arXiv subjects

Miguel Cerviño

Publications and source records attributed to Miguel Cerviño.

At least 19 recordsLinked to original sources

arXiv2026

Semiresolved Stellar Populations as Distance Indicators

Galaxy distances are central to our understanding of the Universe. Despite the success of existing approaches, independent and complementary methods remain valuable for testing systematic effects and extending the applicability range of different distance metrics. Here we demonstrate that the spectrum of an individual semi-resolved stellar population encodes direct information about its distance and that valuable distance constraints can, in principle, be obtained by combining multiple independent measurements. When applied to optical spectra of bulge of the Andromeda galaxy (M\,31), we derive a stellar population-based distance of 756$\pm$57 kpc ($μ_0 = 24.39 \pm 0.15$), in agreement with state-of-the-art measurements. Crucially, semi-resolved stellar population distances does not require secondary calibrations, although its absolute scale remains conditional on the adopted stellar population models. Our findings provide a first assessment of the feasibility of deriving stellar population-based distance estimates from simple stellar population models, motivating further tests of the broader applicability and precision of the method.

astro-ph.GA↗

arXiv2026

The Lockman-SpReSO Project: A Deep X-ray Spectral View of a FIR-selected AGN Population

We present a detailed X-ray spectral analysis of the active galactic nucleus (AGN) population in the Lockman-SpReSO project, a multiwavelength campaign of FIR sources in the Lockman Hole field. Using deep XMM-Newton observations cross-matched with FIR-selected galaxies, we characterize 94 AGNs based on their X-ray spectral properties. The sample is distributed over a large redshift range of $z = 0.07-5$, and reaches a flux limit of $5 \times 10^{-16}\, \mathrm{erg\, s^{-1}\, cm^{-2}}$ in the $0.3-10\, \mathrm{keV}$ band. We model the X-ray spectra using absorbed power-law, reflection, and soft excess components to estimate intrinsic column densities ($N_{\mathrm{H}}$), rest-frame $2-10\, \mathrm{keV}$ luminosities, and iron line equivalent widths $(EW)$. Additionally, we included an advanced model fitting for Compton-thick AGNs (CT-AGNs) using the XCLUMPY model. Our results show an increase in the fraction of obscured AGNs toward higher redshifts, including the identification of one strong and two borderline CT-AGN candidates with $N_{\mathrm{H}} \gtrsim 10^{24}\, \mathrm{cm^{-2}}$. Soft excess emission is detected in 10 AGNs, with an average blackbody temperature of $0.12 \pm 0.02\, \mathrm{keV}$. We also detect the X-ray Baldwin effect in both obscured and unobscured populations, and we found a strong correlation between the torus angular width $(σ_\mathrm{tor})$, dust covering factor $(f_{\mathrm{cov}})$, and X-ray luminosity, described by $f_{\mathrm{cov}} = (-0.1 \pm 0.01) \times \log(L_{2-10\, \mathrm{keV}}/(10^{44}\, \mathrm{erg\, s^{-1}})) + (0.65 \pm 0.01)$, supporting the receding torus scenario. While consistent with deep X-ray surveys, the FIR selection favours the identification of dusty star-forming host galaxies and heavily obscured AGNs.

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arXiv2026

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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arXiv2026

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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arXiv2026

FASTAR -- II. Semi-resolved evolutionary stellar population models

Standard evolutionary synthesis models rely on the assumption of a fully sampled stellar initial mass function (IMF). Under this assumption, the age, chemical composition, and IMF uniquely define the predicted absorption spectra. However, with current instrumentation pushing observations towards higher spatial resolutions and lower surface brightnesses, the assumption of a fully sampled IMF does not always hold true. Here we present the semi-resolved version of the FASTAR models, a comprehensive set of evolutionary synthesis predictions able to reproduce the stochastic behavior of discretely-sampled IMFs. Semi-resolved FASTAR predictions share the same evolutionary principles, ingredients, and features of the integral (fully sampled IMF) version of the FASTAR models, expanding a range of ages from 20 Myr to 14 Gyr, metallicities between -2.5 < [M/H] < +0.3, and several IMF functional forms. Detailed spectroscopic measurements can be carried out within the 3,540-7,400 A wavelength range, and low-resolution spectral energy distributions can also be synthesized over a wider 2,000-to-12,000 A coverage. Semi-resolved FASTAR models also depend on the number of stars contributing to the observed spectra, which determines the effective sampling of the different stellar evolutionary phases along the isochrones. This incomplete sampling implies that semi-resolved FASTAR models are inevitably stochastic. On top of the inherent stochasticity of the models, derived quantities such as equivalent widths, colors, or mass-to-light ratios might present strong deviations compared to standard fully sampled simple stellar population models. This stochasticity dilutes the boundary between model predictions and data, promoting new sampling-based inference approaches. FASTAR semi-resolved models allow for the effective exploration of the parameter space thanks to their optimized, JAX-based computation.

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arXiv2026

Recalibration of the H$α$ surface brightness-radius relation for planetary nebulae using Gaia DR3: new distances and the Milky Way oxygen radial gradient

The spatial distribution of chemical elements in the Galactic disk provides key constraints on models of galaxy evolution. However, studies using planetary nebulae (PNe) as tracers have been historically limited by large uncertainties in their distances. To overcome the long-standing distance uncertainties, we recalibrated the H$α$ surface brightness-radius relation from Frew et al. with Gaia DR3 parallaxes, deriving distances for 1,130 PNe of which 415 have Bayesian distances based on Gaia DR3 parallaxes. The O/H radial gradient for 231 disk PNe is fitted considering three models: a single linear gradient and segmented linear fits with one or two breaks. The segmented fits indicate a change in slope near the solar radius (R ~8 kpc), with a flatter or slightly positive gradient inward and a steeper negative gradient outward. This feature may reflect changes in star formation efficiency driven by the Galactic bar or the corotation resonance of the spiral arms. The breaks in the metallicity radial gradients observed in this work may result from the superposition of distinct stellar populations associated with the thin and thick disks. The two-dimensional O/H distribution in the Galactic plane supports the adopted distances and reveals modest azimuthal asymmetry, with enhanced abundances near the bar at positive longitudes, and a bimodal abundance structure between the inner and outer solar regions. Our results provide new constraints on the chemical evolution of the Milky Way, the impact of non-axisymmetric structures, and the possible existence of distinct radial abundance regimes across the Galactic disk.

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arXiv2025

Science Enabled by a 30-Meter-Class Telescope in the Northern Hemisphere: Massive Stars at Low Metallicity

Massive stars are at the core of our observations of the Universe up to the reionization epoch, both through their intense ionizing fluxes and through the energetic end products that release fresh elements into the interstellar medium. Our interpretation of very high redshift galaxies and transient phenomena depends on knowledge derived from massive star populations in the Milky Way and nearby galaxies, with characteristics that only remotely resemble the conditions in the early Universe. However, the models supporting these interpretations have been tested in a narrow range of environments and carry significant uncertainties when extrapolated. Advancing in our understanding of the Universe beyond the Local Volume therefore requires extending massive star studies to conditions representative of the early Universe. The next generation of telescopes has the potential to accomplish this goal.

astro-ph.IM↗

arXiv2025

GLACE survey: OSIRIS/GTC multi-object spectroscopy of the rich galaxy cluster ZwCl 0024.0+1652 at z~0.4. III. The mass-SFR relation and the quenching of cluster galaxies

Galaxy clusters are among the largest and densest structures in the Universe. Their high density generally increases the suppression of star formation, known as quenching, altering galaxy properties. We study the quenching of emission-line galaxies (ELGs) in the rich cluster ZwCl 0024.0+1652 (Cl0024) at redshift $z\sim0.4$, aiming to determine if and how star formation is suppressed. Using multi-object spectroscopy from the GLACE survey, we extracted fluxes and redshifts of [O II]$λ\lambda3727,3729$, $\mathrm{Hβ}$, and [O III]$\lambda5007$ emission lines to derive star formation rates (SFRs) for 173 ELGs. We also performed spectral energy distribution fitting to obtain key evolutionary parameters such as stellar masses ($M_\star$) and the 4000 Å break ($D4000$) index. We derived the $M_\star-\mathrm{SFR}$ relation for 98 star-forming galaxies (SFGs), finding 34.7% exhibit suppressed SFRs in the cluster, compared to 11.0% in the field. While the SFRs show no significant variation with local density, the fraction of SFGs is 1.55 times higher in the cluster outskirts than in intermediate-density regions. The specific SFR decreases strongly with $D4000$ for active SFGs but remains constant for suppressed galaxies. The fraction of suppressed galaxies in the infall region is 2.6 times higher than in the core, especially in the infalling structure B of the cluster. The cluster's total mass does not appear to be a key factor in SFG quenching. Star formation in Cl0024 galaxies is suppressed by the dense cluster environment. This suppression is evident in SFG fractions and parameters tracing long-term evolution, indicating prolonged quenching. The SFGs preferentially reside in low-density regions, while suppressed galaxies dominate the infall region, supporting a 'delayed-then-rapid' quenching scenario.

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arXiv2025

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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arXiv2025

A reference framework for extremely metal-poor OB star studies: calibrations for stellar parameters and intrinsic colours

We provide the first reference framework for extremely metal-poor (XMP) OB-type stars. We parsed a grid of 0.10 $Z_{\odot}$ FASTWIND models, covering the parameter space of O stars and early-B supergiants, through contemporary spectral classification criteria to deliver a calibration of key stellar properties as a function of spectral type, and tabulated colours for the most common photometric systems. By using an extensive grid of models, we account for the different combinations of stellar parameters that result in the same spectral morphology and provide a range of parameters and colours compatible with each spectral subtype and luminosity class. We supply updated photometric criteria to optimize candidate selection of OB stars in XMP environments. We find 0.10 $Z_{\odot}$ OB stars are 1-6 kK hotter and produce higher ionizing fluxes than their Galactic analogues. In addition, we find a bimodal distribution of the HeII-ionizing flux with spectral type; because of its known dependence on effective temperature and the wind, $\log~q_{HeII}$ for individual XMP late-O type stars could be underestimated by up to 4 orders of magnitude by other calibrations, some of them used by population synthesis codes. Finally, we used our calibrated colours to map the extinction of the 0.10 $Z_{\odot}$ galaxy Sextans A finding that reddening is non-negligible and uneven.

astro-ph.SR↗

arXiv2024

X-ray analysis of Seyfert 1 galaxies with optical polarization: a test for unification models

In accordance with the AGN Unified Model, observed polarization can be related to the orientation of the line of sight with respect to the torus. AGN X-ray emission arises from the central region and carries the imprints of the obscuring material. We aim to test a unified scheme based on optical polarization using X-ray absorption. Using the XMM-Newton data of 19, optically polarized Seyfert 1 sources, we developed a systematic analysis by fitting a baseline model to test the presence of X-ray neutral or ionized (warm) absorption. We find that 100\% of the polar-polarized sources show the presence of absorption, with 70\% favoring the presence of a warm absorber. In contrast, the equatorial-polarized sources show a fraction of absorbed spectra of 75\%, with only 50\% consistent with the presence of a warm absorber.

astro-ph.HE↗

arXiv2024

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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arXiv2024

GLACE survey: OSIRIS/GTC tuneable imaging of the galaxy cluster ZwCl 0024.0+1652 II. The mass--metallicity relationship and the effect of the environment

In this paper, we revisit the data for the galaxy cluster ZwCl 0024.0+1652 provided by the GLACE survey and study the mass--metallicity function and its relationship with the environment. Here we describe an alternative way to reduce the data from OSIRIS tunable filters. This method gives us better uncertainties in the fluxes of the emission lines and the derived quantities. We present an updated catalogue of cluster galaxies with emission in H$α$ and [N\,{\sc{ii}}] $λλ$6548,6583. We also discuss the biases of these new fluxes and describe the way in which we calculated the mass--metallicity relationship and its uncertainties. We generated a new catalogue of 84 emission-line galaxies with reliable fluxes in [N\,{\sc{ii}}] and H$α$ lines from a list of 174 galaxies. We find a relationship between the clustercentric radius and the density of galaxies. We derived the mass--metallicity relationship for ZwCl 0024.0+1652 and compared it with clusters and field galaxies from the literature. We find a difference in the mass--metallicity relationship when compared to more massive clusters, with the latter showing on average higher values of abundance. This could be an effect of the quenching of the star formation, which seems to be more prevalent in low-mass galaxies in more massive clusters. We find little to no difference between ZwCl 0024.0+1652 galaxies and field galaxies located at the same redshift.

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arXiv2024

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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arXiv2022

A new reference catalogue for the very metal-poor Universe: +150 OB stars in Sextans A

Local Group (LG) very metal-poor massive stars are the best proxy for the First Stars of the Universe and fundamental to modelling the evolution of early galaxies. These stars may follow new evolutionary pathways restricted to very low metallicities, such as chemically homogeneous evolution (CHE). However, given the great distance leap needed to reach very metal-poor galaxies of the LG and vicinity, no comprehensive spectroscopic studies have been carried out at metallicities lower than the Small Magellanic Cloud (SMC, Z = 1/5 Z$_{\odot}$) until now. After five observing campaigns at the 10.4-m Gran Telescopio Canarias, we have assembled a low-resolution (R $\sim$ 1000) spectroscopic collection of more than 150 OB stars in the 1/10 Z$_{\odot}$ galaxy Sextans A, increasing by an order of magnitude the number of massive stars known in this galaxy. The catalogue includes 38 BA-type supergiants, 4 red supergiants, and the first candidate 1/10 Z$_{\odot}$ binary systems, CHE sources and systems hosting stripped stars. The sample massive stars mainly overlap the higher concentrations of neutral gas of Sextans A. However, we find some sources in low HI column-density regions. The colour-magnitude diagram of the galaxy presents large dispersion, which suggests uneven, internal extinction in Sextans A. This is the largest catalogue of OB-type stars ever produced at sub-SMC metallicities. This sample constitutes a fundamental first step to unveiling the evolutionary pathways and fates of very metal-poor massive stars, analyzing the dependence of radiation-driven winds with metallicity, and studying binary systems in an environment analogue to the early Universe.

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arXiv2021

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.

astro-ph.IM↗

arXiv2021

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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arXiv2021

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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