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Solvable Lie algebras having at least one Abelian descending central ideal are studied. It is shown that all such Lie algebras can be built up from canonically defined ideals. The nature of such ideals is elucidated and their construction is provided in detail. An approach to study and to classify these Lie algebras is given through the theory of extensions via appropriate cocycles and representations on which a group action is naturally defined. Also, necessary and sufficient conditions for the existence of invariant metrics on the studied extensions are given. It is shown that any solvable quadratic Lie algebra $\g$ having an Abelian descending central ideal is of the form $\g=\h\oplus\a\oplus\h^*$, where $\h^*\simeq \ide(\g)$ and $\a \oplus \h^{*}\simeq \j(\g)$ are in fact two canonically defined Abelian ideals of $\g$ satisfying $\ide(\g)^\perp=\j(\g)$. As an example, a classification of this type of quadratic Lie algebras is given assuming that $\j(\g)/\ide(\g)$ is an $r$-dimensional vector space and $\g/\j(\g)$ is the 3-dimensional Heisenberg Lie algebra., Comment: This is a revised version of the manuscript On Quadratic Lie Algebras With Non-trivial Center [arXiv:1911.05009v3]. We submitted it for publication and the reviewer found a mistake in Lemma 2.6. The problem does not appear for Lie algebras with one Abelian descending central ideal. Thus, we ended up with this manuscript in whose title we have included the additional hypothesis

The formation and the evolution of protoplanetary disks are important stages in the lifetime of stars. The processes of disk evolution and planet formation are intrinsically linked. We spatially resolve with GRAVITY/VLTI in the K-band the sub au-scale region of 27 stars to gain statistical understanding of their properties. We look for correlations with stellar parameters, such as luminosity, mass, temperature and age. Our sample also cover a range of various properties in terms of reprocessed flux, flared or flat morphology, and gaps. We developed semi-physical geometrical models to fit our interferometric data. Our best models correspond to smooth and wide rings, implying that wedge-shaped rims at the dust sublimation edge are favored, as found in the H-band. The closure phases are generally non-null with a median value of ~10 deg, indicating spatial asymmetries of the intensity distributions. Multi-size grain populations could explain the closure phase ranges below 20-25 deg but other scenarios should be invoked to explain the largest ones. Our measurements extend the Radius-Luminosity relation to ~1e4 Lsun and confirm the significant spread around the mean relation observed in the H-band. Gapped sources exhibit a large N-to-K band size ratio and large values of this ratio are only observed for the members of our sample that would be older than 1 Ma, less massive, and with lower luminosity. In the 2 Ms mass range, we observe a correlation in the increase of the relative age with the transition from group II to group I, and an increase of the N-to-K size ratio. However, the size of the current sample does not yet permit us to invoke a clear universal evolution mechanism across the HAeBe mass range. The measured locations of the K-band emission suggest that these disks might be structured by forming young planets, rather than by depletion due to EUV, FUV, and X-ray photo-evaporation., Comment: Accepted for publication in A&A; 23 pages, 16 figures, 7 tables

The aim of this study is to search for evidence of a common emission engine between radio giant pulses (GPs) and very-high-energy (VHE, E>100 GeV) gamma-rays from the Crab pulsar. 16 hours of simultaneous observations of the Crab pulsar at 1.4 GHz with the Effelsberg radio telescope and the Westerbork Synthesis Radio Telescope (WSRT), and at energies above 60 GeV with the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes were performed. We searched for a statistical correlation between the radio and VHE gamma-ray emission with search windows of different lengths and different time lags to the arrival times of a radio GP. A dedicated search for an enhancement in the number of VHE gamma-rays correlated with the occurrence of radio GPs was carried out separately for the P1 and P2 phase ranges respectively. 99444 radio GPs have been detected in the radio data sample. We find no significant correlation between the GPs and VHE photons in any of the search windows. Depending on phase cuts and the chosen search windows we find upper limits at 95% confidence level on an increase in VHE gamma-ray events correlated with radio GPs between 7% and 61% of the average Crab pulsar VHE flux for the P1 and P2 phase ranges respectively. This puts upper limits on the flux increase during a radio GP of 12% to 2900% (depending on search window duration and phase cuts) of the pulsed VHE flux. This is the most stringent upper limit on a correlation between gamma-ray emission and radio GPs reported so far.}, Comment: 15 pages, 7 figures, accepted for publication by Astronomy and Astrophysics

[Abridged] We present the apparent stellar angular momentum of 300 galaxies across the Hubble sequence, using integral-field spectroscopic data from the CALIFA survey. Adopting the same $\lambda_\mathrm{R}$ parameter previously used to distinguish between slow and fast rotating early-type (elliptical and lenticular) galaxies, we show that spiral galaxies as expected are almost all fast rotators. Given the extent of our data, we provide relations for $\lambda_\mathrm{R}$ measured in different apertures, including conversions to long-slit 1D apertures. Our sample displays a wide range of $\lambda_\mathrm{Re}$ values, consistent with previous IFS studies. The fastest rotators are dominated by relatively massive and highly star-forming Sb galaxies, which preferentially reside in the main star-forming sequence. These galaxies reach $\lambda_\mathrm{Re}$ values of $\sim$0.85, are the largest galaxies at a given mass, and display some of the strongest stellar population gradients. Compared to the population of S0 galaxies, our findings suggest that fading may not be the dominant mechanism transforming spirals into lenticulars. Interestingly, we find that $\lambda_\mathrm{Re}$ decreases for late-type Sc and Sd spiral galaxies, with values than in occasions puts them in the slow-rotator regime. While for some of them this can be explained by their irregular morphologies and/or face-on configurations, others are edge-on systems with no signs of significant dust obscuration. The latter are typically at the low-mass end, but this does not explain their location in the classical ($V/\sigma$,$\varepsilon$) and ($\lambda_\mathrm{Re}$,$\varepsilon$) diagrams. Our initial investigations, based on dynamical models, suggest that these are dynamically hot disks, probably influenced by the observed important fraction of dark matter within R$_\mathrm{e}$., Comment: 17 pages, 7 figures, A&A accepted

The upcoming new generation of optical spectrographs on four-meter-class telescopes will provide invaluable information for reconstructing the history of star formation in individual galaxies up to redshifts of about 0.7. We aim at defining simple but robust and meaningful physical parameters that can be used to trace the coexistence of widely diverse stellar components: younger stellar populations superimposed on the bulk of older ones. We produce spectra of galaxies closely mimicking data from the forthcoming Stellar Populations at intermediate redshifts Survey (StePS), a survey that uses the WEAVE spectrograph on the William Herschel Telescope. First, we assess our ability to reliably measure both ultraviolet and optical spectral indices in galaxies of different spectral types for typically expected signal-to-noise levels. Then, we analyze such mock spectra with a Bayesian approach, deriving the probability density function of r- and u-band light-weighted ages as well as of their difference. We find that the ultraviolet indices significantly narrow the uncertainties in estimating the r- and u-band light-weighted ages and their difference in individual galaxies. These diagnostics, robustly retrievable for large galaxy samples even when observed at moderate signal-to-noise ratios, allow us to identify secondary episodes of star formation up to an age of ~0.1 Gyr for stellar populations older than ~1.5 Gyr, pushing up to an age of ~1 Gyr for stellar populations older than ~5 Gyr. The difference between r-band and u-band light-weighted ages is shown to be a powerful diagnostic to characterize and constrain extended star-formation histories and the presence of young stellar populations on top of older ones. This parameter can be used to explore the interplay between different galaxy star-formation histories and physical parameters such as galaxy mass, size, morphology, and environment., Comment: 18 pages, 20 figures, accepted for publication in A&A

The muon collider represents one of the most promising solutions for a future machine exploring the high energy frontier, but several challenges due to the 2.2 $\mu$sec muon lifetime at rest have to be carefully considered. The LEMMA project is investigating the possibility of producing low emittance muon/antimuon pairs from the e$^+$e$^-$ annihilation process at threshold energy, resulting in small transverse emittance beams without any additional beam cooling. However most of the measurements available are performed at higher $\sqrt{s}$ values. It is therefore necessary to measure muons production in positron annihilation at threshold energy and compare the experimental results with the predictions in this specific energy regime. Apart from being a topic of physical interest by itself, these near to threshold measurements can have a sizeable impact on the estimation of the ultimate luminosity achievable in a muon collider with the LEMMA injection scheme., Comment: 13 pages, 8 figures

It is important to determine if massive stars form via disc accretion, like their low-mass counterparts. Theory and observation indicate that protostellar jets are a natural consequence of accretion discs and are likely to be crucial for removing angular momentum during the collapse. However, massive protostars are typically rarer, more distant and more dust enshrouded, making observational studies of their jets more challenging. A fundamental question is whether the degree of ionisation in jets is similar across the mass spectrum. Here we determine an ionisation fraction of $\sim5-12\%$ in the jet from the massive protostar G35.20-0.74N, based on spatially coincident infrared and radio emission. This is similar to the values found in jets from lower-mass young stars, implying a unified mechanism of shock ionisation applies in jets across most of the protostellar mass spectrum, up to at least $\sim10$ solar masses., Comment: Published in Nature Communications. This is author's version. Full article is available here https://rdcu.be/bN6ps . 10 pages, 4 Figures, including methods and references

We present a new methodology for the analysis of the emission lines of the interstellar medium in the Narrow Line Regions around type-2 Active Galactic Nuclei. Our aim is to provide a recipe that can be used for large samples of objects in a consistent way using different sets of optical emission-lines that takes into the account possible variations from the (O/H)-(N/O) relation to use [N II] lines. Our approach consists of a bayesian-like comparison between certain observed emission-line ratios sensitive to total oxygen abundance, nitrogen-to-oxygen ratio and ionization parameter with the predictions from a large grid of photoionization models calculated under the most usual conditions in this environment. We applied our method to a sample of Seyfert 2 galaxies with optical emission-line fluxes and determinations of their chemical properties from detailed models in the literature. Our results agree within the errors with other results and confirm the high metallicity of the objects of the sample, with N/O values consistent wit a large secondary production of N, but with a large dispersion. The obtained ionization parameters for this sample are much larger than those for star-forming object at the same metallicity., Comment: 17 pages. Accepted in MNRAS

The design of a future multi-TeV muon collider needs new ideas to overcome the technological challenges related to muon production, cooling, accumulation and acceleration. In this paper a layout of a positron driven muon source known as the Low EMittance Muon Accelerator (LEMMA) concept is presented. The positron beam, stored in a ring with high energy acceptance and low emittance, is extracted and driven to a multi-target system, to produce muon pairs at threshold. This solution alleviates the issues related to the power deposited and the integrated Peak Energy Density Deposition (PEDD) on the targets. Muons produced in the multi-target system will then be accumulated before acceleration and injection in the collider. A multi-target line lattice has been designed to cope with the focusing of both the positron and muon beams. Studies on the number, material and thickness of the targets have been carried out. A general layout of the overall scheme and a description is presented, as well as plans for future R&D., Comment: 18 pages, 32 figures

The purpose of this paper is to show that there are Hom-Lie algebra structures on $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, where $D$ is a special type of generalized derivation of $\mathfrak{sl}_2(\mathbb{F})$, and $\mathbb{F}$ is an algebraically closed field of characteristic zero. It is shown that the generalized derivations $D$ of $\mathfrak{sl}_2(\mathbb{F})$ that we study in this work, satisfy the Hom-Lie Jacobi identity for the Lie bracket of $\mathfrak{sl}_2(\mathbb{F})$. We study the representation theory of Hom-Lie algebras within the appropriate category and prove that any finite dimensional representation of a Hom-Lie algebra of the form $\mathfrak{sl}_2(\mathbb{F}) \oplus \mathbb{F}D$, is completely reducible, in analogy to the well known Theorem of Weyl from the classical Lie theory. We apply this result to characterize the non-solvable Lie algebras having an invertible generalized derivation of the type of $D$. Finally, using root space decomposition techniques we provide an intrinsic proof of the fact that $\mathfrak{sl}_2(\mathbb{F})$ is the only simple Lie algebra admitting non-trivial Hom-Lie structures.

The 235U(n,f) cross section was measured in a wide energy range at n_TOF relative to 6Li(n,t) and 10B(n,alpha), with high resolution and in a wide energy range, with a setup based on a stack of six samples and six silicon detectors placed in the neutron beam. This allowed us to make a direct comparison of the reaction yields under the same experimental conditions, and taking into account the forward/backward emission asymmetry. A hint of an anomaly in the 10{\div}30 keV neutron energy range had been previously observed in other experiments, indicating a cross section systematically lower by several percent relative to major evaluations. The present results indicate that the evaluated cross section in the 9{\div}18 keV neutron energy range is indeed overestimated, both in the recent updates of ENDF/B-VIII.0 and of the IAEA reference data. Furthermore, these new high-resolution data confirm the existence of resonance-like structures in the keV neutron energy region. The new, high accuracy results here reported may lead to a reduction of the uncertainty in the 1{\div}100 keV neutron energy region. Finally, the present data provide additional confidence on the recently re-evaluated cross section integral between 7.8 and 11 eV., Comment: 22 pages, 20 figures, submitted to PRC

Chemical abundances for 15 elements (C, N, O, Na, Mg, Al, Si, K, Ca, Ti, V, Cr, Mn, Fe, and Ni) are presented for 83 stellar members of the 4 Gyr old solar-metallicity open cluster M67. The sample contains stars spanning a wide range of evolutionary phases, from G dwarfs to red clump stars. The abundances were derived from near-IR ($\lambda$1.5 -- 1.7$\mu$m) high-resolution spectra ($R$ = 22,500) from the SDSS-IV/APOGEE survey. A 1-D LTE abundance analysis was carried out using the APOGEE synthetic spectral libraries, via chi-square minimization of the synthetic and observed spectra with the qASPCAP code. We found significant abundance differences ($\sim$0.05 -- 0.30 dex) between the M67 member stars as a function of the stellar mass (or position on the HR diagram), where the abundance patterns exhibit a general depletion (in [X/H]) in stars at the main-sequence turnoff. The amount of the depletion is different for different elements. We find that atomic diffusion models provide, in general, good agreement with the abundance trends for most chemical species, supporting recent studies indicating that measurable atomic diffusion operates in M67 stars., Comment: Accepted to ApJ

We study and classify the 3-dimensional Hom-Lie algebras over $\mathbb{C}$. We provide first a complete set of representatives for the isomorphism classes of skew-symmetric bilinear products defined on a 3-dimensional complex vector space $\mathfrak{g}$. The well known Lie brackets for the 3-dimensional Lie algebras are included into appropriate isomorphism classes of such products representatives. For each product representative, we provide a complete set of canonical forms for the linear maps $\mathfrak{g} \to \mathfrak{g}$ that turn $g$ into a Hom-Lie algebra, thus characterizing the corresponding isomorphism classes. As by-products, Hom-Lie algebras for which the linear maps $\mathfrak{g} \to \mathfrak{g}$ are not homomorphisms for their products, are exhibited. Examples also arise of non-isomorphic families of HomLie algebras which share, however, a fixed Lie-algebra product on $\mathfrak{g}$. In particular, this is the case for the complex simple Lie algebra $\mathfrak{sl}_2(\mathbb{C})$. Similarly, there are isomorphism classes for which their skew-symmetric bilinear products can never be Lie algebra brackets on $\mathfrak{g}$.

A population of globular clusters (GCs) has been recently established by the Fermi-LAT telescope as a new class of GeV $\gamma$-ray sources. Leptons accelerated to TeV energies, in the inner magnetospheres of MSPs or in their wind regions, should produce $\gamma$-rays through the inverse Compton scattering in the dense radiation field from the huge population of stars. We have conducted deep observations of the globular cluster M15 with the MAGIC telescopes and used 165 hrs in order to search for $\gamma$-ray emission. A strong upper limit on the TeV $\gamma$-ray flux $<3.2\times 10^{-13}\mathrm{cm^{-2}s^{-1}}$ above 300 GeV ($<0.26\%$ of the Crab nebula flux) has been obtained. We interpret this limit as a constraint on the efficiency of the acceleration of leptons in the magnetospheres of the MSPs. We constrain the injection rate of relativistic leptons, $\eta_{\rm e}$, from the MSPs magnetospheres and their surrounding. We conclude that $\eta_{\rm e}$ must be lower than expected from the modelling of high energy processes in MSP inner magnetospheres. For leptons accelerated with the power law spectrum in the MSP wind regions, $\eta_{\rm e}$ is constrained to be much lower than derived for the wind regions around classical pulsars. These constraints are valid for the expected range of magnetic field strengths within the GC and for the range of likely energies of leptons injected from the inner magnetospheres, provided that the leptons are not removed from the globular cluster very efficiently due to advection process. We discuss consequences of these constraints for the models of radiation processes around millisecond pulsars., Comment: 11 pages, 7 figures, accepted for publication in MNRAS

The HAWC Collaboration released the 2HWC catalog of TeV sources, in which 19 show no association with any known high-energy (HE; E > 10 GeV) or very-high-energy (VHE; E > 300 GeV) sources. This catalog motivated follow-up studies by both the MAGIC and Fermi-LAT observatories with the aim of investigating gamma-ray emission over a broad energy band. In this paper, we report the results from the first joint work between HAWC, MAGIC and Fermi-LAT on three unassociated HAWC sources: 2HWC J2006+341, 2HWC J1907+084* and 2HWC J1852+013*. Although no significant detection was found in the HE and VHE regimes, this investigation shows that a minimum 1 degree extension (at 95% confidence level) and harder spectrum in the GeV than the one extrapolated from HAWC results are required in the case of 2HWC J1852+013*, while a simply minimum extension of 0.16 degrees (at 95% confidence level) can already explain the scenario proposed by HAWC for the remaining sources. Moreover, the hypothesis that these sources are pulsar wind nebulae is also investigated in detail., Comment: 12 pages, 3 figures. Accepted for publication in MNRAS

The mechanisms producing fast variability of the $\gamma$-ray emission in active galactic nuclei are under debate. The MAGIC telescopes detected a fast very high energy (VHE, E$>100$ GeV) $\gamma$-ray flare from BL Lacertae on 2015 June 15. The flare had a maximum flux of $(1.5\pm 0.3)\times 10^{-10}$ photons cm$^{-2}$ s$^{-1}$ and halving time of $26\pm8$ minutes. The MAGIC observations were triggered by a high state in the optical and high energy (HE, E$>100$ MeV) $\gamma$-ray bands. In this paper we present the MAGIC VHE $\gamma$-ray data together with multiwavelength data from radio, optical, X-rays, and HE $\gamma$ rays from 2015 May 1 to July 31. Well-sampled multiwavelength data allow us to study the variability in detail and compare it to the other epochs when fast VHE $\gamma$-ray flares have been detected from this source. Interestingly, we find that the behaviour in radio, optical, X-rays and HE $\gamma$-rays is very similar to two other observed VHE $\gamma$-ray flares. In particular, also during this flare there was an indication of rotation of the optical polarization angle and of activity at the 43\,GHz core. These repeating patterns indicate a connection between the three events. We also test modelling of the spectral energy distribution, based on constraints from the light curves and VLBA observations, with two different geometrical setups of two-zone inverse Compton models. In addition we model the $\gamma$-ray data with the star-jet interaction model. We find that all of the tested emission models are compatible with the fast VHE $\gamma$-ray flare, but all have some tension with the multiwavelength observations., Comment: Accepted to Astronomy & Astrophysics

In this work we explore accurate new ways to derive the ionization parameter ($U$) and the equivalent effective temperature ($T_*$) in HII regions using emission-line intensities from the ionized gas. The so-called softness parameter ($\eta$), based on [OII], [OIII], [SII], and [SIII] has been proposed to estimate the hardening of the ionizing incident field of radiation, but the simplest relation of this parameter with $T_*$ also depends on $U$ and metallicity ($Z$). Here we provide a Bayesian-like code (HCm-Teff) that compares the observed emission lines of $\eta$ with the predictions of a large grid of photoionization models giving precise estimations of both $U$ and $T_*$ when $Z$ is known. We also study the radial variation of these parameters in well-studied disc galaxies observed by the CHAOS collaboration. Our results indicate that the observed radial decreasing of $\eta$ can be attributed to a radial hardening of $T_*$, across galactic discs as in NGC~628 and NGC~5457. On the other hand NGC~5194, which presents a positive slope of the fitting of the softness parameter, has a flat slope in $T_*$. On the contrary the three galaxies do not seem to present large radial variations of the ionization parameter. When we inspect a larger sample of galaxies we observe steeper radial variations of $T_*$ in less bright and later-type galaxies, mimicking a similar trend observed for $Z$ but the studied sample should be enlarged to obtain more statistically significant conclusions., Comment: 15 pages, 13 figures, 2 tables, accepted for publication in MNRAS

SNR G24.7+0.6 is a 9.5 kyrs radio and $\gamma$-ray supernova remnant evolving in a dense medium. In the GeV regime, SNR G24.7+0.6 (3FHL\,J1834.1--0706e/FGES\,J1834.1--0706) shows a hard spectral index ($\Gamma$$\sim$2) up to $200$\,GeV, which makes it a good candidate to be observed with Cherenkov telescopes such as MAGIC. We observed the field of view of \snr\ with the MAGIC telescopes for a total of 31 hours. We detect very high energy $\gamma$-ray emission from an extended source located 0.34\degr\ away from the center of the radio SNR. The new source, named \mgc\ is detected up to 5\,TeV, and its spectrum is well-represented by a power-law function with spectral index of $2.74 \pm 0.08$. The complexity of the region makes the identification of the origin of the very-high energy emission difficult, however the spectral agreement with the LAT source and overlapping position at less than 1.5$\sigma$ point to a common origin. We analysed 8 years of \fermi-LAT data to extend the spectrum of the source down to 60\,MeV. \fermi-LAT and MAGIC spectra overlap within errors and the global broad band spectrum is described by a power-law with exponential cutoff at $1.9\pm0.5$\,TeV. The detected $\gamma$-ray emission can be interpreted as the results of proton-proton interaction between the supernova and the CO-rich surrounding., Comment: accepted for publication by MNRAS