Formation of SMBH seeds in Pop III star clusters through collisions : the importance of mass loss

Runaway collisions in dense clusters may lead to the formation of supermassive black hole (SMBH) seeds, and this process can be further enhanced by accretion, as recent models of SMBH seed formation in Population III star clusters have shown. This may explain the presence of supermassive black holes already at high redshift, $z>6$. However, in this context, mass loss during collisions was not considered and could play an important role for the formation of the SMBH seed. Here, we study the effect of mass loss, due to collisions of protostars, in the formation and evolution of a massive object in a dense primordial cluster. We consider both constant mass loss fractions as well as analytic models based on the stellar structure of the collision components. Our calculations indicate that mass loss can significantly affect the final mass of the possible SMBH seed. Considering a constant mass loss of 5% for every collision, we can lose between 60-80% of the total mass that is obtained if mass loss were not considered. Using instead analytical prescriptions for mass loss, the mass of the final object is reduced by 15-40%, depending on the accretion model for the cluster we study. Altogether, we obtain masses of the order of $10^4M_{\odot}$, which are still massive enough to be SMBH seeds.Comment: 12 pages, 9 figures, accepted by MNRA

Stellar collisions in flattened and rotating Pop. III star clusters

Fragmentation often occurs in disk-like structures, both in the early Universe and in the context of present-day star formation. Supermassive black holes (SMBHs) are astrophysical objects whose origin is not well understood; they weigh millions of solar masses and reside in the centers of galaxies. An important formation scenario for SMBHs is based on collisions and mergers of stars in a massive cluster, in which the most massive star moves to the center of the cluster due to dynamical friction. This increases the rate of collisions and mergers since massive stars have larger collisional cross sections. This can lead to runaway growth of a very massive star which may collapse to become an intermediate-mass black hole. Here we investigate the dynamical evolution of Miyamoto-Nagai models that allow us to describe dense stellar clusters, including flattening and different degrees of rotation. We find that the collisions in these clusters depend mostly on the number of stars and the initial stellar radii for a given radial size of the cluster. By comparison, rotation seems to affect the collision rate by at most $20\%$. For flatness, we compared spherical models with systems that have a scale height of about $10\%$ of their radial extent, in this case finding a change in the collision rate of less than $25\%$. Overall, we conclude that the parameters only have a minor effect on the number of collisions. Our results also suggest that rotation helps to retain more stars in the system, reducing the number of escapers by a factor of $2-3$ depending on the model and the specific realization. After two million years, a typical lifetime of a very massive star, we find that about $630$ collisions occur in typical models with $N=10^4$, $R=100$ $\rm~R_\odot$ and a half-mass radius of $0.1$ $\rm~pc$, leading to a mass of about $6.3\times10^3$ $\rm~M_\odot$ for the most massive object.Comment: 10 pages, 7 figure

C-axis electronic Raman scattering in Bi_2Sr_2CaCu_2O_{8+\delta}

We report a c-axis-polarized electronic Raman scattering study of Bi_2Sr_2CaCu_2O_{8+\delta} single crystals. In the normal state, a resonant electronic continuum extends to 1.5 eV and gains significant intensity as the incoming photon energy increases. In the superconducting state, a coherence 2\Delta peak appears around 50 meV, with a suppression of the scattering intensity at frequencies below the peak position. The peak energy, which is higher than that seen with in-plane polarizations, signifies distinctly different dynamics of quasiparticle excitations created with out-of-plane polarization.Comment: 12 pages, REVTEX, 3 postscript figure

Collisions in primordial star clusters: formation pathway for intermediate mass black holes

Collisions were suggested to potentially play a role in the formation of massive stars in present day clusters, and have likely been relevant during the formation of massive stars and intermediate mass black holes within the first star clusters. In the early Universe, the first stellar clusters were particularly dense, as fragmentation typically only occurred at densities above $10^9$cm$^{-3}$, and the radii of the protostars were enhanced due to the larger accretion rates, suggesting a potentially more relevant role of stellar collisions. We present here a detailed parameter study to assess how the number of collisions as well as the mass growth of the most massive object depends on the properties of the cluster, and we characterize the time evolution with three effective parameters, the time when most collisions occur, the duration of the collisions period, as well as the normalization required to obtain the total number of collisions. We apply our results to typical Population III (Pop.III) clusters of about $1000$M$_\odot$, finding that a moderate enhancement of the mass of the most massive star by a factor of a few can be expected. For more massive Pop.III clusters as expected in the first atomic cooling halos, we expect a more significant enhancement by a factor of $15-32$. We therefore conclude that collisions in massive Pop.III clusters were likely relevant to form the first intermediate mass black holes.publishe

C-axis Raman spectra of a normal plane-chain bilayer cuprate and the pseudogap

We investigate the Raman spectra in the geometry where both incident and scattered photon polarizations are parallel to the $\hat{z}$-direction, for a plane-chain bilayer coupled via a single-particle tunneling $t_\perp$. The Raman vertex is derived in the tight-binding limit and in the absence of Coulomb screening, the Raman intensity can be separated into intraband ($\propto t_\perp^4$) and interband ($\propto t_\perp^2$) transitions. In the small-$t_\perp$ limit, the interband part dominates and a pseudogap will appear as it does in the conductivity. Coulomb interactions bring in a two-particle coupling and result in the breakdown of intra- and interband separation. Nevertheless, when $t_\perp$ is small, the Coulomb screening ($\propto t_\perp^4$) has little effect on the intensity to which the unscreened interband transitions contribute most. In general, the total Raman spectra are strongly dependent on the magnitude of $t_\perp$.Comment: 23 pages, 6 figures, submitted to Phys. Rev.

Anomalous Self-Energy Effects of the B_1g Phonon in Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 Films

In Raman spectra of cuprate superconductors the gap shows up both directly, via a redistribution of the electronic background, the so-called "2Delta peaks", and indirectly, e.g. via the renormalization of phononic excitations. We use a model that allows us to study the redistribution and the related phonon self-energy effects simultaneously. We apply this model to the B_1g phonon of Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 films, where Pr or Ca substitution enables us to investigate under- and overdoped samples. While various self-energy effects can be explained by the strength and energy of the 2\Delta peaks, anomalies remain. We discuss possible origins of these anomalies.Comment: 6 pages including 4 figure

C-axis lattice dynamics in Bi-based cuprate superconductors

We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi2201, Bi2212 and Bi2223, we calculate the frequencies of the Brillouin-zone center phonon modes of A2u symmetry and suggest the phonon mode eigenvector patterns. We achieve good agreement between the calculated A2u eigenfrequencies and the experimental values of the c axis TO phonon frequencies which allows us to make a reliable phonon mode assignment for all three Bi-based cuprate superconductors. We also present the results of our shell model calculations for the Gamma-point A1g symmetry modes in Bi2201, Bi2212 and Bi2223 and suggest an assignment that is based on the published experimental Raman spectra. The superconductivity-induced phonon anomalies recently observed in the c axis infrared and resonant Raman scattering spectra in trilayer Bi2223 are consistently explained with the suggested assignment.Comment: 29 pages, 13 figure

A MODEST review

We present an account of the state of the art in the fields explored by the research community invested in 'Modeling and Observing DEnse STellar systems'. For this purpose, we take as a basis the activities of the MODEST-17 conference, which was held at Charles University, Prague, in September 2017. Reviewed topics include recent advances in fundamental stellar dynamics, numerical methods for the solution of the gravitational N-body problem, formation and evolution of young and old star clusters and galactic nuclei, their elusive stellar populations, planetary systems, and exotic compact objects, with timely attention to black holes of different classes of mass and their role as sources of gravitational waves. Such a breadth of topics reflects the growing role played by collisional stellar dynamics in numerous areas of modern astrophysics. Indeed, in the next decade, many revolutionary instruments will enable the derivation of positions and velocities of individual stars in the Milky Way and its satellites and will detect signals from a range of astrophysical sources in different portions of the electromagnetic and gravitational spectrum, with an unprecedented sensitivity. On the one hand, this wealth of data will allow us to address a number of long-standing open questions in star cluster studies; on the other hand, many unexpected properties of these systems will come to light, stimulating further progress of our understanding of their formation and evolution.Comment: 42 pages; accepted for publication in 'Computational Astrophysics and Cosmology'. We are much grateful to the organisers of the MODEST-17 conference (Charles University, Prague, September 2017). We acknowledge the input provided by all MODEST-17 participants, and, more generally, by the members of the MODEST communit

Stellar triples on the edge

Context. Hierarchical triple stars are ideal laboratories for studying the interplay between orbital dynamics and stellar evolution. Both mass loss from stellar winds and strong gravitational perturbations between the inner and outer orbit cooperate to destabilise triple systems. Aims. Our current understanding of the evolution of unstable triple systems is mainly built upon results from extensive binary-single scattering experiments. However, destabilised hierarchical triples cover a different region of phase space. Therefore, we aim to construct a comprehensive overview of the evolutionary pathways of destabilised triple-star systems. Methods. Starting from generic initial conditions, we evolved an extensive set of hierarchical triples using the code TRES, combining secular dynamics and stellar evolution. We detected those triples that destabilise due to stellar winds and/or gravitational perturbations. Their evolution was continued with a direct N-body integrator coupled to stellar evolution. Results. The majority of triples (54–69%) preserve their hierarchy throughout their evolution, which is in contradiction with the commonly adopted picture that unstable triples always experience a chaotic, democratic resonant interaction. The duration of the unstable phase was found to be longer than expected (103 − 4 crossing times, reaching up to millions), so that long-term stellar evolution effects cannot be neglected. The most probable outcome is dissolution of the triple into a single star and binary (42–45%). This occurs through the commonly known democratic channel, during which the initial hierarchy is lost and the lightest body usually escapes, but also through a hierarchical channel, during which the tertiary is ejected in a slingshot, independent of its mass. Collisions are common (13–24% of destabilised triples), and they mostly involve the two original inner binary components still on the main sequence (77–94%). This contradicts the idea that collisions with a giant during democratic encounters dominate (only 5–12%). Together with collisions in stable triples, we find that triple evolution is the dominant mechanism for stellar collisions in the Milky Way. Lastly, our simulations produce runaway and walk-away stars with speeds up to several tens of km/s, with a maximum of a few 100 km s−1. We suggest that destabilised triples can explain – or at least alleviate the tension behind – the origin of the observed (massive) runaway stars. Conclusions. A promising indicator for distinguishing triples that will follow the democratic or hierarchical route, is the relative inclination between the inner and outer orbits. Its influence can be summed up in two rules of thumb: (1) prograde triples tend to evolve towards hierarchical collisions and ejections, and (2) retrograde triples tend to evolve towards democratic encounters and a loss of initial hierarchy, unless the system is compact, which experience collision preferentially. The trends found in this work complement those found previously from binary-single scattering experiments, and together they will help to generalise and improve our understanding on the evolution of unstable triple systems of various origins