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The physical processes by which gas is accreted onto galaxies, transformed into stars and then expelled from galaxies are of paramount importance to galaxy evolution studies. Observationally constraining each of these baryonic components in the same systems however, is challenging. Furthermore, simulations indicate that the stellar mass of galaxies is a key factor influencing CGM properties. Indeed, absorption lines detected against background quasars offer the most compelling way to study the cold gas in the circumgalactic medium (CGM). The MUSE-ALMA Haloes survey is composed of quasar fields covered with VLT/MUSE observations, comprising 32 \ion{H}{i} absorbers at 0.2 $<$ $z$ $<$ 1.4 and 79 associated galaxies, with available or upcoming molecular gas measurements from ALMA. We use a dedicated 40-orbit HST UVIS and IR WFC3 broad-band imaging campaign to characterise the stellar content of these galaxies. By fitting their spectral energy distribution, we establish they probe a wide range of stellar masses: 8.1 $<$ log($M_*$/M$_{\odot}$) $<$ 12.4. Given their star-formation rates, most of these objects lie on the main sequence of galaxies. We also confirm a previously reported anti-correlation between the stellar masses and CGM hydrogen column density N(\ion{H}{i}), indicating an evolutionary trend where higher mass galaxies are less likely to host large amounts of \ion{H}{i} gas in their immediate vicinity up to 120 kpc. Together with other studies from the MUSE-ALMA Haloes survey, these data provide stellar masses of absorber hosts, a key component of galaxy formation and evolution, and observational constraints on the relation between galaxies and their surrounding medium., Comment: accepted in MNRAS

Understanding how galaxies interact with the circumgalactic medium (CGM) requires determining how galaxies morphological and stellar properties correlate with their CGM properties. We report an analysis of 66 well-imaged galaxies detected in HST and VLT MUSE observations and determined to be within $\pm$500 km s$^{-1}$ of the redshifts of strong intervening quasar absorbers at $0.2 \lesssim z \lesssim 1.4$ with H I column densities $N_{\rm H I}$ $>$ $10^{18}$ $\rm cm^{-2}$. We present the geometrical properties (S\'ersic indices, effective radii, axis ratios, and position angles) of these galaxies determined using GALFIT. Using these properties along with star formation rates (SFRs, estimated using the H$\alpha$ or [O II] luminosity) and stellar masses ($M_{*}$ estimated from spectral energy distribution fits), we examine correlations among various stellar and CGM properties. Our main findings are as follows: (1) SFR correlates well with $M_{*}$, and most absorption-selected galaxies are consistent with the star formation main sequence (SFMS) of the global population. (2) More massive absorber counterparts are more centrally concentrated and are larger in size. (3) Galaxy sizes and normalized impact parameters correlate negatively with $N_{\rm H I}$, consistent with higher $N_{\rm H I}$ absorption arising in smaller galaxies, and closer to galaxy centers. (4) Absorption and emission metallicities correlate with $M_{*}$ and sSFR, implying metal-poor absorbers arise in galaxies with low past star formation and faster current gas consumption rates. (5) SFR surface densities of absorption-selected galaxies are higher than predicted by the Kennicutt-Schmidt relation for local galaxies, suggesting a higher star formation efficiency in the absorption-selected galaxies., Comment: Accepted for publication in MNRAS, 25 pages, 19 figures

It may be unsurprising that the most common approach to finding proto-clusters is to search for over-densities of galaxies. Upgrades to submillimetre (submm) interferometers and the advent of the James Webb Space Telescope will soon offer the opportunity to find more distant candidate proto-clusters in deep sky surveys without any spectroscopic confirmation. In this letter, we report the serendipitous discovery of an extremely dense region centred on the blazar, J0217-0820, at z=0.6 in the ALMACAL sky survey. Its density is eight times higher than that predicted by blind submm surveys. Among the seven submm-bright galaxies, three are as bright as conventional single-dish submm galaxies, with S_870um > 3mJy. The over-density is thus comparable to the densest known and confirmed proto-cluster cores. However, their spectra betray a wide range of redshifts. We investigate the likelihood of line-of-sight projection effects using light cones from cosmological simulations, finding that the deeper we search, the higher the chance that we will suffer from such projection effects. The extreme over-density around J0217-0820 demonstrates the strong cosmic variance we may encounter in the deep submm surveys. Thus, we should also question the fidelity of galaxy proto-cluster candidates selected via over-densities of galaxies, where the negative K correction eases the detection of dusty galaxies along an extraordinarily extended line of sight., Comment: 7 pages, 5 figures, update with the accepted version

Despite its crucial role in galaxy evolution, the complex circumgalactic medium (CGM) remains underexplored. Although it is known to be multi-phase, the importance of the molecular gas phase to the total CGM mass budget is, to date, unconstrained. We present the first constraints on the molecular gas covering fraction in the CGM of low-redshift galaxies, using measurements of CO column densities along sightlines towards mm-bright background quasars with intervening galaxies. We do not detect molecular absorption against the background quasars. For the individual, low-redshift, 'normal' galaxy haloes probed here, we can therefore rule out the presence of an extremely molecular gas-rich CGM, as recently reported in high-redshift protoclusters and around luminous active galactic nuclei. We also set statistical limits on the volume filling factor of molecular material in the CGM as a whole, and as a function of radius. ISM-like molecular clouds of ~30 pc in radius with column densities of N(CO) >~ 10^16 cm^-2 have volume filling factors of less than 0.2 per cent. Large-scale smooth gas reservoirs are ruled out much more stringently. The development of this technique in the future will allow deeper constraining limits to be set on the importance (or unimportance) of molecular gas in the CGM., Comment: 5 pages, 5 figures, accepted for publication in MNRAS

The distribution of gas and metals in the circumgalactic medium (CGM) plays a critical role in how galaxies evolve. The MUSE-ALMA Halos survey combines MUSE, ALMA and HST observations to constrain the properties of the multi-phase gas in the CGM and the galaxies associated with the gas probed in absorption. In this paper, we analyse the properties of galaxies associated with 32 strong \ion{H}{i} Ly-$\alpha$ absorbers at redshift $0.2 \lesssim z \lesssim 1.4$. We detect 79 galaxies within $\pm 500$ \kms \!of the absorbers in our 19 MUSE fields. These associated galaxies are found at physical distances from 5.7 kpc and reach star-formation rates as low as $0.1$ \Moyr. The significant number of associated galaxies allows us to map their physical distribution on the $\Delta v$ and $b$ plane. Building on previous studies, we examine the physical and nebular properties of these associated galaxies and find the following: i) 27/32 absorbers have galaxy counterparts and more than 50 per cent of the absorbers have two or more associated galaxies, ii) the \ion{H}{i} column density of absorbers is anti-correlated with the impact parameter (scaled by virial radius) of the nearest galaxy as expected from simulations, iii) the metallicity of associated galaxies is typically larger than the absorber metallicity which decreases at larger impact parameters. It becomes clear that while strong \ion{H}{i} absorbers are typically associated with more than a single galaxy, we can use them to statistically map the gas and metal distribution in the CGM., Comment: 17 pages, 14 figures and 10 pages of appendices. The associated galaxy catalogue will be made available online. Accepted for publication in MNRAS

The gas cycling in the circumgalactic regions of galaxies is known to be multi-phase. The MUSE-ALMA Haloes survey gathers a large multi-wavelength observational sample of absorption and emission data with the goal to significantly advance our understanding of the physical properties of such CGM gas. A key component of the MUSE-ALMA Haloes survey is the multi-facility observational campaign conducted with VLT/MUSE, ALMA and HST. MUSE-ALMA Haloes targets comprise 19 VLT/MUSE IFS quasar fields, including 32 $z_{\rm abs}<$0.85 strong absorbers with measured N$_{HI}$ $\geq 10^{18}$ cm$^{\rm -2}$ from UV-spectroscopy. We additionally use a new complementary HST medium program to characterise the stellar content of the galaxies through a 40-orbit three-band UVIS and IR WFC3 imaging. Beyond the absorber-selected targets, we detect 3658 sources all fields combined, including 703 objects with spectroscopic redshifts. This galaxy-selected sample constitutes the main focus of the current paper. We have secured millimeter ALMA observations of some of the fields to probe the molecular gas properties of these objects. Here, we present the overall survey science goals, target selection, observational strategy, data processing and source identification of the full sample. Furthermore, we provide catalogues of magnitude measurements for all objects detected in VLT/MUSE, ALMA and HST broad-band images and associated spectroscopic redshifts derived from VLT/MUSE observations. Together, this data set provides robust characterisation of the neutral atomic gas, molecular gas and stars in the same objects resulting in the baryon census of condensed matter in complex galaxy structures., Comment: 19 pages, 4 figures. This is the final (proof-corrected) version, published in MNRAS. Galaxy catalogues are available online

We present a pilot, untargeted extragalactic carbon monoxide (CO) emission-line survey using ALMACAL, a project utilizing ALMA calibration data for scientific purposes. In 33 deep (Texp > 40 min) ALMACAL fields we report six CO emission-line detections above S/N > 4, one-third confirmed by MUSE observations. With this pilot survey, we probe a cosmologically significant volume of ~10^5 cMpc^3, widely distributed over many pointings in the southern sky, making the survey largely insusceptible to the effects of cosmic variance. We derive the redshift probability of the CO detections using probability functions from the Shark semi-analytical model of galaxy formation. By assuming typical CO excitations for the detections, we put constraints on the cosmic molecular gas mass density evolution over the redshift range 0 < z < 1.5. The results of our pilot survey are consistent with the findings of other untargeted emission-line surveys and the theoretical model predictions and currently cannot rule out a non-evolving molecular gas mass density. Our study demonstrates the potential of using ALMA calibrator fields as a multi-sightline untargeted CO emission line survey. Applying this approach to the full ALMACAL database will provide an accurate, free of cosmic variance, measurement of the molecular luminosity function as a function of redshift.

Wide, deep, blind continuum surveys at submillimetre/millimetre (submm/mm) wavelengths are required to provide a full inventory of the dusty, distant Universe. However, conducting such surveys to the necessary depth, with sub-arcsec angular resolution, is prohibitively time-consuming, even for the most advanced submm/mm telescopes. Here, we report the most recent results from the ALMACAL project, which exploits the 'free' calibration data from the Atacama Large Millimetre/submillimetre Array (ALMA) to map the lines of sight towards and beyond the ALMA calibrators. ALMACAL has now covered 1,001 calibrators, with a total sky coverage around 0.3 deg2, distributed across the sky accessible from the Atacama desert, and has accumulated more than 1,000h of integration. The depth reached by combining multiple visits to each field makes ALMACAL capable of searching for faint, dusty, star-forming galaxies (DSFGs), with detections at multiple frequencies to constrain the emission mechanism. Based on the most up-to-date ALMACAL database, we report the detection of 186 DSFGs with flux densities down to S870um ~ 0.2mJy, comparable with existing ALMA large surveys but less susceptible to cosmic variance. We report the number counts at five wavelengths between 870um and 3mm, in ALMA bands 3, 4, 5, 6 and 7, providing a benchmark for models of galaxy formation and evolution. By integrating the observed number counts and the best-fitting functions, we also present the resolved fraction of the cosmic infrared background (CIB) and the CIB spectral shape. Combining existing surveys, ALMA has currently resolved about half of the CIB in the submm/mm regime., Comment: 22 pages, 16 figures, accepted for publication in MNRAS

While emission-selected galaxy surveys are biased towards the most luminous part of the galaxy population, absorption selection is a potentially unbiased galaxy selection technique with respect to luminosity. However, the physical properties of absorption-selected galaxies are not well characterised. Here we study the excitation conditions in the interstellar medium (ISM) in damped Ly$\alpha$ (DLA) absorption-selected galaxies. We present a study of the CO spectral line energy distribution (SLED) in four high-metallicity absorption-selected galaxies with previously reported CO detections at intermediate ($z \sim 0.7$) and high ($z \sim 2$) redshifts. We find further evidence for a wide variety of ISM conditions in these galaxies. Two out of the four galaxies show CO SLEDs consistent with that of the Milky Way inner disk. Interestingly, one of these galaxies is at $z \sim 2$ and has a CO SLED below that of main-sequence galaxies at similar redshifts. The other two galaxies at $z>2$ show more excited ISM conditions, with one of them showing thermal excitation of the mid-$J$ (J$=3, 4$) levels, similar to that seen in two massive main-sequence galaxies at these redshifts. Overall, we find that absorption selection traces a diverse population of galaxies., Comment: 10 pages, 5 figures, 6 tables, resubmitted to MNRAS after moderate revision

Absorption-selected galaxies offer an effective way to study low-mass galaxies at high redshift. However, the physical properties of the underlying galaxy population remains uncertain. In particular, the multiphase circum-galactic medium is thought to hold key information on gas flows into and out of galaxies that are vital for galaxy evolution models. Here we present ALMA observations of CO molecular gas in host galaxies of H_2-bearing absorbers. In our sample of six absorbers we detect molecular gas-rich galaxies in five absorber fields although we did not target high-metallicity (>50 per cent solar) systems for which previous studies reported the highest detection rate. Surprisingly, we find that the majority of the absorbers are associated with multiple galaxies rather than single haloes. Together with the large impact parameters these results suggest that the H_2-bearing gas seen in absorption is not part of an extended disk, but resides in dense gas pockets in the circum-galactic and intra-group medium., Comment: Accepted for publication in MNRAS; 8 pages, 7 figures

We present results of MUSE-ALMA Halos, an ongoing study of the Circumgalactic Medium (CGM) of galaxies ($z \leq$ 1.4). Using multi-phase observations we probe the neutral, ionised and molecular gas in a sub-sample containing six absorbers and nine associated galaxies in the redshift range $z \sim 0.3-0.75$. Here, we give an in-depth analysis of the newly CO-detected galaxy Q2131-G1 ($z=0.42974$), while providing stringent mass and depletion time limits for the non-detected galaxies. Q2131-G1 is associated with an absorber with column densities of $\textrm{log}(N_\textrm{HI}/\textrm{cm}^{-2}) \sim 19.5$ and $\textrm{log}(N_{\textrm{H}_2}/\textrm{cm}^{-2}) \sim 16.5$, has a star formation rate of $\textrm{SFR} = 2.00 \pm 0.20 \; \textrm{M}_{\odot} \textrm{yr}^{-1}$, a dark matter fraction of $f_\textrm{DM}(r_{1/2}) = 0.24 - 0.54$ and a molecular gas mass of $M_\textrm{mol} = 3.52 ^{+3.95}_{-0.31} \times 10^9 \; \textrm{M}_{\odot}$ resulting in a depletion time of $\tau_\textrm{dep} < 4.15 \; \textrm{Gyr}$. Kinematic modelling of both the CO (3--2) and [OIII] $\lambda 5008$ emission lines of Q2131-G1 shows that the molecular and ionised gas phases are well aligned directionally and that the maximum rotation velocities closely match. These two gas phases within the disk are strongly coupled. The metallicity, kinematics and orientation of the atomic and molecular gas traced by a two-component absorption feature is consistent with being part of the extended rotating disk with a well-separated additional component associated with infalling gas. Compared to emission-selected samples, we find that HI-selected galaxies have high molecular gas masses given their low star formation rate. We consequently derive high depletion times for these objects., Comment: 18 pages, 9 figures, 3 tables. Accepted for publication in MNRAS

Measurements of the cosmic far-infrared background (CIB) indicate that emission from many extragalactic phenomena, including star formation and black hole accretion, in the Universe can be obscured by dust. Resolving the CIB to study the population of galaxies in which this activity takes place is a major goal of submillimetre astronomy. Here, we present interferometric 650$\mu$m submillimetre number counts. Using the Band 8 data from the ALMACAL survey, we have analysed 81 ALMA calibrator fields together covering a total area of 5.5~arcmin$^2$. The typical central rms in these fields is $\sim 100 \mu$Jy~beam$^{-1}$ with the deepest maps reaching $\sigma = 47 \mu$Jy~beam$^{-1}$ at sub-arcsec resolution. Multi-wavelength coverage from ALMACAL allows us to exclude contamination from jets associated with the calibrators. However, residual contamination by jets and lensing remain a possibility. Using a signal-to-noise threshold of $4.5\sigma$, we find 21 dusty, star-forming galaxies with 650$\mu$m flux densities of $\geq 0.7 $mJy. At the detection limit we resolve $\simeq 100$ per cent of the CIB at 650$\mu$m, a significant improvement compared to low resolution studies at similar wavelength. We have therefore identified all the sources contributing to the EBL at 650 microns and predict that the contribution from objects with flux 0.7

We present results of the MUSE-ALMA Halos, an ongoing study of the Circum-Galactic Medium (CGM) of low redshift galaxies (z < 1.4), currently comprising 14 strong HI absorbers in five quasar fields. We detect 43 galaxies associated with absorbers down to star formation rate (SFR) limits of 0.01-0.1 solar masses/yr, found within impact parameters (b) of 250 kpc from the quasar sightline. Excluding the targeted absorbers, we report a high detection rate of 89 per cent and find that most absorption systems are associated with pairs or groups of galaxies (three to eleven members). We note that galaxies with the smallest impact parameters are not necessarily the closest to the absorbing gas in velocity space. Using a multi-wavelength dataset (UVES/HIRES, HST, MUSE), we combine metal and HI column densities, allowing for derivation of the lower limits of neutral gas metallicity as well as emission line diagnostics (SFR, metallicities) of the ionised gas in the galaxies. We find that groups of associated galaxies follow the canonical relations of N(HI) -- b and W_r(2796) -- b, defining a region in parameter space below which no absorbers are detected. The metallicity of the ISM of associated galaxies, when measured, is higher than the metallicity limits of the absorber. In summary, our findings suggest that the physical properties of the CGM of complex group environments would benefit from associating the kinematics of individual absorbing components with each galaxy member., Comment: Accepted for publication in MNRAS; 23 pages, 25 figures

We are just starting to understand the physical processes driving the dramatic change in cosmic star-formation rate between $z\sim 2$ and the present day. A quantity directly linked to star formation is the molecular gas density, which should be measured through independent methods to explore variations due to cosmic variance and systematic uncertainties. We use intervening CO absorption lines in the spectra of mm-bright background sources to provide a census of the molecular gas mass density of the Universe. The data used in this work are taken from ALMACAL, a wide and deep survey utilizing the ALMA calibrator archive. While we report multiple Galactic absorption lines and one intrinsic absorber, no extragalactic intervening molecular absorbers are detected. However, thanks to the large redshift path surveyed ($\Delta z=182$), we provide constraints on the molecular column density distribution function beyond $z\sim 0$. In addition, we probe column densities of N(H$_2$) > 10$^{16}$ atoms~cm$^{-2}$, five orders of magnitude lower than in previous studies. We use the cosmological hydrodynamical simulation IllustrisTNG to show that our upper limits of $\rho ({\rm H}_2)\lesssim 10^{8.3} \text{M}_{\odot} \text{Mpc}^{-3}$ at $0 < z \leq 1.7$ already provide new constraints on current theoretical predictions of the cold molecular phase of the gas. These results are in agreement with recent CO emission-line surveys and are complementary to those studies. The combined constraints indicate that the present decrease of the cosmic star-formation rate history is consistent with an increasing depletion of molecular gas in galaxies compared to $z\sim 2$., Comment: 11 pages, 10 figures, 2 tables, accepted for publication in MNRAS

Galaxy halos appear to be missing a large fraction of their baryons, most probably hiding in the circumgalactic medium (CGM), a diffuse component within the dark matter halo that extends far from the inner regions of the galaxies. A powerful tool to study the CGM gas is offered by absorption lines in the spectra of background quasars. Here, we present optical (MUSE) and mm (ALMA) observations of the field of the quasar Q1130-1449 which includes a log [N(H I)/cm^-2]=21.71+/-0.07 absorber at z=0.313. Ground-based VLT/MUSE 3D spectroscopy shows 11 galaxies at the redshift of the absorber down to a limiting SFR>0.01 M_sun yr^-1 (covering emission lines of [OII], Hbeta, [OIII], [NII] and Halpha), 7 of which are new discoveries. In particular, we report a new emitter with a smaller impact parameter to the quasar line-of-sight (b=10.6 kpc) than the galaxies detected so far. Three of the objects are also detected in CO(1-0) in our ALMA observations indicating long depletion timescales for the molecular gas and kinematics consistent with the ionised gas. We infer from dedicated numerical cosmological RAMSES zoom-in simulations that the physical properties of these objects qualitatively resemble a small group environment, possibly part of a filamentary structure. Based on metallicity and velocity arguments, we conclude that the neutral gas traced in absorption is only partly related to these emitting galaxies while a larger fraction is likely the signature of gas with surface brightness almost four orders of magnitude fainter that current detection limits. Together, these findings challenge a picture where strong-HI quasar absorbers are associated with a single bright galaxy and favour a scenario where the HI gas probed in absorption is related to far more complex galaxy structures., Comment: Accepted for publication in MNRAS; 20 pages, 9 figures

Gas-rich galaxies are selected efficiently via quasar absorption lines. Recently, a new perspective on such absorption-selected systems has opened up by studying the molecular gas content of absorber host galaxies using ALMA CO emission line observations. Here, we present an analysis of multiple CO transitions ($L'_{\rm CO} \sim 10^9$ K km s$^{-1}$) in two $z \sim 0.5$ galaxies associated with one Ly$\alpha$ absorber towards J0238+1636. The CO spectral line energy distribution (CO SLED) of these galaxies appear distinct from that of typical star-forming galaxies at similar redshifts and is comparable with that of luminous infrared galaxies or AGN. Indeed, these galaxies are associated with optically identified AGN activity. We infer that the CO line ratios and the $\alpha_{\rm CO}$ conversion factor differ from the Galactic values. Our findings suggest that at least a fraction of absorption selected systems shows ISM conditions deviating from those of normal star-forming galaxies. For a robust molecular gas mass calculation, it is therefore important to construct the CO SLED. Absorption-line-selection identifies systems with widely distributed gas, which may preferentially select interacting galaxies, which in turn will have more excited CO SLEDs than isolated galaxies. Furthermore, we raise the question whether quasar absorbers preferentially trace galaxy overdensities., Comment: 5 pages, 3 figures, 3 tables, Accepted for publication in MNRAS

We present a catalogue of ALMA flux density measurements of 754 calibrators observed between August 2012 and September 2017, for a total of 16,263 observations in different bands and epochs. The flux densities were measured reprocessing the ALMA images generated in the framework of the ALMACAL project, with a new code developed by the Italian node of the European ALMA Regional Centre. A search in the online databases yielded redshift measurements for 589 sources ($\sim$78 per cent of the total). Almost all sources are flat-spectrum, based on their low-frequency spectral index, and have properties consistent with being blazars of different types. To illustrate the properties of the sample we show the redshift and flux density distributions as well as the distributions of the number of observations of individual sources and of time spans in the source frame for sources observed in bands 3 (84$-$116 GHz) and 6 (211$-$275 GHz). As examples of the scientific investigations allowed by the catalogue we briefly discuss the variability properties of our sources in ALMA bands 3 and 6 and the frequency spectra between the effective frequencies of these bands. We find that the median variability index steadily increases with the source-frame time lag increasing from 100 to 800 days, and that the frequency spectra of BL Lacs are significantly flatter than those of flat-spectrum radio quasars. We also show the global spectral energy distributions of our sources over 17 orders of magnitude in frequency., Comment: 8 pages, 9 figures, 2 tables, MNRAS accepted

Studying the flow of baryons into and out of galaxies is an important part of understanding the evolution of galaxies over time. We present a detailed case study of the environment around an intervening Ly $\alpha$ absorption line system at $z_{\rm abs} = 0.633$, seen towards the quasar J0423$-$0130 ($z_{\rm QSO} = 0.915$). We detect with ALMA the $^{12}$CO(2--1), $^{12}$CO(3--2) and $1.2$~mm continuum emission from a galaxy at the redshift of the Ly $\alpha$ absorber at a projected distance of $135$ kpc. From the ALMA detections, we infer ISM conditions similar to those in low redshift Luminous Infrared Galaxies. DDT MUSE integral field unit observations reveal the optical counterpart of the $^{12}$CO emission line source and three additional emission line galaxies at the absorber redshift, which together form a galaxy group. The $^{12}$CO emission line detections originate from the most massive galaxy in this group. While we cannot exclude that we miss a fainter host, we reach a dust-uncorrected star-formation rate (SFR) limit of > $0.3 \text{M}_{\odot} \text{ yr}^{-1}$ within $100$ kpc from the sightline to the background quasar. We measure the dust-corrected SFR (ranging from $3$ to $50$ M$_{\odot}$ yr$^{-1}$), the morpho-kinematics and the metallicities of the four group galaxies to understand the relation between the group and the neutral gas probed in absorption. We find that the Ly $\alpha$ absorber traces either an outflow from the most massive galaxy or intra-group gas. This case study illustrates the power of combining ALMA and MUSE to obtain a census of the cool baryons in a bounded structure at intermediate redshift., Comment: 17 pages, 9 figures, 9 tables, accepted for publication in MNRAS

E+A galaxies are post-starburst systems that are identified from their optical spectra. These galaxies contain a substantial young A-type stellar component, but have only little ongoing star formation (SF). HI 21-cm line emission is found in approximately half of the nearby E+A galaxies, indicating that they contain a reservoir of gas that could fuel active SF. Here, we study two HI-rich galaxies, which show a typical E+A spectrum at the centre and SF at larger radii. We present new high spatial resolution radio interferometric observations of the HI 21-cm emission line using the VLA and of the CO(1-0) emission line using ALMA. We combine these data sets to predict the SFR and show that it does not correlate well with the SFR derived from H alpha on sub-kpc scales. We apply a recently developed statistical model for the small scale behaviour of the SF relation to predict and interpret the observed scatter. We find smoothly distributed, regularly rotating HI gas. The CO(1-0) emission line is not detected for both galaxies. The derived upper limit on the CO mass implies a molecular gas depletion time shorter than 20 Myr. However, due to the low metallicity, the CO-to-H2 conversion factor is highly uncertain. In the relations between the H alpha-based SFR and the HI mass, we observe a substantial scatter we demonstrate results from small-number statistics of independent star-forming regions on sub-kpc scales. This finding adds to the existing literature reporting a scale dependence of the molecular SF relation, showing that the atomic and molecular phases are both susceptible to the evolutionary 'cycling' of individual regions. This suggests that the atomic gas reservoirs host substantial substructure, which should be observable with future high-resolution observations. (abridged), Comment: 14 pages, 7 figures, accepted for publication in Astronomy & Astrophysics