The ﬁrst catalogue of spectroscopically conﬁrmed red nuggets at z ∼ 0.7 from the VIPERS survey Linking high-z red nuggets and local relics

Context. ’Red nuggets’ are a rare population of passive compact massive galaxies thought to be the ﬁrst massive galaxies that formed in the Universe. First found at z ∼ 3, they are even less abundant at lower redshifts, and it is believed that with time they mostly transformed through mergers into today’s giant ellipticals. Those red nuggets which managed to escape this fate can serve as unique laboratories to study the early evolution of massive galaxies. Aims. In this paper, we aim to make use of the unprecedented statistical power of the VIMOS Public Extragalactic Redshift Survey to build the largest up-to-date catalogue of spectroscopically conﬁrmed red nuggets at the intermediate redshift 0 . 5 < z < 1 . 0. Methods. Starting from a catalogue of nearly 90000 VIPERS galaxies we select sources with stellar masses M star > 8 × 10 10 M (cid:12) and e ﬀ ective radii R e < 1 . 5 kpc. Among them, we select red, passive galaxies with old stellar population based on colour–colour NUVrK diagram, star formation rate values, and veriﬁcation of their optical spectra. Results. Verifying the inﬂuence of the limit of the source compactness on the selection, we found that the sample size can vary even up to two orders of magnitude, depending on the chosen criterion. Using one of the most restrictive criteria with additional checks on their spectra and passiveness, we spectroscopically identiﬁed only 77 previously unknown red nuggets. The resultant catalogue of 77 red nuggets is the largest such catalogue built based on the uniform set of selection criteria above the local Universe. Number density calculated on the ﬁnal sample of 77 VIPERS passive red nuggets per comoving Mpc 3 increases from 4.7 × 10 − 6 at z ∼ 0 . 61 to 9 . 8 × 10 − 6 at z ∼ 0 . 95, which is higher than values estimated in the local Universe, and lower than the ones found at z > 2. It ﬁlls the gap at intermediate redshift. Conclusions. A catalogue of red nuggets presented in this paper is a golden sample for future studies of this rare population of objects at intermediate redshift. Besides covering a unique redshift range and careful selection of galaxies, the catalogue is spectroscopically identiﬁed.


Introduction
Morphological classification of galaxies splits them into two main groups, early types and late types (Hubble 1926).The early-type galaxies (ETGs) are spheroidal objects with smooth brightness distributions, low star formation rates (SFRs), and stellar content dominated by evolved stars.The late-type galaxies are at the opposite side of Hubble's tuning fork diagram; they are mostly spiral galaxies and contain both young and evolved stars (Kennicutt 1998).
It has been shown that the most massive ETGs in the local Universe differ significantly from their counterparts at high redshifts (z > 2).These high-redshift ETGs are extremely com-pact, a few times smaller in size than their local counterparts (Daddi et al. 2005;Trujillo et al. 2007;Damjanov et al. 2009;van der Wel et al. 2014).According to the two-phase formation scenario, during the initial phase dominated by numerous wet mergers between gas-rich galaxies and characterised by high SFRs, progenitors of ETGs increase their stellar mass rapidly, even up to M star ∼ 10 11 M , but remain compact in size (Oser et al. 2010).Subsequently, star formation in these compact and massive objects quenches quickly, and the galaxies become passive, compact, and massive.At this stage, they are referred to as a red nuggets.In the second, final phase, red nuggets undergo dry mergers with other gas-poor galaxies, which results in the increase in their size and their transformation into giant elliptical galaxies (van Dokkum et al. 2010).This two-phase scenario was predicted by models and simulations (Naab et al. 2009;Zolotov et al. 2015;Flores-Freitas et al. 2021), and has since been confirmed observationally (Barro et al. 2013;Zibetti et al. 2020).
Due to the stochastic nature of mergers, some red nuggets skip the second phase of the two-phase scenario and end as 'relics' (Ferré-Mateu et al. 2017).Red nuggets (relics) provide a unique opportunity to study stellar populations that remained relatively unaltered for billions of years.Even so, direct observational studies of red nuggets have been cursory so far due to the high redshift and the lack of sufficient angular resolution.Moreover, the probability of finding relics in the local Universe is very low as most of them have already merged.High-resolution cosmological simulations predict that the fraction of z ∼ 2 red nuggets that evolve into local Universe relics is less than 15% (Quilis & Trujillo 2013;Wellons et al. 2016;Furlong et al. 2017).These predictions vary depending on the exact description of physical processes influencing the galaxy evolution, in particular stellar winds or active galactic nucleus (AGN) feedback, in the simulations.
Even though there are numerous observational studies dedicated to identifying relics at the lowest redshifts, z ≤ 0.2, the estimated number densities in the different samples differ by a few orders of magnitude (Trujillo et al. 2009;Taylor et al. 2010;Valentinuzzi et al. 2010;Poggianti et al. 2013;Saulder et al. 2015;Tortora et al. 2016;Ferré-Mateu et al. 2017;Scognamiglio et al. 2020).A likely reason for these differences is the different selection criteria for compact sources applied by the authors.At redshifts from 0.2 to 0.5 there are studies that show similar number densities of relics or ultracompact massive galaxies (UCMGs), reporting many of these kinds of objects in systematic wide-field surveys (Tortora et al. 2016;Charbonnier et al. 2017;Buitrago et al. 2018;Scognamiglio et al. 2020).However, the quantitive comparison of the number densities is not straightforward due to different selection compactness criteria.Finally, at redshifts from 0.5 to 3, the limited angular resolution and a lack of systematic wide-field spectroscopic surveys hinder the detection of passive UCMGs (Barro et al. 2013;van der Wel et al. 2014;van Dokkum et al. 2015).
In the present paper we explore the galaxy sample from the VIMOS Public Extragalactic Redshift Survey (VIPERS, Scodeggio et al. 2018), which is a spectroscopic survey of about 90 000 galaxies at redshift 0.4 < z < 1.2, to spectroscopically identify new red nuggets at intermediate redshift.The availability of spectra provides a major improvement over most previous observational studies of red nuggets since it allows us to confirm and precisely measure their redshifts, which is critical for estimating the physical quantities of galaxies.Moreover, our intermediate redshift sample offers a unique opportunity to bridge the gap between high-redshift red nuggets and their local counterparts.
The paper is organised as follows.In Sect. 2 we present the VIPERS survey and observational data relevant for this work, in particular effective radii and stellar masses.We also describe the initial sample selection criteria used for further analysis.Section 3 follows, with a discussion about our spectral energy distribution fitting procedure and re-estimating stellar masses.The final selection of red nuggets, including compactness discrepancy and passiveness criteria is presented in Sect. 4. In Sect. 5 the properties of red nuggets are shown.Finally, a discussion and a comparison with other results are provided in Sect.6, followed by a summary in Sect.7.

Data
The VIMOS Public Extragalactic Redshift Survey (hereafter VIPERS) is a completed ESO Large Program, which was designed to investigate the spatial distribution of galaxies over the z ∼ 1 Universe (Scodeggio et al. 2018).It extends over an area of 23.5 deg 2 and provided a catalogue of spectroscopic redshifts for nearly 90 000 galaxies.Spectroscopic targets were selected within the W1 and W4 fields of the Canada-France-Hawaii Telescope Legacy Survey Wide (CFHTLS-Wide) to a limit of i < 22.5 mag, with a simple and robust (r − i) vs. (u − g) colour-colour pre-selection to effectively remove galaxies at z < 0.5.The spectra were observed using the VIMOS spectrograph (Le Fèvre et al. 2003) with the LR Red grism, providing a wavelength coverage of 5500-9500 Å with a resolution R 220.Taking into account volume and sampling, VIPERS can be considered the intermediate redshift (z ∼ 0.7) equivalent of state-of-the-art local surveys (z < 0.2), such as the 2dF Galaxy Redshift Survey (2dFGRS; Colless et al. 2001) and Sloan Digital Sky Survey (SDSS; York et al. 2000;Ahumada et al. 2020).
The quality of the VIPERS redshift measurement is quantified at the time of validation by attributing a redshift flag (z flag ).The z flag ranges from a value of 4 (>99% confidence that the redshift measurement is secure) to 0 (no redshift estimate).In the following analysis, we consider only objects whose redshift measurement quality was higher than 95%: z flag ∈ {3, 4, 23, 24} (Garilli et al. 2014;Scodeggio et al. 2018), where 23 and 24 stand for >95% confidence of the measured spectroscopic redshift for serendipitous targets.A detailed description of the survey is given by Guzzo et al. (2014) and Scodeggio et al. (2018), and the specifications of the pipeline used for data reduction with the quality flag system are described by Garilli et al. (2014).
In the following analysis, in particular the number density estimations, we also used the spectroscopic success rate (SSR) and the target sampling rate (TSR).Both parameters provide information about the completeness of the VIPERS parent catalogue (more details can be found in Sect. 1 of Scodeggio et al. 2018).The SSR is the fraction of all detected targets with a reliable spectroscopic redshift measurements.Only ∼45% of available targets were assigned a slit.For this reason, TSR is defined as the fraction of candidate galaxies for which spectrum has been acquired.For detailed description, we refer to Garilli et al. (2014).
The VIPERS spectroscopic data are accompanied by a wealth of ancillary information.In particular, in this work we make use of the multiwavelength photometric catalogue (see Sect. 2.1) and physical parameters derived via spectral energy distribution (SED) fitting by Moutard et al. (2016a;see Sect. 2.2), as well as morphological parameters derived by Krywult et al. (2017;see Sect. 2.3).

Photometric data
Photometric data for this analysis has been taken from the VIPERS database (Moutard et al. 2016b) providing multiwavelength observations from the ultraviolet (UV) to the infrared (IR) wavelengths.The catalogue combines Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) T0007-based photometric measurements in u, g, r, i, y, and z filters (the filter i broke in 2006, and was replaced by a similar but not identical A95, page 2 of 16  1 shows the photometric bands used for our data with its centred wavelength.

Stellar mass
Stellar masses, M star , for VIPERS galaxies used in the initial sample selection were derived by Moutard et al. (2016a) using the stellar population synthesis models of Bruzual & Charlot (2003) with Le Phare (Arnouts et al. 1999;Ilbert et al. 2006).
Throughout the procedure of modelling, the authors followed Ilbert et al. (2013).Values of stellar masses correspond to the median of the stellar mass probability distribution marginalised over all other fitted parameters.It should be noted that these stellar masses do not have uncertainties, which has an important impact on our further analysis.For details see Moutard et al. (2016a).

Effective radii and morphological parameters
The radial surface brightness profiles of the galaxies can be modelled by a Sérsic profile (Sérsic 1963(Sérsic , 1968)), where R e is the radius enclosing half of the total light of the galaxy, I e is the mean surface brightness at R e , and n is the Sérsic index.The coefficient b n depends on the value of n and is defined in such a way that R e encloses half of the total light (Graham & Driver 2005).
A single-component 2D Sérsic profile fitting was done by Krywult et al. (2017) on the CFHTLS i-band images of the VIPERS galaxies using GALFIT (Peng et al. 2002).Since GAL-FIT performs an elliptical isophotal fitting, it provides the semimajor axis (a e ) corresponding to the R e , and an axis ratio (b/a) for a galaxy.Therefore, in the following analysis, we use the circularised half-light radius (R e = a e √ b/a) in order to compare our results with other studies.
The goodness of the fit is measured by reduced χ 2 , and we refer to it as χ 2 GALFIT .The accuracy of structural parameters was derived from simulated galaxies on CFHTLS images, returning the uncertainties on effective radii measurements at the level of 4.4% for 68% of the VIPERS sample, and at the level of 12% for 95% of the VIPERS sample.A detailed description of VIPERS morphological parameters can be found in Krywult et al. (2017).

Initial sample selection
The VIPERS survey contains spectroscopic observations of 91 507 sources, including stars and AGN.Aiming at building a sample of VIPERS red nuggets we started from the selection of an initial pure sample.

Secure redshift measurements and redshift range
Firstly, we selected 54 252 objects with secure redshift measurements with a confidence level higher than 95% (with z flag ∈ {3, 4, 23, 24}; see Garilli et al. 2014, for details).In the next step, we selected our sample based on the redshift range.Narrowing the redshift range to 0.5 ≤ z ≤ 1 due to the colour completeness of VIPERS survey (Fritz et al. 2014) further reduced the sample to 44 145 galaxies.

Effective radii quality
In the following step, we restricted this sample to 36 635 sources, for which R e uncertainties were derived.The absence of uncertainties in R e indicates a problem in the convergence of the fitting procedure (for details, see Krywult et al. 2017) and such objects are not suitable for this analysis.We furthermore only considered sources with values of χ 2 GALFIT smaller than 1.2.Moreover, following Krywult et al. (2017), we also removed the galaxies with a Sérsic index n < 0.2, as the estimated morphological properties for such sources may be unreliable.The last criterion to select our pure sample is the reliability of R e measurements with relative errors <100%.Finally, it gave us 36 157 sources (hereafter pure sample).

Stellar mass and compactness
In the next step, we performed a further selection from the pure sample by taking into account the physical properties of the observed objects, namely stellar masses, M star , and effective A95, page 3 of 16 radii, R e , which are already available (see Sects.2.2 and 2.3).The most important criterion used to find the UCMGs is compactness, but the ambiguity in the literature is strong (see Table 3).All of these criteria are based on the position of selected objects in the R e vs. M star diagram.The chosen threshold crucially affects the number of galaxies in the selected sample.In order to maximise our sample of potential UCMGs, we first applied the most liberal threshold proposed by (Damjanov et al. 2015, whose original equation is shown in Table 3).As we do not have information about the uncertainties of given stellar masses, we slightly modified the Damjanov et al. (2015) criterion by adding 0.1 dex to R e : (log(R e ) + 5.74 − 0.1)/ log(M star /M ) < 0.568. (2) This was necessary to ensure that we did not remove any probable UCMGs from further analysis due to inaccurate stellarmass estimates from Le Phare (Arnouts et al. 1999;Ilbert et al. 2006).This additional arbitrary change of 0.1 dex results in 2571 galaxies added to the final analysis.It corresponds to the ∼58% increase in the number of analysed galaxies compared to the original Damjanov et al. (2014) criterion.While our 0.1 dex is arbitrary, as described in the following sections we found no red nugget candidates in the M star -R e space between the original Damjanov et al. ( 2014) criterion and the one enlarged by 0.1 dex.This serves as an additional sanity check that no UCMGs are hiding above the Damjanov et al. (2014) selection.This criterion narrows down the initial sample to 6961 galaxies (hereafter UCMG candidates).The summary of all performed cuts until this point, their order, and their impact on the sample are presented in Table 2.

Pure initial sample
The distribution of the VIPERS pure sample in the M star -R e plane is shown in Fig. 1.The orange dashed line represents the cut defined by Eq. (2).The original limit from Damjanov et al. (2015) is plotted with a magenta dash-dotted line.The blue solid line shows one of the most conservative criteria for compactness found in the literature (Trujillo et al. 2009) and the red points show our final catalogue of 77 VIPERS red nuggets (details in Sect.4).The orange solid line in Fig. 2 represents the seeingdetection limit.The CFHTLS i images used by Krywult et al. (2017) have a pixel scale of 0.186 .The mean seeing, defined by the full width at half maximum (FWHM) of stellar sources, depends on the CFHTLS filter.According to Goranova (2009), it is equal 0.64 for the i/iy-band.The angular size limit is transformed into physical units of R e as a function of redshift, which is shown as an orange solid line in Fig. 2. The vast majority of the pure sample (33 810, ∼93.5%) and the UCMG candidates (5673, ∼81%) have sizes larger than the pixel size.We decided not to remove sources lying below the seeing-detection limit by default, but in the next steps of our analysis we verified their properties more carefully (see Sect. 4).

Stellar mass re-estimation
We decided to recalculate the stellar masses of the UCMG candidates as a part of the quality check.As the stellar mass is one of the two parameters that characterise compact sources, it is necessary to take into account the goodness of the fit and uncertainties, which were not derived so far for VIPERS galaxies.For this purpose we used the state-of-art SED fitting tool called  (Arnouts et al. 1999;Ilbert et al. 2006) and found homogeneous results, which suggests that our SED fitting procedure is independent of the SED fitting methodology.In this analysis we assumed a delayed star formation history, Bruzual & Charlot (2003) single stellar population models with the initial mass function (IMF) given by the Chabrier (2003) and Charlot & Fall (2000) attenuation law, and the dust emission models of Dale et al. (2014) to build a grid of models.
In the case of stellar mass estimation, the used attenuation curve plays a significant role (on average leading to disparities of a factor of two, Małek et al. 2018;Buat et al. 2019).For this reason we decided to test two very well-known attenuation laws: the modified attenuation laws of Charlot & Fall (2000) and Calzetti et al. (2000).As the VIPERS sample lacks reliable IR data we decided to use the Calzetti et al. (2000) law.Here we note that the stellar mass obtained with the Charlot & Fall (2000) recipe is systematically higher by ∼0.1 dex than the Calzetti et al. (2000) value.A more detailed description can be found in Appendix A. Moreover, we suspect that the amount of dust in the galaxies we are looking for is rather low, and therefore we do not expect to find a huge difference between the two methods.Nevertheless, in our SED fitting approach, for the dust attenuation model, we used a wide range of parameters, allowing us to construct and fit templates similar to normal star-forming galaxies with a significant amount of dust.The final input parameters used in SED fitting with CIGALE are presented in Table A.1.A detailed description of each module can be found in Małek et al. (2018) and Boquien et al. (2019).
CIGALE estimates the physical properties of galaxies by evaluating a generated grid of models on data to minimise the likelihood distribution.The quality of the fit is expressed by the reduced value of the χ2 parameter1 .The physical properties and their uncertainties are estimated as the likelihood-weighted means and standard deviations.The mean goodness of the fit in the UCMG candidates sample, assuming input as shown in Table A.1, is χ 2 0.8, and the mean uncertainties of stellar masses are at the level of 19%.Hereafter, every time the stellar masses of UCMG candidates is mentioned, we refer to M star obtained by our SED fitting.

Final selection of red nugget sample
In this section we present the final criteria used to select the population of VIPERS red nuggets from our sample of 6961 UCMG candidates.In particular, we considered different definitions of compactness given by the limits in size, R e , and stellar mass, M star , followed by restricting the sample to red passive galaxies based on their colours and SFRs.

Compactness
The criterion used to select UCMGs, in particular the threshold for stellar mass and effective radius, has a great influence on the size and properties of the selected sample.Several different studies defined the class of massive compact galaxies based on various selection criteria (e.g., Trujillo et al. 2009;Damjanov et al. 2015;Charbonnier et al. 2017).To make a reliable comparison with the literature, we adopted different definitions following the selections that other authors have used.The list of criteria applied to select massive and compact galaxies is given in Table 3. Different criteria can change the number of UCMGs by a factor of ∼50.In particular, using the least conservative criterion proposed by Damjanov et al. (2015) we end up with 4347 UCMGs, while the criterion of Charbonnier et al. (2017) defined in the same redshift range results in 1061 galaxies.In our VIPERS red nuggets catalogue we included only sources that meet one of the most restrictive criteria given by authors.We used the criterion proposed by Trujillo et al. (2009), M star > 8 × 10 10 (log(M star /M ) 10.9) and R e > 1.5 kpc, which limits the sample to only 86 objects (hereafter VIPERS UCMGs).
A95, page 5 of 16 We performed a test and found, when applying compactness and stellar mass completeness cuts together, that the Cassata et al. ( 2011) criterion gives fewer sources above the stellar mass completeness threshold (82 red nugget candidates vs. 86 from the Trujillo et al. 2009 criterion).However, we wanted to focus on truly compact objects, thus we used the Trujillo et al. (2009) criterion, which uses a very strict R e value.Moreover, the Trujillo et al. (2009) criterion is the easiest to perform as it has two separate cuts for stellar mass and effective radius.It allowed us to control the compactness cuts, and also allowed easy comparison with mass completeness.
The Trujillo et al. (2009) criterion was used in the literature to select UCMGs up to z ∼ 0.5 (Tortora et al. 2016;Scognamiglio et al. 2020).Although this work aims to select UCMGs at the intermediate redshift range (0.5 < z < 1.0), we do not expect significant changes in the selection criterion.We assume that if UCMGs survive from z > 3 to the local Universe, z < 1, then their main physical properties such as R e and M star do not change significantly.This implies that they evolved relatively unaltered, without mergers or influence of other galaxies.For this reason, we can use the same compactness criterion for UCMGs from z ∼ 2 to z ∼ 0.
According to Davidzon et al. (2016), applying a cut in stellar mass ensures stellar mass completeness in the VIPERS sample up to z = 0.9 (log(M star /M ) ≥ 10.86).We calculated the stellar mass threshold above which passive galaxies can be considered complete in stellar mass in the redshift range 0.9-1.0.We found, using the Pozzetti et al. (2010) method, which was also used in Davidzon et al. (2016), a stellar mass threshold at the limit of log(M star /M ) = 11.03.However, taking into account the small number of known red nuggets at intermediate redshifts, we decided to enlarge our analysis using the same cut in mass, log(M star /M ) = 10.86, up to redshift 1, even with possible incompleteness bias for the most distant sources.In this step of our selection, we also took into account the seeing-size limit.As we mentioned before, the majority of UCMG candidates (5673, ∼81%) are larger than the size of a pixel, but ∼73% (63 galaxies) of VIPERS UCMGs have size measurements below the seeingdefined limit (see Fig. 2).After visual inspection of a sample of 86 VIPERS UCMGs we found that images of all selected galaxies show compact and elliptical galaxy profiles with no sign of spiral arms or other morphological disturbances, and we decided to use all of them in our further analysis.

Passiveness
To select red and passive galaxies, we performed a multistage selection based on the colours, emission lines, and final visual inspection.

NUVrK diagram
The primary criterion used to select red sources in our work is their position on the colour-colour diagram.We used the NUVrK diagram, which is a tool for selecting a complete and pure sample of red passive galaxies as this combination of colours allows us to break the dust-SFR degeneracy (Arnouts et al. 2013).It is widely used by the VIPERS team, see for example Fritz et al. (2014), Davidzon et al. (2016), Moutard et al. (2016bMoutard et al. ( , 2018)), Gargiulo et al. (2017), Siudek et al. (2018a,b), andTurner et al. (2021).The NUVrK diagram is shown in Fig. 3.The orange line shows the boundary between red and blue galaxies derived by Moutard et al. (2016b) obtained for the VIPERS survey.As can be clearly seen, seven galaxies lie below the limit, even when taking into account the uncertainties.These seven galaxies are indicated by green crosses and have been removed from our sample for the next steps, leaving 79 objects.

Visual inspection of VIPERS spectra
To verify the passiveness of the selected 79 red UCMGs, we checked their spectra obtained by VIPERS.We performed a detailed visual inspection of every object in the sample, searching for characteristic features that indicate star-forming activity, such as oxygen emission lines (Kennicutt 1992), lack of CaII absorption lines, or low Balmer break values (hereafter D4000; Bruzual 1983;Haines et al. 2017).Figure 4 shows examples of possibly active (top panel) and passive (bottom panel) galaxies in our sample of VIPERS UCMGs.The major differences are the presence of a strong O[II] emission line, the lack of the CaII absorption lines, and a weak D4000 in the active spectrum (top panel).In our sample of 79 UCMGs, we found two objects which likely show active galaxy features.At this point, we are left with 77 UCMGs that we consider red nugget candidates.

Sanity check
As a final sanity check of the level of passiveness of the selected sample of 77 passive UCMGs, we examined the stellar mass-SFR relation, also known as the main sequence (MS).Figure 5 shows the SFR as a function of the stellar mass of the 6961 galaxies that belong to the UCMG candidates.The orange solid line shows the limit for passive objects used by Salim et al. (2018), defined as specific SFR (SFR over stellar mass) equal to 10 −11 yr −1 .The blue solid line shows the MS of star-forming galaxies derived by Schreiber et al. (2015).Here we plot the MS at redshift z 0.83, which is the median redshift of the sample of 86 VIPERS UCMGs.In addition, the blue shaded region shows the range where log(SFR/SFR MS ) < log(4) ∼ 0.6 dex.It is a widely used limit to select both starbursting and passive galaxies from the main sequence relation (e.g.,  Red circles and pink triangles indicate VIPERS red nuggets (RN), while green crosses correspond to the UCMGs that we considered as active.The orange line shows the limit for passive galaxies (Salim et al. 2018).The blue line shows the main sequence of galaxies according to Schreiber et al. (2015).The magenta dashed line shows the mass completeness at redshift z = 0.9 for passive galaxies equal to log(M star /M ) ∼ 10.86 according to Davidzon et al. (2016).The three sources with relative errors higher than 45% are indicated as black squares.Elbaz et al. 2018;Buat et al. 2019;Donevski et al. 2020).We found only three sources that were not removed in the previous steps above the Salim et al. (2018) passiveness limit, but considering uncertainties in estimating both the SFR and stellar mass, as well the passive nature of their spectra, we decided to keep them in the sample.Taking into account the uncertainties, none of the 77 UCMGs is considered a MS galaxy.For these reasons, we decided not to remove any additional sources.Finally, we established a sample of confirmed VIPERS red nuggets containing 77 sources.

Final catalogue of VIPERS red nuggetsproperties
In Table 3 we listed the number of selected UCMGs corresponding to different compactness definitions from the literature.Within the VIPERS red nuggets catalogue we only considered the sample obtained using one of the most restrictive criteria for compactness, with M star > 8 × 10 10 M and R e < 1.5 kpc (Trujillo et al. 2009), resulting in 86 UCMGs.We then selected the 77 VIPERS red nuggets based on the NUVrK criterion, visual inspection of their spectra, and additional sanity checks (see Sect. 4.2). Figure B.1 shows four examples of selected red nuggets.We present the images in the u, g, r, i, and z bands from the CFHT survey, and also the normalised spectra with marked oxygen [OII] (3727.5 Å), calcium CaII K (3933.7 Å), and CaII H (3968.5 Å) lines.The VIPERS red nuggets catalogue is publicly available and reported in Appendix C. In the catalogue, we list the VIPERS IDs and positions on the sky, as well as all the important parameters used in analysis, such as redshifts, effective radii, stellar masses, and colours.
One characteristic that sets this study of red nuggets apart from other works is the unique redshift range over a A95, page 7 of 16 wide-field systematic survey.In addition, our sample is already spectroscopically confirmed, which is an improvement in comparison with studies based only on photometry.This means that we present the largest catalogue of spectroscopically identified red nuggets beyond the local Universe.In comparison, there are only 14 confirmed quiescent compact galaxies within the Baryon Oscillation Spectroscopic Survey (BOSS) at redshift 0.2 < z < 0.6 (Damjanov et al. 2014) and about ∼20 found by Charbonnier et al. (2017) in the CFHT equatorial SDSS Stripe 82, also at redshift range 0.2 < z < 0.6.
Within our final catalogue of red nuggets 96% of all galaxies (74 sources) have relative errors of R e lower than 45%.The remaining three red nuggets, with the relative errors of R e equal to 99%, 62%, and 61% included in our sample, are highlighted in Table C with underlined IDs and R e values, and in Fig. 5 with black squares.

Comparison with VIPERS results of unsupervised classification
We performed a cross-match of our 77 red nuggets with detailed classification done by Siudek et al. (2018b).In their paper the authors classified 52 114 VIPERS galaxies with the highest confidence (>90%) of redshift measurements into 12 classes using the unsupervised machine learning algorithm Fisher Expectation-Maximization (FEM; Bouveyron & Brunet 2012).All subclasses found by Siudek et al. (2018b) mirror substructures in the bimodal colour distribution of galaxies, distinguishing subpopulations of passive (red), intermediate (green), and active (blue) galaxies and an additional class of broad-line AGNs.In the following section the definition of the red, green, and blue galaxy populations relies on the FEM classifications: red (subclasses 1-3); green (subclasses 4-6); blue (subclasses 7-11).The reliability of these three classes was checked in Siudek et al. (2018b) via the colour-colour method, spectral features like emission line distribution and the spectral continuum, and morphological parameters like Sérsic index, stellar mass, and SFR.We refer to Siudek et al. (2018aSiudek et al. ( ,b, 2022) ) for a detailed description of the VIPERS classification.In this paper we verify whether VIPERS red nuggets are preferably found in one of the red subclasses.
Our sample of 77 VIPERS red nuggets contains 72 red class galaxies (subclasses 1-3, represented in Fig. 5 as red circles), and 5 green class galaxies (subclasses 4-5, pink triangles).All five green galaxies lie closer to the main sequence relation than the rest of the red nuggets, which additionally supports the reliability of FEM classification from Siudek et al. (2018b).A histogram of red nugget classes is also presented in Fig. 7.We did not find galaxies from the blue classes which supports our classification of passive, massive compact objects.Almost 65% of the red nuggets (49 out of 77) are found in the subclass 1, which gathers massive and small red galaxies (see Table 1 and Sect . 5.3 in Siudek et al. 2022).This confirms the usefulness of applying unsupervised machine-learning algorithms to automatically find 'peculiar' galaxy subclasses (Siudek et al. 2018a(Siudek et al. ,b, 2022)).

The D4000 distribution of intermediate-z red nuggets
The strength of the 4000 Å spectral break (hereafter D4000, defined in Balogh et al. 1999) is one of the main and direct characteristics of the star formation history of galaxies.Its correlation with young and evolved stellar populations makes this spectral index suitable as a passiveness indicator The grey points represent the 77 red nuggets and the red squares represent the median value in every redshift bin (see Table 4).The red line is the best linear fit.The dashed orange line represents D4000 equals 1.55, which is the passiveness limit derived by Kauffmann et al. (2003a) in the local Universe.
Figure 6 shows the D4000-z (top panel) and M star -z (bottom panel) relations.The orange dashed line indicates D4000 = 1.55, the passiveness boundary found by Kauffmann et al. (2003a) for the local Universe based on the SDSS survey.Taking into account the uncertainties of the D4000 measurements, six galaxies lie below the Kauffmann et al. (2003a) limit.Two of these galaxies have z ∼ 0.73, while four are located at the end of our redshift range, at z > 0.85, where we can expect to see a younger population than in the local Universe.
Considering the median values in redshift bins, there is no significant D4000-z dependence for the presented sample, and the median value of D4000 for red nuggets in the redshift range 0.5-1.0stays constant at the level 1.66±0.05,indicating the passiveness of the sample.The bottom panel of Fig. 6 shows the M star -z relation for the sample of 77 red nuggets.We found no clear dependence of the stellar mass on redshift.However, the highest redshift bin may be biased by non-negligible incompleteness.

Influence of compactness criteria on sample size
All the compactness criteria found in literature are functions of R e and M star .The discrepancy of those criteria is shown in Table 3.Unfortunately, we cannot compare sample sizes of UCMGs found by different criteria as not all of them are mass complete.For this reason we additionally limit the criteria by cutting all galaxies with stellar masses below the completeness limit.In the VIPERS survey, the number of sources considered as compact and complete in stellar mass found here varies between 1664, using the Damjanov et al. (2015) criterion, and 82, using the Cassata et al. (2011) ultracompact criterion.We thus see that the choice of compactness criterion can influence the sample size by up to a factor of ∼20.

Evolution of number densities
In order to derive number densities, we divided all red nuggets into four redshift bins containing a roughly equal number of A95, page 8 of 16  Notes.The second column shows the number of sources in each bin, and the third column presents the weighted number of sources, which takes into account the TSR and SSR.In the last column we show the number density per comoving cubic Mpc.
galaxies per bin: 0.50-0.72,0.72-0.82,0.82-0.9,and 0.90-1.00(see Table 4).Taking into account that our sources are not evenly distributed in redshift (see Fig. 7) our bins are not uniform.We then calculated the weighted number of sources based on the TSR and SSR of the parent sample: (for details see Garilli et al. 2014).Finally, we normalised our bins to the comoving volume corresponding to the VIPERS observed area and calculated the number density per cubic comoving Mpc.The results are presented in Table 4 and in Fig. 8. Figure 8 shows number densities (see Table 4) as a function of redshift.Number densities of VIPERS red nuggets calculated in the first three redshift bins are shown as solid red circles, while the results from the redshift bin 0.9-1.0,which can be biased by the mass incompleteness, is shown as an open red circle.Due to the mass incompleteness presented number density for this redshift, we note that this bin should be considered as a lower limit.Presented uncertainties of the number counts take into account fluctuations due to the Poisson noise.
We compared our results with the number densities of quiescent compact galaxies found by Damjanov et al. (2014) in the Baryon Oscillation Spectroscopic Survey.In addition to that, we also plotted the number densities of ultracompact massive Fig. 8. Number density per comoving cubic Mpc vs. redshift.Shown are the results from this work (red), the quiescent compact galaxies found by Damjanov et al. (2014;green), the compact galaxies found by Scognamiglio et al. (2020;black), the ultracompact ETGs analysed by van der Wel et al. (2014;violet), and the quiescent compact galaxies found by Barro et al. (2013;blue).galaxies found in the Kilo Degree Survey by Scognamiglio et al. (2020).As we do not expect to find in this sample a statistically significant number of star-forming massive compact objects (e.g., in our initial sample of 86 UCMGs only ∼10% were considered not passive), it is reasonable to compare those two groups.At higher redshifts we present passive ultracompact galaxies found in the CANDELS field by van der Wel et al. ( 2014) found with the ultracompact criterion (see Table 3).Moreover, we also show the quiescent compact sources found in the GOODS-S and UDS fields of CANDELS by Barro et al. (2013).None of the high-redshift studies provides explicit number densities, and an online tool was used to extract their corresponding values directly from plots2 .
Figure 8 shows that our results are in overall agreement with the lower redshift studies to within an order of magnitude.However, the trends found by Scognamiglio et al. (2020) and Damjanov et al. (2014) are slightly different as those samples were selected using slightly different approaches Damjanov et al. (2014) selected objects with effective radius smaller than R e < 2 kpc (in our work R e < 1.5 kpc), while the cut on stellar mass is the same as that used in this work (M star < 8 × 10 10 ).Moreover, the resulting numbers from Damjanov et al. (2014) are considered as the lower limits for number density, due to sample incompleteness.Scognamiglio et al. (2020) performed a statistical correction, taking into account false positives and false negatives.For the first three bins (redshift lower than 0.4), this correction does not change the number density values significantly (uncorrected results are still inside the error bars).However, the uncorrected value of the last bin is lower by around twice the error value.In Fig. 8 we show only corrected number densities.The criteria used for selecting compact sources are exactly the same as those we used (M star < 8 × 10 10 and R e < 1.5 kpc).However, the authors do not discuss the subject of passiveness.
To summarise, Fig. 8 shows that our results match those presented in Damjanov et al. (2014).Similarly, the results obtained by Scognamiglio et al. (2020), except the number density at z ∼ 0.45, match our results closely.However, as mentioned before, the uncorrected value of the last point is ∼0.3 dex lower.
On the other hand, at high redshifts the differences are significant.However, both van der Wel et al. (2014) and Barro et al. (2013) used radically different, less conservative compactness criteria to those used in this work.In addition, we cannot straightforwardly compare the number of VIPERS UCMGs selected using the same criteria due to the mass completeness.For this reason, here only the mass complete sample sizes are discussed (see Table 3).Considering only mass complete samples of UCMGs, we find that the Trujillo et al. (2009) criterion (our fiducial choice throughout this work) yields roughly 1.5 and 14 times fewer compact sources than the Barro et al. (2013) and van der Wel et al. ( 2014) criteria, respectively.Comparing the number density presented by Barro et al. (2013) at z ∼ 0.75 to the number density of the VIPERS red nuggets at z ∼ 0.63, we find the former to be ∼20 times larger.As the ratio of number densities is similar to our inferred ratio of the number of sources found with the different criteria, we conclude that our results are consistent with those of Barro et al. (2013).Nevertheless, the number density of VIPERS red nuggets at z ∼ 0.95 is roughly five times higher than the number density reported by van der Wel et al. (2014) at z ∼ 1.The cause of this disagreement is unclear.

Summary
We have shown that the sample size of UCMGs in the uniform spectroscopic VIPERS survey is strongly dependent on the compactness criterion, and comparing the different criteria is not straightforward.Our catalogue of 77 VIPERS red nuggets significantly increases the number of known sources.The brand new catalogue of red nuggets presented here is a solid framework for future studies.The very restricted selection cut (based on R e , M star , and passiveness indicators) provides a pure sample of intermediate-redshift red nuggets.The evolution of the number density of red nuggets and relics over cosmic time is still an open issue.The results presented here provide a next step to understanding the evolution of red nuggets.We were able to trace the number densities of red nuggets with a comparable statistical significance to that found at lower redshifts (Charbonnier et al. 2017;Scognamiglio et al. 2020).The detailed analysis of their physical properties that will reveal their nature is left for future work, and their environmental properties are discussed in Siudek et al. (in prep.).

Fig. 1 .
Fig. 1.Stellar mass vs. effective radius distribution of 36 157 galaxies within the pure sample.The magenta dash-dotted line represents the initial Damjanov et al. (2015) cut for massive compact sources, the blue solid line indicates one of the most restrictive criteria proposed by Trujillo et al. (2009), and the orange dashed line visualises the cut adopted in this work to select 6961 UCMG candidates.The red points with error bars represent our final sample of 77 VIPERS red nuggets.The black dashed line shows the stellar mass completeness in the VIPERS catalogue.With other lines different compactness criteria are indicated: blue dot-dashed line -ultracompact Cassata et al. (2011); orange dotted line -Barro et al. (2013); green dashed line -ultracompact van der Wel et al. (2014); red solid line -Charbonnier et al. (2017); brown solid line -Buitrago et al. (2018); violet solid line -Spiniello et al. (2021).

Fig. 2 .
Fig. 2. Distribution of effective radius as a function of redshift for 36 157 galaxies from the VIPERS pure sample (in grey).The orange line represents the VIPERS seeing-detection limit.The UCMG candidates are indicated with red circles.

Fig. 3 .Fig. 4 .
Fig. 3. NUVrK diagram.The distribution of 36 157 galaxies (pure sample) is shown in the background.The orange line ,shows the limit for red galaxies adapted from Moutard et al. (2016b).The red and the green points represent the VIPERS UCMGs sample.Sources indicated by green crosses are thought to be blue (active), and have been removed from our sample.

Fig. 5 .
Fig.5.Relation of SFR vs. stellar mass.In the smoothed background the sample of 6961 UCMG candidates is shown.The points represent our 86 red and green UCMGs.Red circles and pink triangles indicate VIPERS red nuggets (RN), while green crosses correspond to the UCMGs that we considered as active.The orange line shows the limit for passive galaxies(Salim et al. 2018).The blue line shows the main sequence of galaxies according toSchreiber et al. (2015).The magenta dashed line shows the mass completeness at redshift z = 0.9 for passive galaxies equal to log(M star /M ) ∼ 10.86 according toDavidzon et al. (2016).The three sources with relative errors higher than 45% are indicated as black squares.

Fig. 6 .
Fig.6.Relation of D4000 vs. z (top panel) and M star vs. z (bottom panel).The grey points represent the 77 red nuggets and the red squares represent the median value in every redshift bin (see Table4).The red line is the best linear fit.The dashed orange line represents D4000 equals 1.55, which is the passiveness limit derived byKauffmann et al. (2003a) in the local Universe.

Fig. 7 .
Fig. 7. Distribution of VIPERS red nuggets in redshift and in FEM classes (inset).The different colours correspond to our bins.

Table 1 .
Summary of available photometric data in each band used for the SED fitting.Notes.The third column, λ mean , is the centre of the specific filter band given in µm.The last column, N gal , provides the number of detections in the sample of 6961 UCMG candidates.

Table 2 .
Rałowski et al. 2020;ts performed to seleTurner et al. 2021;Pistis et al. 2022; candidates.We used CIGALE as it models the SED of galaxies by conserving the energy balance between the dust-absorbed stellar emission and its re-emission in the IR.The capabilities of this SED fitting tool have already been verified on VIPERS observations (i.e.,Rałowski et al. 2020; Vietri et al. 2021;Turner et al. 2021;Pistis et al. 2022; Figueira et al., in prep.).Previous works have estimated stellar masses, SFRs, and AGN fractions of the VIPERS observed galaxies, and show consistency with each other.Moreover, we checked the stellar masses and absolute magnitudes obtained from CIGALE and Le Phare

Table 3 .
(Cassata et al. 2013;van der Wel et al. 2014ift ranges of sources presented in the literature.The number of UCMG candidates according to each criterion is given in the fourth column.The last column provides the sample size of UCMG candidates that meet the compactness criterion, and the mass completeness above log(M star /M ) ≥ 10.86(Davidzon et al. 2016).Two works(Cassata et al. 2013;van der Wel et al. 2014) applied two different criteria, and we refer to them as a 'compact' and 'ultracompact' for less and more restrictive, respectively.

Table 4 .
Overview of the four redshift bins and the summary of all four bins.