Proof of two conjectures of Zuber on fully packed loop configurations

Two conjectures of Zuber [``On the counting of fully packed loops configurations. Some new conjectures,'' preprint] on the enumeration of configurations in the fully packed loop model on the square grid with periodic boundary conditions, which have a prescribed linkage pattern, are proved. Following an idea of de Gier [``Loops, matchings and alternating-sign matrices,'' Discrete Math., to appear], the proofs are based on bijections between such fully packed loop configurations and rhombus tilings, and the hook-content formula for semistandard tableaux.Comment: 20 pages; AmS-LaTe

First measurements of 15N fractionation in N2H+ toward high-mass star forming cores

We report on the first measurements of the isotopic ratio 14N/15N in N2H+ toward a statistically significant sample of high-mass star forming cores. The sources belong to the three main evolutionary categories of the high-mass star formation process: high-mass starless cores, high-mass protostellar objects, and ultracompact HII regions. Simultaneous measurements of 14N/15N in CN have been made. The 14N/15N ratios derived from N2H+ show a large spread (from ~180 up to ~1300), while those derived from CN are in between the value measured in the terrestrial atmosphere (~270) and that of the proto-Solar nebula (~440) for the large majority of the sources within the errors. However, this different spread might be due to the fact that the sources detected in the N2H+ isotopologues are more than those detected in the CN ones. The 14N/15N ratio does not change significantly with the source evolutionary stage, which indicates that time seems to be irrelevant for the fractionation of nitrogen. We also find a possible anticorrelation between the 14N/15N (as derived from N2H+) and the H/D isotopic ratios. This suggests that 15N enrichment could not be linked to the parameters that cause D enrichment, in agreement with the prediction by recent chemical models. These models, however, are not able to reproduce the observed large spread in 14N/15N, pointing out that some important routes of nitrogen fractionation could be still missing in the models.Comment: 2 Figures, accepted for publication in ApJ

H_2D^+ in the High-mass Star-forming Region Cygnus X

H_2D^+ is a primary ion that dominates the gas-phase chemistry of cold dense gas. Therefore, it is hailed as a unique tool in probing the earliest, prestellar phase of star formation. Observationally, its abundance and distribution is, however, just beginning to be understood in low-mass prestellar and cluster-forming cores. In high-mass star-forming regions, H_2D^+ has been detected only in two cores, and its spatial distribution remains unknown. Here, we present the first map of the ortho-H_2D^+J_(k^+,k^-) = 1_(1,0) → 1_(1,1) and N_2H^+ 4-3 transition in the DR21 filament of Cygnus X with the James Clerk Maxwell Telescope, and N_2D^+ 3-2 and dust continuum with the Submillimeter Array. We have discovered five very extended (≤34, 000 AU diameter) weak structures in H2D+ in the vicinity of, but distinctly offset from, embedded protostars. More surprisingly, the H_2D^+ peak is not associated with either a dust continuum or N_2D^+ peak. We have therefore uncovered extended massive cold dense gas that was undetected with previous molecular line and dust continuum surveys of the region. This work also shows that our picture of the structure of cores is too simplistic for cluster-forming cores and needs to be refined: neither dust continuum with existing capabilities nor emission in tracers like N_2D^+ can provide a complete census of the total prestellar gas in such regions. Sensitive H_2D^+ mapping of the entire DR21 filament is likely to discover more of such cold quiescent gas reservoirs in an otherwise active high-mass star-forming region

Chemical evolution in the environment of intermediate mass young stellar objects: NGC7129--FIRS2 and LkHα\alpha234

We have carried out a molecular survey of the Class 0 IM protostar NGC 7129 -- FIRS 2 (hereafter FIRS 2) and the Herbig Be star LkH$\alpha$ 234 with the aim of studying the chemical evolution of the envelopes of intermediate-mass (IM) young stellar objects (YSOs). Both objects have similar luminosities (~500 Lsun) and are located in the same molecular cloud which minimizes the chemical differences due to different stellar masses or initial cloud conditions. Moreover, since they are located at the same distance, we have the same spatial resolution in both objects. A total of 17 molecular species (including rarer isotopes) have been observed in both objects and the structure of their envelopes and outflows is determined with unprecedent detail. Our results show that the protostellar envelopes are dispersed and warmed up during the evolution to become a pre-main sequence star. In fact, the envelope mass decreases by a factor >5 from FIRS 2 to LkH$\alpha$234, while the kinetic temperature increases from ~13K to 28K. On the other hand, there is no molecular outflow associated with LkH$\alpha$234. The molecular outflow seems to stop before the star becomes visible. These physical changes strongly affect the chemistry of their envelopes. Based on our results in FIRS2 and LkH$\alpha$ 234, we propose some abundance ratios that can be used as chemical clocks for the envelopes of IM YSOs. The SiO/CS, CN/N2H+, HCN/N2H+, DCO+/HCO+ and D2CO/DCO+ ratios are good diagnostics of the protostellar evolutionary stage.Comment: 24 pages, 17 figure

The Deuterium Fractionation Timescale in Dense Cloud Cores: A Parameter Space Exploration

The deuterium fraction [N$_2$D$^+$]/[N$_2$H$^+$], may provide information about the ages of dense, cold gas structures, important to compare with dynamical models of cloud core formation and evolution. Here we introduce a complete chemical network with species containing up to three atoms, with the exception of the Oxygen chemistry, where reactions involving H$_3$O$^+$ and its deuterated forms have been added, significantly improving the consistency with comprehensive chemical networks. Deuterium chemistry and spin states of H$_2$ and H$_3^+$ isotopologues are included in this primarily gas-phase chemical model. We investigate dependence of deuterium chemistry on model parameters: density ($n_{\rm H}$), temperature, cosmic ray ionization rate, and gas-phase depletion factor of heavy elements ($f_{\rm D}$). We also explore the effects of time-dependent freeze-out of gas-phase species and dynamical evolution of density at various rates relative to free-fall collapse. For a broad range of model parameters, the timescales to reach large values of $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$, observed in some low- and high-mass starless cores, are relatively long compared to the local free-fall timescale. These conclusions are unaffected by introducing time-dependent freeze-out and considering models with evolving density, unless the initial $f_{\rm D} \gtrsim$ 10. For fiducial model parameters, achieving $D_{\rm frac}^{\rm N_2H^+} \gtrsim 0.1$ requires collapse to be proceeding at rates at least several times slower than that of free-fall collapse, perhaps indicating a dynamically important role for magnetic fields in the support of starless cores and thus the regulation of star formation.Comment: 23 pages, 18 figures, accepted by Ap

Modelling Online Gaming Metacognitions: The Role of Time Spent Gaming in Predicting Problematic Internet Use

© 2020, The Author(s). In recent years there have been growing concerns about problematic Internet use (PIU) as potential mental health problem. Among the many activities available on the Internet, the time spent gaming appears one of the most frequent risk factors in developing PIU. The aim of the current study was to model the relationship between negative affect, metacognitions about online gaming, frequency of online gaming and PIU. A total of 326 Italian gamers (mean age = 27 years, SD = 5.65 years; 93.3% males) participated in the study. The pattern of relationships specified by the theoretical model was examined through path analysis. Results showed that negative affect was directly associated with all other variables. Specifically, positive, strong and direct associations were found between negative affect and both positive and negative metacognitions about online gaming. Moreover, negative metacognitions about online gaming were strongly linked to PIU. Overall, the theoretical model was supported showing that metacognitions about online gaming may play a role in the association between time spent on online gaming to a broader pattern of PIU. Results are discussed within the context of the metacognitive model of psychopathology and clinical implications based on this model are outlined

Structure, Dynamics and Deuterium Fractionation of Massive Pre-Stellar Cores

High levels of deuterium fraction in N$_2$H$^+$ are observed in some pre-stellar cores. Single-zone chemical models find that the timescale required to reach observed values ($D_{\rm frac}^{{\rm N}_2{\rm H}^+} \equiv {\rm N}_2{\rm D}^+/{\rm N}_2{\rm H}^+ \gtrsim 0.1$) is longer than the free-fall time, possibly ten times longer. Here, we explore the deuteration of turbulent, magnetized cores with 3D magnetohydrodynamics simulations. We use an approximate chemical model to follow the growth in abundances of N$_2$H$^+$ and N$_2$D$^+$. We then examine the dynamics of the core using each tracer for comparison to observations. We find that the velocity dispersion of the core as traced by N$_2$D$^+$ appears slightly sub-virial compared to predictions of the Turbulent Core Model of McKee & Tan, except at late times just before the onset of protostar formation. By varying the initial mass surface density, the magnetic energy, the chemical age, and the ortho-to-para ratio of H$_2$, we also determine the physical and temporal properties required for high deuteration. We find that low initial ortho-to-para ratios ($\lesssim 0.01$) and/or multiple free-fall times ($\gtrsim 3$) of prior chemical evolution are necessary to reach the observed values of deuterium fraction in pre-stellar cores.Comment: 20 pages, 18 figures; accepted for publication in Ap

The dynamical properties of dense filaments in the infrared dark cloud G035.39-00.33

Infrared Dark Clouds (IRDCs) are unique laboratories to study the initial conditions of high-mass star and star cluster formation. We present high-sensitivity and high-angular resolution IRAM PdBI observations of N2H+ (1-0) towards IRDC G035.39-00.33. It is found that G035.39-00.33 is a highly complex environment, consisting of several mildly supersonic filaments (sigma_NT/c_s ~1.5), separated in velocity by <1 km s^-1 . Where multiple spectral components are evident, moment analysis overestimates the non-thermal contribution to the line-width by a factor ~2. Large-scale velocity gradients evident in previous single-dish maps may be explained by the presence of substructure now evident in the interferometric maps. Whilst global velocity gradients are small (<0.7 km s^-1 pc^-1), there is evidence for dynamic processes on local scales (~1.5-2.5 km s^-1 pc^-1 ). Systematic trends in velocity gradient are observed towards several continuum peaks. This suggests that the kinematics are influenced by dense (and in some cases, starless) cores. These trends are interpreted as either infalling material, with accretion rates ~(7 \pm 4)x10^-5 M_sun yr^-1 , or expanding shells with momentum ~24 \pm 12 M_sun km s^-1 . These observations highlight the importance of high-sensitivity and high-spectral resolution data in disentangling the complex kinematic and physical structure of massive star forming regions.Comment: 25 pages, 23 figures, accepted for publication in MNRA

Deuteration as an evolutionary tracer in massive-star formation

Theory predicts, and observations confirm, that the column density ratio of a molecule containing D to its counterpart containing H can be used as an evolutionary tracer in the low-mass star formation process. Since it remains unclear if the high-mass star formation process is a scaled-up version of the low-mass one, we investigated whether the relation between deuteration and evolution can be applied to the high-mass regime. With the IRAM-30m telescope, we observed rotational transitions of N2D+ and N2H+ and derived the deuterated fraction in 27 cores within massive star-forming regions understood to represent different evolutionary stages of the massive-star formation process. Results. Our results clearly indicate that the abundance of N2D+ is higher at the pre-stellar/cluster stage, then drops during the formation of the protostellar object(s) as in the low-mass regime, remaining relatively constant during the ultra-compact HII region phase. The objects with the highest fractional abundance of N2D+ are starless cores with properties very similar to typical pre-stellar cores of lower mass. The abundance of N2D+ is lower in objects with higher gas temperatures as in the low-mass case but does not seem to depend on gas turbulence. Our results indicate that the N2D+-to-N2H+ column density ratio can be used as an evolutionary indicator in both low- and high-mass star formation, and that the physical conditions influencing the abundance of deuterated species likely evolve similarly during the processes that lead to the formation of both low- and high-mass stars.Comment: Accepted by A&AL, 4 pages, 2 figures, 2 appendices (one for Tables, one for additional figures