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ALMA surveys have suggested that protoplanetary disks are not massive enough to form the known exoplanet population, under the assumption that the millimeter continuum emission is optically thin. In this work, we investigate how the mass determination is influenced when the porosity of dust grains is considered in radiative transfer models. The results show that disks with porous dust opacities yield similar dust temperature, but systematically lower millimeter fluxes compared to disks incorporating compact dust grains. Moreover, we recalibrate the relation between dust temperature and stellar luminosity for a wide range of stellar parameters, and calculate the dust masses of a large sample of disks using the traditionally analytic approach. The median dust mass from our calculation is about 6 times higher than the literature result, and this is mostly driven by the different opacities of porous and compact grains. A comparison of the cumulative distribution function between disk dust masses and exoplanet masses show that the median exoplanet mass is about 2 times lower than the median dust mass, if grains are porous, and there are no exoplanetary systems with masses higher than the most massive disks. Our analysis suggests that adopting porous dust opacities may alleviate the mass budget problem for planet formation. As an example illustrating the combined effects of optical depth and porous dust opacities on the mass estimation, we conduct new IRAM/NIKA-2 observations toward the IRAS 04370+2559 disk and perform a detailed radiative transfer modeling of the spectral energy distribution. The best-fit dust mass is roughly 100 times higher than the value from the traditionally analytic calculation. Future spatially resolved observations at various wavelengths are required to better constrain the dust mass., Comment: 11 pages, 7 figures, Accepted for publication in A&A

The composition of protoplanetary disks, and hence the initial conditions of planet formation, may be strongly influenced by the infall and thermal processing of material during the protostellar phase. Composition of dust and ice in protostellar envelopes, shaped by energetic processes driven by the protostar, serves as the fundamental building material for planets and complex organic molecules. As part of the JWST GO program, "Investigating Protostellar Accretion" (IPA), we observed an intermediate-mass protostar HOPS 370 (OMC2-FIR3) using NIRSpec/IFU and MIRI/MRS. This study presents the gas and ice phase chemical inventory revealed with the JWST in the spectral range of $\sim$2.9 to 28 $\mu$m and explores the spatial variation of volatile ice species in the protostellar envelope. We find evidence for thermal processing of ice species throughout the inner envelope. We present the first high-spatial resolution ($\sim 80$ au) maps of key volatile ice species H$_{2}$O, CO$_{2}$, $^{13}$CO$_2$, CO, and OCN$^-$, which reveal a highly structured and inhomogeneous density distribution of the protostellar envelope, with a deficiency of ice column density that coincides with the jet/outflow shocked knots. Further, we observe high relative crystallinity of H$_{2}$O ice around the shocked knot seen in the H$_2$ and OH wind/outflow, which can be explained by a lack of outer colder material in the envelope along the line of sight due to the irregular structure of the envelope. These observations show clear evidence of thermal processing of the ices in the inner envelope, close to the outflow cavity walls, heated by the luminous protostar., Comment: Submitted to ApJ. Main text:16 pages with 11 figures

Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted phylogenetic networks that has been extensively investigated in recent years. In this paper, we give a novel characterisation of a tree-child network $\mathcal{R}$ in terms of cherry-picking sequences that are sequences on the leaves of $\mathcal{R}$ and reduce it to a single vertex by repeatedly applying one of two reductions to its leaves. We show that our characterisation extends to unrooted tree-child networks which are mostly unexplored in the literature and, in turn, also offers a new approach to settling the computational complexity of deciding if an unrooted phylogenetic network can be oriented as a rooted tree-child network.

The spread of a graph $G$ is the difference $\lambda_1 - \lambda_n$ between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determined the graph on $n$ vertices with maximum spread for sufficiently large $n$. In this paper, we study a related question of maximizing the difference $\lambda_{i+1} - \lambda_{n-j}$ for a given pair $(i, j)$ over all graphs on $n$ vertices. We give upper bounds for all pairs $(i, j)$, exhibit an infinite family of pairs where the bound is tight, and show that for the pair $(1, 0)$ the extremal example is unique. These results contribute to a line of inquiry pioneered by Nikiforov aiming to maximize different linear combinations of eigenvalues over all graphs on $n$ vertices., Comment: 9 pages, 2 figures

A normal network is uniquely determined by the set of phylogenetic trees that it displays. Given a set $\mathcal{P}$ of rooted binary phylogenetic trees, this paper presents a polynomial-time algorithm that reconstructs the unique binary normal network whose set of displayed binary trees is $\mathcal{P}$, if such a network exists. Additionally, we show that any two rooted phylogenetic trees can be displayed by a normal network and show that this result does not extend to more than two trees. This is in contrast to tree-child networks where it has been previously shown that any collection of rooted phylogenetic trees can be displayed by a tree-child network. Lastly, we introduce a type of cherry-picking sequence that characterises when a collection $\mathcal{P}$ of rooted phylogenetic trees can be displayed by a normal network and, further, characterise the minimum number of reticulations needed over all normal networks that display $\mathcal{P}$. We then exploit these sequences to show that, for all $n\ge 3$, there exist two rooted binary phylogenetic trees on $n$ leaves that can be displayed by a tree-child network with a single reticulation, but cannot be displayed by a normal network with less than $n-2$ reticulations.

In comparison to phylogenetic trees, phylogenetic networks are more suitable to represent complex evolutionary histories of species whose past includes reticulation such as hybridisation or lateral gene transfer. However, the reconstruction of phylogenetic networks remains challenging and computationally expensive due to their intricate structural properties. For example, the small parsimony problem that is solvable in polynomial time for phylogenetic trees, becomes NP-hard on phylogenetic networks under softwired and parental parsimony, even for a single binary character and structurally constrained networks. To calculate the parsimony score of a phylogenetic network $N$, these two parsimony notions consider different exponential-size sets of phylogenetic trees that can be extracted from $N$ and infer the minimum parsimony score over all trees in the set. In this paper, we ask: What is the maximum difference between the parsimony score of any phylogenetic tree that is contained in the set of considered trees and a phylogenetic tree whose parsimony score equates to the parsimony score of $N$? Given a gap-free sequence alignment of multi-state characters and a rooted binary level-$k$ phylogenetic network, we use the novel concept of an informative blob to show that this difference is bounded by $k+1$ times the softwired parsimony score of $N$. In particular, the difference is independent of the alignment length and the number of character states. We show that an analogous bound can be obtained for the softwired parsimony score of semi-directed networks, while under parental parsimony on the other hand, such a bound does not hold.

Accretion bursts from low-mass young stellar objects (YSOs) are known for many decades. In recent years, the first accretion bursts of massive YSOs (MYSOs) have been observed. These phases of intense protostellar growth are of particular importance for studying massive star formation. Bursts of MYSOs are accompanied by flares of Class II methanol masers (hereafter masers), caused by an increase in exciting mid-infrared (MIR) emission. The G323.46$-$0.08 (hereafter G323) event extends the small sample of known MYSO bursts. Maser observations of the MYSO G323 show evidence of a flare, which was presumed to be caused by an accretion burst. This should be verified with IR data. We used time-dependent radiative transfer (TDRT) to characterize the heating and cooling timescales for eruptive MYSOs and to infer the main burst parameters. The G323 accretion burst is confirmed. It reached its peak in late 2013/early 2014 with a Ks-band increase of 2.5mag. TDRT indicates that the duration of the thermal afterglow in the far-infrared (FIR) can exceed the burst duration by years. The latter was proved by SOFIA observations, which indicate a flux increase of $(14.2\pm4.6)$% at $70\, \rm \mu m$ and $(8.5\pm6.1)$% at $160\, \mu$m in 2022 (2 years after the burst end). A one-sided light echo emerged that was propagating into the interstellar medium. The G323 burst is probably the most energetic MYSO burst observed so far. Within $8.4 \rm \, yrs$, an energy of $(0.9\pm_{0.8}^{2.5}) \times 10^{47}\,\rm erg$ was released. The short timescale points to the accretion of a compact body, while the burst energy corresponds to an accumulated mass of at least $(7\pm_{6}^{20})\,M_{Jup}$ and possibly even more if the protostar is bloated. In this case, the accretion event might have triggered protostellar pulsations, which give rise to the observed maser periodicity.

The spread of a graph $G$ is the difference between the largest and smallest eigenvalue of the adjacency matrix of $G$. In this paper, we consider the family of graphs which contain no $K_{s,t}$-minor. We show that for any $t\geq s \geq 2$ and sufficiently large $n$, there is an integer $\xi_{t}$ such that the extremal $n$-vertex $K_{s,t}$-minor-free graph attaining the maximum spread is the graph obtained by joining a graph $L$ on $(s-1)$ vertices to the disjoint union of $\lfloor \frac{2n+\xi_{t}}{3t}\rfloor$ copies of $K_t$ and $n-s+1 - t\lfloor \frac{2n+\xi_t}{3t}\rfloor$ isolated vertices. Furthermore, we give an explicit formula for $\xi_{t}$ and an explicit description for the graph $L$ for $t \geq \frac32(s-3) +\frac{4}{s-1}$., Comment: Minor revisions. arXiv admin note: text overlap with arXiv:2212.05540

This work aims to utilize the increased sensitivity and resolution of the JWST to quantify the HDO/H$_{2}$O ratio in ices toward young stellar objects (YSOs) and to determine if the HDO/H$_{2}$O ratios measured in the gas phase toward massive YSOs (MYSOs) are representative of the ratios in their ice envelopes. Two protostars observed in the Investigating Protostellar Accretion (IPA) program using JWST NIRSpec were analyzed: HOPS 370, an intermediate-mass YSO (IMYSO), and IRAS 20126+4104, a MYSO. The HDO ice toward these sources was detected above the 3$\sigma$ level and quantified via its 4.1 $\mu$m band. The contributions from the CH$_{3}$OH combination modes to the observed optical depth in this spectral region were constrained via the CH$_{3}$OH 3.53 $\mu$m band to ensure that the integrated optical depth of the HDO feature was not overestimated. H$_{2}$O ice was quantified via its 3 $\mu$m band. From these fits, ice HDO/H$_{2}$O abundance ratios of 4.6$\pm$1.8$\times$10$^{-3}$ and 2.6$\pm$1.2$\times$10$^{-3}$ are obtained for HOPS 370 and IRAS 20126+4104, respectively. The simultaneous detections of both crystalline HDO and crystalline H$_{2}$O corroborate the assignment of the observed feature at 4.1 $\mu$m to HDO ice. The ice HDO/H$_{2}$O ratios are similar to the highest reported gas HDO/H$_{2}$O ratios measured toward MYSOs as well as the hot inner regions of isolated low-mass protostars, suggesting that at least some of the gas HDO/H$_{2}$O ratios measured toward massive hot cores are representative of the HDO/H$_{2}$O ratios in ices. The need for an H$_{2}$O-rich CH$_{3}$OH component in the CH$_{3}$OH ice analysis supports recent experimental and observational results that indicate that some CH$_{3}$OH ice may form prior to the CO freeze-out stage in H$_{2}$O-rich ice layers., Comment: Accepted for publication in A&A. 23 pages, 17 figures, 10 tables

Mid-infrared emission features probe the properties of ionized gas, and hot or warm molecular gas. The Orion Bar is a frequently studied photodissociation region (PDR) containing large amounts of gas under these conditions, and was observed with the MIRI IFU aboard JWST as part of the "PDRs4All" program. The resulting IR spectroscopic images of high angular resolution (0.2") reveal a rich observational inventory of mid-IR emission lines, and spatially resolve the substructure of the PDR, with a mosaic cutting perpendicularly across the ionization front and three dissociation fronts. We extracted five spectra that represent the ionized, atomic, and molecular gas layers, and measured the most prominent gas emission lines. An initial analysis summarizes the physical conditions of the gas and the potential of these data. We identified around 100 lines, report an additional 18 lines that remain unidentified, and measured the line intensities and central wavelengths. The H I recombination lines originating from the ionized gas layer bordering the PDR, have intensity ratios that are well matched by emissivity coefficients from H recombination theory, but deviate up to 10% due contamination by He I lines. We report the observed emission lines of various ionization stages of Ne, P, S, Cl, Ar, Fe, and Ni, and show how certain line ratios vary between the five regions. We observe the pure-rotational H$_2$ lines in the vibrational ground state from 0-0 S(1) to 0-0 S(8), and in the first vibrationally excited state from 1-1 S(5) to 1-1 S(9). We derive H$_2$ excitation diagrams, and approximate the excitation with one thermal (~700 K) component representative of an average gas temperature, and one non-thermal component (~2700 K) probing the effect of UV pumping. We compare these results to an existing model for the Orion Bar PDR and highlight the differences with the observations., Comment: 26 pages, 12 figures, 3 tables. Submitted to A&A, under review (1st revision)

In this paper, we introduce a new notion of curvature on the edges of a graph that is defined in terms of effective resistances. We call this the Ricci--Foster curvature. We study the Ricci flow resulting from this curvature. We prove the existence of solutions to Ricci flow on short time intervals, and prove that Ricci flow preserves graphs with nonnegative (resp. positive) curvature., Comment: 14 pages, 8 figures, comments welcome!

Devriendt and Lambiotte recently introduced the \emph{node resistance curvature}, a notion of graph curvature based on the effective resistance matrix. In this paper, we begin the study of the behavior of the node resistance curvature under the operation of the Cartesian graph product. We study the natural question of global positivity of node resistance curvature of the Cartesian product of positively-curved graphs, and prove that, whenever $m,n\ge3$, the node resistance curvature of the interior vertices of a $m\times n$ grid is always nonpositive, while it is always nonnegative on the boundary of such grids. For completeness, we also prove a number of results on node resistance curvature in $2\times n$ grids and exhibit a counterexample to a generalization. We also give generic bounds and suggest several further questions for future study.

Most low-mass stars form in stellar clusters that also contain massive stars, which are sources of far-ultraviolet (FUV) radiation. Theoretical models predict that this FUV radiation produces photo-dissociation regions (PDRs) on the surfaces of protoplanetary disks around low-mass stars, impacting planet formation within the disks. We report JWST and Atacama Large Millimetere Array observations of a FUV-irradiated protoplanetary disk in the Orion Nebula. Emission lines are detected from the PDR; modelling their kinematics and excitation allows us to constrain the physical conditions within the gas. We quantify the mass-loss rate induced by the FUV irradiation, finding it is sufficient to remove gas from the disk in less than a million years. This is rapid enough to affect giant planet formation in the disk.

Given integers $n > k > 0$, and a set of integers $L \subset [0, k-1]$, an \emph{$L$-system} is a family of sets $\mathcal{F} \subset \binom{[n]}{k}$ such that $|F \cap F'| \in L$ for distinct $F, F'\in \mathcal{F}$. $L$-systems correspond to independent sets in a certain generalized Johnson graph $G(n, k, L)$, so that the maximum size of an $L$-system is equivalent to finding the independence number of the graph $G(n, k, L)$. The \emph{Lov\'asz number} $\vartheta(G)$ is a semidefinite programming approximation of the independence number $\alpha$ of a graph $G$. In this paper, we determine the leading order term of $\vartheta(G(n, k, L))$ of any generalized Johnson graph with $k$ and $L$ fixed and $n\rightarrow \infty$. As an application of this theorem, we give an explicit construction of a graph $G$ on $n$ vertices with a large gap between the Lov\'asz number and the Shannon capacity $c(G)$. Specifically, we prove that for any $\epsilon > 0$, for infinitely many $n$ there is a generalized Johnson graph $G$ on $n$ vertices which has ratio $\vartheta(G)/c(G) = \Omega(n^{1-\epsilon})$, which improves on all known constructions. The graph $G$ \textit{a fortiori} also has ratio $\vartheta(G)/\alpha(G) = \Omega(n^{1-\epsilon})$, which greatly improves on the best known explicit construction., Comment: 21 pages; modified the statement of Theorem 1.6 and expanded the proof of Lemma 2.11; some minor revisions

The structure and composition of simple ices can be modified during stellar evolution by protostellar heating. Key to understanding the involved processes are thermal and chemical tracers that can diagnose the history and environment of the ice. The 15.2 $\mu$m bending mode of $^{12}$CO$_2$ has proven to be a valuable tracer of ice heating events but suffers from grain shape and size effects. A viable alternative tracer is the weaker $^{13}$CO$_2$ isotopologue band at 4.39 $\mu$m which has now become accessible at high S/N with the $\textit{James Webb}$ Space Telescope (JWST). We present JWST NIRSpec observations of $^{13}$CO$_2$ ice in five deeply embedded Class 0 sources spanning a wide range in luminosities (0.2 - 10$^4$ L$_{\odot}$ ) taken as part of the Investigating Protostellar Accretion Across the Mass Spectrum (IPA) program. The band profiles vary significantly, with the most luminous sources showing a distinct narrow peak at 4.38 $\mu$m. We first apply a phenomenological approach and show that a minimum of 3-4 Gaussian profiles are needed to fit the $^{13}$CO$_2$ absorption feature. We then combine these findings with laboratory data and show that a 15.2 $\mu$m $^{12}$CO$_2$ band inspired five-component decomposition can be applied for the isotopologue band where each component is representative of CO$_2$ ice in a specific molecular environment. The final solution consists of cold mixtures of CO$_2$ with CH$_3$OH, H$_2$O and CO as well as segregated heated pure CO$_2$ ice. Our results are in agreement with previous studies of the $^{12}$CO$_2$ ice band, further confirming that $^{13}$CO$_{2}$ is a useful alternative tracer of protostellar heating events. We also propose an alternative solution consisting only of heated CO$_2$:CH$_3$OH and CO$_2$:H$_2$O ices and warm pure CO$_2$ ice for decomposing the ice profiles of the two most luminous sources in our sample.

Recently, there has been a growing interest in the relationships between unrooted and rooted phylogenetic networks. In this context, a natural question to ask is if an unrooted phylogenetic network U can be oriented as a rooted phylogenetic network such that the latter satisfies certain structural properties. In a recent preprint, Bulteau et al. claim that it is computational hard to decide if U has a funneled (resp. funneled tree-child) orientation, for when the internal vertices of U have degree at most 5. Unfortunately, the proof of their funneled tree-child result appears to be incorrect. In this paper, we present a corrected proof and show that hardness remains for other popular classes of rooted phylogenetic networks such as funneled normal and funneled reticulation-visible. Additionally, our results hold regardless of whether U is rooted at an existing vertex or by subdividing an edge with the root.

We aim to investigate the origin of the HI Br$\gamma$ emission in young stars by using GRAVITY to image the innermost region of circumstellar disks, where important physical processes such as accretion and winds occur. With high spectral and angular resolution, we focus on studying the continuum and the HI Br$\gamma$-emitting area of the Herbig star HD58647. Using VLTI-GRAVITY, we conducted observations of HD58647 with both high spectral and high angular resolution. Thanks to the extensive $uv$ coverage, we were able to obtain detailed images of the circumstellar environment at a sub-au scale, specifically capturing the continuum and the Br$\gamma$-emitting region. Through the analysis of velocity-dispersed images and photocentre shifts, we were able to investigate the kinematics of the HI Br$\gamma$-emitting region. The recovered continuum images show extended emission where the disk major axis is oriented along a position angle of 14\degr. The size of the continuum emission at 5-sigma levels is $\sim$ 1.5 times more extended than the sizes reported from geometrical fitting (3.69 mas $\pm$ 0.02 mas). This result supports the existence of dust particles close to the stellar surface, screened from the stellar radiation by an optically thick gaseous disk. Moreover, for the first time with GRAVITY, the hot gas component of HD58647 traced by the Br$\gamma$ ,has been imaged. This allowed us to constrain the size of the Br$\gamma$-emitting region and study the kinematics of the hot gas; we find its velocity field to be roughly consistent with gas that obeys Keplerian motion. The velocity-dispersed images show that the size of the hot gas emission is from a more compact region than the continuum (2.3 mas $\pm$ 0.2 mas). Finally, the line phases show that the emission is not entirely consistent with Keplerian rotation, hinting at a more complex structure in the hot gaseous disk., Comment: accepted in A&A on 20/11/2023

We investigate the bright CO fundamental emission in the central regions of five protostars in their primary mass assembly phase using new observations from JWST's Near-Infrared Spectrograph (NIRSpec) and Mid-Infrared Instrument (MIRI). CO line emission images and fluxes are extracted for a forest of $\sim$150 ro-vibrational transitions from two vibrational bands, $v=1-0$ and $v=2-1$. However, ${}^{13}$CO is undetected, indicating that ${}^{12}$CO emission is optically thin. We use H$_2$ emission lines to correct fluxes for extinction and then construct rotation diagrams for the CO lines with the highest spectral resolution and sensitivity to estimate rotational temperatures and numbers of CO molecules. Two distinct rotational temperature components are required for $v=1$ ($\sim600$ to 1000 K and 2000 to $\sim 10^4$ K), while one hotter component is required for $v=2$ ($\gtrsim 3500$ K). ${}^{13}$CO is depleted compared to the abundances found in the ISM, indicating selective UV photodissociation of ${}^{13}$CO; therefore, UV radiative pumping may explain the higher rotational temperatures in $v=2$. The average vibrational temperature is $\sim 1000$ K for our sources and is similar to the lowest rotational temperature components. Using the measured rotational and vibrational temperatures to infer a total number of CO molecules, we find that the total gas masses range from lower limits of $\sim10^{22}$ g for the lowest mass protostars to $\sim 10^{26}$ g for the highest mass protostars. Our gas mass lower limits are compatible with those in more evolved systems, which suggest the lowest rotational temperature component comes from the inner disk, scattered into our line of sight, but we also cannot exclude the contribution to the CO emission from disk winds for higher mass targets., Comment: 31 pages, 7 figures, 4 tables, received to ApJ December 10 2023, accepted to ApJ August 4 2024

The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research., Comment: 17 pages; minor revisions

In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular sequences or morphological data. Interestingly, it has been known for some time that any binary phylogenetic tree can be (convexly) defined by a set of at most four characters, and that there are binary phylogenetic trees for which three characters are not enough. Thus, it is of interest to characterise those phylogenetic trees that are defined by a set of at most three characters. In this paper, we provide such a characterisation, in particular proving that a binary phylogenetic tree $T$ is defined by a set of at most three characters precisely if $T$ has no internal subtree isomorphic to a certain tree., Comment: 21 pages, 9 figures

Investigating Protostellar Accretion (IPA) is a JWST Cycle~1 GO program that uses NIRSpec IFU and MIRI MRS to obtain 2.9--28~$\mu$m spectral cubes of young, deeply embedded protostars with luminosities of 0.2 to 10,000~L$_{\odot}$ and central masses of 0.15 to 12~M$_{\odot}$. In this Letter, we report the discovery of a highly collimated atomic jet from the Class~0 protostar IRAS~16253$-$2429, the lowest luminosity source ($L_\mathrm{bol}$ = 0.2 $L_\odot$) in the IPA program. The collimated jet is detected in multiple [Fe~II] lines, [Ne~II], [Ni~II], and H~I lines, but not in molecular emission. The atomic jet has a velocity of about 169~$\pm$~15~km\,s$^{-1}$, after correcting for inclination. The width of the jet increases with distance from the central protostar from 23 to~60 au, corresponding to an opening angle of 2.6~$\pm$~0.5\arcdeg. By comparing the measured flux ratios of various fine structure lines to those predicted by simple shock models, we derive a shock {speed} of 54~km\,s$^{-1}$ and a preshock density of 2.0$\times10^{3}$~cm$^{-3}$ at the base of the jet. {From these quantities and using a suite of jet models and extinction laws we compute a mass loss rate between $0.4 -1.1\times10^{-10}~M_{\odot}$~yr~$^{-1}$.} The low mass loss rate is consistent with simultaneous measurements of low mass accretion rate ($2.4~\pm~0.8~\times~10^{-9}~M_{\odot}$~yr$^{-1}$) for IRAS~16253$-$2429 from JWST observations (Watson et al. in prep), indicating that the protostar is in a quiescent accretion phase. Our results demonstrate that very low-mass protostars can drive highly collimated, atomic jets, even during the quiescent phase., Comment: Accepted to ApJL. Comments and feedback welcome

For a $k$-uniform hypergraph $\mathcal{H}$, the \emph{codegree squared sum} $\text{co}_2(\mathcal{H})$ is the square of the $\ell_2$-norm of the codegree vector of $\mathcal{H}$, and for a family $\mathscr{F}$ of $k$-uniform hypergraphs, the codegree squared extremal number $\text{exco}_2(n, \mathscr{F})$ is the maximum codegree squared sum of a hypergraph on $n$ vertices which does not contain any hypergraph in $\mathscr{F}$. Balogh, Clemen and Lidick\'y recently introduced the codegree squared extremal number and determined it for a number of $3$-uniform hypergraphs, including the complete graphs $K_4^3$ and $K_5^3$. In this paper, we give a number of exact or asymptotic results for hypergraph Tur\'an problems in the $\ell_2$-norm, including the first exact results for arbitrary $k$. Namely, we prove a version of the classical Erd\H{o}s-Ko-Rado theorem for the codegree squared extremal number: if $\mathcal{F} \subset \binom{[n]}{k}$ is intersecting and $n\ge 2k$, then \[\text{co}_2(\mathcal{F}) \le \binom{n-1}{k-1}(1+(n-k+1)(k-1)),\] with equality only for the star for $n > 2k$. Our main tool is an inequality of Bey, which also gives a general upper bound on $\text{exco}_2(n, \mathscr{F})$. We also prove versions of the Erd\H{o}s Matching Conjecture and the $t$-intersecting Erd\H{o}s-Ko-Rado theorem for the codegree squared extremal number for large $n$, determine the exact codegree squared extremal number of minimal and linear $3$-paths and $3$-cycles, and determine asymptotically the codegree squared extremal number of minimal and linear $s$-paths and $s$-cycles for $s\ge 4$. Lastly, we derive a number of exact or asymptotic results for graph Tur\'an-type problems in the $\ell_2$-norm from spectral extremal results for certain fobridden subgraph problems and the well-known Hofmeister's inequality., Comment: 26 pages; added some results on graph Tur\'an problems in the $\ell_2$-norm

(Abridged) We investigate the impact of radiative feedback from massive stars on their natal cloud and focus on the transition from the HII region to the atomic PDR (crossing the ionisation front (IF)), and the subsequent transition to the molecular PDR (crossing the dissociation front (DF)). We use high-resolution near-IR integral field spectroscopic data from NIRSpec on JWST to observe the Orion Bar PDR as part of the PDRs4All JWST Early Release Science Program. The NIRSpec data reveal a forest of lines including, but not limited to, HeI, HI, and CI recombination lines, ionic lines, OI and NI fluorescence lines, Aromatic Infrared Bands (AIBs including aromatic CH, aliphatic CH, and their CD counterparts), CO2 ice, pure rotational and ro-vibrational lines from H2, and ro-vibrational lines HD, CO, and CH+, most of them detected for the first time towards a PDR. Their spatial distribution resolves the H and He ionisation structure in the Huygens region, gives insight into the geometry of the Bar, and confirms the large-scale stratification of PDRs. We observe numerous smaller scale structures whose typical size decreases with distance from Ori C and IR lines from CI, if solely arising from radiative recombination and cascade, reveal very high gas temperatures consistent with the hot irradiated surface of small-scale dense clumps deep inside the PDR. The H2 lines reveal multiple, prominent filaments which exhibit different characteristics. This leaves the impression of a "terraced" transition from the predominantly atomic surface region to the CO-rich molecular zone deeper in. This study showcases the discovery space created by JWST to further our understanding of the impact radiation from young stars has on their natal molecular cloud and proto-planetary disk, which touches on star- and planet formation as well as galaxy evolution., Comment: 52 pages, 30 figures, submitted to A&A

Investigating Protostellar Accretion is a Cycle 1 JWST program using the NIRSpec+MIRI integral field units to obtain 2.9--28 $\mu$m spectral cubes of five young protostars with luminosities of 0.2-10,000 L$_{\odot}$ in their primary accretion phase. This paper introduces the NIRSpec 2.9--5.3 $\mu$m data of the inner 840-9000 au with spatial resolutions from 28-300 au. The spectra show rising continuum emission; deep ice absorption; emission from H$_{2}$, H~I, and [Fe~II]; and the CO fundamental series in emission and absorption. Maps of the continuum emission show scattered light cavities for all five protostars. In the cavities, collimated jets are detected in [Fe~II] for the four $< 320$~L$_{\odot}$ protostars, two of which are additionally traced in Br-$\alpha$. Knots of [Fe~II] emission are detected toward the most luminous protostar, and knots of [FeII] emission with dynamical times of $< 30$~yrs are found in the jets of the others. While only one jet is traced in H$_2$, knots of H$_2$ and CO are detected in the jets of four protostars. H$_2$ is seen extending through the cavities, showing that they are filled by warm molecular gas. Bright H$_2$ emission is seen along the walls of a single cavity, while in three cavities narrow shells of H$_2$ emission are found, one of which has an [Fe~II] knot at its apex. These data show cavities containing collimated jets traced in atomic/ionic gas surrounded by warm molecular gas in a wide-angle wind and/or gas accelerated by bow shocks in the jets., Comment: 26 pages, 12 figures

Inclusive e$^+$e$^-$ production has been studied with HADES in $\pi^-$ + p, $\pi^-$ + C and $\pi^- + \mathrm{CH}_2$ reactions, using the GSI pion beam at $\sqrt{s_{\pi p}}$ = 1.49 GeV. Invariant mass and transverse momentum distributions have been measured and reveal contributions from Dalitz decays of $\pi^0$, $\eta$ mesons and baryon resonances. The transverse momentum distributions are very sensitive to the underlying kinematics of the various processes. The baryon contribution exhibits a deviation up to a factor seven from the QED reference expected for the dielectron decay of a hypothetical point-like baryon with the production cross section constrained from the inverse $\gamma$ n$\rightarrow \pi^-$ p reaction. The enhancement is attributed to a strong four-momentum squared dependence of the time-like electromagnetic transition form factors as suggested by Vector Meson Dominance (VMD). Two versions of the VMD, that differ in the photon-baryon coupling, have been applied in simulations and compared to data. VMD1 (or two-component VMD) assumes a coupling via the $\rho$ meson and a direct coupling of the photon, while in VMD2 (or strict VMD) the coupling is only mediated via the $\rho$ meson. The VMD2 model, frequently used in transport calculations for dilepton decays, is found to overestimate the measured dielectron yields, while a good description of the data can be obtained with the VMD1 model assuming no phase difference between the two amplitudes. Similar descriptions have also been obtained using a time-like baryon transition form factor model where the pion cloud plays the major role., Comment: (HADES collaboration)

For a fixed positive integer $k$ and a graph $G$, let $\lambda_k(G)$ denote the $k$-th largest eigenvalue of the adjacency matrix of $G$. In 2017, Tait and Tobin proved that the maximum $\lambda_1(G)$ among all outerplanar graphs on $n$ vertices is achieved by the fan graph $K_1\vee P_{n-1}$. In this paper, we consider a similar problem of determining the maximum $\lambda_2$ among all connected outerplanar graphs on $n$ vertices. For $n$ even and sufficiently large, we prove that the maximum $\lambda_2$ is uniquely achieved by the graph $(K_1\vee P_{n/2-1})\!\!-\!\!(K_1\vee P_{n/2-1})$, which is obtained by connecting two disjoint copies of $(K_1\vee P_{n/2-1})$ through a new edge joining their smallest degree vertices. When $n$ is odd and sufficiently large, the extremal graphs are not unique. The extremal graphs are those graphs $G$ that contain a cut vertex $u$ such that $G\setminus \{u\}$ is isomorphic to $2(K_1\vee P_{n/2-1})$. We also determine the maximum $\lambda_2$ among all 2-connected outerplanar graphs and asymptotically determine the maximum of $\lambda_k(G)$ among all connected outerplanar graphs for any fixed $k$., Comment: 32 pages; minor revisions

The JWST has captured the most detailed and sharpest infrared images ever taken of the inner region of the Orion Nebula, the nearest massive star formation region, and a prototypical highly irradiated dense photo-dissociation region (PDR). We investigate the fundamental interaction of far-ultraviolet photons with molecular clouds. The transitions across the ionization front (IF), dissociation front (DF), and the molecular cloud are studied at high-angular resolution. These transitions are relevant to understanding the effects of radiative feedback from massive stars and the dominant physical and chemical processes that lead to the IR emission that JWST will detect in many Galactic and extragalactic environments. Due to the proximity of the Orion Nebula and the unprecedented angular resolution of JWST, these data reveal that the molecular cloud borders are hyper structured at small angular scales of 0.1-1" (0.0002-0.002 pc or 40-400 au at 414 pc). A diverse set of features are observed such as ridges, waves, globules and photoevaporated protoplanetary disks. At the PDR atomic to molecular transition, several bright features are detected that are associated with the highly irradiated surroundings of the dense molecular condensations and embedded young star. Toward the Orion Bar PDR, a highly sculpted interface is detected with sharp edges and density increases near the IF and DF. This was predicted by previous modeling studies, but the fronts were unresolved in most tracers. A complex, structured, and folded DF surface was traced by the H2 lines. This dataset was used to revisit the commonly adopted 2D PDR structure of the Orion Bar. JWST provides us with a complete view of the PDR, all the way from the PDR edge to the substructured dense region, and this allowed us to determine, in detail, where the emission of the atomic and molecular lines, aromatic bands, and dust originate.

(Abridged) Mid-infrared observations of photodissociation regions (PDRs) are dominated by strong emission features called aromatic infrared bands (AIBs). The most prominent AIBs are found at 3.3, 6.2, 7.7, 8.6, and 11.2 $\mu$m. The most sensitive, highest-resolution infrared spectral imaging data ever taken of the prototypical PDR, the Orion Bar, have been captured by JWST. We provide an inventory of the AIBs found in the Orion Bar, along with mid-IR template spectra from five distinct regions in the Bar: the molecular PDR, the atomic PDR, and the HII region. We use JWST NIRSpec IFU and MIRI MRS observations of the Orion Bar from the JWST Early Release Science Program, PDRs4All (ID: 1288). We extract five template spectra to represent the morphology and environment of the Orion Bar PDR. The superb sensitivity and the spectral and spatial resolution of these JWST observations reveal many details of the AIB emission and enable an improved characterization of their detailed profile shapes and sub-components. While the spectra are dominated by the well-known AIBs at 3.3, 6.2, 7.7, 8.6, 11.2, and 12.7 $\mu$m, a wealth of weaker features and sub-components are present. We report trends in the widths and relative strengths of AIBs across the five template spectra. These trends yield valuable insight into the photochemical evolution of PAHs, such as the evolution responsible for the shift of 11.2 $\mu$m AIB emission from class B$_{11.2}$ in the molecular PDR to class A$_{11.2}$ in the PDR surface layers. This photochemical evolution is driven by the increased importance of FUV processing in the PDR surface layers, resulting in a "weeding out" of the weakest links of the PAH family in these layers. For now, these JWST observations are consistent with a model in which the underlying PAH family is composed of a few species: the so-called 'grandPAHs'., Comment: 25 pages, 10 figures, to appear in A&A

G34.26+0.15 is a region of high-mass star formation that contains a broad range of young stellar objects in different stages of evolution, including a hot molecular core, hyper-compact HII regions and a prototypical cometary ultra-compact HII region. Previous high-sensitivity single dish observations by our group resulted in the detection of broad 6035 MHz OH absorption in this region; the line showed a significant blue-shifted asymmetry indicative of molecular gas expansion. We present high-sensitivity Karl G. Jansky Very Large Array (VLA) observations of the 6035 MHz OH line conducted to image the absorption and investigate its origin with respect to the different star formation sites in the region. In addition, we report detection of 6030 MHz OH absorption with the VLA and further observations of 4.7 GHz and 6.0 GHz OH lines obtained with the Arecibo Telescope. The 6030 MHz OH line shows a very similar absorption profile as the 6035 MHz OH line. We found that the 6035 MHz OH line absorption region is spatially unresolved at $\sim 2$" scales, and it is coincident with one of the bright ionized cores of the cometary HII region that shows broad radio recombination line emission. We discuss a scenario where the OH absorption is tracing the remnants of a pole-on molecular outflow that is being ionized inside-out by the ultra-compact HII region., Comment: 19 pages, 6 figures. Accepted for publication in The Astrophysical Journal

The fragmentation mode of high-mass molecular clumps and the accretion processes that form the most massive stars ($M\gtrsim 8M_\odot$) are still not well understood. To this end, we have undertaken a large observational program (CORE) making use of interferometric observations from the Northern Extended Millimetre Array (NOEMA) for a sample of 20 luminous ($L>10^4L_\odot$) protostellar objects in the 1.37 mm wavelength regime in both continuum and line emission, reaching $\sim$0.4" resolution (800 au at 2 kpc). Using the dense gas tracer CH$_3$CN, we find velocity gradients across 13 cores perpendicular to the directions of bipolar molecular outflows, making them excellent disk candidates. Specific angular momentum ($j$) radial profiles are on average $\sim10^{-3}$ km /s pc and follow $j \propto r^{1.7}$, consistent with a poorly resolved rotating and infalling envelope/disk model. Fitting the velocity profiles with a Keplerian model, we find protostellar masses in the range of $\sim 10-25$ $M_\odot$. Modelling the level population of CH$_3$CN lines, we present temperature maps and find median gas temperatures in the range $70-210$ K. We create Toomre $Q$ maps to study the stability of the disks and find almost all (11 of 13) disk candidates to be prone to fragmentation due to gravitational instabilities at the scales probed by our observations. In particular, disks with masses greater than $\sim10-20\%$ of the mass of their host (proto)stars are Toomre unstable, and more luminous protostellar objects tend to have disks that are more massive and hence more prone to fragmentation. Our finings show that most disks around high-mass protostars are prone to disk fragmentation early in their formation due to their high disk to stellar mass ratio. This impacts the accretion evolution of high-mass protostars which will have significant implications for the formation of the most massive stars., Comment: 27 pages, 12 figures, 6 appendices - accepted for publication in Astronomy and Astrophysics

High-mass protostars (M$_{\star} >$ 8 M$_{\odot}$) are thought to gain the majority of their mass via short, intense bursts of growth. This episodic accretion is thought to be facilitated by gravitationally unstable and subsequently inhomogeneous accretion disks. Limitations of observational capabilities, paired with a lack of observed accretion burst events has withheld affirmative confirmation of the association between disk accretion, instability and the accretion burst phenomenon in high-mass protostars. Following its 2019 accretion burst, a heat-wave driven by a burst of radiation propagated outward from the high-mass protostar G358.93-0.03-MM1. Six VLBI (very long baseline interferometry) observations of the raditively pumped 6.7 GHz methanol maser were conducted during this period, tracing ever increasing disk radii as the heat-wave propagated outward. Concatenating the VLBI maps provided a sparsely sampled, milliarcsecond view of the spatio-kinematics of the accretion disk covering a physical range of $\sim$ 50 - 900 AU. We term this observational approach `heat-wave mapping'. We report the discovery of a Keplerian accretion disk with a spatially resolved four-arm spiral pattern around G358.93-0.03-MM1. This result positively implicates disk accretion and spiral arm instabilities into the episodic accretion high-mass star formation paradigm., Comment: Published in Nature Astronomy in 2023