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The validity of General Relativity, after 100 years, is supported by solid experimental evidence. However, there is a lot of interest in pushing the limits of precision by other experiments. Here we focus our attention on the equivalence principle, in particular the strong form. The results of ground experiments and lunar laser ranging have provided the best upper limit on the Nordtvedt parameter {\eta} that models deviations from the strong equivalence principle. Its uncertainty is currently {\sigma}[{\eta}] =4.4 $\times$ $10^{-4}$. In the first part of this paper we will describe the experiment, to measure {\eta}, that will be done by the future mission BepiColombo. The expected precision on {\eta} is $\approx$ $10^{-5}$. In the second part we will consider the ranging between the Earth and a spacecraft orbiting near the Sun-Earth Lagrangian points to get an independent measurement of {\eta}. In this case, we forecast a constraint similar to that achieved by lunar laser ranging., Comment: 11 pages, 2 figures

ESASky is a science-driven discovery portal to explore the multi-wavelength sky and visualise and access multiple astronomical archive holdings. The tool is a web application that requires no prior knowledge of any of the missions involved and gives users world-wide simplified access to the highest-level science data products from multiple astronomical space-based astronomy missions plus a number of ESA source catalogues. The first public release of ESASky features interfaces for the visualisation of the sky in multiple wavelengths, the visualisation of query results summaries, and the visualisation of observations and catalogue sources for single and multiple targets. This paper describes these features within ESASky, developed to address use cases from the scientific community. The decisions regarding the visualisation of large amounts of data and the technologies used were made in order to maximise the responsiveness of the application and to keep the tool as useful and intuitive as possible., Comment: Published in PASP; ESASky: http://sky.esa.int

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties.

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 $\delta$E(B$-$V)$\approx 0.04$ mag., Comment: accepted for publication in ApJ

We present $\mathrm{^{12}CO}$ and $\mathrm{^{13}CO}$ molecular gas data observed by ALMA, massive early stage young stellar objects identified by applying color-magnitude cuts to \textit{Spitzer} and \textit{Herschel} photometry, and low-mass late stage young stellar objects identified via H$\mathrm{\alpha}$ excess. Using dendrograms, we derive properties for the molecular cloud structures. This is the first time a dendrogram analysis has been applied to extragalactic clouds. The majority of clumps have a virial parameter equal to unity or less. The size-linewidth relations of $\mathrm{^{12}CO}$ and $\mathrm{^{13}CO}$ show the clumps in this study have a larger linewidth for a given size (by factor of 3.8 and 2.5, respectively) in comparison to several, but not all, previous studies. The larger linewidths in 30 Doradus compared to typical Milky Way quiescent clumps are probably due to the highly energetic environmental conditions of 30 Doradus. The slope of the size-linewidth relations of $\mathrm{^{12}CO}$, 0.65 $\pm$ 0.04, and $\mathrm{^{13}CO}$, 0.97 $\pm$ 0.12, are on the higher end but consistent within 3$\mathrm{\sigma}$ of previous studies. Massive star formation occurs in clumps with high masses ($> 1.83 \times 10^{2}\;\mathrm{M_{\odot}}$), high linewidths (v $> 1.18\;\mathrm{km/s}$), and high mass densities ($> 6.67 \times 10^{2}\;\mathrm{M_{\odot}\;pc^{-2}}$). The majority of embedded, massive young stellar objects are associated with a clump. However the majority of more evolved, low-mass young stellar objects are not associated with a clump., Comment: Accepted by ApJ, 65 pages, 17 figures, 6 tables

In this paper we propose a new stable and accurate approximation technique which is extremely effective for interpolating large scattered data sets. The Partition of Unity (PU) method is performed considering Radial Basis Functions (RBFs) as local approximants and using locally supported weights. In particular, the approach consists in computing, for each PU subdomain, a stable basis. Such technique, taking advantage of the local scheme, leads to a significant benefit in terms of stability, especially for flat kernels. Furthermore, an optimized searching procedure is applied to build the local stable bases, thus rendering the method more efficient.

Context: The NIRSpec instrument for the James Webb Space Telescope (JWST) can be operated in multiobject (MOS), long-slit, and integral field (IFU) mode with spectral resolutions from 100 to 2700. Its MOS mode uses about a quarter of a million individually addressable minislits for object selection, covering a field of view of $\sim$9 $\mathrm{arcmin}^2$. Aims: The pipeline used to extract wavelength-calibrated spectra from NIRSpec detector images relies heavily on a model of NIRSpec optical geometry. We demonstrate how dedicated calibration data from a small subset of NIRSpec modes and apertures can be used to optimize this parametric model to the necessary levels of fidelity. Methods: Following an iterative procedure, the initial fiducial values of the model parameters are manually adjusted and then automatically optimized, so that the model predicted location of the images and spectral lines from the fixed slits, the IFU, and a small subset of the MOS apertures matches their measured location in the main optical planes of the instrument. Results: The NIRSpec parametric model is able to reproduce the spatial and spectral position of the input spectra with high fidelity. The intrinsic accuracy (1-sigma, RMS) of the model, as measured from the extracted calibration spectra, is better than 1/10 of a pixel along the spatial direction and better than 1/20 of a resolution element in the spectral direction for all of the grating-based spectral modes. This is fully consistent with the corresponding allocation in the spatial and spectral calibration budgets of NIRSpec., Comment: 17 pages, 11 figures, accepted for publication in A&A

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $\eta$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $\sigma[\eta]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $\sigma[\eta]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $\eta$ by MORE can improve the current precision of about 1~order of magnitude.

General relativity is supported by great experimental evidence. Yet there is a lot of interest in precisely setting its limits with on going and future experiments. A question to answer is about the validity of the Strong Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided the best upper limit on the Nordtvedt parameter $\sigma[\eta]=4.4\times 10^{-4}$. With the future planetary mission BepiColombo, this parameter will be further improved by at least an order of magnitude. In this paper we envisage yet another possible testing environment with spacecraft ranging towards the nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary masses and ephemerides, we forecast $\sigma[\eta]=6.4\,(2.0)\times10^{-4}$ (5 yr integration time) via ranging towards $L_1$ in a realistic (optimistic) scenario depending on current (future) range capabilities and knowledge of the Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead $4.8\,(1.7)\times10^{-4}$. In the optimistic scenario a single measurement of one year would be enough to reach $\approx3\times10^{-4}$. All figures are comparable with Lunar Laser Ranging, but worse than BepiColombo. Performances could be much improved if data were integrated over time and over the number of satellites flying around either of the two Lagrangian points. We point out that some systematics (gravitational perturbations of other planets or figure effects) are much more in control compared to other experiments. We do not advocate a specific mission to constrain the Strong Equivalence Principle, but we do suggest analysing ranging data of present and future spacecrafts flying around $L_1$/$L_2$ (one key mission is, for instance, LISA Pathfinder). This spacecraft ranging would be a new and complementary probe to constrain the Strong Equivalence Principle in space., Comment: 8 pages, 2 figures, 2 tables

We present deep near-infrared HST/WFC3 observations of the young supermassive Galactic star cluster Westerlund 1 and an adjacent control field. The depth of the data is sufficient to derive the mass function for the cluster as a function of radius down to 0.15 M$_\odot$ in the outer parts of the cluster. We identify for the first time a flattening in the mass function (in logarithmic units) at a mass range that is consistent with that of the field and nearby embedded clusters. Through log-normal functional fits to the mass functions we find the nominal peak mass to be comparable to that of the field and nearby embedded star clusters. The width of a log-normal fit appears slightly narrow compared to the width of the field IMF, closer to the values found for globular clusters. The subsolar content within the cluster does not appear to be mass segregated in contrast to the findings for the supersolar content. The total mass of Westerlund 1 is estimated to be 44-57 $\times 10^3$ M$_\odot$ where the main uncertainty is the choice of the isochrone age and the higher mass slope. Comparing the photometric mass with the dynamically determined mass, Westerlund 1 is sufficiently massive to remain bound and could potentially evolve into a low-mass globular cluster., Comment: Accepted by A&A

In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models in case of multi-stability. We propose to reconstruct the domains of attraction via an implicit interpolant using stable radial bases, obtaining the surfaces by partitioning the phase space into disjoint regions. An application to a competition model presenting jointly three stable equilibria is considered.

We present a science-driven discovery portal for all the ESA Astronomy Missions called ESA Sky that allow users to explore the multi-wavelength sky and to seamlessly retrieve science-ready data in all ESA Astronomy mission archives from a web application without prior-knowledge of any of the missions. The first public beta of the service has been released, currently featuring an interface for exploration of the multi-wavelength sky and for single and/or multiple target searches of science-ready imaging data and catalogues. Future releases will enable retrieval of spectra and will have special time-domain exploration features. From a technical point of view, the system offers progressive multi-resolution all-sky projections of full mission datasets using a new generation of HEALPix projections called HiPS, developed at the CDS; detailed geometrical footprints to connect the all-sky mosaics to individual observations; and direct access to science-ready data at the underlying mission-specific science archives., Comment: 4 pages, 2 figures, ADASS XXV conference proceedings; ESA Sky Beta: http://archives.esac.esa.int/esasky-beta/ ; ESA Sky Beta documentation: http://www.cosmos.esa.int/web/esdc/esasky-help

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., Comment: 20 pages, 22 Figures, 3 Tables, Photometric Catalogs and Mosaiced images will be available for download upon publication, accepted for publication on ApJS

We report on the study of interstellar extinction across the Tarantula nebula (30 Doradus), in the Large Magellanic Cloud, using observations from the Hubble Tarantula Treasury Project in the 0.3 - 1.6 micron range. The considerable and patchy extinction inside the nebula causes about 3500 red clump stars to be scattered along the reddening vector in the colour-magnitude diagrams, thereby allowing an accurate determination of the reddening slope in all bands. The measured slope of the reddening vector is remarkably steeper in all bands than in the the Galactic diffuse interstellar medium. At optical wavelengths, the larger ratio of total-to-selective extinction, namely Rv = 4.5 +/- 0.2, implies the presence of a grey component in the extinction law, due to a larger fraction of large grains. The extra large grains are most likely ices from supernova ejecta and will significantly alter the extinction properties of the region until they sublimate in 50 - 100 Myr. We discuss the implications of this extinction law for the Tarantula nebula and in general for regions of massive star formation in galaxies. Our results suggest that fluxes of strongly star forming regions are likely to be underestimated by a factor of about 2 in the optical., Comment: 15 pages, 10 figures, accepted for publication in MNRAS; Updated references, corrected typos in Table 3

Up to ages of ~100 Myr, massive clusters are still swamped in large amounts of gas and dust, with considerable and uneven levels of extinction. At the same time, large grains (ices?) produced by type II supernovae profoundly alter the interstellar medium (ISM), thus resulting in extinction properties very different from those of the diffuse ISM. To obtain physically meaningful parameters of stars, from basic luminosities and effective temperatures to masses and ages, we must understand and measure the local extinction law. This problem affects all the massive young clusters discussed in his volume. We have developed a powerful method to unambiguously determine the extinction law in an uniform way across a cluster field, using multi-band photometry of red giant stars belonging to the red clump (RC). In the Large Magellanic Cloud, with about 20 RC stars per arcmin^2, we can easily derive a solid and self-consistent absolute extinction curve over the entire wavelength range of the photometry. Here, we present the extinction law of the Tarantula nebula (30 Dor) based on thousands of stars observed as part of the Hubble Tarantula Treasury Project., Comment: 2 pages, 2 figures, to appear in the proceedings of IAU Symposium 316, "Formation, Evolution, and Survival of massive star clusters", eds. A. Nota & C. Charbonnel, 2015

We have undertaken a systematic study of pre-main sequence (PMS) stars spanning a wide range of masses (0.5 - 4 Msolar), metallicities (0.1 - 1 Zsolar) and ages (0.5 - 30 Myr). We have used the Hubble Space Telescope (HST) to identify and characterise a large sample of PMS objects in several star-forming regions in the Magellanic Clouds, namely 30 Dor and the SN 1987A field in the LMC, and NGC 346 and NGC 602 in the SMC, and have compared them to PMS stars in similar regions in the Milky Way, such as NGC 3603 and Trumpler 14, which we studied with the HST and Very Large Telescope (VLT). We have developed a novel method that combines broad-band (V, I) photometry with narrow-band Halpha imaging to determine the physical parameters (temperature, luminosity, age, mass and mass accretion rate) of more than 3000 bona-fide PMS stars still undergoing active mass accretion. This is presently the largest and most homogeneous sample of PMS objects with known physical properties and includes not only very young objects, but also PMS stars older than 10 - 20 Myr that are approaching the main sequence (MS). We find that the mass accretion rate scales roughly with the square root of the age, with the mass of the star to the power of 1.5, and with the inverse of the cube root of the metallicity. The mass accretion rates for stars of the same mass and age are thus systematically higher in the Magellanic Clouds than in the Milky Way. These results are bound to have important implications for, and constraints on our understanding of the star formation process., Comment: 14 pages, 7 figures, accepted for publication in Frontier Research in Astrophysics, Eds. F. Giovannelli & L. Sabau-Graziati, PoS(FRAPWS2014)030. arXiv admin note: text overlap with arXiv:1307.8445

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., Comment: Submitted to ApJ

We study Lissajous curves in the 3-cube, that generate algebraic cubature formulas on a special family of rank-1 Chebyshev lattices. These formulas are used to construct trivariate hyperinterpolation polynomials via a single 1-d Fast Chebyshev Transform (by the Chebfun package), and to compute discrete extremal sets of Fekete and Leja type for trivariate polynomial interpolation. Applications could arise in the framework of Lissajous sampling for MPI (Magnetic Particle Imaging).

We have studied the interstellar extinction in a field of ~3' x 3' at the core of the 30 Doradus nebula, including the central R136 cluster, in the Large Magellanic Cloud. Observations at optical and near-infrared wavelengths, obtained with the WFC3 camera on board the Hubble Space Telescope, show that the stars belonging to the red giant clump are spread across the colour-magnitude diagrams because of the considerable and uneven levels of extinction in this region. Since these stars share very similar physical properties and are all at the same distance, they allow us to derive the absolute extinction in a straightforward and reliable way. Thus we have measured the extinction towards about 180 objects and the extinction law in the range 0.3 - 1.6 micron. At optical wavelengths, the extinction curve is almost parallel to that of the diffuse Galactic interstellar medium. Taking the latter as a template, the value of Rv = 4.5 +/- 0.2 that we measure indicates that in the optical there is an extra grey component due to a larger fraction of large grains. At wavelengths longer than ~1 micron, the contribution of this additional component tapers off as lambda^-1.5, like in the Milky Way, suggesting that the nature of the grains is otherwise similar to those in our Galaxy, but with a ~2.2 times higher fraction of large grains. These results are consistent with the addition of "fresh" large grains by supernova explosions, as recently revealed by Herschel and ALMA observations of SN 1987A., Comment: 14 pages, 11 figures, accepted for publication in MNRAS. Updated references

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes whose elements mimic as well as possible the Chebyshev-Lobatto points. In this work we use the simultaneous approximation theory to combine the previous technique with a polynomial regression in order to increase the accuracy of the approximation of a given analytic function. We give indications on how to select the degree of the simultaneous regression in order to obtain polynomial approximant good in the uniform norm and provide a sufficient condition to improve, in that norm, the accuracy of the mock-Chebyshev interpolation with a simultaneous regression. Numerical results are provided., Comment: 17 pages, 9 figures

We present a tally of Milky Way late-type dwarf stars in 68 WFC3 pure-parallel fields (227 arcmin^2) from the Brightest of Reionizing Galaxies (BoRG) survey for high-redshift galaxies. Using spectroscopically identified M-dwarfs in two public surveys, the CANDELS and the ERS mosaics, we identify a morphological selection criterion using the half-light radius (r50), a near-infrared J-H, G-J color region where M-dwarfs are found, and a V-J relation with M-dwarf subtype. We apply this morphological selection of stellar objects, color-color selection of M-dwarfs and optical-near-infrared color subtyping to compile a catalog of 274 M-dwarfs belonging to the disk of the Milky Way with a limiting magnitude of m_F125W < 24. Based on the M-dwarfs statistics, we conclude that (a) the previously identified North/South discrepancy in M-dwarf numbers persists in our sample; there are more M-dwarfs in the Northern fields on average than in Southern ones, (b) the Milky Way's single disk scale-height for M-dwarfs is 0.3-4 kpc, depending on sub-type, (c) {\bf ERRATUM:} we present corrected coordinates (AstroPy) and distances and find a constant $z_0$=600 pc for all types. (d) a second component is visible in the vertical distribution, with a different, much higher scale-height. We report the M-dwarf component of the Sagittarius stream in one of our fields with 11 confirmed M-dwarfs, 7 of which are at the stream's distance. The dwarf scale-height and the relative low incidence in our fields of L- and T-dwarfs in these fields makes it unlikely that these stars will be interlopers in great numbers in color-selected samples of high-redshift galaxies. The relative ubiquity of M-dwarfs however will make them ideal tracers of Galactic Halo substructure with EUCLID and reference stars for JWST observations., Comment: 26 pages, 29 figures, 16 tables, published in ApJ, ERRATUM (6 figures, 1 table) added