arXiv subjects

M. Tosi

Publications and source records attributed to M. Tosi.

At least 55 records · Page 3Linked to original sources

arXiv2017

Exploring the IMF of star clusters: a joint SLUG and LEGUS effort

We present the implementation of a Bayesian formalism within the Stochastically Lighting Up Galaxies (SLUG) stellar population synthesis code, which is designed to investigate variations in the initial mass function (IMF) of star clusters. By comparing observed cluster photometry to large libraries of clusters simulated with a continuously varying IMF, our formalism yields the posterior probability distribution function (PDF) of the cluster mass, age, and extinction, jointly with the parameters describing the IMF. We apply this formalism to a sample of star clusters from the nearby galaxy NGC 628, for which broad-band photometry in five filters is available as part of the Legacy ExtraGalactic UV Survey (LEGUS). After allowing the upper-end slope of the IMF ($α_3$) to vary, we recover PDFs for the mass, age, and extinction that are broadly consistent with what is found when assuming an invariant Kroupa IMF. However, the posterior PDF for $α_3$ is very broad due to a strong degeneracy with the cluster mass, and it is found to be sensitive to the choice of priors, particularly on the cluster mass. We find only a modest improvement in the constraining power of $α_3$ when adding H$α$ photometry from the companion H$α$-LEGUS survey. Conversely, H$α$ photometry significantly improves the age determination, reducing the frequency of multi-modal PDFs. With the aid of mock clusters we quantify the degeneracy between physical parameters, showing how constraints on the cluster mass that are independent of photometry can be used to pin down the IMF properties of star clusters.

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arXiv2017

Legacy ExtraGalactic UV Survey with The Hubble Space Telescope. Stellar cluster catalogues and first insights into cluster formation and evolution in NGC 628

We report the large effort which is producing comprehensive high-level young star cluster (YSC) catalogues for a significant fraction of galaxies observed with the Legacy ExtraGalactic UV Survey (LEGUS) Hubble treasury program. We present the methodology developed to extract cluster positions, verify their genuine nature, produce multiband photometry (from NUV to NIR), and derive their physical properties via spectral energy distribution fitting analyses. We use the nearby spiral galaxy NGC628 as a test case for demonstrating the impact that LEGUS will have on our understanding of the formation and evolution of YSCs and compact stellar associations within their host galaxy. Our analysis of the cluster luminosity function from the UV to the NIR finds a steepening at the bright end and at all wavelengths suggesting a dearth of luminous clusters. The cluster mass function of NGC628 is consistent with a power-law distribution of slopes $\sim -2$ and a truncation of a few times $10^5$ M$_\odot$. After their formation YSCs and compact associations follow different evolutionary paths. YSCs survive for a longer timeframe, confirming their being potentially bound systems. Associations disappear on time scales comparable to hierarchically organized star-forming regions, suggesting that they are expanding systems. We find mass-independent cluster disruption in the inner region of NGC628, while in the outer part of the galaxy there is little or no disruption. We observe faster disruption rates for low mass ($\leq$ $10^4$ M$_\odot$) clusters suggesting that a mass-dependent component is necessary to fully describe the YSC disruption process in NGC628.

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arXiv2016

Hubble Tarantula Treasury Project V. The star cluster Hodge 301: the old face of 30 Doradus

Based on color-magnitude diagrams (CMDs) from the Hubble Space Telescope Hubble Tarantula Treasury Project (HTTP) survey, we present the star formation history (SFH) of Hodge~301, the oldest star cluster in the Tarantula Nebula. The HTTP photometry extends faint enough to reach, for the first time, the cluster pre-main sequence (PMS) turn-on, where the PMS joins the main sequence. Using the location of this feature, along with synthetic CMDs generated with the latest PARSEC models, we find that Hodge~301 is older than previously thought, with an age between 26.5 and 31.5 Myr. From this age, we also estimate that between 38 and 61 supernovae Type-II exploded in the region. The same age is derived from the main sequence turn-off, whereas the age derived from the post-main sequence stars is younger and between 20 and 25 Myr. Other relevant parameters are a total stellar mass of $\approx 8800\,\pm 800$M$_{\odot}$ and average reddening E(B$-$V) $\approx 0.22-0.24$ mag, with a differential reddening $δ$E(B$-$V)$\approx 0.04$ mag.

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arXiv2016

Stellar populations and Star Formation History of the Metal-Poor Dwarf Galaxy DDO 68

We present the star formation history of the extremely metal-poor dwarf galaxy DDO 68, based on our photometry with the Advanced Camera for Surveys. With a metallicity of only $12+\log(O/H)=7.15$ and a very isolated location, DDO 68 is one of the most metal-poor galaxies known. It has been argued that DDO 68 is a young system that started forming stars only $\sim 0.15$ Gyr ago. Our data provide a deep and uncontaminated optical color-magnitude diagram that allows us to disprove this hypothesis, since we find a population of at least $\sim 1$ Gyr old stars. The star formation activity has been fairly continuous over all the look-back time. The current rate is quite low, and the highest activity occurred between 10 and 100 Myr ago. The average star formation rate over the whole Hubble time is $\simeq 0.01$ M$_{\odot}$ yr$^{-1}$, corresponding to a total astrated mass of $\simeq 1.3 \times 10^8$ M$_{\odot}$. Our photometry allows us to infer the distance from the tip of the red giant branch, $D = 12.08 \pm 0.67$ Mpc; however, to let our synthetic color-magnitude diagram reproduce the observed ones we need a slightly higher distance, $D=12.65$ Mpc, or $(m-M)_0 = 30.51$, still inside the errors of the previous determination, and we adopt the latter. DDO 68 shows a very interesting and complex history, with its quite disturbed shape and a long Tail probably due to tidal interactions. The star formation history of the Tail differs from that of the main body mainly for an enhanced activity at recent epochs, likely triggered by the interaction.

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arXiv2016

DDO 68: A flea with smaller fleas that on him prey

We present new photometry of the dwarf irregular galaxy DDO 68, one of the most metal-poor and least massive dwarfs, located in the Lynx-Cancer Void. The images were acquired with the Large Binocular Telescope in the g and r passbands, and show unequivocally that DDO 68 has previously unknown stellar streams related to the accretion of at least two smaller companions: a flea with smaller fleas biting it, to put it in Jonathan Swift's words. Our data provide direct observational evidence of multiple merging occurring at very low galactic mass scales. We present the results of an N-body simulation of the interaction of three dwarf galaxies which reproduces well the main morphological features of DDO 68.

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arXiv2016

The Gaia-ESO Survey: Probes of the inner disk abundance gradient

The nature of the metallicity gradient inside the solar circle (R_GC < 8 kpc) is poorly understood, but studies of Cepheids and a small sample of open clusters suggest that it steepens in the inner disk. We investigate the metallicity gradient of the inner disk using a sample of inner disk open clusters that is three times larger than has previously been studied in the literature to better characterize the gradient in this part of the disk. We used the Gaia-ESO Survey (GES) [Fe/H] values and stellar parameters for stars in 12 open clusters in the inner disk from GES-UVES data. Cluster mean [Fe/H] values were determined based on a membership analysis for each cluster. Where necessary, distances and ages to clusters were determined via comparison to theoretical isochrones. The GES open clusters exhibit a radial metallicity gradient of -0.10+-0.02 dex/kpc, consistent with the gradient measured by other literature studies of field red giant stars and open clusters in the range R_GC ~ 6-12 kpc. We also measure a trend of increasing [Fe/H] with increasing cluster age, as has also been found in the literature. We find no evidence for a steepening of the inner disk metallicity gradient inside the solar circle as earlier studies indicated. The age-metallicity relation shown by the clusters is consistent with that predicted by chemical evolution models that include the effects of radial migration, but a more detailed comparison between cluster observations and models would be premature.

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arXiv2016

The Gaia-ESO Survey: Sodium and aluminium abundances in giants and dwarfs - Implications for stellar and Galactic chemical evolution

Stellar evolution models predict that internal mixing should cause some sodium overabundance at the surface of red giants more massive than ~ 1.5--2.0 Msun. The surface aluminium abundance should not be affected. Nevertheless, observational results disagree about the presence and/or the degree of the Na and Al overabundances. In addition, Galactic chemical evolution models adopting different stellar yields lead to quite different predictions for the behavior of [Na/Fe] and [Al/Fe] versus [Fe/H]. Overall, the observed trends of these abundances with metallicity are not well reproduced. We readdress both issues, using new Na and Al abundances determined within the Gaia-ESO Survey, using two samples: i) more than 600 dwarfs of the solar neighborhood and of open clusters and ii) low- and intermediate-mass clump giants in six open clusters. Abundances of Na in giants with mass below ~2.0 Msun, and of Al in giants below ~3.0 Msun, seem to be unaffected by internal mixing processes. For more massive giants, the Na overabundance increases with stellar mass. This trend agrees well with predictions of stellar evolutionary models. Chemical evolution models that are able to fit well the observed [Na/Fe] vs. [Fe/H] trend in solar neighborhood dwarfs can not simultaneously explain the run of [Al/Fe] with [Fe/H], and viceversa. The comparison with stellar ages is hampered by severe uncertainties. Indeed, reliable age estimates are available for only a half of the stars of the sample. We conclude that Al is underproduced by the models, except for stellar ages younger than about 7 Gyr. In addition, some significant source of late Na production seems to be missing in the models. Either current Na and Al yields are affected by large uncertainties, and/or some important Galactic source(s) of these elements has not been taken into account up to now. [abridged]

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arXiv2015

Hubble Tarantula Treasury Project. III. Photometric Catalog and Resulting Constraints on the Progression of Star Formation in the 30 Doradus Region

We present and describe the astro-photometric catalog of more than 800,000 sources found in the Hubble Tarantula Treasury Project (HTTP). HTTP is a Hubble Space Telescope (HST) Treasury program designed to image the entire 30 Doradus region down to the sub-solar (~0.5 solar masses) mass regime using the Wide Field Camera 3 (WFC3) and the Advanced Camera for Surveys (ACS). We observed 30 Doradus in the near ultraviolet (F275W, F336W), optical (F555W, F658N, F775W), and near infrared (F110W, F160W) wavelengths. The stellar photometry was measured using point-spread function (PSF) fitting across all the bands simultaneously. The relative astrometric accuracy of the catalog is 0.4 mas. The astro-photometric catalog, results from artificial star experiments and the mosaics for all the filters are available for download. Color-magnitude diagrams are presented showing the spatial distributions and ages of stars within 30 Dor as well as in the surrounding fields. HTTP provides the first rich and statistically significant sample of intermediate and low mass pre-main sequence candidates and allows us to trace how star formation has been developing through the region. The depth and high spatial resolution of our analysis highlight the dual role of stellar feedback in quenching and triggering star formation on the giant HII region scale. Our results are consistent with stellar sub-clustering in a partially filled gaseous nebula that is offset towards our side of the Large Magellanic Cloud.

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arXiv2015

Carbon and nitrogen abundances of individual stars in the Sculptor dwarf spheroidal galaxy

We present [C/Fe] and [N/Fe] abundance ratios and CH(λ4300) and S(λ3883) index measurements for 94 red giant branch (RGB) stars in the Sculptor dwarf spheroidal galaxy from VLT/VIMOS MOS observations at a resolving power R= 1150 at 4020 Å. This is the first time that [N/Fe] abundances are derived for a large number of stars in a dwarf spheroidal. We found a trend for the [C/Fe] abundance to decrease with increasing luminosity on the RGB across the whole metallicity range, a phenomenon observed in both field and globular cluster giants, which can be interpreted in the framework of evolutionary mixing of partially processed CNO material. Both our measurements of [C/Fe] and [N/Fe] are in good agreement with the theoretical predictions for stars at similar luminosity and metallicity. We detected a dispersion in the carbon abundance at a given [Fe/H], which cannot be ascribed to measurement uncertainties alone. We interpret this observational evidence as the result of the contribution of different nucleosynthesis sources over time to a not well-mixed interstellar medium. We report the discovery of two new carbon-enhanced, metal-poor stars. These are likely the result of pollution from material enriched by asymptotic giant branch stars, as indicated by our estimates of [Ba/Fe]> +1. We also attempted a search for dissolved globular clusters in the field of the galaxy by looking for the distinctive C-N pattern of second population globular clusters stars in a previously detected, very metal-poor, chemodynamical substructure. We do not detect chemical anomalies among this group of stars. However, small number statistics and limited spatial coverage do not allow us to exclude the hypotheses that this substructure forms part of a tidally shredded globular cluster.

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arXiv2015

Chemical abundances and properties of the ionized gas in NGC 1705

We obtained [O III] narrow-band imaging and multi-slit MXU spectroscopy of the blue compact dwarf (BCD) galaxy NGC 1705 with FORS2@VLT to derive chemical abundances of PNe and H II regions and, more in general, to characterize the properties of the ionized gas. The auroral [O III]\lambda4363 line was detected in all but one of the eleven analyzed regions, allowing for a direct estimate of their electron temperature. The only object for which the [O III]\lambda4363 line was not detected is a possible low-ionization PN, the only one detected in our data. For all the other regions, we derived the abundances of Nitrogen, Oxygen, Neon, Sulfur and Argon out to ~ 1 kpc from the galaxy center. We detect for the first time in NGC 1705 a negative radial gradient in the oxygen metallicity of -0.24 \pm 0.08 dex kpc^{-1}. The element abundances are all consistent with values reported in the literature for other samples of dwarf irregular and blue compact dwarf galaxies. However, the average (central) oxygen abundance, 12 + log(O/H)=7.96 \pm 0.04, is ~0.26 dex lower than previous literature estimates for NGC 1705 based on the [O III]\lambda4363 line. From classical emission-line diagnostic diagrams, we exclude a major contribution from shock excitation. On the other hand, the radial behavior of the emission line ratios is consistent with the progressive dilution of radiation with increasing distance from the center of NGC 1705. This suggests that the strongest starburst located within the central $\sim$150 pc is responsible for the ionization of the gas out to at least $\sim$1 kpc. The gradual dilution of the radiation with increasing distance from the center reflects the gradual and continuous transition from the highly ionized H II regions in the proximity of the major starburst into the diffuse ionized gas.

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arXiv2015

Photometric and spectroscopic study of the intermediate-age open cluster NGC 2355

In this paper we analyse the evolutionary status and properties of the old open cluster NGC 2355, located in the Galactic anticentre direction, as a part of the long term programme BOCCE. NGC 2355 was observed with LBC@LBT using the Bessel $B$, $V$, and $I_c$ filters. The cluster parameters have been obtained using the synthetic colour-magnitude diagram (CMD) method, as done in other papers of this series. Additional spectroscopic observations with FIES@NOT of three giant stars were used to determine the chemical properties of the cluster. Our analysis shows that NGC 2355 has metallicity slightly less than solar, with [Fe/H]$=-0.06$ dex, age between 0.8 and 1 Gyr, reddening $E(B-V)$ in the range 0.14 and 0.19 mag, and distance modulus $(m-M)_0$ of about 11 mag. We also investigated the abundances of O, Na, Al, $α$, iron-peak, and neutron capture elements, showing that NGC 2355 falls within the abundance distribution of similar clusters (same age and metallicity). The Galactocentric distance of NGC~2355 places it at the border between two regimes of metallicity distribution; this makes it an important cluster for the study of the chemical properties and evolution of the disc.

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arXiv2015

The Brightest Young Star Clusters in NGC 5253

The nearby dwarf starburst galaxy NGC5253 hosts a number of young, massive star clusters, the two youngest of which are centrally concentrated and surrounded by thermal radio emission (the `radio nebula'). To investigate the role of these clusters in the starburst energetics, we combine new and archival Hubble Space Telescope images of NGC5253 with wavelength coverage from 1500 Ang to 1.9 micron in 13 filters. These include H-alpha, P-beta, and P-alpha, and the imaging from the Hubble Treasury Program LEGUS (Legacy Extragalactic UV Survey). The extraordinarily well-sampled spectral energy distributions enable modeling with unprecedented accuracy the ages, masses, and extinctions of the 9 optically brightest clusters (M_V < -8.8) and the two young radio nebula clusters. The clusters have ages ~1-15 Myr and masses ~1x10^4 - 2.5x10^5 M_sun. The clusters' spatial location and ages indicate that star formation has become more concentrated towards the radio nebula over the last ~15 Myr. The most massive cluster is in the radio nebula; with a mass 2.5x10^5 M_sun and an age ~1 Myr, it is 2-4 times less massive and younger than previously estimated. It is within a dust cloud with A_V~50 mag, and shows a clear nearIR excess, likely from hot dust. The second radio nebula cluster is also ~1 Myr old, confirming the extreme youth of the starburst region. These two clusters account for about half of the ionizing photon rate in the radio nebula, and will eventually supply about 2/3 of the mechanical energy in present-day shocks. Additional sources are required to supply the remaining ionizing radiation, and may include very massive stars.

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arXiv2015

Hubble Tarantula Treasury Project: Unraveling Tarantula's Web. II. Optical and Near Infrared Star Formation History of the Starburst Cluster NGC 2070 in 30 Doradus

We present a study of the recent star formation of 30 Doradus in the Large Magellanic Cloud (LMC) using the panchromatic imaging survey Hubble Tarantula Treasury Project (HTTP). In this paper we focus on the stars within 20 pc of the center of the massive ionizing cluster of 30 Doradus, NGC 2070. We recovered the star formation history by comparing deep optical and NIR color-magnitude diagrams (CMDs) with state-of-the-art synthetic CMDs generated with the latest PARSEC models, which include all stellar phases from pre-main sequence to post- main sequence. For the first time in this region we are able to measure the star formation using intermediate and low mass stars simultaneously. Our results suggest that NGC2070 experienced a prolonged activity. In particular, we find that the star formation in the region: i) exceeded the average LMC rate ~ 20 Myr ago; ii) accelerated dramatically ~ 7 Myr ago; and iii) reached a peak value 1-3 Myr ago. We did not find significant deviations from a Kroupa initial mass function down to 0.5 Msun. The average internal reddening E(B-V) is found to be between 0.3 and 0.4 mag.

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arXiv2014

The old, metal-poor, anticentre open cluster Trumpler 5

As part of a long term programme, we analyse the evolutionary status and properties of the old and populous open cluster Trumpler 5 (Tr 5), located in the Galactic anticentre direction, almost on the Galactic plane. Tr 5 was observed with WFI@MPG/ESO Telescope using the Bessel $U$, $B$, and $V$ filters. The cluster parameters have been obtained using the synthetic colour-magnitude diagram (CMD) method, i.e. the direct comparison of the observational CMD with a library of synthetic CMDs generated with different stellar evolution sets (Padova, FRANEC, and FST). Age, reddening, and distance are derived through the synthetic CMD method using stellar evolutionary models with subsolar metallicity ($Z=0.004$ or $Z=0.006$). Additional spectroscopic observations with UVES@VLT of three red clump stars of the cluster were used to determine more robustly the chemical properties of the cluster. Our analysis shows that Tr 5 has subsolar metallicity, with [Fe/H]$=-0.403\pm0.006$ dex (derived from spectroscopy), age between 2.9 and 4 Gyr (the lower age is found using stellar models without core overshooting), reddening $E(B-V)$ in the range 0.60 to 0.66 mag complicated by a differential pattern (of the order of $\sim\pm0.1$ mag), and distance modulus $(m-M)_0=12.4\pm0.1$ mag.

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arXiv2014

Legacy ExtraGalactic UV Survey (LEGUS) with The Hubble Space Telescope. I. Survey Description

The Legacy ExtraGalactic UV Survey (LEGUS) is a Cycle 21 Treasury program on the Hubble Space Telescope, aimed at the investigation of star formation and its relation with galactic environment in nearby galaxies, from the scales of individual stars to those of ~kpc-size clustered structures. Five-band imaging, from the near-ultraviolet to the I-band, with the Wide Field Camera 3, plus parallel optical imaging with the Advanced Camera for Surveys, is being collected for selected pointings of 50 galaxies within the local 12 Mpc. The filters used for the observations with the Wide Field Camera 3 are: F275W(2,704 A), F336W(3,355 A), F438W(4,325 A), F555W(5,308 A), and F814W(8,024 A); the parallel observations with the Advanced Camera for Surveys use the filters: F435W(4,328 A), F606W(5,921 A), and F814W(8,057 A). The multi-band images are yielding accurate recent (<~50 Myr) star formation histories from resolved massive stars and the extinction-corrected ages and masses of star clusters and associations. The extensive inventories of massive stars and clustered systems will be used to investigate the spatial and temporal evolution of star formation within galaxies. This will, in turn, inform theories of galaxy evolution and improve the understanding of the physical underpinning of the gas-star formation relation and the nature of star formation at high redshift. This paper describes the survey, its goals and observational strategy, and the initial science results. Because LEGUS will provide a reference survey and a foundation for future observations with JWST and with ALMA, a large number of data products are planned for delivery to the community.

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arXiv2014

The Gaia-ESO Survey: Stellar content and elemental abundances in the massive cluster NGC 6705

Chemically inhomogeneous populations are observed in most globular clusters, but not in open clusters. Cluster mass seems to play a key role in the existence of multiple populations. Studying the chemical homogeneity of the most massive open clusters is necessary to better understand the mechanism of their formation and determine the mass limit under which clusters cannot host multiple populations. Here we studied NGC6705, that is a young and massive open cluster located towards the inner region of the Milky Way. This cluster is located inside the solar circle. This makes it an important tracer of the inner disk abundance gradient. This study makes use of BVI and ri photometry and comparisons with theoretical isochrones to derive the age of NGC6705. We study the density profile of the cluster and the mass function to infer the cluster mass. Based on abundances of the chemical elements distributed in the first internal data release of the Gaia-ESO Survey, we study elemental ratios and the chemical homogeneity of the red clump stars. Radial velocities enable us to study the rotation and internal kinematics of the cluster. The estimated ages range from 250 to 316Myr, depending on the adopted stellar model. Luminosity profiles and mass functions show strong signs of mass segregation. We derive the mass of the cluster from its luminosity function and from the kinematics, finding values between 3700 M$_{\odot}$ and 11 000 M$_{\odot}$. After selecting the cluster members from their radial velocities, we obtain a metallicity of [Fe/H]=0.10$\pm$0.06 based on 21 candidate members. Moreover, NGC6705 shows no sign of the typical correlations or anti-correlations between Al, Mg, Si, and Na, that are expected in multiple populations. This is consistent with our cluster mass estimate, which is lower than the required mass limit proposed in literature to develop multiple populations.

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arXiv2014

STEP: The VST survey of the SMC and the Magellanic Bridge. I. Overview and first results

STEP (the SMC in Time: Evolution of a Prototype interacting late-type dwarf galaxy) is a Guaranteed Time Observation survey being performed at the VST (the ESO VLT Survey Telescope). STEP will image an area of 74 deg$^2$ covering the main body of the Small Magellanic Cloud (32 deg$^2$), the Bridge that connects it to the Large Magellanic Cloud (30 deg$^2$) and a small part of the Magellanic Stream (2 deg$^2$). Our $g,r,i,H_α$ photometry is able to resolve individual stars down to magnitudes well below the main-sequence turnoff of the oldest populations. In this first paper we describe the observing strategy, the photometric techniques, and the upcoming data products of the survey. We also present preliminary results for the first two fields for which data acquisition is completed, including some detailed analysis of the two stellar clusters IC\,1624 and NGC\,419.

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arXiv2014

The Gaia-ESO Survey: Properties of the intermediate age open cluster NGC 4815

NGC 4815 is a populous ~500 Myr open cluster at a Galactocentric radius of 7 kpc observed in the first six months of the Gaia-ESO Survey. Located in the inner Galactic disk, NGC 4815 is an important tracer of the abundance gradient, where few intermediate age open clusters are found. We use the survey derived radial velocities, stellar atmospheric parameters, metallicity, and elemental abundances for stars targeted as potential members of this cluster to carry out an analysis of cluster properties. The radial velocity distribution of stars in the cluster field is used to define the cluster systemic velocity and derive likely cluster membership for stars observed by the Gaia-ESO Survey. We investigate the distributions of Fe and Fe-peak elements, alpha-elements, and the light elements Na and Al and characterize the cluster's internal chemical homogeneity comparing it to the properties of radial velocity non-member stars. Utilizing these cluster properties, the cluster color-magnitude diagram is analyzed and theoretical isochrones are fit to derive cluster reddening, distance, and age. NGC 4815 is found to have a mean [Fe/H]=+0.03. Elemental abundances of cluster members show typically small internal variation, with internal dispersions of ~0.05 dex. [Ca/Fe] and [Si/Fe] show solar ratios, but [Mg/Fe] is moderately enhanced, while [Ti/Fe] appears slightly deficient. As with many open clusters, [Na/Fe] and [Al/Fe] are enhanced, [Na/Fe] significantly so, although the role of internal mixing and the assumption of LTE in the analysis remain to be investigated. From isochrone fits to color-magnitude diagrams, we find a cluster age of 0.5 to 0.63 Gyr, a reddening of E(B-V) = 0.59 to 0.65, and a true distance modulus (m-M) = 11.95 to 12.20, depending on the choice of theoretical models, leading to a Galactocentric distance of 6.9 kpc.

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