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We prove an Amitsur--Levitzki-type theorem for Grassmann algebras, stating that the minimal degree of a standard identity that is a polynomial identity of the ring of $n \times n$ matrices over the $m$-generated Grassmann algebra is at least $2\left\lfloor\frac{m}{2}\right\rfloor+4n-4$ for all $n,m\geq 2$ and this bound is sharp for $m=2,3$ and any $n\geq 2$. The arguments are purely combinatorial, based on computing sums of signs corresponding to Eulerian trails in directed graphs., Comment: 22 pages, 7 figures, since version1 the statement of the lower bound got extended and a conjecture has been added

We analyze a large sample of 885 GCs giants from the APOGEE survey. We used the Cannon results to separate the red giant branch and the asymptotic giant branch stars, not only allowing for a refinement of surface gravity from isochrones, but also providing an independent H-band spectroscopic method to distinguish stellar evolutionary status in clusters. We then use the BACCHUS code to derive metallicity, microturbulence, acroturbulence and many light-element abundances as well as the neutron-capture elements Nd and Ce for the first time from the APOGEE GCs data. Our independent analysis helped us to diagnose issues regarding the standard analysis of the APOGEE DR14 for low-metallicity GC stars. Furthermore, while we confirm most of the known correlations and anti-correlation trends (Na-O, Mg-Al,C-N), we discover that some stars within our most metal-poor clusters show an extreme Mg depletion and some Si enhancement but at the same time show some relative Al depletion, displaying a turnover in the Mg-Al diagram. These stars suggest that Al has been partially depleted in their progenitors by very hot proton-capture nucleosynthetic processes. Furthermore, we attempted to quantitatively correlate the spread of Al abundances with the global properties of GCs. We find an anti-correlation of the Al spread against clusters metallicity and luminosity, but the data do not allow to find clear evidence of a dependence of N against metallicity in the more metal-poor clusters. Large and homogeneously analyzed samples from on-going spectroscopic surveys unveil unseen chemical details for many clusters, including a turnover in the Mg-Al anti-correlation, thus yielding new constrains for GCs formation evolution models., Comment: 17 pages, 23 figures, accepted in A&A

Twenty years have passed since first light for the Sloan Digital Sky Survey (SDSS). Here, we release data taken by the fourth phase of SDSS (SDSS-IV) across its first three years of operation (July 2014-July 2017). This is the third data release for SDSS-IV, and the fifteenth from SDSS (Data Release Fifteen; DR15). New data come from MaNGA - we release 4824 datacubes, as well as the first stellar spectra in the MaNGA Stellar Library (MaStar), the first set of survey-supported analysis products (e.g. stellar and gas kinematics, emission line, and other maps) from the MaNGA Data Analysis Pipeline (DAP), and a new data visualisation and access tool we call "Marvin". The next data release, DR16, will include new data from both APOGEE-2 and eBOSS; those surveys release no new data here, but we document updates and corrections to their data processing pipelines. The release is cumulative; it also includes the most recent reductions and calibrations of all data taken by SDSS since first light. In this paper we describe the location and format of the data and tools and cite technical references describing how it was obtained and processed. The SDSS website (www.sdss.org) has also been updated, providing links to data downloads, tutorials and examples of data use. While SDSS-IV will continue to collect astronomical data until 2020, and will be followed by SDSS-V (2020-2025), we end this paper by describing plans to ensure the sustainability of the SDSS data archive for many years beyond the collection of data., Comment: Paper to accompany DR15. 25 pages, 6 figures. Accepted for publication in ApJSS. The two papers on the MaNGA Data Analysis Pipeline (DAP, Westfall et al. and Belfiore et al., see Section 4.1.2), and the paper on Marvin (Cherinka et al., see Section 4.2) have been submitted for collaboration review and will be posted to arXiv in due course. v2 fixes some broken URLs in the PDF

In this paper, using variational approaches, we investigate the first order planning problem arising in the theory of mean field games. We show the existence and uniqueness of weak solutions of the problem in the case of a large class of Hamiltonians with arbitrary superlinear order of growth at infinity and local coupling functions. We require the initial and final measures to be merely summable. At the same time (relying on the techniques developed recently by Graber and M\'esz\'aros), under stronger monotonicity and convexity conditions on the data, we obtain Sobolev estimates on the solutions of the planning problem both for space and time derivatives., Comment: to appear in Calc. Var. Partial Differential Equations; Section 3 from the previous version removed upon the suggestion of the referee

We map the trends of elemental abundance ratios across the Galactic disk, spanning R = 3-15 kpc and midplane distance |Z|= 0-2 kpc, for 15 elements in a sample of 20,485 stars measured by the SDSS/APOGEE survey (O, Na, Mg, Al, Si, P, S, K, Ca, V, Cr, Mn, Fe, Co, Ni). Adopting Mg rather than Fe as our reference element, and separating stars into two populations based on [Fe/Mg], we find that the median trends of [X/Mg] vs. [Mg/H] in each population are nearly independent of location in the Galaxy. The full multi-element cartography can be summarized by combining these nearly universal median sequences with our measured metallicity distribution functions and the relative proportions of the low-[Fe/Mg] (high-alpha) and high-[Fe/Mg] (low-alpha) populations, which depend strongly on R and |Z|. We interpret the median sequences with a semi-empirical "2-process" model that describes both the ratio of core collapse and Type Ia supernova contributions to each element and the metallicity dependence of the supernova yields. These observationally inferred trends can provide strong tests of supernova nucleosynthesis calculations. Our results lead to a relatively simple picture of abundance ratio variations in the Milky Way, in which the trends at any location can be described as the sum of two components with relative contributions that change systematically and smoothly across the Galaxy. Deviations from this picture and future extensions to other elements can provide further insights into the physics of stellar nucleosynthesis and unusual events in the Galaxy's history., Comment: 29 pp, 22 figs, submitted to AAS journals, comments welcome

Shocks arising in galaxy mergers could accelerate cosmic-ray (CR) ions to TeV-PeV energies. While propagating in the intergalactic medium, these CRs can produce high-energy neutrinos, electron-positron pairs and gamma-rays. In the presence of intergalactic magnetic fields, the secondary pairs will radiate observable emissions through synchrotron radiation and inverse Compton scattering. In this paper, we demonstrate that these emissions can explain the radio and X-ray fluxes of merging galaxies such as NGC 660 and NGC 3256. Using our model in combination with the observations, we can constrain the gas mass, shock velocity, magnetic field and the CR spectral index $s$ of these systems. For NGC 660 a single-zone model with a spectral index $2.1\lesssim s\lesssim2.2$ is able to reproduce simultaneously the radio and X-ray observations, while a simple one-zone scenario with $s\sim2$ can describe the radio and a large fraction of X-ray observations of NGC 3256. Our work provides a useful approach for studying the dynamics and physical parameters of galaxy mergers, which can play an important part in future multi-messenger studies of similar and related extragalactic sources., Comment: 11 pages, 6 figures. Accepted by ApJ

The ANITA collaboration have reported observation of two anomalous events that appear to be $\varepsilon_{\rm cr} \approx 0.6$ EeV cosmic ray showers emerging from the Earth with exit angles of $27^\circ$ and $35^\circ$, respectively. While EeV-scale upgoing showers have been anticipated as a result of astrophysical tau neutrinos converting to tau leptons during Earth passage, the observed exit angles are much steeper than expected in Standard Model (SM) scenarios. Indeed, under conservative extrapolations of the SM interactions, there is no particle that can propagate through the Earth with probability $p > 10^{-6}$ at these energies and exit angles. We explore here whether "beyond the Standard Model" (BSM) particles are required to explain the ANITA events, if correctly interpreted, and conclude that they are. Seeking confirmation or refutation of the physical phenomenon of sub-EeV Earth-emergent cosmic rays in data from other facilities, we find support for the reality of the ANITA events, and three candidate analog events, among the Extremely High Energy Northern Track neutrinos of the IceCube Neutrino Observatory. Properties of the implied BSM particle are anticipated, at least in part, by those predicted for the "stau" slepton ($\tilde{\tau}_R$) in some supersymmetric models of the fundamental interactions, wherein the stau manifests as the next-to-lowest mass supersymmetric partner particle., Comment: PRD submitted. 15 pages, 3 figures

Data and analysis methodology used for the SDSS/APOGEE Data Releases 13 and 14 are described, highlighting differences from the DR12 analysis presented in Holtzman (2015). Some improvement in the handling of telluric absorption and persistence is demonstrated. The derivation and calibration of stellar parameters, chemical abundances, and respective uncertainties are described, along with the ranges over which calibration was performed. Some known issues with the public data related to the calibration of the effective temperatures (DR13), surface gravity (DR13 and DR14), and C and N abundances for dwarfs (DR13 and DR14) are highlighted. We discuss how results from a data-driven technique, The Cannon (Casey 2016), are included in DR14, and compare those with results from the APOGEE Stellar Parameters and Chemical Abundances Pipeline (ASPCAP). We describe how using The Cannon in a mode that restricts the abundance analysis of each element to regions of the spectrum with known features from that element leads to Cannon abundances can lead to significantly different results for some elements than when all regions of the spectrum are used to derive abundances., Comment: 31 pages, 31 figures; Astronomical Journal in press

Data from the SDSS-IV / Apache Point Observatory Galactic Evolution Experiment (APOGEE-2) have been released as part of SDSS Data Releases 13 (DR13) and 14 (DR14). These include high resolution H-band spectra, radial velocities, and derived stellar parameters and abundances. DR13, released in August 2016, contained APOGEE data for roughly 150,000 stars, and DR14, released in August 2017, added about 110,000 more. Stellar parameters and abundances have been derived with an automated pipeline, the APOGEE Stellar Parameter and Chemical Abundance Pipeline (ASPCAP). We evaluate the performance of this pipeline by comparing the derived stellar parameters and abundances to those inferred from optical spectra and analysis for several hundred stars. For most elements -- C, Na, Mg, Al, Si, S, Ca, Cr, Mn, Ni -- the DR14 ASPCAP analysis have systematic differences with the comparisons samples of less than 0.05 dex (median), and random differences of less than 0.15 dex (standard deviation). These differences are a combination of the uncertainties in both the comparison samples as well as the ASPCAP-analysis. Compared to the references, magnesium is the most accurate alpha-element derived by ASPCAP, and shows a very clear thin/thick disk separation, while nickel is the most accurate iron-peak element (besides iron)., Comment: Accepted for publication in AJ

We undertake a critical and comprehensive comparison of the radial velocities and the main stellar atmospheric parameters for stars in common between the latest data releases from the APOGEE and the LAMOST surveys. There is a total of 42,420 dwarfs/giants stars in common between the APOGEE DR14 - LAMOST DR3 stellar catalogs. A comparison between the RVs shows an offset of 4.54 $\pm$ 0.03 km/s, with a dispersion of 5.8 km/s, in the sense that APOGEE RVs are larger. We observe a small offset in the Teff of about 13 K, with a scatter of 155 K. Small offset in [Fe/H] of about 0.06 dex together with a scatter of 0.13 dex is also observed. We notice that the largest offset between the surveys occurs in the surface gravities. Using only surface gravities in calibrated red giants from APOGEE DR14, where there are 24,074 stars in common, a deviation of 0.14 dex is found with substantial scatter. There are 17,482 red giant stars in common between APOGEE DR14 and those in LAMOST tied to APOGEE DR12 via the Cannon. There is generally good agreement between the two data-sets. However, we find dependencies of the differences of the stellar parameters on effective temperature. For metal-rich stars, a different trend for the [Fe/H] discrepancies is found. Surprisingly, we see no correlation between the internal APOGEE DR14 - DR12 differences in Teff and those in DR14 - LAMOST tied to DR12, where a correlation should be expected since LAMOST has been calibrated to APOGEE DR12. We also find no correlation between the [Fe/H] discrepancies, suggesting that LAMOST/Cannon is not well coupled to the APOGEE DR12 stellar parameters scale. A [Fe/H] dependence between the stellar parameters in APOGEE DR12 and those in DR14 is reported. We find a weak correlation in the differences between APOGEE DR14 - DR12 and LAMOST on DR12 surface gravity for stars hotter than 4800 K and in the log g range between 2.0 and 2.8., Comment: 14 pages, 20 figures. Accepted for publication in Astronomy & Astrophysics (A&A)

The detection of gravitational waves and electromagnetic counterparts from a binary neutron star (BNS) merger confirmed that it is accompanied by the launch of fast merger ejecta. Analogous to supernova remnants, forward shocks formed by the interaction of the ejecta with interstellar material will produce high-energy cosmic rays. We investigate the possibility that Galactic neutron star merger remnants (NSMRs) significantly contribute to the observed cosmic rays in the energy range between the knee and the ankle. Using typical parameters obtained by modeling of GW170817, we find that NSMRs can accelerate iron nuclei up to $\sim500$ PeV. We calculate the cosmic-ray spectrum and composition observed on Earth, and show that the Galactic NSMR scenario can account for the experimental cosmic-ray data in the 20 -- 1000 PeV range. Our model can naturally explain the hardening feature around 20 PeV for total cosmic-ray spectrum, which has been observed by the Telescope Array Low Energy extension and the IceTop air shower array., Comment: 8 pages, 1 figure, 1 table, accepted for publication in ApJ

IC 166 is an intermediate-age open cluster ($\sim 1$ Gyr) which lies in the transition zone of the metallicity gradient in the outer disc. Its location, combined with our very limited knowledge of its salient features, make it an interesting object of study. We present the first high-resolution spectroscopic and precise kinematical analysis of IC 166, which lies in the outer disc with $R_{GC} \sim 12.7$ kpc. High resolution \textit{H}-band spectra were analyzed using observations from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. We made use of the Brussels Automatic Stellar Parameter (BACCHUS) code to provide chemical abundances based on a line-by-line approach for up to eight chemical elements (Mg, Si, Ca, Ti, Al, K, Mn and Fe). The $\alpha-$element (Mg, Si, Ca and whenever available Ti) abundances, and their trends with Fe abundances have been analysed for a total of 13 high-likelihood cluster members. No significant abundance scatter was found in any of the chemical species studied. Combining the positional, heliocentric distance, and kinematic information we derive, for the first time, the probable orbit of IC 166 within a Galactic model including a rotating boxy bar, and found that it is likely that IC 166 formed in the Galactic disc, supporting its nature as an unremarkable Galactic open cluster with an orbit bound to the Galactic plane., Comment: 16 pages, 7 tables, 8 figures, accepted for publication in AJ

Due to recent advances in nanosatellite technology, it is now feasible to integrate scintillators with an effective area of hundreds of square-centimeters on a single three-unit cubesat. We present the early test results for the digital payload electronics developed for the proposed CAMELOT (Cubesats Applied for MEasuring and LOcalising Transients) mission. CAMELOT is a fleet of nanosatellites intended to do full-sky monitoring and perform accurate timing-based localization of gamma-ray transients. Here we present the early results on the GPS timestamping capabilities of the CAMELOT payload electronics, concluding that the investigated setup is capable to timestamp the received gamma-ray photons with an accuracy and precision better than 0.02 millisecond, which corresponds to a timing based localization accuracy of $\sim 3.5^{\prime}$. Further refinements will likely allow us to improve the timing accuracy down to the sub-microsecond level., Comment: Proceedings of the SPIE Astronomical Instrumentation Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray

We propose a fleet of nanosatellites to perform an all-sky monitoring and timing based localisation of gamma-ray transients. The fleet of at least nine 3U cubesats shall be equipped with large and thin CsI(Tl) scintillator based soft gamma-ray detectors read out by multi-pixel photon counters. For bright short gamma-ray bursts (GRBs), by cross-correlating their light curves, the fleet shall be able to determine the time difference of the arriving GRB signal between the satellites and thus determine the source position with an accuracy of $\sim10^\prime$. This requirement demands precise time synchronization and accurate time stamping of the detected gamma-ray photons, which will be achieved by using on-board GPS receivers. Rapid follow up observations at other wavelengths require the capability for fast, nearly simultaneous downlink of data using a global inter-satellite communication network. In terms of all-sky coverage, the proposed fleet will outperform all GRB monitoring missions., Comment: Proceedings of the SPIE Astronomical Instrumentation Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray

We study the distribution of the sandpile group of random d-regular graphs. For the directed model, we prove that it follows the Cohen-Lenstra heuristics, that is, the limiting probability that the $p$-Sylow subgroup of the sandpile group is a given $p$-group $P$, is proportional to $|Aut(P)|^{-1}$. For finitely many primes, these events get independent in the limit. Similar results hold for undirected random regular graphs, where for odd primes the limiting distributions are the ones given by Clancy, Leake and Payne. This answers an open question of Frieze and Vu whether the adjacency matrix of a random regular graph is invertible with high probability. Note that for directed graphs this was recently proved by Huang. It also gives an alternate proof of a theorem of Backhausz and Szegedy., Comment: We improved the presentation of the paper. More details are given in several proofs

The observations of a macronova/kilonova accompanied by gravitational waves from a binary neutron star merger (GW170817) confirmed that neutron star coalescences produce copious ejecta. The coincident gamma-ray detection implies the existence of a relativistic jet in this system. During the jet's propagation within the ejecta, high-energy photons and neutrinos can be produced. The photons are absorbed by the ejecta, while the neutrinos escape and can be detected. Here, we estimate such trans-ejecta neutrino emission, and discuss how neutrino observations could be used to differentiate between gamma-ray burst emission scenarios. We find that neutrinos from the internal shocks inside the ejecta may be detectable by IceCube within a few years of operation, and will likely be detected with IceCube-Gen2. The neutrino signals coincident with gravitational waves would enable us to reveal the physical quantities of the choked jets even without electromagnetic signals., Comment: 12 pages, 5 figures, 2 tables, accepted for publication in PRD

We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed by accounting for differences in their solar reference values. We include theoretically motivated corrections to the large frequency spacing ($\Delta \nu$) scaling relation, and we calibrate the zero point of the frequency of maximum power ($\nu_{\rm max}$) relation to be consistent with masses and radii for members of star clusters. For most targets, the parameters returned by different pipelines are in much better agreement than would be expected from the pipeline-predicted random errors, but 22\% of them had at least one method not return a result and a much larger measurement dispersion. This supports the usage of multiple analysis techniques for asteroseismic stellar population studies. The measured dispersion in mass estimates for fundamental calibrators is consistent with our error model, which yields median random and systematic mass uncertainties for RGB stars of order 4\%. Median random and systematic mass uncertainties are at the 9\% and 8\% level respectively for RC stars., Comment: 29 pages, 26 figures. Submitted ApJSupp. Comments welcome. For access to the main data table (Table 5) use https://www.dropbox.com/s/k33td8ukefwy5tv/APOKASC2_Table5.txt?dl=0; for access to the individual pipeline values (Table 6) use https://www.dropbox.com/s/vl9s2p3obftrv8m/APOKASC2_Table6.txt?dl=0

For the first time, a short gamma-ray burst (GRB) was unambiguously associated with a gravitational wave (GW) observation from a binary neutron star (NS) merger. This allows us to link the details of the central engine properties to GRB emission models. We find that photospheric models (both dissipative and non-dissipative variants) have difficulties accounting for the observations. Internal shocks give the most natural account of the observed peak energy, viewing angle and total energy. We also show that a simple external shock model can reproduce the observed GRB pulse with parameters consistent with those derived from the afterglow modeling. We find a simple cocoon shock breakout model is in mild tension with the observed spectral evolution, however it cannot be excluded based on gamma-ray data alone. Future joint observations of brighter GRBs will pose even tighter constraints on prompt emission models., Comment: 14 pages, 6 figures

Metal-poor globular clusters (GCs) exhibit intriguing Al-Mg anti-correlations and possible Si-Al correlations, which are important clues to decipher the multiple-population phenomenon. NGC 5053 is one of the most metal-poor GCs in the nearby Universe, and has been suggested to be associated with the Sagittarius (Sgr) dwarf galaxy, due to its similarity in location and radial velocity with one of the Sgr arms. In this work, we simulate the orbit of NGC 5053, and argue against a physical connection between Sgr and NGC 5053. On the other hand, the Mg, Al, and Si spectral lines, which are difficult to detect in the optical spectra of NGC 5053 stars, have been detected in the near-infrared APOGEE spectra. We use three different sets of stellar parameters and codes to derive the Mg, Al, and Si abundances. Regardless of which method is adopted, we see a large Al variation, and a substantial Si spread. Along with NGC 5053, metal-poor GCs exhibit different Mg, Al, and Si variations. Moreover, NGC 5053 has the lowest cluster mass among the GCs that have been identified to exhibit an observable Si spread until now., Comment: ApJ accepted. 14 pages, 12 figures

We present elemental abundance analysis of high-resolution spectra for five giant stars, deriving Fe, Mg, Al, C, N, O, Si and Ce abundances, and spatially located within the innermost regions of the bulge globular cluster NGC 6522, based on H-band spectra taken with the multi-object APOGEE-north spectrograph from the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey. Of the five cluster candidates, two previously unremarked stars are confirmed to have second-generation (SG) abundance patterns, with the basic pattern of depletion in C and Mg simultaneous with enrichment in N and Al as seen in other SG globular cluster populations at similar metallicity. } In agreement with the most recent optical studies, the NGC 6522 stars analyzed exhibit (when available) only mild overabundances of the s-process element Ce, contradicting the idea of the NGC 6522 stars being formed from gas enriched by spinstars and indicating that other stellar sources such as massive AGB stars could be the primary intra-cluster medium polluters. The peculiar abundance signature of SG stars have been observed in our data, confirming the presence of multiple generations of stars in NGC 6522., Comment: 13 pages, 8 figures, 4 tables, matches the accepted version in A&A

We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for Dushnik-Miller dimension, we have that if $\dim(C)\le d$ for every component $C$ of a poset $P$, then $\dim(P)\le \max\{2,d\}$; also if $\dim(B)\le d$ for every block $B$ of a poset $P$, then $\dim(P)\le d+2$. By way of constrast, local dimension is well behaved with respect to components, but not for blocks: if $\text{ldim}(C)\le d$ for every component $C$ of a poset $P$, then $\text{ldim}(P)\le d+2$; however, for every $d\ge 4$, there exists a poset $P$ with $\text{ldim}(P)=d$ and $\dim(B)\le 3$ for every block $B$ of $P$. In this paper we show that Boolean dimension behaves like Dushnik-Miller dimension with respect to both components and blocks: if $\text{bdim}(C)\le d$ for every component $C$ of $P$, then $\text{bdim}(P)\le 2+d+4\cdot2^d$; also if $\text{bdim}(B)\le d$ for every block of $P$, then $\text{bdim}(P)\le 19+d+18\cdot 2^d$., Comment: 12 pages. arXiv admin note: text overlap with arXiv:1712.06099

The merger of dark matter halos and the gaseous structures embedded in them, such as proto-galaxies, galaxies, and groups and clusters of galaxies, results in strong shocks that are capable of accelerating cosmic rays (CRs) to $\sim10~\rm PeV$. These shocks will produce high-energy neutrinos and $\gamma$-rays through inelastic $pp$ collisions with ambient gaseous environments. In this work, we study the contributions of these halo mergers to the diffuse neutrino flux measured in IceCube and to the non-blazar portion of the extragalactic $\gamma$-ray background measured by $Fermi$. In order to calculate them, we formulate the redshift dependence of the shock velocity, galactic radius, halo gas content and galactic/intergalactic magnetic fields over the dark matter halo distribution up to a redshift $z=10$. We find that high-redshift mergers contribute a significant amount of the cosmic-ray energy luminosity density, and the resulting neutrino spectra could explain a large part of the observed diffuse neutrino flux above 0.1 PeV up to several PeV. We also show that our model can somewhat alleviate tensions with the extragalactic $\gamma$-ray background. First, since a larger fraction of the CR energy luminosity density comes from high redshifts, the accompanying $\gamma$-rays are more strongly suppressed through $\gamma\gamma$ annihilations with the cosmic microwave background (CMB) and the extragalactic background light (EBL). Second, mildly radiative-cooled shocks may lead to a harder CR spectrum with spectral indices of $1.5\lesssim s\lesssim2.0$. Our study suggests that halo mergers, a fraction of which may also induce starbursts in the merged galaxies, can be promising neutrino emitters without violating the existing $Fermi$ $\gamma$-ray constraints on the non-blazar component of the extragalactic $\gamma$-ray background., Comment: 13 pages, 7 figures, ApJ accepted

Recent results from the Pierre Auger Collaboration have shown that the composition of ultrahigh-energy cosmic rays (UHECRs) becomes gradually heavier with increasing energy. Although gamma-ray bursts (GRBs) have been promising sources of UHECRs, it is still unclear whether they can account for the Auger results because of their unknown nuclear composition of ejected UHECRs. In this work, we revisit the possibility that low-luminosity GRBs (LL GRBs) act as the sources of UHECR nuclei, and give new predictions based on the intrajet nuclear composition models considering progenitor dependencies. We find that the nuclear component in the jet can be divided into two groups according to the mass fraction of silicon nuclei, Si-free and Si-rich. Motivated by the connection between LL GRBs and transrelativistic supernovae, we also consider the hypernova ejecta composition. Then, we discuss the survivability of UHECR nuclei in the jet base and internal shocks of the jets, and show that it is easier for nuclei to survive for typical LL GRBs. Finally, we numerically propagate UHECR nuclei ejected from LL GRBs with different composition models and compare the resulting spectra and composition to Auger data. Our results show that both the Si-rich progenitor and hypernova ejecta models match the Auger data well, while the Si-free progenitor models have more difficulty in fitting the spectrum. We argue that our model is consistent with the newly reported cross correlation between the UHECRs and starburst galaxies, since both LL GRBs and hypernovae are expected to be tracers of the star-formation activity. LL GRBs have also been suggested as the dominant origin of IceCube neutrinos in the PeV range, and the LL GRB origin of UHECRs can be critically tested by near-future multimessenger observations., Comment: 17 pages, 16 figures, minor corrections, added the discussion about the possible correlation with starburst galaxies, version accepted by PRD

In this paper we describe the photometric and spectroscopic properties of multiple populations in seven northern globular clusters. In this study we employ precise ground based photometry from the private collection of Stetson, space photometry from the Hubble Space Telescope, literature abundances of Na and O, and APOGEE survey abundances for Mg, Al, C, and N. Multiple populations are identified by their position in the CU,B,I -V pseudo-CMD and confirmed with their chemical composition determined using abundances. We confirm the expectation from previous studies that the RGB in all seven clusters are split and the different branches have different chemical compositions. The Mg-Al anti-correlations were well explored by the APOGEE and Gaia-ESO surveys for most globular clusters, some clusters showing bimodal distributions, while others continuous distributions. Even though the structure (i.e., bimodal vs. continuous) of Mg-Al can greatly vary, the Al-rich and Al-poor populations do not seem to have very different photometric properties, agreeing with theoretical calculations. There is no one-to-one correspondence between the Mg-Al anticorrelation shape (bimodal vs. continuous) and the structure of the RGB seen in the HST pseudo-CMDs, with the HST photometric information usually implying more complex formation/evolution histories than the spectroscopic ones. We report on finding two second generation HB stars in M5, and five second generation AGB stars in M92, which is the most metal-poor cluster to date in which second generation AGB stars have been observed., Comment: Accepted for publication in MNRAS, 13 pages, 7 figures, 5 tables

We discuss the self-enrichment scenario by AGB stars for the formation of multiple populations in globular clusters (GCs) by analyzing data set of giant stars observed in 9 Galactic GCs, covering a wide range of metallicities and for which the simultaneous measurements of C, N, O, Mg, Al, Si are available. To this aim we calculated 6 sets of AGB models, with the same chemical composition as the stars belonging to the first generation of each GC. We find that the AGB yields can reproduce the set of observations available, not only in terms of the degree of contamination shown by stars in each GC but, more important, also the observed trend with metallicity, which agrees well with the predictions from AGB evolution modelling. While further observational evidences are required to definitively fix the main actors in the pollution of the interstellar medium from which new generation of stars formed in GCs, the present results confirm that the gas ejected by stars of mass in the range $4~\rm M_{\odot} \leq \rm M \leq 8~\rm M_{\odot}$ during the AGB phase share the same chemical patterns traced by stars in GCs., Comment: 22 pages and 11 figures; accepted for publication in MNRAS

The Apache Point Observatory Galactic Evolution Experiment (APOGEE) provides spectroscopic information of regions of the inner Milky Way inaccessible to optical surveys. We present the first large study of the metallicity distribution of the innermost Galactic regions based on homogeneous measurements from the SDSS Data Release 12 for 7545 red giant stars within 4.5 kpc of the Galactic center, with the goal to shed light on the structure and origin of the Galactic bulge. Stellar metallicities are found, through multiple-Gaussian decompositions, to be distributed in several components indicative of the presence of various stellar populations such as the bar, or the thin and the thick disk. A super-solar ([Fe/H]=+0.32) and a solar ([Fe/H]=+0.00) metallicity components, tentatively associated with the thin disk and the Galactic bar, respectively, seem to be the major contributors near the midplane. The solar-metallicity component extends outwards in the midplane but is not observed in the innermost regions. The central regions (within 3 kpc of the Galactic center) reveal, on the other hand, the presence of a significant metal-poor population ([Fe/H] =-0.46), tentatively associated with the thick disk, and which becomes the dominant component far from the midplane ($|Z| > +0.75 kpc). Varying contributions from these different components produce a transition region at +0.5 kpc < |Z| < +1.0 kpc characterized by a significant vertical metallicity gradient., Comment: 15 pages, 11 figures

Carbon isotope ratios, along with carbon and nitrogen abundances, are derived in a sample of 11 red-giant members of one of the most metal-rich clusters in the Milky Way, NGC 6791. The selected red-giants have a mean metallicity and standard deviation of [Fe/H]=+0.39+-0.06 (Cunha et al. 2015). We used high resolution H-band spectra obtained by the SDSS-IV Apache Point Observatory Galactic Evolution Experiment (APOGEE). The advantage of using high-resolution spectra in the H-band is that lines of CO are well represented and their line profiles are sensitive to the variation of 12C/13C. Values of the 12C/13C ratio were obtained from a spectrum synthesis analysis. The derived 12C/13C ratios varied between 6.3 and 10.6 in NGC 6791, in agreement with the final isotopic ratios from thermohaline-induced mixing models. The ratios derived here are combined with those obtained for more metal poor red-giants from the literature to examine the correlation between 12C/13C, mass, metallicity and evolutionary status., Comment: Accepted for publication in MNRAS, 9 pages, 4 figures, 2 tables

Solid inflation is a cosmological model where inflation is driven by fields which enter the Lagrangian in the same way as body coordinates of a solid matter enter the equation of state, spontaneously breaking spatial translational and rotational symmetry. We construct a simple generalization of this model by adding a scalar field with standard kinetic term to the action. In our model the scalar power spectrum and the tensor-to-scalar ratio do not differ from the ones predicted by the solid inflation qualitatively, if the scalar field does not dominate the solid matter. The same applies also for the size of the scalar bispectrum measured by the non-linearity parameter, although our model allows it to have different shapes. The tensor bispectra predicted by the two models do not differ from each other in the leading order of the slow-roll approximation. In the case when contribution of the solid matter to the stress-energy tensor is much smaller than the contribution from the scalar field, the tensor-to-scalar ratio and the non-linearity parameter are amplified by factors $\epsilon^{-1}$ and $\epsilon^{-2}$ respectively., Comment: 23 pages, 3 figures

We discuss the electromagnetic radiation from newborn binary black holes (BBHs). As a consequence of the evolution of massive stellar binaries, a binary consisting of a primary black hole (BH) and a secondary Wolf-Rayet star is expected as a BBH progenitor system. We investigate optical transients from the birth of BBHs powered by the Bondi-Hoyle-Lyttleton accretion onto the primary BH, which occur $\sim1-10$ Gyr earlier than gravitational wave signals at the BH-BH merger. When the secondary massive star collapses into a BH, it may eject a fraction of its outer material and may form a disk around the primary BH and induces a powerful disk wind. These primary-induced winds can lead to optical transients with a kinetic energy of $\sim10^{47}-3\times10^{48}$ erg, an ejecta velocity of $10^8-10^9\rm~cm~s^{-1}$, a duration of a few days, and an absolute magnitude ranging from about $-11$ to $-14$. The light curves and late-time spectra of these transients are distinctive from those of ordinary supernovae, and detection of this type of transient is possible by future optical transient surveys if the event rate of this transient is comparable to the merger rate of BBHs. This paper focuses on the emissions from disk-driven transients induced by the primary BH, different from the first paper that focuses on wind-driven transients from the tidally-locked secondary massive star., Comment: 9 pages, 3 figures, accepted for publication in ApJ, arXiv:1702.07337v2 was split into two papers according to referee's suggestion. This is Paper II. See also arXiv:1702.07337v3 for Paper I

The recent detection of gravitational waves and electromagnetic counterparts from the double neutron star merger event GW+EM170817, supports the standard paradigm of short gamma-ray bursts (SGRBs) and kilonovae/macronovae. It is important to reveal the nature of the compact remnant left after the merger, either a black hole or neutron star, and their physical link to the origin of the long-lasting emission observed in SGRBs. The diversity of the merger remnants may also lead to different kinds of transients that can be detected in future. Here we study the high-energy emission from the long-lasting central engine left after the coalescence, under certain assumptions. In particular, we consider the X-ray emission from a remnant disk and the non-thermal nebular emission from disk-driven outflows or pulsar winds. We demonstrate that late-time X-ray and high-frequency radio emission can provide useful constraints on properties of the hidden compact remnants and their connections to long-lasting SGRB emission, and we discuss the detectability of nearby merger events through late-time observations at $\sim30-100$ d after the coalescence. We also investigate the GeV-TeV gamma-ray emission that occurs in the presence of long-lasting central engines, and show the importance of external inverse-Compton radiation due to up-scattering of X-ray photons by relativistic electrons in the jet. We also search for high-energy gamma-rays from GW170817 in the Fermi-LAT data, and report upper limits on such long-lasting emission. Finally, we consider the implications of GW+EM170817 and discuss the constraints placed by X-ray and high-frequency radio observations., Comment: 16 pages, 12 figures, accepted for publication in ApJ, minor changes

First we consider families in the hypercube $Q_n$ with bounded VC dimension. Frankl raised the problem of estimating the number $m(n,k)$ of maximal families of VC dimension $k$. Alon, Moran and Yehudayoff showed that $$n^{(1+o(1))\frac{1}{k+1}\binom{n}{k}}\leq m(n,k)\leq n^{(1+o(1))\binom{n}{k}}.$$ We close the gap by showing that $\log \left(m(n,k)\right)= {(1+o(1))\binom{n}{k}}\log n$ and show how a tight asymptotic for the logarithm of the number of induced matchings between two adjacent small layers of $Q_n$ follows as a corollary. Next, we consider the integrity $I(Q_n)$ of the hypercube, defined as $$I(Q_n) = \min\{ |S| +m(Q_n \setminus S) : S \subseteq V (Q_n) \},$$ where $m(H)$ denotes the number of vertices in the largest connected component of $H$. Beineke, Goddard, Hamburger, Kleitman, Lipman and Pippert showed that $c\frac{2^n}{\sqrt{n}} \leq I(Q_n)\leq C\frac{2^n}{\sqrt{n}}\log n$ and suspected that their upper bound is the right value. We prove that the truth lies below the upper bound by showing that $I(Q_n)\leq C \frac{2^n}{\sqrt{n}}\sqrt{\log n}$., Comment: 7 pages

The coincident detection of a gravitational-wave (GW) event GW170817 with electromagnetic (EM) signals (e.g., a short gamma-ray burst SGRB 170817A or a macronova) from a binary neutron star merger within the nearby galaxy NGC 4933 provides a new, multimessenger test of the weak equivalence principle (WEP), extending the WEP test with GWs and photons. Assuming that the arrival time delay between the GW signals from GW170817 and the photons from SGRB 170817A or the macronova is mainly attributed to the gravitational potential of the Milky Way, we demonstrate that the strict upper limits on the deviation from the WEP are $\Delta \gamma<1.4\times10^{-3}$ for GW170817/macronova and $\Delta \gamma <5.9\times10^{-8}$ for GW170817/SGRB 170817A. A much more severe constraint on the WEP accuracy can be achieved ($\sim0.9\times10^{-10}$) for GW170817/SGRB 170817A when we consider the gravitational potential of the Virgo Cluster, rather than the Milky Way's gravity. This provides the tightest limit to date on the WEP through the relative differential variations of the $\gamma$ parameter for two different species of particles. Compared with other multimessenger (photons and neutrinos) results, our limit is 7 orders of magnitude tighter than that placed by the neutrinos and photons from supernova 1987A, and is almost as good as or is an improvement of 6 orders of magnitude over the limits obtained by the low-significance neutrinos correlated with GRBs and a blazar flare., Comment: 10 pages, no figures. Accepted by JCAP on Nov 8, 2017

We say that a set system $\mathcal{F}\subseteq 2^{[n]}$ shatters a given set $S\subseteq [n]$ if $2^S= \{F~\cap~S:~F~\in~\mathcal{F}\}$. The Sauer-Shelah lemma states that in general, a set system $\mathcal{F}$ shatters at least $|\mathcal{F}|$ sets. Here we concentrate on the case of equality. A set system is called \emph{shattering-extremal} if it shatters exactly $|\mathcal{F}|$ sets. A conjecture of R\'onyai and the second author and of Litman and Moran states that if a family is shattering-extremal then one can add a set to it and the resulting family is still shattering-extremal. Here we prove this conjecture for a class of set systems defined from Sperner families., Comment: 15 pages

The Lidskii formula for the type $A_n$ root system expresses the volume and Ehrhart polynomial of the flow polytope of the complete graph with nonnegative integer netflows in terms of Kostant partition functions. For every integer polytope the volume is the leading coefficient of the Ehrhart polynomial. The beauty of the Lidskii formula is the revelation that for these polytopes its Ehrhart polynomial function can be deduced from its volume function! Baldoni and Vergne generalized Lidskii's result for flow polytopes of arbitrary graphs $G$ and nonnegative integer netflows. While their formulas are combinatorial in nature, their proofs are based on residue computations. In this paper we construct canonical polytopal subdivisions of flow polytopes which we use to prove the Baldoni-Vergne-Lidskii formulas. In contrast with the original computational proof of these formulas, our proof reveal their geometry and combinatorics. We conclude by exhibiting enumerative properties of the Lidskii formulas via our canonical polytopal subdivisions., Comment: 28 pages, 10 figures, v2. includes proof of a second formula for the lattice points and an appendix with examples

SiC based metal-oxide-semiconductor field-effect transistors (MOSFETs) have gained a significant importance in power electronics applications. However, electrically active defects at the SiC/SiO$_2$ interface degrade the ideal behavior of the devices. The relevant microscopic defects can be identified by electron paramagnetic resonance (EPR) or electrically detected magnetic resonance (EDMR). This helps to decide which changes to the fabrication process will likely lead to further increases of device performance and reliability. EDMR measurements have shown very similar dominant hyperfine (HF) spectra in differently processed MOSFETs although some discrepancies were observed in the measured $g$-factors. Here, the HF spectra measured of different SiC MOSFETs are compared and it is argued that the same dominant defect is present in all devices. A comparison of the data with simulated spectra of the C dangling bond (P$_\textrm{bC}$) center and the silicon vacancy (V$_\textrm{Si}$) demonstrates that the P$_\textrm{bC}$ center is a more suitable candidate to explain the observed HF spectra., Comment: Accepted for publication in the Journal of Applied Physics

We investigate current and future prospects for coincident detection of high-energy neutrinos and gravitational waves (GWs). Short gamma-ray bursts (SGRBs) are believed to originate from mergers of compact star binaries involving neutron stars. We estimate high-energy neutrino fluences from prompt emission, extended emission, X-ray flares, and plateau emission, and show that neutrino signals associated with the extended emission are the most promising. Assuming that the cosmic-ray loading factor is $\sim10$ and the Lorentz factor distribution is lognormal, we calculate the probability of neutrino detection from extended emission by current and future neutrino detectors, and find that the quasi-simultaneous detection of high-energy neutrinos, gamma rays, and GWs is possible with future instruments or even with current instruments for nearby SGRBs having extended emission. We also discuss stacking analyses that will also be useful with future experiments such as IceCube-Gen2., Comment: 8 pages, 2 figures, 3 tables, accepted for publication in ApJL

A graph $G$ is terminal-pairable with respect to a demand multigraph $D$ on the same vertex set as $G$, if there exists edge-disjoint paths joining the end vertices of every demand edge of $D$. In this short note, we improve the upper bound on the largest $\Delta(n)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta(n)$. This disproves a conjecture originally stated by Csaba, Faudree, Gy\'arf\'as, Lehel and Schelp., Comment: 4 pages

In this paper we obtain Sobolev estimates for weak solutions of first oder variational Mean Field Game systems with coupling terms that are local function of the density variable. Under some coercivity condition on the coupling, we obtain first order Sobolev estimates for the density variable, while under similar coercivity condition on the Hamiltonian we obtain second order Sobolev estimates for the value function. These results are valid both for stationary and time-dependent problems. In the latter case the estimates are fully global in time, thus we resolve a question which was left open in [PS17]. Our methods apply to a large class of Hamiltonians and coupling functions., Comment: to appear in Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire

High energy neutrino astrophysics has come of age with the discovery by IceCube of neutrinos in the TeV to PeV energy range attributable to extragalactic sources at cosmological distances. At such energies, astrophysical neutrinos must have their origin in cosmic ray interactions, providing information about the sources of high energy cosmic rays, as well as leading to the co-production of high energy gamma-rays. The intimate link with these latter two independently observed types of radiation provides important tools in the search for identifying and understanding the nature of their astrophysical sources. These neutrinons can provide important constraints about the cosmic ray acceleration process, and since they travel essentially unimpeded they can probe our Universe out to the farthest cosmological distances., Comment: 26 pages, 8 figures; accepted in Annual Review of Nuclear and Particle Science; to appear in vol. 67 (2017)