Primordial Star Formation Research Articles

Minimum star-forming halo mass in axion cosmology

ABSTRACT Elucidating the particle physics nature of dark matter (DM) is one of the great challenges in modern science. The current lack of any direct DM detections in the laboratory heightens the need for astrophysical constraints, extending the search to DM models beyond the popular weakly interacting massive particle scenario. We here apply the classical Rees–Ostriker–Silk cooling criterion for galaxy formation to models with ultralight axion DM, also known as fuzzy dark matter (FDM). The resulting constraints provide a heuristic framework for upcoming observations, and our approximate analysis motivates the need for future self-consistent simulations of FDM structure formation. We use observational constraints for the DM hosts of ultra-faint dwarf (UFD) galaxies in the Local Group, together with the redshift constraints for the onset of primordial star formation from the recent EDGES 21-cm cosmology measurement, to illustrate this approach. We find that the existing constraints are straightforward to reconcile with standard ΛCDM, but disfavour FDM axion masses below ${\sim } 10^{-21}\, {\rm eV}/c^2$. The future potential for harnessing astrophysical probes of DM particle physics is compelling.

First star formation in ultralight particle dark matter cosmology

Abstract The formation of the first stars in the high-redshift Universe is a sensitive probe of the small-scale, particle physics nature of dark matter (DM). We carry out cosmological simulations of primordial star formation in ultralight, axion-like particle DM cosmology, with masses of 10−22 and 10−21 eV, with de Broglie wavelengths approaching galactic scales (∼ kpc). The onset of star formation is delayed, and shifted to more massive host structures. For the lightest DM particle mass explored here, first stars form at z ∼ 7 in structures with ∼109 M⊙, compared to the standard minihalo environment within the Λ cold dark matter (ΛCDM) cosmology, where z ∼ 20–30 and ∼105–106 M⊙. Despite this greatly altered DM host environment, the thermodynamic behaviour of the metal-free gas as it collapses into the DM potential well asymptotically approaches a very similar evolutionary track. Thus, the fragmentation properties are predicted to remain the same as in ΛCDM cosmology, implying a similar mass scale for the first stars. These results predict intense starbursts in the axion cosmologies, which may be amenable to observations with the James Webb Space Telescope.

THE IMPACT OF FEEDBACK DURING MASSIVE STAR FORMATION BY CORE ACCRETION

Abstract We study feedback during massive star formation using semi-analytic methods, considering the effects of disk winds, radiation pressure, photoevaporation, and stellar winds, while following protostellar evolution in collapsing massive gas cores. We find that disk winds are the dominant feedback mechanism setting star formation efficiencies (SFEs) from initial cores of ∼0.3–0.5. However, radiation pressure is also significant to widen the outflow cavity causing reductions of SFE compared to the disk-wind only case, especially for > 100 M ⊙ star formation at clump mass surface densities Σ cl ≲ 0.3 g cm − 2 . Photoevaporation is of relatively minor importance due to dust attenuation of ionizing photons. Stellar winds have even smaller effects during the accretion stage. For core masses M c ≃ 10 – 1000 M ⊙ and Σ cl ≃ 0.1 – 3 g cm − 2 , we find the overall SFE to be ε ¯ * f = 0.31 ( R c / 0.1 pc ) − 0.39 , potentially a useful sub-grid star formation model in simulations that can resolve pre-stellar core radii, R c = 0.057 ( M c / 60 M ⊙ ) 1 / 2 ( Σ cl / g cm − 2 ) − 1 / 2 pc . The decline of SFE with M c is gradual with no evidence for a maximum stellar-mass set by feedback processes up to stellar masses of m * ∼ 300 M ⊙ . We thus conclude that the observed truncation of the high-mass end of the IMF is shaped mostly by the pre-stellar core mass function or internal stellar processes. To form massive stars with the observed maximum masses of ∼150– 300 M ⊙ , initial core masses need to be ≳ 500 – 1000 M ⊙ . We also apply our feedback model to zero-metallicity primordial star formation, showing that, in the absence of dust, photoevaporation staunches accretion at ∼ 50 M ⊙ . Our model implies radiative feedback is most significant at metallicities ∼ 10 − 2 Z ⊙ , since both radiation pressure and photoevaporation are effective in this regime.

On the existence of accretion-driven bursts in massive star formation

Abstract Accretion-driven luminosity outbursts are a vivid manifestation of variable mass accretion on to protostars. They are known as the so-called FU Orionis phenomenon in the context of low-mass protostars. More recently, this process has been found in models of primordial star formation. Using numerical radiation hydrodynamics simulations, we stress that present-day forming massive stars also experience variable accretion and show that this process is accompanied by luminous outbursts induced by the episodic accretion of gaseous clumps falling from the circumstellar disc on to the protostar. Consequently, the process of accretion-induced luminous flares is also conceivable in the high-mass regime of star formation and we propose to regard this phenomenon as a general mechanism that can affect protostars regardless of their mass and/or the chemical properties of the parent environment in which they form. In addition to the commonness of accretion-driven outbursts in the star formation machinery, we conjecture that luminous flares from regions hosting forming high-mass stars may be an observational implication of the fragmentation of their accretion discs.

Radiative feedback and cosmic molecular gas: the role of different radiative sources

We present results from multifrequency radiative hydrodynamical chemistry simulations addressing primordial star formation and related stellar feedback from various populations of stars, stellar energy distributions (SEDs) and initial mass functions. Spectra for massive stars, intermediate-mass stars and regular solar-like stars are adopted over a grid of 150 frequency bins and consistently coupled with hydrodynamics, heavy-element pollution and non-equilibrium species calculations. Powerful massive population III stars are found to be able to largely ionize H and, subsequently, He and He$^+$, causing an inversion of the equation of state and a boost of the Jeans masses in the early intergalactic medium. Radiative effects on star formation rates are between a factor of a few and 1 dex, depending on the SED. Radiative processes are responsible for gas heating and photoevaporation, although emission from soft SEDs has minor impacts. These findings have implications for cosmic gas preheating, primordial direct-collapse black holes, the build-up of "cosmic fossils" such as low-mass dwarf galaxies, the role of AGNi during reionization, the early formation of extended disks and angular-momentum catastrophe.

Role of the $\mathrm{H}_2^+$ channel in the primordial star formation under strong radiation field and the critical intensity for the supermassive star formation

We investigate the role of the |$\mathrm{H}_2^+$| channel on H2 molecule formation during the collapse of primordial gas clouds immersed in strong radiation fields which are assumed to have the shape of a diluted blackbody spectra with temperature Trad. Since the photodissociation rate of |$\mathrm{H_2^+}$| depends on its level population, we take full account of the vibrationally resolved |$\mathrm{H}_2^+$| kinetics. We find that in clouds under soft but intense radiation fields with spectral temperature Trad ≲ 7000 K, the |$\mathrm{H_2^+}$| channel is the dominant H2 formation process. On the other hand, for harder spectra with Trad ≳ 7000 K, the H− channel takes over |$\mathrm{H_2^+}$| in the production of molecular hydrogen. We calculate the critical radiation intensity needed for supermassive star formation by direct collapse and examine its dependence on the |$\mathrm{H_2^+}$| level population. Under the assumption of local thermodynamic equilibrium (LTE) level population, the critical intensity is underestimated by a factor of a few for soft spectra with Trad ≲ 7000 K. For harder spectra, the value of the critical intensity is not affected by the level population of |$\mathrm{H_2^+}$|⁠. This result justifies previous estimates of the critical intensity assuming LTE populations since radiation sources like young and/or metal-poor galaxies are predicted to have rather hard spectra.

Preserving chemical signatures of primordial star formation in the first low-mass stars

We model early star forming regions and their chemical enrichment by Population III (Pop III) supernovae with nucleosynthetic yields featuring high [C/Fe] ratios and pair-instability supernova (PISN) signatures. We aim to test how well these chemical abundance signatures are preserved in the gas prior to forming the first long-lived low-mass stars (or second-generation stars). Our results show that second-generation stars can retain the nucleosynthetic signature of their Pop III progenitors, even in the presence of nucleosynthetically normal Pop III core-collapse supernovae. We find that carbon-enhanced metal-poor stars are likely second-generation stars that form in minihaloes. Furthermore, it is likely that the majority of Pop III supernovae produce high [C/Fe] yields. In contrast, metals ejected by a PISN are not concentrated in the first star forming haloes, which may explain the absence of observed PISN signatures in metal-poor stars. We also find that unique Pop III abundance signatures in the gas are quickly wiped out by the emergence of Pop II supernovae. We caution that the observed fractions of stars with Pop III signatures cannot be directly interpreted as the fraction of Pop III stars producing that signature. Such interpretations require modelling the metal enrichment process prior to the second-generation stars' formation, including results from simulations of metal mixing. The full potential of stellar archaeology can likely be reached in ultra-faint dwarf galaxies, where the simple formation history may allow for straightforward identification of second-generation stars.

Formation of primordial supermassive stars by burst accretion

A promising formation channel of SMBHs at redshift 6 is the so-called DC model, which posits that a massive seed BH forms through gravitational collapse of a $\sim 10^5~M_\odot$ SMS. We study the evolution of such a SMS growing by rapid mass accretion. In particular, we examine the impact of time-dependent mass accretion of repeating burst and quiescent phases that are expected to occur with a self-gravitating circumstellar disk. We show that the stellar evolution with such episodic accretion differs qualitatively from that expected with a constant accretion rate, even if the mean accretion rate is the same. Unlike the case of constant mass accretion, whereby the star expands roughly following $R_* \simeq 2.6 \times 10^3 R_\odot (M_*/100~M_\odot)^{1/2}$, the protostar can substantially contract during the quiescent phases between accretion bursts. The stellar effective temperature and ionizing photon emissivity increase accordingly as the star contracts, which can cause strong ionizing feedback and halt the mass accretion onto the star. With a fixed duration of the quiescent phase $\Delta t_{\rm q}$, such contraction occurs in early evolutionary phases, i.e. for $M_* \lesssim 10^3~M_\odot$ with $\Delta t_{\rm q} \simeq 10^3$ yr. For later epochs and larger masses but the same $\Delta t_{\rm q}$, contraction is negligible even during quiescent phases. With larger quiescent times $\Delta t_{\rm q}$, however, the star continues to contract during quiescent phases even for the higher stellar masses. We show that such behavior is well understood by comparing the interval time and the thermal relaxation time for a bloated surface layer. We conclude that the UV radiative feedback becomes effective if the quiescent phase associated by the burst accretion is longer than $\sim 10^3$ yr, which is possible in an accretion disk forming in the direct collapse model.

Primordial star formation under the influence of far ultraviolet radiation: 1540 cosmological haloes and the stellar mass distribution

We perform a large set of cosmological simulations of early structure formation and follow the formation and evolution of 1540 star-forming gas clouds to derive the mass distribution of primordial stars. The star formation in our cosmological simulations is characterized by two distinct populations, the so-called Population III.1 stars and primordial stars formed under the influence of far ultraviolet (FUV) radiation (Population III.2D stars). In this work, we determine the stellar masses by using the dependences on the physical properties of star-forming cloud and/or the external photodissociating intensity from nearby primordial stars, which are derived from the results of two-dimensional radiation hydrodynamic simulations of protostellar feedback. The characteristic mass of the Pop III stars is found to be a few hundred solar masses at z ~ 25, and it gradually shifts to lower masses with decreasing redshift. At high redshifts z > 20, about half of the star-forming gas clouds are exposed to intense FUV radiation and thus give birth to massive Pop III.2D stars. However, the local FUV radiation by nearby Pop III stars becomes weaker at lower redshifts, when typical Pop III stars have smaller masses and the mean physical separation between the stars becomes large owing to cosmic expansion. Therefore, at z < 20, a large fraction of the primordial gas clouds host Pop III.1 stars. At z =< 15, the Pop III.1 stars are formed in relatively cool gas clouds due to efficient radiative cooling by H_2 and HD molecules; such stars have masses of a few x 10 Msun. Since the stellar evolution and the final fate are determined by the stellar mass, Pop III stars formed at different epochs play different roles in the early universe.

A NEW APPROACH TO DETERMINE OPTICALLY THICK H2COOLING AND ITS EFFECT ON PRIMORDIAL STAR FORMATION

We present a new method for estimating the H2 cooling rate in the optically thick regime in simulations of primordial star formation. Our new approach is based on the TreeCol algorithm, which projects matter distributions onto a spherical grid to create maps of column densities for each fluid element in the computational domain. We have improved this algorithm by using the relative gas velocities to weight the individual matter contributions with the relative spectral line overlaps, in order to properly account for the Doppler effect. We compare our new method to the widely used Sobolev approximation, which yields an estimate for the column density based on the local velocity gradient and the thermal velocity. This approach generally underestimates the photon escape probability because it neglects the density gradient and the actual shape of the cloud. We present a correction factor for the true line overlap in the Sobolev approximation and a new method based on local quantities, which fits the exact results reasonably well during the collapse of the cloud, with the error in the cooling rates always being less than 10%. Analytical fitting formulae fail at determining the photon escape probability after formation of the first protostar (error of ∼40%) because they are based on the assumption of spherical symmetry and therefore break down once a protostellar accretion disk has formed. Our method yields lower temperatures and hence promotes fragmentation for densities above ∼1010 cm−3 at a distance of ∼200 AU from the first protostar. Since the overall accretion rates are hardly affected by the cooling implementation, we expect Pop III stars to have lower masses in our simulations, compared to the results of previous simulations that used the Sobolev approximation.

The rich complexity of 21-cm fluctuations produced by the first stars

We explore the complete history of the 21-cm signal in the redshift range z = 7-40. This redshift range includes various epochs of cosmic evolution related to primordial star formation, and should be accessible to existing or planned low-frequency radio telescopes. We use semi-numerical computational methods to explore the fluctuation signal over wavenumbers between 0.03 and 1 Mpc$^{-1}$, accounting for the inhomogeneous backgrounds of Ly-$\alpha$, X-ray, Lyman-Werner and ionizing radiation. We focus on the recently noted expectation of heating dominated by a hard X-ray spectrum from high-mass X-ray binaries. We study the resulting delayed cosmic heating and suppression of gas temperature fluctuations, allowing for large variations in the minimum halo mass that contributes to star formation. We show that the wavenumbers at which the heating peak is detected in observations should tell us about the characteristic mean free path and spectrum of the emitted photons, thus giving key clues as to the character of the sources that heated the primordial Universe. We also consider the line-of-sight anisotropy, which allows additional information to be extracted from the 21-cm signal. For example, the heating transition at which the cosmic gas is heated to the temperature of the cosmic microwave background should be clearly marked by an especially isotropic power spectrum. More generally, an additional cross-power component $P_X$ directly probes which sources dominate 21-cm fluctuations. In particular, during cosmic reionization (and after the just-mentioned heating transition), $P_X$ is negative on scales dominated by ionization fluctuations and positive on those dominated by temperature fluctuations.

PAIR INSTABILITY SUPERNOVAE OF VERY MASSIVE POPULATION III STARS

Numerical studies of primordial star formation suggest that the first stars in the universe may have been very massive. Stellar models indicate that non-rotating Population III stars with initial masses of 140-260 Msun die as highly energetic pair-instability supernovae. We present new two-dimensional simulations of primordial pair-instability supernovae done with the CASTRO code. Our simulations begin at earlier times than previous multidimensional models, at the onset of core collapse, to capture any dynamical instabilities that may be seeded by collapse and explosive burning. Such instabilities could enhance explosive yields by mixing hot ash with fuel, thereby accelerating nuclear burning, and affect the spectra of the supernova by dredging up heavy elements from greater depths in the star at early times. Our grid of models includes both blue supergiants and red supergiants over the range in progenitor mass expected for these events. We find that fluid instabilities driven by oxygen and helium burning arise at the upper and lower boundaries of the oxygen shell $\sim$ 20 - 100 seconds after core bounce. Instabilities driven by burning freeze out after the SN shock exits the helium core. As the shock later propagates through the hydrogen envelope, a strong reverse shock forms that drives the growth of Rayleigh--Taylor instabilities. In red supergiant progenitors, the amplitudes of these instabilities are sufficient to mix the supernova ejecta.

ONE HUNDRED FIRST STARS: PROTOSTELLAR EVOLUTION AND THE FINAL MASSES

We perform a large set of radiation hydrodynamics simulations of primordial star formation in a fully cosmological context. Our statistical sample of 100 First Stars show that the first generation of stars have a wide mass distribution M_popIII = 10 ~ 1000 M_sun. We first run cosmological simulations to generate a set of primordial star-forming gas clouds. We then follow protostar formation in each gas cloud and the subsequent protostellar evolution until the gas mass accretion onto the protostar is halted by stellar radiative feedback. The accretion rates differ significantly among the primordial gas clouds which largely determine the final stellar masses. For low accretion rates the growth of a protostar is self-regulated by radiative feedback effects and the final mass is limited to several tens of solar masses. At high accretion rates the protostar's outer envelope continues to expand and the effective surface temperature remains low; such protostars do not exert strong radiative feedback and can grow in excess to one hundred solar masses. The obtained wide mass range suggests that the first stars play a variety of roles in the early universe, by triggering both core-collapse supernovae and pair-instability supernovae as well as by leaving stellar mass black holes. We find certain correlations between the final stellar mass and the physical properties of the star-forming cloud. These correlations can be used to estimate the mass of the first star from the properties of the parent cloud or of the host halo, without following the detailed protostellar evolution.

Primordial star formation: relative impact of H2three-body rates and initial conditions

Population III stars are the first stars in the Universe to form at z=20-30 out of a pure hydrogen and helium gas in minihalos of 10^5-10^6 M$_\odot$ . Cooling and fragmentation is thus regulated via molecular hydrogen. At densities above 10^8 cm$^{-3}$, the three-body H2 formation rates are particularly important for making the gas fully molecular. These rates were considered to be uncertain by at least a few orders of magnitude. We explore the impact of new accurate three-body H2 formation rates derived by Forrey (2013) for three different minihalos, and compare to the results obtained with three-body rates employed in previous studies. The calculations are performed with the cosmological hydrodynamics code ENZO (release 2.2) coupled with the chemistry package KROME (including a network for primordial chemistry), which was previously shown to be accurate in high resolution simulations. While the new rates can shift the point where the gas becomes fully molecular, leading to a different thermal evolution, there is no trivial trend in how this occurs. While one might naively expect the results to be inbetween the calculations based on Palla et al. (1983) and Abel et al. (2002), the behavior can be close to the former or the latter depending on the dark matter halo that is explored. We conclude that employing the correct three-body rates is about as equally important as the use of appropriate initial conditions, and that the resulting thermal evolution needs to be calculated for every halo individually.

Sturmian theory of three-body recombination: Application to the formation of H2in primordial gas

A Sturmian theory of three-body recombination is presented which provides a unified treatment of bound states, quasi-bound states, and continuum states. The Sturmian representation provides a numerical quadrature of the two-body continuum which may be used to generate a complete set of states within any desired three-body recombination pathway. Consequently, the dynamical calculation may be conveniently formulated using the simplest energy transfer mechanism, even for reactive systems which allow substantial rearrangement. The Sturmian theory generalizes the quantum kinetic theory of Snider and Lowry [J. Chem. Phys. 61, 2330 (1974)] to include metastable states which are formed as independent species. Steady-state rate constants are expressed in terms of a pathway-independent part plus a non-equilibrium correction which depends on tunneling lifetimes and pressure. Numerical results are presented for H$_2$ recombination due to collisions with H and He using quantum mechanical coupled states and infinite order sudden approximations. These results may be used to remove some of the uncertainties that have limited astrophysical simulations of primordial star formation.

PHOTOEVAPORATION OF CIRCUMSTELLAR DISKS REVISITED: THE DUST-FREE CASE

Photoevaporation by stellar ionizing radiation is believed to play an important role in the dispersal of disks around young stars. The mass loss model for dust-free disks developed by Hollenbach et al. is currently regarded as a conventional one and has been used in a wide variety of studies. However, the rate in this model was derived by the crude so-called 1+1D approximation of ionizing radiation transfer, which assumes that diffuse radiation propagates in a direction vertical to the disk. In this study, we revisit the photoevaporation of dust-free disks by solving the 2D axisymmetric radiative transfer for steady-state disks. Unlike that solved by the conventional model, we determine that direct stellar radiation is more important than the diffuse field at the disk surface. The radial density distribution at the ionization boundary is represented by the single power-law with an index -3/2 in contrast to the conventional double power-law. For this distribution, the photoevaporation rate from the entire disk can be written as a function of the ionizing photon emissivity, Phi_EUV, from the central star and the disk outer radius, r_d, as follows: Mdot_PE = 5.4 x 10^-5 x (Phi_EUV/10^49 sec^-1)^1/2 x (r_d/1000 AU)^1/2 Msun/yr. This new rate depends on the outer disk radius rather than on the gravitational radius as in the conventional model, caused by the enhanced contribution to the mass loss from the outer disk annuli. In addition, we discuss its applications to present-day as well as primordial star formation.

RATE OF FORMATION OF HYDROGEN MOLECULES BY THREE-BODY RECOMBINATION DURING PRIMORDIAL STAR FORMATION

Astrophysical models of primordial star formation require rate constants for three-body recombination as input. The current status of these rates for H2 due to collisions with H is far from satisfactory, with published rate constants showing orders of magnitude disagreement at the temperatures relevant for H2 formation in primordial gas. This letter presents an independent calculation of this recombination rate constant as a function of temperature. An analytic expression is provided for the rate constant which should be more reliable than ones currently being used in astrophysical models.

Magnetic fields during high redshift structure formation

AbstractWe explore the amplification of magnetic fields in the high‐redshift Universe. For this purpose, we perform high‐resolution cosmological simulations following the formation of primordial halos with ∼ ⊙ 107 M, revealing the presence of turbulent structures and complex morphologies at resolutions of at least 32 cells per Jeans length. Employing a turbulence subgrid‐scale model, we quantify the amount of unresolved turbulence and show that the resulting turbulent viscosity has a significant impact on the gas morphology, suppressing the formation of low‐mass clumps. We further demonstrate that such turbulence implies the efficient amplification of magnetic fields via the small‐scale dynamo. We discuss the properties of the dynamo in the kinematic and non‐linear regime, and explore the resulting magnetic field amplification during primordial star formation. We show that field strengths of ∼ 10–5 G can be expected at number densities of ∼ 5 cm–3. (© 2013 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Impact of an accurate modelling of primordial chemistry in high-resolution studies

Abstract The formation of the first stars in the Universe is regulated by a sensitive interplay of chemistry and cooling with the dynamics of a self-gravitating system. As the outcome of the collapse and the final stellar masses depend sensitively on the thermal evolution, it is necessary to accurately model the thermal evolution in high-resolution simulations. As previous investigations raised doubts regarding the convergence of the temperature at high resolution, we investigate the role of the numerical method employed to model the chemistry and the thermodynamics. Here we compare the standard implementation in the adaptive-mesh refinement code enzo, employing a first-order backward differentiation formula (BDF), with the fifth-order accurate BDF solver dlsodes. While the standard implementation in enzo shows a strong dependence on the employed resolution, the results obtained with dlsodes are considerably more robust, both with respect to the chemistry and thermodynamics, but also for dynamical quantities such as density, total energy or the accretion rate. We conclude that an accurate modelling of the chemistry and thermodynamics is central for primordial star formation.

The First Billion Years project: the impact of stellar radiation on the co-evolution of Populations II and III

With the first metal enrichment by Population III (Pop III) supernovae (SNe), the formation of the first metal-enriched, Pop II stars becomes possible. In turn, Pop III star formation and early metal enrichment are slowed by the high-energy radiation emitted by Pop II stars. Thus, through the SNe and radiation they produce, Pops II and III co-evolve in the early Universe, one regulated by the other. We present large (4 Mpc)3, high-resolution cosmological simulations in which we self-consistently model early metal enrichment and the stellar radiation responsible for the destruction of the coolants (H2 and HD) required for Pop III star formation. We find that the molecule-dissociating stellar radiation produced both locally and over cosmological distances reduces the Pop III star formation rate at z ≳ 10 by up to an order of magnitude, to a rate per comoving volume of ≲ 10− 4 M⊙ yr− 1 Mpc− 3, compared to the case in which this radiation is not included. However, we find that the effect of Lyman–Werner (LW) feedback is to enhance the amount of Pop II star formation. We attribute this to the reduced rate at which gas is blown out of dark matter haloes by SNe in the simulation with LW feedback, which results in larger reservoirs for metal-enriched star formation. Even accounting for metal enrichment, molecule-dissociating radiation and the strong suppression of low-mass galaxy formation due to reionization at z ≲ 10, we find that Pop III stars are still formed at a rate of ∼ 10− 5 M⊙ yr− 1 Mpc− 3 down to z ∼ 6. This suggests that the majority of primordial pair-instability SNe that may be uncovered in future surveys will be found at z ≲ 10. We also find that the molecule-dissociating radiation emitted from Pop II stars may destroy H2 molecules at a high enough rate to suppress gas cooling and allow for the formation of supermassive primordial stars which collapse to form ∼ 105 M⊙ black holes.