211 and 1.275) resulted
from the high spatial resolution follow-up with NOEMA. The disparity between
the mm molecular and H i 21-cm absorption lines for these and another
intervening system detected in HNC at $z=1.275$, is attributable to radio and
mm sight lines tracing different media. We compare the atomic and molecular
column densities of 14 known high redshift ($z$ ¿ 0.1) molecular absorption
line systems. The associated H i absorption lines are broad, exhibit multiple
components and the molecular absorption generally corresponds to the broader
and weaker 21-cm absorption component. This indicates two distinct phases: one
near galaxy centers with a larger CO-to-H i abundance ratio, and another with
lower molecular abundance in the outer regions of the galaxy. In comparison,
intervening absorption profiles correspond primarily to H i-dominated gas
structure in galaxy outskirts, except for gas at low impact parameters in
gravitationally lensed systems. The comparison of interferometric and single
dish observations presented here shows that the detection of absorption
requires sufficient spatial resolution to overcome the dilution by emission,
and will be an important criterion for mm follow-up of 21-cm absorbers from
ongoing large-scale surveys.

###### Key Words.:

galaxies: ISM, quasars: absorption lines, quasars: individual: PKS0201+113,
PKS 1200$+$045, PKS 1245$-$19, PKS1406-076.

##  1 Introduction

The star formation history of the universe is characterised by a peak about 10
billion years ago. The star formation rate (SFR) density in galaxies, as
reviewed by Madau & Dickinson (2014), evolves across cosmic time: it first
increases with time ($z>$2), peaks at $z\sim$1-2, and then decreases by an
order of magnitude from z$\sim$1 to the present day. Two main factors are
suspected to produce such an evolution: the gas content of galaxies, and their
star formation efficiency (SFE). From studies of main sequence star forming
galaxies across the Hubble time, the gas fraction in the interstellar medium
(ISM) galaxies appears to be the dominant factor in comparison to the SFE
(e.g. Tacconi et al. 2018). It is therefore crucial to constrain the molecular
gas content of galaxies over cosmic time, and also its precursor i.e., the
atomic gas reservoir. Obreschkow & Rawlings (2009a, b) used theoretical models
and the knowledge of molecular gas content of high redshift galaxies to make
very useful predictions of the cosmic evolution of H i and H2 gas components.
The H i evolution was found to be relatively constant over $z$=1-5, from
damped Lyman-$\alpha$ absorber (DLA) studies, while the H2/HI ratio was
steeply declining with time, as (1+$z$)1.6. Since then, many molecular line
surveys have refined our knowledge, and shown that the cosmic H2 evolution
might be flatter (Decarli et al. 2020; Riechers et al. 2020; Lenkić et al.
2020). In this context, it is important to pursue blind surveys, such as
serendipitous discoveries of CO lines in the field of view of the Atacama
Large Millimeter/submillimeter Array (ALMA) calibration sources (e.g.,
Hamanowicz et al. 2023), to obtain an unbiased view of the gas evolution.

Our knowledge of molecular gas in galaxies at high redshift has received major
boosts since the first discovery by Solomon et al. (1992), first by
gravitational lensing, as reviewed by Solomon & Vanden Bout (2005), and then
through the negative K-correction due to which the CO molecule can be observed
all over its rotation ladder, with the flux density increasing strongly with
the J-level (e.g., Combes et al. 1999). Although more difficult to detect,
molecular absorption lines can bring new and complementary information. While
the strength of emission lines decreases as a steep function of redshift,
absorption lines can be observed as easily at high redshift as in the local
Universe, provided there exists a strong background radio source (e.g., Combes
2008). Further, while emission lines are sensitive to dense and warm molecular
gas, absorption lines arise in the low-excitation and diffuse gas (e.g.,
Wiklind & Combes 1994, 1996b, 1997; Menten et al. 2008; Henkel et al. 2009;
Muller et al. 2014; Wiklind et al. 2018). In conclusion, with a 3 millimeter
continuum source flux density of at least $\sim$ 50 mJy, absorption lines can
be potentially used to obtain information about molecular gas in galaxies
undetectable through emission lines.

Absorption lines also have the advantage of the ease of follow up in many
molecular lines other than CO. Indeed, once a high column density absorber has
been discovered, the detection of other lines do not suffer from low filling
factor, as for the emission, nor critical density for excitation. This enables
characterization of the physical and chemical conditions in the absorbing gas
(e.g. Henkel et al. 2005; Bottinelli et al. 2009; Muller et al. 2014, 2016,
2021). The relative strengths of species like H3CN, where the excitation is
dominated by the cosmic microwave background (CMB), can be used to determine
the CMB temperature (e.g. Henkel et al. 2009; Muller et al. 2013). Comparisons
between the redshifts of different transitions (e.g. NH3, CH3OH, OH, etc) can
be used to test for variations in the fundamental constants (e.g. Uzan 2011;
Kanekar 2011; Kanekar et al. 2012; Bagdonaite et al. 2013; Murphy et al.
2022).

Absorption line studies broadly fall in two categories. In case, the absorbing
gas ($z_{abs}$) is located in the same radio source ($z_{em}$), i.e., an
active galactic nuclei (AGN), the absorber is called an associated absorber
($z_{abs}$ $\sim$ $z_{em}$). In this category, the absorbing gas may originate
from circumnuclear disk or represent outflowing or infalling material. In the
second category, the absorbing gas is unrelated to the background AGN and
arises from an intervening galaxy ($z_{abs}$ $<$ $z_{em}$). Through high
spatial resolution observations, the number of associated molecular absorption
line detections in the local Universe is steadily increasing (e.g. Tremblay et
al. 2016; Rose et al. 2019b, a, 2020). These provide extremely useful
information, on gas distribution and kinematics, for example, disentangling
inflow from outflow. Two absorbers are also detected at intermediate redshift:
Abell 2390 ($z$=0.230) and RXCJ0439.0+0520 ($z$=0.208; Rose et al. 2019a).
Both of these are associated with brightest galaxies of the corresponding
galaxy cluster.

Molecular absorptions at higher redshifts are extremely rare. Up to now, only
10 molecular absorption systems in the mm domain are known at $z$$\gtrsim$0.1.
Among these, five are intervening molecular absorptions: three are associated
with lensing galaxies amplifying the background quasars PKS1830-211 and
B0218+357 (e.g. Combes 2008), and PMN0134-0931 (Wiklind et al. 2018); the
fourth is PKS1413+135 and the last is our recent CO/CN absorption detection in
the front of quasar Q0248+430 quasar ($z_{em}$=1.31; Combes et al. 2019). The
quasar sight line in the last case is probing the gas associated with the
tidal tail emanating from a merging galaxy pair, G0248+430 ($z$ = 0.05194), at
an impact parameter of $\sim$15 kpc. The H i and OH absorptions at cm
wavelengths were already detected revealing the presence of cold atomic and
molecular gas towards the sight line (Gupta et al. 2018a), leading to the
above-mentioned CO/CN detection with the the NOrthern Extended Millimeter
Array (NOEMA).

The five high-$z$ associated absorptions, in addition to the two associated
with Brightest Cluster Galaxies mentioned above, are B3 1504+377 (Combes
2008), 4C+12.50 (Dasyra & Combes 2012) and PKS B1740-517 (Allison et al.
2019). This recent CO detection with the ALMA was motivated by a H i 21-cm
absorption detection (Allison et al. 2015). The CO(3-2) spectrum of 4C+12.50
displays both an emission component at the galaxy redshift $z$ = 0.1218, and
an absorption feature $\sim$ 1000 km s-1 from it. The latter is interpreted as
representing outflowing gas. Recently, a search for associated absorption
lines has also been attempted with the calibrators of ALMA, but with no
success (ALMACAL; Klitsch et al. 2019). We also note that it is debatable
whether the absorber towards PKS1413+135 is of associated or intervening
category (Readhead et al. 2021; Combes et al. 2023). Based on the recent
advances, here we will consider it as an intervening absorber.

Interestingly, molecular absorptions of H2 and CO are relatively easy to
detect at high redshift using ultraviolet (UV) lines (e.g. Petitjean et al.
2000; Srianand et al. 2008; Noterdaeme et al. 2015, 2023). The H2 detection
rates among sight lines selected on the basis of the presence of a DLA ($N$(H
i)$>2\times 10^{20}$ cm-2) are low ($\lesssim$10%). H2 is more frequently
detected in DLAs with higher metallicity. More importantly UV lines can detect
molecular column densities one or two orders of magnitude lower ($N$(H2)$\sim
10^{14}$ cm-2) than what is possible with millimeter lines. But at higher
column densities, the background source is obscured by accompanying dust.
Since UV lines are biased against high column density molecular gas, the
millimeter absorption lines are a welcome complementary tool.

We report here a systematic search of CO emission and absorption in a sample
of 30 targets, selected on the basis of the presence of cold atomic gas
already confirmed through the detection of H i 21-cm absorption. This paper is
structured as follows. Our sample is described in Sect. 2. Section 3 presents
the details of millimetre observations using the Institut de Radioastronomie
Millimetrique (IRAM)-30m telescope and NOEMA. The results in terms of optical
depths and column densities are quantified in Section 4. We discuss in Sec. 5
the constraints brought by the negative results on the various absorption
components in comparison with the atomic or ionized gas absorptions. Section 6
summarizes our conclusions. Throughout the present paper, the velocity scale
is defined with respect to redshifts indicated in Table 2. To compute
distances, we adopt a flat $\Lambda$CDM cosmology, with $\Omega_{m}$=0.29,
$\Omega_{\Lambda}$=0.71, and the Hubble constant H0 = 70 km s-1Mpc-1.

##  2 The sample

We have gathered a sample of 30 candidates for molecular absorption and
emission line search. In all of them, the presence of cold atomic gas has
already been confirmed through detection of H i 21-cm absorption. Overall, the
sample consists of 16 associated systems, at the redshift z${}_{abs}\sim$ zem,
and 14 intervening ones, where zabs is significantly lower than zem. The
selected AGNs typically have high ($>$ 100 mJy) flux densities at cm
wavelength. The exceptions are J0229+0044 (3.4 mJy) and J0229+0053 (31.1 mJy)
from Chowdhury et al. (2020) in which H i 21-cm absorption is still detected
due to the presence of large amounts of cold gas. At low-$z$ ($z\sim$ 0.1),
such high 21-cm optical depths are found to be associated with radio sources
embedded in merging galaxy pairs or Ultra Luminous Infrared Galaxies (ULIRGs;
Dutta et al. 2019). The basic properties of the sample are presented in Table
2. The absorption redshifts, $z_{abs}$ in Table 2 are based on the peak of H i
21-cm absorption lines, except for PKS 1200$+$045, where it is the middle of
the absorption range, highly blueshifted with respect to the emission
redshift. The intervening absorption lines are generally narrow with widths of
$\sim$50 km s-1 and, therefore, observed with spectral resolution of a few km
s-1 (e.g., Gupta et al. 2012). The absorption redshifts of these absorbers in
Table 2 have higher accuracy compared to the associated absorbers which are
relatively broader ($\sim$100 km s-1) and observed with coarser spectral
resolution. The interpretation of gas detected in associated absorption
crucially depends on the measurement of systemic redshift, $z_{em}$, based on
optical emission lines. These redshifts are provided in Table 2, most of the
times with an accuracy of four decimal places. We discuss these in detail in
Section 4.

Based on radio morphology and spectral energy distribution (SED) at cm
wavelengths, the associated targets can be classified as compact radio sources
($<$15kpc) expanding through the host galaxy ISM (O’Dea & Saikia 2021). The
expected values of radio continuum at 3mm is taken from the NASA Extragalactic
Database (NED). Since many AGNs have variable fluxes, these are certainly only
approximate. The flux densities from our millimeter observations, which will
be presented in following tables, are also uncertain because these are
obtained with a single dish, through a varying atmosphere. The atmospheric
contribution is best subtracted though rapid wobbling, however it remains
problematic in average weather conditions.

We have searched for molecular absorption at the lowest possible frequency, to
maximize the continuum brightness level, and hence the detectability of
absorption. All sources have been observed in CO lines, and according to their
redshift HCO+ lines, when possible. Our goal was to detect CO in emission or
absorption, and simultaneously high density tracers, like HCO+ or HCN, which
become diffuse gas tracers in absorption. Note that some of the associated
absorbers from the sample have been followed up to search for the OH line in
absorption, with MeerKAT through the approved large program - the MeerKAT
Absorption Line Survey (MALS111$https://mals.iucaa.in/$; Gupta et al. 2016,
2021).

Table 1: Properties of the sample – first 16 associated systems and then 14
intervening absorbers are presented. Columns: (1,2) object coordinates and
favored name; (3,4) redshift of emission and absorption, the latter is based
on H i 21-cm absorption peak, except for PKS1200+045 (see text for details);
(5) Observed frequency, CO(1-0) or CO(2-1) except when indicated otherwise;
(6) 3mm continuum flux density in mJy based on the measurements from NED; (7)
Epoch of IRAM 30-m observations; (8) H i 21-cm absorption references.

Target | Other name | $z_{em}$ | $z_{abs}$ |  $\nu_{obs}$(1) | Scont | Epoch |  H i 21-cm references
---|---|---|---|---|---|---|---
|  |  |  | (GHz) | (mJy) |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8)
J000557.17+382015.1 | B0003+38A | 0.229 | 0.2288 | 93.808 | 900 | 05-19 | Aditya & Kanekar (2018)
J010826.84$-$003724.1 | UM305 | 1.3753 | 1.3710 | 97.232 | 200 | 04-21 | Gupta et al. (2007)
|  |  |  | 112.846a |  | 07-10 |
J014652.79$-$015721.2 | 4C-02.08 | 0.9590 | 0.9589 | 91.059a | 20 | 05-19 | Aditya (2019)
J022928.93+004429.5 | J0229+0044 | 1.2161 | 1.2166 | 104.008 | 0.5 | 04-22 | Chowdhury et al. (2020)
J022947.23+005308.9 | J0229+0053 | - | 1.1630 | 106.582 | 2 | 04-22 | Chowdhury et al. (2020)
J043103.76+203734.2 | PKS0428+20 | 0.219 | 0.2202 | 94.469 | 300 | 07-10 | Vermeulen et al. (2003)
J104830.37+353800.8 | B2 1045+35A | 0.8464 | 0.8471 | 124.811 | 20 | 04-21 | Aditya (2019)
J120321.93+041419.1 | PKS1200+045 | 1.2243 | 1.2111 | 104.263 | 200 | 04-21 | Aditya & Kanekar (2018)
J124823.89$-$195918.8 | PKS1245-19 | 1.275 | 1.2750 | 101.335 | 20 | 04-21 | Aditya & Kanekar (2018)
J132616.51+315409.5 | 4C+32.44 | 0.3680 | 0.3680 | 84.263 | 1000 | 07-10 | Vermeulen et al. (2003)
J134733.36+121724.2 | 4C+12.50 | 0.1217 | 0.1217 | 102.765 | 1500 | 07-10 | Morganti et al. (2004)
J140700.39+282714.7 | Mrk668 | 0.0768 | 0.0775 | 106.980 | 250 | 07-10 | Gupta et al. (2006)
J154015.23$-$145341.9 | J1540-1453 | 2.104 | 2.1139 | 74.035 | 60 | 04-21 | Gupta et al. (2021)
J164801.53+222433.3 | J1648+2224 | 0.8227 | 0.8233 | 126.440 | 100 | 04-21 | Aditya (2019)
J194553.51+705548.7 | 1946+708 | 0.1008 | 0.1008 | 104.716 | 48 | 06-10 | Peck et al. (1999)
J205252.05+363535.3 | B2-2050+36 | 0.354 | 0.3546 | 85.096 | 214 | 06-10 | Vermeulen et al. (2003)
J020346.66+113445.4 | PKS0201+113 | 3.639 | 3.38714 | 131.354 | 100 | 07-10 | Kanekar et al. (2007)
| . |  |  | 105.089 |  | 07-10 |
J025134.54+431515.8 | Q0248+430 | 1.313 | 0.05151 | 109.624 | 150 | 07-10 |  Hwang & Chiou (2004) (1)
J074110.70+311200.2 | 0738+313 | 0.6310 | 0.22124 | 94.389 | 800 | 06-10 |  Kanekar et al. (2001),(2)
J080839.66+495036.5 | SBS0804+499 | 1.4344 | 1.40732 | 95.765 | 200 | 03-19,07-10 |  Gupta et al. (2009), (3)
J083052.09+241059.8 | 0827+243 | 0.9406 | 0.52476 | 75.600 | 900 | 06-10 |  Kanekar & Chengalur (2001), (2)
J092136.24+621552.2 | J0921+6215 | 1.4473 | 1.10360 | 109.592 | 1000 | 03-19 |  Dutta et al. (2017), (4)
J095456.82+174331.2 | 0952+179 | 1.4749 | 0.23780 | 93.126 | 40 | 06-10 | Kanekar & Chengalur (2001)
J124355.79+404358.9 | B3 1241+410 | 1.5266 | 0.01714 | 113.329 | 80 | 07-10 | Gupta et al. (2018b)
J133335.78+164903.9 | HB1331+170 | 2.0835 | 1.77646 | 83.033 | 500 | 03-19 |  Carswell et al. (2011), (2)
J140856.48$-$075226.5 | PKS1406-076 | 1.494 | 1.27464 | 101.351 | 1500 | 03-19,06-10 | Gupta et al. (2012)
J162439.09+234512.2 | 3C336 | 0.9272 | 0.65584 | 107.725a | 100 | 06-10 | Curran et al. (2007)
J163956.36+112758.7 | J1639+1127 | 0.993 | 0.07909 | 106.823 | 70 | 07-10 | Srianand et al. (2013)
J203155.23+121940.4 | PKS2029+121 | 1.215 | 1.11614 | 84.293a | 2000 | 06-10 | Gupta et al. (2012)
J235810.87$-$102008.7 | HB2355-106 | 1.6349 | 1.17304 | 106.090 | 600 | 07-10 |  Gupta et al. (2007), (3)

222 $a$$a$footnotetext: for HCO+(2-1) or (3-2) – Other references (1) Combes
et al. (2019), (2) Berg et al. (2015), (3) Quider et al. (2011), (4) Stickel &
Kuhr (1993)

##  3 Observations and data analysis

All the targets were first observed with the IRAM-30m telescope at Pico
Veleta, Granada, Spain, at the epochs indicated in Table 2. The lines observed
were mainly either CO(1-0) or CO(2-1) at 3mm and CO(3-2) at 2mm, except in
some cases HCO+(2-1) or (3-2). The full width at half-maximum (FWHM) of the
primary beams at the frequencies of 100 GHz and 150 GHz are 25′′ and 17′′,
respectively. The SIS receivers (EMIR) were used for observations in the
wobbler switching mode, with reference positions offset by $\pm$60 arcsec in
azimuth. The main-beam efficiency of IRAM is $\eta_{mb}$ = T${}_{A}^{*}$/Tmb =
0.84 and 0.78 at 100 GHz and 150 GHz, respectively. The system temperatures
ranged between 120 K and 220 K at 3 mm, and between 180 K and 300 K at 2 mm.
The pointing accuracy was regularly checked every 2 h on a nearby planet or a
bright continuum source, and the focus was reviewed after each sunrise, as
well as at the beginning of each night. The integration time is typically 2h
per source, being weather-dependent. Two backends were used simultaneously,
the wideband autocorrelator – WILMA and the Fourier Transform Spectrometer –
FTS. Their respective spectral resolutions are 2 MHz and 0.2 MHz, which
correspond to 6 and 0.6 km s-1 at 3mm. The rms noise levels at 100 GHz and 150
GHz for a velocity resolution of 40 km s-1 were $\sigma\sim$1.0 mK and 1.3 mK
in T${}_{A}^{*}$, respectively. The data were reduced using the Continuum and
Line Analysis Single-dish Software (CLASS) of the Grenoble Image and Line Data
Analysis Software (Gildas).

For two sources detected in line emission, PKS 1200$+$045 and PKS 1245$-$19,
further observations in the 3mm band were carried out with NOEMA using the
PolyFIX correlator in February, March and November, 2022. The CO(2-1) line at
$z$ = 1.226 (PKS 1200$+$045) and 1.275 (PKS 1245$-$19) is redshifted to
103.566 and 101.335 GHz, respectively. The observations were carried out in
dual polarisation mode in 4 basebands, with 3.9 GHz total bandwidth per
baseband, distributed in lower and upper sidebands distant by 15.5 GHz. The
CO(2-1) line was observed in the upper side-band. We observed 80% of the time
in A-configuration, and 20% in C-configuration, with 12 antennas. The total
telescope time per source was 13h (8h on source), with a total of 26h. The
calibrations were performed using strong radio sources, such as 3C273, 3C84,
1222+037 and 1244-255. The absolute flux calibration is accurate at the 10%
level.

The data were calibrated using the Continuum and Line Interferometer
Calibration (CLIC) package and mapped using the MAPPING package of the GILDAS
software. We used self-calibration, which significantly increased the signal-
to-noise ratio. Using CLARK cleaning with natural weighting we obtained images
with synthesized beams of
6$\aas@@fstack{\prime\prime}$9$\times$1$\aas@@fstack{\prime\prime}$3 (PKS
1200$+$045) and
4$\aas@@fstack{\prime\prime}$1$\times$1$\aas@@fstack{\prime\prime}$2 (PKS
1245$-$19) with a position angle (PA) of 10°. Since no other lines were
detected in the rest of the basebands (upper and lower), we used these to
estimate and subtract the continuum level. The velocity resolution was
initially 2 MHz ($\sim$6 km s-1). The data were then smoothed to obtain data
cubes with three resolutions: 10, 50 and 150 km s-1. These final cubes are
256$\times$256 pixels with 0.13″per pixel in the plane of the sky, and have 80
frequency channels. The continuum flux density was also computed using the
images from the wider 7.7 GHz lower side band, with a beam of
7$\aas@@fstack{\prime\prime}$1″$\times$1$\aas@@fstack{\prime\prime}$4, and
4$\aas@@fstack{\prime\prime}$9$\times$1$\aas@@fstack{\prime\prime}$4, with a
PA of 10°. The rms noise is 230 $\mu$Jy/beam in 50 km s-1 channels for the
line and 10 $\mu$Jy/beam for the continuum.

Figure 1:  Detection of CO emission lines towards two intervening (top panels)
and six associated absorbers. The vertical scale is Tmb in mK. The various CO
transitions are indicated at the upper right of each panel. The zero of the
velocity scale corresponds to $z_{abs}$ in Table 2. The velocity range over
which H i 21-cm absorption is detected is indicated by an horizontal bar at
the bottom of each panel.

##  4 Results

In Section 4.1, we first discuss the emission and then absorption line
detections from IRAM-30m observations. The results from NOEMA interferometer
follow-up observations of associated systems PKS 1200$+$045 and PKS 1245$-$19
are presented in Section 4.2.

###  4.1 IRAM-30m

Figure 2: QSO-galaxy pairs, detected in CO emission and absorption: at top,
the HST-F606W image of PKS0201+113, with the galaxies G1 and G2, the latter
considered the most likely DLA candidate by Ellison et al. (2001), and in the
bottom, the PanSTARRS1 z-zg-g image of Q0248+430 and associated galaxies. The
dashed yellow circle indicates the region observed with the 23″beam.

####  4.1.1 Emission

Fig. 1 displays profiles of CO emission lines detected towards eight of the
targets with the IRAM-30m telescope. Out of eight, two correspond to
intervening H i 21-cm absorbers and the remaining to the associated absorbers
(see also Table 2). The detections towards Q0248+430 (J0251+4315; Downes et
al. 1993), 4C+12.50 (J1347+1217; Dasyra & Combes 2012) and Mrk668 (J1407+2827;
Ocaña Flaquer et al. 2010) were previously known, and the remaining are
reported here for the first time.

The two intervening systems detected in CO emission are towards PKS0201+113
(J0203+1134) and Q0248+430 (J0251+4315). Although both can be classified as
QSO-galaxy pairs (QGP) i.e., a foreground galaxy producing absorption in the
sight line of a distant quasar as shown in Fig. 2, the absorber towards
PKS0201+113 was first identified as a DLA at at $z_{abs}$ = 3.38639 (White et
al. 1993) and then subsequently associated to a foreground concentration of
galaxies, with one of them producing the absorption (Ellison et al. 2001). The
absorber galaxy, responsible for the DLA may be G2 in Fig. 2. It is relatively
massive (0.7$L^{*}$) and at an impact parameter of $\sim$20 kpc. The DLA with
N(H i) = $10^{21.26\pm 0.08}$ cm-2 exhibits multiple components spread over
$\sim$270 km s-1. The H i 21-cm absorption exhibits two components spread over
$\sim$115 km s-1 at $z_{abs}$ = 3.387 144(17) and 3.386 141(45) (Kanekar et
al. 2007). The $z_{abs}$ adopted in Table 2 corresponds to the peak of
stronger 21-cm absorption component. The 21-cm absorption peaks do not
coincide with the metal and H2 absorption lines detected in the optical/UV
spectra (Ellison et al. 2001; Kanekar et al. 2007; Srianand et al. 2012). The
CO emission spectrum is in good correspondence with the velocity range over
which [FeII], [CII] and H2 absorption lines are detected (Srianand et al.
2012).

Being nearer ($z\sim$ 0.05), the merging galaxy pair in front of the quasar
Q0248+430 (J0251+4315) at $z$ = 1.313 has been detected in several CO emission
lines (Kuehr 1977; Kollatschny et al. 1991). The CO(1-0) integrated flux
density ($S_{CO}dV$) using the Berkeley-Illinois-Maryland Association (BIMA)
interferometer was 24 Jy km s-1 (Hwang & Chiou 2004). With the IRAM-30m,
Downes et al. (1993) reported $S_{CO}dV$ = 25 Jy km s-1, while from our
observations we estimate, $S_{CO}dV$= 8.5 Jy km s-1. However, in our
observations the telescope was pointed towards the QSO, which is about 15 ″
from the foreground galaxy. Combes et al. (2019) using NOEMA observations have
shown that the CO emission is confined to the few central arcseconds of the
galaxy. Thus, the telescope beam only partially covers CO emission region
associated with the galaxy, as shown in Fig. 2, which explains the discrepancy
with earlier observations. We note that tidal tail emanating from the
foreground galaxy extends across the background QSO and is responsible for the
CO absorption line detection (Combes et al. 2019). Unlike the case of
PKS0201+113, the molecular absorption in this case is coincident with the
narrower and stronger H i 21-cm absorption components (see also Gupta et al.
2018a).

Among six associated molecular emission line detections, the four lower
redshift detections are associated either with radio or Seyfert (Sy) galaxies
(see Table 2). 4C+12.50 (J1347+1217) is associated with a merging galaxy pair
at $z$ = 0.12174 $\pm$ 0.00002 (Holt et al. 2003), with infrared luminosity of
3.2$\times 10^{12}$ L⊙ (Scoville et al. 2000). This has been detected in CO in
emission as well as absorption (Dasyra & Combes 2012; Dasyra et al. 2014). An
image of the associated galaxy pair can be seen in Fig. 5 of Dasyra et al.
(2014). The host of Mrk668 (J1407+2827; OQ208) is an actively star forming
galaxy, with an interacting companion (see Fig. 3), at $z$ = 0.07681 $\pm$
0.00007 (Eracleous & Halpern 2004). It was detected previously by Ocaña
Flaquer et al. (2010) in CO(1-0) and also shows stimulated radio-recombination
lines (Bell & Seaquist 1980). Due to its far infrared luminosity of
2$\times$1011 L⊙, it is classified as LIRG. 1946+708 (J1945+7055) is a radio
galaxy at $z$ = 0.10083 $\pm$ 0.00009 (Snellen et al. 2003). PKS0428+20
(J0431+2037), also a radio galaxy, has a redshift measurement, $z$ = 0.219,
with modest accuracy (Labiano et al. 2007).

The two higher redshift associated detections are PKS1200+045 (J1203+0414) and
PKS1245-19 (J1248-1959) at $z$ = 1.22429 $\pm$ 0.00043 (SDSS) and 1.275
(Labiano et al. 2007), respectively. For PKS1200+045, the double-peaked CO
emission profile agrees with the optical redshift within 1$\sigma$. The H i
21-cm absorption is blueshifted with respect to this by $\sim$2000 km s-1 and
has no overlap with the molecular gas. In contrast, for PKS1245-19 the H i
21-cm absorption and CO emission line peaks are consistent within the random
and systematic errors of measurements with the systemic redshift based on
optical emission lines. In general, except for PKS1200+045, for all the
associated systems the H i 21-cm absorption is detected within the same
velocity range as CO emission (see horizontal bars in Fig. 1).

Figure 3: Mrk668 (OQ208, J1407+282) legacy DR9 image, showing an interacting galaxy with stellar shells. Table 2: Detection of CO emission in two intervening, PKS0201+113 and Q0248+430, and six associated systems. Columns: (1): favored name; (2) $z$ of the CO emission peak; (3) CO transition; (4, 5): emission line peak and FWHM; (6): molecular mass; (7, 8): optical and radio identifications, and 1.4 GHz luminosity for associated systems. Target | $z_{mol}$ | CO | Speak | FWHM | M(H2) | Optical Id. | Radio Id. | log$L_{1.4\,GHz}$
---|---|---|---|---|---|---|---|---
|  |  | (mJy) | (km s-1) | (109M⊙) |  |  | (W Hz-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
PKS0201+113 | 3.38715 | 5-4 | 11$\pm$3 | 289$\pm$50 | 768 | - | - | -
Q0248+430 | 0.05151 | 1-0 | 38$\pm$5 | 225$\pm$23 | 5 | - | - | -
PKS0428+20 | 0.22020 | 1-0 | 10$\pm$2 | 368$\pm$64 | 40 | G | GPS | 26.6
PKS1200+045 | 1.22216 | 2-1 | 6.4$\pm$1 | 750$\pm$90 | 488 | Q | GPS | 27.9
PKS1245$-$19 | 1.27121 | 2-1 | 3.7$\pm$1 | 752$\pm$140 | 327 | Q | GPS | 28.6
| 1.27121 | 3-2 | 3$\pm$1.5 | 733$\pm$180 | 190 |  |  |
4C+12.50 | 0.12170 | 1-0 | 47$\pm$5 | 457$\pm$32 | 71 | Sy/Q | CSS | 26.3
Mrk668 | 0.07642 | 1-0 | 20$\pm$5 | 521$\pm$69 | 13 | Sy | GPS | 24.9
1946+708 | 0.10147 | 2-1 | 4.3$\pm$1 | 222$\pm$90 | 0.6 | G | GPS | 25.3

We compute L${}^{\prime}_{CO}$, the CO luminosity in units of K km s-1pc2,
with the integrated emission in the beam. This CO luminosity is given by

$L^{\prime}_{CO}=3.2510^{7}S_{CO}dV{{D_{L}^{2}}\over{\nu_{rest}^{2}(1+z)}}\hskip
6.0pt\rm{K\hskip 3.0ptkm\hskip 3.0pts^{-1}\hskip 3.0ptpc^{2}},$ (1)

where $S_{CO}dV$ is the integrated flux in Jy km s-1 , $\nu_{rest}$ the rest
frequency in GHz, and $D_{L}$ the luminosity distance in Mpc. Under the
assumption of a standard CO-to-H2 conversion factor (Bolatto et al. 2013), we
compute the H2 mass using M${}_{\rm H_{2}}=\alpha$ L’CO, with $\alpha=4.36$ M⊙
(K km s-1 pc2)-1. The observation of the fundamental CO(1-0) line is the best
measure of the total H2 mass. To convert the CO luminosities measured at
$J$-level higher than one, we adopted the $R_{1J}=T_{1}/T_{J}$ ratios from
Tacconi et al. (2018), i.e. $R_{12}=1.16$, $R_{13}=1.8$, $R_{15}=2.9$. The
molecular gas mass estimates for eight detections are presented in Table 2.

Figure 4:  Detection of absorption with the IRAM-30m, towards two of the
intervening targets – PKS0201+113 in CO(4-3) at left, and PKS1406-076 in
HNC(2-1) at right. The spectra have been normalized to their continuum flux
densities of 0.22 and 1.13 Jy respectively. The zero of the velocity scale
corresponds to the peak of H i 21-cm absorption ($z_{abs}$ in Table 2). The
velocity range over which H i absorption is detected is indicated by an
horizontal bar at the bottom of each panel. For PKS0201+113, the H2 absorption
peak (-25 km s-1) and the velocity range over which the 21-cm (-100, 10) km
s-1 and the [CII]∗ (-80, 0) km s-1 are detected, are reasonably consistent
with the CO absorption (see text for details).

####  4.1.2 Absorption

Fig. 4 displays the spectra of the two molecular absorption line detections.
They are both intervening systems. The values of continuum flux density,
optical depth and column density are provided in Table 3. PKS0201+113 exhibits
a weak absorption ($\sim$3$\sigma$) in the CO(4-3) line. The absorbing galaxy
is also detected in emission in CO(5-4) (see Fig. 1). The continuum flux
density of the quasar is a factor of two higher at the lower frequency of the
CO(4-3) line. The corresponding continuum emission is thus weakened by the
absorption in the beam, while this is not the case at the frequency of the
CO(5-4) line. The CO(4-3) absorption coincides well with the velocity range
(-100, 10) km s-1 over which the H i 21-cm absorption is detected. However,
note that the peaks of 21-cm and H2 absorption lines, despite both being
tracers of cold gas, are disparate by $\sim$25 km s-1 (Srianand et al. 2012).
The differences in absorption line velocities is most likely due to the non-
alignment of radio and optical sight lines. The radio core, especially at cm
wavelengths, is also more extended than the au-sized optical quasar and probes
a larger volume of the absorbing gas.

PKS1406-076 was observed in June 2010 at 101.322 GHz and 151.978 GHz
corresponding to the CO(2-1) and CO(3-2) lines redshifted at $z$=1.2753,
respectively. The H i 21-cm absorption peak is at $-$87 km s-1 with respect to
$z$=1.2753 corresponding to the Mg ii absorption. The observation led only to
upper limits, with a spectral rms of 8 mJy per channels of 20km s-1, along
with rippled baselines, likely due to the high continuum flux density (1.1
Jy). In March 2019, the target was observed again but only in the 3mm band
with a wide configuration, which included CO(2-1) at 101.322 GHz in the upper-
outer sideband, but also HNC(2-1) and HCO+(2-1) at 79.693 GHz and 78.396 GHz
in the lower-outer sideband, respectively. An absorption line was detected
near the HNC(2-1) frequency but blue-shifted by $\sim$600 km s-1 with respect
to the peak of the 21-cm absorption. The HCO+(2-1) frequency was at the edge
of the band and suffered from a rippled baseline.

The continuum flux densities and upper limits for non-detections are presented
in Table 3. The spectral rms ($\sigma$) is estimated for 20 km s-1 channels.
When the continuum is not strong enough, as far as the CO line is concerned,
the emission line upper limit may be estimated by using the rms derived over
80 km s-1channels obtain by dividing $\sigma$ in Table 3 by a factor 2. All
the simultaneously observed lines have not been reported, but only the most
constraining one are considered here.

Assuming a homogeneous and optically thin gas at excitation temperature
$T_{x}$ and with a covering factor $f_{c}$, we can derive the average column
density over the beam corresponding to the mm continuum emission of the quasar
through

$N_{tot}=\frac{8\pi}{c^{3}}\frac{\nu^{3}}{g_{J}A_{J,J+1}}f(T_{x})\int{\tau
dv},$ (2)

where $g_{J}$ is the statistical weight of level $J$, $A_{J,J+1}$ is the
Einstein coefficient for transition $J\rightarrow J+1$, and the function
$f(T_{x})$ is

$f(T_{x})=\frac{Q(T_{x})e^{E_{J}/kT_{x}}}{1-e^{-h\nu/kT_{x}}}$ (3)

We adopt the partition function of local thermal equilibrium (LTE), i.e.,
$Q(T_{x})=\Sigma g_{J}e^{-E_{J}/kT_{x}}$, where $E_{J}$ is the energy of level
$J$ and $T_{x}$ is the excitation temperature of the CO molecule.

Typically, with our integration time of 2h per source, we get at 3mm an rms of
5 mJy in 20 km s-1channels. According to the background radio source flux,
between 100 and 300 mJy of continuum, this leads to a 1$\sigma$ upper limit of
$\sim$ 1.7$\times$ 10-2 to 5$\times$ 10-2 in the optical depth $\tau$, and
$\tau\Delta$V = 0.34 to 1 km s-1 at 1$\sigma$, for a linewidth of $\Delta$V =
20 km s-1. When the observed line is CO(2-1) or HCO+(2-1), this corresponds to
N(CO) = 1.6-5$\times$1015 cm-2, and N(H2) = 1.6-5$\times$1019 cm-2, or N(HCO+)
= 2.6-8$\times$1012 cm-2 respectively, assuming an average excitation
temperature of $T_{x}$= 15K, and a filling factor of $f_{c}$ = 1. We adopt a
typical CO/H2 abundance ratio of $10^{-4}$ (e.g., Rachford et al. 2009).

Table 3: Details of molecular absorption line detections in two intervening and then two associated systems with IRAM-30m and NOEMA, respectively. Columns: (1) favored PKS name of the target; (2) $z$ of the molecular line peak; (3) molecular line transition; (4) continuum flux density; (5) integrated optical depth and (6) total column density of CO or HNC. Target | $z_{mol}$ | Line | Scont |  $\int\tau$dV | $N$
---|---|---|---|---|---
|  |  | (Jy) | (km s-1) | (cm-2)
(1) | (2) | (3) | (4) | (5) | (6)
0201+113 | 3.38715 | CO43 | 0.22 | 6.2$\pm$2 | 6.6E16
1406$-$076 | 1.26949 | HNC21 | 1.13 | 2.4$\pm$0.2 | 2.8E13
1200+045 | 1.21276 | CO21 | 0.058 | 3.1$\pm$0.6 | 1.5E16
1245$-$19 | 1.26605 | CO21 | 0.067 | 7.2$\pm$0.4 | 3.6E16

The column density estimates for the two intervening detections with IRAM-30m
are provided in Table 3. Note that although the column density does not depend
on redshift, the excitation temperature must however be higher than the CMB
temperature, which is already 12 K for PKS0201+113. When the assumed Tx is
20K, instead of 15K, the column density decreases only slightly (13%) for
CO(4-3), and increases by 53% for HNC(2-1). For a typical CO/H2 abundance
ratio of 10-4, the H2 column density is $N$(H2) = 6.6$\times$1020 cm-2 for PKS
0201+113. This is quite comparable to the H i column density of
1.8$\times$1021 cm-2 derived by Ellison et al. (2001) and Kanekar et al.
(2007), from the Lyman-$\alpha$ and H i 21-cm respectively. For PKS1406-076,
we can estimate the abundance of HCN and HNC in the diffuse medium of the
Milky Way, in absorption in front of background radio sources (Liszt & Lucas
2001) as HCN/H2 = 1.4$\times$10-9, and HNC/HCN = 0.2. The H2 column density is
then N(H2) = 1023 cm-2.

###  4.2 NOEMA

The two sources PKS 1200$+$045 and PKS 1245$-$19 are clearly detected in 3mm
continuum emission (see Fig. 5). The CO emission lines are also detected, as
shown in the Figs. 6 and 7, but with much lower amplitude than in the IRAM-30m
spectra. This might be due to extended CO emission getting resolved out by the
limited uv-coverage of the interferometer. However, as the smallest extent of
the synthesized beam is $\sim$ 1″, or $\sim$ 8 kpc, this seems unrealistic.
Another possibility is that the dynamic range is limited to detect a weak line
emission in the presence of a strong continuum source. Indeed the intensity of
latter was found to vary significantly within the baseband, affecting the
accuracy of the subtraction of the continuum. Computed over the lower and
upper sidebands ($\sim$ 20 GHz) the spectral index of the source is close to
-1; -0.6 for PKS 1200$+$045 and -1.5 for PKS 1245$-$19.

We also detect the CO(2-1) absorption lines in both the sources. At V=-1803 km
s-1, the molecular absorption is consistent with the velocity range over which
the H i 21-cm absorption is detected by Aditya & Kanekar (2018). However, the
absorption peaks are shifted by $\sim$200 km s-1 and the molecular line
overlaps with the weaker, shallower absorption component. For PKS 1245$-$19,
the molecular absorption line peak is at V= -1180 km s-1 i.e., the edge of the
blue-shifted wing of the H i 21-cm absorption (Aditya & Kanekar 2018).
Although the CO(2-1) absorption associated with PKS 1245$-$19 appears very
deep in the NOEMA spectrum, it is not incompatible with the non-detection in
the IRAM-30m spectrum: the peak of the absorption is -4 mJy, and the spectral
rms in the IRAM-30m spectrum is 2.5 mJy per 50km s-1 channels.

Table 4: Continuum flux densities and line upper limits based on IRAM-30m for
the associated (top), and then intervening systems (bottom). The spectral rms
($\sigma$) is based on 20 km s-1channels.

Target | $\nu_{obs}$ | Scont | Line | $\sigma$
---|---|---|---|---
| (GHz) | (mJy) |  | (mJy)
B0003+38A | 93.808 | 90 | CO(1-0) | 7
UM305 | 97.232 | 120 | CO(2-1) | 12
| 112.846 | 100 | HCO+(3-2) | 15
4C-02.08 | 91.059 | 20 | HCO+(2-1) | 4.5
J0229+0044 | 104.008 | 10 | CO(2-1) | 2.5
J0229+0053 | 106.582 | 5 | CO(2-1) | 3.5
B2 1045+35A | 96.570 | 45 | HCO+(2-1) | 3.5
| 124.811 | 30 | CO(2-1) | 6
4C+32.44 | 84.263 | 240 | CO(1-0) | 9
J1540-1453 | 74.035 | 25 | CO(2-1) | 7
J1648+2224 | 126.440 | 175 | CO(2-1) | 5
B2-2050+36 | 85.096 | 80 | CO(1-0) | 2.5
0738+313 | 94.389 | 370 | CO(1-0) | 3.5
SBS0804+499 | 95.765 | 440 | CO(2-1) | 12
0827+243 | 151.196 | 610 | CO(2-1) | 5
J0921+6215 | 109.592 | 850 | CO(2-1) | 7
0952+179 | 93.126 | 200 | CO(1-0)a | 3.5
B3 1241+410 | 113.329 | 40 | CO(1-0) | 10
HB1331+170 | 83.033 | 100 | CO(2-1) | 2.5
3C336 | 107.725 | 25 | HCO+(2-1) | 5
| 139.227 | 15 | CO(2-1) | 3.5
J1639+1127 | 106.823 | 340 | CO(1-0) | 10
PKS2029+121 | 84.293 | 900 | HCO+(2-1) | 4
| 163.409 | 505 | CO(3-2) | 5
HB2355-106 | 106.090 | 490 | CO(2-1) | 4.5
333 $a$$a$footnotetext: CO(4-3) detected by ALMA at zem (Audibert et al. 2022)

Figure 5: Left: Continuum image of PKS1200+045 at 3mm, obtained with NOEMA.
Only a 1.5 GHz band has been used around the line frequency, to better
subtract the continuum. The synthesized beam is
6$\aas@@fstack{\prime\prime}$9$\times$1$\aas@@fstack{\prime\prime}$3, with
PA=10°. The compact source has a flux density of 58 mJy and detected at SNR of
303. Right: Same for PKS1245-19. The synthesized beam is
4$\aas@@fstack{\prime\prime}$1$\times$1$\aas@@fstack{\prime\prime}$2, with
PA=10°. The compact source has a flux density of 67 mJy (SNR = 421). In both
the panels, the spatial scale is in arcsecond and the color bar is in Jy
beam-1.  Figure 6: Left: CO(2-1) emission spectrum of PKS1200+045, obtained
with NOEMA, smoothed to 150km s-1. Right: CO(2-1) absorption spectrum towards
PKS1200+045. The spectral resolution is 10 km s-1. In both the panels,
vertical scales are in mJy beam-1 and the horizontal line at the bottom
indicates the velocity range over which the H i 21-cm absorption is detected
(Aditya & Kanekar 2018). Figure 7: CO(2-1) emission and absorption spectrum of
PKS1245-19, obtained with NOEMA, smoothed to 150 km s-1. The vertical scale is
mJy beam-1. The horizontal line at the bottom indicates the velocity range
over which the H i 21-cm absorption is detected (Aditya & Kanekar 2018).

##  5 Discussion

The rarity (5/30) of molecular absorptions among systems with H i 21-cm
absorption, even when the millimeter continuum is strong enough and the CO
emission line is detected, might appear surprising, . But this is likely the
consequence of the low surface filling factor (fs) of the molecular gas. There
may be molecular gas along the line of sight, with a rather wide beam of 10
kpc scales as seen in the cases with CO emission, but the surface may be
filled at f${}_{s}\sim$1% or lower (Wiklind & Combes 1997). In contrast, the
filling factor of the atomic gas is higher for the same column density. In
addition, radio continuum emission is more extended at cm wavelength than at
mm wavelength. Both these factors lead to more favorable conditions for the
detection of cold atomic gas in absorption at longer wavelengths, than
molecular gas at mm wavelengths.

When the CO lines are detected in emission, higher spatial resolution
observations are required to isolate the compact nuclear continuum emission
and avoid that the emission line outshines the absorption signal. NOEMA was
used for two of the associated systems detected in emission. Although the
continuum is strongly detected, the absorption signal is rather weak.
Detection of weak absorption signals is made in fact more difficult by the
influence of strong continuum emission on the noise level, and the baseline
stability. Alternatively, it is possible to detect absorption in the high-
density tracers, such as HCO+, HCN or HNC, which are not detectable in
emission. This is indeed the case of the intervening system towards
PKS1406-076.

The eight CO emission line detections in our sample correspond to $M$(H2) =
$10^{9}-7\times 10^{11}$ M⊙. Six of these are associated systems and the
majority i,e., four are at low redshift ($z<$0.25). Among intervening systems,
one detection is at $z$=3.3871 and the other at 0.05151. It is interesting to
stack all the non-detection spectra listed in Table 3, by aligning these to
the same velocity scale centered at the peak of the H i 21-cm absorption. They
were stacked with no particular weight related to continuum level or redshift,
just taking into account their rms. The latter was comparable for all sources,
therefore no individual one dominates. The stacked spectrum in Fig. 8 reveals
a weak emission, not incompatible with a superposed absorption, but lost in
the noise. The FWHM of the feature is rather large (870 km s-1), and is most
likely due to non-alignment of the H i absorption with the systemic velocity
of the galaxies. The integrated flux is 1.75$\pm$0.3 Jykm s-1. We also stacked
the associated and intervening non-detections separately, but then the
resulting spectra do not show any detectable feature.

###  5.1 Comparison of H i and H2 column densities

We compare the atomic and molecular column densities of 14 known high redshift
($z>0.1$) molecular absorption line systems. Table 5 provides a compilation of
their basic properties from the literature. Seven of these are associated
targets. One of these is not detected in H i 21-cm absorption, although the
upper limit is quite shallow. For estimating molecular column densities, the
excitation temperature was adopted from the original reference, when
physically justified, or taken as the default, Tx = 15K, for CO. Estimating
the spin temperature for H i is more problematic. For intervening absorbers,
based on the Milky Way ISM, a value of 100 K is generally taken. The spin
temperature may be at least as high as 1000 K in the associated absorbers
(e.g., Maloney et al. 1996). In Table 5, we adopt Ts = 1000 and 100 K for
associated and intervening absorbers, respectively. Fig. 9 shows H i and H2
column densities for both types of systems. Clearly, there is no correlation,
when the bias of higher absorption depth at largest distances i.e., at higher
$z$, emission is more difficult to detect and only absorption may be detected,
is taken into account. The $N$(H2)/$N$(H i) ratio is in the range 0.03 – 2.7
for the associated systems. For the intervening systems it is 0.2 - 1000, with
top three (22 - 1000) corresponding to the lensed systems. The scatter
decreases if we adopt Ts = 100 for both the associated and intervening
systems. But a uniform spin temperature for both types of systems can not be
justified simply on the basis of H2/H i ratios. The associated systems exhibit
broader lines, with a median FWHM of $\sim$150 km s-1 in H i and, as discussed
in Section 5.3, comprise gas from two distinct components – the circumnuclear
disk and the galaxy-wide ISM. On the other hand, the intervening H i
absorption lines are narrower (FWHM$\sim$40 km s-1) and represent multiple
clouds with overlapping velocities from the quiescent galaxy disk (see Section
5.2).

Actually, several additional redshift-dependent biases ought to be considered
for the detectability of absorption: first, contrary to the dust emission
which benefits from a negative K-correction, the AGN synchrotron emission
intrinsically decreases with frequency, and becomes fainter at higher
redshift. Second, for a given observing frequency, the lines to be observed at
higher redshift correspond to higher J-level, which are increasingly difficult
to be excited in diffuse media, may favor detection through absorption. Also
at higher redshifts, higher spatial resolution is required to resolve the line
emission, and detect the underlying absorption signal.

Table 5: Comparison of 14 known – first 7 associated and then intervening – H
i 21-cm and molecular absorption line systems. Columns: (1, 2) favored name
and systemic optical redshift; (3) redshift based on H i 21-cm absorption peak
(4, 6) total H i column density, adopting $T_{\rm s}$ = 1000 K (100 K) for
associated (intervening) targets, and integrated optical depth; (5) FWHM of
the main absorption component; (7 - 9): molecular column density, FWHM and
total integrated optical based on line in column (10); (11): redshift based on
the peak of molecular line. (12) and (13): references for H i 21-cm and
molecular absorption line. In columns (5) and (8), we give also in parentheses
the full velocity extent of the absorption.

Target |  ze |  z${}_{21}^{*}$ | N(HI) | FWHM |  $\int\tau$dV |  N(H2) | FWHM |  $\int\tau$dV | Line | $z_{mol}$ | Ref | Ref
---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  |  (cm-2) |  (km s-1) |  (km s-1) |  (cm-2) |  (km s-1) |  (km s-1) |  |  |  (H i) | (Mol.)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
J0439+0520 | 0.2076 | – |  $<$5e22 |  $<$200 |  $<$28. | 2.0e21 | 126 (210) | 5.4 | CO(1-0) | 0.2077 | H1 | C1
PKS1200+045 | 1.2243 | 1.2111 | 4.6e21 | 100 (800) | 2.52 | 1.5e20 | 87 (225) | 3.1 | CO(2-1) | 1.21276 | H2 | C2
PKS1245-197 | 1.275 | 1.2750 | 8.3e21 | 200 (1000) | 4.54 | 3.6e20 | 113 (400) | 7.2 | CO(2-1) | 1.26605 | H2 | C2
4C+12.50 | 0.1217 | 0.1217 | 6.6e21 | 250 (1800) | 3.6 | 1.8e22 | 250 (600) | 55.0 | CO(3-2) | 0.11806 | H3 | C3
B1504+377 | 0.674 | 0.67343 | 3.8e22 | 130 (175) | 21.0 | 6.0e20 | 75 (100) | 10.4 | CO(2-1) | 0.67343 | H4 | C4
B1740-517 | 0.4423 | 0.44129 | 5.0e21 | 5 (210) | 2.7 | 1.5e20 | 37 (120) | 4.8 | CO(2-1) | 0.44185 | H5 | H5
Abell 2390 | 0.2304 | 0.2310 | 2.5e+22 | 154 (1100) | 13.7 | 8.0e21 | 122 (300) | 28.2 | CO(1-0) | 0.2312 | H6,H1 | C1
PMN0134-0931 | 2.225 | 0.76344 | 9.0e20 | 107 (200) | 4.93 | 2.0e21 | 53 (200) | 70.3 | CO(2-1) | 0.76391 | H7 | C5
PKS0201+113 | 3.639 | 3.38714 | 1.8e21 | 19 (125) | 0.7 | 6.6e20 | 57 (400) | 6.2 | CO(4-3) | 3.38715 | H8 | C2
B0218+357 | 0.944 | 0.68466 | 4.0e20 | 43 (75) | 2.19 | 4.0e23 | 20 (30) | 20.3 |  C18O(2-1) | 0.68466 | H9 | C6,C7
G0248+430 | 1.313 | 0.05151 | 9.7e19 | 19 (90) | 0.53 | 2.9e19 | 16 (30) | 0.25 | CO(1-0) | 0.05151 | H10 | C8
PKS1406-076 | 1.494 | 1.27464 | 2.5e20 | 11 (50) | 0.51 | 1.0e23 | 77 (155) | 2.4 | HNC(2-1) | 1.26949 | H11 | C2
PKS1413+135 |  $\sim$0.3 | 0.24671 | 2.0e21 | 18 (180) | 10.86 | 4.6e20 | 2 (5) | 3.64 | CO(1-0) | 0.24671 | H12 | C9
PKS1830-211 | 2.510 | 0.88489 | 1.8e21 | 180 (400) | 10.1 | 4.0e22 | 40 (400) | 30. | CO(4-3) | 0.88582 | H13 | C10

H i -ref – H1: Hogan (2014), H2 Aditya & Kanekar (2018), H3: Morganti et al.
(2004), H4: Carilli et al. (1997), H5: Allison et al. (2019), , H6: Hernández
et al. (2008), , H7: Carilli et al. (1993), H8: Kanekar et al. (2007), H9:
Koopmans & de Bruyn (2005), H10: Gupta et al. (2018a), H11: Gupta et al.
(2012), H12: Carilli et al. (1993); Combes et al. (2023), H13: Kanekar &
Briggs (2003).

CO-ref – C1: Rose et al. (2019a), C2: present work, C3: Dasyra & Combes
(2012), C4: Wiklind & Combes (1996a), C5: Wiklind et al. (2018), C6: Wiklind &
Combes (1995), C7: Combes & Wiklind (1995), C8: Combes et al. (2019), C9:
Wiklind & Combes (1997), C10: Wiklind & Combes (1998).

  * *

$z_{21}$ is the redshift of peak H i 21-cm absorption depth, except for PKS
1200$+$045, where it is the center of the velocity range over which the
absorption is detected.

Figure 8: Spectrum stacked from of all upper limits, described in Table 3. The
spectra were all aligned at the observed H i absorption velocity. The vertical
scale is Tmb in mK. All continuum levels have been ignored.

###  5.2 Nature of the gas detected in intervening systems

Due to the low low surface filling factor of the molecular gas and compact
size of the AGN continuum emission, the probability to detect gas in distant
galaxies through emission lines may be much higher than through line
absorption. Indeed, CO as well as [C ii] emission from strong metal absorbers
or high-$z$ DLAs at $z\sim$0.1 - 4 have been detected recently with ALMA and
NOEMA Neeleman et al. (2016, 2019); Kaur et al. (2021, 2022). Typically, the H
i column densities along the background quasar are of the order of 1021 cm-2,
and the galaxies have far-infrared luminosities higher than the Milky Way.
Although the projected separation between the galaxy and quasar can be
relatively high, 10-45 kpc for [C ii] and as much as 100 kpc for CO, the
velocities of emission and absorption signals are reasonably consistent. The
inferred molecular gas masses are in the range of 109 to 1010.5 M⊙. The
intervening emission line detection in our sample have masses $M$(H2) =
$7\times 10^{11}$ M⊙ ($z=3.38715$) and $1.5\times 10^{10}$ M⊙ ($z=0.05151$)
(see Table 2). The CO emission detection rate is 2/14 i.e., $\sim
14^{+19}_{-9}$%. Among 19 DLAs at $z\sim 2$ with CO emission searches reported
in the literature, the CO detection rate can be as high as $56^{+38}_{-24}$%
but only for high metallicity ([M/H]$>$-0.3) absorbers, otherwise it is merely
$\sim 11^{+26}_{-9}$% (Kaur et al. 2022). Notably, the $z=3.38715$ detection
presented here has the lowest absorption metallicity [M/H] = -1.2 (Kanekar et
al. 2007) and the highest molecular mass among the DLAs searched for CO
emission till date.

Next, we turn our attention to the molecular absorption line detections. Among
seven associated systems in Table 5, three are associated with lensing
galaxies. Towards PMN0134-0931, molecular absorption separated by $\sim$200 km
s-1 is seen towards two sight lines separated by 5 kpc (Wiklind et al. 2018).
The spatially unresolved 21-cm absorption spectrum shows smoother absorption
coinciding with most of the molecular absorption (Kanekar & Briggs 2003). The
H i and molecular absorption line column densities in Table 5 correspond to
the deeper 21-cm absorption component with $N$(CO)/$N$(H i) = $2.2\times
10^{-4}$ ($N$(H2)/$N$(H i) = 2.2). The other absorption component exhibit
different properties with a factor of $\sim 5$ lower abundance ratio. As
previously noted, for PKS0201+113 the 21-cm and H2 absorption do not coincide,
the peaks are separated by about $\sim$25 km s-1 (Srianand et al. 2012).
Interestingly, the 21-cm absorption and CO absorption components coincide
rather well i.e., within 5 km s-1(Fig. 3). These may be good candidates to
constrain the variation of fundamental constants of physics using CO and 21-cm
absorption, albeit with better quality spectra. The total integrated H i
column density in Table 5 provides $N$(CO)/$N$(H i) = $3.7\times 10^{-5}$
($N$(H2)/$N$(H i) = 0.4). This is a factor of two higher if only the H i in
main absorption component is considered. In general, the CO absorption does
not extend over all 21-cm components, due to the difference in radio continuum
extent. The H2 column density based on Lyman and Werner band absorption lines
is $N$(H2) = $10^{14.6-16.0}$ cm-2 (Srianand et al. 2012), which is about five
orders of magnitude less than the value inferred from the CO absorption. This
and the disparity between H2 and 21-cm/CO absorption line shifts suggest
parsec scale structure in the cloud.

The H i 21-cm absorption towards another lensed system B0218+37 is much
broader than the molecular line but the absorption peaks match well within 10
km s-1 (Wiklind & Combes 1995). The $N$(CO)/$N$(H i) = 0.1 ($N$(H2)/$N$(H i) =
103). The CO and 13CO lines are optically thick, and the column density is
obtained through the C18O(2-1) line (Combes & Wiklind 1995). We have to warn
that due to the different continuum sizes, the H i and H2 column densities are
not averaged over the same apertures. As previously noted, the atomic and
molecular absorption also match well for G0248+430, with $N$(CO)/$N$(H i) =
2.9 $\times$10-4 ($N$(H2)/$N$(H i) = 2.9), and 90% of the 21-cm optical depth
is within the extent of molecular absorption. Towards PKS1413+135 the H i
absorption is broad but the molecular absorption is extremely narrow, and
$N$(H2)/$N$(H i) = 0.2. PKS1830-211 is also a lensed system. It is
particularly known to be rich in gas and dust exhibiting more than sixty
molecular transitions (Muller et al. 2014). Both the H i and CO absorptions
are broad ($\sim$400 km s-1), and the overall $N$(H2)/$N$(H i) = 22, is among
the highest.

The case of PKS1406-076 is intriguing with no overlap between the molecular
and 21-cm line absorptions. The background radio source is a blazar, exhibits
proper motion (0.3 mas yr-1) and at mas scales exhibits complex morphology
over 180 pc. The H i 21-cm absorption profile in the GMRT spectra shows three
well detached components and tentative variability over seven months (Gupta et
al. 2012). The disparity between the 21-cm and mm molecular absorptions is
attributable to the parsec scale structure in the cloud i.e., radio and mm
sight lines tracing different media. Unfortunately, the presence of H i 21-cm
absorption corresponding to the HNC absorption is unknown. The GMRT
observation to detect H i 21-cm absorption used a narrow (1 MHz) bandwidth to
target the Mg ii absorption and did not cover the 21-cm line frequency
corresponding to the HNC absorption.

To summarize, in the case of intervening absorbers, the H i absorption is
broader and the narrower molecular absorption line is generally close to the H
i absorption peak, although shifted by 10-20 km s-1. The exceptions are
PKS1406-076 and the three lensed systems where the situation is complicated by
multiple sightlines towards the lensed source. Nevertheless, the observed
velocity structure of H i and molecular absorption profiles imply sight lines
piercing through layered molecular clouds i.e., molecular gas embedded in
outer layers of predominantly H i gas.

Figure 9: Comparison between H2 and H i (21-cm) column densities for the known
molecular absorption lines systems at high redshift. Ts = 1000 K (100 K) is
adopted for associated (intervening) systems shown as circles (squares). The
color of the symbols represent the redshift, as indicated by the right color
bar, and the size of the symbol traces the velocity extent of the absorption,
averaged over the H i and H2 components.

###  5.3 Nature of the gas detected in associated systems

Both associated targets, PKS 1200$+$045 and PKS 1245$-$19, detected in
molecular absorption are GPS sources. In general, such sources are extremely
compact ($<1$ kpc) and believed to represent the early stages of evolution of
powerful radio galaxies (O’Dea & Saikia 2021). They are known to exhibit
highest H i 21-cm absorption detection rates ($\sim$45%; Gupta et al. 2006).
Indeed, five out of six CO emission line detections from our sample are also
GPS sources (Table 2). In all the cases, CO emission line peak coincides with
the systemic optical redshift within $\sim$200 km s-1(Fig. 1). The CO emission
line widths (FWHM) are 200 - 800 km s-1, implying that these may have
contributions from the gas clouds from (i) the host galaxy ISM through which
the young radio source is expanding, and (ii) the circumnuclear disk,
especially the regions close to the central AGN. The emission and absorption
detected towards Abell 2390 is complex – CO emission is extended and exhibits
large scale outflows and the H i 21-cm absorption has narrow feature with
broader components on either side or covering the entire velocity (Hernández
et al. 2008; Rose et al. 2019a). Nevertheless, the H i absorption line peak in
all but one i.e., PKS 1200$+$045, is also within the velocity range over which
CO emission is detected. Thus, to the first order H i 21-cm absorption and CO
mm emission lines are originating from the same regions.

In general, at cm wavelengths the absorption is more likely to be detected in
front of radio jets and lobes whereas at mm wavelengths the gas in front of
flat spectrum ‘core’ will dominate the detected signal. In addition, molecular
gas is embedded in ISM clouds with outer layers of higher atomic gas fraction.
Both these factors, i.e., geometrical effects due to orientation and frequency
dependent structure of the radio source, and varying molecular gas fraction
within the cloud may lead to differences in the observed properties of the gas
detected in atomic and molecular absorption lines.

In addition to the two associated CO absorbers reported here, associated
molecular absorption lines have been detected in 5 other systems (see Table
5). In general, associated H i 21-cm absorption lines are known to exhibit a
deep narrow and a broad shallow component. The former, when coincident with
the systemic redshift is believed to originate from the circumnuclear disk or
torus. The latter depending on whether it is blueshifted or redshifted with
respect to the systemic redshift is interpreted as outflowing gas due to jet-
ISM interaction or infalling gas that may eventually fuel the AGN. In Fig. 10,
we present the extent of overall H i 21-cm absorption (in blue) and associated
secondary i.e., broader/ shallower component (in cyan) for 6 AGNs444BCG
J0439+0520 with no H i 21-cm absorption is excluded.. In 5/6 cases H i
absorption peak, shown as vertical line on blue, matches with the systemic
redshift within $\pm$200 km s-1. Interestingly, there is a tendency among the
associated systems, to present CO absorption (in red) coincident with the
weaker 21-cm absorption component.

Figure 10: Velocity offsets of H i 21-cm and CO absorption lines. The zero of
the velocity scale corresponds to $z_{21}$. For H i, both the extent of the
full and secondary absorption are shown. The vertical ticks mark the location
of H i and CO absorption peaks, and the systemic velocity, except for PKS
1200$+$045, based on optical emission lines is shown as $\star$.

For PKS 1200$+$045, the observed offset ($\sim$2000 km s-1) between the H i
21-cm and CO absorption lines with respect to molecular and optical/UV
emission lines is particularly intriguing. The large velocity offset with
respect to the CO emission lines and systemic redshift, and the widths of H i
21-cm ($\sim$800 km s-1) and CO ($\sim$200 km s-1) absorption lines suggest
that the absorbing gas represents a distinct and scarce population of cold gas
clouds in the host galaxy. The associated radio emission at 1.4 GHz with a
projected linear size of 60 mas (500 pc at $z_{abs}$) exhibits three
components, one of which lying at one end contains more than 90% of the total
flux density (Liu et al. 2007). The nature of this one-sided morphology as a
core-jet structure is confirmed by the higher frequency milliarcsecond scale
images at 2.3, 4.3 and 8.7 GHz available from the Very Long Baseline Array
(VLBA) calibrator catalog555https://obs.vlba.nrao.edu/cst/. The one-sided
core-jet morphology and orientation of the jet-axis likely ensures that the
sight lines to the radio source do not pass through the circumnuclear disk
detected in CO emission. The absorbing gas may then correspond to quiescent
clouds in the host galaxy ISM or gas interacting with the jet. The large
velocity widths of H i 21-cm ($\sim$800 km s-1) and CO ($\sim$200 km s-1)
absorption lines suggest that it is the latter, detectable in absorption
primarily due to the orientation of the radio source.

For PKS 1200$+$045 one possibility is that only the radio ‘core’ is
responsible for the absorption detected at cm and mm wavelengths. The H i
absorption consists of two components separated by $\sim$200 km s-1 and CO
absorption is coincident only with the secondary weaker component (Fig. 10).
Assuming complete coverage of the radio ‘core’ for the total integrated
columns of the atomic and molecular gas and $T_{\rm s}$ = 1000 K, we estimate
the CO-to-H i column density ratio, $N$(CO)/$N$(H i) = $3\times 10^{-6}$ i.e.,
$N(H_{2})$/$N$(H i) = $3\times 10^{-2}$. Alternatively, it is also possible
that only the CO and secondary H i absorption component are originating from
the gas in the front of radio ‘core’. The molecular to H i column density
ratio would then be a factor of two higher. The deeper H i absorption
component would then correspond to the gas in the front of weaker radio
components associated with the jet and the lobe. The projected distance of
this gas component would at least be a few 100 pc from the ‘core’, explaining
the absence of CO absorption at the corresponding velocities.

The second possibility for PKS 1200$+$045 is similar to the scenario observed
for 4C+12.50, a CSS source hosted in a gas rich Seyfert galaxy. At 1.4 GHz,
4C+12.50 exhibits distorted radio morphology with an overall extent of 150 mas
($\sim$325 pc). The mas-scale spectroscopy reveal the deep narrow H i 21-cm
absorption component to be detected towards fainter northern lobe rather than
the ‘core’ or brighter southern hotspot (Morganti et al. 2004). The weaker H i
absorption component coincides with the CO absorption. The CO-to-H i column
density ratio is $6\times 10^{-4}$ ($N(H_{2})$/$N$(H i) = 6) for $N$(H i) =
$3\times 10^{21}$ cm-2 based on Na i or H i 21-cm absorption ($T_{\rm s}$ =
1000 K) associated with absorption component coincident with the molecular
absorption. This is about 200 times higher than the ratio observed for PKS
1200$+$045 and likely because 4C+12.50 (i) is hosted in a gas rich Seyfert
galaxy, and (ii) being a radio galaxy has orientation such that the sight line
to the radio core passes through the circumnuclear disk.

In contrast to PKS 1200$+$045, the CO absorption associated with PKS 1245$-$19
is offset with respect to 21-cm absorption by $-$1180 km s-1 but within the
range over which CO emission is detected (Fig. 7). The 21-cm absorption
coincides well with the CO emission (Fig. 7). At 2.3 and 8.6 GHz, the radio
source exhibits two prominent steep spectrum ($\alpha<$-0.5) components of
similar strength separated by $\sim$25 mas (Sokolovsky et al. 2011). The radio
core is not detected in these low frequency images but may be responsible for
the CO absorption. The sight lines at cm wavelength, especially towards the
counter jet and lobe, pass through the circumnuclear disk as well as host
galaxy ISM. The non-detection of H i 21-cm absorption, adopting $T_{\rm
s}=1000$ K and line FWHM = 200 km s-1 based on the detected CO absorption,
corresponds to a CO-to-H i column density ratio of $>7\times 10^{-5}$
($N(H_{2})$/$N$(H i) $>$ 0.7). This is significantly higher and lower than the
ratio observed PKS 1200$+$045 and 4C+12.50, respectively. Overall, both the
21-cm and CO absorption lines seem to be tracing the galaxy-wide cold gas from
the ISM and the circumnuclear disk detected in CO emission. The disparity
between H i and CO absorption lines is most likely due to the differences in
the sight lines at cm and mm wavelengths.

Molecular absorption lines have also been detected towards B1504+377, hosted
in a disk galaxy. The associated radio emission at cm wavelengths consists of
a dominant ‘core’ component, with some diffuse emission at a distance of 55
mas (390 pc at $z$=0.674). There is coincidence between the broader H i and CO
absorption (FWHM$\sim$75 km s-1) components at $z$ = 0.67343, both of which
are coincident with the systemic velocity (Wiklind & Combes 1996a; Carilli et
al. 1997). But no H i absorption is detected in the narrow (FWHM$\sim$15 km
s-1) molecular absorption component at $z=0.67150$ (see Fig. 10). For the
broader component the CO-to-H i column density ratio is $2\times 10^{-6}$
($N(H_{2})$/$N$(H i) $>$ 0.02). The orientation and the morphology of the
radio source suggest that it is tracing the gas through the circumnuclear disk
as intercepted by the ‘core’. The non-detection of H i 21-cm absorption in the
narrow CO absorption component corresponds to a column density ratio of
$>3\times 10^{-5}$ ($N(H_{2})$/$N$(H i) $>$ 0.3), which is comparable to other
similar systems discussed here but at least a factor of 10 higher than the
broader component. Based on the large shift ($-$450 km s-1) but narrow width
(15 km s-1) it likely represents a cloud in the inner circumnuclear disk. The
H i 21-cm absorption non-detection is due to the relatively higher CO-to-H i
abundance ratio.

Another molecular absorber is B1740-517, which is a GPS source associated with
a radio galaxy (Sy). At 2.3 GHz, radio emission is resolved into two
components separated by $\sim$50 mas ($\sim$300 pc at $z$=0.442 and the
CO(2-1) absorption coincides with weaker H i absorption component (Allison et
al. 2019). No CO absorption is detected at the narrow, deep 21-cm absorption
peak blue-shifted with respect to CO absorption and systemic redshift by
$\sim$130 km s-1. It is unclear whether the two radio components are core-jet
or two lobes. The CO-to-H i column density ratio for absorption component with
H i and CO absorption, $2\times 10^{-5}$ ($N(H_{2})$/$N$(H i) $=$ 0.2), is
comparable to the other associated systems. It may represent gas closer to the
central AGN whereas the narrow component represents distant towards the jet
and the lobe.

Overall, CO absorption is generally detected in broader and weaker 21-cm
absorption component with typical CO-to-H i abundance ratio of $10^{-6}$ –
$10^{-5}$ ($N(H_{2})$/$N$(H i) = 0.01 - 0.1). Except for B1504+377, the CO
absorption is never coinciding with the deep / strong 21-cm absorption
component. This suggests that absorbing gas has two different phases: one
phase near galaxy centers with a larger CO-to-H i abundance ratio, and another
with lower CO abundance which shows only H i and might correspond to the gas
in outer regions of galaxies. These two phases are well known through emission
line observations of nearby galaxies (e.g., Bigiel & Blitz 2012). The
molecular absorption detection rate from our survey is 2/16 i.e.,
$13^{+16}_{-8}$. As previously noted, it is not expected to detect molecular
absorption in all associated systems with 21-cm absorption, because of the
smaller filling factor of the molecular component, and the much smaller
continuum sizes at millimeter frequency.

##  6 Conclusions

We have searched for molecular emission and absorption in 30 H i 21-cm
absorbers at $0.1<z<4$: 16 of these are associated with the AGN and the
remaining 14 are from intervening galaxies. We report the detection of CO
emission in 8 systems, of which 5 are new. The derived molecular masses,
assuming standard conversion ratios, range from 109 to 7$\times$ 1011 M⊙. The
majority of the these correspond to associated systems belonging to young
radio AGN, i.e. intrinsically compact radio sources with a peaked radio
spectrum. Four of them are at low redshift ($z<$0.25). CO emission in
intervening galaxies are rarer (2/14 = $\sim 14^{+19}_{-9}$%). The two
detections reported here from our sample have masses $M$(H2) = $7\times
10^{11}$ M⊙ (PKS0201+113; $z=3.38715$) and $1.5\times 10^{10}$ M⊙ (Q0248+430;
$z=0.05151$). Notably, the $z=3.38715$ detection presented here has the lowest
absorption metallicity ([M/H] = -1.2) and the highest molecular mass among the
DLAs searched for CO emission till date (Kaur et al. 2022). We have also
stacked together the spectra from 21 undetected sources (10 associated and 11
intervening) and found a hint of emission, at a flux level about an order of
magnitude lower than the individual detections. It is not possible to draw
conclusions on the corresponding masses, because of the varied distances.

Millimeter molecular absorptions are still very rare, at moderate and high
redshift: only 10 systems have been found (Combes 2008; Dasyra & Combes 2012;
Wiklind et al. 2018; Allison et al. 2019; Combes et al. 2019; Rose et al.
2019a): five are associated absorbing systems, and the remaining five
intervening systems, of which 3 are gravitational lenses. Here, we report five
i.e., two associated and three intervening absorption line detections. The two
associated systems, PKS 1200$+$045 ($z$ = 1.2111) and PKS 1245$-$19 ($z$ =
1.2750), are made possible by the high spatial resolution NOEMA follow-up of
our IRAM 30-m detection of CO emission, and demonstrate the complexity faced
in detecting absorption in the presence of emission. Alternatively, it is
possible to detect absorption in the high-density tracers, such as HCO+, HCN
or HNC, which are not detectable in emission. This is indeed the case of the
intervening system towards PKS1406-076 ($z$ = 1.27464) reported here.

The other two intervening detections are towards PKS0201+113 ($z$ = 3.38714)
and Q0248+430 (0.05151). For PKS0201+113 the 21-cm and H2 (ultraviolet)
absorption do not coincide, the peaks are separated by about $\sim$25 km s-1
(Srianand et al. 2012). Interestingly, the 21-cm absorption and CO absorption
components coincide rather well i.e., within 5 km s-1(Fig. 3), and the latter
could be good candidates to constrain the variations of fundamental constants
of physics. The disparity between H2 and 21-cm/CO absorption line shifts
suggest parsec scale structure in the cloud. The case of PKS1406-076 is even
more intriguing with no overlap between the molecular and 21-cm line
absorptions. The disparity between the 21-cm and mm molecular absorptions is
attributable to complex radio morphology i.e., radio and mm sight lines
tracing different media.

We compare the atomic and molecular column densities of 14 known high redshift
($z>0.1$) molecular absorption line systems. Among associated systems, CO
absorption is generally detected in broader and weaker 21-cm absorption
component with typical CO-to-H i abundance ratio of $10^{-6}$ – $10^{-5}$
($N(H_{2})$/$N$(H i) = 0.01 - 0.1). The CO absorption very rarely coincides
with the deep / strong 21-cm absorption component. This suggests that
absorbing gas has two different phases: one phase near galaxy centers with a
larger CO-to-H i abundance ratio, and another with lower CO abundance which
shows only H i and might correspond to the gas in outer regions of galaxies.
These two phases are well known through emission line observations of nearby
galaxies (e.g., Bigiel & Blitz 2012).

In the case of intervening absorbers, the H i absorption is broader and the
narrower molecular absorption line is generally close to the H i absorption
peak, although shifted by 10-20 km s-1. The exceptions are PKS1406-076 and the
three lensed systems where the situation is complicated by multiple sightlines
towards the lensed source. Nevertheless, the observed velocity structure of H
i and molecular absorption profiles imply sight lines piercing through layered
molecular clouds i.e., molecular gas embedded in outer layers of predominantly
H i gas.

With the advent of large surveys at cm wavelengths the number of H i 21-cm
absorbers is expected to steeply increase. However, currently H i 21-cm line
spectroscopy at z$>$0.5 can be performed only at spatial resolutions
$>5^{\prime\prime}$, which may be inadequate to reveal the origin of the
absorbing gas. The work presented here demonstrates that the limitation can be
overcome through the combination of millimeter emission and absorption
spectroscopy probing, and understand the role played by cold gas in the
evolution of normal and active galaxies.

###### Acknowledgements.

This work is based on observations carried out with the IRAM-30m telescope,
and the NOEMA Interferometer. IRAM is supported by INSU/CNRS (France), MPG
(Germany), and IGN (Spain). We acknowledge the help of the IRAM teams for the
observations and thank Vinodiran Arumugam for his support with the data
reduction. The data were processed using the Gildas package. This project has
benefited from support from the Programme National Cosmologie et Galaxies. We
made use of the NASA/IPAC Extragalactic Database (NED), and of the HyperLeda
database (http://leda.univ-lyon1.fr).

## References

  * Aditya (2019) Aditya, J. N. H. S. 2019, MNRAS, 482, 5597
  * Aditya & Kanekar (2018) Aditya, J. N. H. S. & Kanekar, N. 2018, MNRAS, 473, 59
  * Allison et al. (2019) Allison, J. R., Mahony, E. K., Moss, V. A., et al. 2019, MNRAS, 482, 2934
  * Allison et al. (2015) Allison, J. R., Sadler, E. M., Moss, V. A., et al. 2015, MNRAS, 453, 1249
  * Audibert et al. (2022) Audibert, A., Dasyra, K. M., Papachristou, M., et al. 2022, A&A, 668, A67
  * Bagdonaite et al. (2013) Bagdonaite, J., Jansen, P., Henkel, C., et al. 2013, Science, 339, 46
  * Bell & Seaquist (1980) Bell, M. B. & Seaquist, E. R. 1980, ApJ, 238, 818
  * Berg et al. (2015) Berg, T. A. M., Ellison, S. L., Prochaska, J. X., Venn, K. A., & Dessauges-Zavadsky, M. 2015, MNRAS, 452, 4326
  * Bigiel & Blitz (2012) Bigiel, F. & Blitz, L. 2012, ApJ, 756, 183
  * Bolatto et al. (2013) Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207
  * Bottinelli et al. (2009) Bottinelli, S., Hughes, A. M., van Dishoeck, E. F., et al. 2009, ApJ, 690, L130
  * Carilli et al. (1997) Carilli, C. L., Menten, K. M., Reid, M. J., & Rupen, M. P. 1997, ApJ, 474, L89
  * Carilli et al. (1993) Carilli, C. L., Rupen, M. P., & Yanny, B. 1993, ApJ, 412, L59
  * Carswell et al. (2011) Carswell, R. F., Jorgenson, R. A., Wolfe, A. M., & Murphy, M. T. 2011, MNRAS, 411, 2319
  * Chowdhury et al. (2020) Chowdhury, A., Kanekar, N., & Chengalur, J. N. 2020, ApJ, 900, L30
  * Combes (2008) Combes, F. 2008, Ap&SS, 313, 321
  * Combes et al. (2019) Combes, F., Gupta, N., Jozsa, G. I. G., & Momjian, E. 2019, A&A, 623, A133
  * Combes et al. (2023) Combes, F., Gupta, N., Muller, S., et al. 2023, A&A, 671, A43
  * Combes et al. (1999) Combes, F., Maoli, R., & Omont, A. 1999, A&A, 345, 369
  * Combes & Wiklind (1995) Combes, F. & Wiklind, T. 1995, A&A, 303, L61
  * Curran et al. (2007) Curran, S. J., Tzanavaris, P., Murphy, M. T., Webb, J. K., & Pihlström, Y. M. 2007, MNRAS, 381, L6
  * Dasyra & Combes (2012) Dasyra, K. M. & Combes, F. 2012, A&A, 541, L7
  * Dasyra et al. (2014) Dasyra, K. M., Combes, F., Novak, G. S., et al. 2014, A&A, 565, A46
  * Decarli et al. (2020) Decarli, R., Aravena, M., Boogaard, L., et al. 2020, ApJ, 902, 110
  * Downes et al. (1993) Downes, D., Solomon, P. M., & Radford, S. J. E. 1993, ApJ, 414, L13
  * Dutta et al. (2019) Dutta, R., Srianand, R., & Gupta, N. 2019, MNRAS, 489, 1099
  * Dutta et al. (2017) Dutta, R., Srianand, R., Gupta, N., et al. 2017, MNRAS, 465, 4249
  * Ellison et al. (2001) Ellison, S. L., Pettini, M., Steidel, C. C., & Shapley, A. E. 2001, ApJ, 549, 770
  * Eracleous & Halpern (2004) Eracleous, M. & Halpern, J. P. 2004, ApJS, 150, 181
  * Gupta et al. (2018a) Gupta, N., Momjian, E., Srianand, R., et al. 2018a, ApJ, 860, L22
  * Gupta et al. (2006) Gupta, N., Salter, C. J., Saikia, D. J., Ghosh, T., & Jeyakumar, S. 2006, MNRAS, 373, 972
  * Gupta et al. (2016) Gupta, N., Srianand, R., Baan, W., et al. 2016, in MeerKAT Science: On the Pathway to the SKA, 14
  * Gupta et al. (2018b) Gupta, N., Srianand, R., Farnes, J. S., et al. 2018b, MNRAS, 476, 2432
  * Gupta et al. (2012) Gupta, N., Srianand, R., Petitjean, P., et al. 2012, A&A, 544, A21
  * Gupta et al. (2007) Gupta, N., Srianand, R., Petitjean, P., et al. 2007, ApJ, 654, L111
  * Gupta et al. (2009) Gupta, N., Srianand, R., Petitjean, P., Noterdaeme, P., & Saikia, D. J. 2009, MNRAS, 398, 201
  * Gupta et al. (2021) Gupta, N., Srianand, R., Shukla, G., et al. 2021, ApJS, 255, 28
  * Hamanowicz et al. (2023) Hamanowicz, A., Zwaan, M. A., Péroux, C., et al. 2023, MNRAS, 519, 34
  * Henkel et al. (2005) Henkel, C., Jethava, N., Kraus, A., et al. 2005, A&A, 440, 893
  * Henkel et al. (2009) Henkel, C., Menten, K. M., Murphy, M. T., et al. 2009, A&A, 500, 725
  * Hernández et al. (2008) Hernández, H., Ghosh, T., Salter, C. J., & Momjian, E. 2008, in American Institute of Physics Conference Series, Vol. 1035, The Evolution of Galaxies Through the Neutral Hydrogen Window, ed. R. Minchin & E. Momjian, 214–217
  * Hogan (2014) Hogan, M. T. 2014, PhD thesis, Durham University, UK
  * Holt et al. (2003) Holt, J., Tadhunter, C. N., & Morganti, R. 2003, MNRAS, 342, 227
  * Hwang & Chiou (2004) Hwang, C.-Y. & Chiou, S.-H. 2004, ApJ, 600, 52
  * Kanekar (2011) Kanekar, N. 2011, ApJ, 728, L12
  * Kanekar & Briggs (2003) Kanekar, N. & Briggs, F. H. 2003, A&A, 412, L29
  * Kanekar & Chengalur (2001) Kanekar, N. & Chengalur, J. N. 2001, A&A, 369, 42
  * Kanekar et al. (2007) Kanekar, N., Chengalur, J. N., & Lane, W. M. 2007, MNRAS, 375, 1528
  * Kanekar et al. (2001) Kanekar, N., Ghosh, T., & Chengalur, J. N. 2001, A&A, 373, 394
  * Kanekar et al. (2012) Kanekar, N., Langston, G. I., Stocke, J. T., Carilli, C. L., & Menten, K. M. 2012, ApJ, 746, L16
  * Kaur et al. (2022) Kaur, B., Kanekar, N., Rafelski, M., et al. 2022, ApJ, 933, L42
  * Kaur et al. (2021) Kaur, B., Kanekar, N., Rafelski, M., et al. 2021, ApJ, 921, 68
  * Klitsch et al. (2019) Klitsch, A., Péroux, C., Zwaan, M. A., et al. 2019, MNRAS, 490, 1220
  * Kollatschny et al. (1991) Kollatschny, W., Dietrich, M., Borgeest, U., & Schramm, K. J. 1991, A&A, 249, 57
  * Koopmans & de Bruyn (2005) Koopmans, L. V. E. & de Bruyn, A. G. 2005, MNRAS, 360, L6
  * Kuehr (1977) Kuehr, H. 1977, A&AS, 29, 139
  * Labiano et al. (2007) Labiano, A., Barthel, P. D., O’Dea, C. P., et al. 2007, A&A, 463, 97
  * Lenkić et al. (2020) Lenkić, L., Bolatto, A. D., Förster Schreiber, N. M., et al. 2020, AJ, 159, 190
  * Liszt & Lucas (2001) Liszt, H. & Lucas, R. 2001, A&A, 370, 576
  * Liu et al. (2007) Liu, X., Cui, L., Luo, W. F., Shi, W. Z., & Song, H. G. 2007, A&A, 470, 97
  * Madau & Dickinson (2014) Madau, P. & Dickinson, M. 2014, ARA&A, 52, 415
  * Maloney et al. (1996) Maloney, P. R., Hollenbach, D. J., & Tielens, A. G. G. M. 1996, ApJ, 466, 561
  * Menten et al. (2008) Menten, K. M., Güsten, R., Leurini, S., et al. 2008, A&A, 492, 725
  * Morganti et al. (2004) Morganti, R., Oosterloo, T. A., Tadhunter, C. N., et al. 2004, A&A, 424, 119
  * Muller et al. (2013) Muller, S., Beelen, A., Black, J. H., et al. 2013, A&A, 551, A109
  * Muller et al. (2014) Muller, S., Combes, F., Guélin, M., et al. 2014, A&A, 566, A112
  * Muller et al. (2016) Muller, S., Müller, H. S. P., Black, J. H., et al. 2016, A&A, 595, A128
  * Muller et al. (2021) Muller, S., Ubachs, W., Menten, K. M., Henkel, C., & Kanekar, N. 2021, A&A, 652, A5
  * Murphy et al. (2022) Murphy, M. T., Molaro, P., Leite, A. C. O., et al. 2022, A&A, 658, A123
  * Neeleman et al. (2019) Neeleman, M., Kanekar, N., Prochaska, J. X., Rafelski, M. A., & Carilli, C. L. 2019, ApJ, 870, L19
  * Neeleman et al. (2016) Neeleman, M., Prochaska, J. X., Zwaan, M. A., et al. 2016, ApJ, 820, L39
  * Noterdaeme et al. (2023) Noterdaeme, P., Balashev, S., Cuellar, R., et al. 2023, A&A, 673, A89
  * Noterdaeme et al. (2015) Noterdaeme, P., Petitjean, P., & Srianand, R. 2015, A&A, 578, L5
  * Obreschkow & Rawlings (2009a) Obreschkow, D. & Rawlings, S. 2009a, ApJ, 696, L129
  * Obreschkow & Rawlings (2009b) Obreschkow, D. & Rawlings, S. 2009b, MNRAS, 394, 1857
  * Ocaña Flaquer et al. (2010) Ocaña Flaquer, B., Leon, S., Combes, F., & Lim, J. 2010, A&A, 518, A9
  * O’Dea & Saikia (2021) O’Dea, C. P. & Saikia, D. J. 2021, A&A Rev., 29, 3
  * Peck et al. (1999) Peck, A. B., Taylor, G. B., & Conway, J. E. 1999, ApJ, 521, 103
  * Petitjean et al. (2000) Petitjean, P., Srianand, R., & Ledoux, C. 2000, A&A, 364, L26
  * Quider et al. (2011) Quider, A. M., Nestor, D. B., Turnshek, D. A., et al. 2011, AJ, 141, 137
  * Rachford et al. (2009) Rachford, B. L., Snow, T. P., Destree, J. D., et al. 2009, ApJS, 180, 125
  * Readhead et al. (2021) Readhead, A. C. S., Ravi, V., Liodakis, I., et al. 2021, ApJ, 907, 61
  * Riechers et al. (2020) Riechers, D. A., Boogaard, L. A., Decarli, R., et al. 2020, ApJ, 896, L21
  * Rose et al. (2019a) Rose, T., Edge, A. C., Combes, F., et al. 2019a, MNRAS, 489, 349
  * Rose et al. (2019b) Rose, T., Edge, A. C., Combes, F., et al. 2019b, MNRAS, 485, 229
  * Rose et al. (2020) Rose, T., Edge, A. C., Combes, F., et al. 2020, MNRAS, 496, 364
  * Scoville et al. (2000) Scoville, N. Z., Evans, A. S., Thompson, R., et al. 2000, AJ, 119, 991
  * Snellen et al. (2003) Snellen, I. A. G., Lehnert, M. D., Bremer, M. N., & Schilizzi, R. T. 2003, MNRAS, 342, 889
  * Sokolovsky et al. (2011) Sokolovsky, K. V., Kovalev, Y. Y., Pushkarev, A. B., Mimica, P., & Perucho, M. 2011, A&A, 535, A24
  * Solomon et al. (1992) Solomon, P. M., Radford, S. J. E., & Downes, D. 1992, Nature, 356, 318
  * Solomon & Vanden Bout (2005) Solomon, P. M. & Vanden Bout, P. A. 2005, ARA&A, 43, 677
  * Srianand et al. (2012) Srianand, R., Gupta, N., Petitjean, P., et al. 2012, MNRAS, 421, 651
  * Srianand et al. (2013) Srianand, R., Gupta, N., Rahmani, H., et al. 2013, MNRAS, 428, 2198
  * Srianand et al. (2008) Srianand, R., Noterdaeme, P., Ledoux, C., & Petitjean, P. 2008, A&A, 482, L39
  * Stickel & Kuhr (1993) Stickel, M. & Kuhr, H. 1993, A&AS, 101, 521
  * Tacconi et al. (2018) Tacconi, L. J., Genzel, R., Saintonge, A., et al. 2018, ApJ, 853, 179
  * Tremblay et al. (2016) Tremblay, G. R., Oonk, J. B. R., Combes, F., et al. 2016, Nature, 534, 218
  * Uzan (2011) Uzan, J.-P. 2011, Living Reviews in Relativity, 14, 2
  * Vermeulen et al. (2003) Vermeulen, R. C., Pihlström, Y. M., Tschager, W., et al. 2003, A&A, 404, 861
  * White et al. (1993) White, R. L., Kinney, A. L., & Becker, R. H. 1993, ApJ, 407, 456
  * Wiklind & Combes (1994) Wiklind, T. & Combes, F. 1994, A&A, 286, L9
  * Wiklind & Combes (1995) Wiklind, T. & Combes, F. 1995, A&A, 299, 382
  * Wiklind & Combes (1996a) Wiklind, T. & Combes, F. 1996a, A&A, 315, 86
  * Wiklind & Combes (1996b) Wiklind, T. & Combes, F. 1996b, Nature, 379, 139
  * Wiklind & Combes (1997) Wiklind, T. & Combes, F. 1997, A&A, 328, 48
  * Wiklind & Combes (1998) Wiklind, T. & Combes, F. 1998, ApJ, 500, 129
  * Wiklind et al. (2018) Wiklind, T., Combes, F., & Kanekar, N. 2018, ApJ, 864, 73