Primordial Star Formation Research Articles

Formation of Stellar Clusters and the Importance of Thermodynamics for Fragmentation

AbstractWe discuss results from numerical simulations of star cluster formation in the turbulent interstellar medium (ISM). The thermodynamic behavior of the star-forming gas plays a crucial role in fragmentation and determines the stellar mass function as well as the dynamic properties of the nascent stellar cluster. This holds for star formation in molecular clouds in the solar neighborhood as well as for the formation of the very first stars in the early universe. The thermodynamic state of the ISM is a result of the balance between heating and cooling processes, which in turn are determined by atomic and molecular physics and by chemical abundances. Features in the effective equation of state of the gas, such as a transition from a cooling to a heating regime, define a characteristic mass scale for fragmentation and so set the peak of the initial mass function of stars (IMF). As it is based on fundamental physical quantities and constants, this is an attractive approach to explain the apparent universality of the IMF in the solar neighborhood as well as the transition from purely primordial high-mass star formation to the more normal low-mass mode observed today.

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).

Feedback from First Radiation Sources: H - Photodissociation

During the epoch of reionization, the formation of radiation sources is accompanied by the growth of a H- photodissociating flux. We estimate the impact of this flux on the formation of molecular hydrogen and cooling in the first galaxies, assuming different types of radiation sources (e.g., Population II and Population III stars, miniquasars). We find that H- photodissociation reduces the formation of H2 molecules by a factor of Fs ~ 1 + 103ksxfδ-1, where x is the mean ionized fraction in the intergalactic medium, fesc is the fraction of ionizing photons that escape from their progenitor halos, δ is the local gas overdensity, and ks is an order unity constant that depends on the type of radiation source. By the time a significant fraction of the universe becomes ionized, H- photodissociation may significantly reduce the H2 abundance and, with it, the primordial star formation rate, delaying the progress of reionization.

Three-body recombination of hydrogen during primordial star formation

We consider the formation and destruction of H 2 and HD during the gravitational contraction of condensations of the primordial gas, which led to the formation of the first generation of stars (Population III stars). The determination of the populations of the bound rovibrational levels of molecular hydrogen is considered in detail. Initially, the rates per unit volume at which these levels are populated and depopulated are not in equilibrium. As the density increases, equilibrium between the rates of population and depopulation is established first, and then the levels gradually thermalize (i.e. their populations tend towards a Boltzmann distribution at the kinetic temperature of the gas), with the lowest energy levels thermalizing first. Ultimately, both the bound and the continuum states thermalize (i.e. attain a Saha distribution), but this process is not complete until densities n H ≈10 13 cm -3 are reached. Using the principle of microscopic reversibility, we derive an expression for the rate coefficient for three-body recombination of hydrogen which is found to differ significantly from the much used expression of Jacobs et al.

The role of HD cooling in primordial star formation

The role of HD cooling in the formation of primordial objects is examined by means of a great number of 1-D models of the collapse of halos, exploring a wide range of masses and virialization redshifts. We find that HD has very little effect upon the critical mass separating the objects which are likely to form stars from those which are not. We also find that, once the proto-stellar collapse has started, HD effects are quite negligible. Instead, HD effects can be important during the intermediate stage of gas fragmentation: objects below a certain mass scale (� 3×10 5 M⊙ at zvir = 20 in our “fiducial” case) can be cooled by HD down to T � 50 100 K, whereas H2 cooling never takes the gas below T � 200 K. The lower temperature implies a reduction of a factor � 10 in the Jeans mass of the fragmenting gas, and stars forming in such low-mass halos are probably less massive than their counterparts in larger halos. We estimate the importance of this mode of star formation through a variation of the Press-Schechter formalism, and find that it never exceeds the contribution of halos which are cooled by H2 only. Halos where HD is important account at best for a fraction �0.25 of the total primordial star formation. However, HD cooling might provide a channel through which long-lived low mass stars could be formed in primordial conditions.

Formation of Primordial Stars in a ΛCDM Universe

We study the formation of the first generation of stars in the standard cold dark matter model, using a very high-resolution hydordynamic simulations. Our simulation achieves a dynamic range of 10^{10} in length scale. With accurate treatment of atomic and molecular physics, it allows us to study the chemo-thermal evolution of primordial gas clouds to densities up to n = 10^{16}/cc without assuming any a priori equation of state; a six orders of magnitudes improvement over previous three-dimensional calculations. All the relevant atomic and molecular cooling and heating processes, including cooling by collision-induced continuum emission, are implemented. For calculating optically thick H2 cooling at high densities, we use the Sobolev method. To examine possible gas fragmentation owing to thermal instability, we compute explicitly the growth rate of isobaric perturbations. We show that the cloud core does not fragment in either the low-density or high-density regimes. We also show that the core remains stable against gravitational deformation and fragmentation. We obtain an accurate gas mass accretion rate within a 10 Msun innermost region around the protostar. The protostar is accreting the surrounding hot gas at a rate of 0.001-0.01 Msun/yr. From these findings we conclude that primordial stars formed in early minihalos are massive. We carry out proto-stellar evolution calculations using the obtained accretion rate. The resulting mass of the first star is M_ZAMS = 60-100 Msun, with the exact mass dependent on the actual accretion rate.

Population III Star Formation in a ΛWDM Universe

In this paper we examine aspects of primordial star formation in a gravitino warm dark matter universe with a cosmological constant (ΛWDM). We compare a set of simulations using a single cosmological realization but with a wide range of WDM particle masses that have not yet been conclusively ruled out by observations. The addition of a WDM component to the initial power spectrum results in a delay in the collapse of high-density gas at the center of the most massive halo in the simulation and, as a result, an increase in the virial mass of this halo at the onset of baryon collapse. Both of these effects become more pronounced as the WDM particle mass becomes smaller. A cosmology using a gravitino WDM power spectrum assuming a particle mass of mWDM 40 keV is effectively indistinguishable from the cold dark matter case, whereas the mWDM 15 keV case delays star formation in the parent halo by 108 yr. There is remarkably little scatter between simulations in the final properties of the protostar that forms at the center of the halo. The detailed evolution of the collapsing halo core in two representative WDM cosmologies is described. At low densities (nb 105 cm-3) the evolution of the two calculations is qualitatively similar, but occurs on significantly different timescales, with the halo in the lower particle mass calculation taking much longer to evolve over the same density range and reach runaway collapse. Once the gas in the center of the halo reaches relatively high densities (nb 105 cm-3), the overall evolution is essentially identical in the two calculations.

On the first generation of stars

We argue that the first stars may have spanned the conventional mass range rather than be identified with the very massive objects (∼100-10 3 M ⊙ ) favoured by numerical simulations. Specifically, we find that magnetic field generation processes acting in the first protostellar systems suffice to produce fields that exceed the threshold for magneto-rotational instability (MRI) to operate, and thereby allow the MRI dynamo to generate equipartition-amplitude magnetic fields on protostellar mass scales below ∼50 M ⊙ . Such fields allow primordial star formation to occur at essentially any metallicity by regulating angular momentum transfer, fragmentation, accretion and feedback in much the same way as occurs in conventional molecular clouds.

The HiiRegion of the First Star

Simulations predict that the first stars in a ΛCDM universe formed at redshifts z > 20 in minihalos with masses of about 106 M☉. We have studied their radiative feedback by simulating the propagation of ionization fronts (I-fronts) created by these first Population III stars (M* = 15-500 M☉) at z = 20, within the density field of a cosmological simulation of primordial star formation, outward through the host minihalo and into the surrounding gas. A three-dimensional ray-tracing calculation tracks the I-front once the H II region evolves a champagne flow inside the minihalo, after the early D-type I-front detaches from the shock and runs ahead, becoming R type. We take account of the hydrodynamic back-reaction by an approximate model of the central wind. We find that the escape fraction of ionizing radiation from the host halo increases with stellar mass, with 0.7 fesc 0.9 for 80 M*/M☉ 500. To quantify the ionizing efficiency of these stars as they begin cosmic reionization, we find that for M* 80 M☉, the ratio of gas mass ionized to stellar mass is ~60,000, roughly half the number of ionizing photons released per stellar baryon. Nearby minihalos are shown to trap the I-front, so their centers remain neutral. This is contrary to the recent suggestion that these stars would trigger formation of a second generation by fully ionizing neighboring minihalos, stimulating H2 formation in their cores. Finally, we discuss how the evacuation of gas from the host halo reduces the growth and luminosity of miniquasars that may form from black hole remnants of the first stars.

Cosmological Magnetic Field: A Fossil of Density Perturbations in the Early Universe

The origin of the substantial magnetic fields that are found in galaxies and on even larger scales, such as in clusters of galaxies, is yet unclear. If the second-order couplings between photons and electrons are considered, then cosmological density fluctuations, which explain the large-scale structure of the universe, can also produce magnetic fields on cosmological scales before the epoch of recombination. By evaluating the power spectrum of these cosmological magnetic fields on a range of scales, we show here that magnetic fields of 10(-18.1) gauss are generated at a 1-megaparsec scale and can be even stronger at smaller scales (10(-14.1) gauss at 10 kiloparsecs). These fields are large enough to seed magnetic fields in galaxies and may therefore have affected primordial star formation in the early universe.

The Number of Supernovae from Primordial Stars in the Universe

Recent simulations of the formation of the first luminous objects in the universe predict isolated very massive stars to form in dark matter halos with virial temperatures large enough to allow significant amounts of molecular hydrogen to form. We construct a semi-analytic model based on the Press-Schechter formalism and calibrate the minimum halos mass that may form a primordial star with the results from extensive adaptive mesh refinement simulations. The model also includes star formation in objects with virial temperatures in excess of ten thousand Kelvin. The free parameters are tuned to match the optical depth measurements by the WMAP satellite. The models explicitly includes the negative feedback of the destruction of molecular hydrogen by a soft UV background which is computed self-consistently. We predict high redshift supernova rates as one of the most promising tools to test the current scenario of primordial star formation. The supernova rate from primordial stars peaks at redshifts ~20. Using an analytic model for the luminosities of pair-instability supernovae we predict observable magnitudes and discuss possible observational strategies. Such supernovae would release enough metals corresponding to a uniform enrichment to a few hundred thousands of solar metalicity. If some of these stars produce gamma ray bursts our rates will be directly applicable to understanding the anticipated results from the SWIFT satellite. This study highlights the great potential for the James Webb space telescope in probing cosmic structure at redshifts greater than 20.

Chemical Evolution in Hierarchical Models of Cosmic Structure. I. Constraints on the Early Stellar Initial Mass Function

I present a new Galactic chemical evolution model motivated by and grounded in the hierarchical theory of galaxy formation, as expressed by a halo merger history of the Galaxy. This model accurately reproduces the "metallicity distribution function" (MDF) for Population II stars residing today in the Galactic halo. Model MDFs are calculated for a fiducial Galaxy formation scenario and a range of assumptions about the astrophysics of star formation and chemical enrichment at early times. The observed MDF and the apparent absence of true Population III stars from the halo strongly imply that there is some critical metallicity, Zcr ≲ 10-4 Z☉, below which low-mass star formation is inhibited and perhaps impossible. The observed constraints from the halo MDF, relative metal abundances from extremely metal-poor Galactic halo stars, and the ionizing photon budget needed to reionize the IGM together imply a stellar IMF below Zcr that is peaked in the range of massive stars that experience core-collapse supernovae, with mean mass ⟨M⟩ = 8-42 M☉. This mass range is similar to the masses predicted by models of primordial star formation that account for formation feedback. A set of five plausible IMF cases is presented, ranging from broadly peaked with mean mass ~15 M☉ to narrowly peaked at mean mass ~70 M☉. These IMF cases cannot be distinguished formally by the available constraints, but the models with lower characteristic mass produce overall better fits to the available data. The model also implies that metal-poor halo stars below [Fe/H] ≲ -3 had only 1-10 metal-free stars as their supernova precursors, such that the relative abundances in these halo stars exhibit IMF-weighted averages over the intrinsic yields of the first supernovae. This paper is the first part of a long-term project to connect the high-redshift in situ indicators of early star formation with the low-z, old remnants of the first stars.

The Formation Of The First Stars In The Universe

In this review, I survey our current understanding of how the very first stars in the universe formed, with a focus on three main areas of interest: the formation of the first protogalaxies and the cooling of gas within them, the nature and extent of fragmentation within the cool gas, and the physics – in particular the interplay between protostellar accretion and protostellar feedback – that serves to determine the final stellar mass. In each of these areas, I have attempted to show how our thinking has developed over recent years, aided in large part by the increasing ease with which we can now perform detailed numerical simulations of primordial star formation. I have also tried to indicate the areas where our understanding remains incomplete, and to identify some of the most important unsolved problems.

Nucleosynthesis, Reionization, and the Mass Function of the First Stars

We critique the hypothesis that the first stars were very massive stars (VMSs; M > 140 M☉). We review the two major lines of evidence for the existence of VMSs: (1) that the relative metal abundances of extremely metal-poor Galactic halo stars show evidence of VMS enrichment and (2) that the high electron-scattering optical depth (τe) to the cosmic microwave background found by the Wilkinson Microwave Anisotropy Probe (WMAP) requires VMSs for reionization in a concordance ΛCDM cosmology. The yield patterns of VMSs exploding as pair-instability supernovae are incompatible with the Fe-peak and r-process abundances in halo stars. Models including Type II supernovae and/or hypernovae from zero-metallicity progenitors with M = 8-40 M☉ can better explain the observed trends. We use the nucleosynthesis results and stellar evolution models to construct an initial mass function (IMF) for reionization. With a simple metal transport model, we estimate that halo enrichment curtails metal-free star formation after ~108 yr at z ~ 20. Because the lifetime-integrated ionizing photon efficiency of metal-free stars peaks at ~120 M☉ and declines at higher mass, an IMF with an approximate lower bound at M ~ 10-20 M☉ and no VMS can maximize the ionizing photon budget and still be consistent with the nucleosynthetic evidence. An IMF devoid of low-mass stars is justified independently by models of the formation of primordial stars. Using a semianalytic model for H I and He II reionization, we find that such an IMF can reproduce τe 0.10-0.14, consistent with the range from WMAP, without extreme astrophysical assumptions, provided that metal-free star formation persists 107-108 yr after star formation begins. Because stars in the mass range 50-140 M☉ are the most efficient sources of ionizing photons but are expected to collapse to black holes without releasing metals, this IMF effectively decouples early metal enrichment and early ionization. Such an IMF may allow the unique properties of the zero-metallicity IMF to persist longer than they would in the pure VMS case and to contribute significantly to the global ionizing photon budget before halo self-enrichment and/or interhalo metal transport truncates metal-free star formation. We conclude, on the basis of these results, that VMSs are not necessary to meet the existing constraints commonly taken to motivate them.

Induced formation of primordial low-mass stars

We show that the explosion of the first supernovae can trigger low-mass star formation via gravitational fragmentation of the supernova-driven gas shell. If the shell mass does not exceed the host galaxy gas mass, all explosions with energies E SN⩾10 51 erg can lead to shell fragmentation. However, the minimum ambient density required to induce such fragmentation is much larger, n 0>300 cm −3, for Type II supernovae than for pair-instability ones, which can induce star formation even at lower ambient densities. The typical mass of the unstable fragments is ∼10 4−7 M ⊙; their density is in the range 110–6×10 7 cm −3. Fragments have a metallicity strictly lower than 10 −2.6 Z ⊙ and large values of the gravitational-to-pressure force ratio f≃8. Based on these findings, we conclude that the second generation of stars produced by such self-propagating star formation is predominantly constituted by low-mass, long-living, extremely metal-poor (or even metal-free, if mixing is suppressed) stars. We discuss the implications of such results for Pop III star formation scenarios and for the most iron-poor halo star HE0107-5240.

The role of dust in “active” and “passive” low-metallicity star formation

We investigate the role of dust in star formation activity of extremely metal-poor blue compact dwarf galaxies (BCDs). Observations suggest that star formation in BCDs occurs in two different regimes: and passive. The BCDs host super star clusters (SSCs), and are characterised by compact size, rich H2 content, large dust optical depth, and high dust temperature; the passive BCDs are more diffuse with cooler dust, and lack SSCs and large amounts of H2. By treating physical processes concerning formation of stars and dust, we are able to simultaneously reproduce all the above properties of both modes of star formation (active and passive). We find that the difference between the two regimes can be understood through the variation of the compactness of the star-forming region: an mode emerges if the region is compact (with radius 500 cm −3 ). The dust, supplied from Type II supernovae in a compact star-forming region, effectively reprocesses the heating photons into the infrared and induces a rapid H2 formation over a period of several Myr. This explains the high infrared luminosity, high dust temperature, and large H2 content of active BCDs. Moreover, the gas in galaxies cools ( 100 pc and gas number density <100 cm −3 ). We finally discuss primordial star formation in high-redshift galaxies in the context of the and passive star formation scenario.

Primordial star formation triggered by UV photons from UHECR

The presence of ultra-high energy cosmic rays in the universe in the pre-ionization epoch enhances significantly H$_2$ kinetics in virialized halos. It results in more efficient radiative cooling and decreases the lower mass limit of the first star-forming systems. Consequently, the fraction of baryons contained in the first luminous objects and their contribution to the reionization of the universe can significantly increase in comparison with the standard scenario.

Detectability of Long Gamma‐Ray Burst Afterglows from Very High Redshifts

Gamma-ray bursts (GRBs) are promising tools for tracing the formation of high-redshift stars, including the first generation. At very high redshifts the reverse shock emission lasts longer in the observer frame, and its importance for detection and analysis purposes relative to the forward shock increases. We consider two different models for the GRB environment, based on current ideas about the redshift dependence of gas properties in galaxies and primordial star formation. We calculate the observed flux as a function of the redshift and observer time for typical GRB afterglows, taking into account intergalactic photoionization and Lyα absorption opacity, as well as extinction by the Milky Way. The fluxes in the X-ray and near-IR bands are compared with the sensitivity of different detectors such as Chandra, XMM, Swift XRT, and the James Webb Space Telescope (JWST). Using standard assumptions, we find that Chandra, XMM, and Swift XRT can potentially detect GRBs in the X-ray band out to very high redshifts z 30. In the K and M bands, the JWST and ground-based telescopes are potentially able to detect GRBs even 1 day after the trigger out to z ~ 16 and 33, if present. While the X-ray band is insensitive to the external density and to reverse shocks, the near-IR bands provide a sensitive tool for diagnosing both the environment and the reverse shock component.

The Formation of the First Stars. I. Mass Infall Rates, Accretion Disk Structure, and Protostellar Evolution

We present a theoretical model for primordial star formation. First we describe the structure of the initial gas cores as virialized, quasi-hydrostatic objects in accord with recent high-resolution numerical studies. The accretion rate can then be related to characteristic densities and temperatures that are set by the cooling properties of molecular hydrogen. We allow for rotation of the gas core, assuming angular momentum conservation inside the sonic point of the flow. In the typical case, most mass then reaches the star via an accretion disk. The structure of the inner region of this disk is described with the standard theory of viscous disks, but with allowance for the substantial energies absorbed in ionizing and dissociating the gas. The size of the protostar and its luminosity depend on the accretion rate, the energetics of the accreting gas, and the ability of the radiation to escape from the stellar accretion shock. We combine these models for the infall rate, inner disk structure, and protostellar evolution to predict the radiation field that is the basis for radiative feedback processes acting against infall (second paper in the series). For realistic initial angular momenta, the photosphere of the protostar is much smaller and hotter than in the spherical case, leading to stronger radiative feedback at earlier stages in the evolution. In particular, once the star is older than its Kelvin-Helmholtz time, contraction toward the main sequence causes a rapid increase in ionizing and far-ultraviolet luminosity at masses ~30 M? in the fiducial case. Since the cores out of which the first stars formed were much more massive than 30 M? and since feedback is dynamically unimportant at lower masses, we conclude that the first stars should have had masses 30 M?.

Stars of extragalactic origin in the solar neighborhood

For 77 main-sequence F–G stars in the solar neighborhood with published iron, magnesium, and europium abundances determined from high-dispersion spectra and with the ages estimated from theoretical isochrones, we calculated the spatial velocities using Hipparcos data and the Galactic orbital elements. A comparison with the orbital elements of the globular clusters that are known to have been accreted by our Galaxy in the past reveals stars of extragalactic origin. We show that the abundance ratios of r-and α-elements in all the accreted stars differ sharply from those in the stars that are genetically associated with the Galaxy. According to current theoretical models, europium is produced mainly in low-mass type-II supernovae (SNe II), while magnesium is synthesized in large quantities in high-mass SN II progenitors. Since all the old accreted stars of our sample exhibit a significant Eu overabundance relative to Mg, we conclude that the maximum masses of the SN II progenitors outside the Galaxy were much lower than those inside it. On the other hand, only a small number of young accreted stars exhibit low negative ratios [Eu/Mg]<0. This can be explained by the delay of primordial star formation and the explosions of high-mass SNe II in a relatively small part of extragalactic space. We provide evidence that the interstellar medium was weakly mixed at the early evolutionary stages of the Galaxy formed from a single protogalactic cloud, and that the maximum mass of the SN II progenitors increased in it with time simultaneously with the increase in mean metallicity.