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Mario Gennaro

Publications and source records attributed to Mario Gennaro.

At least 37 records · Page 2Linked to original sources

A HST Study of the Substellar Population of NGC 2024

We performed a HST/WFC3-IR imaging survey of the young stellar cluster NGC 2024 in three filters probing the 1.4~$μ$m H$_2$O absorption feature, characteristic of the population of low mass and sub-stellar mass objects down to a few Jupyter masses. We detect 812 point sources, 550 of them in all 3 filters with signal to noise greater than 5. Using a distance-independent two-color diagram we determine extinction values as high as $A_V\simeq 40$. We also find that the change of effective wavelengths in our filters results in higher $A_V$ values as the reddening increases. Reconstructing a dereddened color-magnitude diagram we derive a luminosity histogram for both the full sample of candidate cluster members and for an extinction-limited sub-sample containing the 50% of sources with $A_V\lesssim 15$. Assuming a standard extinction law like Cardelli et al. (1989) with a nominal $R_V$=3.1 we produce a luminosity function in good agreement with the one resulting from a Salpeter-like Initial Mass Function for a 1~Myr isochrone. There is some evidence of an excess of luminous stars in the most embedded region. We posit that the correlation may be due to those sources being younger, and therefore overluminous than the more evolved and less extinct cluster's stars. We compare our classification scheme based on the depth of the 1.4$μ$m photometric feature with the results from the spectroscopic survey of Levine et al. (2006), and we report a few peculiar sources and morphological features typical of the rich phenomenology commonly encountered in young star-forming regions.

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Roman Early-Definition Astrophysics Survey Opportunity: Galactic Roman Infrared Plane Survey (GRIPS)

A wide-field near-infrared survey of the Galactic disk and bulge/bar(s) is supported by a large representation of the community of Galactic astronomers. The combination of sensitivity, angular resolution and large field of view make Roman uniquely able to study the crowded and highly extincted lines of sight in the Galactic plane. A ~1000 deg2 survey of the bulge and inner Galactic disk would yield an impressive dataset of ~120 billion sources and map the structure of our Galaxy. The effort would foster subsequent expansions in numerous dimensions (spatial, depth, wavelengths, epochs). Importantly, the survey would benefit from early defintion by the community, namely because the Galactic disk is a complex environment, and different science goals will require trade offs.

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First Sample of H$α$+[O III] $λ$5007 Line Emitters at $z > 6$ Through JWST/NIRCam Slitless Spectroscopy: Physical Properties and Line Luminosity Functions

We present a sample of four emission-line galaxies at $z=6.11-6.35$ that were serendipitously discovered using the commissioning data for the JWST/NIRCam wide-field slitless spectroscopy (WFSS) mode. One of them (at $z=6.11$) has been reported previously while the others are new discoveries. These sources are selected by the secure detections of both [O III] $λ$5007 and H$α$ lines with other fainter lines tentatively detected in some cases (e.g., [O II] $λ$3727, [O III] $λ$4959). In the [O III]/H$β$ - [N II]/H$α$ Baldwin-Phillips-Terlevich diagram, these galaxies occupy the same parameter space as that of $z\sim2$ star-forming galaxies, indicating that they have been enriched rapidly to sub-solar metallicities ($\sim$0.4 $Z_{\odot}$), similar to galaxies with comparable stellar masses at much lower redshifts. The detection of strong H$α$ lines suggests a higher ionizing photon production efficiency within galaxies in the early Universe. We find brightening of the [O III] $λ$5007 line luminosity function (LF) from $z=3$ to 6, and weak or no redshift evolution of the H$α$ line LF from $z=2$ to 6. Both LFs are under-predicted at $z\sim6$ by a factor of $\sim$10 in certain cosmological simulations. This further indicates a global Ly$α$ photon escape fraction of 7-10% at $z\sim6$, slightly lower than previous estimates through the comparison of the UV-derived star-formation rate density and Ly$α$ luminosity density. Our sample recovers $66^{+128}_{-44}$% of $z=6.0-6.6$ galaxies in the survey volume with stellar masses greater than $5\times10^8$ $M_{\odot}$, suggesting the ubiquity of strong H$α$ and [O III] line emitters in the Epoch of Reionization, which will be further uncovered in the era of JWST.

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The JWST Resolved Stellar Populations Early Release Science Program III: Photometric Star-Galaxy Separations for NIRCam

We present criteria for separately classifying stars and unresolved background galaxies in photometric catalogs generated with the point spread function (PSF) fitting photometry software DOLPHOT from images taken of Draco II, WLM, and M92 with the Near Infrared Camera (NIRCam) on JWST. Photometric quality metrics from DOLPHOT in one or two filters can recover a pure sample of stars. Conversely, colors formed between short-wavelength (SW) and long-wavelength (LW) filters can be used to effectively identify pure samples of galaxies. Our results highlight that the existing DOLPHOT output parameters can be used to reliably classify stars in our NIRCam data without the need to resort to external tools or more complex heuristics.

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The JWST Resolved Stellar Populations Early Release Science Program II. Survey Overview

We present the JWST Resolved Stellar Populations Early Release Science (ERS) science program. We obtained 27.5 hours of NIRCam and NIRISS imaging of three targets in the Local Group (Milky Way globular cluster M92, ultra-faint dwarf galaxy Draco II, star-forming dwarf galaxy WLM), which span factors of $\sim10^5$ in luminosity, $\sim10^4$ in distance, and $\sim10^5$ in surface brightness. We describe the survey strategy, scientific and technical goals, implementation details, present select NIRCam color-magnitude diagrams (CMDs), and validate the NIRCam exposure time calculator (ETC). Our CMDs are among the deepest in existence for each class of target. They touch the theoretical hydrogen burning limit in M92 ($<0.08$ $M_{\odot}$; SNR $\sim5$ at $m_{F090W}\sim28.2$; $M_{F090W}\sim+13.6$), include the lowest-mass stars observed outside the Milky Way in Draco II (0.09 $M_{\odot}$; SNR $=10$ at $m_{F090W}\sim29$; $M_{F090W}\sim+12.1$), and reach $\sim1.5$ magnitudes below the oldest main sequence turnoff in WLM (SNR $=10$ at $m_{F090W}\sim29.5$; $M_{F090W}\sim+4.6$). The PARSEC stellar models provide a good qualitative match to the NIRCam CMDs, though are $\sim0.05$ mag too blue compared to M92 F090W$-$F150W data. The NIRCam ETC (v2.0) matches the SNRs based on photon noise from DOLPHOT stellar photometry in uncrowded fields, but the ETC may not be accurate in more crowded fields, similar to what is known for HST. We release beta versions of DOLPHOT NIRCam and NIRISS modules to the community. Results from this ERS program will establish JWST as the premier instrument for resolved stellar populations studies for decades to come.

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JWST NIRCam Defocused Imaging: Photometric Stability Performance and How it Can Sense Mirror Tilts

We use JWST NIRCam short wavelength photometry to capture a transit lightcurve of the exoplanet HAT-P-14 b to assess performance as part of instrument commissioning. The short wavelength precision is 152 ppm per 27 second integration as measured over the full time series compared to a theoretical limit of 107 ppm, after corrections to spatially correlated 1/f noise. Persistence effects from charge trapping are well fit by an exponential function with short characteristic timescales, settling on the order of 5-15 minutes. The short wavelength defocused photometry is also uniquely well suited to measure the realtime wavefront error of JWST. Analysis of the images and reconstructed wavefront maps indicate that two different hexagonal primary mirror segments exhibited "tilt events" where they changed orientation rapidly in less than ~1.4 seconds. In some cases, the magnitude and timing of the flux jumps caused by tilt events can be accurately predicted with a telescope model. These tilt events can be sensed by simultaneous longer-wavelength NIRCam grism spectral images alone in the form of changes to the point spread function, diagnosed from the FWHM. They can also be sensed with the FGS instrument from difference images. Tilt events possibly from sudden releases of stress in the backplane structure behind the mirrors were expected during the commissioning period because they were found in ground-based testing. Tilt events have shown signs of decreasing in frequency but have not disappeared completely. The detectors exhibit some minor (less than 1%) deviations from linear behavior in the first few groups of each integration, potentially impacting absolute fluxes and transit depths on bright targets where only a handful of groups are possible. Overall, the noise is within 50% of the theoretical photon noise and read noise. This bodes well for high precision time series measurements.

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The JWST Resolved Stellar Populations Early Release Science Program I.: NIRCam Flux Calibration

We use globular cluster data from the Resolved Stellar Populations Early Release Science (ERS) program to validate the flux calibration for the Near Infrared Camera (NIRCam) on the James Webb Space Telescope (JWST). We find a significant flux offset between the eight short wavelength detectors, ranging from 1-23% (about 0.01-0.2 mag) that affects all NIRCam imaging observations. We deliver improved zeropoints for the ERS filters and show that alternate zeropoints derived by the community also improve the calibration significantly. We also find that the detector offsets appear to be time variable by up to at least 0.1 mag.

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JWST/NIRCam Coronagraphy: Commissioning and First On-Sky Results

In a cold and stable space environment, the James Webb Space Telescope (JWST or "Webb") reaches unprecedented sensitivities at wavelengths beyond 2 microns, serving most fields of astrophysics. It also extends the parameter space of high-contrast imaging in the near and mid-infrared. Launched in late 2021, JWST underwent a six month commissioning period. In this contribution we focus on the NIRCam Coronagraphy mode which was declared "science ready" on July 10 2022, the last of the 17 JWST observing modes. Essentially, this mode will allow to detect fainter/redder/colder (less massive for a given age) self-luminous exoplanets as well as other faint astrophysical signal in the vicinity of any bright object (stars or galaxies). Here we describe some of the steps and hurdles the commissioning team went through to achieve excellent performances. Specifically, we focus on the Coronagraphic Suppression Verification activity. We were able to produce firm detections at 3.35$μ$m of the white dwarf companion HD 114174 B which is at a separation of $\simeq$ 0.5" and a contrast of $\simeq$ 10 magnitudes ($10^{4}$ fainter than the K$\sim$5.3 mag host star). We compare these first on-sky images with our latest, most informed and realistic end-to-end simulations through the same pipeline. Additionally we provide information on how we succeeded with the target acquisition with all five NIRCam focal plane masks and their four corresponding wedged Lyot stops.

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First Peek with JWST/NIRCam Wide-Field Slitless Spectroscopy: Serendipitous Discovery of a Strong [O III]/H$α$ Emitter at $z=6.11$

We report the serendipitous discovery of an [O III] $λλ$4959/5007 and H$α$ line emitter in the Epoch of Reionization (EoR) with the JWST commissioning data taken in the NIRCam wide field slitless spectroscopy (WFSS) mode. Located $\sim$55" away from the flux calibrator P330-E, this galaxy exhibits bright [O III] $λλ$4959/5007 and H$α$ lines detected at 3.7, 9.9 and 5.7$σ$, respectively, with a spectroscopic redshift of $z=6.112\pm0.001$. The total H$β$+[O III] equivalent width is 664$\pm$98 Å (454$\pm$78 Å from the [O III] $λ$5007 line). This provides direct spectroscopic evidence for the presence of strong rest-frame optical lines (H$β$+[O III] and H$α$) in EoR galaxies as inferred previously from the analyses of Spitzer/IRAC spectral energy distributions. Two spatial and velocity components are identified in this source, possibly indicating that this system is undergoing a major merger, which might have triggered the ongoing starburst with strong nebular emission lines over a timescale of $\sim$2 Myr as our SED modeling suggests. The tentative detection of He II $λ$4686 line ($1.9σ$), if real, may indicate the existence of very young and metal-poor star-forming regions with a hard UV radiation field. Finally, this discovery demonstrates the power and readiness of the JWST/NIRCam WFSS mode, and marks the beginning of a new era for extragalactic astronomy, in which EoR galaxies can be routinely discovered via blind slitless spectroscopy through the detection of rest-frame optical emission lines.

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Planet populations inferred from debris discs: insights from 178 debris systems in the ISPY, LEECH and LIStEN planet-hunting surveys

We know little about the outermost exoplanets in planetary systems, because our detection methods are insensitive to moderate-mass planets on wide orbits. However, debris discs can probe the outer-planet population, because dynamical modelling of observed discs can reveal properties of perturbing planets. We use four sculpting and stirring arguments to infer planet properties in 178 debris-disc systems from the ISPY, LEECH and LIStEN planet-hunting surveys. Similar analyses are often conducted for individual discs, but we consider a large sample in a consistent manner. We aim to predict the population of wide-separation planets, gain insight into the formation and evolution histories of planetary systems, and determine the feasibility of detecting these planets in the near future. We show that a `typical' cold debris disc likely requires a Neptune- to Saturn-mass planet at 10-100 au, with some needing Jupiter-mass perturbers. Our predicted planets are currently undetectable, but modest detection-limit improvements (e.g. from JWST) should reveal many such perturbers. We find that planets thought to be perturbing debris discs at late times are similar to those inferred to be forming in protoplanetary discs, so these could be the same population if newly formed planets do not migrate as far as currently thought. Alternatively, young planets could rapidly sculpt debris before migrating inwards, meaning that the responsible planets are more massive (and located further inwards) than debris-disc studies assume. We combine self-stirring and size-distribution modelling to show that many debris discs cannot be self-stirred without having unreasonably high masses; planet- or companion-stirring may therefore be the dominant mechanism in many (perhaps all) debris discs. Finally, we provide catalogues of planet predictions, and identify promising targets for future planet searches.

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Predicted Trends in Milky Way Bulge Proper Motion Rotation Curves: future Prospects for HST and LSST

We use an $N$-body+smoothed particle hydrodynamics simulation of an isolated barred galaxy to study the age dependence of bulge longitudinal proper motion ($μ_l$) rotation curves. We show that close to the minor axis ($|l| \sim 0^\circ$) the relatively young stars rotate more rapidly than the old stars, as found by Hubble Space Telescope in the Milky Way's (MW's) bulge. This behaviour would be expected also if the MW were unbarred. At larger $|l|$ a different behaviour emerges. Because younger stars trace a strong bar, their galactocentric radial motions dominate their $μ_l$ at $|l| \sim 6^\circ$, leading to a reversal in the sign of $\left< μ_l \right>$. This results in a rotation curve with forbidden velocities (negative $\left< μ_l \right>$ at positive longitudes, and positive $\left< μ_l \right>$ at negative longitudes). The old stars, instead, trace a much weaker bar and thus their kinematics are more axisymmetric, resulting in no forbidden velocities. We develop metrics of the difference in the $\left< μ_l \right>$ rotation curves of young and old stars, and forbidden velocities. We use these to predict the locations where rotation curve reversals can be observed by HST and the Vera Rubin Telescope. Such measurements would represent support for the amplitude of the bar being a continuous function of age, as predicted by kinematic fractionation, in which the bar strength variations are produced purely by differences in the random motions of stellar populations at bar formation.

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Measuring Young Stars in Space and Time -- I. The Photometric Catalog and Extinction Properties of N44

In order to better understand the role of high-mass stellar feedback in regulating star formation in giant molecular clouds, we carried out a Hubble Space Telescope (HST) Treasury Program "Measuring Young Stars in Space and Time" (MYSST) targeting the star-forming complex N44 in the Large Magellanic Cloud (LMC). Using the F555W and F814W broadband filters of both the ACS and WFC3/UVIS, we built a photometric catalog of 461,684 stars down to $m_\mathrm{F555W} \simeq 29$ mag and $m_\mathrm{F814W} \simeq 28$ mag, corresponding to the magnitude of an unreddened 1 Myr pre-main-sequence star of $\approx0.09$ $M_\odot$ at the LMC distance. In this first paper we describe the observing strategy of MYSST, the data reduction procedure, and present the photometric catalog. We identify multiple young stellar populations tracing the gaseous rim of N44's super bubble, together with various contaminants belonging to the LMC field population. We also determine the reddening properties from the slope of the elongated red clump feature by applying the machine learning algorithm RANSAC, and we select a set of Upper Main Sequence (UMS) stars as primary probes to build an extinction map, deriving a relatively modest median extinction $A_{\mathrm{F555W}}\simeq0.77$ mag. The same procedure applied to the red clump provides $A_{\mathrm{F555W}}\simeq 0.68$ mag.

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Measuring Young Stars in Space and Time -- II. The Pre-Main-Sequence Stellar Content of N44

The Hubble Space Telescope (HST) survey Measuring Young Stars in Space and Time (MYSST) entails some of the deepest photometric observations of extragalactic star formation, capturing even the lowest mass stars of the active star-forming complex N44 in the Large Magellanic Cloud. We employ the new MYSST stellar catalog to identify and characterize the content of young pre-main-sequence (PMS) stars across N44 and analyze the PMS clustering structure. To distinguish PMS stars from more evolved line of sight contaminants, a non-trivial task due to several effects that alter photometry, we utilize a machine learning classification approach. This consists of training a support vector machine (SVM) and a random forest (RF) on a carefully selected subset of the MYSST data and categorize all observed stars as PMS or non-PMS. Combining SVM and RF predictions to retrieve the most robust set of PMS sources, we find $\sim26,700$ candidates with a PMS probability above 95% across N44. Employing a clustering approach based on a nearest neighbor surface density estimate, we identify 18 prominent PMS structures at $1$ $σ$ significance above the mean density with sub-clusters persisting up to and beyond $3$ $σ$ significance. The most active star-forming center, located at the western edge of N44's bubble, is a subcluster with an effective radius of $\sim 5.6$ pc entailing more than 1,100 PMS candidates. Furthermore, we confirm that almost all identified clusters coincide with known H II regions and are close to or harbor massive young O stars or YSOs previously discovered by MUSE and Spitzer observations.

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Stellar Parameter Determination from Photometry using Invertible Neural Networks

Photometric surveys with the Hubble Space Telescope (HST) allow us to study stellar populations with high resolution and deep coverage, with estimates of the physical parameters of the constituent stars being typically obtained by comparing the survey data with adequate stellar evolutionary models. This is a highly non-trivial task due to effects such as differential extinction, photometric errors, low filter coverage, or uncertainties in the stellar evolution calculations. These introduce degeneracies that are difficult to detect and break. To improve this situation, we introduce a novel deep learning approach, called conditional invertible neural network (cINN), to solve the inverse problem of predicting physical parameters from photometry on an individual star basis and to obtain the full posterior distributions. We build a carefully curated synthetic training data set derived from the PARSEC stellar evolution models to predict stellar age, initial/current mass, luminosity, effective temperature and surface gravity. We perform tests on synthetic data from the MIST and Dartmouth models, and benchmark our approach on HST data of two well-studied stellar clusters, Westerlund 2 and NGC 6397. For the synthetic data we find overall excellent performance, and note that age is the most difficult parameter to constrain. For the benchmark clusters we retrieve reasonable results and confirm previous findings for Westerlund 2 on cluster age ($1.04_{-0.90}^{+8.48}\,\mathrm{Myr} $), mass segregation, and the stellar initial mass function. For NGC 6397 we recover plausible estimates for masses, luminosities and temperatures, however, discrepancies between stellar evolution models and observations prevent an acceptable recovery of age for old stars.

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HST astrometry in the Orion Nebula Cluster: census of low-mass runaways

We present a catalog of high-precision proper motions in the Orion Nebula Cluster (ONC), based on Treasury Program observations with the Hubble Space Telescope's (HST) ACS/WFC camera. Our catalog contains 2,454 objects in the magnitude range of $14.2<m_{\rm F775W}<24.7$, thus probing the stellar masses of the ONC from $\sim$0.4 $M_\odot$ down to $\sim$0.02 $M_\odot$ over an area of $\sim$550 arcmin$^2$. We provide a number of internal velocity dispersion estimates for the ONC that indicate a weak dependence on the stellar location and mass. There is good agreement with the published velocity dispersion estimates, although nearly all of them (including ours at $σ_{v,x}=0.94$ and $σ_{v,y}=1.25$ mas yr$^{-1}$) might be biased by the overlapping young stellar populations of Orion A. We identified 4 new ONC candidate runaways based on HST and the Gaia DR2 data, all with masses less than $\sim$1 $M_\odot$. The total census of known candidate runaway sources is 10 -- one of the largest samples ever found in any Milky Way open star cluster. Surprisingly, none of them has the tangential velocity exceeding 20 km s$^{-1}$. If most of them indeed originated in the ONC, it may compel re-examination of dynamical processes in very young star clusters. It appears that the mass function of the ONC is not significantly affected by the lost runaways.

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HST survey of the Orion Nebula Cluster in the H$_2$O 1.4 $μ$m absorption band: III. The population of sub-stellar binary companions

We present new results concerning the sub-stellar binary population in the Orion Nebula Cluster (ONC). Using the Karhunen-Loève Image Projection (KLIP) algorithm, we have reprocessed images taken with the IR channel of the Wide Field Camera 3 mounted on the Hubble Space Telescope to unveil faint close companions in the wings of the stellar PSFs. Starting with a sample of $1392$ bona-fide not saturated cluster members, we detect $39$ close-pairs cluster candidates with separation $0.16''-0.77''$. The primary masses span a range M$_p$ $\sim 0.015-1.27$ M$_{\odot}$ whereas for the companions we derive M$_c$ $\sim 0.004-0.54$ M$_{\odot}$. Of these $39$ binary systems, $18$ were already known while the remaining $21$ are new detections. Correcting for completeness and combining our catalog with previously detected ONC binaries, we obtain an overall binary fraction of $11.5\% \pm 0.9\%$. Compared to other star forming regions, our multiplicity function is $\sim 2$ smaller than e.g. Taurus, while compared to the binaries in the field we obtain comparable values. We analyze the mass function of the binaries, finding differences between the mass distribution of binaries and single stars and between primary and companion mass distributions. The mass ratio shows a bottom-heavy distribution with median value of $M_c/M_p \sim 0.25$. Overall our results suggest that ONC binaries may represent a template for the typical population of field binaries, supporting the hypothesis that the ONC may be regarded as a most typical star forming region in the Milky Way.

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HST survey of the Orion Nebula Cluster in the H$_2$O 1.4 $μ$m absorption band: II. The substellar IMF down to planetary masses

We exploit the ability of the Hubble Space Telescope to probe near infrared water absorption present in the atmosphere of low-mass stars, brown dwarfs and planetary mass objects to create a very pure sample of Orion Nebula Cluster (ONC) members, not affected by contamination from background stars and galaxies which lack water absorption. Thanks to these data we infer the Initial Mass Function (IMF) of the ONC in the $0.005 - 1.4$M$_{\odot}$ regime, i.e. down to few Jupiter masses. The young age of the ONC, $\sim1$ Myr, provides a snapshot of the outcome of star formation for the present-day conditions (metallicity, temperature, pressure) of typical Milky Way disk molecular clouds. We demonstrate that the IMF of the ONC is well described by either a log-normal function or a broken power-law, with parameter values qualitatively in agreement with the canonical Chabrier or Kroupa forms for the Milky Way disk IMF. This continuity in the mass distribution provides clues to the fact that the same physical processes may be regulating formation of stars, brown dwarfs, and planetary mass objects. Both the canonical IMF forms under-predict the observed number of very low mass members (below $0.1$ M$_\odot$), a regime where our data allows more precise constraints. Nevertheless, we do not observe a rise or secondary peak in the brown dwarfs or planetary mass regimes. Our study thus contradicts findings based on broad-band near infrared ground-based photometry, which predict an extremely high number of free-floating planets, but likely suffer from unaccounted background contamination.

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HST survey of the Orion Nebula Cluster in the H$_2$O 1.4 $μ$m absorption band: I. A census of substellar and planetary mass objects

In order to obtain a complete census of the stellar and sub-stellar population, down to a few M$_{Jup}$ in the $\sim1$ Myr old Orion Nebula Cluster, we used the infrared channel of the Wide Field Camera 3 of the Hubble Space Telescope with the F139M and F130N filters. These bandpasses correspond to the $1.4 μ$m H$_2$O absorption feature and an adjacent line-free continuum region. Out of $4,504$ detected sources, $3,352$ (about $75\%$) appear fainter than m$_{130}=14$ (Vega mag) in the F130N filter, a brightness corresponding to the hydrogen-burning limit mass (M$\simeq 0.072 M_\odot$) at $\sim 1$ Myr. Of these, however, only $742$ sources have a negative F130M-139N color index, indicative of the presence of H$_2$O vapor in absorption, and can therefore be classified as bona-fide M and L dwarfs, with effective temperatures T$\lesssim 2850$ K at an assumed $1$ Myr cluster age. On our color-magnitude diagram, this population of sources with H$_2$O absorption appears clearly distinct from the larger background population of highly reddened stars and galaxies with positive F130M-F139N color index, and can be traced down to the sensitivity limit of our survey, m$_{130}\simeq 21.5$, corresponding to a $1$ Myr old $\simeq 3 $M$_{Jup}$, planetary mass object under about 2 magnitudes of visual extinction. Theoretical models of the BT-Settl family predicting substellar isochrones of $1, 2$ and $3$ Myr (down to $\sim 1 $M$_{Jup}$) fail to reproduce the observed H$_2$O color index at M$\lesssim 20 $M$_{Jup}$. We perform a Bayesian analysis to determine extinction, mass and effective temperature of each sub-stellar member of our sample, together with its membership probability.

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