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Abstract In the present work we revisit the problem of the generalised Korteweg–de Vries equation parametrically, as a function of the relevant nonlinearity exponent, to examine the emergence of blow-up solutions, as traveling waveforms lose their stability past a critical point of the relevant parameterp, here atp = 5. We provide anormal formof the associated collapse dynamics, and illustrate how this captures the collapsing branch bifurcating from the unstable traveling branch. We also systematically characterise the linearisation spectrum of not only the traveling states, but importantly of the emergent collapsing waveforms in the so-called co-exploding frame where these waveforms are identified as stationary states. This spectrum, in addition to two positive real eigenvalues which are shown to be associated with the symmetries of translation and scaling invariance of the original (non-exploding) frame features complex patterns of negative eigenvalues that we also fully characterise. We show that the phenomenology of the latter is significantly affected by the boundary conditions and is far more complicated than in the corresponding symmetric Laplacian case of the nonlinear Schrödinger problem that has recently been explored. In addition, we explore the dynamics of the unstable solitary waves forp > 5 in the co-exploding frame. 

Abstract We present JWST NIRCam imaging targeting 13z ~ 3 infrared-luminous (L_IR ∼ 5 × 10¹²L_⊙) galaxies from the ALESS survey with uniquely deep, high-resolution (0 $\stackrel{\text{″}}{.}$08–0 $\stackrel{″}{.}$16) Atacama Large Millimeter/submillimeter Array 870μm imaging. The 2.0–4.4μm (observed frame) NIRCam imaging reveals the rest-frame near-infrared stellar emission in these submillimeter-selected galaxies at the same (sub)kiloparsec resolution as the 870μm dust continuum. The newly revealed stellar morphologies show striking similarities with the dust continuum morphologies at 870μm, with the centers and position angles agreeing for most sources, clearly illustrating that the spatial offsets reported previously between the 870μm and Hubble Space Telescope morphologies were due to strong differential dust obscuration. The F444W sizes are 78% ± 21% larger than those measured at 870μm, in contrast to recent results from hydrodynamical simulations that predict larger 870μm sizes. We report evidence for significant dust obscuration in F444W for the highest-redshift sources, emphasizing the importance of longer-wavelength MIRI imaging. The majority of the sources show evidence that they are undergoing mergers/interactions, including tidal tails/plumes—some of which are also detected at 870μm. We find a clear correlation between NIRCam colors and 870μm surface brightness on  ∼1 kpc scales, indicating that the galaxies are primarily red due to dust—not stellar age—and we show that the dust structure on  ∼kpc scales is broadly similar to that in nearby galaxies. Finally, we find no strong stellar bars in the rest-frame near-infrared, suggesting the extended bar-like features seen at 870μm are highly obscured and/or gas-dominated structures that are likely early precursors to significant bulge growth. 

Key Points These indices are not totally interchangeable, consideration should be given to index choice in model validation or cross‐study comparison Hourly averaged SMR and SYM‐H return levels track Dst for return periods below 10 years. Above that they exceed Dst; at 100 years by >10% One minute cadence SMR and SYM‐H 5, 10, 50, and 100 year return levels exceed that of Dst by about 10%, 12%, 20%, and 25% respectively 

Abstract We present the average rest-frame spectrum of the final catalog of dusty star-forming galaxies (DSFGs) selected from the South Pole Telescope's SPT-SZ survey and measured with Band 3 of the Atacama Large Millimeter/submillimeter Array. This work builds on the previous average rest-frame spectrum, given in Spilker et al. (2014) for the first 22 sources, and is comprised of a total of 78 sources, normalized by their respective apparent dust masses. The spectrum spans 1.9 <z< 6.9 and covers rest-frame frequencies of 240–800 GHz. Combining this data with low-JCO observations from the Australia Telescope Compact Array, we detect multiple bright line features from¹²CO, [Ci], and H₂O, as well as fainter molecular transitions from¹³CO, HCN, HCO⁺, HNC, CN, H₂O⁺, and CH. We use these detections, along with limits from other molecules, to characterize the typical properties of the interstellar medium (ISM) for these high-redshift DSFGs. We are able to divide the large sample into subsets in order to explore how the average spectrum changes with various galaxy properties, such as effective dust temperature. We find that systems with hotter dust temperatures exhibit differences in the bright¹²CO emission lines, and contain either warmer and more excited dense gas tracers or larger dense gas reservoirs. These observations will serve as a reference point to studies of the ISM in distant luminous DSFGs (L_IR> 10¹²L_⊙), and will inform studies of chemical evolution before the peak epoch of star formation atz= 2–3. 

High-redshift dusty star-forming galaxies with very high star formation rates (500−3000 M ⊙ yr −1 ) are key to understanding the formation of the most extreme galaxies in the early Universe. Characterising the gas reservoir of these systems can reveal the driving factor behind the high star formation. Using molecular gas tracers such as, high- J CO lines, neutral carbon lines, and the dust continuum, we can estimate the gas density and radiation field intensity in their interstellar media. In this paper, we present high resolution (∼0.4″) observations of CO(7−6), [CI](2−1), and dust continuum of three lensed galaxies from the South pole telescope – sub-millimetre galaxies (SPT-SMG) sample at z  ∼ 3 with the Atacama Large Millimetre/submillimetre Array. Our sources have high intrinsic star formation rates (> 850 M ⊙ yr −1 ) and rather short depletion timescales (< 100 Myr). Based on the L [CI](2−1) / L CO(7 − 6) and L [CI](2−1) / L IR ratios, our galaxy sample has similar radiation field intensities and gas densities compared to other submillimetre galaxies. We performed visibility-based lens modelling on these objects to reconstruct the kinematics in the source plane. We find that the cold gas masses of the sources are compatible with simple dynamical mass estimates using ULIRG-like values of the CO-H 2 conversion factor α CO , but not Milky Way-like values. We find diverse source kinematics in our sample: SPT0103−45 and SPT2147−50 are likely rotating disks, while SPT2357−51 is possibly a major merger. The analysis presented in the paper could be extended to a larger sample to determine better statistics of morphologies and interstellar medium properties of high- z dusty star-forming galaxies. 

ABSTRACT We present APEX-LABOCA 870-μm observations of the fields surrounding the nine brightest high-redshift unlensed objects discovered in the South Pole Telescope’s (SPT) 2500 deg2 survey. Initially seen as point sources by SPT’s 1-arcmin beam, the 19-arcsec resolution of our new data enables us to deblend these objects and search for submillimetre (submm) sources in the surrounding fields. We find a total of 98 sources above a threshold of 3.7σ in the observed area of 1300 arcmin2, where the bright central cores resolve into multiple components. After applying a radial cut to our LABOCA sources to achieve uniform sensitivity and angular size across each of the nine fields, we compute the cumulative and differential number counts and compare them to estimates of the background, finding a significant overdensity of $$\delta \, {\approx }\,$$10 at $$S_{870}= 14$$ mJy. The large overdensities of bright submm sources surrounding these fields suggest that they could be candidate protoclusters undergoing massive star formation events. Photometric and spectroscopic redshifts of the unlensed central objects range from $z= $3 to 7, implying a volume density of star-forming protoclusters of approximately 0.1 Gpc−3. If the surrounding submm sources in these fields are at the same redshifts as the central objects, then the total star formation rates of these candidate protoclusters reach 10 000 M⊙ yr−1, making them much more active at these redshifts than seen so far in either simulations or observations. 

ABSTRACT We present Gemini-S and Spitzer-IRAC optical-through-near-IR observations in the field of the SPT2349-56 proto-cluster at z = 4.3. We detect optical/IR counterparts for only 9 of the 14 submillimetre galaxies (SMGs) previously identified by ALMA in the core of SPT2349-56. In addition, we detect four z ∼ 4 Lyman-break galaxies (LBGs) in the 30 arcsec-diameter region surrounding this proto-cluster core. Three of the four LBGs are new systems, while one appears to be a counterpart of one of the nine observed SMGs. We identify a candidate brightest cluster galaxy (BCG) with a stellar mass of $$(3.2^{+2.3}_{-1.4})\times 10^{11}$$ M⊙. The stellar masses of the eight other SMGs place them on, above, and below the main sequence of star formation at z ≈ 4.5. The cumulative stellar mass for the SPT2349-56 core is at least (12.2 ± 2.8) × 1011 M⊙, a sizeable fraction of the stellar mass in local BCGs, and close to the universal baryon fraction (0.19) relative to the virial mass of the core (1013 M⊙). As all 14 of these SMGs are destined to quickly merge, we conclude that the proto-cluster core has already developed a significant stellar mass at this early stage, comparable to z = 1 BCGs. Importantly, we also find that the SPT2349-56 core structure would be difficult to uncover in optical surveys, with none of the ALMA sources being easily identifiable or constrained through g, r, and i colour selection in deep optical surveys and only a modest overdensity of LBGs over the more extended structure. SPT2349-56 therefore represents a truly dust-obscured phase of a massive cluster core under formation.