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Open Access
Issue
A&A
Volume 677, September 2023
Article Number A44
Number of page(s) 21
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202346143
Published online 06 September 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1. Introduction

The series of processes involved in the formation and evolution of galaxies across cosmic time is still far from being fully understood. What we undoubtedly know is that the amount of cold gas inside a galaxy is the main factor deciding its fate, as it is the fuel of star formation. Indeed, gas can cool down and condense to form stars that, during their lifetime, alter the state and growth of a galaxy (see e.g., Tumlinson et al. 2017; Péroux & Howk 2020; Tacconi et al. 2020 for reviews). In particular, massive stars are able to inject energy and momentum in their surroundings through stellar winds and supernova (SN) explosions, modifying the properties of the interstellar medium (ISM) by enriching it with heavy elements and sweeping the gas out of the galaxy via fast and powerful outflows (e.g., Murray et al. 2005; Veilleux et al. 2005; Hopkins et al. 2012; Erb 2015; Heckman et al. 2015). At the same time, SNe can trigger interstellar turbulence regulating the star-formation rate (SFR) of a galaxy, which in turn plays a key role in providing new sources of radiation and feedback (e.g., Faucher-Giguère et al. 2013; Martizzi et al. 2016; Orr et al. 2018; Ostriker & Kim 2022). Along with other mechanisms, such as radiation pressure (e.g., Thompson et al. 2005; Veilleux et al. 2005; Murray et al. 2011; Hopkins et al. 2012), cosmic rays (e.g., Samui et al. 2010; Hanasz et al. 2013; Salem & Bryan 2014), and active galactic nuclei (AGNs; e.g., Murray et al. 2005; Faucher-Giguère & Quataert 2012; Harrison et al. 2014; Rupke et al. 2017), stellar feedback rules the baryon cycle in galaxies, and it is essential in galaxy evolution models and simulations based on the Lambda-cold dark matter (Λ-CDM) framework in order to reproduce their observational properties (e.g., Springel 2005; Vogelsberger et al. 2014; Schaye et al. 2015; Pillepich et al. 2018). For instance, feedback from SNe and AGNs is invoked to suppress star-formation efficiency in low- and high-mass galaxies, respectively, lessening the discrepancies between the observed shape of the galaxy luminosity function and the predicted dark matter halo mass function (e.g., Silk & Mamon 2012; Behroozi et al. 2013). This is also needed to explain the co-evolution of central supermassive black holes with their host galaxies (e.g., Tremaine et al. 2002; Kormendy & Ho 2013; King & Pounds 2015), and many fundamental scaling relations, such as the mass-metallicity (e.g., Mannucci et al. 2009; Lilly et al. 2013; Kashino et al. 2016; Lian et al. 2018; Curti et al. 2020) or Tully-Fisher relations (e.g., McGaugh 2012; Somerville & Davé 2015).

Dwarf starburst galaxies (with stellar mass M* < 1010 M⊙; e.g., Sartori et al. 2015; McCormick et al. 2018; Marasco et al. 2023) represent the ideal targets to investigate the impact of stellar feedback on galaxy evolution. In these sources, galactic winds are thought to be driven by the radiation from young stellar populations and SN explosions, and, because of the shallow gravitational potential wells of their hosts, they can be much more effective than in high-mass galaxies in carrying large amounts of metals and dust into the circumgalactic (or even intergalactic) medium (CGM or IGM; e.g., Gnedin & Kravtsov 2010; Booth et al. 2012; Côté et al. 2015; Schaye et al. 2015; Davé et al. 2017; Christensen et al. 2018). Moreover, dwarf low-metallicity galaxies are thought to be analogs of high-z sources (e.g., Patej & Loeb 2015; Izotov et al. 2021; Shivaei et al. 2022), allowing us to provide valuable insights into the processes shaping the evolution of their counterparts in the early Universe. A key parameter for characterizing the power and efficiency of galactic outflows is the ratio between the rate at which the material in the ISM is expelled out of the galaxy (i.e., the mass outflow rate Ṁout) and its SFR, also known as the mass-loading factor (η = Ṁout/SFR).

On the theoretical side, predictions on the outflow efficiency can be obtained through cosmological hydrodynamical simulations. These models are able to simulate a large number of galaxies at different cosmic times, with an aim of reproducing the overall properties of the observed Universe (e.g., Davé et al. 2011; Vogelsberger et al. 2014; Muratov et al. 2015; Nelson et al. 2019). However, they do not have enough resolution to unveil the physical processes of the stellar feedback taking place on the smallest scales, for which zoomed-in simulations and semi-analytical models are needed (e.g., Somerville et al. 2008; Hopkins et al. 2014; Côté et al. 2015; Kim & Ostriker 2018). In addition, chemical evolution models are another useful tool to investigate the need of galactic outflows in shaping the baryon cycle of galaxies (e.g., Côté et al. 2016; Nanni et al. 2020; Galliano et al. 2021). As a matter of fact, all these models typically require large values of the mass-loading factor (η > 1) in order to reproduce the observational properties of low-mass galaxies, although with a large scatter in their predictions. For instance, Nanni et al. (2020) made use of the One-zone Model for the Evolution of GAlaxies (OMEGA; Côté et al. 2017) to model the chemical evolution of local low-metallicity dwarf galaxies from the Dwarf Galaxy Survey (DGS; Madden et al. 2013, 2014), along with high-redshift Lyman-break galaxies (LBGs). They found that galactic outflows are crucial in order to reproduce, for instance, the observed, relatively low content of dust compared to stars in older sources, and they are more efficient than grain destruction by Type II SNe in removing dust from the ISM of both local and high-redshift galaxies. However, the mass-loading factors they provide as input for their models depend on the initial gas mass in the galaxies, and they could span a very broad range of values (i.e., η ∼ 0 − 80) to cover the whole parameter space of their sources. Therefore, observational constraints on this parameter are pivotal for a better description of stellar feedback, as well as for disentangling different mechanisms of gas and dust production and destruction into the ISM of galaxies.

Unsurprisingly, the mass-loading factor is challenging to constrain as it depends on assumptions on the outflow physical size, geometry, and composition (e.g., its temperature, density, or chemistry), and it could thus be subject to many uncertainties (e.g., Veilleux et al. 2005; Maiolino et al. 2012; Chisholm et al. 2017; Fluetsch et al. 2019; Lutz et al. 2020). Furthermore, outflows are composed of multiple gas phases (i.e., hot, warm, and cold) which require different techniques and instruments for an in-depth investigation. Such observations span the whole electromagnetic spectrum, ranging from the rest-frame UV/optical emission for the warm, ionized, and cold atomic and molecular gas (e.g., Contursi et al. 2013; Heckman et al. 2015; González-Alfonso et al. 2017; Fluetsch et al. 2019; Herrera-Camus et al. 2019; Concas et al. 2022), to the X-ray emission for the hot phase (e.g., Heckman et al. 1995; Ott et al. 2005; Tombesi et al. 2015; McQuinn et al. 2018). The expelled material is typically detected as a blueshift in the profile of UV/optical and far-infrared (FIR) absorption lines with respect to the systemic velocity of the galaxy (e.g., Pettini et al. 2002; Erb et al. 2012; Veilleux et al. 2013; Heckman et al. 2015; Falgarone et al. 2017; González-Alfonso et al. 2017; Talia et al. 2017; Riechers et al. 2021; Calabrò et al. 2022), or by searching for a broad emission (that is supposed to trace the outflow) on top of a narrow component (related to the virial motion of stars) in the spectrum of observed emission lines (e.g., Rupke & Veilleux 2013; Arribas et al. 2014; Förster Schreiber et al. 2014; Janssen et al. 2016; Herrera-Camus et al. 2019; Marasco et al. 2023).

In particular, the fine-structure transition of C+ at 158 μm (hereafter, [CII]) has proven to be suitable for characterizing a number of properties of the ISM of both local and high-redshift sources. This represents the brightest emission line in the rest-frame FIR spectra of star-forming galaxies (SFGs), being one of the major coolant of their ISM (e.g., Stacey et al. 1991; Carilli & Walter 2013). The bulk of its emission comes from neutral atomic gas arising in photo-dissociation regions (PDRs) surrounding young stars (Hollenbach & Tielens 1999); however, given its low ionization potential (11.3 eV, compared to the 13.6 eV of neutral hydrogen), it can also be emitted by the partly ionized (e.g., Cormier et al. 2012; Pineda et al. 2014) and molecular medium (e.g., Zanella et al. 2018; Madden et al. 2020). Furthermore, [CII] was recently used to infer the neutral hydrogen (HI) gas mass in galaxies out to z ∼ 6 both with observations and simulations (e.g., Heintz et al. 2021; Vizgan et al. 2022). High-velocity outflows have been detected in the broad wings of the [CII] line profile in individual high-redshift luminous quasars (QSOs; e.g., Maiolino et al. 2012; Cicone et al. 2015) and in normal SFGs at z > 4 (e.g., Ginolfi et al. 2020; Herrera-Camus et al. 2021) thanks to the IRAM Plateau de Bure Interferometer and ALMA observations, respectively. In the local Universe, Herschel data have been exploited to trace atomic (and possibly molecular) outflows in the broad [CII] wings of ultra-luminous infrared galaxies (ULIRGs; e.g., Janssen et al. 2016) as well.

The aim of this work is to further investigate the importance of stellar feedback in the evolution of galaxies by constraining the efficiency of galactic outflows in local dwarf sources. To do that, we made use of archival spectroscopic [CII] observations as collected by Herschel/PACS in a sample of local dwarf galaxies drawn from the DGS. We explored both the individual and average properties of outflows in these sources, trying to characterize their efficiency, origin, and impact on their host galaxies and external environment. Our results will be used as input in state-of-the-art chemical evolution models in order to better understand the processes involved in the cycle of baryons into galaxies at different cosmic times (Nanni et al. in prep.).

The paper is structured as follows. In Sect. 2, we provide a description of the dwarf galaxy sample used in our analysis. The data retrieving and reduction are described in Sect. 3. In Sect. 4, we describe the methods used to identify galactic outflows in individual galaxies and by stacking of their spectra and data cubes. We present our results in Sect. 5, including estimates of the outflow efficiencies and depletion timescales, as well as discussions on their ability to enrich the environment of their hosts, and their powering mechanisms. The summary and conclusions are reported in Sect. 6. Throughout this work, we adopt a Λ−CDM cosmology with H0 = 70 km s−1 Mpc−1, Ωm = 0.3, and ΩΛ = 0.7. We also assume a Chabrier (2003) initial mass function (IMF).

2. Sample description

The DGS1 (Madden et al. 2013, 2014) collected Herschel observations of 48 low-metallicity (7.14 < 12 + log(O/H) < 8.43, ranging from 1/50 to 1/2 Z⊙) local dwarf galaxies, with distances smaller than 200 Mpc and stellar masses in the range of log(M*/M⊙)∼6 − 10. The DGS sample was initially selected from several surveys targeting emission-line and blue compact dwarf galaxies, including the Hamburg/SAO survey and the First and Second Byurakan Surveys (e.g., Markarian & Stepanian 1983; Izotov et al. 1991; Ugryumov et al. 2003), with the aim of maximizing the number of sources with available multi-wavelength ancillary data over a wide metallicity range. The PACS (Poglitsch et al. 2010) and SPIRE (Griffin et al. 2010) instruments on board the Herschel Space Observatory (Pilbratt et al. 2010) provided a full photometric and spectroscopic coverage of the FIR emission, retrieving information on the different phases of the ISM, as well as on the dust properties and star-formation mechanisms in these galaxies (e.g., Rémy-Ruyer et al. 2013; Cormier et al. 2015, 2019).

The sample is divided into 37 compact objects (fitting within the PACS footprint; see Sect. 3) and 11 more extended sources that are also the closest to our galaxy. As the latter were observed only partially with the PACS spectrometer, we decided to exclude them from our analysis, focusing on the compact sample whose galaxies were entirely covered by the PACS pointings. Additionally, two faint sources were dropped from the PACS spectroscopy program because of time constraints (Cormier et al. 2015), resulting in 35 compact galaxies.

2.1. Physical parameters estimation

The stellar masses and SFRs for the DGS galaxies are presented in Madden et al. (2013, 2014). However, such quantities are not available for all the observed sources, and they were retrieved with different methods; for example, SFRs were obtained both from the IR luminosity or (when IR data were not present) from Hα and Hβ lines. In order to have more homogeneously derived physical quantities, we used the latest version of the Code Investigating GALaxy Emission (CIGALE; Burgarella et al. 2005; Noll et al. 2009; Boquien et al. 2019) to recompute the physical parameters of our galaxies through spectral energy distribution (SED) fitting.

We adopted the same photometry as in Burgarella et al. (2020), which includes UV and optical fluxes from the NASA/IPAC Extragalactic Database2 (NED), 2MASS J, H, and K near-IR bands, Spitzer IRAC, IRAS, and WISE fluxes for the mid-IR, as well as Herschel PACS and SPIRE coverage of the FIR regime. CIGALE modules and input parameters are also taken from Burgarella et al. (2020) for local low-metallicity galaxies, with the exception of the following additional quantities that have been fixed in the fit, based on previous works on DGS galaxies. As the gas-phase metallicity (Zgas) in the DGS sample spans more than an order of magnitude, we set it for each source to the closest value from Madden et al. (2013). Based on that, we made multiple runs each time fixing the stellar metallicity (Z) to the available input values lower than Zgas (e.g., Lian et al. 2018; Fraser-McKelvie et al. 2022), finally taking the one providing the best fit to the data. Furthermore, Rémy-Ruyer et al. (2015) adopted semi-empirical models by Galliano et al. (2011) to fit the observed dust SED of DGS galaxies, recovering information on the formation and evolution of dust in these low-metallicity sources. In particular, we took advantage of their predictions on the mass fraction of polycyclic aromatic hydrocarbon (qPAH), the minimum value of the radiation field (Umin), and the power-law slope of the distribution of its intensity per dust mass (α, being dU/dMd ∝ Uα). Constraints on the ionization parameter (U) were provided by Cormier et al. (2019), which made use of the spectral synthesis code Cloudy (Ferland et al. 2017) to model the ISM phases of the DGS sources with the aim of reproducing the corresponding IR luminosities estimated by Rémy-Ruyer et al. (2015) at the same time. For each of these quantities, we took the values closer to the corresponding model grids, and we gave those as input in CIGALE. We added more freedom to each fit by letting these input parameters to vary within their uncertainties, reaching an average reduced χ2 ∼ 1.9. Final modules and input parameters are reported in Table 1.

Table 1.

Parameters used in CIGALE for modeling the SEDs of our galaxies.

We thus obtained, in a consistent way, new estimates of M* for all the galaxies in our sample. Our results are in agreement with previous findings by Burgarella et al. (2020), although systematically lower (up to ∼1 dex in a few cases, as similarly found in Nanni et al. 2020) than original results by Madden et al. (2013). In their work, Madden et al. (2013) computed DGS stellar masses based on Spitzer IRAC 3.6 and 4.5 μm bands, assuming a constant near-IR mass-to-light ratio, without accounting for any dependence on metallicity and age (Eskew et al. 2012; Wen et al. 2013). Here, we made a detailed SED fitting of each galaxy by modeling their emission from UV/optical to FIR wavelengths, individually tuning their gas and dust properties from previous analysis and observations (see Table 1). Clearly, the adopted star-formation history (SFH) and/or IMF could have an impact on the estimated M* (see e.g., discussion in Appendix B.2 of Galliano et al. 2021). Before picking out the delayed one, Burgarella et al. (2020) explored different SFHs in CIGALE to reproduce the SEDs of the DGS galaxies, finding no significant improvement of the fits. Furthermore, recent results by Motiño Flores et al. (2021) for local dwarf galaxies (including a few DGS sources) suggest no evidence of old stellar populations for the majority of their sample, in contrast with the SFHs assumed by Galliano et al. (2021) that are modeled on two (old and young) stellar populations and more in agreement with those adopted in this work (see also Sect. 5.1). Finally, we note that the mass-to-light ratio used by Madden et al. (2013) to compute M* is calibrated on a Salpeter (1955) IMF. Applying a systematic scaling of a factor of ∼0.6 to our stellar masses (to convert from the Chabrier 2003 to the Salpeter 1955 IMF; e.g., Madau & Dickinson 2014; Galliano et al. 2021) would alleviate the tension between our estimates and those by Madden et al. (2013). For all these reasons, we are confident about our new M* results, although further investigation is needed to reduce the difference in the stellar mass computation among various methods.

About SFRs, we decided to compute them from observations. In particular, we adopted the prescription presented by De Looze et al. (2014), which was specifically calibrated on the DGS galaxies (i.e., log(SFR) = ( − 5.73 ± 0.32)+(0.80 ± 0.05)×log(L[CII])) using the observed [CII] luminosity as a tracer of the total SFR (see Sect. 4.1). On average, we found that our new estimates of the SFRs from [CII] (i.e., SFR[CII]) are in agreement with those obtained with CIGALE within the uncertainties. We also note here that SFRs used to calibrate the [CII]-SFR relation by De Looze et al. (2014) are not the same as those estimated by Madden et al. (2013). In particular, De Looze et al. (2014) used the GALEX FUV and MIPS 24 μm fluxes to probe the dust unobscured and obscured star formation, respectively, both available for 32 out of 48 DGS sources.

The final stellar masses and SFRs are reported in Table 2 and shown in Fig. 1 in the SFR-M* diagram (e.g., Noeske et al. 2007; Rodighiero et al. 2011; Speagle et al. 2014). For comparison, we show (as density contours) the sample of ∼15 750 nearby galaxies from Leroy et al. (2019) observed by the Wide-field Infrared Survey Explorer (WISE; Wright et al. 2010) and by the Galaxy Evolution Explorer (GALEX; Martin et al. 2005). Their best fit to the local star-forming main sequence3 and associated 3σ scatter is also reported. Most of our sources lie within and in the upper side of the main sequence, with a few galaxies with larger stellar mass and SFR tending toward the starburst-dominated region.

thumbnail Fig. 1.

SFR-M* diagram for all the sources in our sample (teal circles). Gray contours show the distribution of nearby galaxies from Leroy et al. (2019). Here, contours increase in steps of 20%, with the lowest one including 90% of the local sample. The pink solid line represents the best-fit relation (by Leroy et al. 2019) to local SFGs (selected in the log(M*/M⊙) = 9.5 − 11 range), probing the local star-forming main sequence. We also show the extrapolation of such a relation to the lower stellar mass regime covered by our galaxy sample (pink dotted line). Pink dashed lines are the 3σ scatter associated with the relation. Circles highlighted in white represent galaxies from our sample with individual outflow detections.

Table 2.

Physical properties of our sample of galaxies.

3. Observations and data reduction

We downloaded the fully calibrated science-ready data of the 35 compact objects in our sample from the Herschel Science Archive4. In this study, we focused on [CII] 158 μm emission, which mostly traces the atomic gas in our galaxies and was observed for the full sample.

The field of view (FoV) of the PACS spectrometer is a footprint of 5 × 5, 9.4″-sized spatial pixels (spaxels), for a total coverage of 47″ × 47″. The spectral resolution is 240 km s−1 at 158 μm, which is consistent with the average full width at half maximum (FWHM) of our sample, allowing us to identify possible flux excess at higher velocities (see Sect. 4.1). To obtain the spectra and extract the fluxes needed for our analysis, we used the Herschel Interactive Processing Environment (HIPE; Ott 2010), version 15.0.1, on the re-binned cubes. These are the main science-use cubes produced by the HIPE standard pipelines, with the native footprint of the PACS FoV and an increased spectral resolution as defined by the parameters upsample and oversample. By default, these two quantities are set to four and two, respectively, resulting in a final sampling in the spectral direction of 30 km s−1 at 158 μm (see PACS documentation for more). The re-binned cubes are unique for pointed observations of the most compact objects. For slightly more extended galaxies, mapping observations were made and multiple cubes are created for each source. In those cases, we plotted the different footprints on the corresponding PACS photometry image, taking only the re-binned cube in which the source was located at (or near to) the central spaxel.

We obtained three different spectra from each data cube with the HIPE tool. In particular, we used standard HIPE tasks to extract the spectrum from (i) the central spaxel, (ii) the sum of the 3 × 3 inner spaxels, and (iii) the sum of the full 5 × 5 spaxel coverage. To each spectrum, a point-source correction was applied to take into account the size of the PACS beam (i.e., ∼12″ at 158 μm) and the flux loss between spaxels (due to the fact that the PACS footprint is not regular and the spaxels are not contiguous to each other). By looking at the spatial extension of each source across the PACS footprint and by comparing the three spectra, we took the one with the largest flux and a high signal-to-noise ratio (S/N) in order to include as much information as possible from the line emission. For 6 out of 35 sources, the final spectrum was too noisy to be characterized, thus we excluded such objects from our analysis (see Appendix A). Therefore, the final sample is composed of 29 galaxies whose properties are reported in Tables 2 and 3. We made a first Gaussian fit of the line to obtain an initial estimate of its FWHM and used this value to define the continuum emission as the region from 2 − 5 × FWHM (both redward and blueward of the line peak), so as to avoid the possible wings of the outflow component and the noisy end of the spectrum. To fit the emission profiles, we used SCIPY.OPTIMIZE.CURVE_FIT (Virtanen et al. 2020), providing the expected wavelength of [CII] emission (based on the available spectroscopic redshift of each source), the maximum flux value around that position, and the PACS spectral resolution as initial guesses for the center, peak, and FWHM of the line, respectively. Because the shape of the continuum emission could be rather variable in our spectra, we followed Lebouteiller et al. (2012) and Cormier et al. (2015), and modeled the continuum with a polynomial curve of the order of one or two, or with a third-degree Chebyshev series5 (Rivlin 1974). Then, we simultaneously fit the line and continuum for each source, taking the one providing the minimum reduced χ2, after further checking the goodness of the fit through visual inspection, as the best continuum modeling. Finally, we subtracted the continuum to each spectrum in order to better analyze the line and wing profiles.

Table 3.

Information on [CII] spectra acquisition and Gaussian fit.

4. Analysis and results

We started searching for outflow signatures in the spectra of each individual galaxy by fitting their [CII] emission lines with a single and double Gaussian profile (the latter including a narrow and broad component), and by inspecting the corresponding residuals. In this case, we used the output value of the central wavelength obtained from the fit in the previous section as initial guess for both the Gaussian components, leaving the peak flux as a free parameter. We then adopted the PACS resolution as a guess for the FWHM of the narrow component and twice its value for the broad component. In some cases, the presence of outflowing gas is clearly evidenced by the broad component, which, by matching the high-velocity wings of the spectra, improves the quality of the fit. To quantify such an improvement, we compared the reduced χ2 of the fit with the single ( χ single 2 $ \chi^2_{\rm single} $) and double ( χ double 2 $ \chi^2_{\rm double} $) Gaussian profiles, considering the presence of the possible outflow component only when χ double 2 $ \chi^2_{\rm double} $ <  χ single 2 $ \chi^2_{\rm single} $. As a result, we found that 11 out of 29 galaxies show clear signs of outflowing atomic gas as traced by the [CII] emission, while in the remaining sources the outflow (if present) is too faint to be individually detected (see Sect. 4.2). In the following, we first compute the properties of the 11 sources with outflow evidence, and then we estimate the average outflow features from the entire galaxy sample through line and cube stacking.

4.1. Individual outflow detection

The galaxies with clear outflow detections are characterized by evident wings in the spectra at typical velocities of ±400 km s−1, where the residuals between the single Gaussian model and the line present an excess of emission. In these cases, such residuals are reduced to the noise level by adopting a double Gaussian profile, including a broad component to account for the high-velocity wings in the spectra (see Appendix B).

We retrieved different quantities from the [CII] spectra that we use in the following sections to investigate the strength and efficiency of the outflow in the 11 galaxies described above. First, we computed the FWHM of the narrow and broad components as FWHM= (FWH M obs 2 −FWH M inst 2 ) 1/2 $ FWHM=(FWHM_{\rm obs}^2 - FWHM_{\rm inst}^2)^{1/2} $, where FWHMobs = 2.355σ is the observed width of the line (with σ the standard deviation of the corresponding Gaussian function), and FWHMinst is the PACS instrumental line width (i.e., 240 km s−1 for [CII])6. We found that the broad component has, on average, a FWHM more than two times larger than the narrow component, with means of ∼526 and 213 km s−1, respectively. Then, we obtained the [CII] luminosity of both components by following Solomon et al. (1992):

L [ CII ] = 1.04 × 10 − 3 S [ CII ] Δ v D L ( z [ CII ] ) 2 ν obs [ L ⊙ ] , $$ \begin{aligned} L_{\rm {[CII]}} = 1.04 \times 10^{-3}~S_{\rm [CII]}~\Delta { v}~D_{\rm L}(z_{\rm [CII]})^2~\nu _{\rm obs}~[{L_\odot }], \end{aligned} $$(1)

where S[CII]Δv is the velocity-integrated line flux in units of Jy km s−1, νobs is the observed peak frequency in GHz, and DL is the luminosity distance in Mpc at the redshift derived from the centroid of the single Gaussian fit of the [CII] line (i.e., z[CII]). In particular, we used the [CII] luminosity of the narrow component to estimate the SFR[CII] of each galaxy (see Sect. 2). To obtain the error on L[CII], we perturbed the [CII] integrated flux N = 1000 times within its uncertainty. We then took the 16th and 84th percentiles of the resulting distribution as the error on S[CII]Δv, propagating it to L[CII] based on Eq. (1).

We found that, for three galaxies (i.e., Haro3, Mrk1089, and UM448), a three-Gaussian fit (with two narrow and one broad components) provided better residuals than obtained from the two-Gaussian fit, improving the modeling of their global [CII] profiles. Interestingly, the morphology and kinematics of these sources show evidence for merging activity (e.g., Dopita et al. 2002; Johnson & Conti 2000; Johnson et al. 2004; Cairós et al. 2007; Galametz et al. 2009; James et al. 2013). For instance, James et al. (2013) made use of the Fibre Large Array Multi Element Spectrograph (FLAMES; Pasquini et al. 2002) at the Very Large Telescope (VLT) to detect Hα emission over UM448. They found a complex emission line profile, composed of two narrow components and a third broad component possibly associated with an outflow. Similarly, we modeled the [CII] spectrum of UM448 adding a third narrow Gaussian component to the fit. As the goodness of this fit was better than the double-Gaussian one for all three sources and given the evidence of mergers, thereafter we used the parameters from the three-component modeling for Haro3, Mrk1089, and UM448. A few examples of individual spectral fitting for the galaxies in our sample are shown in Appendix B. All the quantities derived in this section are reported in Table 3.

4.2. Spectral stacking

In order to obtain the average outflow properties of our full galaxy sample and to investigate the possible presence of the outflows in the 18 sources with no individual detection, we performed a stacking of their [CII] spectra. First, we used the computed z[CII] to align each continuum-subtracted spectrum to the [CII] rest-frame frequency. Then, following, for instance, Gallerani et al. (2018) and Ginolfi et al. (2020), we tested the null hypothesis that the [CII] line profiles in our sample can be fully reproduced by a single Gaussian component. To do so, we computed the residuals of each galaxy by subtracting the best-fitting Gaussian function to the corresponding observed flux. We thus combined the obtained residuals with a variance-weighted stacking as

R stack = ∑ i = 1 N R i · w i ∑ i = 1 N w i , $$ \begin{aligned} R_{\mathrm{stack} } = \frac{\sum _{i=1}^{N} R_i \cdot { w}_i}{\sum _{i=1}^{N} { w}_i}, \end{aligned} $$(2)

where Ri represents the residual of the i-th galaxy, N is the number of stacked sources, and w i =1/ σ i 2 $ {\it w}_i=1/\sigma^2_{i} $ is the weighting factor (with σi being the noise associated with each spectrum). To estimate σi, we avoided the velocity range of [−800; +800] km s−1 to exclude contamination from the [CII] emission and the broad wings.

The resulting stacked residuals are shown in Fig. 2, where a clear excess of emission is evidenced by the two peaks at velocities of ±400 km s−1, reaching a significance of ∼3σ. This proves that an additional component is needed in order to reproduce the observed [CII] fluxes. Indeed, if our spectra were fully characterized by a single Gaussian function, the residuals in Fig. 2 should be consistent with the noise over the full spectral range (see left panel of Fig. B.1). Two weaker negative peaks are also visible at velocities of ±200 km s−1. As also discussed by Ginolfi et al. (2020), these represent another signature of the poor single Gaussian fits to the [CII] line profiles of our galaxies, which tend to underestimate the flux at low velocities in order to attribute some flux at the high-velocity wings (see, e.g., middle and right panels in Fig. B.1).

thumbnail Fig. 2.

Variance-weighted stacked residuals obtained after subtracting the best-fit single component Gaussian function to each [CII] spectrum. Red bins represent the residuals within ±800 km s−1, whereas the blue bins mark the spectral region used for estimating the noise. The dotted horizontal line sets the zero level, while the shaded area represents the noise at ±1σ. An ∼3σ excess is visible at velocities ±400 km s−1, suggesting that a further Gaussian component is needed to model the [CII] emission in our galaxies.

At this point, we proceeded with a stacking of the [CII] spectra of all the galaxies in our sample. Similarly to what was done for the residuals, we defined the stacked spectrum as

S stack = ∑ i = 1 N S i · w i ∑ i = 1 N w i , $$ \begin{aligned} S_{\mathrm{stack} } = \frac{\sum _{i=1}^{N} S_i \cdot { w}_i}{\sum _{i=1}^{N} { w}_i}, \end{aligned} $$(3)

where Si is the flux of the i-th galaxy, and all the other parameters are the same as for Eq. (2). Figure 3 (left panel) shows the result of this procedure. As done for the individual outflow detections, we fitted the stacked spectrum with both a single and double Gaussian profile, comparing the corresponding reduced χ2 and residuals. The spectrum shows clear signs of broad wings at velocities of ± ∼ 400 km s−1, as evidenced by the corresponding large residuals obtained by using a single Gaussian function to fit the line profile. The two-component model clearly improves the fit, resulting in a better reduced χ2 and a residual flux consistent with the noise over the entire velocity range.

thumbnail Fig. 3.

Average [CII] line profiles. Left: Stacked, variance-weighted [CII] spectrum (black histogram) of the whole sample as a function of velocity. Both the fit with a single Gaussian function (in blue) and that with a double Gaussian profile (in pink) are reported. The latter is the sum of a narrow (green line) and broad (orange line and shaded area) component. The FWHM of both components and the corresponding reduced χ2 are also shown in the figure. A zoomed-in view of the spectral region dominated by outflows is shown as an inset plot on the right. The bottom panel reports the residuals from the single (blue) and double (pink) Gaussian functions. The dotted horizontal line marks the zero level, while the shaded area represents the noise of each spectrum at ±1σ, computed as described in the text. Right: Same as left panel, but for the stacking of only the sources with non-detected outflows.

To ensure that the stacking result was not biased by the presence of a few sources with stronger evidence of outflows, we performed a delete-d jackknife resampling (Shao & Wu 1989). We recomputed the stacked spectrum 500 times by excluding ∼10% of the sample (i.e., 3 galaxies) each time, in order to obtain an estimate of the wing variation while still preserving a large enough sample to stack. The resulting FWHM distributions of both Gaussian components are in agreement with what we obtained by stacking the whole sample, implying that our results are not affected by outliers. We repeated the stacking with only the 18 sources with no individual outflow detection to investigate the presence of broad wings in this subsample. This is shown in Fig. 3 (right panel), where the high-velocity tails are still visible in the spectrum and recovered with a broad component, although they are weaker than those found in the stack of the whole sample. Again, the jackknife statistics did not find any track of outliers, as expected given that none of the galaxies in this subsample show significant evidence of outflowing gas.

It is interesting to note that most of the galaxies with individual outflow detections lie in the top right corner of the main-sequence diagram with the largest stellar masses and SFRs (see Fig. 1). This suggests that the stronger broad component in the stacked spectrum of the whole sample could be driven by sources with the largest star-formation activity, as also found at high redshift (Ginolfi et al. 2020) and as expected by the well-known [CII]-SFR relation (e.g., De Looze et al. 2014; Schaerer et al. 2020; Romano et al. 2022).

As done for the individual sources showing broad wings, we estimated the [CII] luminosity of the broad component of both the stacked spectra through Eq. (1), as well as their FWHM. These values are listed in Table 3 and they will be used later to constrain the outflow efficiency of the average population of dwarf galaxies.

4.3. Spatial stacking

To characterize the average spatial extent of the atomic outflows in our galaxies, we produced a stacked [CII] cube. As done for the spectra in Sect. 4.2, we first aligned the spectral axes of each continuum-subtracted cube to the [CII] rest-frame emission. Then, we spatially aligned the cubes by centering them on the peak of the corresponding [CII] intensity map produced by summing the fluxes from the spectral channels including the emission line. We used a variance-weighted stacking as in Eq. (3), where the σ in the weighting factor now represents the spatial rms estimated in each channel of the cube in regions free of emission.

In Fig. 4 (top panel), we show the channel maps of the [CII] emission of the stacked cube from the central 80″ × 80″ region and within ∼2000 km s−1 of the spectral line. The [CII] emission is clearly detected at high velocities (i.e., where the broad wings in the [CII] stacked spectrum arise), with a bulk in the core of the line at v ∼ [ − 250; 250] km s−1. As our aim is to obtain the average size of the outflow, we produced velocity-integrated [CII] maps of the wings in the low- and high-velocity tails at [−500, −250] and [250; 500] km s−1, respectively (Fig. 4, bottom panels), which resulted in high-significance detections of ≳20σ. We then summed the two maps together to obtain the total outflow emission (detected at ≳30σ), used to obtain the average outflow radius. In particular, we fitted a 2D Gaussian function to the total intensity map of the wings obtaining the outflow circularized effective radius defined as R out = ab $ R_{\mathrm{out}} = \sqrt{ab} $, where a and b are the best-fit beam-deconvolved semi-major and semi-minor axes of the Gaussian, respectively. We found Rout = 0.99 ± 0.18 kpc, where the uncertainty was computed through the errors of a and b from the fit. Our result is in good agreement with previous assumptions and estimations from the literature in local galaxies (e.g., Arribas et al. 2014; Fluetsch et al. 2019; Marasco et al. 2023).

thumbnail Fig. 4.

Spatial extent of the average [CII] emission. Top: Channel maps of the stacked cube covering ∼2000 km s−1 around the peak of the emission line. Velocity bins are in steps of ∼106 km s−1 for a better representation. Each spectral channel shows the [CII] emission from a 80″ × 80″ region. Contour levels are shown in white at 3, 5, and 7σ, where σ is the rms computed in each channel. Bottom: [CII] integrated intensity maps of the outflow and core emission. Left and right panels are obtained by summing the emission of the broad wings in the velocity ranges [−500, −250] and [250; 500] km s−1, respectively, while the central panel represents the core emission at [−250; 250] km s−1. The bottom panel is the sum of the two velocity-integrated maps of the broad wings (as pointed out by the arrows) representing the whole outflow emission. Contour levels are shown in white at 3, 5, and 7 σ, where σ is the rms of the integrated intensity map. Both figures report the PACS beam (as shown in the lower-left corner of the first panel) and a reference scale of 5 kpc.

The core of the stacked [CII] line emission results to be quite extended. By fitting the corresponding intensity map with the same method adopted for the estimation of the outflow radius, we obtained a deconvolved size of R[CII] = 1.49 ± 0.05 kpc, with some residuals surrounding the edge of the core suggesting the presence of a more extended emission. We thus compared the average [CII] size of our galaxies with the stellar distribution as traced by their rest-frame UV emission. To measure the individual UV sizes of our sources, we used the NUV band (λmean ∼ 2345 Å) photometry from GALEX, obtaining an average of RUV = 0.67 ± 0.03 kpc. Overall, we found that the [CII] emission in our dwarf galaxies is ∼2 times more extended than the UV. Interestingly, these results are in good agreement with those found for SFGs at z ≳ 4 (e.g., Fujimoto et al. 2020; Herrera-Camus et al. 2020; Lambert et al. 2023), which suggests the presence of circumgalactic [CII] halos likely produced by galactic outflows or past merging activity (e.g., Fujimoto et al. 2019, 2020; Ginolfi et al. 2020). We will further explore these results in a future work (Romano et al. in prep.).

5. Discussion

5.1. Outflow efficiency

To fully characterize the outflows and their impact on the evolution of dwarf galaxies, a key parameter is the so-called mass-loading factor, that is, the ratio between the rate of gas mass expelled out of the galaxy and the rate of star formation (η = Ṁout/SFR). This quantity is an estimate of the outflow efficiency and it represents a fundamental ingredient for simulations trying to explain the baryon cycle in galaxies.

We used the [CII] luminosity of the broad component (both for individual outflow detections and stacked spectra) to estimate the mass of the outflowing atomic gas (e.g., Maiolino et al. 2012; Bischetti et al. 2019; Ginolfi et al. 2020). In particular, we considered the following relation by Hailey-Dunsheath et al. (2010):

M out / M ⊙ = 0.77 ( 0.7 L [ CII ] , broad L ⊙ ) ( 1.4 × 10 − 4 X C + ) × 1 + 2 e − 91 K / T + n crit / n 2 e − 91 K / T , , $$ \begin{aligned} \begin{aligned} M_{\mathrm{out} }/M_{\odot } =&0.77 \left(\frac{0.7 L_{\mathrm{[CII],broad} }}{L_{\odot }} \right) \left(\frac{1.4\times 10^{-4}}{X_{\rm C^{+} }} \right)\\&\times \frac{1+2e^{-91K/T}+n_{\mathrm{crit} }/n}{2e^{-91K/T}}, \end{aligned} ,\end{aligned} $$(4)

where XC+ is the C+ abundance per hydrogen atom, ncrit ∼ 3 × 103 cm−3 is the critical density of the [CII] transition (e.g., Carilli & Walter 2013), and T and n are the gas temperature and density, respectively. Equation (4) was derived under the assumption of an optically thin [CII] emission (e.g., Hailey-Dunsheath et al. 2010; Cicone et al. 2015; Ginolfi et al. 2020), and assuming XC+ = 1.4 × 10−4 (Savage & Sembach 1996), T in the range of 60–200 K (see Ginolfi et al. 2020 and references therein), and n ≫ ncrit, all typical of PDRs. In addition, the factor 0.7 in the parentheses of Eq. (4) represents the fraction of [CII] emission arising from PDRs, while the remaining 30% is supposed to come from the other phases of the ISM (e.g., Stacey et al. 1991, 2010; Díaz-Santos et al. 2017; Cormier et al. 2019).

It is worth noting that the assumptions on the physical properties of the outflowing gas (i.e., the optically thin emission, the large number density) are conservative (as discussed in Maiolino et al. 2012), providing us lower limits on Mout. Furthermore, in this work we are only accounting for the atomic gas as traced by the [CII] emission, not considering that part of the outflow could be composed by the other ISM phases (i.e., molecular and ionized gas) that may also contribute to the evolution of the host galaxy (e.g., Veilleux et al. 2005; Maiolino et al. 2012; Muratov et al. 2015; Fluetsch et al. 2019).

We thus computed the atomic mass outflow rate within the time-averaged expelled shells or clumps scenario (Rupke et al. 2005a):

M ˙ out = v out × M out R out , $$ \begin{aligned} \dot{M}_{\mathrm{out} } = \frac{{ v}_{\mathrm{out} }\times M_{\mathrm{out} }}{R_{\mathrm{out} }}, \end{aligned} $$(5)

where vout = FWHMbroad/2 + |vbroad − vnarrow| is the outflow velocity (with FWHMbroad the full width at half maximum of the broad component, while vbroad and vnarrow are the velocity peaks of the broad and narrow components, respectively; Rupke et al. 2005b) and Rout is the outflow radius as obtained in Sect. 4.3. This model is consistent with a constant outflow rate over time. However, different outflow histories and geometries could also be adopted, leading to different results. For instance, a spherical or multi-conical geometry (i.e., a decaying outflow history) can provide outflow rates up to three times larger than those found with Eq. (5) (e.g., Maiolino et al. 2012; Cicone et al. 2014), although this seems to be disfavored by many observations of local galaxies (see Lutz et al. 2020 and references therein). With this caveat in mind, we obtained the outflow properties reported in Table 4, along with their corresponding mass-loading factors.

Table 4.

Outflow properties.

It is worth noting that the outflow velocities of the cold gas found in our work are comparable with those obtained from [CII]-based studies in normal SFGs (e.g., Gallerani et al. 2018; Ginolfi et al. 2020; Herrera-Camus et al. 2021). Such velocities could be slightly larger than what was found through measurements of absorption lines (e.g., NaDλλ 5890, 5896 Å, OH) tracing the cold gas (e.g., Cazzoli et al. 2016; Janssen et al. 2016; Roberts-Borsani & Saintonge 2019; see also Veilleux et al. 2005 and Heckman et al. 2017), whose absorption line studies revealed the presence of fast (≳500 km s−1) cool outflowing gas in different systems), and sometimes (i.e., for vout ≳ 250 km s−1) not predicted by numerical or hydrodynamic simulations (e.g., Kim et al. 2020; Andersson et al. 2023). On the other hand, Scannapieco (2017) used a suite of three-dimensional simulations to reproduce the evolution of initially hot material (typically quite fast and highly ionized) ejected by starburst-driven galactic outflows, suggesting that an explanation for the different velocity range of cold outflowing gas found in observations could be that absorption lines probe the cold gas at the smallest radii of a galaxy, while emission lines trace cold material condensed from an initial hot medium at larger distances7. Schneider et al. (2018) made use of a suite of high-resolution isolated galaxy models to investigate the origin of fast-moving cool gas in outflows. They found that such gas can originate from a rapid cooling of the hot gas phase, which can generate cool gas outflows at velocities up to ∼1000 km s−1. Interestingly, Pizzati et al. (2020) used semi-analytical models to simulate [CII] emission from supernova-driven cooling outflows. Similarly to Scannapieco (2017), they predicted that gas can cool very rapidly within the central kiloparsec of the galaxies, so as to guarantee the formation and survival of [CII] ions in the outflows. Particularly, they found that [CII] can be transported by the neutral outflows at velocities of 300 − 500 km s−1 (as found in this work and previous observations, e.g., Ginolfi et al. 2020), likely producing the extended [CII] halos observed around high-z (and possibly local; see Sect. 4.3 and Fig. 4) galaxies (e.g., Fujimoto et al. 2020). Future comparisons between observations and tailored simulations will hopefully allow us to fully characterize the multi-phase nature of galactic outflows.

In Fig. 5, we show the atomic outflow rate as a function of the SFR as obtained from the spectral stacking of our galaxies and from individual detections of the broad component, and color-coded by their mass-loading factors. We also report the best-fit relations between molecular outflow rate and SFR for both local AGNs and starburst/SFGs as found by Fluetsch et al. (2019)8. AGN hosts are characterized by η ≫ 1 in the range of SFR spanned by our sample, while SFGs have typically lower outflow efficiencies. Most of our galaxies lie along the 1:1 relation (i.e., η = 1) as also found in previous observations of local SFGs (e.g., Cicone et al. 2014; Fluetsch et al. 2019), with an average mass-loading factor of η ∼ 1.3. We note that if we assume that all the phases of the ISM contribute equally to the outflow rate (e.g., Fluetsch et al. 2019), we could obtain an average outflow efficiency three times larger than estimated (i.e., η ≳ 3). From the stacking, we found similar results, that is η = 0.97 for the whole sample and η = 1.76 for the non-detected outflows only, as obtained by assuming the corresponding median SFRs of the two subsamples, that is, 0.22 and 0.06 M⊙ yr−1, respectively. The best fit to the individual outflow detections provided log(Ṁout) = 1.13 log(SFR[CII]) + 0.07, with the slope in agreement with that found by Fluetsch et al. (2019) for local SFGs, but closer to the 1:1 relation.

thumbnail Fig. 5.

Atomic outflow rate as a function of the SFR, for both individual detections of broad wings (circles) and from line stacking of the whole sample and of the sources with non-detected outflow (big and small squares, respectively). The pink and violet lines are the best-fit relations between molecular outflow rate and SFR for local AGN hosts and star-forming/starburst galaxies by Fluetsch et al. (2019), respectively, while the shaded regions are the corresponding uncertainties. The solid gray line with the shaded area represents a linear fit to the DGS galaxies with individual outflow detections and its uncertainty, respectively. The dashed line reports the 1:1 relation. We also show the results from [CII] stacking of z ≳ 5 SFGs by Gallerani et al. (2018; hexagon) and Ginolfi et al. (2020; diamond). All markers are color-coded for their mass-loading factors.

Furthermore, we compare our results to those found at high redshift by Gallerani et al. (2018) and Ginolfi et al. (2020), which took advantage of [CII] emission detected in a sample of nine SFGs at z ∼ 5.5 (Capak et al. 2015), and in the sample of normal SFGs at 4 < z < 6 as part of the ALMA Large Program to INvestigate [CII] at Early times (ALPINE; Béthermin et al. 2020; Faisst et al. 2020; Le Fèvre et al. 2020), respectively. Both results are in agreement with our low-redshift dwarf galaxies, suggesting that similar feedback mechanisms can be in place in this kind of sources. The interpretation of this is not straightforward, being the environment and physical processes ruling the formation and evolution of high-z galaxies quite different from those occurring in the local Universe. Cosmological simulations predict a roughly constant mass-loading factor at different redshifts for galaxies with log(M*/M⊙) < 10, along with an increase with lower stellar masses (e.g., Nelson et al. 2019). However, many observations (including this work) find no significant differences in the efficiency of outflows in primordial main-sequence galaxies and local less massive sources (e.g., Gallerani et al. 2018; Ginolfi et al. 2020; Calabrò et al. 2022). An explanation of this can reside in the fact that local low-metallicity dwarf galaxies could be considered as analogs of high-z sources, as they can share similar properties in terms of morphology, size, metal content, or specific SFR (e.g., Patej & Loeb 2015; Izotov et al. 2021; Motiño Flores et al. 2021; Henkel et al. 2022; Shivaei et al. 2022). For instance, Motiño Flores et al. (2021) studied the properties of a sample of 11 potential local analogs to high-z galaxies, selected to have similar SEDs to those of z ≳ 2 objects. They computed the SFHs of their sources, finding that half of the candidates (with 3 of them also included in our sample) are characterized by a lack of star-formation activity at look-back times ≳1 Gyr (i.e., they have no old stellar populations), and thus they resemble early objects. This is further supported by the recent results from Shivaei et al. (2022), who constrained the infrared SEDs of z ∼ 2.3 subsolar-metallicity galaxies and compared them with those of local dwarfs (including DGS sources) and (U)LIRGs. They found that infrared SEDs of sources in their sample have properties much more similar to those of local dwarf galaxies than to the SEDs of nearby (U)LIRGs, suggesting that local dwarfs and high-z galaxies could share analogous ISM ionization properties and dust populations. In addition, their galaxies present rather high specific SFRs relative to the z ∼ 2 main sequence, as also found for some sources in our DGS sample (see Fig. 1). Following this, local dwarfs and high-z galaxies could also share comparable outflow efficiencies. On the other hand, the external environment may also have an impact on η. Calabrò et al. (2022) characterized galactic outflows by analyzing ISM absorption lines in the spectra of 330 galaxies from the VANDELS survey (Pentericci et al. 2018; McLure et al. 2018; Garilli et al. 2021) distributed over a wide redshift range, that is, 2 < z < 5. Again, they obtained an average mass-loading factor on the order of unity, with no redshift evolution. Interestingly, they found evidence of a larger contribution of inflows at earlier cosmic times that, combined with the more turbulent ISM and higher merging activity (e.g., De Breuck et al. 2014; Jones et al. 2021; Romano et al. 2021), could level out the outflow efficiency in these galaxies.

5.2. Are outflows able to escape dark matter halos?

Theoretical models predict that, because of their small potential wells, outflows could quite easily bring gas outside of low-mass galaxies, clearing these sources of their metal and dust content and enriching the IGM (e.g., Dekel & Silk 1986; Springel & Hernquist 2003). In order to test such predictions, we computed the escape velocities of our dwarf galaxies (vesc), which are needed by outflows to escape their gravitational potential.

Following Fluetsch et al. (2019), we assumed a Navarro-Frenk-White (NWF) dark matter density profile (Navarro et al. 1996) resulting in

v esc ( r ) = 2 | Φ ( r ) | = 2 M halo G r ( ln ( 1 + c ) − c / ( 1 + c ) ) ln ( 1 + r / r s ) , $$ \begin{aligned} { v}_{\rm esc}(r)=\sqrt{2 |\Phi (r)|} = \sqrt{\frac{2 M_{\rm halo} G}{r(\mathrm{ln} (1+c) - c/(1+c))} \mathrm{ln} (1+r/r_s)}, \end{aligned} $$(6)

where G is the gravitational constant, c is the concentration parameter9, Mhalo is the mass of the halo, and rs = rhalo/c is the characteristic radius, with rhalo being the virial radius. The halo mass was obtained from the stellar mass of the corresponding galaxy through abundance-matching techniques (Behroozi et al. 2010), while the virial radius is defined as (e.g., Łokas & Mamon 2001; Huang et al. 2017)

r halo = [ 3 M halo 4 π 200 ρ crit , 0 ] 1 / 3 , $$ \begin{aligned} r_{\rm halo} = \left[ \frac{3 M_{\rm halo}}{4 \pi ~200~\rho _{\mathrm{crit},0}} \right]^{1/3}, \end{aligned} $$(7)

with ρcrit, 0 being the present critical density. All the above-mentioned parameters are listed in Table 4.

Figure 6 shows the velocity of the outflow as a function of the escape velocity for each galaxy with individual outflow detection. As a comparison, we display the results for ionized gas outflows by Heckman et al. (2015) in a sample of ∼40 local starbursts10, and by Manzano-King et al. (2019) from Keck spectroscopy of local dwarf galaxies (including AGNs and SFGs) drawn from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) catalog by Oh et al. (2011). The most massive galaxies (i.e., log(M*/M⊙)≳10) lie below the 1:1 relation at large escape velocities, implying that outflows in these sources (at least from the ionized phase) are not able to expel material outside of their dark matter halos. Conversely, all of our sources are close to or above the relation, with outflow velocities higher than (or comparable to) the escape ones, in agreement with the results for ionized outflows in local dwarf galaxies by Manzano-King et al. (2019). This suggests that galactic winds in these objects are able to bring material at least in their CGM, having a large impact on their baryon cycle.

thumbnail Fig. 6.

Relation between outflow velocity and escape velocity. Galaxies of our sample with individual outflow detections are shown as circles with their size increasing with larger escape fractions. Local starbursts are represented as hexagons (Heckman et al. 2015). Nearby dwarf galaxies, including AGNs and star forming and composite galaxies (based on their optical classification), are shown as squares, stars, and pentagons, respectively (Manzano-King et al. 2019). The dashed line reports the 1:1 relation. All data are color-coded for their stellar mass.

To understand how much gas can be expelled out of our galaxies, we estimated their escape fractions (fesc), defined as the fraction of the outflowing gas with velocity higher than the escape velocity. In particular, we integrated the [CII] emission of the broad component at velocities larger than vesc, and divided by the total amount of gas carried by the outflow. We found values ranging from ∼20 to 90% depending on the outflow velocity and potential well of the galaxy, with an average escape fraction of 40%. This is more than a factor four larger than what was found by Fluetsch et al. (2019) in local SFGs and AGNs. However, as those authors pointed out, their sample does not include low-mass galaxies, for which a significant fraction of gas is expected to leave the galaxy and its halo enriching the IGM. Our results are instead consistent with nearby ULIRGs, as found through molecular OH-based (∼25%; González-Alfonso et al. 2017) or CO-based (15–40%; Pereira-Santaella et al. 2018; Herrera-Camus et al. 2020) analyses. In general, except for a few galaxies in our sample that are able to expel a large fraction of material directly into the IGM, the majority of the atomic gas in the outflow will remain bound to the gravitational potential of the galaxy (i.e., it will stay in the CGM), and it could later be re-accreted and used for future star formation, still contributing to the baryon cycle of its host. Interestingly, the galaxies with the larger escape fractions are also those with the lowest metallicities, suggesting that a significant fraction of metals in these sources is likely residing inside (or outside) their halos, as also predicted by theoretical models (e.g., Recchi & Hensler 2013).

We note here that our estimates on the escape velocity could be affected by the method used to compute the halo mass of the galaxies. For instance, Östlin et al. (2015) made use of velocity dispersion obtained from ionized emission lines to estimate the dynamical mass of Haro11, that is, ∼1011 M⊙. Their result is ∼0.2 dex lower than what we found from abundance matching (thus causing a lower escape velocity and allowing outflowing gas to escape more easily from the galaxy), but it relies on the assumption that the observed line widths are mainly due to virial motions. However, turbulence produced by feedback driven by star formation could also have a large impact on the broadening of emission lines, significantly affecting the resulting estimates (e.g., Green et al. 2010; Moiseev & Lozinskaya 2012). As the galaxies in our sample are hosting outflows, we decided to compute our halo masses based on abundance-matching methods.

Finally, we want to highlight that the total fraction of gas (atomic, molecular, and ionized) entrained outside of the galaxy by outflows could be larger than what was estimated here based on [CII] emission. For instance, the warm/hot ionized outflowing gas is found to reach typically higher velocities than the cool molecular and atomic phases (e.g., Rupke et al. 2005a; Veilleux et al. 2005; Heckman et al. 2017), likely producing larger escape fractions. However, different works suggest that the ionized phase contributes only minimally to the total outflow mass as compared to the other ISM phases (e.g., Rupke & Veilleux 2013; Carniani et al. 2015; Fluetsch et al. 2019; Ramos Almeida et al. 2019), lowering its significance with respect to the cool gas traced in this work. Molecular gas is instead a fundamental component of the mass and energy budget of the outflow, as it could contribute up to 50% to the total mass outflow rate (e.g., Fluetsch et al. 2019). Therefore, multi-phase studies of the outflowing gas in these galaxies are needed to carefully describe the relative contribution of each outflow phase to the CGM enrichment and baryon cycle.

5.3. Depletion timescales

In this section, we compare the depletion timescale due to outflows with that due to gas consumption by star formation. We define these timescales as the time needed for the molecular gas inside the galaxy to be swept out by the outflow or consumed by star formation, respectively, providing that both the outflow rate and SFR are constant over time and that no supply of fresh gas is in place, for instance, via merging or cold accretion. Under these assumptions, τdep,out = MH2,TOT/Ṁout and τdep, SF = MH2, TOT/SFR. Here, MH2, TOT is the total mass of molecular gas derived from the luminosity of the narrow component of the [CII] line (see Table 3) by following Madden et al. (2020), that is, MH2,TOT = 102.12 × (L[CII],narrow)0.97. In particular, this relation derives from the application of the spectral synthesis code Cloudy (Ferland et al. 2017) to the DGS sample, and from the finding that a large fraction (70 to 100%) of the H2 mass is not traced by the CO(1–0) transition (usually considered to deduce the total molecular hydrogen) in dwarf galaxies (i.e., CO-dark gas mass), but it is well traced by [CII].

Figure 7 shows the relation between the two depletion timescales for our dwarf galaxies with detected outflow. Their typical error bar is displayed on the top right corner of the figure. This was computed by propagating the errors of MH2, TOT and Ṁout (SFR) on τdep, out (τdep, SF) and by considering that the quantities involved in the computation of both timescales are correlated to each other. The uncertainty on the molecular gas mass was instead estimated with the error propagation on the equation by Madden et al. (2020) and by assuming a standard deviation of 0.14 dex on that relation, as reported in their work. In the same figure, we also compare our results with a compilation of local sources including AGNs, LINERs, and starburst galaxies analyzed by Cicone et al. (2014). They found molecular outflow depletion timescales ranging from a few up to a few hundred million years for AGN-host and starburst galaxies11, respectively, with the former populating the area with depletion timescales due to outflows much shorter than those due to star formation. In our sample, we find that the two timescales are similar, in agreement with the starburst-dominated galaxies by Cicone et al. (2014). In particular, the outflow depletion timescales of our dwarf sources range from one hundred million years up to a few billion years, with ∼60 − 90% of our sample characterized by τdep, out ≲ τdep, SF, as a consequence of the mass-loading factors larger than (or consistent with) unity. This could imply a fundamental role of galactic outflows in regulating star formation in dwarf galaxies. It is also worth noting that, in our computation of the outflow depletion timescale, the outflow rate is only due to the atomic gas and it could be larger when accounting for the ionized and molecular ISM phases (e.g., Fluetsch et al. 2019). For this reason, our values must be considered as upper limits, moving to lower τdep, out in case of higher η and strengthening the importance of feedback in such sources.

thumbnail Fig. 7.

Comparison between depletion timescale due to outflows and gas consumption due to star formation. DGS galaxies from this work are shown as circles. The typical uncertainty on both timescales is shown in the top right corner. Squares, stars, and pentagons are the results from local AGNs, starburst galaxies, and LINERs, respectively (Cicone et al. 2014). The dashed line reports the 1:1 relation. The area below this line is populated by galaxies whose outflows are more efficient than star formation in consuming gas (i.e., τdep, out < τdep, SF). All data are color-coded for their mass-loading factors.

5.4. Outflow energetics

Stellar winds can inject a significant amount of mechanical energy and momentum in the ISM of starburst galaxies, producing shocks that propagate outwards sweeping away the gas. Depending on the efficiency of radiative losses during this process, we can distinguish between “energy-driven” and “momentum-driven” outflows. The former are associated with adiabatic expansion of the gas powered by SN explosions, with shocks preserving their mechanical luminosity. On the other hand, radiative cooling is significant in momentum-driven outflows, which are typically induced by the radiation pressure on dust grains produced by young stellar populations (e.g., Murray et al. 2005; Faucher-Giguère & Quataert 2012; Hopkins et al. 2012; Côté et al. 2015; Thompson et al. 2015).

To investigate the driving mechanisms of the outflows in our galaxies, we computed their kinetic power (Ėout) and momentum rate (Ṗout) as follows:

E ˙ out = 1 2 M ˙ out v 2 out , $$ \begin{aligned} \dot{E}_\mathrm{out} = \frac{1}{2} \dot{M}_{\mathrm{out} } {{ v}^2}_{\mathrm{out} }, \end{aligned} $$(8)

P ˙ out = M ˙ out v out . $$ \begin{aligned} \dot{P}_{\mathrm{out} } = \dot{M}_{\mathrm{out} } {{ v}}_{\mathrm{out} }. \end{aligned} $$(9)

We compared these quantities with the momentum and kinetic energy supplied by starburst-driven winds, that is, (ṖSB) and (ĖSB), respectively. In particular, Veilleux et al. (2005) used evolutionary models of the populations of massive stars (Starburst99; Leitherer et al. 1999) to calculate the power injected by SNe into the ISM of starburst galaxies, finding ĖSB(erg s−1) = 7 × 1041 SFR(M⊙ yr−1). Similarly, the total momentum supplied from starbursts (with the wind driven by a combination of massive star ejecta and radiation pressure) can be obtained as ṖSB(g cm s−2) = 4.6 × 1033 SFR(M⊙ yr−1), following, for instance, Heckman et al. (2015) and Xu et al. (2022). As a check, we computed the total radiative momentum for our galaxies as Lbol/c, where Lbol is the bolometric luminosity given by the sum of the stellar and dust luminosities from CIGALE, finding a good agreement with ṖSB. The outflow kinetic power and momentum rate are reported in Table 4.

In Fig. 8, we show the relation between the kinetic energy (left panel) and momentum (right panel) carried by outflows and the corresponding quantities provided by starbursts. Points are color-coded by the “momentum boost” of each source, defined as the ratio between the outflow momentum and the radiative momentum of the galaxy (i.e., Ṗout/ṖSB). Most of our galaxies are characterized by kinetic powers of the outflows between 1% and 20% of the kinetic power produced by SNe and momentum rates comparable with (or lower than) those supplied by starbursts.

thumbnail Fig. 8.

Outflow energetics. Left: Kinetic power of outflow as a function of kinetic power generated by SN-driven winds. The solid lines report the relations Ėout = 0.01,0.1,1 ĖSB, as indicated in the figure. Right: Outflow momentum rate as a function of momentum supplied by starburst galaxies. The solid lines refer to Ṗout= 0.1,1,10 ṖSB, as reported in the figure. Both panels also show the results by Cicone et al. (2014), Heckman et al. (2015), and Chisholm et al. (2017) for local starburst (stars, hexagons, and crosses) and AGN-dominated (squares and pentagons) sources. Big circles display the results from this work and are color-coded according to the momentum boost, as described in the text.

Our findings are in good agreement with previous results from the literature for ionized and molecular outflows in local galaxies. For instance, Heckman et al. (2015) analyzed the properties of ionized outflows in a sample of ∼40 low-z starburst galaxies through UV absorption lines. We show their results in the right panel of Fig. 8 for the momentum rate, and we derived our own values of the kinetic power based on their estimates of SFR, vout, and Ṁout, as done for our sources. In their work, they found a net distinction between stronger (Ṗout ≳ 1034 g cm s−2) and weaker outflows, with the former usually carrying a larger fraction of the starburst momentum (mostly lying along the 1:1 relation) and ultimately suggesting a momentum-driven outflow scenario. Similarly, Cicone et al. (2014) studied the properties of molecular outflows in a sample of ∼20 local starburst and AGN host galaxies. We report their results in Fig. 8. They found large momentum boosts (≳10) and kinetic powers for AGN-dominated sources, requiring energy-conserving mechanisms. On the other hand, starbursts are characterized by outflow kinetic power corresponding to only a few percent of that produced by SNe, and momentum rates comparable to Lbol/c, from which they conclude that molecular outflows in these sources are mostly momentum-driven. Finally, we also show the results by Chisholm et al. (2017) who constrained the energetic of ionized outflows in a sample of eight local SFGs. They found that up to 20 per cent of the energy released by SNe is converted into kinetic energy of the outflow and that outflows are more efficient in galaxies with lower stellar mass, for which additional sources of momentum apart from SN momentum are needed.

Our galaxies populate the parameter space covered by these previous works, although with some scatter. The computed kinetic powers show that only a few galaxies would require large coupling efficiencies, on the order of 20%, in order for their outflows to be driven by SNe, while the objects with the lowest momentum boost have outflow kinetic power in agreement with a SN-driven wind with coupling efficiencies below 10%, as predicted by models (e.g., Efstathiou 2000; Veilleux et al. 2005; Harrison et al. 2014; Hu 2019). At the same time, the momentum budget shows that most of our galaxies are comparable to ṖSB, suggesting that radiation pressure on dusty clouds can contribute significantly to (or even dominate) the outflow powering mechanism, supporting the momentum-driven scenario (e.g., Cicone et al. 2014; Costa et al. 2018).

Finally, we note that other feedback mechanisms can be invoked in order to explain the outflow energetics. For instance, stellar activity can produce cavities of hot gas in the ISM of galaxies. SNe can inject energy into these cavities, producing bubble-like structures that can expand outwards. Eventually, these bubbles can merge together into super-bubbles that can reach the edge of the gaseous disk of a galaxy and break out, forming an outflow and ejecting a large fraction of metals into the CGM (e.g., Recchi & Hensler 2013; Côté et al. 2015; Hu 2019). Plenty of ionized and molecular gas observations have evidenced the presence of super-bubbles in the ISM of local galaxies, including a few DGS sources (e.g., Cresci et al. 2017; McQuinn et al. 2018, 2019; McCormick et al. 2018; Suzuki et al. 2018; Menacho et al. 2019; Watkins et al. 2023). These observations are supported by as many analytical models and hydrodynamic simulations trying to describe the evolution and propagation of super-bubbles across the galaxy ISM (e.g., Veilleux et al. 2005; Faucher-Giguère & Quataert 2012; Côté et al. 2015; Kim et al. 2017; Fielding et al. 2018; Oku et al. 2022; Orr et al. 2022). Assuming typical properties of the bubbles observed in local galaxies (e.g., Menacho et al. 2019; McCormick et al. 2018; Watkins et al. 2023), these models predict momentum rates in the range of 1031–1035 g cm s−2 (e.g., Veilleux et al. 2005; Orr et al. 2022), comparable with what found for our outflows and in agreement with the typical mechanical momentum released by star formation and SNe in starburst-driven winds (see Fig. 8, right panel). This suggests that SN super-bubbles could be an important channel for the origin of galactic outflows in dwarf galaxies and for the CGM/IGM enrichment. However, these estimates are based on many assumptions such as the size and velocity of the expanding bubbles, SN rate, or ambient number density (e.g., Veilleux et al. 2005; Kim et al. 2020), and can be affected by large uncertainties, preventing us from making firm conclusions.

All of the feedback processes introduced in this section could jointly concur to the wind’s powering mechanism. Therefore, additional data and increased statistics are needed to properly constrain their individual contribution to the outflow energetics.

6. Summary and conclusions

In this work, we investigated the impact of galactic outflows in a sample of 29 local low-metallicity dwarf galaxies drawn from the DGS (Madden et al. 2013, 2014). These sources benefit from Herschel/PACS spectroscopic coverage of the rest-frame FIR, as well as from a collection of multi-wavelength ancillary data, making them an ideal sample to study how feedback affects their evolution. We took advantage of [CII] observations from PACS to carry out a systematic analysis of atomic outflows in these galaxies by looking at the broad wings in their spectra. Our main results are summarized as follows.

  • We fitted the [CII] line profiles of all the galaxies in our sample with a single Gaussian model, and inspect the corresponding residuals searching for an excess of emission at the high-velocity tails of the spectra (suggestive of the presence of outflowing gas, see Sect. 4.1). We found such an excess in 11 out of 29 galaxies, with three of them better described with a three-Gaussian model likely because of past or undergoing merging activity.

  • Having excluded the null hypothesis that the average [CII] emission of our galaxies could be modeled with a single Gaussian component only (see Sect. 4.2, Fig. 2), we proceeded with a variance-weighted stacking of the [CII] spectra of both the whole sample of 29 dwarf galaxies, and the subsample of 18 sources with no individual wings detection, in order to include the remaining galaxies with no or weak outflow emission (Fig. 3). In the two cases, we observed significant residuals at velocities of ± ∼ 400 km s−1, which are reduced to the noise level by fitting the spectra with a double-Gaussian model. From the stacking of both samples, we measured average FWHM of ∼240 and ∼460 km s−1 for the narrow and broad components, respectively.

  • We implemented a spatial stacking of the [CII] data cubes to measure the average size of the outflow (Sect. 4.3, Fig. 4). By fitting the intensity map of the stacked wings, we found a typical outflow radius of Rout ∼ 1 kpc, in agreement with previous estimates for local galaxies (e.g., Arribas et al. 2014; Fluetsch et al. 2019). Furthermore, we found that the core of the stacked [CII] emission is significantly more extended than the typical UV size of these sources (tracing their stellar contribution), likely highlighting the presence of [CII] halos around them, as also found at higher redshift (e.g., Fujimoto et al. 2019; Ginolfi et al. 2020).

  • We constrained the outflow efficiency in our galaxies by providing an estimate of their mass-loading factor (i.e., by dividing their outflow mass rate for the SFR). We obtained η[CII] ∼ 1 for most of the sources, in agreement with both local and high-z SFGs (e.g., Gallerani et al. 2018; Fluetsch et al. 2019; Ginolfi et al. 2020), thus suggesting that the evolution of these galaxies could be ruled by similar feedback mechanisms (see Sect. 5.1, Fig. 5).

  • We compared the outflow velocities with the escape velocities needed by galactic winds to bring gas outside of their host halos (Sect. 5.2, Fig. 6). We found that, despite the low mass-loading factors, galactic outflows are able to sweep ISM material out of dwarf galaxies (i.e., directly into the IGM), with an average fraction of expelled atomic gas of 40%, that increases up to ∼90% for very low-mass and low-metallicity sources.

  • Assuming a constant outflow rate and SFR, we derived the depletion timescales due to outflows and gas consumption by star formation, respectively (Sect. 5.3, Fig. 7). Our results cover a similar interval in both timescales, ranging from one hundred million to a few billion years. At least 60% of our sample is characterized by τdep, out ≲ τdep, SF, with the fraction rising to ∼90% if accounting for the other phases of the ISM (i.e., ionized and molecular). This suggests a possible main role of galactic outflows in regulating the amount of gas in dwarf galaxies and their SFHs.

  • We investigated the energetic of the outflows by computing their kinetic power and momentum rate (see Sect. 5.4). By comparing these quantities with the energetic expected by starburst-driven winds (e.g., Veilleux et al. 2005; Heckman et al. 2015), we found that our outflows are likely powered by the radiation pressure of young stars on dusty clouds (i.e., momentum-driven scenario), as also observed in local starbursts (e.g., Cicone et al. 2014). However, we cannot exclude that SNe contribute in accelerating the outflows (i.e., energy-driven scenario), as the majority of our sources are still comparable with theoretical models assuming a coupling efficiency ≲10% (see Fig. 8). Moreover, both observations and simulations suggest that SN super-bubbles can also produce galactic winds in local dwarf galaxies and (under specific assumptions on the properties and composition of the bubbles) they could account for the momentum rates observed in the outflows.

Our results highlight the importance of galactic feedback in the evolution of low-mass sources and their environment. Although they are not as much efficient as AGN-driven winds, outflows powered by star formation are still able to mold the history of (especially) dwarf galaxies, for which they can easily bring dust and gas into their CGM (with a significant fraction of them even further, i.e., into the IGM). In a forthcoming paper, we will show how our constraints on the mass-loading factor impact the description of the physical processes responsible for the formation and destruction of dust in these galaxies (Nanni et al. in prep.). Further investigation is needed in order to provide a more complete picture of the effect of feedback on local galaxies. More observations, both from archival research or via follow-ups with, for instance, NOEMA, ALMA, JWST, or Keck telescopes, will allow us to extend our present sample, and to collect ionized and molecular data to complement all the phases of the outflows, making an in-depth study of their interplay.

1

An overview of the survey, the sample selection, and the information available for each galaxy can be found at https://irfu.cea.fr/Pisp/diane.cormier/dgsweb/index.html.

2

The NASA/IPAC Extragalactic Database (NED) is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

3

The best-fit relation to the star-forming main sequence in Leroy et al. (2019) was obtained by selecting SFGs with log(M*/M⊙) = 9.5 − 11. We show their original fit in Fig. 1, extrapolating the relation to the lower stellar mass regime probed by our dwarf galaxies.

5

The Chebyshev series is defined as P ( x ) = ∑ i = 0 i = 3 C i · T i ( x ) $ P(x)= \sum\nolimits_{i=0}^{i=3} C_i \cdot T_i(x) $, where Ti(x) is the Chebyshev polynomial of first kind and degree i, and Ci are the coefficients of the fitting.

6

We applied the deconvolution for the spectral resolution of the instrument only to intrinsic line widths larger than 150 km s−1 (see Cormier et al. 2015).

7

In this regard, the [CII] line has already been proven to trace large-scale cold gas emission around galaxies (e.g., Fujimoto et al. 2020; Ginolfi et al. 2020).

8

As reported in Fluetsch et al. (2019), the ionized, neutral, and molecular phases of the ISM could contribute to the outflow rate at the same level. Therefore, we point out that the comparison between the atomic and molecular outflow rates in Fig. 5 is reasonable, as we are probing the contribution of one ISM phase in both cases.

9

Instead of assuming a single value of c for each galaxy, we used the z = 0 relation by Duffy et al. (2008) to link the concentration parameter to the halo mass as log(c) = 0.76 − 0.1 log(Mhalo).

10

We computed the escape velocities for the galaxies in Heckman et al. (2015) by collecting the redshift and stellar mass of each galaxy in their work and using our Eq. (6).

11

We caution the reader that the results found by Cicone et al. (2014) were obtained under the assumption of a spherical or multi-conical geometry. Adapting their values to the outflow geometry adopted in this paper would result in outflow depletion timescales that are three times larger, and conversely for the mass-loading factors and for the outflow properties derived in Sect. 5.4.

Acknowledgments

We warmly thank the referee for her/his useful comments and suggestions that nicely improved the quality of our paper. M.R. would like to thank Denis Burgarella and Katarzyna Małek for helpful discussions. HIPE is a joint development by the Herschel Science Ground Segment Consortium, consisting of ESA, the NASA Herschel Science Center, and the HIFI, PACS and SPIRE consortia. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. M.R., A.N., and P.S. acknowledge support from the Narodowe Centrum Nauki (UMO-2020/38/E/ST9/00077). G.C.J. acknowledges funding from ERC Advanced Grant 789056 “FirstGalaxies” under the European Union’s Horizon 2020 research and innovation programme. J. is grateful for the support from the Polish National Science Centre via grant UMO-2018/30/E/ST9/00082. D.D. acknowledges support from the National Science Center (NCN) grant SONATA (UMO-2020/39/D/ST9/00720).

References

  1. Andersson, E. P., Agertz, O., Renaud, F., & Teyssier, R. 2023, MNRAS, 521, 2196 [NASA ADS] [CrossRef] [Google Scholar]
  2. Arribas, S., Colina, L., Bellocchi, E., Maiolino, R., & Villar-Martín, M. 2014, A&A, 568, A14 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Behroozi, P. S., Conroy, C., & Wechsler, R. H. 2010, ApJ, 717, 379 [Google Scholar]
  4. Behroozi, P. S., Wechsler, R. H., & Conroy, C. 2013, ApJ, 770, 57 [NASA ADS] [CrossRef] [Google Scholar]
  5. Béthermin, M., Fudamoto, Y., Ginolfi, M., et al. 2020, A&A, 643, A2 [Google Scholar]
  6. Bischetti, M., Maiolino, R., Carniani, S., et al. 2019, A&A, 630, A59 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  7. Booth, C. M., Schaye, J., Delgado, J. D., & Dalla Vecchia, C. 2012, MNRAS, 420, 1053 [NASA ADS] [CrossRef] [Google Scholar]
  8. Boquien, M., Burgarella, D., Roehlly, Y., et al. 2019, A&A, 622, A103 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  9. Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000 [NASA ADS] [CrossRef] [Google Scholar]
  10. Burgarella, D., Buat, V., & Iglesias-Páramo, J. 2005, MNRAS, 360, 1413 [NASA ADS] [CrossRef] [Google Scholar]
  11. Burgarella, D., Nanni, A., Hirashita, H., et al. 2020, A&A, 637, A32 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  12. Cairós, L. M., Caon, N., García-Lorenzo, B., et al. 2007, ApJ, 669, 251 [CrossRef] [Google Scholar]
  13. Calabrò, A., Pentericci, L., Talia, M., et al. 2022, A&A, 667, A117 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  14. Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682 [NASA ADS] [CrossRef] [Google Scholar]
  15. Capak, P. L., Carilli, C., Jones, G., et al. 2015, Nature, 522, 455 [NASA ADS] [CrossRef] [Google Scholar]
  16. Carilli, C. L., & Walter, F. 2013, ARA&A, 51, 105 [NASA ADS] [CrossRef] [Google Scholar]
  17. Carniani, S., Marconi, A., Maiolino, R., et al. 2015, A&A, 580, A102 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  18. Cazzoli, S., Arribas, S., Maiolino, R., & Colina, L. 2016, A&A, 590, A125 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  19. Chabrier, G. 2003, PASP, 115, 763 [Google Scholar]
  20. Chisholm, J., Tremonti, C. A., Leitherer, C., & Chen, Y. 2017, MNRAS, 469, 4831 [NASA ADS] [CrossRef] [Google Scholar]
  21. Christensen, C. R., Davé, R., Brooks, A., Quinn, T., & Shen, S. 2018, ApJ, 867, 142 [CrossRef] [Google Scholar]
  22. Cicone, C., Maiolino, R., Sturm, E., et al. 2014, A&A, 562, A21 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  23. Cicone, C., Maiolino, R., Gallerani, S., et al. 2015, A&A, 574, A14 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  24. Concas, A., Maiolino, R., Curti, M., et al. 2022, MNRAS, 513, 2535 [NASA ADS] [CrossRef] [Google Scholar]
  25. Contursi, A., Poglitsch, A., Graciá Carpio, J., et al. 2013, A&A, 549, A118 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Cormier, D., Lebouteiller, V., Madden, S. C., et al. 2012, A&A, 548, A20 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  27. Cormier, D., Madden, S. C., Lebouteiller, V., et al. 2015, A&A, 578, A53 [CrossRef] [EDP Sciences] [Google Scholar]
  28. Cormier, D., Abel, N. P., Hony, S., et al. 2019, A&A, 626, A23 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  29. Costa, T., Rosdahl, J., Sijacki, D., & Haehnelt, M. G. 2018, MNRAS, 473, 4197 [Google Scholar]
  30. Côté, B., Martel, H., & Drissen, L. 2015, ApJ, 802, 123 [CrossRef] [Google Scholar]
  31. Côté, B., West, C., Heger, A., et al. 2016, MNRAS, 463, 3755 [CrossRef] [Google Scholar]
  32. Côté, B., O’Shea, B. W., Ritter, C., Herwig, F., & Venn, K. A. 2017, ApJ, 835, 128 [Google Scholar]
  33. Cresci, G., Vanzi, L., Telles, E., et al. 2017, A&A, 604, A101 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  34. Curti, M., Mannucci, F., Cresci, G., & Maiolino, R. 2020, MNRAS, 491, 944 [Google Scholar]
  35. Davé, R., Oppenheimer, B. D., & Finlator, K. 2011, MNRAS, 415, 11 [Google Scholar]
  36. Davé, R., Rafieferantsoa, M. H., Thompson, R. J., & Hopkins, P. F. 2017, MNRAS, 467, 115 [NASA ADS] [Google Scholar]
  37. De Breuck, C., Williams, R. J., Swinbank, M., et al. 2014, A&A, 565, A59 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  38. Dekel, A., & Silk, J. 1986, ApJ, 303, 39 [Google Scholar]
  39. De Looze, I., Cormier, D., Lebouteiller, V., et al. 2014, A&A, 568, A62 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  40. Díaz-Santos, T., Armus, L., Charmandaris, V., et al. 2017, ApJ, 846, 32 [Google Scholar]
  41. Dopita, M. A., Pereira, M., Kewley, L. J., & Capaccioli, M. 2002, ApJS, 143, 47 [NASA ADS] [CrossRef] [Google Scholar]
  42. Draine, B. T., Aniano, G., Krause, O., et al. 2014, ApJ, 780, 172 [Google Scholar]
  43. Duffy, A. R., Schaye, J., Kay, S. T., & Dalla Vecchia, C. 2008, MNRAS, 390, L64 [Google Scholar]
  44. Efstathiou, G. 2000, MNRAS, 317, 697 [NASA ADS] [CrossRef] [Google Scholar]
  45. Erb, D. K. 2015, Nature, 523, 169 [Google Scholar]
  46. Erb, D. K., Quider, A. M., Henry, A. L., & Martin, C. L. 2012, ApJ, 759, 26 [CrossRef] [Google Scholar]
  47. Eskew, M., Zaritsky, D., & Meidt, S. 2012, AJ, 143, 139 [NASA ADS] [CrossRef] [Google Scholar]
  48. Faisst, A. L., Schaerer, D., Lemaux, B. C., et al. 2020, ApJS, 247, 61 [NASA ADS] [CrossRef] [Google Scholar]
  49. Falgarone, E., Zwaan, M. A., Godard, B., et al. 2017, Nature, 548, 430 [NASA ADS] [CrossRef] [Google Scholar]
  50. Faucher-Giguère, C.-A., & Quataert, E. 2012, MNRAS, 425, 605 [Google Scholar]
  51. Faucher-Giguère, C.-A., Quataert, E., & Hopkins, P. F. 2013, MNRAS, 433, 1970 [Google Scholar]
  52. Ferland, G. J., Chatzikos, M., Guzmán, F., et al. 2017, Rev. Mex. Astron. Astrofis, 53, 385 [Google Scholar]
  53. Fielding, D., Quataert, E., & Martizzi, D. 2018, MNRAS, 481, 3325 [CrossRef] [Google Scholar]
  54. Fluetsch, A., Maiolino, R., Carniani, S., et al. 2019, MNRAS, 483, 4586 [NASA ADS] [Google Scholar]
  55. Förster Schreiber, N. M., Genzel, R., Newman, S. F., et al. 2014, ApJ, 787, 38 [Google Scholar]
  56. Fraser-McKelvie, A., Cortese, L., Groves, B., et al. 2022, MNRAS, 510, 320 [Google Scholar]
  57. Fujimoto, S., Ouchi, M., Ferrara, A., et al. 2019, ApJ, 887, 107 [Google Scholar]
  58. Fujimoto, S., Silverman, J. D., Bethermin, M., et al. 2020, ApJ, 900, 1 [Google Scholar]
  59. Galametz, M., Madden, S., Galliano, F., et al. 2009, A&A, 508, 645 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  60. Gallerani, S., Pallottini, A., Feruglio, C., et al. 2018, MNRAS, 473, 1909 [Google Scholar]
  61. Galliano, F., Hony, S., Bernard, J. P., et al. 2011, A&A, 536, A88 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  62. Galliano, F., Nersesian, A., Bianchi, S., et al. 2021, A&A, 649, A18 [EDP Sciences] [Google Scholar]
  63. Garilli, B., McLure, R., Pentericci, L., et al. 2021, A&A, 647, A150 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  64. Ginolfi, M., Jones, G. C., Béthermin, M., et al. 2020, A&A, 633, A90 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  65. Gnedin, N. Y., & Kravtsov, A. V. 2010, ApJ, 714, 287 [NASA ADS] [CrossRef] [Google Scholar]
  66. González-Alfonso, E., Fischer, J., Spoon, H. W. W., et al. 2017, ApJ, 836, 11 [Google Scholar]
  67. Green, A. W., Glazebrook, K., McGregor, P. J., et al. 2010, Nature, 467, 684 [NASA ADS] [CrossRef] [Google Scholar]
  68. Griffin, M. J., Abergel, A., Abreu, A., et al. 2010, A&A, 518, L3 [EDP Sciences] [Google Scholar]
  69. Hailey-Dunsheath, S., Nikola, T., Stacey, G. J., et al. 2010, ApJ, 714, L162 [Google Scholar]
  70. Hanasz, M., Lesch, H., Naab, T., et al. 2013, ApJ, 777, L38 [NASA ADS] [CrossRef] [Google Scholar]
  71. Harrison, C. M., Alexander, D. M., Mullaney, J. R., & Swinbank, A. M. 2014, MNRAS, 441, 3306 [Google Scholar]
  72. Heckman, T. M., & Thompson, T. A. 2017, in Handbook of Supernovae, eds. A. W. Alsabti, & P. Murdin, 2431 [CrossRef] [Google Scholar]
  73. Heckman, T. M., Dahlem, M., Lehnert, M. D., et al. 1995, ApJ, 448, 98 [NASA ADS] [CrossRef] [Google Scholar]
  74. Heckman, T. M., Alexandroff, R. M., Borthakur, S., Overzier, R., & Leitherer, C. 2015, ApJ, 809, 147 [Google Scholar]
  75. Heintz, K. E., Watson, D., Oesch, P. A., Narayanan, D., & Madden, S. C. 2021, ApJ, 922, 147 [NASA ADS] [CrossRef] [Google Scholar]
  76. Henkel, C., Hunt, L. K., & Izotov, Y. I. 2022, Galaxies, 10, 11 [NASA ADS] [CrossRef] [Google Scholar]
  77. Herrera-Camus, R., Tacconi, L., Genzel, R., et al. 2019, ApJ, 871, 37 [NASA ADS] [CrossRef] [Google Scholar]
  78. Herrera-Camus, R., Janssen, A., Sturm, E., et al. 2020, A&A, 635, A47 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  79. Herrera-Camus, R., Förster Schreiber, N., Genzel, R., et al. 2021, A&A, 649, A31 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  80. Hollenbach, D. J., & Tielens, A. G. G. M. 1999, Rev. Mod. Phys., 71, 173 [Google Scholar]
  81. Hopkins, P. F., Quataert, E., & Murray, N. 2012, MNRAS, 421, 3522 [Google Scholar]
  82. Hopkins, P. F., Kereš, D., Oñorbe, J., et al. 2014, MNRAS, 445, 581 [NASA ADS] [CrossRef] [Google Scholar]
  83. Hu, C.-Y. 2019, MNRAS, 483, 3363 [NASA ADS] [CrossRef] [Google Scholar]
  84. Huang, K.-H., Fall, S. M., Ferguson, H. C., et al. 2017, ApJ, 838, 6 [NASA ADS] [CrossRef] [Google Scholar]
  85. Izotov, I. I., Guseva, N. G., Lipovetskii, V. A., Kniazev, A. I., & Stepanian, J. A. 1991, A&A, 247, 303 [NASA ADS] [Google Scholar]
  86. Izotov, Y. I., Guseva, N. G., Fricke, K. J., et al. 2021, A&A, 646, A138 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  87. James, B. L., Tsamis, Y. G., Barlow, M. J., Walsh, J. R., & Westmoquette, M. S. 2013, MNRAS, 428, 86 [NASA ADS] [CrossRef] [Google Scholar]
  88. Janssen, A. W., Christopher, N., Sturm, E., et al. 2016, ApJ, 822, 43 [NASA ADS] [Google Scholar]
  89. Johnson, K. E., & Conti, P. S. 2000, AJ, 119, 2146 [NASA ADS] [CrossRef] [Google Scholar]
  90. Johnson, K. E., Indebetouw, R., Watson, C., & Kobulnicky, H. A. 2004, AJ, 128, 610 [NASA ADS] [CrossRef] [Google Scholar]
  91. Jones, G. C., Vergani, D., Romano, M., et al. 2021, MNRAS, 507, 3540 [NASA ADS] [CrossRef] [Google Scholar]
  92. Kashino, D., Renzini, A., Silverman, J. D., & Daddi, E. 2016, ApJ, 823, L24 [NASA ADS] [CrossRef] [Google Scholar]
  93. Kim, C.-G., & Ostriker, E. C. 2018, ApJ, 853, 173 [NASA ADS] [CrossRef] [Google Scholar]
  94. Kim, C.-G., Ostriker, E. C., & Raileanu, R. 2017, ApJ, 834, 25 [Google Scholar]
  95. Kim, C.-G., Ostriker, E. C., Fielding, D. B., et al. 2020, ApJ, 903, L34 [NASA ADS] [CrossRef] [Google Scholar]
  96. King, A., & Pounds, K. 2015, ARA&A, 53, 115 [NASA ADS] [CrossRef] [Google Scholar]
  97. Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511 [Google Scholar]
  98. Lambert, T. S., Posses, A., Aravena, M., et al. 2023, MNRAS, 518, 3183 [Google Scholar]
  99. Lebouteiller, V., Cormier, D., Madden, S. C., et al. 2012, A&A, 548, A91 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  100. Le Fèvre, O., Béthermin, M., Faisst, A., et al. 2020, A&A, 643, A1 [Google Scholar]
  101. Leitherer, C., Schaerer, D., Goldader, J. D., et al. 1999, ApJS, 123, 3 [Google Scholar]
  102. Leroy, A. K., Sandstrom, K. M., Lang, D., et al. 2019, ApJS, 244, 24 [Google Scholar]
  103. Lian, J., Thomas, D., & Maraston, C. 2018, MNRAS, 481, 4000 [Google Scholar]
  104. Lilly, S. J., Carollo, C. M., Pipino, A., Renzini, A., & Peng, Y. 2013, ApJ, 772, 119 [NASA ADS] [CrossRef] [Google Scholar]
  105. Łokas, E. L., & Mamon, G. A. 2001, MNRAS, 321, 155 [CrossRef] [Google Scholar]
  106. Lutz, D., Sturm, E., Janssen, A., et al. 2020, A&A, 633, A134 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  107. Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415 [Google Scholar]
  108. Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2013, PASP, 125, 600 [NASA ADS] [CrossRef] [Google Scholar]
  109. Madden, S. C., Rémy-Ruyer, A., Galametz, M., et al. 2014, PASP, 126, 1079 [CrossRef] [Google Scholar]
  110. Madden, S. C., Cormier, D., Hony, S., et al. 2020, A&A, 643, A141 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  111. Maiolino, R., Gallerani, S., Neri, R., et al. 2012, MNRAS, 425, L66 [Google Scholar]
  112. Mannucci, F., Cresci, G., Maiolino, R., et al. 2009, MNRAS, 398, 1915 [Google Scholar]
  113. Manzano-King, C. M., Canalizo, G., & Sales, L. V. 2019, ApJ, 884, 54 [NASA ADS] [CrossRef] [Google Scholar]
  114. Marasco, A., Belfiore, F., Cresci, G., et al. 2023, A&A, 670, A92 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  115. Markarian, B. E., & Stepanian, D. A. 1983, Astrofizika, 19, 639 [NASA ADS] [Google Scholar]
  116. Martin, D. C., Fanson, J., Schiminovich, D., et al. 2005, ApJ, 619, L1 [Google Scholar]
  117. Martizzi, D., Fielding, D., Faucher-Giguère, C.-A., & Quataert, E. 2016, MNRAS, 459, 2311 [NASA ADS] [CrossRef] [Google Scholar]
  118. McCormick, A., Veilleux, S., Meléndez, M., et al. 2018, MNRAS, 477, 699 [NASA ADS] [CrossRef] [Google Scholar]
  119. McGaugh, S. S. 2012, AJ, 143, 40 [Google Scholar]
  120. McLure, R. J., Pentericci, L., Cimatti, A., et al. 2018, MNRAS, 479, 25 [NASA ADS] [Google Scholar]
  121. McQuinn, K. B. W., Skillman, E. D., Heilman, T. N., Mitchell, N. P., & Kelley, T. 2018, MNRAS, 477, 3164 [NASA ADS] [CrossRef] [Google Scholar]
  122. McQuinn, K. B. W., van Zee, L., & Skillman, E. D. 2019, ApJ, 886, 74 [NASA ADS] [CrossRef] [Google Scholar]
  123. Menacho, V., Östlin, G., Bik, A., et al. 2019, MNRAS, 487, 3183 [CrossRef] [Google Scholar]
  124. Moiseev, A. V., & Lozinskaya, T. A. 2012, MNRAS, 423, 1831 [NASA ADS] [CrossRef] [Google Scholar]
  125. Motiño Flores, S. M., Wiklind, T., & Eufrasio, R. T. 2021, ApJ, 921, 130 [CrossRef] [Google Scholar]
  126. Muratov, A. L., Kereš, D., Faucher-Giguère, C.-A., et al. 2015, MNRAS, 454, 2691 [NASA ADS] [CrossRef] [Google Scholar]
  127. Murray, N., Quataert, E., & Thompson, T. A. 2005, ApJ, 618, 569 [NASA ADS] [CrossRef] [Google Scholar]
  128. Murray, N., Ménard, B., & Thompson, T. A. 2011, ApJ, 735, 66 [NASA ADS] [CrossRef] [Google Scholar]
  129. Nanni, A., Burgarella, D., Theulé, P., Côté, B., & Hirashita, H. 2020, A&A, 641, A168 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  130. Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563 [Google Scholar]
  131. Nelson, D., Pillepich, A., Springel, V., et al. 2019, MNRAS, 490, 3234 [Google Scholar]
  132. Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, ApJ, 660, L43 [CrossRef] [Google Scholar]
  133. Noll, S., Burgarella, D., Giovannoli, E., et al. 2009, A&A, 507, 1793 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  134. Oh, K., Sarzi, M., Schawinski, K., & Yi, S. K. 2011, ApJS, 195, 13 [NASA ADS] [CrossRef] [Google Scholar]
  135. Oku, Y., Tomida, K., Nagamine, K., Shimizu, I., & Cen, R. 2022, ApJS, 262, 9 [NASA ADS] [CrossRef] [Google Scholar]
  136. Orr, M. E., Hayward, C. C., Hopkins, P. F., et al. 2018, MNRAS, 478, 3653 [NASA ADS] [CrossRef] [Google Scholar]
  137. Orr, M. E., Fielding, D. B., Hayward, C. C., & Burkhart, B. 2022, ApJ, 932, 88 [NASA ADS] [CrossRef] [Google Scholar]
  138. Östlin, G., Marquart, T., Cumming, R. J., et al. 2015, A&A, 583, A55 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  139. Ostriker, E. C., & Kim, C.-G. 2022, ApJ, 936, 137 [NASA ADS] [CrossRef] [Google Scholar]
  140. Ott, S. 2010, in Astronomical Data Analysis Software and Systems XIX, eds. Y. Mizumoto, K. I. Morita, & M. Ohishi, ASP Conf. Ser., 434, 139 [Google Scholar]
  141. Ott, J., Walter, F., & Brinks, E. 2005, MNRAS, 358, 1453 [NASA ADS] [CrossRef] [Google Scholar]
  142. Pasquini, L., Avila, G., Blecha, A., et al. 2002, The Messenger, 110, 1 [Google Scholar]
  143. Patej, A., & Loeb, A. 2015, ApJ, 815, L28 [NASA ADS] [CrossRef] [Google Scholar]
  144. Pentericci, L., McLure, R. J., Garilli, B., et al. 2018, A&A, 616, A174 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  145. Pereira-Santaella, M., Colina, L., García-Burillo, S., et al. 2018, A&A, 616, A171 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  146. Péroux, C., & Howk, J. C. 2020, ARA&A, 58, 363 [CrossRef] [Google Scholar]
  147. Pettini, M., Rix, S. A., Steidel, C. C., et al. 2002, ApJ, 569, 742 [NASA ADS] [CrossRef] [Google Scholar]
  148. Pilbratt, G. L., Riedinger, J. R., Passvogel, T., et al. 2010, A&A, 518, L1 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  149. Pillepich, A., Springel, V., Nelson, D., et al. 2018, MNRAS, 473, 4077 [Google Scholar]
  150. Pineda, J. L., Langer, W. D., & Goldsmith, P. F. 2014, A&A, 570, A121 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  151. Pizzati, E., Ferrara, A., Pallottini, A., et al. 2020, MNRAS, 495, 160 [Google Scholar]
  152. Poglitsch, A., Waelkens, C., Geis, N., et al. 2010, A&A, 518, L2 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  153. Ramos Almeida, C., Acosta-Pulido, J. A., Tadhunter, C. N., et al. 2019, MNRAS, 487, L18 [NASA ADS] [CrossRef] [Google Scholar]
  154. Recchi, S., & Hensler, G. 2013, A&A, 551, A41 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  155. Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2013, A&A, 557, A95 [Google Scholar]
  156. Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2015, A&A, 582, A121 [Google Scholar]
  157. Riechers, D. A., Cooray, A., Pérez-Fournon, I., & Neri, R. 2021, ApJ, 913, 141 [NASA ADS] [CrossRef] [Google Scholar]
  158. Rivlin, T. 1974, The Chebyshev Polynomials, A Wiley-Interscience publication (Wiley) [Google Scholar]
  159. Roberts-Borsani, G. W., & Saintonge, A. 2019, MNRAS, 482, 4111 [NASA ADS] [Google Scholar]
  160. Rodighiero, G., Daddi, E., Baronchelli, I., et al. 2011, ApJ, 739, L40 [Google Scholar]
  161. Romano, M., Cassata, P., Morselli, L., et al. 2021, A&A, 653, A111 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  162. Romano, M., Morselli, L., Cassata, P., et al. 2022, A&A, 660, A14 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  163. Rupke, D. S. N., & Veilleux, S. 2013, ApJ, 768, 75 [Google Scholar]
  164. Rupke, D. S., Veilleux, S., & Sanders, D. B. 2005a, ApJS, 160, 115 [Google Scholar]
  165. Rupke, D. S., Veilleux, S., & Sanders, D. B. 2005b, ApJ, 632, 751 [NASA ADS] [CrossRef] [Google Scholar]
  166. Rupke, D. S. N., Gültekin, K., & Veilleux, S. 2017, ApJ, 850, 40 [NASA ADS] [CrossRef] [Google Scholar]
  167. Salem, M., & Bryan, G. L. 2014, MNRAS, 437, 3312 [CrossRef] [Google Scholar]
  168. Salpeter, E. E. 1955, ApJ, 121, 161 [Google Scholar]
  169. Samui, S., Subramanian, K., & Srianand, R. 2010, MNRAS, 402, 2778 [NASA ADS] [CrossRef] [Google Scholar]
  170. Sartori, L. F., Schawinski, K., Treister, E., et al. 2015, MNRAS, 454, 3722 [CrossRef] [Google Scholar]
  171. Savage, B. D., & Sembach, K. R. 1996, ApJ, 470, 893 [Google Scholar]
  172. Scannapieco, E. 2017, ApJ, 837, 28 [NASA ADS] [CrossRef] [Google Scholar]
  173. Schaerer, D., Ginolfi, M., Béthermin, M., et al. 2020, A&A, 643, A3 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  174. Schaye, J., Crain, R. A., Bower, R. G., et al. 2015, MNRAS, 446, 521 [Google Scholar]
  175. Schneider, E. E., Robertson, B. E., & Thompson, T. A. 2018, ApJ, 862, 56 [NASA ADS] [CrossRef] [Google Scholar]
  176. Shao, J., & Wu, C. F. J. 1989, Ann. Stat., 17, 1176 [CrossRef] [Google Scholar]
  177. Shivaei, I., Popping, G., Rieke, G., et al. 2022, ApJ, 928, 68 [NASA ADS] [CrossRef] [Google Scholar]
  178. Silk, J., & Mamon, G. A. 2012, Res. Astron. Astrophys., 12, 917 [Google Scholar]
  179. Solomon, P. M., Downes, D., & Radford, S. J. E. 1992, ApJ, 398, L29 [Google Scholar]
  180. Somerville, R. S., & Davé, R. 2015, ARA&A, 53, 51 [Google Scholar]
  181. Somerville, R. S., Hopkins, P. F., Cox, T. J., Robertson, B. E., & Hernquist, L. 2008, MNRAS, 391, 481 [NASA ADS] [CrossRef] [Google Scholar]
  182. Speagle, J. S., Steinhardt, C. L., Capak, P. L., & Silverman, J. D. 2014, ApJS, 214, 15 [Google Scholar]
  183. Springel, V. 2005, MNRAS, 364, 1105 [Google Scholar]
  184. Springel, V., & Hernquist, L. 2003, MNRAS, 339, 289 [Google Scholar]
  185. Stacey, G. J., Geis, N., Genzel, R., et al. 1991, ApJ, 373, 423 [NASA ADS] [CrossRef] [Google Scholar]
  186. Stacey, G. J., Hailey-Dunsheath, S., Ferkinhoff, C., et al. 2010, ApJ, 724, 957 [NASA ADS] [CrossRef] [Google Scholar]
  187. Suzuki, T., Kaneda, H., Onaka, T., et al. 2018, MNRAS, 477, 3065 [NASA ADS] [CrossRef] [Google Scholar]
  188. Tacconi, L. J., Genzel, R., & Sternberg, A. 2020, ARA&A, 58, 157 [NASA ADS] [CrossRef] [Google Scholar]
  189. Talia, M., Brusa, M., Cimatti, A., et al. 2017, MNRAS, 471, 4527 [NASA ADS] [CrossRef] [Google Scholar]
  190. Thompson, T. A., Quataert, E., & Murray, N. 2005, ApJ, 630, 167 [Google Scholar]
  191. Thompson, T. A., Fabian, A. C., Quataert, E., & Murray, N. 2015, MNRAS, 449, 147 [NASA ADS] [CrossRef] [Google Scholar]
  192. Tombesi, F., Meléndez, M., Veilleux, S., et al. 2015, Nature, 519, 436 [NASA ADS] [CrossRef] [Google Scholar]
  193. Tremaine, S., Gebhardt, K., Bender, R., et al. 2002, ApJ, 574, 740 [NASA ADS] [CrossRef] [Google Scholar]
  194. Tumlinson, J., Peeples, M. S., & Werk, J. K. 2017, ARA&A, 55, 389 [Google Scholar]
  195. Ugryumov, A. V., Engels, D., Pustilnik, S. A., et al. 2003, A&A, 397, 463 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  196. Veilleux, S., Cecil, G., & Bland-Hawthorn, J. 2005, ARA&A, 43, 769 [NASA ADS] [CrossRef] [Google Scholar]
  197. Veilleux, S., Meléndez, M., Sturm, E., et al. 2013, ApJ, 776, 27 [Google Scholar]
  198. Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nat. Methods, 17, 261 [Google Scholar]
  199. Vizgan, D., Heintz, K. E., Greve, T. R., et al. 2022, ApJ, 939, L1 [NASA ADS] [CrossRef] [Google Scholar]
  200. Vogelsberger, M., Genel, S., Springel, V., et al. 2014, MNRAS, 444, 1518 [Google Scholar]
  201. Watkins, E. J., Kreckel, K., Groves, B., et al. 2023, A&A, 676, A67 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  202. Wen, X.-Q., Wu, H., Zhu, Y.-N., et al. 2013, MNRAS, 433, 2946 [NASA ADS] [CrossRef] [Google Scholar]
  203. Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868 [Google Scholar]
  204. Xu, X., Heckman, T., Henry, A., et al. 2022, ApJ, 933, 222 [NASA ADS] [CrossRef] [Google Scholar]
  205. Zanella, A., Daddi, E., Magdis, G., et al. 2018, MNRAS, 481, 1976 [Google Scholar]

Appendix A: Spectra extraction

We show here two examples of spectra extraction from the PACS data cubes, as described in Sect. 3. The top panels in Fig. A.1 report the case of the galaxy HS1319+3224. On the left, the spectra retrieved from each spaxel at the position of the corresponding PACS footprint of the galaxy are shown. The spectrum from the central spaxel, and those obtained from the sum of the 3 × 3 and 5 × 5 grids are also displayed on the right. This galaxy is not present in our final sample, as it is one of the six sources we discarded because of their noisy [CII] spectra (see Sect. 3). Indeed, by looking at the figure, none of the spectra show a clear emission feature to be used for our analysis. For comparison, we also show the [CII] spectra of Haro11, one of the 29 sources of our sample, at the bottom of Fig. A.1. Contrarily to HS1319+3224, this represents an example of the good quality of our data, which was impossible to reach for the above-mentioned excluded DGS galaxies. Haro11 is placed at the center of the PACS footprint, where the signal is larger than in the outskirts. The 3 × 3 inner spectrum resulted to be the one with the largest flux and S/N (see Table 3), and we used it to search for broad wings in its high-velocity tails, clearly visible in the figure as a flux excess with respect to the single Gaussian component fitted to the emission profile.

thumbnail Fig. A.1.

Examples of spectra extraction for two galaxies with bad (top) and good (bottom) quality of the [CII] data. For both galaxies: Left panel shows [CII] spectra obtained for each spaxel of the PACS data cube (with the pair numbers in the top left of each plot associated with the corresponding position on the PACS footprint); in the right panel, the solid lines represent the spectra from the central spaxel (orange) and from the inner 3 × 3 (green) and 5 × 5 (teal) spaxel grids, while the shaded areas show their uncertainties. For Haro11, the right panel reports the continuum-subtracted spectra, while the dashed black line displays the single component Gaussian fit on the 3 × 3 inner spectrum.

Appendix B: Individual spectral fitting

In this appendix, we report three examples of spectral fitting to individual galaxies, as discussed in Sect. 4.1. In the left panel of Fig. B.1, we show the case of the galaxy SBS1533+574, which is one of the 18 sources of our sample with no evidence for a broad component in their [CII] spectra. On the other hand, the middle panel reports the [CII] spectrum of Haro11 (the same spectrum is also shown in the bottom panel of Fig. A.1 as a green line), in which the presence of the broad component is clearly evidenced by the large residuals at ∼ ± 400 km s−1, obtained with a single-component Gaussian fit of the line. Finally, the right panel shows the case of one of the three galaxies of our sample (Mrk1089), for which we found that a three-component modeling was a better description of their [CII] line profiles. As stated in Sect. 4.1, previous studies found evidence of possible merging activity in these objects. Following them, we fitted their spectra with one broad and two narrow components, resulting in better residuals than obtained with a double Gaussian fit only.

thumbnail Fig. B.1.

Continuum-subtracted [CII] spectra (black histograms) as a function of the velocity offset computed with respect to the line peak. The figure shows three different galaxies with no detection of a broad component (left panel), and with individual outflow detection in the case of a single source (middle panel) and a possible merger (right panel). For each galaxy (whose name is reported at the top of the figure), the line profile is fitted with a single Gaussian function (in blue). A double (triple) Gaussian profile (in pink), that is the sum of one (green line) or two (green and grey lines) narrow and a broad (orange line) components, is also shown in the middle and right panels. The FWHM of both components and the corresponding reduced χ2 are reported in each figure. For Mrk1089, FWHMnarrow is obtained from the Gaussian profile resulting from the sum of the two narrow components. The bottom panels display the residuals from the single (blue) and double/triple (pink) Gaussian functions. The dotted horizontal line marks the zero level, while the shaded area represents the rms of each spectrum at ±1σ. Flux densities and residuals are both normalized to the corresponding maximum values.

All Tables

Table 1.

Parameters used in CIGALE for modeling the SEDs of our galaxies.

In the text
Table 2.

Physical properties of our sample of galaxies.

In the text
Table 3.

Information on [CII] spectra acquisition and Gaussian fit.

In the text
Table 4.

Outflow properties.

In the text

All Figures

thumbnail Fig. 1.

SFR-M* diagram for all the sources in our sample (teal circles). Gray contours show the distribution of nearby galaxies from Leroy et al. (2019). Here, contours increase in steps of 20%, with the lowest one including 90% of the local sample. The pink solid line represents the best-fit relation (by Leroy et al. 2019) to local SFGs (selected in the log(M*/M⊙) = 9.5 − 11 range), probing the local star-forming main sequence. We also show the extrapolation of such a relation to the lower stellar mass regime covered by our galaxy sample (pink dotted line). Pink dashed lines are the 3σ scatter associated with the relation. Circles highlighted in white represent galaxies from our sample with individual outflow detections.
In the text
thumbnail Fig. 2.

Variance-weighted stacked residuals obtained after subtracting the best-fit single component Gaussian function to each [CII] spectrum. Red bins represent the residuals within ±800 km s−1, whereas the blue bins mark the spectral region used for estimating the noise. The dotted horizontal line sets the zero level, while the shaded area represents the noise at ±1σ. An ∼3σ excess is visible at velocities ±400 km s−1, suggesting that a further Gaussian component is needed to model the [CII] emission in our galaxies.
In the text
thumbnail Fig. 3.

Average [CII] line profiles. Left: Stacked, variance-weighted [CII] spectrum (black histogram) of the whole sample as a function of velocity. Both the fit with a single Gaussian function (in blue) and that with a double Gaussian profile (in pink) are reported. The latter is the sum of a narrow (green line) and broad (orange line and shaded area) component. The FWHM of both components and the corresponding reduced χ2 are also shown in the figure. A zoomed-in view of the spectral region dominated by outflows is shown as an inset plot on the right. The bottom panel reports the residuals from the single (blue) and double (pink) Gaussian functions. The dotted horizontal line marks the zero level, while the shaded area represents the noise of each spectrum at ±1σ, computed as described in the text. Right: Same as left panel, but for the stacking of only the sources with non-detected outflows.
In the text
thumbnail Fig. 4.

Spatial extent of the average [CII] emission. Top: Channel maps of the stacked cube covering ∼2000 km s−1 around the peak of the emission line. Velocity bins are in steps of ∼106 km s−1 for a better representation. Each spectral channel shows the [CII] emission from a 80″ × 80″ region. Contour levels are shown in white at 3, 5, and 7σ, where σ is the rms computed in each channel. Bottom: [CII] integrated intensity maps of the outflow and core emission. Left and right panels are obtained by summing the emission of the broad wings in the velocity ranges [−500, −250] and [250; 500] km s−1, respectively, while the central panel represents the core emission at [−250; 250] km s−1. The bottom panel is the sum of the two velocity-integrated maps of the broad wings (as pointed out by the arrows) representing the whole outflow emission. Contour levels are shown in white at 3, 5, and 7 σ, where σ is the rms of the integrated intensity map. Both figures report the PACS beam (as shown in the lower-left corner of the first panel) and a reference scale of 5 kpc.
In the text
thumbnail Fig. 5.

Atomic outflow rate as a function of the SFR, for both individual detections of broad wings (circles) and from line stacking of the whole sample and of the sources with non-detected outflow (big and small squares, respectively). The pink and violet lines are the best-fit relations between molecular outflow rate and SFR for local AGN hosts and star-forming/starburst galaxies by Fluetsch et al. (2019), respectively, while the shaded regions are the corresponding uncertainties. The solid gray line with the shaded area represents a linear fit to the DGS galaxies with individual outflow detections and its uncertainty, respectively. The dashed line reports the 1:1 relation. We also show the results from [CII] stacking of z ≳ 5 SFGs by Gallerani et al. (2018; hexagon) and Ginolfi et al. (2020; diamond). All markers are color-coded for their mass-loading factors.
In the text
thumbnail Fig. 6.

Relation between outflow velocity and escape velocity. Galaxies of our sample with individual outflow detections are shown as circles with their size increasing with larger escape fractions. Local starbursts are represented as hexagons (Heckman et al. 2015). Nearby dwarf galaxies, including AGNs and star forming and composite galaxies (based on their optical classification), are shown as squares, stars, and pentagons, respectively (Manzano-King et al. 2019). The dashed line reports the 1:1 relation. All data are color-coded for their stellar mass.
In the text
thumbnail Fig. 7.

Comparison between depletion timescale due to outflows and gas consumption due to star formation. DGS galaxies from this work are shown as circles. The typical uncertainty on both timescales is shown in the top right corner. Squares, stars, and pentagons are the results from local AGNs, starburst galaxies, and LINERs, respectively (Cicone et al. 2014). The dashed line reports the 1:1 relation. The area below this line is populated by galaxies whose outflows are more efficient than star formation in consuming gas (i.e., τdep, out < τdep, SF). All data are color-coded for their mass-loading factors.
In the text
thumbnail Fig. 8.

Outflow energetics. Left: Kinetic power of outflow as a function of kinetic power generated by SN-driven winds. The solid lines report the relations Ėout = 0.01,0.1,1 ĖSB, as indicated in the figure. Right: Outflow momentum rate as a function of momentum supplied by starburst galaxies. The solid lines refer to Ṗout= 0.1,1,10 ṖSB, as reported in the figure. Both panels also show the results by Cicone et al. (2014), Heckman et al. (2015), and Chisholm et al. (2017) for local starburst (stars, hexagons, and crosses) and AGN-dominated (squares and pentagons) sources. Big circles display the results from this work and are color-coded according to the momentum boost, as described in the text.
In the text
thumbnail Fig. A.1.

Examples of spectra extraction for two galaxies with bad (top) and good (bottom) quality of the [CII] data. For both galaxies: Left panel shows [CII] spectra obtained for each spaxel of the PACS data cube (with the pair numbers in the top left of each plot associated with the corresponding position on the PACS footprint); in the right panel, the solid lines represent the spectra from the central spaxel (orange) and from the inner 3 × 3 (green) and 5 × 5 (teal) spaxel grids, while the shaded areas show their uncertainties. For Haro11, the right panel reports the continuum-subtracted spectra, while the dashed black line displays the single component Gaussian fit on the 3 × 3 inner spectrum.
In the text
thumbnail Fig. B.1.

Continuum-subtracted [CII] spectra (black histograms) as a function of the velocity offset computed with respect to the line peak. The figure shows three different galaxies with no detection of a broad component (left panel), and with individual outflow detection in the case of a single source (middle panel) and a possible merger (right panel). For each galaxy (whose name is reported at the top of the figure), the line profile is fitted with a single Gaussian function (in blue). A double (triple) Gaussian profile (in pink), that is the sum of one (green line) or two (green and grey lines) narrow and a broad (orange line) components, is also shown in the middle and right panels. The FWHM of both components and the corresponding reduced χ2 are reported in each figure. For Mrk1089, FWHMnarrow is obtained from the Gaussian profile resulting from the sum of the two narrow components. The bottom panels display the residuals from the single (blue) and double/triple (pink) Gaussian functions. The dotted horizontal line marks the zero level, while the shaded area represents the rms of each spectrum at ±1σ. Flux densities and residuals are both normalized to the corresponding maximum values.
In the text

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