arXiv subjects

Matthew R. Bate

Publications and source records attributed to Matthew R. Bate.

At least 19 recordsLinked to original sources

arXiv2026

Cosmological simulations of the high-redshift galaxy population adopting a variable stellar initial mass function

JWST surveys reveal a greater space density of high-redshift UV-bright galaxies than predicted by conventional galaxy formation models. We present results from a $L=100$ cMpc cosmological simulation evolved to $z=5$ with a variation of the COLIBRE galaxy formation model that adopts a density-dependent stellar initial mass function (IMF), such that stellar populations formed from dense gas are born with a top-heavy IMF. Crucially, heavy element and dust yields, and supernova feedback energetics, are self-consistently adjusted to the changing IMF. We model UV/optical emission (including nebular emission) from galaxies and its attenuation by dust. By allowing a significant fraction of high-redshift star formation to proceed with a top-heavy IMF, the rest-frame far-UV luminosities of early galaxies are elevated by up to a factor of $\simeq4$ with respect to the fiducial COLIBRE L100m6 simulation, which assumes a universal Chabrier IMF. This enables the formation of galaxies with observed brightness up to $M_{\rm UV} \simeq -20$ at $z=15$ (c.f. $M_{\rm UV} \simeq -18.5$ in the fiducial simulation), illustrating the potential of star formation with a top-heavy IMF to alleviate tensions with JWST data. Later, the boost in far-UV emission is partly offset by attenuation due to increased dust surface densities from i) additional dust grain ejection from core-collapse supernovae and ii) efficient grain growth promoted by more metal-rich interstellar gas. The simulation reproduces the $z=5$ galaxy stellar mass function and rest-frame optical luminosity function with comparable accuracy to the fiducial simulation, and both simulations exhibit UV continuum slopes that are consistent with JWST observations.

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arXiv2025

Modelling dust coagulation, dynamical drag and turbulent mixing during star and disc formation

Planet formation in the discs around young stars involves the coagulation of sub-micron sized dust grains into much larger grains that may be mixed by turbulence and migrate through the disc. In this paper, we describe how we have combined a method for modelling the coagulation of a population of dust grains with the MULTIGRAIN algorithm for modelling the dynamical evolution of a population of dust grains that are subject to strong gas drag. We solve the dynamical evolution of the dust grains due to gas drag using a recently-developed implicit integration method, and we introduce a new implicit method to model the diffusion of the dust due to unresolved hydrodynamic turbulence. The resulting smoothed particle hydrodynamics (SPH) code allows us, for the first time, to model the growth, mixing and migration of dust grain populations during the early stages of star formation and the formation, growth and evolution of a young protoplanetary disc using three-dimensional hydrodynamical simulations. In doing so, we find that including turbulent dust diffusion within the disc provides a substantial enhancement of the rate of dust grain growth due to the fact that the turbulent diffusion provides a source of small and intermediate dust grains to the regions in which the largest dust grains are growing.

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arXiv2025

Common envelopes in massive stars III. The obstructive role of radiation transport in envelope ejection

We present 3D radiation hydrodynamics simulations of common-envelope (CE) evolution involving a 12 solar mass red supergiant donor and a 3 solar mass companion. Existing 3D simulations are predominantly adiabatic, focusing strongly on low-mass donors on the red giant and asymptotic giant branches. However, the adiabatic assumption breaks down once the perturbed CE material becomes optically thin or when entering a longer-timescale evolutionary phase after the dynamical plunge-in. This is especially important for high-mass red supergiant donors, which have short thermal timescales, adding significant uncertainty to our understanding of how massive binary stars evolve into gravitational-wave sources, X-ray binaries, stripped-envelope supernovae, and more. We compare our radiation hydrodynamics simulations with an adiabatic simulation from Paper I that is otherwise identical, finding that radiative diffusion strongly inhibits CE ejection. The fraction of ejected mass is roughly half that of the adiabatic case without accounting for recombination energy release. Almost no material is ejected during the dynamical plunge-in, and longer-timescale ejection during the slow spiral-in is suppressed. However, the orbital separation reached at the end of the dynamical plunge-in does not differ significantly. The large amount of remaining bound mass tentatively supports the emerging view that the dynamical plunge-in is followed by a non-adiabatic phase, during which a substantial fraction of the envelope is ejected and the binary orbit may continue to evolve.

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arXiv2025

Variation of the low-mass end of the stellar initial mass function with redshift and metallicity

We report the stellar mass functions obtained from 20 radiation hydrodynamical simulations of star cluster formation in 500 M$_\odot$ molecular clouds with metallicities of 3, 1, 1/10 and 1/100 of the solar value, with the clouds subjected to levels of the cosmic microwave background radiation that are appropriate for star formation at redshifts z=0, 3, 5, 7, and 10. The calculations include a thermochemical model of the diffuse interstellar medium and treat dust and gas temperatures separately. We find that the stellar mass distributions obtained become increasingly bottom light as the redshift and/or metallicity are increased. Mass functions that are similar to a typical Galactic initial mass function are obtained for present-day star formation (z=0) independent of metallicity, and also for the lowest-metallicity (1/100 solar) at all redshifts up to z=10, but for higher metallicities there is a larger deficit of brown dwarfs and low-mass stars as the metallicity and redshift are increased. These effects are a result of metal-rich gas being unable to cool to as lower temperatures at higher redshift due to the warmer cosmic microwave background radiation. Based on the numerical results we provide a parameterisation that may be used to vary the stellar initial mass function with redshift and metallicity; this could be used in simulations of galaxy formation. For example, a bottom-light mass function reduces the mass-to-light ratio compared to a typical Galactic stellar initial mass function, which may reduce the estimated masses of high-redshift galaxies.

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arXiv2024

An implicit algorithm for simulating the dynamics of small dust grains with smoothed particle hydrodynamics

We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves casting the dust diffusion equation into implicit form, rearranging into its resolvent cubic equation and solving analytically. This method is relevant for small grains that are tightly coupled to the gas, such as sub-micron dust grains in the interstellar medium or millimetre-sized dust grains in protoplanetary discs. The method avoids problems with the variable used to evolve the dust fraction becoming negative when evolved explicitly and is fast and accurate, avoiding the need for dust stopping time limiters and significantly reducing computational expense. Whilst this method is an improvement over using the explicit terminal velocity approximation method, as with any dust-as-mixture method it still fails to give accurate solutions in the limit of large (weakly coupled) grains.

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arXiv2024

Probing initial distributions of orbital eccentricity and disc misalignment via polar discs

In a population of multiple protostellar systems with discs, the sub-population of circumbinary discs whose orbital plane is highly misaligned with respect to the binary's orbital plane constrains the initial distribution of orbital parameters of the whole population. We show that by measuring the polar disc fraction and the average orbital eccentricity in the polar discs, one can constrain the distributions of initial eccentricity and mutual inclination in multiple stellar systems at birth.

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arXiv2023

On the frequencies of circumbinary discs in protostellar systems

We report the analysis of circumbinary discs formed in a radiation hydrodynamical simulation of star cluster formation. We consider both pure binary stars and pairs within triple and quadruple systems. The protostellar systems are all young (ages < $10^5$ yrs). We find that the systems that host a circumbinary disc have a median separation of $\approx 11$ au, and the median characteristic radius of the discs is $\approx 64$ au. We find that $89$ per cent of pure binaries with semi-major axes $a<1$ au have a circumbinary disc, and the occurrence rate of circumbinary discs is bimodal with log-separation in pure binaries with a second peak at $a \approx 50$ au. Systems with $a>100$ au almost never have a circumbinary disc. The median size of a circumbinary disc is between $\approx 5-6\ a$ depending on the order of the system, with higher order systems having larger discs relative to binary separation. We find the underlying distribution of mutual inclinations between circumbinary discs and binary orbit of both observed and simulated discs to not differ statistically.

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arXiv2022

The statistical properties of stars at redshift, z=5, compared with the present epoch

We report the statistical properties of stars and brown dwarfs obtained from three radiation hydrodynamical simulations of star cluster formation with metallicities of 1, 1/10 and 1/100 of the solar value. The star-forming clouds are subjected to cosmic microwave background radiation that is appropriate for star formation at a redshift z=5. The results from the three calculations are compared to each other, and to similar previously published calculations that had levels of background radiation appropriate for present-day (z=0) star formation. Each of the calculations treat dust and gas temperatures separately and include a thermochemical model of the diffuse interstellar medium. We find that whereas the stellar mass distribution is insensitive to the metallicity for present-day star formation, at z=5 the characteristic stellar mass increases with increasing metallicity and the mass distribution has a deficit of brown dwarfs and low-mass stars at solar metallicity compared to the Galactic initial mass function. We also find that the multiplicity of M-dwarfs decreases with increasing metallicity at z=5. These effects are a result of metal-rich gas being unable to cool to as low temperatures at z=5 compared to at z=0 due to the hotter cosmic microwave background radiation, which inhibits fragmentation at high densities.

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arXiv2022

Dust coagulation during the early stages of star formation: molecular cloud collapse and first hydrostatic core evolution

Planet formation in protoplanetary discs requires dust grains to coagulate from the sub-micron sizes that are found in the interstellar medium into much larger objects. For the first time, we study the growth of dust grains during the earliest phases of star formation using three-dimensional hydrodynamical simulations. We begin with a typical interstellar dust grain size distribution and study dust growth during the collapse of a molecular cloud core and the evolution of the first hydrostatic core, prior to the formation of the stellar core. We examine how the dust size distribution evolves both spatially and temporarily. We find that the envelope maintains its initial population of small dust grains with little growth during these phases, except that in the inner few hundreds of au the smallest grains are depleted. However, once the first hydrostatic core forms rapid dust growth to sizes in excess of $100~μ$m occurs within the core (before stellar core formation). Progressively larger grains are produced at smaller distances from the centre of the core. In rapidly-rotating molecular cloud cores, the `first hydrostatic core' that forms is better described as a pre-stellar disc that may be gravitationally unstable. In such cases, grain growth is more rapid in the spiral density waves leading to the larger grains being preferentially found in the spiral waves even though there is no migration of grains relative to the gas. Thus, the grain size distribution can vary substantially in the first core/pre-stellar disc even at these very early times.

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arXiv2022

Supernovae and photoionizing feedback in spiral arm molecular clouds

We explore the interplay between supernovae and the ionizing radiation of their progenitors in star forming regions. The relative contributions of these stellar feedback processes are not well understood, particularly on scales greater than a single star forming cloud. We focus predominantly on how they affect the interstellar medium. We re-simulate a 500 pc^2 region from previous work that included photoionization and add supernovae. Over the course of 10 Myr more than 500 supernovae occur in the region. The supernovae remnants cool very quickly in the absence of earlier photoionization, but form much larger and more spherical hot bubbles when photoionization is present. Overall, the photoionization has a significantly greater effect on gas morphology and the sites of star formation. However, the two processes are comparable when looking at their effect on velocity dispersion. When combined, the two feedback processes increase the velocity dispersions by more than the sum of their parts, particularly on scales above 5 pc.

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arXiv2022

On the origin of magnetic fields in stars II: The effect of numerical resolution

Are the kG-strength magnetic fields observed in young stars a fossil field left over from their formation or are they generated by a dynamo? Our previous numerical study concluded that magnetic fields must originate by a dynamo process. Here, we continue that investigation by performing even higher numerical resolution calculations of the gravitational collapse of a 1~M$_\odot$ rotating, magnetised molecular cloud core through the first and second collapse phases until stellar densities are reached. Each model includes Ohmic resistivity, ambipolar diffusion, and the Hall effect. We test six numerical resolutions, using between $10^5$ and $3\times10^7$ particles to model the cloud. At all but the lowest resolutions, magnetic walls form in the outer parts of the first hydrostatic core, with the maximum magnetic field strength located within the wall rather than at the centre of the core. At high resolution, this magnetic wall is disrupted by the Hall effect, producing a magnetic field with a spiral-shaped distribution of intensity. As the second collapse occurs, this field is dragged inward and grows in strength, with the maximum field strength increasing with resolution. As the second core forms, the maximum field strength exceeds 1~kG in our highest resolution simulations, and the stellar core field strength exceeds this threshold at the highest resolution. Our resolution study suggests that kG-strength magnetic fields may be implanted in low-mass stars during their formation, and may persist over long timescales given that the diffusion timescale for the magnetic field exceeds the age of the Universe.

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arXiv2021

The statistical properties of protostellar discs and their dependence on metallicity

We present the analysis of the properties of large samples of protostellar discs formed in four radiation hydrodynamical simulations of star cluster formation. The four calculations have metallicities of 0.01, 0.1, 1 and 3 times solar metallicity. The calculations treat dust and gas temperatures separately and include a thermochemical model of the diffuse interstellar medium. We find the radii of discs of bound protostellar systems tend to decrease with decreasing metallicity, with the median characteristic radius of discs in the 0.01 and 3 times solar metallicity calculations being $\approx20$ and $\approx65$ au, respectively. Disc masses and radii of isolated protostars also tend to decrease with decreasing metallicity. We find that the circumstellar discs and orbits of bound protostellar pairs, and the two spins of the two protostars are all less well aligned with each other with lower metallicity than with higher metallicity. These variations with metallicity are due to increased small scale fragmentation due to lower opacities and greater cooling rates with lower metallicity, which increase the stellar multiplicity and increase dynamical interactions. We compare the disc masses and radii of protostellar systems from the solar metallicity calculation with recent surveys of discs around Class 0 and I objects in the Orion and Perseus star-forming regions. The masses and radii of the simulated discs have similar distributions to the observed Class 0 and I discs.

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arXiv2021

The impact of non-ideal magnetohydrodynamic processes on discs, outflows, counter-rotation and magnetic walls during the early stages of star formation

Non-ideal magnetohydrodynamic (MHD) processes -- namely Ohmic resistivity, ambipolar diffusion and the Hall effect -- modify the early stages of the star formation process and the surrounding environment. Collectively, they have been shown to promote disc formation and promote or hinder outflows. But which non-ideal process has the greatest impact? Using three-dimensional smoothed particle radiation non-ideal MHD simulations, we model the gravitational collapse of a rotating, magnetised cloud through the first hydrostatic core phase to shortly after the formation of the stellar core. We investigate the impact of each process individually and collectively. Including any non-ideal process decreases the maximum magnetic field strength by at least an order of magnitude during the first core phase compared to using ideal MHD, and promotes the formation of a magnetic wall. When the magnetic field and rotation vectors are anti-aligned and the Hall effect is included, rotationally supported discs of $r \gtrsim 20$~au form; when only the Hall effect is included and the vectors are aligned, a counter-rotating pseudo-disc forms that is not rotationally supported. Rotationally supported discs of $r \lesssim 4$~au form if only Ohmic resistivity or ambipolar diffusion are included. The Hall effect suppresses first core outflows when the vectors are anti-aligned and suppresses stellar core outflows independent of alignment. Ohmic resistivity and ambipolar diffusion each promote first core outflows and delay the launching of stellar core outflows. Although each non-ideal process influences star formation, these results suggest that the Hall effect has the greatest influence.

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arXiv2020

A triple star system with a misaligned and warped circumstellar disk shaped by disk tearing

Young stars are surrounded by a circumstellar disk of gas and dust, within which planet formation can occur. Gravitational forces in multiple star systems can disrupt the disk. Theoretical models predict that if the disk is misaligned with the orbital plane of the stars, the disk should warp and break into precessing rings, a phenomenon known as disk tearing. We present observations of the triple star system GWOrionis, finding evidence for disk tearing. Our images show an eccentric ring that is misaligned with the orbital planes and the outer disk. The ring casts shadows on a strongly warped intermediate region of the disk. If planets can form within the warped disk, disk tearing could provide a mechanism for forming wide-separation planets on oblique orbits.

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arXiv2020

Photoionising feedback in spiral arm molecular clouds

We present simulations of a 500 pc$^2$ region, containing gas of mass 4 $\times$ 10$^6$ M$_\odot$, extracted from an entire spiral galaxy simulation, scaled up in resolution, including photoionising feedback from stars of mass > 18 M$_\odot$. Our region is evolved for 10 Myr and shows clustered star formation along the arm generating $\approx$ 5000 cluster sink particles $\approx$ 5% of which contain at least one of the $\approx$ 4000 stars of mass > 18 M$_\odot$. Photoionisation has a noticeable effect on the gas in the region, producing ionised cavities and leading to dense features at the edge of the HII regions. Compared to the no-feedback case, photoionisation produces a larger total mass of clouds and clumps, with around twice as many such objects, which are individually smaller and more broken up. After this we see a rapid decrease in the total mass in clouds and the number of clouds. Unlike studies of isolated clouds, our simulations follow the long range effects of ionisation, with some already-dense gas becoming compressed from multiple sides by neighbouring HII regions. This causes star formation that is both accelerated and partially displaced throughout the spiral arm with up to 30% of our cluster sink particle mass forming at distances > 5 pc from sites of sink formation in the absence of feedback. At later times, the star formation rate decreases to below that of the no-feedback case.

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arXiv2020

Ionization and dissociation induced fragmentation of a tidally disrupted star into planets around a supermassive black hole

We show results from the radiation hydrodynamics (RHD) simulations of tidal disruption of a star on a parabolic orbit by a supermassive black hole (SMBH) based on a three-dimensional smoothed particle hydrodynamics code with radiative transfer. We find that such a tidally disrupted star fragment and form clumps soon after its tidal disruption. The fragmentation results from the endothermic processes of ionization and dissociation that reduce the gas pressure, leading to local gravitational collapse. Radiative cooling is less effective because the stellar debris is still highly optically thick in such an early time. Our simulations reveal that a solar-type star with a stellar density profile of n=3 disrupted by a 10^6 solar mass black hole produces $\sim20$ clumps of masses in the range of 0.1 to 12 Jupiter masses. The mass fallback rate decays with time, with pronounced spikes from early to late time. The spikes provide evidence for the clumps of the returning debris, while the clumps on the unbound debris can be potentially freely-floating planets and brown dwarfs. This ionization and dissociation induced fragmentation on a tidally disrupted star are a promising candidate mechanism to form low-mass stars to planets around an SMBH.

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arXiv2019

There is no magnetic braking catastrophe: Low-mass star cluster and protostellar disc formation with non-ideal magnetohydrodynamics

We present results from the first radiation non-ideal magnetohydrodynamics (MHD) simulations of low-mass star cluster formation that resolve the fragmentation process down to the opacity limit. We model 50~M$_\odot$ turbulent clouds initially threaded by a uniform magnetic field with strengths of 3, 5 10 and 20 times the critical mass-to-magnetic flux ratio, and at each strength, we model both an ideal and non-ideal (including Ohmic resistivity, ambipolar diffusion and the Hall effect) MHD cloud. Turbulence and magnetic fields shape the large-scale structure of the cloud, and similar structures form regardless of whether ideal or non-ideal MHD is employed. At high densities ($10^6 \lesssim n_{\rm H} \lesssim 10^{11}$~cm$^{-3}$), all models have a similar magnetic field strength versus density relation, suggesting that the field strength in dense cores is independent of the large-scale environment. Albeit with limited statistics, we find no evidence for the dependence of the initial mass function on the initial magnetic field strength, however, the star formation rate decreases for models with increasing initial field strengths; the exception is the strongest field case where collapse occurs primarily along field lines. Protostellar discs with radii $\gtrsim 20$~au form in all models, suggesting that disc formation is dependent on the gas turbulence rather than on magnetic field strength. We find no evidence for the magnetic braking catastrophe, and find that magnetic fields do not hinder the formation of protostellar discs.

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arXiv2019

Resolving numerical star formation: A cautionary tale

Resolution studies of test problems set baselines and help define minimum resolution requirements, however, resolution studies must also be performed on scientific simulations to determine the effect of resolution on the specific scientific results. We perform a resolution study on the formation of a protostar by modelling the collapse of gas through 14 orders of magnitude in density. This is done using compressible radiative non-ideal magnetohydrodynamics. Our suite consists of an ideal magnetohydrodynamics (MHD) model and two non-ideal MHD models, and we test three resolutions for each model. The resulting structure of the ideal MHD model is approximately independent of resolution, although higher magnetic field strengths are realised in higher resolution models. The non-ideal MHD models are more dependent on resolution, specifically the magnetic field strength and structure. Stronger magnetic fields are realised in higher resolution models, and the evolution of detailed structures such as magnetic walls are only resolved in our highest resolution simulation. In several of the non-ideal MHD models, there is an off-set between the location of the maximum magnetic field strength and the maximum density, which is often obscured or lost at lower resolutions. Thus, understanding the effects of resolution on numerical star formation is imperative for understanding the formation of a star.

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