# Posts Tagged mass ratio

## Recent Postings from mass ratio

### Two-body gravitational spin-orbit interaction at linear order in the mass ratio

We analytically compute, to linear order in the mass-ratio, the "geodetic" spin precession frequency of a small spinning body orbiting a large (non-spinning) body to the eight-and-a-half post-Newtonian order, thereby extending previous analytical knowledge which was limited to the third post-Newtonian level. These results are obtained applying analytical gravitational self-force theory to the first-derivative level generalization of Detweiler’s gauge-invariant redshift variable. We compare our analytic results with strong-field numerical data recently obtained by S.~R.~Dolan et al. [Phys.\ Rev.\ D {\bf 89}, 064011 (2014)]. Our new, high-post-Newtonian-order results capture the strong-field features exhibited by the numerical data. We argue that the spin-precession will diverge as $\approx -0.14/(1-3y)$ as the light-ring is approached. We transcribe our kinematical spin-precession results into a corresponding improved analytic knowledge of one of the two (gauge-invariant) effective gyro-gravitomagnetic ratios characterizing spin-orbit couplings within the effective-one-body formalism. We provide simple, accurate analytic fits both for spin-precession and the effective gyro-gravitomagnetic ratio. The latter fit predicts that the linear-in-mass-ratio correction to the gyro-gravitomagnetic ratio changes sign before reaching the light-ring. This strong-field prediction might be important for improving the analytic modeling of coalescing spinning binaries.

### Photometric Investigation of the K-type Extreme-Shallow Contact Binary V1799 Orion

New multi-color light curves of the very short period K-type eclipsing binary V1799 Ori were obtained and analyzed with the W-D code. The photometric solutions reveal that the system is a W-type shallow-contact binary with a mass ratio of $q=1.335(\pm0.005)$ and a degree of contact about $f = 3.5(\pm1.1)\%$. In general, the results are in good agreement with which is reported by Samec. The remarkable O’Connell effects in the light curves are well explained by employing star spots on the binary surface, which confirms that the system is active at present. Several new times of light minimum were obtained. All the available times of light minimum were collected, along with the recalculated and new obtained. Applying a least-squares method to the constructed O-C diagram, a new ephemeris was derived for V1799 Ori. The orbital period is found to show a continuous weak increase at a rate of $1.8(\pm0.6)\times10^{-8}$ days$\cdot$yr$^{-1}$. The extreme-shallow contact, together with the period increase, suggests that the binary may be at a critical stage predicted by the TRO theory. \keywords{binaries : close — binaries : eclipsing — stars: individual (V1799 Ori)

### OGLE-2008-BLG-355Lb: A Massive Planet around A Late type Star

We report the discovery of a massive planet OGLE-2008-BLG-355Lb. The light curve analysis indicates a planet:host mass ratio of q = 0.0118 +/- 0.0006 at a separation of 0.877 +/- 0.010 Einstein radii. We do not measure a significant microlensing parallax signal and do not have high angular resolution images that could detect the planetary host star. Therefore, we do not have a direct measurement of the host star mass. A Bayesian analysis, assuming that all host stars have equal probability to host a planet with the measured mass ratio implies a host star mass of M_h = 0.37_{-0.17}^{+0.30} M_Sun and a companion of mass M_P = 4.6^{+3.7}_{-2.2} M_Jup, at a projected separation of r_proj = 1.70^{+0.29}_{-0.30} AU. The implied distance to the planetary system is D_L = 6.8 +/- 1.1 kpc. A planetary system with the properties preferred by the Bayesian analysis would be a challenge to the core-accretion model of planet formation, as the core-accretion model predicts that massive planets are far more likely to form around more massive host stars. This core accretion model prediction is not consistent with our Bayesian prior of an equal probability of host stars of all masses to host a planet with the measured mass ratio. So, if the core accretion model prediction is right, we should expect that follow-up high angular resolution observations will detect a host star with a mass in the upper part of the range allowed by the Bayesian analysis. That is, the host would probably be a K or G dwarf.

### The Self-Force Problem: Local Behaviour of the Detweiler-Whiting Singular Field

The growing reality of gravitational wave astronomy is giving age-old problems a new lease of life; one such problem is that of the self-force. A charged or massive particle moving in a curved background space-time produces a field that affects its motion, pushing it off its expected geodesic. This self-field gives rise to a so-called self-force acting on the particle. In modelling this motion, the self-force approach uses a perturbative expansion in the mass ratio. One of the most interesting sources of gravitational waves are extreme mass ratio inspirals – systems perfectly suited to self-force modelling. One of the key problems within the self-force model is the divergence of the field at the particle. To resolve this, the field is split into a singular component and a smooth regular field. This regular-singular split, introduced by Detweiler and Whiting, is used in most modern self-force calculations. In this thesis, we derive high-order expansions of the Detweiler-Whiting singular field, and use these to push the boundaries on current precision limits of self-force calculations. Within the mode-sum scheme, we give over 14 previously unknown regularisation parameters, almost doubling the current regularisation parameter database. We also produce smooth effective sources to high order, and propose an application of the higher terms to improve accuracy in the m-mode scheme. Finally, we investigate the status of the cosmic censorship conjecture and the role that the self-force plays. To this end, we give regularisation parameters for non-geodesic motion. We also show the necessity of our results in the exciting area of second order self-force calculations, which benefit significantly from high-order coordinate expansions of the singular field. We calculate several parameters that these schemes require, and highlight the further advancements possible from the results of this thesis.

### Analytic determination of the eight-and-a-half post-Newtonian self-force contributions to the two-body gravitational interaction potential

We {\it analytically} compute, to the eight-and-a-half post-Newtonian order, and to linear order in the mass ratio, the radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies, thereby extending previous analytic results. These results are obtained by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. We emphasize the increase in \lq\lq transcendentality" of the numbers entering the post-Newtonian expansion coefficients as the order increases, in particular we note the appearance of $\zeta(3)$ (as well as the square of Euler’s constant $\gamma$) starting at the seventh post-Newtonian order. We study the convergence of the post-Newtonian expansion as the expansion parameter $u=GM/(c^2r)$ leaves the weak-field domain $u\ll 1$ to enter the strong field domain $u=O(1)$.

### Evolution of Cool Close Binaries -- Rapid Mass Transfer and Near Contact Binaries

[Abridged] We test the evolutionary model of cool close binaries on the observed properties of near contact binaries (NCBs). Those with a more massive component filling the Roche lobe are SD1 binaries whereas in SD2 binaries the Roche lobe filling component is less massive. Our evolutionary model assumes that, following the Roche lobe overflow by the more massive component (donor), mass transfer occurs until mass ratio reversal. A binary in an initial phase of mass transfer, before mass equalization, is identified with SD1 binary. We show that the transferred mass forms an equatorial bulge around the less massive component (accretor). Its presence slows down the mass transfer rate to the value determined by the thermal time scale of the accretor, once the bulge sticks out above the Roche lobe. It means, that in a binary with a (typical) mass ratio of 0.5 the SD1 phase lasts at least 10 times longer than resulting from the standard evolutionary computations neglecting this effect. This is why we observe so many SD1 binaries. Our explanation is in contradiction to predictions identifying the SD1 phase with a broken contact phase of the Thermal Relaxation Oscillations model. The continued mass transfer, past mass equalization, results in mass ratio reversed. SD2 binaries are identified with this phase. Our model predicts that the time scales of SD1 and SD2 phases are comparable to one another. Analysis of the observations of 22 SD1 binaries, 27 SD2 binaries and 110 contact binaries (CBs) shows that relative number of both types of NCBs favors similar time scales of both phases of mass transfer. Total masses, orbital angular momenta and orbital periods of SD1 and SD2 binaries are indistinguishable from each other whereas they differ substantially from the corresponding parameters of CBs. We conclude that the results of the analysis fully support the model presented in this paper.

### Chaotic enhancement of dark matter density in binary systems and galaxies

Using symplectic map description we study the capture of galactic dark matter particles (DMP) in two-body and few-body galaxies. This approach allows to model scattering of $10^{16}$ DMP following time evolution of captured particle on about $10^9$ orbital periods. We obtain DMP density distribution inside such galaxies and determine the enhancement factor of their density in galactic center compared to its inter-galactic value as a function of mass ratio of galactic bodies and a ratio of body velocity to velocity of galactic DMP wind. We find that the enhancement factor can be of the order of ten thousands.

### Observational Signatures of Binary Supermassive Black Holes

Observations indicate that most massive galaxies contain a supermassive black hole, and theoretical studies suggest that when such galaxies have a major merger, the central black holes will form a binary and eventually coalesce. Here we discuss two spectral signatures of such binaries that may help distinguish them from ordinary AGN. These signatures are expected when the mass ratio between the holes is not extreme and the system is fed by a circumbinary disk. One such signature is a notch in the thermal continuum that has been predicted by other authors; we point out that it should be accompanied by a spectral revival at shorter wavelengths and also discuss its dependence on binary properties such as mass, mass ratio, and separation. In particular, we note that the wavelength $\lambda_n$ at which the notch occurs depends on these three parameters in such a way as to make the number of systems displaying these notches $\propto \lambda_n^{16/3}$; longer wavelength searches are therefore strongly favored. A second signature, first discussed here, is hard X-ray emission with a Wien-like spectrum at a characteristic temperature $\sim 100$ keV produced by Compton cooling of the shock generated when streams from the circumbinary disk hit the accretion disks around the individual black holes. We investigate the observability of both signatures. The hard X-ray signal may be particularly valuable as it can provide an indicator of black hole merger a few decades in advance of the event.

### Photometric data analysis of the eclipsing binary system AH Tauri

Two sets of photometric observations of the system AH Tauri have been analyzed using the latest version of the Wilson-Devinney code. The results show that AH Tauri may classified as A-type of W-UMa eclipsing binary. The mass ratio of q = 0.81, an over-contact degree of f = 0.095, and a slightly temperature difference between the two components have been obtained. The asymmetry of its light curve explained by the presence of a dark spot on the massive component. The physical, geometrical, and absolute parameters have been derived and compared with previous work.

### Spectroscopy of the inner companion of the pulsar PSR J0337+1715

The hierarchical triple system PSR J0337+1715 offers an unprecedented laboratory to study secular evolution of interacting systems and to explore the complicated mass-transfer history that forms millisecond pulsars and helium-core white dwarfs. The latter in particular, however, requires knowledge of the properties of the individual components of the system. Here we present precise optical spectroscopy of the inner companion in the PSR J0337+1715 system. We confirm it as a hot, low-gravity DA white dwarf with Teff=15,800+/-100 K and log(g)=5.82+/-0.05. We also measure an inner mass ratio of 0.1364+/-0.0015, entirely consistent with that inferred from pulsar timing, and a systemic radial velocity of 29.7+/-0.3 km/s. Combined with the mass (0.19751 Msun) determined from pulsar timing, our measurement of the surface gravity implies a radius of 0.091+/-0.005 Rsun; combined further with the effective temperature and extinction, the photometry implies a distance of 1300+/-80 pc. The high temperature of the companion is somewhat puzzling: with current models, it likely requires a recent period of unstable hydrogen burning, and suggests a surprisingly short lifetime for objects at this phase in their evolution. We discuss the implications of these measurements in the context of understanding the PSR J0337+1715 system, as well as of low-mass white dwarfs in general.

### Spectroscopy of the inner companion of the pulsar PSR J0337+1715 [Replacement]

The hierarchical triple system PSR J0337+1715 offers an unprecedented laboratory to study secular evolution of interacting systems and to explore the complicated mass-transfer history that forms millisecond pulsars and helium-core white dwarfs. The latter in particular, however, requires knowledge of the properties of the individual components of the system. Here we present precise optical spectroscopy of the inner companion in the PSR J0337+1715 system. We confirm it as a hot, low-gravity DA white dwarf with Teff=15,800+/-100 K and log(g)=5.82+/-0.05. We also measure an inner mass ratio of 0.1364+/-0.0015, entirely consistent with that inferred from pulsar timing, and a systemic radial velocity of 29.7+/-0.3 km/s. Combined with the mass (0.19751 Msun) determined from pulsar timing, our measurement of the surface gravity implies a radius of 0.091+/-0.005 Rsun; combined further with the effective temperature and extinction, the photometry implies a distance of 1300+/-80 pc. The high temperature of the companion is somewhat puzzling: with current models, it likely requires a recent period of unstable hydrogen burning, and suggests a surprisingly short lifetime for objects at this phase in their evolution. We discuss the implications of these measurements in the context of understanding the PSR J0337+1715 system, as well as of low-mass white dwarfs in general.

### Dynamics and microinstabilities at perpendicular collisionless shock: A comparison of large-scale two-dimensional full particle simulations with different ion to electron mass ratio [Cross-Listing]

Large-scale two-dimensional (2D) full particle-in-cell simulations are carried out for studying the relationship between the dynamics of a perpendicular shock and microinstabilities generated at the shock foot. The structure and dynamics of collisionless shocks are generally determined by Alfven Mach number and plasma beta, while microinstabilities at the shock foot are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the ratio of the plasma-to-cyclotron frequency. With a fixed Alfven Mach number and plasma beta, the ratio of the upstream bulk velocity to the electron thermal velocity is given as a function of the ion-to-electron mass ratio. The present 2D full PIC simulations with a relatively low Alfven Mach number (M_A ~ 6) show that the modified two-stream instability is dominant with higher ion-to-electron mass ratios. It is also confirmed that waves propagating downstream are more enhanced at the shock foot near the shock ramp as the mass ratio becomes higher. The result suggests that these waves play a role in the modification of the dynamics of collisionless shocks through the interaction with shock front ripples.

### Dynamics and microinstabilities at perpendicular collisionless shock: A comparison of large-scale two-dimensional full particle simulations with different ion to electron mass ratio [Replacement]

Large-scale two-dimensional (2D) full particle-in-cell simulations are carried out for studying the relationship between the dynamics of a perpendicular shock and microinstabilities generated at the shock foot. The structure and dynamics of collisionless shocks are generally determined by Alfven Mach number and plasma beta, while microinstabilities at the shock foot are controlled by the ratio of the upstream bulk velocity to the electron thermal velocity and the ratio of the plasma-to-cyclotron frequency. With a fixed Alfven Mach number and plasma beta, the ratio of the upstream bulk velocity to the electron thermal velocity is given as a function of the ion-to-electron mass ratio. The present 2D full PIC simulations with a relatively low Alfven Mach number (M_A ~ 6) show that the modified two-stream instability is dominant with higher ion-to-electron mass ratios. It is also confirmed that waves propagating downstream are more enhanced at the shock foot near the shock ramp as the mass ratio becomes higher. The result suggests that these waves play a role in the modification of the dynamics of collisionless shocks through the interaction with shock front ripples.

### Dust grain growth and the formation of the extremely primitive star SDSS J102915+172927

Dust grains in low-metallicity star-forming regions may be responsible for the formation of the first low-mass stars. The minimal conditions to activate dust-induced fragmentation require the gas to be pre-enriched above a critical dust-to-gas mass ratio Dcr=[2.6--6.3]x10^-9 with the spread reflecting the dependence on the grain properties. The recently discovered Galactic halo star SDSS J102915+172927 has a stellar mass of 0.8 Msun and a metallicity of Z=4.5×10^-5 Zsun and represents an optimal candidate for the dust-induced low-mass star formation. Indeed, for the two most plausible Population III supernova progenitors, with 20 Msun and 35 Msun, the critical dust-to-gas mass ratio can be overcome provided that at least 0.4 Msun of dust condenses in the ejecta, allowing for moderate destruction by the reverse shock. Here we show that even if dust formation in the first supernovae is less efficient or strong dust destruction does occur, grain growth during the collapse of the parent gas cloud is sufficiently rapid to activate dust cooling and likely fragmentation into low-mass and long-lived stars. Silicates and magnetite grains can experience significant grain growth in the density range 10^9 /cc < nH<10^12 /cc by accreting gas-phase species (SiO, SiO2, and Fe) until their gas-phase abundance drops to zero, reaching condensation efficiencies =1. The corresponding increase in the dust-to-gas mass ratio allows dust-induced cooling and fragmentation to be activated at 10^12 /cc < nH < 10^14 /cc, before the collapsing cloud becomes optically thick to continuum radiation. We show that for all the initial conditions that apply to the parent cloud of SDSS J102915+172927, dust-driven fragmentation is able to account for the formation of the star.

### The Double Contact Nature of TT Herculis

We present new radial velocities and photometry of the short-period Algol TT Herculis. Previous attempts to model the light curves of the system have met with limited success, primarily because of the lack of a reliable mass ratio. Our spectroscopic observations are the first to result in radial velocities for the secondary star, and thus provide a spectroscopic mass ratio. Simultaneous analysis of the radial velocities and new photometry shows that the system is a double contact binary, with a rapidly rotating primary that fills its limiting lobe.

### Reduction the secular solution to the periodic solution in the generalized restricted three-body problem

The aim of the present work is to reduce the secular solution around the triangular equilibrium points to periodic solution in the frame work of the generalized restricted thee-body problem. This model is generalized in sense that both the primaries are oblate and radiating as well as the gravitational potential from a belt. We show that the linearized equation of motion of the infinitesimal body around the triangular equilibrium points has a secular solution when the value of mass ratio equals the critical mass value. Moreover, we reduce this solution to periodic solution, as well as some numerical and graphical investigations for the effects of the perturbed forces are introduced. This model can be used to examine the existence of a dust particle near the triangular points of an oblate and radiating binary stars system surrounded by a belt.

### HT Cas - eclipsing dwarf nova during its superoutburst in 2010

We present results of a world-wide observing campaign of the eclipsing dwarf nova – HT Cas during its superoutburst in November 2010. Using collected data we were able to conduct analysis of the light curves and we calculated $O-C$ diagrams. The CCD photometric observations enabled us to derive the superhump period and with the timings of eclipses the orbital period was calculated. Based on superhump and orbital period estimations the period excess and mass ratio of the system were obtained.

### Satellite galaxies around present-day massive ellipticals

Using the spectroscopic and photometric catalogues of the Sloan Digital Sky Survey (SDSS DR7), we have explored the satellite distribution around $\sim$1000 massive (M$_\star$$\gtrsim2\times10^{11}M_\odot) visually classified elliptical galaxies down to a satellite mass ratio of 1:400 (i.e. 5\times$$10^{8}$$\lesssimM_{sat}$$\lesssim$2$\times$10$^{11}$M$_\odot$). Our host galaxies were selected to be representative of a mass complete sample. The satellites of these galaxies were searched within a projected radial distance of 100 kpc to their hosts. We have found that only 17-23% of the massive ellipticals has at least a satellite down to a mass ratio 1:10. This number increases to 40-52% if we explore satellites down to 1:100 and is $>$55-70% if we go further down to 1:400. The average projected radial distance of the satellites to their hosts is $\sim$59 kpc (which can be decreased down to 49-51 kpc if we account for incompleteness effects). The number of satellites per galaxy host only increases very mildly at decreasing the satellite mass. The fraction of mass which is contained in the satellites down to a mass ratio of 1:400 is 7.4% of the total mass contained by the hosts. Satellites with a mass ratio from 1:2 to 1:5 (with $\sim$27% of the total mass of the satellites) are the main contributor to the total satellite mass. If the satellites eventually infall into the host galaxies, the merger channel will be largely dominated by satellites with a mass ratio down to 1:10 (as these objects have 66% of the total mass in satellites).

### Satellite galaxies around present-day massive ellipticals [Replacement]

Using the spectroscopic NYU-VAGC and the photometric PHOTOZ catalogues of the Sloan Digital Sky Survey (SDSS DR7), we have explored the satellite distribution around ~1000 massive (M_star > 2×10^11 M_sun) visually classified elliptical galaxies down to a satellite mass ratio of 1:400 (i.e. 5×10^8 < M_sat < 2×10^11 M_sun). Our host galaxies were selected to be representative of a mass complete sample. The satellites of these galaxies were searched within a projected radial distance of 100 kpc to their hosts. We have found that only 20-23% of the massive ellipticals has at least a satellite down to a mass ratio 1:10. This number increases to 45-52% if we explore satellites down to 1:100 and is $>$60-70% if we go further down to 1:400. The average projected radial distance of the satellites to their hosts is ~59 kpc (which can be decreased at least down to 50 kpc if we account for incompleteness effects). The number of satellites per galaxy host only increases very mildly at decreasing the satellite mass. The fraction of mass which is contained in the satellites down to a mass ratio of 1:400 is 8% of the total mass contained by the hosts. Satellites with a mass ratio from 1:2 to 1:5 (with ~28% of the total mass of the satellites) are the main contributor to the total satellite mass. If the satellites eventually infall into the host galaxies, the merger channel will be largely dominated by satellites with a mass ratio down to 1:10 (as these objects have 68% of the total mass in satellites).

### High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations [Replacement]

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

### High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations

We extend the analytical determination of the main radial potential describing (within the effective one-body formalism) the gravitational interaction of two bodies beyond the 4th post-Newtonian approximation recently obtained by us. This extension is done to linear order in the mass ratio by applying analytical gravitational self-force theory (for a particle in circular orbit around a Schwarzschild black hole) to Detweiler’s gauge-invariant redshift variable. By using the version of black hole perturbation theory developed by Mano, Suzuki and Takasugi, we have pushed the analytical determination of the (linear in mass ratio) radial potential to the 6th post-Newtonian order (passing through 5 and 5.5 post-Newtonian terms). In principle, our analytical method can be extended to arbitrarily high post-Newtonian orders.

### Accretion disks around binary black holes of unequal mass: GRMHD simulations near decoupling [Cross-Listing]

We report on simulations in general relativity of magnetized disks onto black hole binaries. We vary the binary mass ratio from 1:1 to 1:10 and evolve the systems when they orbit near the binary-disk decoupling radius. We compare (surface) density profiles, accretion rates (relative to a single, non-spinning black hole), variability, effective $\alpha$-stress levels and luminosities as functions of the mass ratio. We treat the disks in two limiting regimes: rapid radiative cooling and no radiative cooling. The magnetic field lines clearly reveal jets emerging from both black hole horizons and merging into one common jet at large distances. The magnetic fields give rise to much stronger shock heating than the pure hydrodynamic flows, completely alter the disk structure, and boost accretion rates and luminosities. Accretion streams near the horizons are among the densest structures; in fact, the 1:10 no-cooling evolution results in a refilling of the cavity. The typical effective temperature in the bulk of the disk is $\sim 10^5 (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4} {\rm K}$ yielding characteristic thermal frequencies $\sim 10^{15} (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4}(1+z)^{-1}{\rm Hz}$. These systems are thus promising targets for many extragalactic optical surveys, such as LSST, WFIRST, and PanSTARRS.

### Accretion disks around binary black holes of unequal mass: GRMHD simulations near decoupling

We report on simulations in general relativity of magnetized disks onto black hole binaries. We vary the binary mass ratio from 1:1 to 1:10 and evolve the systems when they orbit near the binary-disk decoupling radius. We compare (surface) density profiles, accretion rates (relative to a single, non-spinning black hole), variability, effective $\alpha$-stress levels and luminosities as functions of the mass ratio. We treat the disks in two limiting regimes: rapid radiative cooling and no radiative cooling. The magnetic field lines clearly reveal jets emerging from both black hole horizons and merging into one common jet at large distances. The magnetic fields give rise to much stronger shock heating than the pure hydrodynamic flows, completely alter the disk structure, and boost accretion rates and luminosities. Accretion streams near the horizons are among the densest structures; in fact, the 1:10 no-cooling evolution results in a refilling of the cavity. The typical effective temperature in the bulk of the disk is $\sim 10^5 (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4} {\rm K}$ yielding characteristic thermal frequencies $\sim 10^{15} (M/10^8 M_\odot)^{-1/4} (L/L_{\rm edd})^{1/4}(1+z)^{-1}{\rm Hz}$. These systems are thus promising targets for many extragalactic optical surveys, such as LSST, WFIRST, and PanSTARRS.

### Black hole remnant of black hole-neutron star coalescing binaries with arbitrary black hole spin

A model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with arbitrary initial black hole spin angular momentum, binary mass ratio, and neutron star mass and cold equation of state is formulated. Tests against numerical-relativity results are carried out, showing that both the dimensionless spin parameter and the final mass are accurately reproduced. For the first time, the behaviour of both quantities and of the l = 2, m = 2, n = 0 quasinormal mode frequency is inspected throughout the parameter space. Predictions of this frequency may be exploited to guide gravitational wave modelling and detection efforts, and to extract physical information from detected gravitational wave signals that would help us break degeneracies between binary black hole and black hole-neutron star systems, improve our understanding of compact binary formation, and constrain the neutron star equation of state.

### Black hole remnant of black hole-neutron star coalescing binaries with arbitrary black hole spin [Replacement]

A model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with arbitrary initial black hole spin angular momentum, binary mass ratio, and neutron star mass and cold equation of state is formulated. Tests against numerical-relativity results are carried out, showing that both the dimensionless spin parameter and the final mass are accurately reproduced. For the first time, the behaviour of both quantities and of the l = 2, m = 2, n = 0 quasinormal mode frequency is inspected throughout the parameter space. Predictions of this frequency may be exploited to guide gravitational wave modelling and detection efforts, and to extract physical information from detected gravitational wave signals that would help us break degeneracies between binary black hole and black hole-neutron star systems, improve our understanding of compact binary formation, and constrain the neutron star equation of state.

### Black hole remnant of black hole-neutron star coalescing binaries with arbitrary black hole spin [Cross-Listing]

A model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with arbitrary initial black hole spin angular momentum, binary mass ratio, and neutron star mass and cold equation of state is formulated. Tests against numerical-relativity results are carried out, showing that both the dimensionless spin parameter and the final mass are accurately reproduced. For the first time, the behaviour of both quantities and of the l = 2, m = 2, n = 0 quasinormal mode frequency is inspected throughout the parameter space. Predictions of this frequency may be exploited to guide gravitational wave modelling and detection efforts, and to extract physical information from detected gravitational wave signals that would help us break degeneracies between binary black hole and black hole-neutron star systems, improve our understanding of compact binary formation, and constrain the neutron star equation of state.

### Black hole remnant of black hole-neutron star coalescing binaries with arbitrary black hole spin [Replacement]

A model for determining the dimensionless spin parameter and mass of the black hole remnant of black hole-neutron star mergers with arbitrary initial black hole spin angular momentum, binary mass ratio, and neutron star mass and cold equation of state is formulated. Tests against numerical-relativity results are carried out, showing that both the dimensionless spin parameter and the final mass are accurately reproduced. For the first time, the behaviour of both quantities and of the l = 2, m = 2, n = 0 quasinormal mode frequency is inspected throughout the parameter space. Predictions of this frequency may be exploited to guide gravitational wave modelling and detection efforts, and to extract physical information from detected gravitational wave signals that would help us break degeneracies between binary black hole and black hole-neutron star systems, improve our understanding of compact binary formation, and constrain the neutron star equation of state.

### The puzzle of the CNO abundances of {\alpha} Cygni variables resolved by the Ledoux criterion?

Recent stellar evolution computations show that the blue supergiant (BSG) stars could come from two distinct populations: a first group arising from massive stars that just left the main sequence (MS) and are crossing the Hertzsprung-Russell diagram (HRD) towards the red supergiant (RSG) branch, and a second group coming from stars that have lost considerable amount of mass during the RSG stage and are crossing the HRD for a second time towards the blue region. Due to very different luminosity-to- mass ratio, only stars from the second group are expected to have excited pulsations observable at the surface. In a previous work, we have shown that our models were able to reproduce the pulsational properties of BSGs. However, these models failed to reproduce the surface chemical composition of stars evolving back from a RSG phase. In this paper, we show how the use of the Ledoux criterion instead of the Schwarzschild one for convection allows to significantly improve the agreement with the observed chemical composition, while keeping the agreement with the pulsation periods. This gives some support to the Ledoux criterion.

### Conditions for Sustained Orbital Resonances in Extreme Mass Ratio Inspirals

We investigate the possibility of sustained orbital resonances in extreme mass ratio inspirals. Using a near-identity averaging transformation, we reduce the equations of motion for a particle moving in Kerr spacetime with self-force corrections in the neighbourhood of a resonant geodesic to a one dimensional equation for a particle moving in an effective potential. From this effective equation we obtain the necessary and sufficient conditions that the self-force needs to satisfy to allow inspiralling orbits to be captured in sustained resonance. Along the way we also obtain the full non-linear expression for the jump in the adiabatic constants of motion incurred as an inspiral transiently evolves through a strong resonance to first-order in the mass ratio. Finally, we find that if the resonance is strong enough to allow capture in sustained resonance, only a small fraction (order of the square root of mass-ratio) of all inspirals will indeed be captured. This makes observation of sustained resonances in EMRIs—if they exist—very unlikely for space based observatories like eLisa.

### The growth of galactic bulges through mergers in LCDM haloes revisited. II. Morphological mix evolution [Replacement]

The mass aggregation and merger histories of present-day distinct haloes selected from the cosmological Millennium Simulations I and II are mapped into stellar mass aggregation and galaxy merger histories of central galaxies by using empirical stellar-to-halo and stellar-to-gas mass relations. The growth of bulges driven by the galaxy mergers/interactions is calculated using dynamical prescriptions. The predicted bulge demographics at redshift z~0 is consistent with observations (Zavala+2012). Here we present the evolution of the morphological mix (traced by the bulge-to-total mass ratio, B/T) as a function of mass up to z=3. This mix remains qualitatively the same up to z~1: B/T<0.1 galaxies dominate at low masses, 0.1<B/T<0.45 at intermediate masses, and B/T>0.45 at large masses. At z>1, the fractions of disc-dominated and bulgeless galaxies increase strongly, and by z~2 the era of pure disc galaxies is reached. Bulge-dominated galaxies acquire such a morphology, and most of their mass, following a downsizing trend. Since our results are consistent with most of the recent observational studies of the morphological mix at different redshifts, a LCDM-based scenario of merger-driven bulge assembly does not seem to face critical issues. However, if the stellar-to-halo mass relation changes too little with redshift, then some tensions with observations appear.

### The growth of galactic bulges through mergers in LCDM haloes revisited. II. Morphological mix evolution

The mass aggregation and merger histories of present-day distinct haloes selected from the cosmological Millennium Simulations I and II are mapped into stellar mass aggregation and galaxy merger histories of central galaxies by using empirical stellar-to-halo and stellar-to-gas mass relations. The growth of bulges driven by the galaxy mergers/interactions is calculated using analytical recipes. The predicted bulge demographics at redshift z~0 is consistent with observations (Zavala+2012). Here we present the evolution of the morphological mix (traced by the bulge-to-total mass ratio, B/T) as a function of mass up to z=3. This mix remains qualitatively the same up to z~1: B/T<0.1 galaxies dominate at low masses, 0.1<B/T<0.45 at intermediate masses, and B/T>0.45 at large masses. At z>1, the fractions of disc-dominated and bulgeless galaxies increase strongly, and by z~2 the era of pure disc galaxies is reached. Bulge-dominated galaxies acquire such a morphology, and most of their mass, following a downsizing trend. Since our results are consistent with several recent observational studies of the morphological mix at different redshifts, a LCDM-based scenario of merger-driven bulge assembly does not seem to face significant issues. However, if the stellar-to-halo mass relation changes too little with redshift, then some tensions with observations appear.

### Love can be Tough to Measure

The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation of state effects. The latter first enter at 5 post-Newtonian (PN) order (i.e. proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5 PN order, with higher order terms only known to leading-order in the mass-ratio. We here find that not including point-particle terms at 4PN order to leading- and first-order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state.

### Love can be Tough to Measure [Cross-Listing]

The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation of state effects. The latter first enter at 5 post-Newtonian (PN) order (i.e. proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5 PN order, with higher order terms only known to leading-order in the mass-ratio. We here find that not including point-particle terms at 4PN order to leading- and first-order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state.

### Love can be Tough to Measure [Replacement]

The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation of state effects. The latter first enter at 5 post-Newtonian (PN) order (i.e. proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5 PN order, with higher order terms only known to leading-order in the mass-ratio. We here find that not including point-particle terms at 4PN order to leading- and first-order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state. This problem can be solved if one uses numerical waveforms once their own systematic errors are under control.

### Love can be Tough to Measure [Replacement]

The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation of state effects. The latter first enter at 5 post-Newtonian (PN) order (i.e. proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5 PN order, with higher order terms only known to leading-order in the mass-ratio. We here find that not including point-particle terms at 4PN order to leading- and first-order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state. This problem can be solved if one uses numerical waveforms once their own systematic errors are under control.

### Resonant periodic orbits in the exoplanetary systems [Replacement]

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance. Both planar and spatial cases are examined. In the spatial problem, families of periodic orbits are obtained after analytical continuation of vertical critical orbits. The linear stability of orbits is also examined. Concerning initial conditions nearby stable periodic orbits, we obtain long-term planetary stability, while unstable orbits are associated with chaotic evolution that destabilizes the planetary system. Stable periodic orbits are of particular importance in planetary dynamics, since they can host real planetary systems. We found stable orbits up to $60^\circ$ of mutual planetary inclination, but in most families, the stability does not exceed $20^\circ$-$30^\circ$, depending on the planetary mass ratio. Most of these orbits are very eccentric. Stable inclined circular orbits or orbits of low eccentricity were found in the $4/3$ and $5/2$ resonance, respectively.

### Resonant periodic orbits in the exoplanetary systems [Replacement]

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance. Both planar and spatial cases are examined. In the spatial problem, families of periodic orbits are obtained after analytical continuation of vertical critical orbits. The linear stability of orbits is also examined. Concerning initial conditions nearby stable periodic orbits, we obtain long-term planetary stability, while unstable orbits are associated with chaotic evolution that destabilizes the planetary system. Stable periodic orbits are of particular importance in planetary dynamics, since they can host real planetary systems. We found stable orbits up to $60^\circ$ of mutual planetary inclination, but in most families, the stability does not exceed $20^\circ$-$30^\circ$, depending on the planetary mass ratio. Most of these orbits are very eccentric. Stable inclined circular orbits or orbits of low eccentricity were found in the $4/3$ and $5/2$ resonance, respectively.

### Resonant periodic orbits in the exoplanetary systems

The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance. Both planar and spatial cases are examined. In the spatial problem families of periodic orbits are obtained after analytical continuation of vertical critical orbits. The linear stability of orbits is also examined. Concerning initial conditions nearby stable periodic orbits, we obtain long-term planetary stability, while unstable orbits are associated with chaotic evolution that destabilizes the planetary system. Stable periodic orbits are of particular importance in planetary dynamics, since they can host real planetary systems. We found stable orbits up to $60^\circ$ of mutual planetary inclination, but in most families the stability does not exceed $20^\circ$-$30^\circ$, depending on the planetary mass ratio. Most of these orbits are very eccentric. Stable inclined circular orbits or orbits of low eccentricity were found in the $4/3$ and $5/2$ resonance, respectively.

### Dust May Be More Rare Than Expected in Metal Poor Galaxies

‘Normal’ galaxies observed at z>6, when the Universe was <1 billion years old, thus far show no evidence of the cold dust that accompanies star formation in the local Universe, where the dust-to-gas mass ratio is 1%. A prototypical example is ‘Himiko’ (z=6.6), which a mere 840 Myr after the Big Bang is forming stars at a rate of 30-100 Msun/yr, yielding a mass assembly time M^{star}/SFR 150×10^6 yr. Himiko is estimated to have a low fraction (2-3% of the Solar value) of elements heavier than helium (metallicity), and although its gas mass cannot be asserted at this time its dust-to-stellar mass ratio is constrained to be <0.05%. The local galaxy I Zw 18, with a metallicity 4% solar and forming stars less rapidly than Himiko but still vigorously for its mass (M^{star}/SFR 1.6×10^9 yr), is also very dust deficient and perhaps one of the best analogues of primitive galaxies accessible to detailed study. Here we report observations of dust emission from I Zw 18 from which we determine its dust mass to be 450-1800 Msun, yielding a dust-to-stellar mass ratio \approx 10^{-6}-10^{-5} and a dust-to-gas mass ratio 3.2-13×10^{-6}. If I Zw 18 is a reasonable analog of Himiko, then Himiko’s dust mass is \approx 50,000 Msun, a factor of 100 below the current upper limit. These numbers are considerably uncertain, but if most high-z galaxies are more like Himiko than like the quasar host SDSS J114816.64+525150.3, then the prospects for detecting the gas and dust in them are much poorer than hitherto anticipated.

### Binary Black Hole Accretion From a Circumbinary Disk: Gas Dynamics Inside the Central Cavity

We present the results of 2D hydrodynamical simulations of circumbinary disk accretion using the finite-volume code DISCO. This code solves the 2D viscous Navier-Stokes equations on a high-resolution moving mesh which shears with the fluid flow, greatly reducing advection errors in comparison with a fixed grid. We perform a series of simulations for binary mass ratios in the range 0.026 < q < 1.0, each lasting longer than a viscous time so that we reach a quasi-steady accretion state. In each case, we find that gas is efficiently stripped from the inner edge of the circumbinary disk and enters the cavity along accretion streams, which feed persistent "mini-disks" surrounding each black hole. We find that for q > 0.1, the binary excites eccentricity in the inner region of the circumbinary disk, creating an overdense lump which gives rise to enhanced periodicity in the accretion rate. The dependence of the periodicity on mass ratio may provide a method for observationally inferring mass ratios from measurements of the accretion rate. We also find that for all mass ratios studied, the magnitude of the accretion onto the secondary is sufficient to drive the binary toward larger mass ratio. This suggests a mechanism for biasing mass ratio distributions toward equal mass.

### How Cold is Cold Dark Matter? [Replacement]

If cold dark matter consists of particles, these must be non-interacting and non-relativistic by definition. In most cold dark matter models however, dark matter particles inherit a non-vanishing velocity dispersion from interactions in the early universe, a velocity that redshifts with cosmic expansion but certainly remains non-zero. In this article, we place model-independent constraints on the dark matter temperature to mass ratio, whose square root determines the dark matter velocity dispersion. We only assume that dark matter particles decoupled kinetically while non-relativistic, when galactic scales had not entered the horizon yet, and that their momentum distribution has been Maxwellian since that time. Under these assumptions, using cosmic microwave background and matter power spectrum observations, we place upper limits on the temperature to mass ratio of cold dark matter today (away from collapsed structures). These limits imply that the present cold dark matter velocity dispersion has to be smaller than 54 m/s. Cold dark matter has to be quite cold, indeed.

### Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples [Replacement]

Kozai-Lidov (KL) oscillations can accelerate compact object mergers via gravitational wave (GW) radiation by driving the inner binaries of hierarchical triples to high eccentricities. We perform direct three-body integrations of high mass ratio compact object triple systems using Fewbody including post-Newtonian terms. We find that the inner binary undergoes rapid eccentricity oscillations (REOs) on the timescale of the outer orbital period which drive it to higher eccentricities than secular theory would otherwise predict, resulting in substantially reduced merger times. For a uniform distribution of tertiary eccentricity ($e_2$), ~40% of systems merge within ~1-2 eccentric KL timescales whereas secular theory predicts that only ~20% of such systems merge that rapidly. This discrepancy becomes especially pronounced at low $e_2$, with secular theory overpredicting the merger time by many orders of magnitude. We show that a non-negligible fraction of systems have eccentricity > 0.8 when they merge, in contrast to predictions from secular theory. Our results are applicable to high mass ratio triple systems containing black holes or neutron stars. In objects in which tidal effects are important, such as white dwarfs, stars, and planets, REOs can reduce the tidal circularization timescale by an order of magnitude and bring the components of the inner binary into closer orbits than would be possible in the secular approximation.

### Rapid Eccentricity Oscillations and the Mergers of Compact Objects in Hierarchical Triples [Replacement]

Kozai-Lidov (KL) oscillations can accelerate compact object mergers via gravitational wave (GW) radiation by driving the inner binaries of hierarchical triples to high eccentricities. We perform direct three-body integrations of high mass ratio compact object triple systems using Fewbody including post-Newtonian terms. We find that the inner binary undergoes rapid eccentricity oscillations (REOs) on the timescale of the outer orbital period which drive it to higher eccentricities than secular theory would otherwise predict, resulting in substantially reduced merger times. For a uniform distribution of tertiary eccentricity ($e_2$), ~40% of systems merge within ~1-2 eccentric KL timescales whereas secular theory predicts that only ~20% of such systems merge that rapidly. This discrepancy becomes especially pronounced at low $e_2$, with secular theory overpredicting the merger time by many orders of magnitude. We show that a non-negligible fraction of systems have eccentricity > 0.8 when they merge, in contrast to predictions from secular theory. Our results are applicable to high mass ratio triple systems containing black holes or neutron stars. In objects in which tidal effects are important, such as white dwarfs, stars, and planets, REOs can reduce the tidal circularization timescale by an order of magnitude and bring the components of the inner binary into closer orbits than would be possible in the secular approximation.

### Analysis of Molecular Hydrogen Absorption toward QSO B0642-5038 for a Varying Proton-to-Electron Mass Ratio [Replacement]

Rovibronic molecular hydrogen (H$_2$) transitions at redshift $z_{\rm abs} \simeq 2.659$ towards the background quasar B0642$-$5038 are examined for a possible cosmological variation in the proton-to-electron mass ratio, $\mu$. We utilise an archival spectrum from the Very Large Telescope/Ultraviolet and Visual Echelle Spectrograph with a signal-to-noise ratio of $\sim$35 per 2.5-km$\,$s$^{-1}$ pixel at the observed H$_2$ wavelengths (335–410 nm). Some 111 H$_2$ transitions in the Lyman and Werner bands have been identified in the damped Lyman $\alpha$ system for which a kinetic gas temperature of $\sim$84 K and a molecular fraction $\log f = -2.18\pm0.08$ is determined. The H$_2$ absorption lines are included in a comprehensive fitting method, which allows us to extract a constraint on a variation of the proton-electron mass ratio, $\Delta\mu/\mu$, from all transitions at once. We obtain $\Delta\mu/\mu = (17.1 \pm 4.5_{\rm stat} \pm3.7_{\rm sys})\times10^{-6}$. However, we find evidence that this measurement has been affected by wavelength miscalibration errors recently identified in UVES. A correction based on observations of objects with solar-like spectra gives a smaller $\Delta\mu/\mu$ value and contributes to a larger systematic uncertainty: $\Delta\mu/\mu = (12.7 \pm 4.5_{\rm stat} \pm4.2_{\rm sys})\times10^{-6}$.

### A census of transient orbital resonances encountered during binary inspiral [Replacement]

Transient orbital resonances have recently been identified as potentially important to the inspiral of small bodies into large black holes. These resonances occur as the inspiral evolves through moments in which two fundamental orbital frequencies, $\Omega_\theta$ and $\Omega_r$, are in a small integer ratio to one another. Previous work has demonstrated that a binary’s parameters are "kicked" each time the inspiral passes through a resonance, changing the orbit’s characteristics relative to a model that neglects resonant effects. In this paper, we use exact Kerr geodesics coupled to an accurate but approximate model of inspiral to survey orbital parameter space and estimate how commonly one encounters long-lived orbital resonances. We find that the most important resonances last for a few hundred orbital cycles at mass ratio $10^{-6}$, and that resonances are almost certain to occur during the time that a large mass ratio binary would be a target of gravitational-wave observations. Resonances appear to be ubiquitous in large mass ratio inspiral, and to last long enough that they are likely to affect binary evolution in observationally important ways.

### A census of transient orbital resonances encountered during binary inspiral [Replacement]

Transient orbital resonances have recently been identified as potentially important to the inspiral of small bodies into large black holes. These resonances occur as the inspiral evolves through moments in which two fundamental orbital frequencies, $\Omega_\theta$ and $\Omega_r$, are in a small integer ratio to one another. Previous work has demonstrated that a binary’s parameters are "kicked" each time the inspiral passes through a resonance, changing the orbit’s characteristics relative to a model that neglects resonant effects. In this paper, we use exact Kerr geodesics coupled to an accurate but approximate model of inspiral to survey orbital parameter space and estimate how commonly one encounters long-lived orbital resonances. We find that the most important resonances last for a few hundred orbital cycles at mass ratio $10^{-6}$, and that resonances are almost certain to occur during the time that a large mass ratio binary would be a target of gravitational-wave observations. Resonances appear to be ubiquitous in large mass ratio inspiral, and to last long enough that they are likely to affect binary evolution in observationally important ways.

### Where angular momentum goes in a precessing black hole binary [Replacement]

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant’s mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$.

### Where angular momentum goes in a precessing black hole binary [Replacement]

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant’s mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$.

### Where angular momentum goes in a precessing black hole binary [Replacement]

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant’s mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$.

### Where angular momentum goes in a precessing black hole binary [Replacement]

We evolve a set of 32 equal-mass black-hole binaries with collinear spins (with intrinsic spin magnitudes $|\vec{S}_{1,2}/m^2_{1,2}|=0.8$) to study the effects of precession in the highly nonlinear plunge and merger regimes. We compare the direction of the instantaneous radiated angular momentum, $\hat{\delta J}_{\rm rad}(t)$, to the directions of the total angular momentum, $\hat{J}(t)$, and the orbital angular momentum, $\hat{L}(t)$. We find that $\hat{\delta J}_{\rm rad}(t)$ approximately follows $\hat{L}$ throughout the evolution. During the orbital evolution and merger, we observe that the angle between $\vec{L}$ and total spin $\vec{S}$ is approximately conserved to within $1^\circ$, which allows us to propose and test models for the merger remnant’s mass and spin. For instance, we verify that the \hangup effect is the dominant effect and largely explains the observed total energy and angular momentum radiated by these precessing systems. We also verify that the total angular momentum, which significantly decreases in magnitude during the inspiral, varies in direction by less than $\sim 5^\circ$. The maximum variation in the direction of $\vec J$ occurs when the spins are nearly antialigned with the orbital angular momentum. Based on our results, we conjecture that transitional precession, which would lead to large variations in the direction of $\vec J$, is not possible for similar-mass binaries and would require a mass ratio $m_1/m_2\lesssim1/4$.