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We revisit the conditions present in supermassive discs (SMDs) formed by the merger of gas-rich, metal-enriched galaxies at red-shift $z\sim 10$. We find that SMDs naturally form hydrostatic cores which go through a rapidly accreting supermassive star phase, before directly collapsing into massive black holes via the general relativistic instability. The growth and collapse of the cores occurs within $\sim 5\times 10^5$ yr from the formation of the SMD, producing bright electromagnetic, neutrino and gravitational wave transients with a typical duration of a few minutes and, respectively, a typical flux and a typical strain amplitude at Earth of $\sim 10^{-8}$ erg s$^{-1}$ cm$^{-2}$ and $\sim4\times 10^{-21}$. We provide a simple fitting formula for the the resulting black hole masses, which range from a few $10^6$ M$_{\odot}$ to $10^8$ M$_{\odot}$ depending on the initial SMD configuration. Crucially, our analysis does not require any specific assumption on the thermal properties of the gas, nor on the angular momentum loss mechanisms within the SMD. Led by these findings, we argue that the merger-driven scenario provides a robust pathway for the rapid formation of supermassive black holes at $z > 6$. It provides an explanation for the origin of the brightest and oldest quasars without the need of a sustained growth phase from a much smaller seed. Its smoking gun signatures can be tested directly via multi-messenger observations., Published by MNRAS. Comments welcome!!

Context: The sizes of dust in the interstellar medium follows a distribution where most of the dust mass is in smaller grains. However, the re-distribution from larger grains towards smaller sizes especially by means of rotational disruption is poorly understood. Aims: We aim to study the dynamics of porous grain aggregates under accelerated ration. Especially, we determine the deformation of the grains and the maximal angular velocity up to the rotational disruption event by caused by centrifugal forces. Methods: We pre-calculate aggregates my means of ballistic aggregation analogous to the interstellar dust as input for subsequent numerical simulations. In detail, we perform three-dimensional N-body simulations mimicking the radiative torque spin-up process up to the point where the grain aggregates become rotationally disrupted. Results: Our simulations results are in agreement with theoretical models predicting a characteristic angular velocity $\omega_{\mathrm{disr}}$ of the order of ${ 10^8 - 10^9\ \mathrm{rad\ s^{-1}} }$, where grains become rotationally disrupted. In contrast to theoretical predictions, we show that for large porous aggregates ($< 300\ \mathrm{nm}$) $\omega_{\mathrm{disr}}$ reaches a lower asymptotic value. Hence, such grains can withstand an accelerated ration more efficiently up to a factor of 10 because the displacement of mass by centrifugal forces and the subsequent mechanical deformation supports the buildup of new connections within the aggregate. Furthermore, we report that the rapid rotation of grains deforms an ensemble with initially 50:50 prolate and oblate shapes, respectively, preferentially into oblate shapes. Finally, we present a best fit formula to predict the average rotational disruption of an ensemble of porous dust aggregates dependent on internal grain structure, total number of monomers, and applied material properties., Comment: 17 pages, 10 figures, 3 tables

Population III stars, born from the primordial gas in the Universe, lose a negligible fraction of their mass via stellar winds and possibly follow a top-heavy mass function. Hence, they have often been regarded as the ideal progenitors of massive black holes (BHs), even above the pair instability mass gap. Here, we evolve a large set of Population III binary stars (metallicity $Z=10^{-11}$) with our population-synthesis code SEVN, and compare them with Population II binary stars ($Z=10^{-4}$). In our models, the lower edge of the pair-instability mass gap corresponds to a BH mass of $\approx{86}$ ($\approx{91}$) M$_\odot$ for single Population III (II) stars. Overall, we find only mild differences between the properties of binary BHs (BBHs) born from Population III and II stars, especially if we adopt the same initial mass function and initial orbital properties. Most BBH mergers born from Population III and II stars have primary BH mass below the pair-instability gap, and the maximum secondary BH mass is $ < 50$ M$_\odot$. Only up to $\approx{3.3}$% ($\approx{0.09}$%) BBH mergers from Population III (II) progenitors have primary mass above the gap. Unlike metal-rich binary stars, the main formation channel of BBH mergers from Population III and II stars involves only stable mass transfer episodes in our fiducial model., 15 pages, 17 figures, comments are welcome

The first generation of stars, often called Population III (or Pop III), form from metal-free primordial gas at redshifts 30 and below. They dominate the cosmic star formation history until redshifts 15 to 20, at which point the formation of metal-enriched Pop II stars takes over. We review current theoretical models for the formation, properties and impact of Pop III stars, and discuss existing and future observational constraints. Key takeaways from this review include the following: (1) Primordial gas is highly susceptible to fragmentation and Pop III stars form as members of small clusters with a logarithmically flat mass function. (2) Feedback from massive Pop III stars plays a central role in regulating subsequent star formation, but major uncertainties remain regarding its immediate impact. (3) In extreme conditions, supermassive Pop III stars can form, reaching masses of several 10^5 Msun. Their remnants may be the seeds of the supermassive black holes observed in high-redshift quasars. (4) Direct observations of Pop III stars in the early Universe remain extremely challenging. Indirect constraints from the global 21cm signal or gravitational waves are more promising. (5) Stellar archeological surveys allow us to constrain both the low-mass and the high-mass ends of the Pop III mass distribution. Observations suggest that most massive Pop III stars end their lives as core-collapse supernovae rather than as pair-instability supernovae., Comment: To appear in Annual Reviews of Astronomy and Astrophysics (75 pages, 14 figures, 600 references)

The CO-to-H$_2$ conversion factor ($\alpha_\rm{CO}$) is central to measuring the amount and properties of molecular gas. It is known to vary with environmental conditions, and previous studies have revealed lower $\alpha_\rm{CO}$ in the centers of some barred galaxies on kpc scales. To unveil the physical drivers of such variations, we obtained ALMA Band 3, 6, and 7 observations toward the inner 2 kpc of NGC 3627 and NGC 4321 tracing $^{12}$CO, $^{13}$CO, and C$^{18}$O lines on 100 pc scales. Our multi-line modeling and Bayesian likelihood analysis of these datasets reveal variations of molecular gas density, temperature, optical depth, and velocity dispersion, which are among the key drivers of $\alpha_\rm{CO}$. The central 300 pc nuclei in both galaxies show strong enhancement of temperature $T_\rm{k}>100$ K and density $n_\rm{H_2}>10^3$ cm$^{-3}$. Assuming a CO-to-H$_2$ abundance of $3\times10^{-4}$, we derive 4-15 times lower $\alpha_\rm{CO}$ than the Galactic value across our maps, which agrees well with previous kpc-scale measurements. Combining the results with our previous work on NGC 3351, we find a strong correlation of $\alpha_\rm{CO}$ with low-J $^{12}$CO optical depths ($\tau_\rm{CO}$), as well as an anti-correlation with $T_\rm{k}$. The $\tau_\rm{CO}$ correlation explains most of the $\alpha_\rm{CO}$ variation in the three galaxy centers, whereas changes in $T_\rm{k}$ influence $\alpha_\rm{CO}$ to second order. Overall, the observed line width and $^{12}$CO/$^{13}$CO 2-1 line ratio correlate with $\tau_\rm{CO}$ variation in these centers, and thus they are useful observational indicators for $\alpha_\rm{CO}$ variation. We also test current simulation-based $\alpha_\rm{CO}$ prescriptions and find a systematic overprediction, which likely originates from the mismatch of gas conditions between our data and the simulations., Comment: Accepted for publication in ApJ; 30 pages of main text + 3 appendices

Observations of the 21cm line of neutral hydrogen are poised to revolutionize our knowledge of cosmic reionization and the high-redshift population of galaxies. However, harnessing such information requires robust and comprehensive theoretical modeling. We study the non-linear effects of hydrodynamics and astrophysical feedback processes, including stellar and AGN feedback, on the 21cm signal by post-processing three existing cosmological hydrodynamical simulations of galaxy formation: Illustris, IllustrisTNG, and Eagle. Overall and despite their different underlying galaxy-formation models, the three simulations return similar predictions for the global 21cm rightness temperature and its power spectrum. At fixed redshift, most differences are attributable to differences in the history of reionization, in turn driven by differences in the build-up of stellar sources of radiation. However, the impact of astrophysics is imprinted in the 21cm power spectrum through several unique signatures. First, we find significant small scale ($k \geq 10\, \rm {Mpc}^{-1}$) differences between Illustris and IllustrisTNG, where higher velocity winds generated by supernova feedback soften density peaks and lead to lower 21cm power in TNG. Second, we find more 21cm power at intermediate scales ($k \approx 0.8\, \rm {Mpc}^{-1}$) in Eagle, due to differences in ionization driven by highly effective stellar feedback, leading to lower star formation, older and redder stellar populations, and thus lower ionizing luminosities. Though subtle, these features could allow future observations of the 21cm signal, in conjunction with other reionization observables, to constrain theoretical models for galactic feedback at high redshift., Comment: submitted to MNRAS (12/05/23)

JWST observations of polycyclic aromatic hydrocarbon (PAH) emission provide some of the deepest and highest resolution views of the cold interstellar medium (ISM) in nearby galaxies. If PAHs are well mixed with the atomic and molecular gas and illuminated by the average diffuse interstellar radiation field, PAH emission may provide an approximately linear, high resolution, high sensitivity tracer of diffuse gas surface density. We present a pilot study that explores using PAH emission in this way based on MIRI observations of IC 5332, NGC 628, NGC 1365, and NGC 7496 from the PHANGS-JWST Treasury. Using scaling relationships calibrated in Leroy et al. (2022), scaled F1130W provides 10--40 pc resolution and 3$\sigma$ sensitivity of $\Sigma_{\rm gas} \sim 2$ M$_\odot$ pc$^{-2}$. We characterize the surface densities of structures seen at $< 7$ M$_\odot$ pc$^{-2}$ in our targets, where we expect the gas to be HI-dominated. We highlight the existence of filaments, inter-arm emission, and holes in the diffuse ISM at these low surface densities. Below $\sim 10$ M$_\odot$ pc$^{-2}$ for NGC 628, NGC 1365, and NGC 7496 the gas distribution shows a ``Swiss cheese''-like topology due to holes and bubbles pervading the relatively smooth distribution of diffuse ISM. Comparing to recent galaxy simulations, we observe similar topology for the low surface density gas, though with notable variations between simulations with different setups and resolution. Such a comparison of high resolution, low surface density gas with simulations is not possible with existing atomic and molecular gas maps, highlighting the unique power of JWST maps of PAH emission., Comment: 18 pages, 6 figures, accepted as part of a PHANGS-JWST Focus Issue to appear in ApJ

Mapping star-formation rates (SFR) within galaxies is key to unveiling their assembly and evolution. Calibrations exist for computing SFR from a combination of ultraviolet and infrared bands for galaxies as integrated systems, but their applicability to sub-galactic (kpc) scales remains largely untested. Here we use integral field spectroscopy of 19 nearby ($D, accepted in A&A

The complex physical, kinematic, and chemical properties of galaxy centres make them interesting environments to examine with molecular line emission. We present new $2-4$" (${\sim}75{-}150$ pc at $7.7$ Mpc) observations at 2 and 3 mm covering the central $50$" (${\sim}1.9$ kpc) of the nearby double-barred spiral galaxy NGC 6946 obtained with the IRAM Plateau de Bure Interferometer. We detect spectral lines from ten molecules: CO, HCN, HCO$^+$, HNC, CS, HC$_3$N, N$_2$H$^+$, C$_2$H, CH$_3$OH, and H$_2$CO. We complemented these with published 1mm CO observations and 33 GHz continuum observations to explore the star formation rate surface density ${\Sigma_{\mathrm{SFR}}}$ on 150 pc scales. In this paper, we analyse regions associated with the inner bar of NGC 6946 $-$ the nuclear region (NUC), the northern (NBE), and southern inner bar end (SBE) and we focus on short-spacing corrected bulk (CO) and dense gas tracers (HCN, HCO$^+$, and HNC). We find that HCO$^+$ correlates best with ${\Sigma_{\mathrm{SFR}}}$, but the dense gas fraction ($f_{\mathrm{dense}}$) and star formation efficiency of the dense gas (${\mathrm{SFE_{dense}}}$) fits show different behaviours than expected from large-scale disc observations.The SBE has a higher ${\Sigma_{\mathrm{SFR}}}$, $f_{\mathrm{dense}}$, and shocked gas fraction than the NBE. We examine line ratio diagnostics and find a higher CO(2-1)/CO(1-0) ratio towards NBE than for the NUC. Moreover, comparison with existing extragalactic datasets suggests that using the HCN/HNC ratio to probe kinetic temperatures is not suitable on kiloparsec and sub-kiloparsec scales in extragalactic regions. Lastly, our study shows that the HCO$^+$/HCN ratio might not be a unique indicator to diagnose AGN activity in galaxies., Comment: 38 pages, 23 figures, accepted for publication in A&A

The ultra-faint dwarf galaxy Reticulum~II was enriched by a single rare and prolific r-process event. The r-process content of Reticulum~II thus provides a unique opportunity to study metal mixing in a relic first galaxy. Using multi-object high-resolution spectroscopy with VLT/GIRAFFE and Magellan/M2FS, we identify 32 clear spectroscopic member stars and measure abundances of Mg, Ca, Fe, and Ba where possible. We find $72^{+10}_{-12}$% of the stars are r-process-enhanced, with a mean $\left\langle\mbox{[Ba/H]}\right\rangle=-1.68~\pm~0.07$ and unresolved intrinsic dispersion $\sigma_{\rm [Ba/H]} < 0.20$. The homogeneous r-process abundances imply that Ret~II's metals are well-mixed by the time the r-enhanced stars form, which simulations have shown requires at least 100 Myr of metal mixing in between bursts of star formation to homogenize. This is the first direct evidence of bursty star formation in an ultra-faint dwarf galaxy. The homogeneous dilution prefers a prompt and high-yield r-process site, such as collapsar disk winds or prompt neutron star mergers. We also find evidence from [Ba/H] and [Mg/Ca] that the r-enhanced stars in Ret~II formed in the absence of substantial pristine gas accretion, perhaps indicating that ${\approx}70$% of Ret~II stars formed after reionization., Comment: 37 pages, 12 figures, 10 tables, accepted to AJ

We use PHANGS-JWST data to identify and classify 1271 compact 21 $μ$m sources in four nearby galaxies using MIRI F2100W data. We identify sources using a dendrogram-based algorithm, and we measure the background-subtracted flux densities for JWST bands from 2 $μ$m to 21 $μ$m. Using the SED in JWST as well as HST bands, plus ALMA and MUSE/VLT observations, we classify the sources by eye. Then we use this classification to define regions in color-color space, and so establish a quantitative framework for classifying sources. We identify 1085 sources as belonging to the ISM of the target galaxies with the remainder being dusty stars or background galaxies. These 21 $μ$m sources are strongly spatially associated with HII regions ($>92\%$ of sources), while 74$\%$ of sources are coincident with a stellar association defined in the HST data. Using SED fitting, we find that the stellar masses of the 21 $μ$m sources span a range of 10$^{2}$ to 10$^{4}~M_\odot$ with mass-weighted ages down to 2 Myr. There is a tight correlation between attenuation-corrected H$α$ and 21 $μ$m luminosity for $L_{ν,\mathrm{F2100W}}>10^{19}~\mathrm{W~Hz}^{-1}$. Young embedded source candidates selected at 21 $μ$m are found below this threshold and have $M_\star < 10^{3}~M_\odot$., 15 pages, 5 figures, Accepted as part of a PHANGS-JWST Focus Issue to appear in ApJ

We study the evolution of embedded star clusters as possible progenitors to reproduce 30 Doradus, specifically the compact star cluster known as R136 and its surrounding stellar family, which is believed to be part of an earlier star formation event. We employ the high-precision stellar dynamics code NBODY6++GPU to calculate the dynamics of the stars embedded in different evolving molecular clouds modelled by the 1D cloud/clusters evolution code WARPFIELD. We explore clouds with initial masses of $M_\text{cloud}=3.16 \times 10^{5}$ M$_\odot$ that (re)-collapse allowing for the birth of a second generation of stars. We explore different star formation efficiencies in order to find the best set of parameters that can reproduce the observation measurements. Our best-fit models correspond to a first stellar generation with masses between $1.26 \times 10^4$ - $2.85 \times 10^4 $M$_\odot$ and for the second generation we find a $M \approx 6.32\times 10^4$ M$_\odot$. Our models can match the observed stellar ages, cloud shell radius, and the fact that the second generation of stars is more concentrated than the first one. This is found independently of the cluster starting initially with mass segregation or not. By comparing our results with recent observational measurements of the mass segregation and density profile of the central zone we find close agreement, and thus provide supporting evidence for a centrally focused (re)-collapse origin to the multiple ages., 13 pages, 7 figures, 2 tables

In this paper we examine the factors that shape the distribution of molecular gas surface densities on the 150 pc scale across 67 morphologically diverse star-forming galaxies in the PHANGS-ALMA CO (2-1) survey. Dividing each galaxy into radial bins, we measure molecular gas surface density contrasts, defined here as the ratio between a fixed high percentile of the CO distribution and a fixed reference level in each bin. This reference level captures the level of the faint CO floor that extends between bright filamentary features, while the intensity level of the higher percentile probes the structures visually associated with bright, dense ISM features like spiral arms, bars, and filaments. We compare these contrasts to matched percentile-based measurements of the 3.6 $��$m emission measured using Spitzer/IRAC imaging, which trace the underlying stellar mass density. We find that the logarithms of CO contrasts on 150 pc scales are 3-4 times larger than, and positively correlated with, the logarithms of 3.6 $��$m contrasts probing smooth non-axisymmetric stellar bar and spiral structures. The correlation appears steeper than linear, consistent with the compression of gas as it flows supersonically in response to large-scale stellar structures, even in the presence of weak or flocculent spiral arms. Stellar dynamical features appear to play an important role in setting the cloud-scale gas density in our galaxies, with gas self-gravity perhaps playing a weaker role in setting the 150 pc-scale distribution of gas densities., Accepted for publication in ApJ, 16 pages, 7 figures

Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02, respectively. We find that l_s agrees with the relation l_s / L = phi_s Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is either the driving scale of turbulence or the diameter of a molecular cloud. If L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily because of the separation between the driving scale and the start of the supersonic cascade. For a supersonic cascade extending beyond the cloud scale, we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find that the supersonic cascade transitions smoothly to the subsonic cascade over a factor of 3 in scale, instead of a sharp transition. Our measurements provide quantitative input for turbulence-regulated models of filament structure and star formation in molecular clouds., 22 pages, 9 figures, Nat Astron (2021)

In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse problem is ambiguous: one measurement may map to multiple different sets of parameters. In this setting, the posterior parameter distribution, conditioned on an input measurement, has to be determined. We argue that a particular class of neural networks is well suited for this task -- so-called Invertible Neural Networks (INNs). Although INNs are not new, they have, so far, received little attention in literature. While classical neural networks attempt to solve the ambiguous inverse problem directly, INNs are able to learn it jointly with the well-defined forward process, using additional latent output variables to capture the information otherwise lost. Given a specific measurement and sampled latent variables, the inverse pass of the INN provides a full distribution over parameter space. We verify experimentally, on artificial data and real-world problems from astrophysics and medicine, that INNs are a powerful analysis tool to find multi-modalities in parameter space, to uncover parameter correlations, and to identify unrecoverable parameters.

Understanding turbulence is critical for a wide range of terrestrial and astrophysical applications. Here we present first results of the world's highest-resolution simulation of turbulence ever done. The current simulation has a grid resolution of 10048^3 points and was performed on 65536 compute cores on SuperMUC at the Leibniz Supercomputing Centre (LRZ). We present a scaling test of our modified version of the FLASH code, which updates the hydrodynamical equations in less than 3 micro seconds per cell per time step. A first look at the column density structure of the 10048^3 simulation is presented and a detailed analysis is provided in a forthcoming paper., Comment: 2 pages, 3 figures, book contribution to "High Performance Computing in Science und Engineering - Garching/Munich 2016", eds. S. Wagner, A. Bode, H. Br\"uchle, and M. Brehm

CR7 is the brightest Lyman-$��$ emitter observed at $z>6$, which shows very strong Lyman-$��$ and HeII 1640�� line luminosities, but no metal line emission. Previous studies suggest that CR7 hosts either young primordial stars with a total stellar mass of $\sim 10^7\,\mathrm{M}_\odot$ or a black hole of $\gtrsim 10^6\,\mathrm{M}_\odot$. Here, we explore different formation scenarios for CR7 with a semianalytical model, based on the random sampling of dark matter merger trees. We are unable to reproduce the observational constraints with a primordial stellar source, given our model assumptions, due to the short stellar lifetimes and the early metal enrichment. Black holes that are the remnants of the first stars are either not massive enough, or reside in metal-polluted haloes, ruling out this possible explanation of CR7. Our models instead suggest that direct collapse black holes, which form in metal-free haloes exposed to large Lyman-Werner fluxes, are more likely the origin of CR7. However, this result is derived under optimistic assumptions and future observations are necessary to further constrain the nature of CR7., 21 pages, 17 figures, 2 tables, MNRAS in press

Interstellar space is filled with a dilute mixture of charged particles, atoms, molecules and dust grains, called the interstellar medium (ISM). Understanding its physical properties and dynamical behavior is of pivotal importance to many areas of astronomy and astrophysics. Galaxy formation and evolution, the formation of stars, cosmic nucleosynthesis, the origin of large complex, prebiotic molecules and the abundance, structure and growth of dust grains which constitute the fundamental building blocks of planets, all these processes are intimately coupled to the physics of the interstellar medium. However, despite its importance, its structure and evolution is still not fully understood. Observations reveal that the interstellar medium is highly turbulent, consists of different chemical phases, and is characterized by complex structure on all resolvable spatial and temporal scales. Our current numerical and theoretical models describe it as a strongly coupled system that is far from equilibrium and where the different components are intricately linked together by complex feedback loops. Describing the interstellar medium is truly a multi-scale and multi-physics problem. In these lecture notes we introduce the microphysics necessary to better understand the interstellar medium. We review the relations between large-scale and small-scale dynamics, we consider turbulence as one of the key drivers of galactic evolution, and we review the physical processes that lead to the formation of dense molecular clouds and that govern stellar birth in their interior., Comment: Lecture notes given at the 43rd Saas Fee Advanced School, March 11-16, 2013, Villars-sur-Ollon, Switzerland -- 191 pages, 23 figures. Links to the video recording of the lectures : http://lastro.epfl.ch/conferences/sf2013/videos2.cgi

Understanding the formation of the first objects in the universe critically depends on knowing whether the properties of small dark matter structures at high-redshift (z > 15) are different from their more massive lower-redshift counterparts. To clarify this point, we performed a high-resolution N-body simulation of a cosmological volume 1 Mpc/h comoving on a side, reaching the highest mass resolution to date in this regime. We make precision measurements of various physical properties that characterize dark matter haloes (such as the virial ratio, spin parameter, shape, and formation times, etc.) for the high-redshift (z > 15) dark matter mini-haloes we find in our simulation, and compare them to literature results and a moderate-resolution comparison run within a cube of side-length 100 Mpc/h. We find that dark matter haloes at high-redshift have a log-normal distribution of the dimensionless spin parameter centered around �� $\sim$ 0.03, similar to their more massive counterparts. They tend to have a small ratio of the length of the shortest axis to the longest axis (sphericity), and are highly prolate. In fact, haloes of given mass that formed recently are the least spherical, have the highest virial ratios, and have the highest spins. Interestingly, the formation times of our mini-halos depend only very weakly on mass, in contrast to more massive objects. This is expected from the slope of the linear power spectrum of density perturbations at this scale, but despite this difference, dark matter structures at high-redshift share many properties with their much more massive counterparts observed at later times., 17 pages. Accepted for publication in MNRAS

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple appoximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form $\mathrm{P}_v(\rho)\propto\rho^{-1.54}$ for the (volume-weighted) PDF and $\mathrm{P}_m(\rho)\propto\rho^{-0.54}$ for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates. Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured star formation rates are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall., Comment: accepted for publication, 13 pages

We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetised gas cloud. We focus on the dependence of the growth and saturation level of the dynamo generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetised cloud. In order to follow the evolution of the magnetic field in both the kinematic and the nonlinear regime, we choose an initial field strength of $\simeq 1\,\mkG$ with the magnetic to kinetic energy ratio, $E_{\rm m}/E_{\rm k} \sim 10^{-4}$. Both gravitational compression and the small-scale dynamo initially amplify the magnetic field. Further into the evolution, the dynamo-generated magnetic field saturates but the total magnetic field continues to grow because of compression. The saturation of the small-scale dynamo is marked by a change in the slope of $B/\rho^{2/3}$ and by a shift in the peak of the magnetic energy spectrum from small scales to larger scales. For the range of initial Mach numbers explored in this study, the dynamo growth rate increases as the Mach number increases from $v_{\rm rms}/c_{\rm s}\sim 0.2$ to 0.4 and then starts decreasing from $v_{\rm rms}/c_{\rm s}\sim 1.0$. We obtain saturation values of $E_{\rm m}/E_{\rm k} = 0.2 - 0.3$ for these runs. Simulations with different initial injection scales of turbulence also show saturation at similar levels. For runs with different initial rotation of the cloud, the magnetic energy saturates at $E_{\rm m}/E_{\rm k}\sim 0.2 - 0.4$ of the equipartition value. (Abridged), Comment: submitted to MNRAS, reviewer's comments addressed

We derive the mass function of condensations (clumps) which were formed through a turbulent cascade over a range of spatial scales $L\le20$ pc during early, predominantly turbulent evolution of a molecular cloud. The approach rests upon the assumption of a statistical clump mass-density relationship $n\propto m^x$ with a scale dependence of the exponent $x$ obtained from equipartition relations between various forms of energy of clumps. The derived clump mass function (ClMF) could be represented by series of 2 or 3 power laws, depending on the chosen equipartition relation, the velocity scaling index and the type of turbulent forcing. The high-mass ClMF exhibits an average slope $\Gamma\simeq-1$, typical for fractal clouds, whereas its intermediate-mass part is shallower or flattened, in agreement with some observational studies., Comment: Accepted in MNRAS; 12 pages, 6 figures

We present a cluster analysis of the bright main-sequence and faint pre--main-sequence stellar populations of a field ~ 90 x 90 pc centered on the HII region NGC 346/N66 in the Small Magellanic Cloud, from imaging with HST/ACS. We extend our earlier analysis on the stellar cluster population in the region to characterize the structuring behavior of young stars in the region as a whole with the use of stellar density maps interpreted through techniques designed for the study of the ISM structuring. In particular, we demonstrate with Cartwrigth & Whitworth's Q parameter, dendrograms, and the Delta-variance wavelet transform technique that the young stellar populations in the region NGC 346/N66 are hierarchically clustered, in agreement with other regions in the Magellanic Clouds observed with HST. The origin of this hierarchy is currently under investigation., 4 pages, 3 figures; to appear in proceedings of the conference "The Labyrinth of Star Formation", (eds.) D. Stamatellos, S. Goodwin, and D. Ward-Thompson, Springer

The linewidth (sigma) - size (R) relationship has been extensively measured and analysed, in both the local ISM and in nearby normal galaxies. Generally, a power-law describes the relationship well with an index ranging from 0.2-0.6, now referred to as one of "Larson's Relationships." The nature of turbulence and star formation is considered to be intimately related to these relationships, so evaluating the sigma-R correlations in various environments is important for developing a comprehensive understanding of the ISM. We measure the sigma-R relationship in the Central Molecular Zone (CMZ) of the Galactic Centre using spectral line observations of the high density tracers N2H+, HCN, H13CN, and HCO+. We use dendrograms, which map the hierarchical nature of the position-position-velocity (PPV) data, to compute sigma and R of contiguous structures. The dispersions range from ~2-30 km/s in structures spanning sizes 2-40 pc, respectively. By performing Bayesian inference, we show that a power-law with exponent 0.3-1.1 can reasonably describe the sigma-R trend. We demonstrate that the derived sigma-R relationship is independent of the locations in the PPV dataset where sigma and R are measured. The uniformity in the sigma-R relationship suggests turbulence in the CMZ is driven on the large scales beyond >30 pc. We compare the CMZ sigma-R relationship to that measured in the Galactic molecular cloud Perseus. The exponents between the two systems are similar, suggestive of a connection between the turbulent properties within a cloud to its ambient medium. Yet, the velocity dispersion in the CMZ is systematically higher, resulting in a coefficient that is nearly five times larger. The systematic enhancement of turbulent velocities may be due to the combined effects of increased star formation activity, larger densities, and higher pressures relative to the local ISM., 11 pages, 8 figures, Accepted for publication in MNRAS

Understanding the origin of high-mass stars is central to modern astrophysics. We shed light on this problem with simulations using a novel, adaptive-mesh, ray-tracing algorithm. These simulations consistently follow the gravitational collapse of a massive molecular cloud core, the subsequent build-up and fragmentation of the accretion disk surrounding the nascent star, and, for the first time, the interaction between its intense UV radiation field and the infalling material. We show that ionization feedback can neither stop protostellar mass growth nor suppress fragmentation. We discuss the effects of feedback by ionizing and non-ionizing radiation on the evolution of the stellar cluster. The accretion is not limited by radiative feedback but by the formation of low-mass companions in a process we call "fragmentation-induced starvation". This behavior consistently reproduces the observed relation between the most massive star and the total mass of stars in a cluster. We show that magnetic fields reduce the star formation rate and lead to the formation of more massive stars., Comment: to appear in the proceedings of "Stellar Clusters & Associations: A RIA Workshop on GAIA", Granada, 23-27 May 2011

We investigate how the X factor, the ratio of H_2 column density (NH2) to velocity-integrated CO intensity (W), is determined by the physical properties of gas in model molecular clouds (MCs). We perform radiative transfer calculations on chemical-MHD models to compute X. Using integrated NH2 and W reproduces the limited range in X found in observations, resulting in a mean value X=2\times10^20 s/cm^2/K^1/km^1 from the Galactic MC model. However, in limited velocity intervals, X can take on a much larger range due to CO line saturation. Thus, X strongly depends on both the range in gas velocities and volume densities. The temperature (T) variations within individual MCs do not strongly affect X, as dense gas contributes most to setting X. For fixed velocity and density structure, gas with higher T has higher W, yielding X ~ T^-1/2 for T~20-100 K. We demonstrate that the linewidth-size scaling relation does not influence the X factor - only the range in velocities is important. Clouds with larger linewidths, regardless of the linewidth-size relation, have a higher W, corresponding to a lower value of X, scaling roughly as X ~ sigma^-1/2. The "mist" model, consisting of optically thick cloudlets with well-separated velocities, does not accurately reflect the conditions in a turbulent MC. We propose that the observed cloud-average values of X ~ XGal is simply a result of the limited range in NH2, temperatures, and velocities found in Galactic MCs - a ~constant value of X therefore does not require any linewidth-size relation, or that MCs are virialized objects. Since gas properties likely differ (slightly) between clouds, masses derived through a standard X should only be considered as a rough first estimate. For temperatures T~10-20 K, velocity dispersions ~1-6 km/s, and NH2~2-20\times10^21 cm^-2, we find cloud-averaged X ~ 2-4\times10^20 s/cm^2/K^1/km^1 for Solar-metallicity models., Comment: 24 pages, including 21 Figures, Accepted to MNRAS

(abridged) The nature of early Class 0/I protostellar discs is not clearly understood. Early protostellar discs are needed to drive molecular outflows and jets observed in star forming regions, but there has been some debate to how they form. From a theoretical perspective, the consequences of disc and outflow generation are crucial to understanding the very nature of how stars are assembled. We have performed 3D ideal magnetohydrodynamic (MHD) simulations of collapsing Bonnor-Ebert spheres, employing sink particles with a radius of 3.2 AU alongside an AMR grid and using a cooling function to model radiative cooling of the gas. This has allowed us to explore 2-8x10^4 yr further into the evolution of an early Class 0 disc-outflow system than previous simulations. Our outflow is precessing, kinked, turbulent, contains internal shocks and has a scale of 0.1 pc end-to-end. We form a rotationally dominated disc with a radius of 100 AU embedded inside a transient, unstable, flattened, rotating core extending out to 2000 AU. The larger flattened structure launches a low speed wind (v_r < 1.5 km/s) dominated by B_phi, while the inner disc launches a centrifugally driven jet dominated by B_p with speeds up to 20$ km/s. From the inner disk, the value of dM/dt_out/dM/dt_in ~ 0.1, wheras in the outer core dM/dt_out/dM/dt_in ~ 1.0. The inner disc becomes unstable to a warping instability due to the magnetic structure of the outflow and warps to 30 deg with respect to the z-axis by the end of the simulation. The envelope is cleared out and is less massive than the disc. We measure star formation efficiencies of eta_core=0.63 (and growing), higher than theoretical predictions. This indicates that outflows are not as efficient at expelling envelope mass as some current models estimate. We discuss the relevance of our disc misalignment concerning the formation of mis-aligned hot Jupiters., This paper has changed. We are re-submitting the same research, but divided into two papers focused on the formation of magnetized discs and the evolution of outflows respectively. We will post these two papers when they are accepted

We introduce a prescription for the luminosity from accreting protostars into smoothed particle hydrodynamics simulation, and apply the method to simulations of five primordial minihalos generated from cosmological initial conditions. We find that accretion luminosity delays fragmentation within the halos, but does not prevent it. In halos that slowly form a low number of protostars, the accretion luminosity can reduce the number of fragments that are formed before the protostars start ionising their surroundings. However, halos that rapidly form many protostars become dominated by dynamical processes, and the effect of accretion luminosity becomes negligible. Generally the fragmentation found in the halos is highly dependent on the initial conditions. Accretion luminosity does not substantially affect the accretion rates experienced by the protostars, and is far less important than dynamical interactions, which can lead to ejections that effectively terminate the accretion. We find that the accretion rates onto the inner regions of the disks (20 AU) around the protostars are highly variable, in contrast to the constant or smoothly decreasing accretion rates currently used in models of the pre-main sequence evolution of Population III stars., Comment: 12 pages, 10 figures and 3 tables. Accepted by MNRAS

We present TreeCol, a new and efficient tree-based scheme to calculate column densities in numerical simulations. Knowing the column density in any direction at any location in space is a prerequisite for modelling the propagation of radiation through the computational domain. TreeCol therefore forms the basis for a fast, approximate method for modelling the attenuation of radiation within large numerical simulations. It constructs a HEALPix sphere at any desired location and accumulates the column density by walking the tree and by adding up the contributions from all tree nodes whose line of sight contributes to the pixel under consideration. In particular when combined with widely-used tree-based gravity solvers the new scheme requires little additional computational cost. In a simulation with $N$ resolution elements, the computational cost of TreeCol scales as $N \log N$, instead of the $N^{5/3}$ scaling of most other radiative transfer schemes. TreeCol is naturally adaptable to arbitrary density distributions and is easy to implement and to parallelize. We discuss its accuracy and performance characteristics for the examples of a spherical protostellar core and for the turbulent interstellar medium. We find that the column density estimates provided by TreeCol are on average accurate to better than 10 percent. In another application, we compute the dust temperatures for solar neighborhood conditions and compare with the result of a full-fledged Monte Carlo radiation-transfer calculation. We find that both methods give very similar answers. We conclude that TreeCol provides a fast, easy to use, and sufficiently accurate method of calculating column densities that comes with little additional computational cost when combined with an existing tree-based gravity solver., Comment: 11 pages, 10 figures, submitted to MNRAS

In this contribution we review our recent numerical work discussing the essential role of the local cluster environment in assembling massive stars. First we show that massive stars are formed from low mass pre-stellar cores and become massive due to accretion. Proto-stars that benefit from this accretion are those situated at the centre of a cluster's potential well, which is the focal point of the contraction of the cluster gas. Given that most of the mass which makes up a massive star in this model comes from the cluster environment rather than the core, it is important to model the molecular cloud environment accurately. Preliminary results of a simulation which accurately treats the chemistry and time-dependent thermodynamics of a molecular cloud show quantitatively similar star formation to previous models, but allow a true comparison to be made between simulation and observations. This method can also be applied to cases with varying metallicities allowing star formation in primordial gas to be studied. In general, these numerical studies of clustered star formation yield IMFs which are compatible with the Salpeter mass function. The only possible exception to this is in low density unbound regions of molecular clouds which lack very low and high mass stars., Comment: Conference Proceedings: UP2010, Have Observations Revealed a Variable Upper End of the Initial Mass Function? 8 pages

The observed slope at the high-mass end of the initial mass function (IMF) displays a remarkable universality in a wide variety of physical environments. We predict that competitive accretion, the ongoing accretion of gas from a common reservoir by a collection of protostellar cores, can provide a natural explanation for such a universal slope in star forming regions with metallicities roughly greater than 1e-5 the solar value. In our discussion, we point out that competitive accretion will occur whenever a gaseous region has multiple Jeans masses of material and contains large-scale motions that are controlled by the gravitational potential well. We describe how and when these conditions can be reached during the chemical enrichment of the Universe, showing that they can occur for a wide range of metallicities and environmental conditions. We also discuss the ability of other physical processes to limit the effects of further accretion onto protostellar cores. Current theoretical and numerical studies show that competitive accretion is robust against disrupting effects - such as feedback from young stars, supersonic turbulence and magnetic fields - in all but the most extreme cases., Comment: Submitted to ApJ: 11 pages, 1 figure

Using smoothed particle hydrodynamics in combination with the special-purpose hardware device GRAPE, we follow the fragmentation process and dynamical evolution in the interior of molecular clouds until most of the gas is converted to form a cluster of protostellar cores. The properties of this protostellar cluster are compared to observational data from star forming regions., Comment: 4 pages including three figures, LaTeX, to appear in the proceedings to the Riken Symposium on Supercomputing, held September 1 --3 1997 in Tokyo, (resolution of fig. 1 has been degraded to fit size requirements)

Determining the sequence of events in the formation of stars and planetary systems and their timescales is essential for understanding those processes, yet establishing ages is fundamentally difficult because we lack direct indicators. In this review we discuss the age challenge for young stars, specifically those less than ~ 100 m.y. old. Most age determination methods that we discuss are primarily applicable to groups of stars but can be used to estimate the age of individual objects. A reliable age scale is established above 20 m.y. from measurement of the lithium depletion boundary (LDB) in young clusters, and consistency is shown between these ages and those from the upper-main-sequence (UMS) and main-sequence (MS) tum-off - if modest core convection and rotation is included in the models of higher-mass stars. Other available methods for age estimation include the kinematics of young groups, placing stars in Hertzsprung-Russell diagrams (HRDs), pulsations and seismology, surface gravity measurement, rotation and activity, and Li abundance. We review each of these methods and present known strengths and weaknesses. Below ~20 m.y., both model-dependent and observational uncertainties grow, the situation is confused by the possibility of age spreads, and no reliable absolute ages yet exist. The lack of absolute age calibration below 20 m.y. should be born in mind when considering the lifetimes of protostellar phases and circumstellar material.

We are still in the early days of exoplanet discovery. Astronomers are beginning to model the atmospheres and interiors of exoplanets and have developed a deeper understanding of processes of planet formation and evolution. However, we have yet to map out the full complexity of multi-planet architectures or to detect Earth analogs around nearby stars. Reaching these ambitious goals will require further improvements in instrumentation and new analysis tools. In this chapter, we provide an overview of five observational techniques that are currently employed in the detection of exoplanets: optical and infrared (IR) Doppler measurements, transit photometry, direct imaging, microlensing, and astrometry. We provide a basic description of how each of these techniques works and discuss forefront developments that will result in new discoveries. We also highlight the observational limitations and synergies of each method and their connections to future space missions.

Results from recent space missions, in particular Spitzer and Herschel, have led to significant progress in our understanding of the formation and transport of water from clouds to disks, planetesimals, and planets. [n this review, we provide the underpinnings for the basic molecular physics and chemistry of water and outline these advances in the context of water formation in space, its transport to a forming disk, its evolution in the disk, and finally the delivery to forming terrestrial worlds and accretion by gas giants. Throughout, we pay close attention to the disposition of water as vapor or solid and whether it might be subject to processing at any stage. The context of the water in the solar system and the isotopic ratios (D/H) in various bodies are discussed as grounding data points for this evolution. Additional advances include growing knowledge of the composition of atmospheres of extrasolar gas giants, which may be influenced by the variable phases of water in the protoplanetary disk. Furthermore, the architecture of extrasolar systems leaves strong hints of dynamical interactions, which are important for the delivery of water and subsequent evolution of planetary systems. We conclude with an exploration of water on Earth and note that all the processes and key parameters identified here should also hold for exoplanetary systems.