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We use polarization data from SOFIA HAWC+ to investigate the interplay between magnetic fields and stellar feedback in altering gas dynamics within the high-mass star-forming region RCW 36, located in Vela C. This region is of particular interest as it has a bipolar HII region powered by a massive star cluster which may be impacting the surrounding magnetic field. To determine if this is the case, we apply the Histogram of Relative Orientations (HRO) method to quantify the relative alignment between the inferred magnetic field and elongated structures observed in several datasets such as dust emission, column density, temperature, and spectral line intensity maps. The HRO results indicate a bimodal alignment trend, where structures observed with dense gas tracers show a statistically significant preference for perpendicular alignment relative to the magnetic field, while structures probed by photo-dissociation region (PDR) tracers tend to align preferentially parallel relative to the magnetic field. Moreover, the dense gas and PDR associated structures are found to be kinematically distinct such that a bimodal alignment trend is also observed as a function of line-of-sight velocity. This suggests that the magnetic field may have been dynamically important and set a preferred direction of gas flow at the time that RCW 36 formed, resulting in a dense ridge developing perpendicular to the magnetic field. However on filament-scales near the PDR region, feedback may be energetically dominating the magnetic field, warping its geometry and the associated flux-frozen gas structures, causing the observed the preference for parallel relative alignment., Comment: 40 pages (25 pages main paper, 15 pages appendix), 24 figures, 5 tables, accepted for publication in ApJ

We investigate the dynamical and physical structures of bright-rimmed clouds (BRCs) in a nearby HII region. We focused on carbon- and oxygen-bearing species that trace photon-dominated regions (PDRs) and warm molecular cloud surfaces in order to understand the effect of UV radiation from the exciting stars on the cloud structure. We mapped four regions around the most prominent BRCs at scales of 4--10 arcmin in the HII region IC 1396 in [CII] 158 micron with (up)GREAT on board SOFIA. IC 1396 is predominantly excited by an O6.5V star. Toward IC 1396A, we also observed [OI] 63 micron and 145 micron. We combined these observations with JCMT archive data, which provide the low-J transitions of CO, $^{13}$CO, and C$^{18}$O. All spectra are velocity-resolved. The line profiles show a variety of velocity structures, which we investigated in detail for all observed emission lines. We find no clear sign of photoevaporating flows in the [CII] spectra, although the uncertainty in the location of the BRCs along the line of sight makes this interpretation inconclusive. Our analysis of the [$^{13}$CII] emission in IC 1396A suggests that the [CII] is likely mostly optically thin. The heating efficiency, measured by the ([CII]+[OI] 63 micron)/far-infrared intensity ratio, is higher in the northern part of IC 1396A than in the southern part, which may indicate a difference in the dust properties of the two areas. The complex velocity structures identified in the BRCs of IC 1396, which is apparently a relatively simple HII region, highlight the importance of velocity-resolved data for disentangling different components along the line of sight and thus facilitating a detailed study of the dynamics of the cloud. We also demonstrate that the optically thin [$^{13}$CII] and [OI] 145 micron emission lines are essential for a conclusive interpretation of the [CII] 158 micron and [OI] 63 micron line profiles., Comment: Accepted for publication in A&A, 26 pages including Appendices

This study is aimed to contribute to a more comprehensive understanding of the molecular hydrogen distribution in the galaxy M33 by introducing novel methods for generating high angular resolution (18.2$''$, equivalent to 75 pc) column density maps of molecular hydrogen ($N_{\rm H_2}$). M33 is a local group galaxy that has been observed with Herschel in the far-infrared wavelength range from 70 to 500 $\mu$m. Previous studies have presented total hydrogen column density maps ($N_{\rm H}$), using these FIR data (partly combined with mid-IR maps), employing various methods. We first performed a spectral energy distribution fit to the 160, 250, 350, and 500 $\mu$m continuum data obtain $N_{\rm H}$, using a technique similar to one previously reported in the literature. We also use a second method which involves translating only the 250 $\mu$m map into a $N_{\rm H}$ map at the same angular resolution. An $N_{\rm H_2}$ map via each method is then obtained by subtracting the HI component. Distinguishing our study from previous ones, we adopt a more versatile approach by considering a variable emissivity index, $\beta$ and dust absorption coefficient, $\kappa_0$. This choice enables us to construct a $\kappa_0$ map, thereby enhancing the depth and accuracy of our investigation of the hydrogen column density. We address the inherent biases and challenges within both methods (which give similar results) and compare them with existing maps available in the literature. Moreover, we calculate a map of the carbon monoxide CO-to-H$_2$ conversion factor ($X_\mathrm{CO}$ factor), which shows a strong dispersion around an average value of $1.8\times10^{20}\,\mathrm{cm^{-2}/(K\,km\,s^{-1})}$ throughout the disk. We obtain column density probability distribution functions (N-PDFs) from the $N_{\rm H}$, $N_{\rm H_2}$, and $N_{HI}$ maps and discuss their shape.

A game has approximate equilibria if for every $\epsilon >0$ there is an $\epsilon$-equilibrium. We show that there is a stochastic game that lacks approximate equilibria. This game has finitely many players and actions, their payoffs are Borel measurable functions on the pathways of play, and all players have perfect knowledge of the past histories and the present state., Comment: The proof is flawed

Preserving privacy is an undeniable benefit to users online. However, this benefit (unfortunately) also extends to those who conduct cyber attacks and other types of malfeasance. In this work, we consider the scenario in which Privacy Preserving Technologies (PPTs) have been used to obfuscate users who are communicating online with ill intentions. We present a novel methodology that is effective at deobfuscating such sources by synthesizing measurements from key locations along protocol transaction paths. Our approach links online personas with their origin IP addresses based on a Pattern of Life (PoL) analysis, and is successful even when different PPTs are used. We show that, when monitoring in the correct places on the Internet, DNS over HTTPS (DoH) and DNS over TLS (DoT) can be deobfuscated with up to 100% accuracy, when they are the only privacy-preserving technologies used. Our evaluation used multiple simulated monitoring points and communications are sampled from an actual multiyear-long social network message board to replay actual user behavior. Our evaluation compared plain old DNS, DoH, DoT, and VPN in order to quantify their relative privacy-preserving abilities and provide recommendations for where ideal monitoring vantage points would be in the Internet to achieve the best performance. To illustrate the utility of our methodology, we created a proof-of-concept cybersecurity analyst dashboard (with backend processing infrastructure) that uses a search engine interface to allow analysts to deobfuscate sources based on observed screen names and by providing packet captures from subsets of vantage points.

We investigate the physical structure and conditions of photodissociation regions (PDRs) and molecular gas within the Pillars of Creation in the Eagle Nebula using SOFIA FEEDBACK observations of the [C II] 158 micron line. These observations are velocity resolved to 0.5 km s$^{-1}$ and are analyzed alongside a collection of complimentary data with similar spatial and spectral resolution: the [O I] 63 micron line, also observed with SOFIA, and rotational lines of CO, HCN, HCO$^{+}$, CS, and N$_2$H$^{+}$. Using the superb spectral resolution of SOFIA, APEX, CARMA, and BIMA, we reveal the relationships between the warm PDR and cool molecular gas layers in context of the Pillars' kinematic structure. We assemble a geometric picture of the Pillars and their surroundings informed by illumination patterns and kinematic relationships and derive physical conditions in the PDRs associated with the Pillars. We estimate an average molecular gas density $n_{{\rm H}_2} \sim 1.3 \times 10^5$ cm$^{-3}$ and an average atomic gas density $n_{\rm H} \sim 1.8 \times 10^4$ cm$^{-3}$ and infer that the ionized, atomic, and molecular phases are in pressure equilibrium if the atomic gas is magnetically supported. We find pillar masses of 103, 78, 103, and 18 solar masses for P1a, P1b, P2, and P3 respectively, and evaporation times of $\sim$1-2 Myr. The dense clumps at the tops of the pillars are currently supported by the magnetic field. Our analysis suggests that ambipolar diffusion is rapid and these clumps are likely to collapse within their photoevaporation timescales., Comment: 42 pages, 16 figures. Accepted for publication in The Astronomical Journal

Molecular hydrogen clouds are a key component of the interstellar medium because they are the birthplaces for stars. They are embedded in atomic gas that pervades the interstellar space. However, the details of how molecular clouds assemble from and interact with the atomic gas are still largely unknown. As a result of new observations of the 158~$\mu$m line of ionized carbon CII in the Cygnus region within the FEEDBACK program on SOFIA (Stratospheric Observatory for Infrared Astronomy), we present compelling evidence that CII unveils dynamic interactions between cloud ensembles. This process is neither a head-on collision of fully molecular clouds nor a gentle merging ofonly atomic clouds. Moreover, we demonstrate that the dense molecular clouds associated with the DR21 and W75N star-forming regions and a cloud at higher velocity are embedded in atomic gas and all components interact over a large range of velocities (20 km/s). The atomic gas has a density of 100 cm$^{-3}$ and a temperature of 100 K. We conclude that the CII 158 $\mu$m line is an excellent tracer to witness the processes involved in cloud interactions and anticipate further detections of this phenomenon in other regions, Comment: Nature Astronomy in press

We present new observations of [CII] fine structure line emission from an isolated molecular cloud using the upGREAT instrument onboard SOFIA. These data are analyzed together with archival CO=1-0 and HI 21 cm emission spectra to investigate the role of converging atomic gas flows in the formation of molecular clouds. Bright [CII] emission is detected throughout the mapped area that likely originates from photodissociation regions excited by UV radiation fields produced by newborn stars within the cloud. Upon spatial averaging of the [CII] spectra, we identify weak [CII] emission within velocity intervals where the HI 21 cm line is brightest; these are blue-shifted relative to velocities of the CO and bright [CII] emission by 4 km/s. The brightness temperatures, velocity dispersions, and alignment with HI 21 cm velocities connect this [CII] emission component to the cold, neutral atomic gas of the interstellar medium (CNM). We propose that this CNM feature is an accretion flow onto the far--side of the existing molecular cloud. The mass infall rate is 3.2x10**{-4} Msun/yr. There is no direct evidence of a comparable red--shifted component in the [CII] or HI 21 cm spectral lines that would indicate the presence of a converging flow., Comment: 11 pages, 7 figures, accepted by ApJ

We define "paradoxical colouring rule", show its relation to measure theoretic paradoxes, and demonstrate that proper vertex colouring can be a paradoxical colouring rule., Comment: arXiv admin note: text overlap with arXiv:1805.10225

Given a probability space $(X, {\cal B}, m)$, measure preserving transformations $g_1, \dots , g_k$ of $X$, and a colour set $C$, a colouring rule is a way to colour the space with $C$ such that the colours allowed for apoint $x$ are determined by that point's location and the colours of the finitely $g_1 (x), \dots , g_k(x)$ with $g_i(x) \not= x$ for all $i$ and almost all $x$. We represent a colouring rule as a correspondence $F$ defined on $X\times C^k$ with values in $C$. A function $f: X\rightarrow C$ satisfies the rule at $x$ if $f(x) \in F( x, f(g_1 x), \dots , f(g_k x))$. A colouring rule is paradoxical if it can be satisfied in some way almost everywhere with respect to $m$, but not in {\bf any} way that is measurable with respect to a finitely additive measure that extends the probability measure $m$ defined on ${\cal B}$ and for which the finitely many transformations $g_1, \dots , g_k$ remain measure preserving. Can a colouring rule be paradoxical if both $X$ and the colour set $C$ are convex and compact sets and the colouring rule says if $c: X\rightarrow C$ is the colouring function then the colour $c(x)$ must lie ($m$ a.e.) in $F(x, c(g_1(x) ), \dots , c(g_k(x)))$ for a non-empty upper-semi-continuous convex-valued correspondence $F$ defined on $X\times C^k$? The answer is yes, and we present such an example. We show that this result is robust, including that any colouring that approximates the correspondence by $\epsilon$ for small enough positive $\epsilon$ also cannot be measurable in the same finitely additive way. Because non-empty upper-semi-continuous convex-valued correspondences on Euclidean space can be approximated by continuous functions, there are paradoxical colouring rules that are defined by continuous functions.

Given a probability space $(X, {\cal B}, m)$, measure preserving transformations $g_1, \dots , g_k$ of $X$, and a colour set $C$, a colouring rule is a way to colour the space with $C$ such that the colours allowed for a point $x$ are determined by that point's location and the colours of the finitely $g_1 (x), \dots , g_k(x)$ with $g_i(x) \not= x$ for all $i$ and almost all $x$. We represent a colouring rule as a correspondence $F$ defined on $X\times C^k$ with values in $C$. A function $f: X\rightarrow C$ satisfies the rule at $x$ if $f(x) \in F( x, f(g_1 x), \dots , f(g_k x))$. A colouring rule is paradoxical if it can be satisfied in some way almost everywhere with respect to $m$, but not in {\bf any} way that is measurable with respect to a finitely additive measure that extends the probability measure $m$ and for which the finitely many transformations $g_1, \dots , g_k$ remain measure preserving. We show that a colouring rule can be paradoxical when the $g_1, \dots, g_k$ are members of a group $G$, the probability space $X$ and the colour set $C$ are compact sets, $C$ is convex and finite dimensional, and the colouring rule says if $c: X\rightarrow C$ is the colouring function then the colour $c(x)$ must lie ($m$ a.e.) in $F(x, c(g_1(x) ), \dots , c(g_k(x)))$ for a non-empty upper-semi-continuous convex-valued correspondence $F$ defined on $X\times C^k$. We show that any colouring that approximates the correspondence by $\epsilon$ for small enough positive $\epsilon$ cannot be measurable in the same finitely additive way. Furthermore any function satisfying the colouring rule illustrates a paradox through finitely many measure preserving shifts defining injective maps from the whole space to subsets of measure summing up to less than one.

Radiative and mechanical feedback of massive stars regulates star formation and galaxy evolution. Positive feedback triggers the creation of new stars by collecting dense shells of gas, while negative feedback disrupts star formation by shredding molecular clouds. Although key to understanding star formation, their relative importance is unknown. Here, we report velocity-resolved observations from the SOFIA (Stratospheric Observatory for Infrared Astronomy) legacy program FEEDBACK of the massive star-forming region RCW 120 in the [CII] 1.9-THz fine-structure line, revealing a gas shell expanding at 15 km/s. Complementary APEX (Atacama Pathfinder Experiment) CO J=3-2 345-GHz observations exhibit a ring structure of molecular gas, fragmented into clumps that are actively forming stars. Our observations demonstrate that triggered star formation can occur on much shorter time scales than hitherto thought (<0.15 million years), suggesting that positive feedback operates on short time periods., Comment: 8 Pages, 4 Figures, 1 Table (+16 Page Supplementary Materials with 10 Figures). Published in Science Advances on April 9th, 2021, with free open access to the online article available at https://advances.sciencemag.org/content/7/15/eabe9511

For a set-valued function $F$ on a compact subset $W$ of a manifold, spanning is a topological property that implies that $F(x) \ne 0$ for interior points $x$ of $W$. A myopic equilibrium applies when for each action there is a payoff whose functional value is not necessarily affine in the strategy space. We show that if the payoffs satisfy the spanning property, then there exist a myopic equilibrium (though not necessarily a Nash equilibrium). Furthermore, given a parametrized collection of games and the spanning property to the structure of payoffs in that collection, the resulting myopic equilibria and their payoffs have the spanning property with respect to that parametrization. This is a far reaching extension of the Kohberg-Mertens Structure Theorem. There are at least four useful applications, when payoffs are exogenous to a finite game tree (for example a finitely repeated game followed by an infinitely repeated game), when one wants to understand a game strategically entirely with behaviour strategies, when one wants to extends the subgame concept to subsets of a game tree that are known in common, and for evolutionary game theory. The proofs involve new topological results asserting that spanning is preserved by relevant operations on set-valued functions.

We report the first detection of the isotopologues 13CCC and C13CC. We used the heterodyne receivers GREAT and upGREAT on board SOFIA to search for the ro-vibrational transitions Q(2) and Q(4) of 13CCC and C13CC at 1.9 THz along the line of sight towards SgrB2(M). For both species the ro-vibrational absorption lines Q(2) and Q(4) have been identified, primarily arising from the warm gas physically associated with the strong continuum source SgrB2(M). In addition, to determine the local excitation temperature we analyzed data from nine ro-vibrational transitions of the main isotopologue CCC in the frequency range between 1.6-1.9 THz which were taken from the Herschel Science Data Archive, and derived a gas excitation temperature of Tex = 44.4(+4.7/-3.9) K and a total column density of N(CCC)=3.88(+0.39/-0.35)x10^15 cm^-2. Assuming the excitation temperatures of C13CC and 13CCC to be the same as for CCC, we obtained column densities of the 13C-isotopologues of N(C13CC) = 2.1(+0.9/-0.6)X10^14 cm^-2 and N(13CCC)=2.4(+1.2/-0.8)x10^14 cm^-2. The derived 12C/13C abundance ratio in the C3 molecules is 20.5(4.2), which is in agreement with the elemental ratio of 20, typically observed in SgrB2(M). However, we find the N(13CCC) / N(C13CC) ratio to be 1.2(0.1), which is shifted from the statistically expected value of 2. We propose that the discrepant abundance ratio arises due to the lower zero-point energy of C13CC which makes position exchange reaction converting 13CCC to C13CC energetically favorable., Comment: 7 pages, 4 figures, 5 tables

Understanding the matter cycle in the interstellar medium of galaxies from the assembly of clouds to star formation and stellar feedback remains an important and exciting field in comtemporary astrophysics. Many open questions regarding cloud and structure formation, the role of turbulence, and the relative importance of the various feedback processes can only be addressed with observations of spectrally resolved lines. We here stress the importance of two specific sets of lines: the finestructure lines of atomic carbon as a tracer of the dark molecular gas and mid-J CO lines as tracers of the warm, active molecular gas in regions of turbulence dissipation and feedback. The observations must cover a wide range of environments (i.e., physical conditions), which will be achieved by large scale surveys of Galactic molecular clouds, the Galactic Center, the Magellanic clouds, and nearby galaxies. To date, such surveys are completely missing and thus constitute an important science opportunity for the next decade and beyond. For the successful interpretation of the observations, it will be essential to combine them with results from (chemical) modelling and simulations of the interstellar medium., Comment: 7 pages, 1 figure