Luminous Red Novae (LRNe) form a novel class of stellar transients with luminosities intermediate between novae and core-collapse supernovae (SNe). These gap transients (Kasliwal 2012; Pastorello & Fraser 2019 ) have a characteristic double-peak light curve, early spectra similar to those of Type IIn SNe and late spectra that migrate from matching those of intermediate stellar types to those of mid-tolate M-type stars (see, Pastorello et al. 2019a , and references therein). These properties allow us to securely discriminate LRNe from the so-called Intermediate-Luminosity Red Transients (ILRTs 1 , e.g. Botticella et al. 2009; Bond et al. 2009; Cai et al. 2018; Stritzinger et al. 2020a) , which are believed to originate from eruptions or terminal explosions of superasymptotic giant branch (S-AGB) stars. Nonetheless, some observational overlap between the two classes has been occasionally noted, giving rise to controversial cases (e.g., M85-2006OT1 and AT 2018hso; Kulkarni et al. 2007; Pastorello et al. 2007; Cai et al. 2019) .
The LRN phenomenon can be comfortably explained in terms of post common envelope evolution and eventually co-1 ILRTs always show a very slow spectral evolution, and prominent Ca lines, in particular the typical narrow [Ca II] λλ 7291, 7324 doublet in emission. alescence in binary systems whose components span a wide range of masses. However, the physical processes leading to the common envelope ejection and the path to coalescence are still debated (e.g" Ivanova et al. 2013; Pejcha et al. 2017; Segev et al. 2019; MacLeod et al. 2018; Soker 2020; Soker & Kaplan 2020) . The characterization of this species of gap transients is also necessary to provide reliable estimates of their rates, both in the Galaxy and within a volume of universe, although it is now clear that the frequency of LRNe depends significantly on their luminosity and the total mass of the system (Kochanek et al. 2014; Howitt et al. 2020 ). Finally, the study of the evolution of massive binaries is a hot topic, as this has important implications in the formation of close compact binaries (Klencki et al. 2020) , that are sources of gravitational waves (Abbott et al. , 2017 .
Collecting good datasets covering all the crucial phases of the LRN evolution is a necessary condition to develop reliable theoretical models (see, e.g., Pejcha et al. 2016a,b; Segev et al. 2019; MacLeod & Loeb 2020a,b) . However, so far only a limited number of LRNe are available in the literature with extensive light curves, including pre-outburst detections, and well-sampled spectral sequences. For this reason, within the NOT Unbiased Transient Survey 2 A&A proofs: manuscript no. LRN2_pastorello (NUTS2 2 ; Holmbo et al. 2019 ) collaboration, we are leading a program of systematic follow-up of LRNe (e.g., Cai et al. 2019; Pastorello et al. 2019a,b) .
In this paper, we present the outcomes of our monitoring campaigns of two LRNe in the nearby Universe: AT 2020hat and AT 2020kog. These two objects, along with AT 2019zhd in M 31 (whose study is presented in a companion paper, Pastorello et al. 2020) , were discovered in the observing semester from December 2019 to May 2020. Our team committed substantial effort for following-up these three objects, and provided excellent datasets for all of them, although the monitoring campaigns were severely complicated by the fact that many observational facilities had to suspend operations during the global lock-down resulting from the Covid-19 pandemic emergency.
The paper is structured as follows: Sect. 2 reports information on the discovery, classification, host-galaxy properties, distance and reddening of AT 2020hat and AT 2020kog; their light curves and spectral evolution are presented in Sect. 3 and Sect. 4, respectively; archive photometry of the quiescent progenitor system of AT 2020hat is analysed in Sect. 5; the evolution of the bolometric luminosity, temperature and radius is illustrated in Sect. 6; and a general discussion on the physical properties of LRNe and final remarks follow in Sect. 7.
AT 2020hat 3 was discovered on 2020 April 12.48 UT in the Sctype galaxy NGC 5068 by the Asteroid Terrestrial-impact Last Alert System (ATLAS, Tonry et al. 2018; Smith et al. 2020) , at an ATLAS orange-band magnitude o = 17.83 ± 0.08 mag. The coordinates of the object are RA = 13 h 19 m 01 s .927, Dec = −21 • 03 ′ 16 ′′ . 37 (equinox J 2000.0), which is offset by 55 ′′ . 4 south and 99 ′′ . 6 east from the centre of the host galaxy (see Fig. 1 , top panel). The object was classified as a LRN after maximum light by Reguitti et al. (2020) . The transient was also observed in the radio domain, but no counterpart was found down to 3σ limits of about 0.06 mJy at 5.5 GHz, and 0.04 mJy at 9.0 GHz (Ryder et al. 2020 ). The host, NGC 5068, is a nearby face-on Sc-type galaxy 4 with redshift z = 0.002235 ± 0.000003 (Pisano et al. 2011) . Given its proximity, the redshift does not provide a good constraint on the galaxy distance. For this reason, in this paper we adopt the distance estimate obtained through the tip of red-giant branch method, which provides a distance d = 5.16 ± 0.21 Mpc (Karachentsev et al. 2017) , hence a distance modulus µ = 28.56 ± 0.08 mag. We note that this value is remarkably similar to another estimate based on the planetary nebulae luminosity function (µ = 28.68 ± 0.08 mag, Herrmann et al. 2008) .
The reddening towards AT 2020hat is dominated by the Milky Way component, E(B − V) MW = 0.09 mag (Schlafly & Finkbeiner 2011) . In fact, the analysis of the spectra of the transient (as we will see in Sect. 4) does not indicate additional host galaxy reddening, as expected considering the peripheral location of the object in its host.
AT 2020kog, also known as PS20dgq, was discovered by the Pan-STARRS Search for Kilonovae (Smartt et al. 2019 ), on 2020 May 18.49 UT, in an outer spiral arm of the Sc-type galaxy NGC 6106. The coordinates of the object are RA = 16 h 18 m 47 s .652, Dec = +07 • 25 ′ 16 ′′ . 86 (equinox J 2000.0), with an offset of 42 ′′ . 7 north and 9 ′′ . 1 east from the core of the host galaxy (Fig. 1, bottom panel) . The survey discovery magnitude was w = 20.30 ± 0.10 mag (Fulton et al. 2020) .
The redshift of NGC 6106 is z = 0.00483 ± 0.00002. Adopting a standard cosmology with H 0 = 73 km s −1 Mpc −1 , Ω matter = 0.27 and Ω vacuum = 0.73, a distance of 23.8 ± 1.7 Mpc (corrected for Virgo Infall) 5 is obtained (Mould et al. 2000) , which provides µ = 31.89 ± 0.15 mag. Numerous distance estimates have been published using the Tully-Fisher method, spanning a wide range of inferred values (from about 21 to 28 Mpc). Here we Tully et al. (2016) adapted to our cosmological assumptions: d = 22.5 ± 2.0 Mpc, which gives µ = 31.76 ± 0.45 mag. This distance, that will be adopted hereafter in the paper, is slightly lower than the kinematic distance. The dust extinction within the Milky Way in the direction of the transient is E(B − V) MW = 0.06 mag (Schlafly & Finkbeiner 2011) . In addition, the detection of a prominent narrow interstellar feature of Na I λλ5890,5896 (Na ID) in the spectra of the transient suggests the existence of additional reddening within the host galaxy. With a host galaxy contribution of E(B − V) host = 0.31 ± 0.06 mag (see Sect. 4.2 for details), we find a total colour excess due to line-of-sight dust extinction is E(B − V) tot = 0.37 ± 0.07 mag.
The photometric follow-up campaigns of AT 2020hat and AT 2020kog have been performed after their discovery using a number of instruments available to our collaboration. The details of the instrumental configurations are provided in the photometry tables (available in electronic form at the CDS).
Due to its faint apparent magnitude, AT 2020kog was not detected by most of the surveys. However, important early data have been obtained by the Panoramic Survey Telescope & Rapid Response System (Pan-STARRS; Chambers et al. 2019; Flewelling et al. 2019; Magnier et al. 2019) , with the wide w-band filter. In contrast, AT 2020hat had a brighter apparent magnitude, and was routinely observed by numerous surveys, including the D < 40 Mpc SN survey (DLT40; Tartaglia et al. 2018, unfiltered data) , the Zwicky Transient Facility (ZTF; Masci et al. 2018 , in the Sloan-g and r bands), 6 the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014; Kochanek et al. 2017 , in the g band) 7 , the Asteroid Terrestrial-impact Last Alert System project (ATLAS: Tonry et al. 2018 , in the ATLAS-cyan and orange bands) and Pan-STARRS (in the i and z bands). We remark that in our paper the unfiltered DLT40 data were calibrated to Sloan-r magnitudes, while the observations with ATLAS-orange (o) and ATLAS-cyan (c) filters were left in their original photometric systems. Finally, although no transformation was applied to the Pan-STARRS-w band magnitudes provided by the survey, these data match very well our Sloan-r observations.
Our imaging data needed some preliminary processing, including bias, flat-field and (when useful) fringing pattern corrections. Near-infrared (NIR) images required additional prelimi-6 ZTF forced photometry is released through the Lasair (https://lasair.roe.ac.uk/) and ALeRCE (https://alerce.online/) brokers. 7 ASAS-SN photometry is publicly released through the Sky Patrol ASAS-SN interface (https://asas-sn.osu.edu).
A&A proofs: manuscript no. LRN2_pastorello Table 2 . Log of spectroscopic observations of the two LRNe. Phases are from their r-band light curve peak, that in AT 2020hat and AT 2020kog are at MJD r,max = 58954.0 ± 1.5 MJD r,max = 58991.9 ± 0.7, respectively. nary steps, including building a sky image for each filter obtained from median-combining dithered science frames. Then, the sky image was subtracted from individual science frames, which were finally combined to increase the signal-to-noise (S/N) ratio. Optical and NIR imaging data were reduced using the python/pyraf SNOoPY pipeline (Cappellaro 2014) . The software allowed us to perform astrometric calibration of the images, PSF-fitting photometry of the transient (with or without template subtraction) 8 and the subsequent photometric calibration making use of catalogues of reference stars. For the optical Sloan band images, we used the Sloan catalogue, while for the NIR data we used the Two Micron All-Sky Survey (2MASS) catalogue (Skrutskie et al. 2006) . The unfiltered DLT40 photometry was calibrated with reference to the Sloan-r photometry.
The final light curves of the two objects are shown in Fig. 2 , while the optical photometry tables 9 are made available in electronic form at the CDS. The NIR observations of AT 2020hat are instead reported in Table 1 .
The field of AT 2020hat was routinely sampled before the LRN discovery by public surveys. These observations are crucial to build the light curve before the LRN outburst ( Fig. 2 , left panel). In particular, a faint source at the position of the transient is observed starting about three months before the AT 2020hat peak luminosity. In the pre-outburst phase, the light curve shows some fluctuations over a general brightening trend. 8 AT 2020kog was located in a crowded region of its host galaxy, hence we subtracted template images of NGC 6106 obtained from the Pan-STARRS survey (griz filters) and SDSS (u filter). In contrast, AT 2020hat was in a clean and peripheral location of the host galaxy, hence template subtraction was not necessary. 9 Table E1 contains the following information on the optical photometry of AT 2020hat: column 1 lists the dates of the optical band observations, column 2 reports the MJDs, columns 3 to 16 give the optical (u, g, r, i, z, c, o) magnitudes and their errors, and column 17 reports a number coding the instrumental configuration. Table E2 contains the following information on the photometry of AT 2020kog: column 1 lists the date of the observations, column 2 reports the MJDs, columns 3 to 12 provide the optical (u, g, r, i, z) magnitudes and their errors, and column 13 reports the code of the instrumental configuration.
From about one month before maximum, the best-sampled rband light curve shows a much more evident luminosity rise of about 2.5 mag, reaching the peak at r max = 17.79 ± 0.02 mag (on MJD r,max = 58954.0 ± 1.5) 10 . The low-contrast light-curve peak is followed by a nearly linear decline in the blue bands, while a sort of plateau lasting about 70-80 d is observed in the red bands. This phase is followed by a rapid decline that unfortunately was not well sampled due to the modest visibility from our northern facilities. The decline rates in the different bands between the maximum and ∼ +70 d are: γ u = 5.22 ± 0.61, γ g = 2.59 ± 0.07, γ r = 0.97 ± 0.03, γ o = 0.61 ± 0.06, γ i = 0.43 ± 0.03, and γ z = 0.04 ± 0.05 mag (100 d) −1 . The late-time (>80 d) decline rates in the Sloan-r and ATLAS-o bands steepen to γ r = 6.7±0.9 mag (100 d) −1 and γ o = 9.4 ± 0.8 mag (100 d) −1 , respectively.
A few observations of AT 2020hat were also obtained in the NIR domain by the 2.0 m Liverpool Telescope (LT) with IO:I and the 2.56 m Nordic Optical Telescope (NOT) with NOTCam. While only two epochs were obtained in the J and K bands, observations in the H band were obtained at five epochs during the plateau, with the object staying at roughly constant luminosity, around H ∼ 15.8 mag (Fig. 2, left panel) .
AT 2020kog was detected by Pan-STARRS a couple of months before the outburst peak (see Fig. 2 , right panel). During the pre-outburst phase, until one month before maximum, the r-band light curve initially rises with a rate of 2.4±0.3 mag (100 d) −1 . The r-band light curve brightening becomes faster in the following two weeks, with a rate of 5.8±0.2 mag (100 d) −1 , to finally increase by further ∼2 mag in about 10 days by the time of the first blue peak. The epoch of the maximum and the peak magnitude of the r-band light curve of AT 2020kog can be inferred from a low-order polynomial fit: we obtain MJD r,max = 58991.9 ± 0.7 and r max = 19.48±0.02 mag. Premaximum information is not available for the g band, so we adopt MJD g,max ∼ 58991.0 and g max ∼ 19.88 mag as indicative parameters for the g-band maximum. After the peak, the r-band light curve fades with a slope of γ r = 8.2±0.2 mag (100 d) −1 and reaches a local minimum of r ∼ 20.3 mag at about 10 d past-maximum, followed by a modest rebrightening (r ∼ 20.1 mag). From three weeks after maximum, the light curve declines almost linearly, with a rate γ r = 1.3 ± 0.1 mag (100 d) −1 . A much larger steepening is observed from about 80 d after maximum in all bands, although the decline rates are less steep in the Sloan-i and z bands. At phases > 80 d, we find γ r = 5.7 ± 0.2, γ i = 4.6 ± 0.7, and γ z = 2.0 ± 0.2 mag (100 d) −1 .
Spectroscopic observations of the two objects were performed using the 10.4 m Gran Telescopio Canarias (GTC) equipped with OSIRIS, the 3.58 m Telescopio Nazionale Galileo (TNG) equipped with Dolores (LRS), the NOT with ALFOSC and the 2.0 m LT with SPRAT. All these telescopes are hosted at the Observatorio del Roque de los Muchachos, in La Palma (Canary Islands, Spain). Information of the instrumental configurations used for the spectroscopic data is given in Table 2 . The spectra were reduced using standard tasks in IRAF 11 , with the exception of the ALFOSC data that were reduced using the Python-based FOSCGUI pipeline 12 developed by E. Cappellaro. After the traditional bias and flat-field correction of the science frames, 1-d spectra were optimally extracted, and wavelength calibrated using arc-lamp spectra. The accuracy of the wavelength calibration was checked by measuring the wavelengths of the [O I] night sky lines. Then, the spectra were flux calibrated using spectrophotometric standards taken during the same night as the LRN observation. The flux calibration was finally fine-tuned using the photometric information, and the telluric absorption bands of O 2 and H 2 O were removed using the spectra of hot standard stars.
AT 2020hat was discovered quite late, and we could not follow it spectroscopically during the pre-maximum evolution. Nonetheless, the observational cadence after discovery is excellent, and spans over 100 days of its evolution. The observational campaign of AT 2020kog is more complete, although hampered by the faint apparent magnitude of the transient and, because of its northern declination, the lack of support of southern facilities. As a consequence, the object was only observed with GTC and NOT, from soon after the blue peak to +100 d. Despite the limited number of spectra, we have been able to sample all the crucial phases of the evolution of AT 2020kog. The two spectral sequences are shown in Fig. 3 .
The spectra of AT 2020hat are typical of the cooler, red-peak (or plateau) phase of LRNe. This implies that we failed to see an earlier hotter phase (which is unlikely), or that this LRN did not become very hot at the early phases of the outburst, as occasionally observed in lower luminosity Galactic LRNe such as V1309Sco (Mason et al. 2010; Tylenda et al. 2011) and V838 Mon (Munari et al. 2002; Goranskij et al. 2002; Kimeswenger et al. 2002; Crause et al. 2003; Tylenda 2005) . Fig. 4 . Blow-up of the Hα region in the mid-resolution OSIRIS spectrum of AT 2020hat at phase +33 d, compared with two low-resolution spectra taken at earlier (+6 d) and later (+75.9 d) phases. As no H II regions in the proximity of AT 2020hat have been spectroscopically observed for more accurately estimate the redshift at the LRN location, the spectra have been corrected for the average redshift of NGC 5068 (z = 0.002235).
The spectra show weak Balmer lines with P Cygni profiles, and a forest of narrow absorptions due to metal lines. These features are responsible for line blanketing at the blue wavelengths, although many multiplets are clearly detected at longer wavelengths. Ca II H&K and Ca II NIR triplet are among the most prominent absorption lines in the spectra of AT 2020hat. We also possibly identify O I λλ7772,7777, although O I λ8446 is not unequivocally seen.
Detailed line identification and more precise velocity measurements can be performed in the region 560-760 nm using the moderate-resolution GTC+OSIRIS R2500R spectrum of AT 2020hat at phase +33 d. Hα shows a resolved broader emission component with a full-width at half-maximum (FWHM) velocity (v FWH M ) of 250 ± 30 km s −1 (after correction for spectral resolution), atop of which a narrower absorption feature is observed. Adopting a redshift of z = 0.002235 (see Sect. 2), this feature is blueshifted by about 120±5 km s −1 from the rest wavelength (Fig. 4 ). An indicative estimate for the photosperic velocity at +33 d can be inferred by measuring the position of the minima of the prominent Ba II (multiplet 2) lines, which is found to be 175±10 km s −1 . In Fig. 5 (top panel) , we compare the R2500R spectrum with the combined R1000B+R1000R spectrum obtained at the same epoch. The comparison shows that the narrow features observed in the R2500R spectrum match those observed in the lower resolution configuration, confirming that these are real spectral absorption lines, and not noise patterns. Line identification on the R2500R spectrum is shown in Fig. 5  (bottom panel) . The spectrum shows a number of multiplets of metals, identified following Moore (1945) , including Ca I, Ba I, Ba II, Sc I, Sc II, Fe I, Fe II, V I, V II, Ti I, Ti II, and Na I. Y II and Mn II are also tentatively identified, as these ions do not generate prominent features in the AT 2020hat spectrum.
The first two spectra of AT 2020kog (Fig. 3, bottom panel) were obtained a few days after the initial blue peak. These early spec- F606W and F814W filters at a combined S/N> 5. A foreground reddening A V = 0.29 mag and distance modulus µ = 28.56 mag have been corrected for. The sharp diagonal detection cut is due to limiting magnitude, as determined by the S/N threshold. Pink points are sources within 1 ′′ of AT 2020hat as indicated in the left panel, for which the S/N>5 detection threshold has been relaxed (as a consequence, they are plotted with large error bars). The green point is the progenitor candidate for AT 2020hat. tra have also been used to estimate the host galaxy reddening towards AT 2020kog. The narrow interstellar feature of Na ID is well detected in these low-resolution spectra, with an equivalent width (EW) of 2.0 ± 0.4 Å. Adopting the relation between EW(Na ID) and E(B − V) presented by Turatto et al. (2002) 13 , an host galaxy extinction value of E(B−V) host = 0.31±0.06 mag is inferred, hence a total colour excess E(B − V) = 0.37 ± 0.07 mag.
After correcting for the total reddening, the continuum temperature can be inferred through a black-body fit to the continuum. We find it to be T BB = 11400 ± 1000 K in the +4.3 d spectrum, and rapidly declines to T BB = 10200 ± 1100 K at +9.3 d, T BB = 8800 ± 700 K at +22.2 d, and T BB = 6600 ± 1100 K at 37.1 d. In the early spectra, along with the prominent emission lines of H, we identify P Cygni lines of Ca II, O I and Fe II. In particular, the most prominent Fe II lines are those of the multiplet 42. At phase +4.3 d, Hα has a Lorentzian profile with v FWH M ≈ 470 km s −1 after correcting for spectral resolution, and 380 ± 10 km s −1 at +9.3 d. In our third spectrum at +22.2 d, the Hα profile becomes asymmetric, and shows two unresolved Gaussian components, with a more prominent emission component at the rest wavelength, and a weaker emission redshifted by about +350 km s −1 . In our fourth spectrum (phase ∼ 37.1 d), Hα is very faint, showing now a P Cygni profile, whose minimum is blue-shifted by ∼ 220 km s −1 . The evolution of the Fe II lines 13 We remark, however, that the extimates of interstellar extinction inferred through EW(Na ID) should be taken with caution, in particular when EW(Na ID) > 1 Å (see, e.g., discussions in Munari & Zwitter 1997; Poznanski et al. 2012; Phillips et al. 2013; Stritzinger et al. 2018 ). is quite modest, with an expansion velocity inferred from the P Cygni minimum which declines from about 330 km s −1 in our +4.3 d spectrum, to ∼ 280 km s −1 at 22.2 d.
Two spectra were also taken at phase ∼87 d, with the continuum becoming redder, Hα relatively prominent again, and there is now evidence for the presence of broad absorption features due to molecules (mostly TiO). We note that these spectra are remarkably similar the the spectrum of AT 2020hat at +75.9 d (see Fig. 3 , top panel). Both the narrow Hα in emission and the broad molecular bands in absorption becomes much stronger in the 100 d spectrum of AT 2020kog. Among the molecular band features, we clearly identify TiO features at about 6150-6270 Å, 6570-6880 Å, 7050-7270 Å, 7590-7860 Å and above 9200 Å. This late evolution is consistent with the expectations for a LRN (e.g., Martini et al. 1999; Kamiński et al. 2009; Mason et al. 2010; Barsukova et al. 2014; Smith et al. 2016; Blagorodnova et al. 2017; Pastorello et al. 2019a,b; Cai et al. 2019; Blagorodnova et al. 2020 ).
Due to its proximity, the host of AT 2020hat was frequently monitored in the past. In particular, the Hubble Space Telescope (HST) fortuitously observed NGC 5068 with the Advanced Camera for Surveys (ACS) Wide-Field Channel on 2017 February 11, a little over three years prior to the discovery of AT 2020hat. Two images with exposure time 515 s each were taken in each of the F606W and F814W filters. These data were downloaded from the Mikulski Archive for Space Telescopes 14 .
In order to locate the position of AT 2020hat on these images, we obtained deep imaging from the NOT+ALFOSC on the night of 2020 June 8. To avoid saturation on the transient, we selected 15 × 60 s images in the Sloan-r band which were subsequently co-added to give a deep image with a measured FWHM of 0.9 ′′ . We used 22 point-like sources common to the drizzled (_drc) HST+ACS F606W and NOT+ALFOSC images in order to derive an astrometric transformation between the two images. We find an RMS scatter of these sources of only 0.14, 0.13 ALFOSC pixels in x and y (hence ∼ 28 mas) on the transformation. After measuring the pixel coordinates of AT 2020hat on the ALFOSC image, we were hence able to transform this to the ACS image with a 1σ uncertainty of only 0.44 pixels.
A source (henceforth the progenitor candidate) is clearly visible at the transformed position in Fig. 6 . We use the dolphot package (Dolphin 2000) to measure Vega-scale magnitudes of F606W = 25.48 ± 0.04 mag, F814W = 24.25 ± 0.03 mag. The source is 0.7 pixels offset from our transformed position for AT 2020hat and, as this is 1.6σ, we regard it as a strong candidate for the progenitor. In addition, two fainter sources were detected to the south and west which are potentially consistent with the position of AT 2020hat (Fig. 6) . The magnitudes and colours of these sources are F606W = 27.42 ± 0.18, with F606W −F814W = 0.19±0.34 mag, and F606W = 28.51±0.44 mag, with with F606W−F814W = 1.55±0.50 mag, respectively. This would imply absolute magnitudes of nearly −1 to 0 mag at our adopted distance, and we do not consider them any further here.
For our adopted distance and extinction, the progenitor candidate has an absolute magnitude in M F606W = −3.33±0.09 mag, and an F606W − F814W colour = 1.13 ± 0.05 mag, which is significantly redder than the detected progenitors of other LRNe (see discussion in section 5 of Pastorello et al. 2019a) . While, in analogy with other LRNe, these photometric parameters are most likely the integrated values of the binary system stellar components, the absolute magnitude is too faint to be consistent with a system dominated by a massive (> 8 M ⊙ ) star that could later explode as a core-collapse SN. It appears to be more consistent with a system dominated by a lower mass (below 8 M ⊙ ) giant star of mid-K spectral type.
Using the light curves presented in Sect. 3, along with the distance and reddening values computed in Sect. 2, we can estimate the evolution of the luminosity through a blackbody fit to the spectral energy distribution (SED) at selected epochs. This procedure has been previously applied for other LRN studies (e.g., Blagorodnova et al. 2017; Cai et al. 2019; Pastorello et al. 2019b Pastorello et al. , 2020 .
For AT 2020hat, the SED fits have been computed by accounting for the contributions of the following bands: Sloanu (until phase ∼+50 d after maximum); Sloan-g and ATLAS-c (until phase ∼+100 d); Sloan-r, i, z and ATLAS-o; J, H, K (from ∼+20 to ∼+100 d). For AT 2020kog, only the contribution of Sloan filter data have been considered, while the PanSTARRS-w data were roughly approximated to Sloan-r. The flux contribution of the missing bands in the pre-outburst epochs has been computed through the gross assumption that the source had the same colours as at maximum light. For both AT 2020hat and 14 http://archive.stsci.edu/ AT 2020kog, the SEDs are fairly well fitted by single blackbody functions, and the bolometric luminosity for each epoch was computed by integrating the inferred blackbody flux over the entire electromagnetic spectrum. The resulting bolometric light curves are compared in Fig. 7 (top panel) with that of AT 2015dl/M101-2015OT1 (Blagorodnova et al. 2017) , an object whose luminosity is intermediate between those of the two LRNe discussed here.
The comparison with AT 2015dl is interesting because it has an intermediate luminosity between AT 2020hat and AT 2020kog. After the rise, AT 2020kog peaks at almost 9 ×10 40 erg s −1 , then rapidly declines until reaching the plateau at about 3 × 10 40 erg s −1 . Instead, AT 2020hat is about one order of magnitude fainter at maximum, peaking at 8 × 10 39 erg s −1 , and then its luminosity declines by almost a factor of 2 at phase ∼70 d after peak. AT 2015dl stays in the middle, although it has a much more prominent second maximum, while both AT 2020hat and AT 2020kog show a longer lasting plateau. An interpretation of the shapes of the LRN light curves will be given in Sect. 7.
The blackbody temperature (T bb ) evolution of the three LRNe is shown in Fig. 7 (middle panel) . While AT 2020kog is initially hot (with temperatures T bb ∼ 10000 − 11000 K), AT 2020hat is much cooler, having about 4700 K at maximum (hence comparable with the photosphere of an intermediate Ktype star), with a temperature which is similar (slightly higher) than that of AT 2015dl. We note, however, that the pre-maximum A&A proofs: manuscript no. LRN2_pastorello temperatures of the two LRNe are highly uncertain, due to the incomplete colour information in the pre-outburst epochs. With time, the temperature of AT 2020hat declines very slowly (T bb ∼ 3300 K at about 3 months after maximum, consistent with that of an intermediate M-type star), while the temperature of AT 2020kog goes down much more rapidly, decreasing by a factor of two in two months, and by a factor of three in the final epochs of the monitoring campaign. Fig. 7 (bottom panel panel) shows the evolution of the photospheric radii of AT 2020hat and AT 2020kog, obtained through the Stefan-Boltzmann law. For both objects, the pre-outburst radius is relatively small, at about 2 AU. Then, at the maximum light, the photospheric radius of AT 2020hat and AT 2020kog increases to 10.3 and 7 AU (hence, about 2200 and 1500 R ⊙ ), respectively. At ∼3 months after peak, the radii of AT 2020hat and AT 2020kog monotonically rise with time reaching about 16 AU (i.e., ∼3400 R ⊙ ) and 25 AU (∼5400 R ⊙ ), respectively. At phases >+100 days, when the optical light curves decline very rapidly and the SED peak shifts towards the NIR domain, the photospheric radius is expected to rise significantly. In the case of AT 2020kog, the radius increases by 50 per cent in about two weeks. We also note that, at early phases, the photospheric radii of AT 2020hat and AT 2020kog are much smaller than that of AT 2015dl, but become reasonably similar at late phases. In addition, while AT 2015dl shows a photospheric radius receding from 6500 to 4300 R ⊙ from the the peak to ∼50 days after, this behaviour is not seen in AT 2020hat and AT 2020kog that have a low-contrast early peak.
AT 2020hat and AT 2020kog belong to the growing group of LRNe that have been detected before the luminous outburst. The absolute magnitude of AT 2020hat in the last three months before the outburst ranges from M r ≈ −8.0 mag to M r ≈ −8.9 mag, with the light curve showing some fluctuations superposed on a general trend of luminosity rise (Fig. 8) . The pre-outburst phase of AT 2020kog was less densely sampled also because of its faintness. However, in the last ∼50 d before the outburst, the object monotonically brightens from M r ≈ −9.1 mag to M r ≈ −10.4 mag (see, Fig. 8) .
The pre-outurst light curves of AT 2020hat and, more marginally, AT 2020kog are similar to those observed in other LRNe, such as V1309 Sco (Tylenda et al. 2011 ) and M31-LRN2015 (phases 1 to 3 as described in Blagorodnova et al. 2020 , see their figure 2). The initial slow luminosity rise observed in these LRNe accompanied by a low-contrast modulation in the light curve is usually interpreted as due to an increasing mass loss through the L2 point that generates an expanding photosphere . When this common envelope engulfs the binary, the luminosity decreases and the light curve shows a minimum, along with the disappearance of the superposed light-curve modulation. Further mass loss or shock interaction produced by the L2 outflow may cause a modest, later rebrightening, as those observed also in AT 2020hat and AT 2020kog. This phase is followed by a major outburst, during which AT 2020hat and AT 2020kog reach M r ≈ −11.0 ± 0.1 mag and M r ≈ −13.2 ± 0.5 mag, respectively. This light curve peak is likely due to a hot, high-velocity gas outflow in polar direction following the system coalescence . We note that AT 2020hat has a modest early peak, while it is much more prominent in AT 2020kog. The differences in the early LRN light curve shapes can be explained through the Fig. 8 . Absolute light curves of AT 2020hat and AT 2020kog in the Sloan-r bands, showing also the pre-outburst detections. As a comparison, we also show the R-band absolute light curves of the luminous SNhunt248 (Kankare et al. 2015; Mauerhan et al. 2015) and the relatively faint V838 Mon (Munari et al. 2002; Goranskij et al. 2002; Kimeswenger et al. 2002; Crause et al. 2003) , scaled to the AB mag system. geometry of the system and the variety of masses involved in the process. This phase is then followed by a 2-3 month lasting plateau, reminiscent of that seen in Type IIP SNe, rather than a broad, red second peak observed in the most luminous events (Pastorello et al. 2019a) . Radiative shocks generated in the interaction between the newly expelled fast outflow and slower circumstellar material ejected before the coalescence power the plateau . The material gathered through the shocks then produces a cool dense shell where dust may form in short time scales. The progressively increasing photospheric radius and the slow decline of temperature observed in this phase (see Sect. 6) are fairly well explained with this scenario. Nonetheless, the mechanisms producing the heterogeneous photometric observables of LRNe are still under debate (e.g., MacLeod et al. 2017) .
Despite the uncertainties in the mechanism powering the light curves of LRNe, it is reasonable to assume that the ejected and total masses involved are key parameters to explain the widely heterogeneous photometric properties of these gap transients. Pastorello et al. (2019a) proposed that individual features of the light curve (the V-band absolute magnitudes of the preoutburst rise, the first peak and the second peak/plateau) are correlated with the intrinsic luminosity of the quiescent progenitor, while Kochanek et al. (2014) stated that the light curve peak magnitudes are correlated with the total mass of the progenitor system.
Unfortunately ultra-deep pre-explosion images of the host of AT 2020kog are not available, hence very few constraints can be placed on the luminosity of its progenitor. The stacked Pan-STARRS images allow us to only set detection limits for the progenitor of AT 2020kog down to g = 23.30 and r = 22.97 mag. The pre-outburst brightest Pan-STARRS w-band magnitude of AT 2020kog is converted to Johnson-V through the relations given by Tonry et al. (2012) , while Johnson-V magnitudes of the two main peaks are obtained from the g-band magnitudes adopting the prescriptions of Chronis & Gaskell (2008) and the available colour information. In order to obtain the desired magnitudes of the pre-outburst maximum of AT 2020hat, along with those of the two main peaks, we use the available Sloan-g and r magnitudes, transformed to Johnson-V following Chronis & Gaskell (2008) . When Sloan filter magnitudes are not available, they are estimated from the ATLAS-cyan and orange magnitudes using the relations of Tonry et al. (2018) and Tonry et al. (2012, to account for the conversion from Pan-STARRS to Sloan photometry systems). A similar approach was also adopted for other LRNe without V-band observation at the crucial epochs discussed here (see, also, Pastorello et al. 2019a) . Following these prescriptions, from the stacked Pan-STARRS images we infer an upper limit for the absolute magnitude of the quiescent progenitor of AT 2020kog of M V > −8.9 mag.
A&A proofs: manuscript no. LRN2_pastorello
As discussed in in Sect. 5, we can place much tighter constraints on the progenitor of AT 2020hat. Using the conversion formula between HST F606W and Johnson-V (Dolphin 2000) , the quiescent progenitor of AT 2020hat would have a relatively faint absolute magnitude, i.e. M V = −2.99 ± 0.09 mag. For these two objects and the recent LRN AT 2019zhd (Pastorello et al. 2020) , we can compute the absolute magnitudes of the brightest pre-outburst phase, and those of the blue peak and the red peak/plateau. Their photometric parameters can be compared with those of other LRNe from the literature in the updated version of the diagram originally presented in Pastorello et al. (2019a) (see Fig. 9 ). In the top-left panel, we also report where LRNe are located in the diagram showing the ratio between blue and red peak optical luminosities vs. the time during which the LRN light curves stay in the luminosity range between 0.1L peak and L peak .
We note that the parameters of M31-LRN2015 (Williams et al. 2015; Kurtenkov et al 2015; Lipunov et al 2017; Blagorodnova et al. 2020 ), M31-RV (Boschi & Munari 2004 , and references therein) 15 and OGLE-2002-BLG-360 (Tylenda et al. 2013 ) have been updated with respect to those discussed in Pastorello et al. (2019a) . In particular, as the light curve of OGLE-2002-BLG-360 is peculiar and shows a triple peak, we discussed two scenarios: Scenario (a), in which the first maximum corresponds to the brightest pre-merging detection, the second maximum is the blue peak, and the third one is the red peak; Scenario (b) assumes that the first light-curve maximum is coincident with the blue peak, the second maximum is the red peak, while the third maximum is an unprecedented late optical rebrightening, so far never observed in other LRNe. 16 While here we confirm the existence of a correlation between the progenitor absolute magnitude and the light curve luminosity as discussed in Pastorello et al. (2019a) , and we also note another general trend among LRNe: objects with a larger blue peak to red peak luminosity ratio have light curves fading more rapidly in luminosity ( Fig. 9 ; top-left panel).
On the bright extreme of the LRN luminosity function (see Fig. 9 ), we find extra-galactic events such as NGC 4490-2011OT1 (Smith et al. 2016; Pastorello et al. 2019a ), SNhunt248 (Kankare et al. 2015; Mauerhan et al. 2015) and AT 2015dl (Goranskij et al. 2016; Blagorodnova et al. 2017; Pastorello et al. 2019a ). On the faint side, we have faint Galactic transients, such as V1309 Sco (Mason et al. 2010; Tylenda et al. 2011; Walter et al. 2012) , V4332 Sgr (Martini et al. 1999; Kimeswenger 2006; Goranskij & Barsukova 2007 ) and OGLE 2002 -BLG-360 (Tylenda et al. 2013 . While the former were likely produced by massive, hot stellar systems (a few tens M ⊙ ; Smith et al. 2016; Blagorodnova et al. 2017; Mauerhan et al. 2018; Pastorello et al. 2019a) , the latter were likely produced by cooler low mass binaries, with a primary of about 1 M ⊙ , and a secondary of 0.1M ⊙ (or even less). As a consequence, the final outcome of high-luminosity LRNe are massive stars that will complete the nuclear burning cycles, finally exploding as core-collapse SNe. A significant fraction of core-collapse SNe is in fact expected to arise in close binary systems, including those producing a massive merger (e.g., Zapartas et al. 2017) . The massive stellar merger, for instance, was proposed to explain the peculiar circumstellar 15 The V-band light curve parameters of M31-RV have been fine-tuned including a few observations from Bryan & Royer (1992) , which were not considered in Boschi & Munari (2004) . 16 To date, a late third light curve peak has been only observed in LRN AT 2017jfs, but in the NIR domain (Pastorello et al. 2019b ). environment of SN 1987A and its blue supergiant progenitor (Morris & Podsiadlowski 2007) . On the other hand, the faint events will likely end their life without producing a SN explosion. In this framework, AT 2020kog can be regarded among the most luminous events generating massive mergers, while AT 2020hat has intermediate photometric properties similar to those of AT 2015dl. AT 2019zhd (whose progenitor was over three mag fainter and redder than that of AT 2020hat, Pastorello et al. 2020) shares instead some similarity with other LRNe discovered in M 31 (and more marginally with V838 Mon), hence the merger is likely a low to moderate-mass star, which is not expected to end its life as a core-collapse SN.
While light curve modelling (e.g., MacLeod et al. 2017; has improved our knowledge of the LRN outburst mechanisms, very little is known about their progenitor systems. Strategies with high-cadence multiband observations are necessary to better understand the binary properties and the masses of the two components during the premerger phase of orbital instability, as done for V1309 Sco (Tylenda et al. 2011) and (with less accuracy) M31-LRN2015 (Blagorodnova et al. 2020 ). In addition, future deep images with high spatial resolution will verify our predictions on the fate of the final merger, in particular through information provided by multi-domain observations, as imaging in a single domain (e.g., Bond & Siegel 2006; Bond 2018) has ofter remained ambiguous.