An asymptotically correct implicit-explicit time integration scheme for finite volume radiation-hydrodynamics.

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of time-scales, and where the relative importance of these processes often varies by orders of magnitude across the computational domain. Here, we present a new implicit-explicit method for numerical RHD that has a number of desirable properties that have not previously been combined in a single method. Our scheme is based on moments and allows machine-precision conservation of energy and momentum, making it highly suitable for adaptive mesh refinement applications; it requires no more communication than hydrodynamics and includes no non-local iterative steps, making it highly suitable for massively parallel and Graphics Processing Unit (GPU)-based systems where communication is a bottleneck; and we show that it is asymptotically accurate in the streaming, static diffusion, and dynamic diffusion limits, including in the so-called asymptotic diffusion regime where the computational grid does not resolve the photon mean-free path. We implement our method in the GPU-accelerated RHD code quokka and show that it passes a wide range of numerical tests.

The cosmic ray ionization and γ-ray budgets of star-forming galaxies.

Cosmic rays in star-forming galaxies are a dominant source of both diffuse γ-ray emission and ionization in gas too deeply shielded for photons to penetrate. Though the cosmic rays responsible for γ-rays and ionization are of different energies, they are produced by the same star formation-driven sources, and thus galaxies' star formation rates, γ-ray luminosities, and ionization rates should all be linked. In this paper, we use up-to-date cross-section data to determine this relationship, finding that cosmic rays in a galaxy of star formation rate [Formula: see text] and gas depletion time t dep produce a maximum primary ionization rate ζ ≈ 1 × 10-16(t dep/Gyr)-1 s-1 and a maximum γ-ray luminosity [Formula: see text] erg s-1 in the 0.1-100 GeV band. These budgets imply either that the ionization rates measured in Milky Way molecular clouds include a significant contribution from local sources that elevate them above the Galactic mean, or that CR-driven ionization in the Milky Way is enhanced by sources not linked directly to star formation. Our results also imply that ionization rates in starburst systems are only moderately enhanced compared to those in the Milky Way. Finally, we point out that measurements of γ-ray luminosities can be used to place constraints on galactic ionization budgets in starburst galaxies that are nearly free of systematic uncertainties on the details of cosmic ray acceleration.

Environmental variation of the low-mass IMF.

We use a series of magnetohydrodynamic simulations including both radiative and protostellar outflow feedback to study environmental variation of the initial mass function (IMF). The simulations represent a carefully-controlled experiment whereby we keep all dimensionless parameters of the flow constant except for those related to feedback. We show that radiation feedback suppresses the formation of lower mass objects more effectively as the surface density increases, but this only partially compensates for the decreasing Jeans mass in denser environments. Similarly, we find that protostellar outflows are more effective at suppressing the formation of massive stars in higher surface density environments. The combined effect of these two trends is towards an IMF with a lower characteristic mass and a narrower overall mass range in high surface density environments. We discuss the implications for these findings for the interpretation of observational evidence of IMF variation in early type galaxies.

The diffuse γ-ray background is dominated by star-forming galaxies.

The Fermi Gamma-ray Space Telescope has revealed a diffuse γ-ray background at energies from 0.1 gigaelectronvolt to 1 teraelectronvolt, which can be separated into emission from our Galaxy and an isotropic, extragalactic component1. Previous efforts to understand the latter have been hampered by the lack of physical models capable of predicting the γ-ray emission produced by the many candidate sources, primarily active galactic nuclei2-5 and star-forming galaxies6-10, leaving their contributions poorly constrained. Here we present a calculation of the contribution of star-forming galaxies to the γ-ray background that does not rely on empirical scalings and is instead based on a physical model for the γ-ray emission produced when cosmic rays accelerated in supernova remnants interact with the interstellar medium11. After validating the model against local observations, we apply it to the observed cosmological star-forming galaxy population and recover an excellent match to both the total intensity and the spectral slope of the γ-ray background, demonstrating that star-forming galaxies alone can explain the full diffuse, isotropic γ-ray background.

A scaling relation for the molecular cloud lifetime in Milky Way-like galaxies.

We study the time evolution of molecular clouds across three Milky Way-like isolated disc galaxy simulations at a temporal resolution of 1 Myr and at a range of spatial resolutions spanning two orders of magnitude in spatial scale from ∼10 pc up to ∼1 kpc. The cloud evolution networks generated at the highest spatial resolution contain a cumulative total of ∼80 000 separate molecular clouds in different galactic-dynamical environments. We find that clouds undergo mergers at a rate proportional to the crossing time between their centroids, but that their physical properties are largely insensitive to these interactions. Below the gas-disc scale height, the cloud lifetime τlife obeys a scaling relation of the form τlife∝ℓ-0.3 with the cloud size ℓ, consistent with over-densities that collapse, form stars, and are dispersed by stellar feedback. Above the disc scale height, these self-gravitating regions are no longer resolved, so the scaling relation flattens to a constant value of ∼13 Myr, consistent with the turbulent crossing time of the gas disc, as observed in nearby disc galaxies.

Magnetic field amplification in accretion discs around the first stars: implications for the primordial IMF.

Magnetic fields play an important role in the dynamics of present-day molecular clouds. Recent work has shown that magnetic fields are equally important for primordial clouds, which form the first stars in the Universe. While the primordial magnetic field strength on cosmic scales is largely unconstrained, theoretical models strongly suggest that a weak seed field existed in the early Universe. We study how the amplification of such a weak field can influence the evolution of accretion discs around first stars, and thus affect the primordial initial mass function (IMF). We perform a suite of 3D ideal magneto-hydrodynamic simulations with different initial field strengths and numerical resolutions. We find that, in simulations with sufficient spatial resolution to resolve the Jeans scale during the collapse, even initially weak magnetic fields grow exponentially to become dynamically important due to both the so-called small-scale turbulent dynamo and the large-scale mean-field dynamo. Capturing the small-scale dynamo action depends primarily on how well we resolve the Jeans length, while capturing the large-scale dynamo depends on the Jeans resolution as well as the maximum absolute resolution. Provided enough resolution, we find that fragmentation does not depend strongly on the initial field strength, because even weak fields grow to become strong. However, fragmentation in runs with magnetic fields differs significantly from those without magnetic fields. We conclude that the development of dynamically strong magnetic fields during the formation of the first stars is likely inevitable, and that these fields had a significant impact on the primordial IMF.

Distribution and kinematics of 26Al in the Galactic disc.

26Al is a short-lived radioactive isotope thought to be injected into the interstellar medium (ISM) by massive stellar winds and supernovae (SNe). However, all-sky maps of 26Al emission show a distribution with a much larger scale height and faster rotation speed than either massive stars or the cold ISM. We investigate the origin of this discrepancy using an N-body + hydrodynamics simulation of a Milky-Way-like galaxy, self-consistently including self-gravity, star formation, stellar feedback, and 26Al production. We find no evidence that the Milky Way's spiral structure explains the 26Al anomaly. Stars and the 26Al bubbles they produce form along spiral arms, but, because our simulation produces material arms that arise spontaneously rather than propagating arms forced by an external potential, star formation occurs at arm centres rather than leading edges. As a result, we find a scale height and rotation speed for 26Al similar to that of the cold ISM. However, we also show that a synthetic 26Al emission map produced for a possible Solar position at the edge of a large 26Al bubble recovers many of the major qualitative features of the observed 26Al sky. This suggests that the observed anomalous 26Al distribution is the product of foreground emission from the 26Al produced by a nearby, recent SN.

The life cycle of the Central Molecular Zone - II. Distribution of atomic and molecular gas tracers.

We use the hydrodynamical simulation of our inner Galaxy presented in Armillotta et al. to study the gas distribution and kinematics within the Central Molecular Zone (CMZ). We use a resolution high enough to capture the gas emitting in dense molecular tracers such as NH3 and HCN, and simulate a time window of 50 Myr, long enough to capture phases during which the CMZ experiences both quiescent and intense star formation. We then post-process the simulated CMZ to calculate its spatially dependent chemical and thermal state, producing synthetic emission data cubes and maps of both H i and the molecular gas tracers CO, NH3, and HCN. We show that, as viewed from Earth, gas in the CMZ is distributed mainly in two parallel and elongated features extending from positive longitudes and velocities to negative longitudes and velocities. The molecular gas emission within these two streams is not uniform, and it is mostly associated with the region where gas flowing towards the Galactic Centre through the dust lanes collides with gas orbiting within the ring. Our simulated data cubes reproduce a number of features found in the observed CMZ. However, some discrepancies emerge when we use our results to interpret the position of individual molecular clouds. Finally, we show that, when the CMZ is near a period of intense star formation, the ring is mostly fragmented as a consequence of supernova feedback, and the bulk of the emission comes from star-forming molecular clouds. This correlation between morphology and star formation rate should be detectable in observations of extragalactic CMZs.

slug IV: a novel forward-modelling method to derive the demographics of star clusters.

We describe a novel method for determining the demographics of a population of star clusters, for example distributions of cluster mass and age, from unresolved photometry. This method has a number of desirable properties: it fully exploits all the information available in a data set without any binning, correctly accounts for both measurement error and sample incompleteness, naturally handles heterogenous data (e.g. fields that have been imaged with different sets of filters or to different depths), marginalizes over uncertain extinctions, and returns the full posterior distributions of the parameters describing star cluster demographics. We demonstrate the method using mock star cluster catalogues and show that our method is robust and accurate, and that it can recover the demographics of star cluster populations significantly better than traditional fitting methods. For realistic sample sizes, our method is sufficiently powerful that its accuracy is ultimately limited by the accuracy of the underlying physical models for stellar evolution and interstellar dust, rather than by statistical uncertainties. Our method is implemented as part of the Stochastically Lighting Up Galaxies (slug) stellar populations code, and is freely available.

Suppression of star formation in dwarf galaxies by photoelectric grain heating feedback.

Photoelectric heating--heating of dust grains by far-ultraviolet photons--has long been recognized as the primary source of heating for the neutral interstellar medium. Simulations of spiral galaxies have shown some indication that photoelectric heating could suppress star formation; however, simulations that include photoelectric heating have typically shown that it has little effect on the rate of star formation in either spiral galaxies or dwarf galaxies, which suggests that supernovae are responsible for setting the gas depletion time in galaxies. This result is in contrast with recent work indicating that a star formation law that depends on galaxy metallicity--as is expected with photoelectric heating,but not with supernovae--reproduces the present-day galaxy population better than does a metallicity-independent one. Here we report a series of simulations of dwarf galaxies, the class of galaxy in which the effects of both photoelectric heating and supernovae are expected to be strongest. We simultaneously include space and time-dependent photoelectric heating in our simulations, and we resolve the energy-conserving phase of every supernova blast wave, which allows us to directly measure the relative importance of feedback by supernovae and photoelectric heating in suppressing star formation. We find that supernovae are unable to account for the observed large gas depletion times in dwarf galaxies. Instead, photoelectric heating is the dominant means by which dwarf galaxies regulate their star formation rate at any given time,suppressing the rate by more than an order of magnitude relative to simulations with only supernovae.

Early turbulent mixing as the origin of chemical homogeneity in open star clusters.

The abundances of elements in stars are critical clues to stars' origins. Observed star-to-star variations in logarithmic abundance within an open star cluster--a gravitationally bound ensemble of stars in the Galactic plane--are typically only about 0.01 to 0.05 over many elements, which is noticeably smaller than the variation of about 0.06 to 0.3 seen in the interstellar medium from which the stars form. It is unknown why star clusters are so homogenous, and whether homogeneity should also prevail in regions of lower star formation efficiency that do not produce bound clusters. Here we report simulations that trace the mixing of chemical elements as star-forming clouds assemble and collapse. We show that turbulent mixing during cloud assembly naturally produces a stellar abundance scatter at least five times smaller than that in the gas, which is sufficient to explain the observed chemical homogeneity of stars. Moreover, mixing occurs very early, so that regions with star formation efficiencies of about 10 per cent are nearly as well mixed as those with formation efficiencies of about 50 per cent. This implies that even regions that do not form bound clusters are likely to be well mixed, and improves the prospects of using 'chemical tagging' to reconstruct (via their unique chemical signatures, or tags) star clusters whose constituent stars have become unbound from one another and spread across the Galactic disk.

The intense starburst HDF 850.1 in a galaxy overdensity at z ≈ 5.2 in the Hubble Deep Field.

The Hubble Deep Field provides one of the deepest multiwavelength views of the distant Universe and has led to the detection of thousands of galaxies seen throughout cosmic time. An early map of the Hubble Deep Field at a wavelength of 850 micrometres, which is sensitive to dust emission powered by star formation, revealed the brightest source in the field, dubbed HDF 850.1 (ref. 2). For more than a decade, and despite significant efforts, no counterpart was found at shorter wavelengths, and it was not possible to determine its redshift, size or mass. Here we report a redshift of z = 5.183 for HDF 850.1, from a millimetre-wave molecular line scan. This places HDF 850.1 in a galaxy overdensity at z ≈ 5.2, corresponding to a cosmic age of only 1.1 billion years after the Big Bang. This redshift is significantly higher than earlier estimates and higher than those of most of the hundreds of submillimetre-bright galaxies identified so far. The source has a star-formation rate of 850 solar masses per year and is spatially resolved on scales of 5 kiloparsecs, with an implied dynamical mass of about 1.3 × 10(11) solar masses, a significant fraction of which is present in the form of molecular gas. Despite our accurate determination of redshift and position, a counterpart emitting starlight remains elusive.

The formation of massive star systems by accretion.

Massive stars produce so much light that the radiation pressure they exert on the gas and dust around them is stronger than their gravitational attraction, a condition that has long been expected to prevent them from growing by accretion. We present three-dimensional radiation-hydrodynamic simulations of the collapse of a massive prestellar core and find that radiation pressure does not halt accretion. Instead, gravitational and Rayleigh-Taylor instabilities channel gas onto the star system through nonaxisymmetric disks and filaments that self-shield against radiation while allowing radiation to escape through optically thin bubbles. Gravitational instabilities cause the disk to fragment and form a massive companion to the primary star. Radiation pressure does not limit stellar masses, but the instabilities that allow accretion to continue lead to small multiple systems.

A minimum column density of 1 g cm(-2) for massive star formation.

Massive stars are very rare, but their extreme luminosities make them both the only type of young star we can observe in distant galaxies and the dominant energy sources in the Universe today. They form rarely because efficient radiative cooling keeps most star--forming gas clouds close to isothermal as they collapse, and this favours fragmentation into stars of one solar mass or lower. Heating of a cloud by accreting low-mass stars within it can prevent fragmentation and allow formation of massive stars, but the necessary properties for a cloud to form massive stars-and therefore where massive stars form in a galaxy--have not yet been determined. Here we show that only clouds with column densities of at least 1 g cm(-2) can avoid fragmentation and form massive stars. This threshold, and the environmental variation of the stellar initial mass function that it implies, naturally explain the characteristic column densities associated with massive star clusters and the difference between the radial profiles of Halpha and ultraviolet emission in galactic disks. The existence of a threshold also implies that the initial mass function should show detectable variation with environment within the Galaxy, that the characteristic column densities of clusters containing massive stars should vary between galaxies, and that star formation rates in some galactic environments may have been systematically underestimated.

The formation of stars by gravitational collapse rather than competitive accretion.

There are two dominant models of how stars form. Under gravitational collapse, star-forming molecular clumps, of typically hundreds to thousands of solar masses (M(o)), fragment into gaseous cores that subsequently collapse to make individual stars or small multiple systems. In contrast, competitive accretion theory suggests that at birth all stars are much smaller than the typical stellar mass (approximately 0.5M(o)), and that final stellar masses are determined by the subsequent accretion of unbound gas from the clump. Competitive accretion models interpret brown dwarfs and free-floating planets as protostars ejected from star-forming clumps before they have accreted much mass; key predictions of this model are that such objects should lack disks, have high velocity dispersions, form more frequently in denser clumps, and that the mean stellar mass should vary within the Galaxy. Here we derive the rate of competitive accretion as a function of the star-forming environment, based partly on simulation, and determine in what types of environments competitive accretion can occur. We show that no observed star-forming region can undergo significant competitive accretion, and that the simulations that show competitive accretion do so because the assumed properties differ from those determined by observation. Our result shows that stars form by gravitational collapse, and explains why observations have failed to confirm predictions of the competitive accretion model.