Runaway Collapse Research Articles

Formation of an embryonic supermassive star in the first galaxy

Abstract We studied the gravitational collapse of a warm (∼8000 K) primordial-gas cloud as a candidate progenitor for a supermassive star (SMS; ≳ 105 M⊙) using a three-dimensional hydrodynamical simulation including all the relevant cooling processes of both H2 and H, which can potentially induce cloud fragmentation. This is the first simulation of this kind to resolve protostar formation. We find that from a weakly turbulent initial condition, the cloud undergoes runaway collapse without a major episode of fragmentation. Although the H2 fraction jumps by a large factor via the three-body reaction at ∼10−13 g cm−3, its cooling remains inefficient due to the optical thickness, and the temperature remains ≳ 3000 K. When the central core of the cloud becomes opaque to continuum radiation at ∼10−8 g cm−3, a hydrostatic protostar with ≃0.2 M⊙ is formed. The protostar grows to the mass ≃1 M⊙ and the radius ≃2 au within ∼1 yr via rapid accretion of dense filamentary flows. With high accretion rate, ∼2 M⊙ yr−1, the protostar is expected to turn into an SMS within its lifetime, eventually collapsing to a seed for the supermassive black hole observed in the early Universe at z ∼ 7.

NON-IDEAL MAGNETOHYDRODYNAMIC SIMULATIONS OF THE TWO-STAGE FRAGMENTATION MODEL FOR CLUSTER FORMATION

We model molecular cloud fragmentation with thin disk non-ideal magnetohydrodynamic simulations that include ambipolar diffusion and partial ionization that transitions from primarily ultraviolet dominated to cosmic ray dominated regimes. These simulations are used to determine the conditions required for star clusters to form through a two-stage fragmentation scenario. Recent linear analyses have shown that the fragmentation length and time scales can undergo a dramatic drop across the column density boundary that separates the ultraviolet and cosmic ray dominated ionization regimes. As found in earlier studies, the absence of an ionization drop and regular perturbations leads to a single-stage fragmentation on parsec scales in transcritical clouds, so that the nonlinear evolution yields the same fragment sizes as predicted by linear theory. However, we find that a combination of initial transcritical mass-to-flux ratio, evolution through a column density regime in which the ionization drop takes place, and regular small perturbations to the mass-to-flux ratio are sufficient to cause a second stage of fragmentation during the nonlinear evolution. Cores of size ~0.1 pc are formed within an initial fragment of ~ pc size. Regular perturbations to the mass-to-flux ratio also accelerate the onset of runaway collapse.

Consumer Fronts, Global Change, and Runaway Collapse in Ecosystems

Consumer fronts occur when grazers or predators aggregate in bands along the edges of a resource. Our review reveals that consumer fronts are a common phenomenon in nature, occur in many different ecosystems, and are triggered by universal mechanisms: External forces locally increase top-down control beyond prey carrying and/or renewal capacity, and resource-dependent movement leads to consumer aggregation along the edge of the remaining prey population. Once formed, consumer fronts move through systems as spatially propagating waves, self-reinforced via intense overexploitation and amplified by density-dependent feedbacks. When consumer fronts are spatially restricted, they generate patchiness. In contrast, when consumer fronts are expansive, they can lead to runaway responses that cause large-scale ecosystem degradation and regime shifts. We conceptualize a synergistic stress hypothesis and model that highlight how coupled intensification of physical stress and enhanced consumer pressure can trigger increased occurrence of consumer fronts and decreased system stability and resilience. With escalating climate change and food-web modification, the physical and biological conditions favoring consumer-front formation will likely become a common feature of many ecosystems.

Accretion does not drive the turbulence in galactic discs

Rapid accretion of cold gas plays a crucial role in getting gas into galaxies. It has been suggested that this accretion proceeds along narrow streams that might also directly drive the turbulence in galactic gas, dynamical disturbances, and bulge formation. In cosmological simulations, however, it is impossible to isolate and hence disentangle the effect of accretion from internal instabilities and mergers. Moreover, in most cosmological simulations, the phase structure and turbulence in the ISM arising from stellar feedback are treated in a sub-grid manner, so that feedback cannot generate ISM turbulence. In this paper we therefore test the effects of cold streams in extremely high-resolution simulations of otherwise isolated galaxy disks using detailed models for star formation and feedback; we then include or exclude mock cold flows falling onto the galaxies with accretion rates, velocities and geometry set to maximize their effect on the disk. We find: (1) Turbulent velocity dispersions in gas disks are identical with or without the cold flow; the energy injected by the flow is dissipated where it meets the disk. (2) In runs without stellar feedback, the presence of a cold flow has essentially no effect on runaway local collapse, resulting in star formation rates (SFRs) that are far too large. (3) Disks in runs with feedback and cold flows have higher SFRs, but only insofar as they have more gas. (4) Because flows are extended relative to the disk, they do not trigger strong resonant responses and so induce weak morphological perturbation (bulge formation via instabilities is not accelerated). (5) However, flows can thicken the disk by direct contribution of out-of-plane streams. We conclude that while inflows are critical over cosmological timescales to determine the supply and angular momentum of gas disks, they have weak instantaneous dynamical effects on galaxies.

Fragmentation of Primordial Filamentary Clouds under Far-Ultraviolet Radiation

The collapse and fragmentation of uniform filamentary clouds under isotropic far-ultraviolet external radiation are investigated. Especially, the impact of the photodissociation of hydrogen molecules during collapse is considered. The dynamical and thermal evolutions of collapsing filamentary clouds are calculated by solving the virial equation and the energy equation while taking into account non-equilibrium chemical reactions. It is found that thermal evolution is hardly affected by external radiation if the initial density is high ($ n_0$$ \gt$ 10$ ^{2}$ cm$ ^{-3}$ ). On the other hand, if the line mass of the filamentary cloud is moderate and the initial density is low ($ n_0$$ \le$ 10$ ^{2}$ cm$ ^{-3}$ ), the thermal evolution of the filamentary cloud tends to be adiabatic, owing to the effect of external dissociation radiation. In this case, the collapse of the filamentary cloud is suppressed, and the filamentary cloud fragments into very massive clouds ($ \sim$ 10$ ^{4-5}\ M_\odot$ ) in the early stage of collapse. The analytic criterion for the filamentary clouds to fragment into such massive clouds is discussed. We also investigate the collapse and fragmentation of the filamentary clouds with an improved model. This model can partly capture the effect of run-away collapse. Also, in this model filamentary clouds with low initial density ($ n_0$$ \le$ 10$ ^{2}$ cm$ ^{-3}$ ) fragment into massive clouds ($ \sim$ 10$ ^{4}\ M_\odot$ ) owing to the effect of external radiation.

Star formation in the first galaxies - I. Collapse delayed by Lyman-Werner radiation

We investigate the process of metal-free star formation in the first galaxies with a high-resolution cosmological simulation. We consider the cosmologically motivated scenario in which a strong molecule-destroying Lyman-Werner (LW) background inhibits effective cooling in low-mass haloes, delaying star formation until the collapse or more massive haloes. Only when molecular hydrogen (H2) can self-shield from LW radiation, which requires a halo capable of cooling by atomic line emission, will star formation be possible. To follow the formation of multiple gravitationally bound objects, at high gas densities we introduce sink particles which accrete gas directly from the computational grid. We find that in a 1 Mpc^3 (comoving) box, runaway collapse first occurs in a 3x10^7 M_sun dark matter halo at z~12 assuming a background intensity of J21=100. Due to a runaway increase in the H2 abundance and cooling rate, a self-shielding, supersonically turbulent core develops abruptly with ~10^4 M_sun in cold gas available for star formation. We analyze the formation of this self-shielding core, the character of turbulence, and the prospects for star formation. Due to a lack of fragmentation on scales we resolve, we argue that LW-delayed metal-free star formation in atomic cooling haloes is very similar to star formation in primordial minihaloes, although in making this conclusion we ignore internal stellar feedback. Finally, we briefly discuss the detectability of metal-free stellar clusters with the James Webb Space Telescope.

Gentrifying Climate Change: Ecological Modernisation and the Cultural Politics of Definition

Gentrifying Climate Change: Ecological Modernisation and the Cultural Politics of Definition

The structure of the interstellar medium of star-forming galaxies

We present numerical methods for including stellar feedback in galaxy-scale simulations. We include heating by SNe (I & II), gas recycling and shock-heating from O-star & AGB winds, HII photoionization, and radiation pressure from stellar photons. The energetics and time-dependence are taken directly from stellar evolution models. We implement these in simulations with pc-scale resolution, modeling galaxies from SMC-like dwarfs and MW analogues to massive z~2 starburst disks. Absent feedback, gas cools and collapses without limit. With feedback, the ISM reaches a multi-phase steady state in which GMCs continuously form, disperse, and re-form. Our primary results include: (1) Star forming galaxies generically self-regulate at Toomre Q~1. Most of the volume is in diffuse hot gas with most of the mass in dense GMC complexes. The phase structure and gas mass at high densities are much more sensitive probes of stellar feedback physics than integrated quantities (Toomre Q or gas velocity dispersion). (2) Different feedback mechanisms act on different scales: radiation & HII pressure are critical to prevent runaway collapse of dense gas in GMCs. SNe and stellar winds dominate the dynamics of volume-filling hot gas; however this primarily vents out of the disk. (3) The galaxy-averaged SFR is determined by feedback. For given feedback efficiency, restricting star formation to molecular gas or modifying the cooling function has little effect; but changing feedback mechanisms directly translates to shifts off the Kennicutt-Schmidt relation. (4) Self-gravity leads to marginally-bound GMCs with an ~M^-2 mass function with a cutoff at the Jeans mass; they live a few dynamical times before being disrupted by stellar feedback and turn ~1-10% of their mass into stars (increasing from dwarfs through starburst galaxies). Low-mass GMCs are preferentially unbound.

Observational Identification of First Cores: Non-LTE Radiative Transfer Simulation

A first core is a first hydrostatic object formed in the course of dynamical contraction of a molecular cloud core. Since the inflow pattern changes drastically both before and after first core formation, it is regarded as a milestone in the star-formation process. In order to identify the first core from a mapping observation, the features expected for the first core are studied for CS rotation transitions at radio wavelengths. The non-LTE (local thermodynamical equilibrium) radiation transfer is calculated for the results of radiation magnetohydrodynamical simulations of the contraction of the magnetized molecular cloud core in rotation (Tomida et al. (2010b), ApJ, 714, L58). We used the Monte-Carlo method to solve the non-LTE radiation transfer in a nested grid hierarchy. In the first core phase, an outflow arises from the vicinity of the first core due to a twisted magnetic field amplified by rotation of the contracting gas disk. The disk and outflow system has several characteristic observational features: (i) relatively opaque lines indicate asymmetry in the emission lines in which the blue side is stronger than the red side (an infall signature of the envelope); (ii) in the edge-on view, the disk has a signature of simultaneous rotation and infall, i.e., the integrated intensity of the approaching side is brighter than that of the receding side and the gradient in the intensity-weighted velocity is larger in the approaching side; (iii) the observed outflow indicates rotation around the rotation axis. The size of the outflow gives the approximate age after the first core is formed, since the outflow is not expected for the earlier runaway isothermal collapse phase.

Self-regulated star formation in galaxies via momentum input from massive stars

Feedback from massive stars is believed to play a critical role in shaping the galaxy mass function, the structure of the interstellar medium (ISM), and the low efficiency of star formation, but the exact form of the feedback is uncertain. In this paper, the first in a series, we present and test a novel numerical implementation of stellar feedback resulting from momentum imparted to the ISM by radiation, supernovae, and stellar winds. We employ a realistic cooling function, and find that a large fraction of the gas cools to <100K, so that the ISM becomes highly inhomogeneous. Despite this, our simulated galaxies reach an approximate steady state, in which gas gravitationally collapses to form giant molecular clouds (GMCs), dense clumps, and stars; subsequently, stellar feedback disperses the GMCs, repopulating the diffuse ISM. This collapse and dispersal cycle is seen in models of SMC-like dwarfs, the Milky-Way, and z~2 clumpy disk analogues. The simulated global star formation efficiencies are consistent with the observed Kennicutt-Schmidt relation. Moreover, the star formation rates are nearly independent of the numerically imposed high-density star formation efficiency, density threshold, and density scaling. This is a consequence of the fact that, in our simulations, star formation is regulated by stellar feedback limiting the amount of very dense gas available for forming stars. In contrast, in simulations without stellar feedback, i.e. under the action of only gravity and gravitationally-induced turbulence, the ISM experiences runaway collapse to very high densities. In these simulations without feedback, the global star formation rates exceed observed galactic star formation rates by 1-2 orders of magnitude, demonstrating that stellar feedback is crucial to the regulation of star formation in galaxies.

GRAVITATIONAL WAVES FROM INTERMEDIATE-MASS BLACK HOLES IN YOUNG CLUSTERS

Massive young clusters (YCs) are expected to host intermediate-mass black holes (IMBHs) born via runaway collapse. These IMBHs are likely in binaries and can undergo mergers with other compact objects, such as stellar mass black holes (BHs) and neutron stars (NSs). We derive the frequency of such mergers starting from information available in the Local Universe. Mergers of IMBH-NS and IMBH-BH binaries are sources of gravitational waves (GWs), which might allow us to reveal the presence of IMBHs. We thus examine their detectability by current and future GW observatories, both ground- and space-based. In particular, as representative of different classes of instruments we consider Initial and Advanced LIGO, the Einstein gravitational-wave Telescope (ET) and the Laser Interferometer Space Antenna (LISA). We find that IMBH mergers are unlikely to be detected with instruments operating at the current sensitivity (Initial LIGO). LISA detections are disfavored by the mass range of IMBH-NS and IMBH-BH binaries: less than one event per year is expected to be observed by such instrument. Advanced LIGO is expected to observe a few merger events involving IMBH binaries in a 1-year long observation. Advanced LIGO is particularly suited for mergers of relatively light IMBHs (~100 Msun) with stellar mass BHs. The number of mergers detectable with ET is much larger: tens (hundreds) of IMBH-NS (IMBH-BH) mergers might be observed per year, according to the runaway collapse scenario for the formation of IMBHs. We note that our results are affected by large uncertainties, produced by poor observational constraints on many of the physical processes involved in this study, such as the evolution of the YC density with redshift.[abridged]

Magnetically-regulated fragmentation induced by nonlinear flows and ambipolar diffusion

We present a parameter study of simulations of fragmentation regulated by gravity, magnetic fields, ambipolar diffusion, and nonlinear flows. The thin-sheet approximation is employed with periodic lateral boundary conditions, and the nonlinear flow field (“turbulence”) is allowed to freely decay. In agreement with previous results in the literature, our results show that the onset of runaway collapse (formation of the first star) in subcritical clouds is significantly accelerated by nonlinear flows in which a large-scale wave mode dominates the power spectrum. In addition, we find that a power spectrum with equal energy on all scales also accelerates collapse, but by a lesser amount. For a highly super-Alfvénic initial velocity field with most power on the largest scales, the collapse occurs promptly during the initial compression wave. However, for trans-Alfvénic perturbations, a subcritical magnetic field causes a rebound from the initial compression, and the system undergoes several oscillations before runaway collapse occurs. Models that undergo prompt collapse have highly supersonic infall motions at the core boundaries. Cores in magnetically subcritical models with trans-Alfvénic initial perturbations also pick up significant systematic speeds by inheriting motions associated with magnetically-driven oscillations. Core mass distributions are much broader than in models with small-amplitude initial perturbations, although the disturbed structure of cores that form due to nonlinear flows does not guarantee subsequent monolithic collapse. Our simulations also demonstrate that significant power (if present initially) can be maintained with negligible dissipation in large-scale compressive modes of a magnetic thin sheet, in the limit of perfect flux freezing.

A New Design Method for Industrial Portal Frames in Fire

Industrial portal frames near to other buildings must keep their vertical walls standing in fire in order to prevent fire spread. A recently developed analysis, implemented in the program Vulcan, using a combination of static and dynamic solvers, has shown that the strong base connections recommended by the current design method may not always lead to conservative design. A second-phase failure mechanism observed in numerical modelling, and the critical temperature at which final run-away collapse occurs, may be higher than the temperature at which the roof frame initially loses its stability, because a re-stabilisation often happens. A new method for estimating critical temperatures of portal frames in fire, using these two failure mechanisms, is presented. Numerical tests on typical industrial frames are used to calibrate this new method.

Uncertainties in H2and HD chemistry and cooling and their role in early structure formation

At low temperatures, the main coolant in primordial gas is molecular hydrogen, H 2 . Recent work has shown that primordial gas that is not collapsing gravitationally but is cooling from an initially ionized state forms hydrogen deuteride, HD, in sufficient amounts to cool the gas to the temperature of the cosmic microwave background. This extra cooling can reduce the characteristic mass for gravitational fragmentation and may cause a shift in the characteristic masses of Population III stars. Motivated by the importance of the atomic and molecular data for the cosmological question, we assess several chemical and radiative processes that have hitherto been neglected: the sensitivity of the low-temperature H 2 cooling rate to the ratio of ortho-H 2 to para-H 2 , the uncertainty in the low-temperature cooling rate of H 2 excited by collisions with atomic hydrogen, the effects of cooling from H 2 excited by collisions with protons and electrons, and the large uncertainties in the rates of several of the reactions responsible for determining the H 2 fraction in the gas. It is shown that the most important of neglected processes is the excitation of H 2 by collisions with protons and electrons. Their effect is to cool the gas more rapidly at early times, and consequently to form less H 2 and HD at late times. This fact, as well as several of the chemical uncertainties presented here, significantly affects the thermal evolution of the gas. We anticipate that this may lead to clear differences in future detailed three-dimensional studies of first structure formation. In such calculations it has previously been shown that the details of the timing between cooling and merger events decide between immediate runaway gravitational collapse and a slower collapse delayed by turbulent heating. Finally, we show that although the thermal evolution of the gas is in principle sensitive to the ortho-para ratio, in practice the standard assumption of a 3:1 ratio produces results that are almost indistinguishable from those produced by a more detailed treatment.

Nonlinear evolution of gravitational fragmentation regulated by magnetic fields and ambipolar diffusion

We present results from an extensive set of simulations of gravitational fragmentation in the presence of magnetic fields and ambipolar diffusion. The thin-sheet approximation is employed, with an ambient magnetic field that is oriented perpendicular to the plane of the sheet. Nonlinear development of fragmentation instability leads to substantial irregular structure and distributions of fragment spacings, fragment masses, shapes, and velocity patterns in model clouds. We study the effect of dimensionless free parameters that characterize the initial mass-to-flux ratio, neutral-ion coupling, and external pressure associated with the sheet. The average fragmentation spacing in the nonlinear phase of evolution is in excellent agreement with the prediction of linear perturbation theory. Both significantly subcritical and highly supercritical clouds have average fragmentation scales 〈 λ 〉 ≈ 2 π Z 0 , where Z 0 is the initial half-thickness of the sheet. In contrast, the qualitatively unique transcritical modes can have 〈 λ 〉 that is at least several times larger. Conversely, fragmentation dominated by external pressure can yield dense cluster formation with much smaller values of 〈 λ 〉 . The time scale for nonlinear growth and runaway collapse of the first core is ≈10 times the calculated growth time τ g,m of the eigenmode with minimum growth time, when starting from a uniform background state with small-amplitude white-noise perturbations. Subcritical and transcritical models typically evolve on a significantly longer time scale than the supercritical models. Infall motions in the nonlinear fully-developed contracting cores are subsonic on the core scale in subcritical and transcritical clouds, but are somewhat supersonic in supercritical clouds. Core mass distributions are sharply peaked with a steep decline to large masses, consistent with the existence of a preferred mass scale for each unique set of dimensionless free parameters. However, a sum total of results for various initial mass-to-flux ratios yields a broad distribution reminiscent of observed core mass distributions. Core shapes are mostly near-circular in the plane of the sheet for subcritical clouds, but become progressively more elongated for clouds with increasing initial mass-to-flux ratio. Field lines above the cloud midplane remain closest to vertical in the ambipolar-drift driven core formation in subcritical clouds, and there is increasing amount of magnetic field curvature for clouds of increasing mass-to-flux ratio. Based on our results, we conclude that fragmentation spacings, magnitude of infall motions, core shapes, and, especially, the curvature of magnetic field morphology, may serve as indirect observational means of determining a cloud’s ambient mass-to-flux ratio.

Formation of Massive Primordial Stars in a Reionized Gas

We use cosmological hydrodynamic simulations with unprecedented resolution to study the formation of primordial stars in an ionized gas at high redshifts. Our approach includes all the relevant atomic and molecular physics to follow the thermal evolution of a prestellar gas cloud to very high densities of ~1018 cm-3. We locate a star-forming gas cloud within a reionized region in our cosmological simulation. The gas cloud cools down to a few tens of kelvins by HD line cooling, and this is lower than possible by H2 cooling only. Owing to the low temperature, the first runaway collapse is triggered when the gas cloud's mass is ~40 M☉. We show that the cloud core remains stable against chemothermal instability and also against gravitational deformation throughout its evolution. Consequently, a single protostellar seed is formed, which accretes the surrounding hot gas at the rate 10-3 M☉ yr-1. We carry out protostellar evolution calculations using the inferred accretion rate. The resulting mass of the star when it reaches the zero-age main sequence is MZAMS ~ 40 M☉. Since the obtained MZAMS is as large as the mass of the collapsing parent cloud, the final stellar mass is likely close to this value. Such massive, rather than exceptionally massive, primordial stars are expected to cause early chemical enrichment of the universe by exploding as black hole-forming super/hypernovae and may also be progenitors of high-redshift γ-ray bursts. The elemental abundance patterns of recently discovered hyper-metal-poor stars suggest that they might have been born from the interstellar medium that was metal-enriched by the supernovae of these massive primordial stars.

Dissipation of Magnetic Flux in Primordial Star Formation: From Run-away Phase to Mass-Accretion Phase

Abstract We investigate the dissipation of magnetic flux in primordial star-forming clouds throughout their collapse, including the run-away collapse phase as well as the accretion phase. We solve the energy equation and the non-equilibrium chemical reactions in the collapsing gas, in order to obtain the radial distribution of the ionized fraction during the collapse. As a result, we find that the ionized fraction is high enough for the magnetic field to couple with the gas throughout evolution of the cloud. This result suggests that the jet formation from protostars as well as the activation of magneto–rotational instability in the accretion disk are enabled in the presence of the cosmological seed magnetic flux proposed by Langer, Puget, and Aghanim (2003, Phys. Rev. D67, 43505).

Early Cosmological Hii/HeiiiRegions and Their Impact on Second‐Generation Star Formation

We present the results of three-dimensional radiation hydrodynamics simulations of the formation and evolution of early H II/He III regions around the first stars. Cooling and recollapse of the gas in the relic H II region is also followed in a full cosmological context, until second-generation stars are formed. We first carry out ray-tracing simulations of ionizing radiation transfer from the first star. Hydrodynamics is directly coupled with photoionization heating as well as radiative and chemical cooling. The photoionized hot gas is evacuated out of the host halo at a velocity of ~30 km s-1. This radiative feedback effect quenches further star formation within the halo for over tens to a hundred million years. We show that the thermal and chemical evolution of the photoionized gas in the relic H II region is remarkably different from that of a neutral primordial gas. Efficient molecular hydrogen production in the recombining gas enables it to cool to ~100 K, where fractionation of HD/H2 occurs. The gas further cools by HD line cooling down to a few tens of kelvins. Interestingly, at high redshifts (z > 10), the minimum gas temperature is limited by that of the cosmic microwave background with TCMB = 2.728(1 + z). The gas cloud experiences runaway collapse when its mass is ~40 M☉, which is significantly smaller than a typical clump mass of ~200-300 M☉ for early primordial gas clouds. We argue that massive, rather than very massive, primordial stars may form in the relic H II region. Such stars might be responsible for early metal enrichment of the interstellar medium from which recently discovered hyper-metal-poor stars were born.

Galaxy Bulge Formation: Interplay with Dark Matter Halo and Central Supermassive Black Hole

We present a simple scenario where the formation of galactic bulges was regulated by the dark halo gravity and regulates the growth of the central supermassive black hole. Assuming the angular momentum is low, we suggest that bulges form in a runaway collapse due to the "gravothermal" instability once the central gas density or pressure exceeds a certain threshold. We emphasize that the threshold is nearly universal, set by the background NFW dark matter gravity gDM ~ 1.2 × 10-8 cm s-2 in the central cusps of halos. Unlike known thresholds for gradual formation of galaxy disks, we show that the universal "halo-regulated" star formation threshold for spheroids matches the very high star formation rate and star formation efficiency seen in high-redshift observations of central starburst regions. The starburst feedback also builds up a pressure shortly after the collapse. This large pressure could act both outward to halt further infall of gas from larger scales and inward to counter the Compton-thick wind launched from the central black hole in an Eddington accretion. Assuming the feedback balances inward and outward forces, our scenario naturally gives rise to the black hole-bulge relationships observed in the local universe.

Composite steel-framed structures in fire with protected and unprotected edge beams

The structural behaviour of a steel–concrete composite frame subject to a natural fire is analysed using a numerical model. The behaviour is compared when fire protection is applied to only the external beams and when no beams are fire protected. The behaviour of the structure in the two cases is significantly different. When the edge beams are protected the floor slab tends to span in 2 directions because the edge beams provide sufficient support around the perimeter of the floor for tensile membrane action to develop. When the edge beams are unprotected the slab tends to span in only one direction in a manner similar to a beam in catenary action. Catenary action is a weaker load carrying mechanism than tensile membrane action. As a consequence of the weaker mechanism, when the edge beams are unprotected, the columns displace inwards towards the end of the fire indicating the possibility of imminent runaway collapse. The pattern of mechanical strains in the floor slab reinforcement depends on the load carrying mechanism and therefore on whether edge beam protection is included. Although the average mechanical tensile strains are higher when the edge beams are protected the highest strains occur when the beams are unprotected. Conversely, an instability in the primary beam occurs at much lower temperatures when the edge beams are protected. It is concluded that fire protecting the edge beams of the structural layout studied has a number of effects on the fire resistance of the structure, some beneficial, some detrimental, however, in general, fire protecting the edge beams provides an increased level of fire resistance.