A JWST Project on 47 Tucanae. Overview, Photometry, and Early Spectroscopic Results of M Dwarfs and Observations of Brown Dwarfs

James Webb Space Telescope (JWST) observations have been demonstrated to be efficient in detecting multiple stellar populations in globular clusters (GCs) in the low-mass regime of M dwarfs. We present an overview, and first results, of different projects that can be explored by using the JWST observations gathered under program GO2560 for 47 Tucanae, the first program entirely devoted to the investigation of multiple populations in very-low-mass stars, which includes spectroscopic data for the faintest GC stars for which spectra are available. Our color–magnitude diagram (CMD) shows some substructures for ultracool stars, including gaps and breaks in slope. In particular, we observe both a gap and a minimum in the F322W2 luminosity function less than 1 mag apart, and discuss which it could be associated with the H-burning limit. We detect stars fainter than this minimum, very likely brown dwarfs. We corroborate the ubiquity of the multiple populations across different masses, from ∼0.1 M ⊙ up to red giants (∼0.8 M ⊙). The oxygen range inferred for the M dwarfs, both from the CMD and from the spectra of two M dwarfs associated with different populations, is similar to that observed for giants. We have not detected any difference between the fractions of stars in distinct populations across stellar masses ≳ 0.1 M ⊙. This work demonstrates the JWST's capability in uncovering multiple populations within M dwarfs and illustrates the possibility to analyze very-low-mass stars in GCs approaching the H-burning limit and the brown-dwarf sequence.


INTRODUCTION
Corresponding author: A. F. Marino anna.marino@inaf.itThe majority of Globular Clusters (GCs) harbors diverse stellar populations characterized by distinct chemical compositions.This includes a first population (1P) of stars with compositions akin to field stars exhibiting comparable metallicity, alongside one or more 'second' populations (2Ps) enriched in helium, nitrogen, aluminum, and sodium, while being depleted in carbon and oxygen (e.g.Kraft 1994;Bastian & Lardo 2018;Gratton et al. 2019;Milone & Marino 2022).
Since first discoveries, the intricate complexities underlying the coexistence of distinct stellar populations in GCs have posed a challenge to our understanding of both stellar evolution and star formation in the early Universe.In the past decades, a huge observational effort has been devoted to the study of multiple populations in GCs and several physical processes have been proposed for their formation.However, a consensus regarding the origin of the phenomenon is still missing (see reviews by Renzini et al. 2015;Bastian & Lardo 2018;Milone & Marino 2022, and references therein).
The current understanding of the "observed framework" provides two main competing scenarios.According to the multiple generations scenarios, multiple populations are attributed to distinct bursts of star formation at different epochs.Second-generation (2P) stars are born from material processed and ejected by the first-generation (1P, e.g.Dantona et al. 1983;Cottrell & Da Costa 1981;Renzini et al. 2022).Various kinds of 1P polluters have been proposed, including massive binary, Asymptotic Giant Branch (AGB), rotating, and supermassive stars (e.g.Ventura et al. 2001;Decressin et al. 2007;de Mink et al. 2009;Krause et al. 2013;Denissenkov & Hartwick 2014;D'Antona et al. 2016;Calura et al. 2019;Lacchin et al. 2024).However, regardless of proposed polluters, the amount of available material for 2P star formation is only a small fraction of the total presentday mass of 1P stars, a challenge known as the "mass budget problem".To cope with it, the 1P is required to be substantially more massive at its formation and the progenitors of GCs should have lost a large fraction of it, thus providing a significant contribution to the mass of the Galactic Halo.In this context, it has been argued that GCs would have formed inside dwarf galaxies as a result of a cooling catastrophe, with a fraction of the dwarf itself having contributed material for the formation of 2Ps (Renzini et al. 2022).As opposed to a compact, massive progenitor that would not lose much mass, a dense GC embedded in an extended envelope would easily survive tidal interaction while loosing most of the envelope itself, e.g., as suggested by N-body simulations (Lacchin et al. 2024).
Alternatively, it has been suggested that a fraction of stars from the same generation successively accreted material processed and ejected by massive stars of their own generation (Bastian et al. 2013;Gieles et al. 2018).This scenario was proposed as an attempt to cope with the mass budget issue, assuming that a much lesser amount of processed material would be required to produce the 2Ps, compared to the multiple stellar generations case.However, if only a small amount of accreted material was sufficient to produce the 2Ps, then one would expect this material to be mixed over the whole envelope as stars reach the red giant branch (RGB), thus producing a difference in composition with respect to main sequence (MS) stars, which is not observed.Even more funda-mentally, as 2P stars are enriched in helium, the putative accreted material would have a higher mean molecular weight compared to underlying layers, thus causing Rayleigh Taylor instability to mix the accreted material with most of the star.Thus, accretion seems not to solve the mass budget problem, as it hardly account for the discreteness of multiple populations (Renzini et al. 2015).More recently, the occurrence of stellar mergers within forming binary-rich globular clusters has been suggested as an explanation for multiple populations observed in GCs (Wang et al. 2020).
The two scenarios (multiple stellar generations and accretion) result in different expectations for the population pattern across stellar masses.Based on the multiple generations scenario, the population pattern should be identical for stars with different masses, which means that both high-mass and lowmass stars formed during each burst of star formation should exhibit similar chemical compositions.On the other hand, in the accretion scenario the amount of accreted material depends on stellar mass, and it is proportional to the square of the stellar mass (e.g., ∝ M 2 ) (in the case of Bondi-like accretion Bondi & Hoyle 1944).Being very-low mass stars less efficient in accreting polluted material, the differences in helium, carbon, nitrogen, and oxygen (O) abundances commonly observed among red giants, would systematically decrease in the M dwarf domain.
The predictions of the two scenarios also diverge concerning the mass function (MF) of the Multiple Populations (MPs).If the 2P grew out of Bondi accretion, the MF of 2P should be significantly flatter compared to that of 1P (Ballesteros-Paredes et al. 2015).In contrast, if there were multiple star-formation episodes, a much less pronounced difference, if any, is expected between the MF slopes of 1P and 2P stars.Being the multiple stellar population pattern across different masses a key ingredient to constrain the formation scenarios, the comparison of stellar population properties in the very-low mass regime of M dwarfs with those, already known, of red giants, holds the promise of shedding light on the origin of this enigmatic phenomenon.
First analyses of multiple stellar populations below the MS knee have been conducted with data from the Hubble Space Telescope (HS T ) for the GC NGC 2808, which already showed the endurance of different stellar populations among low mass stars (Milone et al. 2012b).Other GCs were successively investigated including NGC 6121 (M 4 Milone et al. 2014), Omega Centauri (Milone et al. 2017a), NGC 6752 (Milone et al. 2019).This work highlights the presence of similar chemical variations among low and higher mass stars supporting the multiple generations scenario.Dondoglio et al. (2022) presents an analysis of a sample of GCs below the MS knee, and provided for the first time, their MFs of multiple populations in NGC 2808 and M 4 along a wide range of stellar masses, from ∼0.2 to ∼0.8 M ⊙ , finding that the fraction of MPs does not depend on the stellar mass, thus further challenging the accretion scenario.First evidence of multiple stellar populations in very low mass stars from JWS T data have been reported fo 47 Tucanae (Milone et al. 2023a), M 92 (Ziliotto et al. 2023), and NGC 6440 (Cadelano et al. 2023).In this paper we exploit deep JWS T data to reach well below the hydrogen-buring limit in 47 Tucanae, and into the brown dwarf regime.
This work provides an overview of a project, mainly based on observations gathered under the JWS T program GO-2560.The project aims at the analysis of multiple stellar populations among very low mass stars, in the domain of M dwarfs, in the GC NGC 104 (47 Tucanae).Since the seventies, the presence of multiple stellar populations with different light-element abundances in this GC has been strongly established from the analysis of bright RGB stars (e.g.Dickens et al. 1979;Bell et al. 1983;Brown et al. 1990;Briley et al. 1991).Nowadays, we know that 47 Tucanae hosts two main stellar populations of 1P and 2P stars, which have been photometrically detected along the main evolutionary phases, including the MS, SGB, RGB, HB, and AGB (e.g.Anderson et al. 2009;Milone et al. 2012a;Lagioia et al. 2021;Jang et al. 2022;Tailo et al. 2020;Lee 2022), and correspond to stars with different light-element abundances (Marino et al. 2019).A range of ∼0.4 dex in [C/Fe], ∼0.5 dex in [O/Fe], and ∼1.0 dex in [N/Fe], (Carretta et al. 2009;Marino et al. 2016;Dobrovolskas et al. 2014) has been observed, whereas helium spans an interval of δY =0.05 in mass fraction (Milone et al. 2018b).Astrometric plus spectroscopic analysis, mostly based on RGB stars or bright MS stars, shows that these stellar populations exhibit different radial distributions and internal kinematics (e.g.Richer et al. 2013;Milone et al. 2018a;Cordoni et al. 2020).
In this work, we exploit the JWS T capabilities to explore the regime of low mass stars in 47 Tucanae, ranging from ∼0.1 M ⊙ , and reaching the H-burning limit and beyond.First photometric data for this program, observed on July, 13, 2022 have recently demonstrated the JWS T 's capability in uncovering multiple populations within the low-mass realm of M dwarfs marking indeed a pivotal advancement in the possibility of understanding the formation and evolution of GCs (Milone et al. 2023a).
Here, we present the latest observations collected in September 2023, including both photometric and spectroscopic data, which allowed us to explore the faintest stars of 47 Tucanae, encompassing a number of astrophysics issues, from the analysis of multiple stellar populations to the observation of brown dwarfs, and to the spectral detection of chemical variations.For the first time, we provide indeed direct spectroscopic evidence of multiple populations among M dwarfs, obtained from the first spectra ever observed in the faint MS of a GC.
The overview of this work is as follows: Section 2 describes the data set; Section 3 presents the color-magnitude diagrams (CMDs) obtained from NIRCam images, and focuses on very low mass stars, including M-dwarfs and the brown dwarfs, which are poorly explored in GCs.This section includes the analysis of multiple populations among Mdwarfs, based on the CMDs.We also present in Section 4 early results based on the spectra of two M dwarfs associated with stellar populations with very different chemical composition, whereas Section 5 compares the fraction of 1P and 2P stars among stars with different masses.Finally, Section 6 discusses and summarizes our results.

DATA AND DATA REDUCTION
To investigate low-mass stars in 47 Tucanae with photometry, we used images collected with the near infrared camera (NIRCam) on board JWS T , the Wide-field Channel of the Advanced Camera (WFC/ACS), the Ultraviolet and Visual channel and the Infrared Channel of the Wide Field Camera 3 of HS T (UVIS/WFC3 and IR/WFC3).The dataset consists in NIRCam images of a field, denoted as C and positioned approximately 11 arcminutes (corresponding to ∼3.5 half light radii, assuming a half light radius of 3.17 ′ from Harris (1996)) westward from the cluster center, (RA∼00 h 21 m 16 s , DEC∼ −72 d 06 m 16 s ), which is observed as part as GO-2560 (PI A. F. Marino).We acquired images of field C simultaneously using the F115W filter of the short-wavelength channel and the F322W2 filter of the long-wavelength channel.These images were captured using the DEEP8 readout pattern and were dithered to effectively cover the gaps between the A and B detectors of the short-wavelength channel.In addition, we used data of a different field, denoted as A (RA∼00 h 22 m 37 s , DEC∼ −72 d 04 m 06 s ) and located about 5 arcmin (∼1.5 half light radii) westward from the center of 47 Tucanae.In particular, we analyzed three regions of field A that have been observed as part of three distinct visits of JWS T (GO-2559, PI I. Caiazzo).
The footprints of these images are shown in Figure 1, where we also show the images of Field B (RA∼00 h 22 m 36 s , DEC∼ −72 d 09 m 27 s ) studied by Milone et al. (2023a).The main properties of the JWS T images of fields A and C and the HS T images of field C are summarized in Table 1, whereas we refer to Milone et al. (2023a) for details on the other images of fields A and B 1 .For completeness, we note that the line-of-sight based rotation axis of 47 Tucanae has inclination of ∼136 • north to east (Bianchini et al. 2013;Cordoni et al. 2020).
To measure stellar fluxes and positions we used a method that is based on two main steps.First-step photometry and astrometry is obtained by using the computer program img2xym.Originally devised by Jay Anderson (e.g. Anderson & King 2006) for the reduction of HS T images, the methodology involves independently measuring stellar fluxes and positions in each image.This is achieved by employing a spatially variable point-spread-function (PSF) model (Anderson & King 2000) along with a 'perturbation PSF' that fine-tunes the fitting process to accommodate slight variations in the telescope focus.The perturbation PSF is obtained through unsaturated, bright, and isolated stars.All magnitude determinations derived from individual filters and cameras have been standardized to a common photometric zero point, aligning with the zero point of the deepest exposure in the chosen filter, which serves as the reference frame for constructing the photometric master frame.This alignment was achieved by utilizing bright, unsaturated stars well-fitted by the PSF to calculate the magnitude differences between the master frame and each exposure.The mean of these differences was then used to transform star measurements in each exposure into the reference frame.For geometric distortion correction, solutions provided by Anderson (2022), Bellini et al. (2011), andMilone et al. (2023a) were applied to adjust stellar positions of UVIS/IR, UVIS/WFC3, and NIRCam images.The coordinates of stars in all cluster images were transformed into a common reference system based on Gaia Data Release 3 (DR3) catalogs (Gaia Collaboration et al. 2021).This transformation ensures alignment with the West and North directions for the abscissa and ordinate, respectively.
The second-step photometry and astrometry of all sources has been carried out with the computer program KS2, which is developed by Jay Anderson and is based on the program kitchen sync by Anderson et al. (2008) (see Sabbi et al. 2016;Bellini et al. 2017;Milone et al. 2023b, for details).
KS2 employs three distinct methods for measuring stars, and each method provides optimal photometry for stars with varying levels of brightness.In method I, which works well for bright stars, the stellar fluxes and positions were independently derived in each individual exposure by using the most suitable effective point-spread function (PSF) model for their specific location on the detector.The sky brightness is measured over an annular region between 4 and 8 pixels from the center of the star.
Method II combines information from all exposures to derive the magnitudes of stars in each exposure by means of aperture photometry, after subtracting the nearby stars.Specifically, we used a 5×5 pixel aperture and determined the sky as in method I.This method works well for faint stars, which often do not have enough photons to constrain their fluxes and positions in the individual exposures.Method III is similar to method II.The main difference is that the aperture photometry is computed by considering a circular region with a radius of 0.75 pixels, and the background sky is determined from the annulus located between 2 and 4 pixels away from the initially identified position.Subsequently, the multiple measurements for each star were averaged to obtain the most accurate estimations of their magnitudes and positions.
We used the parameters that are indicative of the astrometric and photometric quality provided by the KS2 computer programs to select the stars that are well-fitted by the PSF model.To do this, we used the procedure by Milone et al. (2023b, see their section 2.4).Photometry has been calibrated to the Vega system as in Milone et al. (2023b) and by using the zero points available in the Space Telescope Science Institute webpage2 for WFC3 and NIRCam.We verified that the photometry is not affected by significant reddening variations across the field of view (Legnardi et al. 2023).Hence, we did not correct the photometry for differential reddening.
Proper motions are derived as in Milone et al. (2023a, see their section 2.3) by comparing the distortion-corrected positions of stars measured at different epochs.The propermotion diagram derived for field-C stars brighter than m F322W2 = 24.0 is plotted in the left panel of Figure 2, showcasing two primary stellar clumps encompassing the majority of cluster members and Small Magellanic Cloud (SMC) stars.The red circle is used to distinguish probable 47 Tucanae members from field stars, which are colored black and red, respectively, in the m F322W2 vs.
The m F115W vs. m F115W − m F322W2 CMD of all stars with available proper motions is plotted in the left panel of Figure 3.We computed for each star the proper motion relative to the average proper motion of 47 Tucanae, µ R , and plotted this quantity against the F115W magnitude.For magnitudes brighter than m F115W = 26.1 mag the stars of 47 Tucanae and the SMC stars exhibit distinct proper motions.Hence, we draw by eye the vertical aqua line to separate the bulk of cluster members from the field stars, which are colored black and red, respectively in the left and middle panels of Figure 2. Due to the large observational errors, the proper motions of stars fainter than m F115W = 26.1 mag do not allow us to disentangle field stars from cluster members.
To estimate the amount of faint field stars that we expect in the field C, we compare the observed m F322W2 vs. m F115W − m F322W2 CMD of all stars with available NIRCam photome-Table 1. Description of the images used in the paper.For each dataset, we indicate the mission (JWS T or HS T ), the camera, the filter, the date, the exposure times, the GO program, and the principal investigator.We also indicate the visit numbers of GO-2559 observations.The observations collected during visit 1, 2, and 3 are centered around (RA,DEC)=(0 h 22 m 6.0 s , −72 d 03 m 51 s ), (0 h 22 m 13.9 s , −72

Artificial stars and completeness
We conducted artificial star (AS) experiments to estimate the photometric uncertainties and the completeness level of our sample by using the procedure adopted in previous papers (e.g.Anderson et al. 2008).These stars were distributed across the field of view similarly to the cluster stars and along the fiducial lines of the main sequence (MS) of 47 Tucanae that we derived from the observed CMDs.The ASs have been reduced by using exactly the same procedure adopted for the real stars.The KS2 computer program generates the same diagnostic measurements of photometric and astrometric quality for ASs as it does for real stars.In our analysis, we considered only a subset of artificial stars that are relatively isolated, exhibit good PSF fitting, and show small root mean square (rms) values in magnitudes.These artificial stars were selected using the same criteria we applied to real stars in our investigation.
We partitioned the NIRCam field for each field into five concentric anuli, centered on 47 Tucanae.Within each annulus, we analyzed the results of the artificial star experiments in a number of N distinct 0.5 magnitude bins, spanning from the saturation limit to approximately one F322W2 magnitude below the faintest star that we detected.For each of the 5×N grid positions, we calculated the average completeness by comparing the number of recovered ASs with the input artificial stars within that particular bin.

NIRSpec spectra
NIRSpec has been used in the multi-object spectroscopy (MOS) mode, involving a micro-shutter assembly (MSA) configuration, which allowed us the simultaneous collec- tion of 29 source spectra of sufficient quality, within a 3.4 ′ × 3.6 ′ field of view centered on field B. We choose the G235M/F170LP disperser and filter combination, which observes the wavelength range 1.66-3.07µm, at a nominal resolving power of ∼1,000.
The improved reference sampling and subtraction (IRS 2 ) readout mode, with the NRSIRS2 pattern, which has 5 frames averaged into a single group, has been employed for our MOS observations.Each source has been observed with a 2-Shutter nod in Slitlet pattern with two identical configurations and each configuration has been executed ten times.Each exposure was observed for 1,182s (with 16 groups per integration), for a total on-target time of 47,280s.However, a dither of 20 ′′ in the dispersion direction has been applied to close the detector gap.In the end, of our 29 observed stars, 17 are covered by both dither positions, hence have all the 40 exposures, while 12 have only one dither position (20 exposures).
We have analysed the NIRSpec 1-D extracted spectra processed with the JWS T Science Calibration Pipeline (Bushouse et al. 2023).While for a full analysis of the individual stars we refer to a forthcoming paper devoted to the oxygen estimates, we anticipate in this paper the results for spectra of M-dwarfs with extreme chemical compositions.

THE NIRCAM CMD OF 47 TUCANAE
The m F322W2 vs. m F115W −m F322W2 CMD of stars in the field C is illustrated in the lower panels of Figure 4, whereas the upper panels show portions of the NIRCam field of view.We notice that the m F115W − m F322W2 color broadening of the upper MS of 47 Tucanae (m F322W2 ≲ 18.7) is comparable with the broadening due to the observational errors alone.In contrast, the MS color spread for stars fainter than the MS knee is much wider than the observational errors.This phenomenon, which is due to the presence of multiple populations among the M-dwarfs, will be further investigated in Section 3.3.In the following Section 3.1 we investigate the stars at faintest magnitudes approaching the H-burning limit.

Ultracool dwarfs
We analyse here the faintest 47 Tucanae stars appearing in the m F322W2 vs. m F115W −m F322W2 CMD of Figure 4.In particular, we focus on the faintest portion of the CMD, composed by a plume of stars extending from the bottom of the vertical sequence (at m F322W2 ∼ 23.3 mag) down to m F322W2 ∼ 27.0 mag.This sparsely populated group of stars covers a wide color range (∼2 mag) and it appears as an extension of the bluest portion of the vertical sequence composed by the cluster's M dwarfs.A quick glance at this sequence suggests that its stars, which have masses less than ∼ 0.1 M ⊙ , are not continuously distributed.In particular, we notice the presence of compelling features, namely, possible clumps at m F322W2 ∼ 23.3, a sharp gap ∼ 24.2 mag, and a distinct change in slope at ∼ 24.5 mag (see also Figure 4   The observed luminosity function approaches its minimum value around m F322W2 ∼ 25.3, and rises up toward fainter luminosities, where we observe the bright portion of the browndwarf sequence.As an example of the analysed field of view, the upper-right panels of Figure 4 show a zoom of the stacked F322W2 and F115W images that include two probable brown dwarfs (red and blue circles).
To further investigate the lower MS of 47 Tucanae, we show in the left panel of Figure 5  The luminosity and mass functions may provide additional information of low mass stars in 47 Tucanae.Unfortunately, isochrones that reproduce both massive and lowmass stars in 47 Tucanae are not available to us as shown in the left panel of Figure 6, where we compare the m F322W2 vs. m F115W − m F322W2 CMD with three isochrones.We have marked with black dots the probable cluster MS and brown dwarfs that we selected by eye, whereas the white dwarfs of 47 Tucanae and the Small Magellanic Cloud (SMC) stars are colored grey.The red and the blue isochrones provide the best fit of 1P and 2P stars with extreme chemical composition, respectively, and comprise stars more massive than ∼ 0.1 M ⊙ .These isochrones, which refer specifically to 47 Tucanae and are described in detail by Milone et al. (2023a), are extracted from the Dartmouth database (Dotter et al. 2008)   To derive the mass-luminosity relation for stars less massive than ∼ 0.1 M ⊙ we tentatively used the tracks by Phillips et al. (2020) (brown isochrone plotted in the left panel of Figure 6), which however are based on model atmospheres and evolution models for brown dwarfs and giant exoplanets with solar metallicity.Clearly, this isochrone, which is computed for an age of 10 Gyr, does not match the browndwarf sequence of 47 Tucanae, and differs from those derived by Gerasimov et al. (2023) that qualitatively reproduce the observed CMDs.In a recent paper, Nardiello et al. (2023) identified ten candidate brown dwarfs by using the m F322W2 vs. m F115W − m F322W2 CMD of field-B stars in 47 Tucanae.These stars, are distributed along the isochrone by Phillips et al. (2020) and span F322W2 magnitudes between ∼25.2 and 25.8 mag are superimposed on the SMC MS and may then belong to SMC rather than to 47 Tucanae.Accurate stellar proper motions, which are mandatory to disentangle SMC stars and possible cluster members, are not available for these very faint stars.Hence, we neither exclude nor confirm the presence of brown dwarfs in 47 Tucanae following the Phillips et al. isochrone.In the following, we only focus on the sequence of ultracool stars analyzed in this paper.
The luminosity functions of 47 Tucanae stars are plotted in the top-right and middle-right panel of Figure 6, for the stars observed with the detectors A and B of the long NIRCam channels and for all stars together.Specifically, we plotted the logarithm of the numbers of stars per square arcmin, cor-rected for completeness, as a function of the m F322W2 magnitude.The star counts are calculated in 0.4-mag wide bins.The luminosity function exhibits a peak around m F322W2 ∼ 20.2.As we move towards fainter luminosities, the star count per unit magnitude consistently decreases, reaching its minimum around m F322W2 ∼ 25.3 mag.Beyond this point, the number of stars increases for fainter values of m F322W2 .
The bottom-right panel of Figure 6 shows a tentative determination of the mass function, which is derived from the luminosity function plotted in the middle-right panel.For simplicity, we did not account for the multiple populations in 47 Tucanae, and we used the red isochrone plotted in the left panel to convert the luminosities into stellar masses for stars  4, where we used black colors to mark the probable MS and brown dwarfs of 47 Tucanae.We superimposed on the CMD the best-fit isochrones for MS stars (Dotter et al. 2008;Milone et al. 2023a) and the isochrone by Phillips et al. (2020) for low-mas stars.The horizontal lines mark the magnitudes corresponding to four stellar masses inferred from the red isochrone and from Gerasimov et al. (2023).Right.F322W2 luminosity function of 47 Tucanae stars along the MS and the brown-dwarf sequence obtained by using 0.4-wide magnitude bins.The open circles are derived from stars where the correction for the incompleteness of the photometric sample is smaller than 50%.The top panel shows the luminosity functions of stars in the detectors A and B of the long-wavelength channel of NIRCam, separately, which have different radial distances of ∼11.5 and 14.5 arcmin from the cluster center.The middle panel shows the results from the entire field of view.The grey points in the middle panel are derived by using 0.4-wide magnitude bins but by changing the starting magnitude value of the LF by 0.1, 0.2, and 0.3 mag with respect to the value used for the black points.The bottom panel shows the mass function for stars in the entire field of view.The vertical dotted line corresponds to 0.11 solar masses.See the text for details.
brighter than m F322W2 ∼ 22.5, which have masses larger than ∼ 0.1 M ⊙ , In this mass interval, we find that the mass function exhibits a peak at ∼0.5 M ⊙ and declines toward lower masses.
Due to the lack of appropriate isochrones for stars with masses lower than ∼ 0.1 M ⊙ , it is not possible to provide accurate mass functions for these stars.Nevertheless, we assumed that the luminosity m F322W2 = 25.3 corresponds to a stellar mass of 0.074 M ⊙ , which according to Gerasimov et al. (2023) corresponds to the hydrogen-burning limit, whereas stars with m F322W2 = 27 have 0.06 solar masses, as predicted by Gerasimov and collaborators.The results are plotted in the bottom-right panel of Figure 6, showing an abrupt change in the mass function slope at the assumed hydrogen-burning limit.We are reluctant to take for good this result, because of the tentative mass-luminosity relation we have adopted.

The M-Dwarf to Brown-Dwarf Transition in
47 Tucanae.
As emphasised by Gerasimov et al. (2023), the termination of the hydrogen-burning MS is expected to exhibit a gap in the CMD between the faintest MS stars and the brightest brown dwarfs.Thus, it is tantalising to identify this gap (i.e., the termination of the MS) with the evident gap at m F322W2 ∼ 24.2 seen in Figure 5.In their simulations Gerasimov et al. do not find a similar gap at this luminosity (their Figure 6), whereas a gap may appear at a much fainter luminosity, m F322W2 ∼ 26 (their Figure 10).This corresponds to the minimum in their synthetic luminosity function at this latter magnitude, as illustrated in their Figure 9. Thus, Gerasimov et al. (2023) associate this minimum with the hydrogen-burning limit.
Our observed luminosity function shows also a sharp minimum (see Figure 6), but it is found at m F322W2 ∼ 25.3, i.e., around half magnitude brighter than predicted by Gerasimov et al.So, where is the hydrogen-burning limit in 47 Tuc?Is it at m F322W2 ∼ 24.2, at 25.3, or at 26? What would be needed is an extended set of isochrones, possibly with options in the input physics.The data we present here represents a major jump in depth and completeness, for coeval M and brown dwarfs all at the same distance and extending down to unprecedented faint luminosities.These data demand a new, parallel effort in modelling M dwarfs and brown dwarfs.
In the meantime, we can still speculate on the nature of of the gap at m F322W2 ∼ 24.2 and the origin of the different luminosities at the minimum of the luminosity function, just mentioned above.If the gap does not correspond to the hydrogenburning limit, what else can cause it?These M dwarfs are fully convective, so convection effects could hardly result in such a sharp discontinuity (note that a drop is not evident in the luminosity function at this magnitude because of the binning, except in the case of blue points in Figure 6).Could atmospheric effects cause it?We don't know, so it remains an unsolved issue.
Similarly, we cannot unambiguously pinpoint the origin of the mag discrepancy in the minimum of the luminosity function.Both sets use Vega magnitudes, so it cannot be a zeropoint issue.Maybe it is due to a systematic effect on the stellar models, in a regime in which a small difference in mass can result in a large difference in luminosity.On the observational side, at these faint magnitudes the luminosity function of galaxies is raising steeply, so we cannot exclude that our luminosity function of 47 Tucanae is partly contaminated by faint galaxies.Still we have excluded morphologically non-stellar objects in constructing the luminosity functions of 47 Tucanae.

Multiple stellar populations
The m F322W2 vs. m F115W −m F322W2 CMD of Figure 4 clearly shows that the MS color broadening, which is comparable with that expected from observational errors for stars brighter than the MS knee, suddenly increases among Mdwarfs fainter than the MS knee, and approaches a value of more than 0.2 mag in the F322W2 interval between ∼20 and 23 mag.
Figure 7 provides additional information on the color distribution of MS stars.We derived by eye the aqua dashed-dot line shown in panel a) to define the blue boundary of the MS.Subsequently, we utilized this line to generate the verticalized m F322W2 vs. δ(m F115W − m F322W2 ) diagram represented in panel b).To achieve this, we subtracted the color of each star from the color of the aqua fiducial associated with the identical F322W2 magnitude.Panels c) show the histograms and the kernel-density distributions of δ(m F115W − m F322W2 ) in six intervals of F322W2 magnitude.The latter is obtained by using a Gaussian kernel with dispersion, σ=0.02 mag.
When considering a MS portion with nearly constant F322W2 magnitude, the majority of M-dwarfs in this luminosity interval exhibits blue colors.In particular, the histograms of Figure 7c exhibit a peak around δ(m F115W − m F322W2 )=0.02 mag, which corresponds to the bulk of 1P stars.However, there is a tail of stars that extends towards red colors.
The color broadening is mostly due to the star-to-star oxygen variations, which are associated with multiple stellar populations.The main culprit is the absorption of different chemical species containing oxygen, mainly H 2 O (the primary absorber) and OH.The absorption features of these molecules strongly affect the flux in F322W2 band whereas the F115W filter is poorly sensitive to oxygen variations.As a consequence, the 1P stars, which have higher oxygen abundances than the 2P, exhibit fainter F322W2 magnitudes and bluer m F115W − m F322W2 colors than stars with similar atmospheric parameters (Milone et al. 2012b(Milone et al. , 2023a;;Dotter et al. 2015;VandenBerg et al. 2022;Ziliotto et al. 2023).
To quantify the amount of oxygen that is needed to reproduce the m F115W − m F322W2 MS broadening, we compared isochrones with different oxygen abundances (Dotter et al. 2008;Milone et al. 2023a) with the observed CMD.Specifically, we considered the isochrones with [O/Fe]=0.4and [O/Fe]=−0.1.To properly compare the relative colours of 47 Tucanae stars with those of the isochrones, we have calculated the colour difference between the O-poor isochrone and the O-rich one and shifted both verticalized isochrones by δ(m F115W − m F322W2 )=0.02 mag, in such a way that the red isochrone is superimposed on the bulk of 1P stars.The δ(m F115W − m F322W2 ) interval spanned by stars brighter than m F322W2 ∼ 22.5 mag, which have masses larger than ∼0.1 M ⊙ , is consistent with an oxygen variation of ∼0.5 dex, comparable with the [O/Fe] range inferred for RGB stars from high-resolution spectroscopy (e.g.Carretta et al. 2009;Dobrovolskas et al. 2014).We conclude that the stars in the mass interval between ∼0.1 and 0.9 solar masses span a similar range of [O/Fe].
Intriguingly, as noticed by Milone et al. (2023a) for the stars in the field B, the MS color broadening of stars fainter than m F322W2 ∼ 23 mag appears to be much smaller than that observed for brighter M-dwarfs in F322W2 magnitude range ∼20.0-22.5.Unfortunately, there are no available isochrones that account for multiple stellar populations among ultracool stars.Hence, we can not provide a firm conclusion on whether or not this fact is due to the lack of stellar populations with extreme chemical composition among these very low-mass stars.Additional qualitative information on multiple populations among stars less massive than ∼0.1 solar masses is provided by the visual comparison between the ob-  10), which accounts for the chemical compositions of the multiple populations of 47 Tucanae.The simulated CMD exhibits a wide m F150W2 − m F322W2 color range of ∼0.5 mag for stars with m F322W2 ∼ 24 mag, which seems in contrast with the narrow sequence of ultracool stars with similar luminosity observed in Figure 5.This fact suggests a possible lack of very O-poor 2P stars among ultracool stars.
Additional information on multiple populations in 47 Tucanae is provided by the m F814W vs. C F606W,F814W,F322W2 pseudo CMD of the stars in field B shown in the top panel of Figure 8.In this diagram, the stars fainter than the MSknee, identified at approximately m F814W = 20.0 mag, reveal hints of four discrete sequences.According to the isochrones provided by Dotter et al. (2008) and Milone et al. (2023a), which consider the chemical composition of multiple populations, the reddest sequence is composed of 1P stars, while the 2P stars with particularly extreme chemical compositions display bluer C F606W,F814W,F322W2 pseudocolors.

THE CHEMICAL COMPOSITION OF M-DWARFS FROM NIRSPEC SPECTRA
In this Section we present NIRSpec spectra for two M dwarfs photometrically associated with different stellar populations.The location of these stars in the photometric diagrams is shown in Figure 8.The large dots superimposed on the pseudo-CMD and the ChM of Figure 8 mark indeed two stars with comparable F814W magnitudes.However, these stars exhibit distinct values for ∆ CF606W,F814W,F322W2 and ∆ F606W,F814W .Based on their location in Figure 8, upper panel, the red-and blue-dot stars are labelled as 1P and 2P, respectively.
The two targets have been spectroscopically observed as part of GO-2560, and their NIRSpec spectra are displayed in the bottom-left panel of Figure 8.The red spectrum represents the star with RA=0 h 22 m 22.14 s and DEC=−72 d 04 m 10.5 s while the blue spectrum correspond to the star with RA=0 h 22 m 12.36 s and DEC=−72 d 04 m 30.8 s .In present-ing the spectra, we applied the same shift to both spectra, plotting them such that the average value of −2.5 log 10 (flux) in the region with λ < 1.75 µm for the blue spectrum equals zero.
Clearly, the spectrum of the 1P star exhibits much stronger molecular bands than that of the 2P star.In principle, such large difference in the spectra could be either due to different atmospheric parameters or to different chemical composition.The location of the two stars at similar m F814W magnitudes suggests that they have similar atmospheric parameters.Indeed, by fitting the m F814W vs. m F606W −m F814W CMD with the isochrones by Dotter et al. (2008) and Milone et al. (2023a) we obtain T eff /log g=3700/5.0and 3600/5.0for the blue and the red star, respectively.Such a small difference in the atmospheric parameters alone cannot account for the differences of the observed spectra.
As outlined in the spectra of Figure 8, the main molecular feature appearing in the observed spectral range are due to rotational-vibrational H 2 O band heads at 1.9 and 2.7 µm, and some contribution from the CO second overtone bands are rather masked by the H 2 O bands.The water vapour molecular bands in the near-IR are good indicators of oxygen abundance.
While for a full detailed spectroscopic analysis of all the observed NIRSpec spectra we refer the reader to an upcoming paper, here we illustrate two synthetic spectra constructed with the atmospheric parameters assumed for our two M dwarfs to infer a first estimate of the O range in the low mass regime of 47 Tucanae.
The bottom-right panel of Figure 8 shows the comparison of the observed spectra with simulated spectra with different light-element abundances.The simulated spectra are derived as in our previous works (Milone et al. 2023a;Ziliotto et al. 2023).In a nutshell, we calculated the model atmospheres using the ATLAS 12 computer program, employing the opacity-sampling technique and assuming local thermodynamic equilibrium (Kurucz 1970;Sbordone et al. 2004).We incorporated molecular line lists for all diatomic molecules listed on Kurucz's website, in addition to including H 2 O molecules from Partridge & Schwenke (1997).We used the SYNTHE computer program (Kurucz & Avrett 1981;Castelli 2005;Kurucz 2005;Sbordone et al. 2007) to compute the spectra in the region between 1.7 and 3.2 µm covered by the available NIRSpec spectra.Specifically, the crimson spectrum has oxygen content [O/Fe]=0.3dex, whereas the teal one has [O/Fe]=−0.1 dex.Noticeably, the blue spectrum has higher effective temperature than the red one by 70 K.This effective temperature difference is consistent with the fact that 2P stars of 47 Tucanae are helium enhanced with respect to the 1P (e.g.Lagioia et al. 2018;Milone et al. 2018b).(Dotter et al. 2008;Milone et al. 2023a).Panels c illustrate the δ(m F115W − m F322W2 ) histogram distributions for stars in six F322W2 magnitude intervals and the corresponding kernel-density distributions.
We conclude that the comparison of the spectra of the two M dwarfs belonging to different stellar populations indicates that M dwarfs exhibit a range in the O abundances very similar to that reported in the literature on higher mass stars along the RGB.The result presented here is the first detection of the O range directly performed on stellar spectra of M dwarfs, and strongly corroborates our previous findings about the similarity of the multiple stellar populations in stars with different masses (from the RGB to M dwarfs), already suggested by photometric diagrams.

POPULATION RATIOS
To derive the fraction of stars in the main stellar populations of 47 Tucanae we started using the ∆ F110W,F160W,F115W,F322W2 vs. ∆ F606W,F110W ChM of stars in field C, which is derived from the m F322W2 vs. m F110W − m F160W + m F115W − m F322W2 pseudo-CMD plotted in Figure 2 and the m F322W2 vs. m F606W − m F110W CMD.
The results are plotted in the left panel of Figure 9.The 1P stars are clustered around the origin of the ChM, while the 2P defines a sequence ranging from (∆ F606W,F110W ,∆ F110W,F160W,F115W,F322W2 ) (∼ −0.2, 0.1) towards the top left corner of the ChM.
To assess the proportion of stars within each population, we expanded upon the approach outlined by Zennaro et al. (2019) to derive the fraction of stars in the four stellar populations of the GC NGC 2419 and apply it to the ChM of 47 Tucanae (see also Milone et al. 2012aMilone et al. , 2020;;Nardiello et al. 2018).In a nutshell, we estimated the mean values of ∆ F606W,F110W and ∆ F110W,F160W,F115W,F322W2 for the stars within each population (depicted as colored dots in Figure 9).In the case of 1P stars, we used two values for the center to account for sub-populations with different metallicity (Legnardi et al. 2022;Marino et al. 2023).These values served to define five distinct regions denoted as R 1 , R 2A , R 2B , R 2C , and R 2D and delimited by the colored solid lines.Owing to photometric errors, each region may encompass stars from all populations.As an example, the observed count of stars   within region R1 is: (1) where N 1P , N 2PA , N 2PB , N 2PC , and N 2PD , are the numbers of 1P, 2P A , 2P B , 2P C , and 2P D stars in each population in our sample.
The number of stars within the regions R 2A , R 2B , R 2C , and R 2D are linked to the fraction of stars of each population through four comparable equations.The values of N R1 , N R2A , N R2B , N R2C , and N R2D used in these equations are derived by counting the stars within the corresponding regions.
The fractions of 1P, 2P A , 2P B , 2P C , and 2P D stars within the region R1, f R1 1P , f R1 2PA , f R1 2PB , f R1 2PC , and f R1 2PD are derived from simulated ChMs composed of ASs, and we did the same for inferring the fractions of stars of each populations in the regions of the ChM R 2A , R 2B , R 2C , and R 2D .To do this, we simulated 50,000 ASs for each population, disposed along the centers of each population in the ChM.
The numbers of stars in the five populations of 47 Tucanae, N 1P , N 2PA , N 2PB , N 2PC , N 2PD , are calculated by solving for these five equations.The results are provided in Table 2, where we also provide the fractions of stars in the five stellar populations that we obtain by extending the same procedure to the ChM shown in Figure 8 for stars in field A. In particular, we find that 1P stars comprise the 38.1±1.2% and the 46.3±4.2% of the total number of ChM stars of field A and field C, respectively.
The fraction of 2P stars in 47 Tucanae inferred from either RGB or HB stars significantly changes as a function of the radial distance.It ranges from about 80% near the cluster centers to less than 60% for distances larger than ∼5 arcmin (Milone et al. 2012c(Milone et al. , 2017b;;Cordero et al. 2014;Don-doglio et al. 2021;Lee 2022).Figure 10 compares the values of the fractions of 2P stars derived by Dondoglio et al. (2021) from HB stars with different radial distances (black points) and those obtained in this paper from M-dwarfs (red triangles).We conclude that there is no significant difference between the fractions of 2P stars derived from stars with different masses.In the context of the multiple generations scenario, where the 2P stars form in the dense cluster center, this would imply that the IMF does not depend on the density of the environment.

SUMMARY AND CONCLUSIONS
We have presented our JWS T project on multiple stellar populations in the GC 47 Tucanae.Our main dataset comprised ∼13h observing time with NIRSpec+NIRCam parallel observations, allowing us to infer crucial constraints on the multiple-population phenomenon both from spectroscopic and photometric analysis.This is the first project specifically devoted to the analysis of multiple stellar populations in GCs conducted with the JWS T .However, in addition to studies on multiple populations, our dataset demonstrated to have the potential to investigate the general properties of the poorly-explored stellar populations, such as the Mdwarfs and brown-dwarfs.In this work, we present early results which allowed us to study the low mass stars, in the domain of M dwarfs and beyond, down to the hydrogen-burning limit and the brown-dwarf sequence.
This overview sheds light on multiple populations among low-mass stars of 47 Tucanae.The main results can be summarized as follows.
• The photometric diagrams constructed with the F322W2 filter of NIRCam, including the m F322W2 vs. m F115W − m F322W2 CMD and the m F322W2 vs. C F606W,F814W,F322W2 pseudo-CMD, reveal that, below the knee, MS stars with masses larger than ∼ 0.1 M ⊙ and similar F322W2 luminosities span a wide color, or pseudo color, range.This result corroborates the evidence of multiple stellar populations among M-dwarfs (see e.g., Dondoglio et al. 2022;Milone & Marino 2022;Milone et al. 2023a;Cadelano et al. 2023, for previous photometric studies of multiple populations among very low mass stars in 47 Tucanae).
• The comparison between isochrones with different chemical compositions and the observed CMD reveals that the MS color broadening observed among M-dwarfs more-massive than ∼0.1 solar masses is consistent with stellar populations with different oxygen abundances.The [O/Fe] range of ∼0.5 dex that is needed to reproduce the observations is comparable with that observed among RGB stars by means • We present the NIRSpec spectra for two stars with similar F814W magnitude that occupy extreme positions in the ChM and are associated with the populations 1P and 2P C .For a fixed wavelength, the 1Pstar spectrum is more-absorbed than the spectrum of the 2P C star.The comparison with synthetic spectra with different chemical compositions reveals that the two stars have different oxygen abundances, with the 2P C M-dwarf being depleted by [O/Fe]=0.4dex with respect to the 1P star.Hence, the flux difference can be attributed to molecules consisting of oxygen (predominantly H 2 O), which exhibit strong absorption in the spectra of 1P stars, known for their oxygen-rich composition.This outcome represents the first spectroscopic determination of the chemical composition of M-dwarfs within a GC.It validates the earlier prediction, derived from synthetic spectra, that the observed color variation among M-dwarfs in GCs is attributable to multiple stellar populations characterized by varying oxygen abundances (Milone et al. 2012b).
• The 2P M dwarfs consists in ∼62% and 54% of the total number of M dwarfs, respectively at ∼ 5 and ∼ 11 arcmin from the cluster center.These values are similar to the fraction of 2P stars measured among HB and RGB stars with similar radial distance (Dondoglio et al. 2021;Milone et al. 2012c), thus indicating that the fractions of 2P stars do not depend on stellar mass, at least for stars more massive than ∼0.1 M ⊙ .This result, together with the evidence that M-dwarfs and giant stars span a similar range of [O/Fe], provides a serious challenge to the scenarios for the formation of multiple populations that are based on accretion.
The deep NIRCam photometry collected as part of GO-2560 has allowed us to detect objects in the field of 47 Tucanae down to m F322W2 = 27.0.We have thus explored the faintest MS and brown dwarf regions, which are poorly investigated in GCs.The corresponding results can be summarised as follows: • Based on both the m F322W2 vs. m F115W − m F322W2 and the m F322W2 vs. m F150W2 − m F322W2 CMDs, we detected a main discontinuity along the sequence of very low mass stars (masses smaller than ∼0.1 M ⊙ ) at m F322W2 ∼ 24.2 mag.We also notice clear changes of the MS slope around m F322W2 = 23.3 and 24.5 mag.
• The F322W2 luminosity function of MS stars exhibits a drop in the number of stars around m F322W2 = 25.3 mag, and the number of stars per magnitude interval rises up at fainter luminosities.We tentatively associate this gap with the hydrogen-burning limit.Hence, the deep CMD obtained from GO-2560 photometry unveils, for the first time in a GC, the brown dwarfs cooling sequence.
We can conclude by emphasising that the initial observations of GCs carried out with the JWS T have showcased the telescope's capability to effectively separate multiple populations among M dwarfs and explore the properties of very low mass stars.The results mark the opening of new horizons in the exploration of the lower mass regime.The heightened sensitivity of JWS T to the infrared domain will be indeed instrumental in enabling an efficient and systematic exploration of cool, low-mass stars across a substantial sample of GCs.A current limitation is represented by the insufficient availability of theoretical isochrones and mass-luminosity relations down to the faint limits now reached with JWS T .
try and the simulated CMD calculated by the Trilegal code(Girardi et al. 2005) for a Galactic field with the same area and the same Galactic coordinates as field C. The result is plotted in the right panel of Figure3where we observe that a negligible fraction of Milky Way field star interlopers are expected to contaminate the observed CMD sequences of 47 Tucanae.

Figure 1 .
Figure 1.Footprints of the images used in our work on 47 Tucanae.Cyan and azure colors represent the JWS T and HS T images, respectively, of field A, whereas the JWS T and HS T footprints of field B are colored yellow and orange, respectively.Light and dark green colors indicate JWS T and HS T images of field C. North is up, and east is left.

Figure 2 .
Figure 2. Left.Proper motions for stars in field C brighter than m F322W2 = 24.0mag.Stars in 47 Tucanae, within the red dotted circle, and SMC are clearly separated in this plot.Right.m F322W2 vs. m F110W − m F160W + m F115W − m F322W2 pseudo-CMD for probable cluster members (black circles), which are located within the red dotted circle in the left-panel diagram, and for SMC stars (red crosses).

Figure 3 .
Figure3.m F115W vs. m F115W − m F322W2 CMD for stars in the field C with available proper motions (left panel).The middle panel shows the F115W magnitude as a function of the proper motion relative to 47 Tucanae.The vertical aqua line separates the bulk of cluster members (black points in the left and middle panel) from the field stars (red crosses).The stars below the aqua horizontal line, where the proper motions do not allow us to disentangle field stars from cluster members, are represented with grey crosses.Probable white dwarfs, selected from the m F606W vs. m F606W − m F115W CMD are represented with blue triangles in the left and middle panels.In the right panel we show the m F322W2 vs. m F115W − m F322W2 CMD for all stars in the field CMD (grey points) with the stars simulated by the trilegal Galactic model (red starred symbols,Girardi et al. 2005) for a field with the same area as field C in the direction of 47 Tucanae.
the m F150W2 vs. m F150W2 − m F322W2 CMD of stars in Field A. As highlighted by the Hess diagram plotted in the inset, we confirm the main gap and bend in the CMD already evident in Figure 4.In particular, this diagram clearly shows the change in the slope of the sequence of ultracool stars at m F322W2 = 24.5 mag.The right panels of Figure 5 compare the m F322W2 vs. m F150W2 −m F322W2 (top) and the m F322W2 vs. m F115W − m F322W2 CMDs (bottom)zoomed around the bottom of the MS, that are derived from GO-2559 and GO-2560 data.The dashed lines, derived by eye, enclose the bulk of stars along the MS and the browndwarf sequence that we marked with black circles.The colored symbols mark the stars for which photometry from both GO-2559 and GO-2560 is available.
and share the same age (13 Gyr), iron abundance ([Fe/H]=−0.75) and [α/Fe]=+0.4dex.However, they have different abundances of He, C, N, and O, in such a way that the blue isochrone is enhanced in helium mass fraction by ∆Y=0.04 and in [N/Fe] by 1.2 dex, and depleted in [C/Fe] and [O/Fe] by −0.35 and 0.50 dex, respectively, relative to

Figure 4 .
Figure 4. Top.Three-color (RGB) image of a portion of the studied field of view (field C).We used the stacked F115W and F322W2 images for the B and R channels, respectively, whereas the G channel is obtained by averaging the F115W and F322W2 stacked images (left).The right panels show the F322W2 (top) and F115W (bottom) stacked images for the region within the yellow box highlighted in the field of view on the left panel.Bottom.m F322W2 vs. m F115W − m F322W2 CMD of stars in field C (left).The arrows indicate the location of the possible gaps or discontinuities along the sequence of ultracool 47 Tucanae stars.Stars fainter than m F322W2 ∼ 25.3 mag and with colors redder than m F115W − m F322W2 ∼ 1.5 mag are probable brown dwarfs.The blue and red circles in the CMD highlight two of them, which are also marked in the top-right panel.We choose these two stars, among the brown dwarf sample, for illustrative purposes, as they are located in a relatively small region of the field of view.A zoom around the MS region of 47 Tucanae populated by M-dwarfs is shown in the right panel. the red isochrone that has Y=0.248, [O/Fe]=0.4and solar carbon and nitrogen abundances.To derive the mass-luminosity relation for stars less massive than ∼ 0.1 M ⊙ we tentatively used the tracks byPhillips et al. (2020) (brown isochrone plotted in the left panel of Figure6), which however are based on model atmospheres and evolution models for brown dwarfs and giant exoplanets with solar metallicity.Clearly, this isochrone, which is

Figure 5 .
Figure 5. Left.m F322W2 vs. m F150W2 − m F322W2 CMD of stars in field A (left).The inset shows the Hess diagram of the low MS of 47 Tucanae, where the main gaps and discontinuities are marked with colored arrows.Specifically the crimson arrows indicate the changes in slope at m F322W2 around 23.3 and 24.5 mag, while the teal arrows correspond to the sharp gap at m F322W2 ∼24.2, and the observed minimum in the luminosity function at m F322W2 ∼25.3 mag.Right.m F322W2 vs. m F150W2 − m F322W2 (top) and m F322W2 vs. m F115W − m F322W2 CMDs (bottom) for faint MS stars and brown-dwarfs.The stars observed in both CMDs are represented with colored symbols, specifically: the aqua, orange, and red colors indicate the dwarfs that populate the main MS segments, whereas the likely brown dwarfs observed in both datasets are colored brown.

Figure 6 .
Figure 6.Left.Reproduction of the m F322W2 vs. m F115W − m F322W2 CMD of Figure4, where we used black colors to mark the probable MS and brown dwarfs of 47 Tucanae.We superimposed on the CMD the best-fit isochrones for MS stars(Dotter et al. 2008;Milone et al. 2023a) and the isochrone byPhillips et al. (2020) for low-mas stars.The horizontal lines mark the magnitudes corresponding to four stellar masses inferred from the red isochrone and fromGerasimov et al. (2023).Right.F322W2 luminosity function of 47 Tucanae stars along the MS and the brown-dwarf sequence obtained by using 0.4-wide magnitude bins.The open circles are derived from stars where the correction for the incompleteness of the photometric sample is smaller than 50%.The top panel shows the luminosity functions of stars in the detectors A and B of the long-wavelength channel of NIRCam, separately, which have different radial distances of ∼11.5 and 14.5 arcmin from the cluster center.The middle panel shows the results from the entire field of view.The grey points in the middle panel are derived by using 0.4-wide magnitude bins but by changing the starting magnitude value of the LF by 0.1, 0.2, and 0.3 mag with respect to the value used for the black points.The bottom panel shows the mass function for stars in the entire field of view.The vertical dotted line corresponds to 0.11 solar masses.See the text for details.
served m F322W2 vs. m F150W2 − m F322W2 CMD shown in Figure 5 and the CMD simulated by Gerasimov et al. (2023, see their figure

Figure 7 .
Figure 7. Reproduction of the m F322W2 vs. m F115W − m F322W2 CMD of Figure 4 zoomed around the bottom of the MS of 47 Tucanae (panel a).The aqua line is the blue boundary of the MS and is used to derive the m F322W2 vs. δ(m F115W − m F322W2 ) verticalized diagram shown in panel b.The red and blue lines are the best-fit isochrones for MS stars with [O/Fe]=0.4and [O/Fe]=−0.1 dex, respectively(Dotter et al. 2008;Milone et al. 2023a).Panels c illustrate the δ(m F115W − m F322W2 ) histogram distributions for stars in six F322W2 magnitude intervals and the corresponding kernel-density distributions.

Figure 9 .
Figure 9. ∆ F110W,F160W,F115W,F322W2 vs. ∆ F606W,F110W ChM of M-dwarfs in field C (panel a).Panels b-e illustrate the procedure to estimate the fractions of 1P and 2P stars.The observed ChM is further reproduced in panel (b), while panel (c) shows the simulated ChM where simulated 1P stars are coloured in red.The colored solid lines delimit the four regions used to infer the fraction of stars in each population, while the colored dots mark the average positions in the ChM of the simulated stellar populations.Panels d and e show the ∆ F110W,F160W,F115W,F322W2 and ∆ F606W,F110W kernel distributions for the observed (black line) and the simulated (grey line) stars.

Figure 10 .
Figure 10.Fraction of 2P stars as a function of the radial distance from the cluster centers.Black dots are derived by Dondoglio et al. (2021) by using HB stars, whereas the results obtained in this paper from M-dwarfs are represented with red triangles.The horizontal lines mark the radial interval associated with each point.The dotted and dashed vertical lines mark the core and the half-light radii from the 2010 version of the Harris (1996) catalog.

Table 2 .
Fractions of stars in the five stellar populations of 47 Tucanae for the fields A and C. 381±0.0120.352±0.0120.148±0.0090.065±0.0060.054±0.006C 0.463±0.0420.329±0.0350.122±0.0280.049±0.0210.036±0.014 of high-resolution spectroscopy.We notice that the m F115W − m F322W2 color broadening of very-faint stars (m F322W2 > 23 appears to be narrower than that observed among the M-dwarfs with brighter luminosity, similar with what was observed by Milone et al. (2023a) for stars in field B. An appropriate comparison with isochrones that accounts for the chemical compositions of multiple populations is needed to associate this fact with the possible lack of stellar populations with extreme chemical compositions among ultracool stars.