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Jakub Nadolny

Publications and source records attributed to Jakub Nadolny.

At least 19 recordsLinked to original sources

Rubin LSST DP2 unveils almost-dark galaxies in the Virgo Cluster

Galaxies with the faintest surface brightness are currently known only in the Local Group. Similar objects should exist beyond our vicinity and are crucial for understanding galaxy evolution, structure, and dark matter content, yet surveys have not reached the depth required to detect them systematically. We present a population of seven almost-dark galaxies identified in Data Preview 2 of the Rubin Legacy Survey of Space and Time. They surround M49 in the vicinity of the Virgo Cluster, and exhibit central surface brightnesses in the range of $26.9 - 28.5 \, \mathrm{mag \, arcsec^{-2}}$ in the $g$-band, with half-light radii of $0.6 - 4.6 \, \mathrm{kpc}$ at the distance of Virgo, and stellar masses of $10^6 - 10^7 \, \mathrm{M_\odot}$. Their characteristics are analogous to those of the faintest and low-mass galaxies identified among satellite galaxies And XXI, And XXIII, and And XXV in the Local Group. This discovery demonstrates the power of the forthcoming Rubin LSST 10-year survey to uncover extremely faint galaxies at scale, promising the large statistical samples needed to constrain the faint-end luminosity function and the nature of dark matter.

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The OTELO Survey: The main sequence of low-mass galaxies

This paper describes the relationship between the star formation rate and the stellar mass, the so-called main sequence (MS), of low-mass galaxies at three different redshifts from the OTELO survey. In particular, we study Halpha at z=0.38, [OIII] at z=0.83, and [OII] at z=1.43 emission line galaxies (ELGs). This is done to characterise the properties of low-mass ELGs. We fitted the spectral energy distribution (SED) of each emitter and obtained the stellar masses, the total infrared luminosity, and the star formation rate. We found that 100% of the Halpha emitters and about 90% of the [OIII] and [OII] emitters are low-mass galaxies (< 1E10M_sun). We generated a MS for each redshift regime, employing all galaxies and binning them in stellar mass. We obtained the parameters of the fit (turnover mass and slope of the low-mass regime) and compared them to results from the literature. We found that the colour-magnitude method employed to select ELGs leaves out a significant number of them. We also found that the whole sample contains few luminous infrared galaxies and no ultra-luminous infrared galaxies. We also found that the lack of infrared constraints in the input SEDs may generate problems when determining the total infrared luminosity. When comparing the MS obtained for our sample of low-mass ELGs with those from the bibliography, we found, in general, very good agreement. We can consider the MS to be almost the same for the relatively unexplored regime of low-mass galaxies. However, the turnover mass obtained by this work is higher for all redshifts compared with the ones from the literature. We suggest that this is an effect of the different methods and samples used in the generation of the MS compared to those of the bibliography.

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Star formation at z$\sim$0.9 from the OTELO survey: A comprehensive view combining deep optical spectroscopy and infrared data

We aim to quantify the star formation rate (SFR) from deep optical spectroscopic data and far-infrared (FIR) photometry from a sample of galaxies at $z\sim 0.9$ from the OTELO survey and compare the activity estimated by optical tracers and FIR emission. We used the multi-wavelength OTELO catalogue to construct a sample of FIR sources. We identified and separated galaxies with active nuclei and derived the physical properties of the rest. We analysed their spectral energy distribution, obtaining estimates for stellar mass, dust attenuation, luminosity, and SFR based on infrared luminosity. We also studied H$β$ and [OIII] emission-line galaxies without significant FIR emission from previous works. This approach allowed us to perform a comparative analysis among the SFR obtained through different calibrators, in particular H$β$, presented in a previous work. We find that FIR-based SFR estimates uncover a significant fraction of hidden star formation. We determined that the SFR density obtained from the FIR emission is three times larger than that obtained from only emission-line sources. Likely related to the fact that each SFR tracer provides insight into star formation over different timescales, we suggest that such indicators are also more or less suited for different galaxy populations. Specifically, while optical emission lines effectively trace star formation in lower-mass galaxies, FIR-derived SFRs provide a more reliable measure in massive dust-rich systems. By accounting for both optically visible and obscured star formation, we provide a more comprehensive view of the star-forming main sequence at $z \sim 0.9$ and reinforce the importance of infrared tracers in studying galaxy evolution.

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Atomic gas properties at the positions of supernovae Type Ia, II, and Ib/c

Understanding which stars explode as which type of supernovae (SNe) is crucial to measure their contribution to the metal production and feedback halting star formation. Most of the studies of the gas in the environment of SNe are limited by a small sample size ($<10$). The goal of this paper is to present the first analysis of atomic gas properties at the positions of a statistically significant sample of SNe in order to constrain their nature. We selected 133 SNe (29 Ia, 77 II, 27 Ib/c) which have exploded in galaxies with existing atomic gas data. In order to test whether SN positions trace enhancements in the atomic gas distribution, we analyzed the fraction of pixels on the {\hi} map which are fainter than the pixel in which SN is located and the fraction of the {\hi} flux contributed by these pixels. All types of SNe deviate from the completely random distribution. From the three types of SNe, Type II showed the largest offset from the {\hi} distribution, preferring even higher concentrations of atomic gas. This type of SNe deviated also from being proportional to the stellar surface density of the host. The results are, however, complicated by the limits of the survey in size, and in the un-even resolution of the {\hi} observations. Furthermore, by direct comparison between the three SN types, we observed that the distributions of these populations are still consistent with each other. The obtained results fail to ascertain that Ib/c core-collapse SNe, and possibly also Type II SNe, are connected with the densest concentrations of atomic gas in their hosts, unlike what has been suggested for GRBs and Ic-BL SNe. Hence, the birth of progenitors of Type II and Ib/c SNe is still consistent with being connected with the current star formation in their hosts, whereas the progenitors of GRBs and Type Ic-BL SNe require more special conditions to form, for example low metallicity.

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The OTELO survey: New evidence of downsizing from the specific star formation rates, stellar mass functions, and star formation histories of a sample of low-mass galaxies at 0.38<z<1.43

We present an analysis of the emitters (\ha, \hb, and \oii) from the OTELO survey, in order to characterize the star formation properties of low-mass galaxies ($<10^9$ M$_{\odot}$ stellar masses). We calculated the specific star formation rate function, the stellar mass function, and, by integrating them, the associated densities for both quantities: the specific star formation rate density and the stellar mass density. We obtained the star formation history of our low-mass sample galaxies by fitting the spectral energy distribution of the galaxies. We also compared our results with those from the literature at different mass regimes and redshifts. The specific star formation rate density and the stellar mass density for low-mass galaxies do not depend on the redshift, contrary to the behaviour presented by the high-mass galaxies. We found that the star formation histories of low-mass galaxies are characterized by a constant star formation rate, in contrast to high-mass galaxies. We interpret these results, in the context of the downsizing effect, as representative of the faster evolution of massive galaxies compared with low-mass ones.

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Evolution of the star formation rate surface density main sequence. Insights from a semi-analytic simulation since $z = 12$

Recent high-redshift ($z>4$) spatially resolved observations with the James Webb Space Telesescope have shown the evolution of the star formation rate (SFR) surface density ($Σ_{\rm SFR}$) and its main sequence in the $Σ_{\rm SFR}$-$M_*$ diagram ($Σ_{\rm SFR}{\rm MS}$). The $Σ_{\rm SFR}{\rm MS}$\ is already observed at cosmic morning ($z\sim7.5$). The use of $Σ_{\rm SFR}$\ is physically motivated because it is normalized by the area in which the star formation occurs, and this indirectly considers the gas density. The $Σ_{\rm SFR}$-$M_*$ diagram has been shown to complement the widely used (specific) SFR-$M_*$, particularly when selecting passive galaxies. We establish the $Σ_{\rm SFR}$\ evolution since $z=12$ in the framework of the L-Galaxies2020 semi-analytical model (SAM), and we interpret recent observations. We estimated $Σ_{\rm SFR}$(-$M_*$) and the cosmic star formation rate density (CSFRD) for the simulated galaxy population and for the subsamples, which were divided into stellar mass bins in the given redshift. The simulated $Σ_{\rm SFR}$\ decreases by $\sim3.5$ dex from $z=12$ to $z=0$. We show that galaxies with different stellar masses have different paths of $Σ_{\rm SFR}$\ evolution. We find that $Σ_{\rm SFR}{\rm MS}$\ is already observed at $z\sim11$. The simulated $Σ_{\rm SFR}{\rm MS}$\ agrees with the observed one at $z=0, 1, 2, 5$, and $7.5$ and with individual galaxies at $z>10$. We show that the highest $Σ_{\rm SFR}{\rm MS}$\ slope of $0.709\pm0.005$ is at $z\sim3$ and decreases to $\sim0.085\pm0.003$ at $z=0$. This is mostly driven by a rapid decrease in SFR with an additional size increase for the most massive galaxies in this redshift range. This coincides with the dominance of the most massive galaxies in the CSFRD from the SAM.

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Binary progenitor systems for Type Ic supernovae

Core-collapse supernovae are explosions of massive stars at the end of their evolution. They are responsible for metal production and for halting star formation, having a significant impact on galaxy evolution. The details of these processes depend on the nature of supernova progenitors, but it is unclear if Type Ic supernovae (without hydrogen or helium lines in their spectra) originate from core-collapses of very massive stars (> 30 Msun) or from less massive stars in binary systems. Here we show that Type II (with hydrogen lines) and Ic supernovae are located in environments with similar molecular gas densities, therefore their progenitors have comparable lifetimes and initial masses. This supports a binary interaction for most Type Ic supernova progenitors, which explains the lack of hydrogen and helium lines. This finding can be implemented in sub-grid prescriptions in numerical cosmological simulations to improve the feedback and chemical mixing.

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The fate of the interstellar medium in early-type galaxies. IV. The impact of stellar feedback, mergers, and black holes on the cold ISM in simulated galaxies

Removing cold interstellar medium (ISM) from a galaxy is central to quenching star formation. However, the exact mechanism of this process remains unclear. The objective of this work is to find the mechanism responsible for dust and gas removal in simulated early-type galaxies (ETGs). A statistically significant sample of massive (M_*>$10^{10}$M$_\odot$), simulated ETG in a redshift range of 0.02--0.32 is studied in the context of its ISM properties. In particular, we investigate the cold dust and gas removal timescales, the cold gas inflows, and their relation with black hole (BH) mass. We also investigate the evolution of galaxies in the dust vs. star formation rate (SFR) plane and the influence of merger events. We find agreement with previous observational works considering the timescales of dust and HI removal from ETGs. When considering the dust-to-stellar mass ratio as a function of time in simulations, we recovered a similar decline as in the observational sample as a function of stellar age, validating its use for timing the ISM decline. Moreover, we recover the observed relation between dust mass and SFR for actively star-forming galaxies as well as for passive ETGs. We also show that starburst galaxies form their own sequence on the dust vs. SFR plot in a form $\log(M_{\rm dust, SB})= 0.913\times \log({\rm SFR}) + 6.533$ with $2σ$ scatter of 0.32. Finally, we find that type II supernova reverse shocks dominate the dust destruction at the early stages of ETG evolution, while at later times stellar feedback becomes more important. We show that merger events lead to morphological transformations by increasing the bulge-to-total stellar mass ratio followed by an increase in BH masses. The BH feedback resulting from radio mode accretion prevents the hot halo gas from cooling, indirectly leading to a decrease in the SFR.

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The Lockman--SpReSO project. Main properties of infrared selected star-forming galaxies

Methods.We applied distinct selection criteria to attain an SFG sample with minimal AGN contamination. Multiple approaches were used to estimate the intrinsic extinction, SFR and gas-phase metallicity for the SFGs. In conjunction with findings in the literature, we examined the correlation between SFRs and stellar masses ($M_*$), as well as the metallicity evolution depending on $M_*$. Finally, the 3D relationship between $M_*$, SFR and metallicity, is also studied.} Results. From the initial spectroscopic sample of 409 FIR-selected objects from the Lockman--SpReSO catalogue, 69 (17\%) AGNs have been identified and excluded, which is nearly double the percentage found in local studies, leaving a sample of 340 SFGs. The analysis of the $M_*$--SFR relationship revealed that Lockman--SpReSO IR-selected SFGs show signs of evolution at redshifts $z>0.4$, shifting above the main sequence, with a mean value of $\sim0.4$ dex. They are located within the starburst galaxy region since 78\% of the galaxies fall into this category. In addition, no evident flattening was found in the relation to specific SFR with redshift for $\log M_* (M_\odot) \gtrsim 10.5$. In line with the $M_*$--metallicity relation (MZR) outcomes published in previous studies for optically selected SFGs, however, during the analysis of the MZR, it was found that IR-selected SFGs exhibit lower metallicities than those anticipated on the basis of their $M_*$ and redshift. During the investigation of the 3D $M_*$--SFR--metallicity relation (FP), it was established that the research sample is consistent with relations in the existing literature, with an average scatter of $\sim0.2$ dex. However, a re-calibration of the FP when using the SFR obtained from the IR luminosity is required and, in this case, no attenuation in the correlation for $\log M_* (M_\odot) \gtrsim 10.5$ is observed.

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The Lockman-SpReSO project. Galactic flows in a sample of far-infrared galaxies

Methods. We performed measurements of the \MgII, \MgI, \FeIIa, \FeIIb, and \FeIIc\ spectral lines present in the spectra of the selected sample to determine the EW and velocity of the flows observed in the star-forming galaxies. Subsequently, we conducted $10^7$ bootstrap simulations using Spearman's rank correlation coefficient ($ρ_s$) to explore correlations with galaxy properties. Furthermore, we calculated the covering factor, gas density, and optical depth for the measured \ion{Fe}{II} doublets. Results. Our analysis revealed strong correlations between the EW of \ion{Mg}{II} lines and both $M_{*}$ ($ρ_s=0.43$, 4.5$σ$) and SFR ($ρ_s=0.42$, 4.4$σ$). For the \ion{Fe}{II} lines, we observed strong correlations between the EW and SFR ($ρ_s\sim0.65$, $>3.9σ$), with a weaker correlation for $M_{*}$ ($ρ_s\sim0.35$, $>1.9σ$). No notable correlations were found between velocity measurements of \ion{Mg}{II} line and $M_{*}$, SFR, or sSFR of the objects ($ρ_s\sim0.1)$. However, a negative strong correlation was found between the velocity of the \ion{Fe}{II} lines and the SFR of the galaxies ($ρ_s\sim-0.45$, $\sim3σ$). Our results align with previous studies but studying FIR-selected objects. Finally, we detected a candidate \textit{loitering outflow}, a recently discovered subtype of FeLoBAL quasar, at redshift of $z=1.4399$, exhibiting emission in \ion{C}{III}] and low line velocities ($|v|\lesssim$ 200 km/s).

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The Fate of the Interstellar Medium in Early-type Galaxies. II. Observational Evidence for Morphological Quenching

The mechanism by which galaxies stop forming stars and get rid of their interstellar medium (ISM) remains elusive. Here, we study a sample of more than two thousand elliptical galaxies in which dust emission has been detected. This is the largest sample of such galaxies ever analysed. We infer the timescale for removal of dust in these galaxies and investigate its dependency on physical and environmental properties. We obtain a dust removal timescale in elliptical galaxies of $τ$ = 2.26 $\pm$ 0.18 Gyr, corresponding to a half-life time of 1.57 $\pm$ 0.12 Gyr. This timescale does not depend on environment, stellar mass or redshift. We observe a departure of dusty elliptical galaxies from the star formation rate vs. dust mass relation. This is caused by the star-formation rates declining faster than the dust masses and indicates that there exists an internal mechanism, which affects star formation, but leaves the ISM intact. Morphological quenching together with ionisation or outflows caused by older stellar populations (supernova type Ia or planetary nebulae) are consistent with these observations.

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Main Sequence to Starburst Transitioning Galaxies: Gamma-ray Burst Hosts at $z\sim2$

Star-forming galaxies populate a main sequence (MS), a well-defined relation between stellar mass (M*) and star-formation rate (SFR). Starburst (SB) galaxies lie significantly above the relation whereas quenched galaxies lie below the sequence. In order to study the evolution of galaxies on the SFR-M* plane and its connection to the gas content, we use the fact that recent episodes of star formation can be pinpointed by the existence of gamma-ray bursts (GRBs). Here we present sensitive [CI]-nondetections of z$\sim$2 ultra luminous infrared (ULIRG) GRB host galaxies. We find that our GRB hosts have similar molecular masses to those of other ULIRGs. However, unlike other ULIRGs, the GRB hosts are located at the MS or only a factor of a few above it. Hence, our GRB hosts are caught in the transition toward the SB phase. This is further supported by the estimated depletion times, which are similar to those of other transitioning galaxies. The GRB hosts are [CI]-dark galaxies, defined as having a [CI]/CO temperature brightness ratio of <0.1. Such a low [CI]/CO ratio has been found in high-density environments (nH > 10$^4$ cm$^{-3}$) where CO is shielded from photodissociation, leading to under-abundances of [CI]. This is consistent with the merger process that is indeed suggested for our GRB hosts by their morphologies.

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Non-Sequential Neural Network for Simultaneous, Consistent Classification and Photometric Redshifts of OTELO Galaxies

Context. Computational techniques are essential for mining large databases produced in modern surveys with value-added products. Aims. This paper presents a machine learning procedure to carry out simultaneously galaxy morphological classification and photometric redshift estimates. Currently, only spectral energy distribution (SED) fitting has been used to obtain these results all at once. Methods. We used the ancillary data gathered in the OTELO catalog and designed a non-sequential neural network that accepts optical and near-infrared photometry as input. The network transfers the results of the morphological classification task to the redshift fitting process to ensure consistency between both procedures. Results. The results successfully recover the morphological classification and the redshifts of the test sample, reducing catastrophic redshift outliers produced by SED fitting and avoiding possible discrepancies between independent classification and redshift estimates. Our technique may be adapted to include galaxy images to improve the classification.

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The OTELO survey: the star formation rate evolution of low-mass galaxies

We present the analysis of a sample of \ha\,, \hb\ and \oii\ emission line galaxies from the \otelo\ survey, with masses typically below $log(M_*/M_\sun) \sim 9.4$ and redshifts between $z \sim 0.4$ and 1.43. We study the star formation rate, star formation rate density, and number density and their evolution with redshift. We obtain a robust estimate of the specific star formation rate -- stellar mass relation based on the lowest mass sample published so far. We also determine a flat trend of the star formation rate density and number density with redshift. Our results suggest a scenario of no evolution of the number density of galaxies, regardless of their masses, up to redshift $z\sim1.4$. This implies a gradual change of the relative importance of the star forming processes, from high-mass galaxies to low-mass galaxies, with decreasing redshift. We also find little or no variation of the star formation rate density in the redshift range of $0.4<z<1.43$.

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The OTELO survey: Revealing a population of low-luminosity current/active star-forming galaxies at z$\sim0.9$

We study a sample of H$β$ emission line sources at $z\sim$0.9 to identify the star-forming (SF) galaxies sample and characterise them in terms of line luminosity, stellar mass, SFR, and morphology. The final aim is to obtain the H$β$ luminosity function (LF) of the SF galaxies at this redshift. We used the instrument OSIRIS at GTC to obtain the pseudo spectra of emission line sources in the OTELO field. From these pseudo spectra, we identified the objects with H$β$ emission. As the resolution of the pseudo spectra allowed us to separate H$β$ from O[III], we derive the H$β$ flux without contamination. Using data from the extended OTELO catalogue, we discriminated AGNs and studied the SFR, the stellar mass, and the morphology of the SF galaxies. We find that our sample is located on the main sequence of SF galaxies. The sources are morphologically classified, mostly as disc-like galaxies (76%), and 90% of the sample are low-mass galaxies ($M_*<10^{10}\;\mathrm{M}_\odot$). The low-mass SF galaxies at $z \sim 0.9$ that were detected by OTELO present similar properties as low-mass SF galaxies in the local universe, suggesting that these kinds of objects do not have a favorite epoch of formation and star formation enhancement from $z \sim 1$ to now. Our sample of 40 H$β$ SF galaxies includes the faintest H$β$ emitters detected so far. This allows us to constrain the faint end of the LF for the H$β$ line alone with a minimum luminosity of $\log L = 39 \;\mathrm{erg\,s}^{-1}$, which is a hundred times fainter than previous surveys. The dust-corrected OTELO H$β$ LF established the faint-end slope as $α=-1.36\pm 0.15$. We increased the scope of the analysis to the bright end by adding ancillary data from the literature, which was not dust-corrected in this case. The obtained slope for this extended LF is $α= -1.43\pm 0.12$.

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Dust in the central parsecs of unobscured AGN: more challenges to the torus

A parsec-scale dusty torus is thought to be the cause of Active Galactic Nuclei (AGN) dichotomy in the 1/2 types, narrow/broad emission lines. In a previous work, on the basis of parsec-scale resolution infrared / optical dust maps it was found that dust filaments, few parsecs wide, several hundred parsecs long, were ubiquitous features crossing the centre of type 2 AGN, their optical thickness being sufficient to fully obscure the optical nucleus. This work presents the complementary view for type 1 and intermediate-type AGN. The same type of narrow, collimated, dust filaments are equally found at the centre of these AGN. The difference now resides in their location with respect to the nucleus, next to it but not crossing it, as it is the case in type 2, and their reduced optical thickness towards the centre, $A_V \lesssim 1.5 \rm{mag}$, insufficient to obscure at UV nucleus wavelengths. It is concluded that large scale, hundred pc to kpc long, dust filaments and lanes, reminiscent of those seen in the Milky Way, are a common ingredient to the central parsec of galaxies. Their optical thickness changes along their structure, in type 2 reaching optical depths high enough to obscure the nucleus in full. Their location with respect to the nucleus and increasing gradient in optical depth towards the centre could naturally lead to the canonical type 1/2 AGN classification, making these filaments to play the role of the torus. Dust filaments and lanes show equivalent morphologies in molecular gas. Available gas kinematic indicates mass inflows at rates $ < ~ 1 M\odot~ yr^{-1}$.

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The OTELO survey: Faint end of the luminosity function of [OII] emitters at = 1.43

In this paper, we aim to study the main properties and luminosity function (LF) of the [OII] emitters detected in the OTELO survey in order to characterise the star formation processes in low-mass galaxies at $z\sim1.43$ and to constrain the faint-end of the LF. Here, we describe the selection method and analysis of the emitters obtained from narrow-band scanning techniques. In addition, we present several relevant properties of the emitters and discuss the selection biases and uncertainties in the determination of the LF and the star formation rate density (SFRD). We confirmed a total of 60 sources from a preliminary list of 332 candidates as [OII] emitters. Approximately 93% of the emitters have masses in the range of $10^{8}<M_{*}/{\rm M_{\odot}}<10^{9}$. All of our emitters are classified as late-type galaxies, with a lower value of $(u-v)$\, when compared with the rest of the emitters of the OTELO survey. We find that the cosmic variance strongly affects the normalisation ($ϕ^*$) of the LF and explains the discrepancy of our results when compared with those obtained from surveys of much larger volumes. However, we are able to determine the faint-end slope of the LF, namely, $α=-1.42\pm0.06$, by sampling the LF down to $\sim1$\,dex lower than in previous works. We present our calculation of the SFRD of our sample and compare it to the value obtained in previous studies from the literature.

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The OTELO survey as a morphological probe. Last ten Gyr of galaxy evolution. The mass--size relation up to z=2

The morphology of galaxies provide us with a unique tool for relating and understanding other physical properties and their changes over the course of cosmic time. It is only recently that we have been afforded access to a wealth of data for an unprecedented number galaxies thanks to large and deep surveys, We present the morphological catalogue of the OTELO survey galaxies detected with the Hubble Space Telescope (HST)-ACS F814W images. We explore various methods applied in previous works to separate early-type (ET) and late-type (LT) galaxies classified via spectral energy distribution (SED) fittings using galaxy templates. Together with this article, we are releasing a catalogue containing the main morphological parameters in the F606W and F814W bands derived for more than 8\,000 sources. The morphological analysis is based on the single-Sérsic profile fit. We used the GALAPAGOS2 software to provide multi-wavelength morphological parameters fitted simultaneously in two HST-ACS bands. The GALAPAGOS2 software detects, prepares guess values for GALFTI-M, and provides the best-fitting single-Sérsic model in both bands for each source. Stellar masses were estimated using synthetic rest-frame magnitudes recovered from SED fittings of galaxy templates. The morphological catalogue is complemented with concentration indexes from a separate SExtractor dual, high dynamical range mode. A total of 8,812 sources were successfully fitted with single-Sérsic profiles. The analysis of a carefully selected sample of ~3,000 sources up to phot_z=2 is presented in this work, of which 873 sources were not detected in previous studies. We found no statistical evidence for the evolution of the low-mass end of mass-size relation for ET and LT since z=2. Furthermore, we found a good agreement for the median size evolution for ET and LT galaxies, for a given stellar mass, with the data from the literature.

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