Long-Term Evolution of Massive Black Hole Binaries. III. Binary Evolution in Collisional Nuclei

[Abridged] In galactic nuclei with sufficiently short relaxation times, binary supermassive black holes can evolve beyond their stalling radii via continued interaction with stars. We study this "collisional" evolutionary regime using both fully self-consistent N-body integrations and approximate Fokker-Planck models. The N-body integrations employ particle numbers up to 0.26M and a direct-summation potential solver; close interactions involving the binary are treated using a new implementation of the Mikkola-Aarseth chain regularization algorithm. Even at these large values of N, two-body scattering occurs at high enough rates in the simulations that they can not be simply scaled to the large-N regime of real galaxies. The Fokker-Planck model is used to bridge this gap; it includes, for the first time, binary-induced changes in the stellar density and potential. The Fokker-Planck model is shown to accurately reproduce the results of the N-body integrations, and is then extended to the much larger N regime of real galaxies. Analytic expressions are derived that accurately reproduce the time dependence of the binary semi-major axis as predicted by the Fokker-Planck model. Gravitational wave coalescence is shown to occur in <10 Gyr in nuclei with velocity dispersions below about 80 km/s. Formation of a core results from a competition between ejection of stars by the binary and re-supply of depleted orbits via two-body scattering. Mass deficits as large as ~4 times the binary mass are produced before coalescence. After the two black holes coalesce, a Bahcall-Wolf cusp appears around the single hole in one relaxation time, resulting in a nuclear density profile consisting of a flat core with an inner, compact cluster, similar to what is observed at the centers of low-luminosity spheroids.Comment: 21 page

Massive perturbers and the efficient merger of binary massive black holes

We show that dynamical relaxation in the aftermath of a galactic merger and the ensuing formation and decay of a binary massive black hole (MBH), are dominated by massive perturbers (MPs) such as giant molecular clouds or clusters. MPs accelerate relaxation by orders of magnitude relative to 2-body stellar relaxation alone, and efficiently scatter stars into the binary MBH's orbit. The 3-body star-binary MBH interactions shrink the binary MBH to the point where energy losses from the emission of gravitational waves (GW) lead to rapid coalescence. We model this process based on observed and simulated MP distributions and take into account the decreased efficiency of the star-binary MBH interaction due to acceleration in the galactic potential. We show that mergers of gas-rich galactic nuclei lead to binary MBH coalescence well within the Hubble time. Moreover, lower-mass binary MBHs (<10^8 Msun) require only a few percent of the typical gas mass in a post-merger nucleus to coalesce in a Hubble time. The fate of a binary MBH in a gas poor galactic merger is less certain, although massive stellar structures (e.g. clusters, stellar rings) could likewise lead to efficient coalescence. These coalescence events are observable by their strong GW emission. MPs thus increase the cosmic rate of such GW events, lead to a higher mass deficit in the merged galactic core and suppress the formation of triple MBH systems and the resulting ejection of MBHs into intergalactic space.Comment: 14 pages, 4 figures, 3 tables. More detailed explanations and changes in structure. Section on hypervelocity stars moved to another paper (in preparation). Results and conclusions unchanged. Accepted to Ap

Binding energy referencing for XPS in Alkali metal-based battery materials research (II): Application to complex composite electrodes

X-ray photoelectron spectroscopy (XPS) is a key method for studying (electro-)chemical changes in metal-ion battery electrode materials. In a recent publication, we pointed out a conflict in binding energy (BE) scale referencing at alkali metal samples, which is manifested in systematic deviations of the BEs up to several eV due to a specific interaction between the highly reactive alkali metal in contact with non-conducting surrounding species. The consequences of this phenomenon for XPS data interpretation are discussed in the present manuscript. Investigations of phenomena at surface-electrolyte interphase regions for a wide range of materials for both lithium and sodium-based applications are explained, ranging from oxide-based cathode materials via alloys and carbon-based anodes including appropriate reference chemicals. Depending on material class and alkaline content, specific solutions are proposed for choosing the correct reference BE to accurately define the BE scale. In conclusion, the different approaches for the use of reference elements, such as aliphatic carbon, implanted noble gas or surface metals, partially lack practicability and can lead to misinterpretation for application in battery materials. Thus, this manuscript provides exemplary alternative solutions

Wavelength-dependent reflectivity changes on gold at elevated electronic temperatures

Upon the excitation by an ultrashort laser pulse the conditions in a material can drastically change, altering its optical properties and therefore the relative amount of absorbed energy, a quan- tity relevant for determining the damage threshold and for developing a detailed simulation of a structuring process. The subject of interest in this work is the d-band metal gold which has an absorption edge marking the transition of free valence electrons and an absorbing deep d-band with bound electrons. Reflectivity changes are observed in experiment over a broad spectral range at ablation conditions. To understand the involved processes the laser excitation is modeled by a com- bination of first principle calculations with a two-temperature model. The description is kept most general and applied to realistically simulate the transfer of the absorbed energy of a Gaussian laser pulse into the electronic system at every point in space at every instance of time. An electronic temperature-dependent reflectivity map is calculated, describing the out of equilibrium reflectivity during laser excitation for photon energies from 0.9 - 6.4 eV, including inter- and intra-band transi- tions and a temperature-dependent damping factor. The main mechanisms are identified explaining the electronic temperature-dependent change in reflectivity: broadening of the edge of the occu- pied/unoccupied states around the chemical potential $\mu$, also leading to a shift of the $\mu$ and an increase of the collision rate of free s/p-band electrons with bound d-band holes

Renormalized spin coefficients in the accumulated orbital phase for unequal mass black hole binaries

We analyze galactic black hole mergers and their emitted gravitational waves. Such mergers have typically unequal masses with mass ratio of the order 1/10. The emitted gravitational waves carry the inprint of spins and mass quadrupoles of the binary components. Among these contributions, we consider here the quasi-precessional evolution of the spins. A method of taking into account these third post-Newtonian (3PN) effects by renormalizing (redefining) the 1.5 PN and 2PN accurate spin contributions to the accumulated orbital phase is developed.Comment: 10 pages, to appear in Class. Quantum Grav. GWDAW13 Proceedings Special Issue, v2: no typos conjectur