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A crucial aspect in addressing the challenge of measuring the core mass function, that is pivotal for comprehending the origin of the initial mass function, lies in constraining the temperatures of the cores. We aim to measure the luminosity, mass, column density and dust temperature of star-forming regions imaged by the ALMA-IMF large program. High angular resolution mapping is required to capture the properties of protostellar and pre-stellar cores and to effectively separate them from larger features, such as dusty filaments. We employed the point process mapping (PPMAP) technique, enabling us to perform spectral energy distribution fitting of far-infrared and submillimeter observations across the 15 ALMA-IMF fields, at an unmatched 2.5" angular resolution. By combining the modified blackbody model with near-infrared data, we derived bolometric luminosity maps. We estimated the errors impacting values of each pixel in the temperature, column density, and luminosity maps. Subsequently, we employed the extraction algorithm getsf on the luminosity maps in order to detect luminosity peaks and measure their associated masses. We obtained high-resolution constraints on the luminosity, dust temperature, and mass of protoclusters, that are in agreement with previously reported measurements made at a coarser angular resolution. We find that the luminosity-to-mass ratio correlates with the evolutionary stage of the studied regions, albeit with intra-region variability. We compiled a PPMAP source catalog of 313 luminosity peaks using getsf on the derived bolometric luminosity maps. The PPMAP source catalog provides constraints on the mass and luminosity of protostars and cores, although one source may encompass several objects. Finally, we compare the estimated luminosity-to-mass ratio of PPMAP sources with evolutionary tracks and discuss the limitations imposed by the 2.5" beam., Comment: 35 pages, 19 figures, 5 tables Accepted by A&A

We use the H$41\alpha$ recombination line to create templates of the millimeter free-free emission in the ALMA-IMF continuum maps, which allows to separate it from dust emission. This method complements spectral-index information and extrapolation from centimeter wavelength maps. We use the derived maps to estimate the properties of up to 34 HII regions across the ALMA-IMF protoclusters. The hydrogen ionizing-photon rate $Q_0$ and spectral types follow the evolutionary trend proposed by Motte et al. The youngest protoclusters lack detectable ionized gas, followed by protoclusters with increasing numbers of OB stars. The total $Q_0$ increases from $\sim 10^{45}$ s$^{-1}$ to $> 10^{49}$ s$^{-1}$. We used the adjacent He$41\alpha$ line to measure the relative number abundances of helium, finding values consistent with the Galactic interstellar medium, although a few outliers are discussed. A search for sites of maser amplification of the H$41\alpha$ line returned negative results. We looked for possible correlations between the electron densities ($n_e$), emission measures (EM), and $Q_0$ with HII region size $D$. The latter are the better correlated, with $Q_0 \propto D^{2.49\pm0.18}$. This favors interpretations where smaller ultracompact HII regions are not necessarily the less dynamically evolved versions of larger ones, but rather are ionized by less massive stars. Moderate correlations were found between dynamical width $\Delta V_\mathrm{dyn}$ with $D$ and $Q_0$. $\Delta V_\mathrm{dyn}$ increases from about one to two times the ionized-gas sound speed. Finally, an outlier HII region south of W43-MM2 is discussed. We suggest that this source could harbor an embedded stellar or disk wind., Comment: Accepted to AAS Journals (ApJS). Data available at https://dataverse.harvard.edu/dataverse/h41a-freefree

The ALMA-IMF Large Program provides multi-tracer observations of 15 Galactic massive protoclusters at matched sensitivity and spatial resolution. We focus on the dense gas kinematics of the G353.41 protocluster traced by N$_2$H$^+$ (1$-$0), with an spatial resolution $\sim$0.02 pc. G353.41, at a distance of $\sim$2 kpc, has a mass of $\sim$2500 M$_{\odot}$ within $1.3\times1.3$ pc$^2$. We extract the N$_2$H$^+$ isolated line component and we decompose it by fitting up to 3 Gaussian velocity components. This allows us to identify velocity structures that are impossible to identify in the traditional position-velocity diagram. We identify multiple velocity gradients on large ($\sim$1 pc) and small scales ($\sim$0.2 pc). We find good agreement between the N$_2$H$^+$ velocities and the previously reported DCN core velocities, suggesting that cores are kinematically coupled to the dense gas in which they form. We measure 9 converging ``V-shaped'' velocity gradients ($\sim20$ km/s/pc), located in filaments, which are sometimes associated with cores near their point of convergence. The average inflow timescale is $\sim67$ kyr, or about twice the free-fall time of cores in the same area ($\sim33$ kyr) but substantially shorter than protostar lifetime estimates ($\sim$0.5 Myr). We derive mass accretion rates in the range of $(0.35-8.77)\,\times\,10^{-4}$ M$_{\odot}$/yr. This feeding might lead to further filament collapse and formation of new cores. We suggest that the protocluster is collapsing on large scales, but the velocity signature of collapse is slow compared to pure free-fall. These data are consistent with a comparatively slow global protocluster contraction under gravity, and faster core formation within, suggesting the formation of multiple generations of stars over the protocluster lifetime., Comment: Accepted in A&A, 22 pages, 21 figures, 1 interactive figure, 4 tables

An integral framed, closed pure n-braid B' in the 3-sphere describes a positive Artin presentation, if the braid B can be put on a disk with holes such that each relation describes a positive path and these paths are disjoint. In the present paper we classify the closed, pure n-braids B' in the 3-sphere, such that B represents a positive Artin presentation. Also we prove that if such B describes a positive Artin presentation then B' is strongly invertible. Such positive Artin presentation give us the fundamental group of closed, connected and orientable 3-manifolds M, and in fact, by giving an example, we show that there exist 3-manifolds whose fundamental group does not admit a positive Artin presentation., Comment: 18 pages, 11 figures

We present the combination of ALMA-IMF and single-dish continuum images from the Mustang-2 Galactic Plane Survey (MGPS90) at 3 millimeters and the Bolocam Galactic Plane Survey (BGPS) at 1 millimeter. Six and ten out of the fiffteen ALMA-IMF fields are combined with MGPS90 and BGPS, respectively. The combination is made via the feathering technique. We used the dendrogram algorithm throughout the combined images, and performed further analysis in the six fields with combination in both bands (G012.80, W43-MM1, W43-MM2, W43-MM3, W51-E, W51-IRS2). In these fields, we calculated spectral index maps and used them to separate regions dominated by dust or free-free emission, and then performed further structural analysis. We report the basic physical parameters of the dust-dominated (column densities, masses) and ionized (emission measures, hydrogen ionization photon rates) structures. We also searched for multi-scale relations in the dust-dominated structures across the analyzed fields, finding that the fraction of mass in dendrogram leaves (which we label as "Leaf Mass Eficiency", LME) as a function of molecular gas column density follows a similar trend: a rapid, exponential-like growth, with maximum values approaching 100% in most cases. The observed behaviour of the LME with gas column is tentatively interpreted as an indicator of large star formation activity within the ALMA-IMF protoclusters. W51-E and G012.80 stand out as cases with comparatively large and reduced potential for further star formation, respectively., Comment: Accepted to The Astrophysical Journal Supplement

Let {$\{S_n\}_{n\geqslant 0}$} be the sequence of orthogonal polynomials with respect to the Laguerre-Sobolev inner product $$ \langle f,g\rangle_S =\!\int_{0}^{+\infty}\! f(x) g(x)x^{\alpha}e^{-x}dx+\sum_{j=1}^{N}\sum_{k=0}^{d_j}\lambda_{j,k} f^{(k)}(c_j)g^{(k)}(c_j), $$ where $\lambda_{j,k}\geqslant 0$, $\alpha >-1$ and $c_i \in (-\infty, 0)$ for $i=1,2,\dots,N$. We provide a formula that relates the Laguerre-Sobolev polynomials $S_n$ to the standard Laguerre orthogonal polynomials. We find the ladder operators for the polynomial sequence $\{S_n\}_{n\geqslant 0}$ and a second-order differential equation with polynomial coefficients for $\{S_n\}_{n\geqslant 0}$. We establish a sufficient condition for an electrostatic model of the zeros of orthogonal Laguerre-Sobolev polynomials. Some examples are given where this condition is either satisfied or not., Comment: arXiv admin note: substantial text overlap with arXiv:2308.06171

We study the sequence of polynomials $\{S_n\}_{n\geq 0}$ that are orthogonal with respect to the general discrete Sobolev-type inner product $$ \langle f,g \rangle_{\mathsf{s}}=\!\int\! f(x) g(x)d\mu(x)+\sum_{j=1}^{N}\sum_{k=0}^{d_j}\lambda_{j,k} f^{(k)}(c_j)g^{(k)}(c_j), $$ where $\mu$ is a finite Borel measure whose support $\supp{\mu}$ is an infinite set of the real line, $\lambda_{j,k}\geq 0$, and the mass points $c_i$, $i=1,\dots,N$ are real values outside the interior of the convex hull of $\supp{\mu}$ ($c_i\in\RR\setminus\inter{\ch{\supp{\mu}}}$). Under some restriction of order in the discrete part of $\langle \cdot, \cdot \rangle_{\mathsf{s}}$, we prove that $S_n$ has at least $n-d^*$ zeros on $\inter{\ch{\supp{\mu}}}$, being $d^*$ the number of terms in the discrete part of $\langle \cdot, \cdot \rangle_{\mathsf{s}}$. Finally, we obtain the outer relative asymptotic for $\{S_n\}$ in the case that the measure $\mu$ is the classical Laguerre measure, and for each mass point, only one order derivative appears in the discrete part of $\langle \cdot, \cdot \rangle_{\mathsf{s}}$.

ALMA-IMF is an Atacama Large Millimeter/submillimeter Array (ALMA) Large Program designed to measure the core mass function (CMF) of 15 protoclusters chosen to span their early evolutionary stages. It further aims to understand their kinematics, chemistry, and the impact of gas inflow, accretion, and dynamics on the CMF. We present here the first release of the ALMA-IMF line data cubes (DR1), produced from the combination of two ALMA 12m-array configurations. The data include 12 spectral windows, with eight at 1.3mm and four at 3mm. The broad spectral coverage of ALMA-IMF (~6.7 GHz bandwidth coverage per field) hosts a wealth of simple atomic, molecular, ionised, and complex organic molecular lines. We describe the line cube calibration done by ALMA and the subsequent calibration and imaging we performed. We discuss our choice of calibration parameters and optimisation of the cleaning parameters, and we demonstrate the utility and necessity of additional processing compared to the ALMA archive pipeline. As a demonstration of the scientific potential of these data, we present a first analysis of the DCN (3-2) line. We find that DCN traces a diversity of morphologies and complex velocity structures, which tend to be more filamentary and widespread in evolved regions and are more compact in the young and intermediate-stage protoclusters. Furthermore, we used the DCN (3-2) emission as a tracer of the gas associated with 595 continuum cores across the 15 protoclusters, providing the first estimates of the core systemic velocities and linewidths within the sample. We find that DCN (3-2) is detected towards a higher percentage of cores in evolved regions than the young and intermediate-stage protoclusters and is likely a more complete tracer of the core population in more evolved protoclusters. The full ALMA 12m-array cubes for the ALMA-IMF Large Program are provided with this DR1 release., Comment: 75 pages (21 main body; 54 appendix), 37 figures. The ALMA-IMF DR1 line release is hosted at https://dataverse.harvard.edu/dataverse/alma-imf

Among the most central open questions regarding the initial mass function (IMF) of stars is the impact of environment on the shape of the core mass function (CMF) and thus potentially on the IMF. The ALMA-IMF Large Program aims to investigate the variations in the core distributions with cloud characteristics, as diagnostic observables of the formation process and evolution of clouds. The present study focuses on the W43-MM2&MM3 mini-starburst, whose CMF has recently been found to be top-heavy with respect to the Salpeter slope. W43-MM2&MM3 harbors a rich cluster that contains a statistically significant number of cores, which was previously characterized in Paper III. We applied a multi-scale decomposition technique to the ALMA 1.3 mm and 3 mm continuum images to define six subregions. For each subregion we characterized the high column density probability distribution function, n-PDF, and the shape of the cloud gas using the 1.3 mm image. Using the core catalog, we investigate correlations between the CMF and cloud and core properties. We classify the subregions into different stages of evolution, from quiescent to burst to post-burst, based on the surface number density of cores, number of outflows, and UCHii presence. The high-mass end of the subregion CMFs varies from being close to the Salpeter slope (quiescent) to top-heavy (burst and post-burst). Moreover, the second tail of the n-PDF varies from steep, to flat like observed for the high mass star-forming clouds. We found that subregions with flat second n-PDF tails display top-heavy CMFs. The CMF may evolve from Salpeter to top-heavy throughout the star formation process from the quiescent to the burst phase. This scenario raises the question of if the CMF might revert again to Salpeter as the cloud approaches the end of its star formation stage, a hypothesis that remains to be tested., Comment: Accepted for publication in A&A (december, 5th 2022) after language editing; 25 pages, 14 figures

We present the first data release of the ALMA-IMF Large Program, which covers the 12m-array continuum calibration and imaging. The ALMA-IMF Large Program is a survey of fifteen dense molecular cloud regions spanning a range of evolutionary stages that aims to measure the core mass function (CMF). We describe the data acquisition and calibration done by the Atacama Large Millimeter/submillimeter Array (ALMA) observatory and the subsequent calibration and imaging we performed. The image products are combinations of multiple 12m array configurations created from a selection of the observed bandwidth using multi-term, multi-frequency synthesis imaging and deconvolution. The data products are self-calibrated and exhibit substantial noise improvements over the images produced from the delivered data. We compare different choices of continuum selection, calibration parameters, and image weighting parameters, demonstrating the utility and necessity of our additional processing work. Two variants of continuum selection are used and will be distributed: the "best-sensitivity" data, which include the full bandwidth, including bright emission lines that contaminate the continuum, and "cleanest", which select portions of the spectrum that are unaffected by line emission. We present a preliminary analysis of the spectral indices of the continuum data, showing that the ALMA products are able to clearly distinguish free-free emission from dust emission, and that in some cases we are able to identify optically thick emission sources. The data products are made public with this release., Comment: Data released on Zenodo at https://zenodo.org/record/5702966. Accepted for publication in A&A

The ALMA-IMF Large Program imaged a total noncontiguous area of 53pc2, covering 15 extreme, nearby protoclusters of the Milky Way. They were selected to span relevant early protocluster evolutionary stages. Our 1.3mm and 3mm observations provide continuum images that are homogeneously sensitive to point-like cores with masses of 0.2 and 0.6Msun, respectively, with a matched spatial resolution of 2000au. We also detect lines that probe the protocluster structure, kinematics, chemistry, and feedback over scales from clouds to filaments to cores. We classify ALMA-IMF protoclusters as Young, Intermediate, or Evolved based on the amount of dense gas in the cloud that has potentially been impacted by HII regions. The ALMA-IMF catalog contains 700 cores that span a mass range of 0.15-250Msun at a typical size of 2100au. We show that this core sample has no significant distance bias and can be used to build core mass functions at similar physical scales. Significant gas motions, which we highlight here in the G353.41 region, are traced down to core scales and can be used to look for inflowing gas streamers and to quantify the impact of the possible associated core mass growth on the shape of the CMF with time. Our first analysis does not reveal any significant evolution of the matter concentration from clouds to cores or from the youngest to more evolved protoclusters, indicating that cloud dynamical evolution and stellar feedback have for the moment only had a slight effect on the structure of high-density gas in our sample. Furthermore, the first-look analysis of the line richness toward bright cores indicates that the survey encompasses several tens of hot cores, of which we highlight the most massive in the G351.77 cloud. Their homogeneous characterization can be used to constrain the emerging molecular complexity in protostars of high to intermediate masses., Comment: 27 pages, 9 figures, accepted for publication by A&A

We present unprecedented high fidelity radio images of the M87 jet. We analyzed Jansky Very Large Array (VLA) broadband, full polarization, radio data from 4 to 18 GHz. The observations were taken with the most extended configuration (A configuration), which allow the study of the emission of the jet up to kpc scales with a linear resolution $\sim$10 pc. The high sensitivity and resolution of our data allow to resolve the jet width. We confirm a double-helix morphology of the jet material between $\sim$300 pc and $\sim$1 kpc. We found a gradient of the polarization degree with a minimum at the projected axis and maxima at the jet edges, and a gradient in the Faraday depth with opposite signs at the jet edges. We also found that the behavior of the polarization properties along the wide range of frequencies is consistent with internal Faraday depolarization. All these characteristics strongly support the presence of a helical magnetic field in the M87 jet up to 1 kpc from the central black hole although the jet is most likely particle dominated at these large scales. Therefore, we propose a plausible scenario in which the helical configuration of the magnetic field has been maintained to large scales thanks to the presence of Kelvin-Helmholtz instabilities., Comment: Published on ApJL

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev $p$-norm ($1

The Gaia DR2 catalog is the best source of stellar astrometric and photometric data available today. The history of the Milky Way galaxy is written in stone in this data set. Parallaxes and photometry tell us where the stars are today, when were they formed, and with what chemical content, i.e. their star formation history (SFH). We develop a Bayesian hierarchical model suited to reconstruct the SFH of a resolved stellar population. We study the stars brighter than $G\,=\,15$ within 100 pc of the Sun in Gaia DR2 and derive a SFH of the solar neighbourhood in agreement with previous determinations and improving upon them because we detect chemical enrichment. Our results show a maximum of star formation activity about 10 Gyr ago, producing large numbers of stars with slightly below solar metallicity (Z=0.014), followed by a decrease in star formation up to a minimum level occurring around 8 Gyr ago. After a quiet period, star formation rises to a maximum at about 5 Gyr ago, forming stars of solar metallicity (Z=0.017). Finally, star formation has been decreasing until the present, forming stars of Z=0.03 at a residual level. We test the effects introduced in the inferred SFH by ignoring the presence of unresolved binary stars in the sample, reducing the apparent limiting magnitude, and modifying the stellar initial mass function., Comment: 33 pages, 28 figures

Let $p\geq 1$, $\ell\in \NN$, $\alpha,\beta>-1$ and $\varpi=(\omega_0,\omega_1, \dots, \omega_{\ell-1})\in \RR^{\ell}$. Given a suitable function $f$, we define the discrete-continuous Jacobi-Sobolev norm of $f$ as: $$ \normSp{f}:= \left(\sum_{k=0}^{\ell-1} \left|f^{(k)}(\omega_{k})\right|^{p} + \int_{-1}^{1} \left|f^{(\ell)}(x)\right|^{p} d\Jm(x)\right)^{\frac{1}{p}}, $$ where $ d\Jm(x)=(1-x)^{\alpha} (1+x)^{\beta}dx$. Obviously, $\normSp[2]{\cdot}= \sqrt{\IpS{\cdot}{\cdot}}$, where $\IpS{\cdot}{\cdot}$ is the inner product. $$ \IpS{f}{g}:= \sum_{k=0}^{\ell-1} f^{(k)}(\omega_{k}) \, g^{(k)}(\omega_{k}) + \int_{-1}^{1} f^{(\ell)}(x) \,g^{(\ell)}(x) d\Jm(x). $$ In this paper, we summarize the main advances on the convergence of the Fourier-Sobolev series, in norms of type $L^p$, cases continuous and discrete. We study the completeness of the Sobolev space of functions associated with the norm $\normSp{\cdot}$ and the denseness of the polynomials. Furthermore, we obtain the conditions for the convergence in $\normSp{\cdot}$ norm of the partial sum of the Fourier-Sobolev series of orthogonal polynomials with respect to $\IpS{\cdot}{\cdot}$ .

In this paper, we study the sequence of orthogonal polynomials $\{S_n\}_{n=0}^{\infty}$ with respect to the Sobolev-type inner product $$\langle f,g \rangle= \int_{-1}^{1} f(x) g(x) \,d\mu(x) +\sum_{j=1}^{N} \eta_{j} \,f^{(d_j)}(c_{j}) g^{(d_j)}(c_{j}), $$ where $\mu$ is in the Nevai class $\mathbf{M}(0,1)$, $\eta_j >0$, $N,d_j \in \mathbb{Z}_{+}$ and $\{c_1,\dots,c_N\}\subset \mathbb{R} \setminus [-1,1]$. Under some restriction of order in the discrete part of $\langle\cdot,\cdot \rangle$, we prove that for sufficiently large $n$ the zeros of $S_n$ are real, simple, $n-N$ of them lie on $(-1,1)$ and each of the mass points $c_j$ ``attracts'' one of the remaining $N$ zeros. The sequences of associated polynomials $\{S_n^{[k]}\}_{n=0}^{\infty}$ are defined for each $k\in \mathbb{Z}_{+}$. We prove an analogous of Markov's Theorem on rational approximation to a function of certain class of holomorphic functions and we give an estimate of the ``speed'' of convergence.