# Posts Tagged mass ratio

## Recent Postings from mass ratio

### Search for a drifting proton--electron mass ratio from H$_2$

An overview is presented of the H$_2$ quasar absorption method to search for a possible variation of the proton--electron mass ratio $\mu=m_p/m_e$ on a cosmological time scale. Details of the analysis of astronomical spectra, obtained with large 8--10 m class optical telescopes, equipped with high-resolution echelle grating based spectrographs, are explained. The methods and results of the laboratory molecular spectroscopy of H$_2$, in particular the laser-based metrology studies for the determination of rest wavelengths of the Lyman and Werner band absorption lines, are reviewed. Theoretical physics scenarios delivering a rationale for a varying $\mu$ will be discussed briefly, as well as alternative spectroscopic approaches to probe variation of $\mu$, other than the H$_2$ method. Also a recent approach to detect a dependence of the proton-to-electron mass ratio on environmental conditions, such as the presence of strong gravitational fields, will be highlighted. Currently some 56 H$_2$ absorption systems are known and listed. Their usefulness to detect $\mu$-variation is discussed, in terms of column densities and brightness of background quasar sources, along with future observational strategies. The astronomical observations of ten quasar systems analyzed so far set a constraint on a varying proton-electron mass ratio of $|\Delta\mu/\mu| < 5 \times 10^{-6}$ (3-$\sigma$), which is a null result, holding for redshifts in the range $z=2.0-4.2$. This corresponds to look-back times of 10--12.4 billion years into cosmic history. Attempts to interpret the results from these 10 H$_2$ absorbers in terms of a spatial variation of $\mu$ are currently hampered by the small sample size and their coincidental distribution in a relatively narrow band across the sky.

### KIC 4739791: A New R CMa-type Eclipsing Binary with a Pulsating Component

The {\it Kepler} light curve of KIC 4739791 exhibits partial eclipses, inverse O'Connell effect, and multiperiodic pulsations. Including a starspot on either of the binary components, the light-curve synthesis indicates that KIC 4739791 is in detached or semi-detached configurations with both a short orbital period and a low mass ratio. Multiple frequency analyses were performed in the light residuals after subtracting the binarity effects from the original {\it Kepler} data. We detected 14 frequencies: six in the low-frequency region (0.1$-$2.3 d$^{-1}$) and eight in the high-frequency region (18.2$-$22.0 d$^{-1}$). Among these, six high frequencies with amplitudes of 0.62$-$1.97 mmag were almost constant over time for 200 d. Their pulsation periods and pulsation constants are in the ranges of 0.048$-$0.054 d and 0.025$-$0.031 d, respectively. In contrast, the other frequencies may arise from the alias effects caused by the orbital frequency or combination frequencies. We propose that KIC 4739791 is a short-period R CMa binary with the lowest mass ratio in the known classical Algols and that its primary component is a $\delta$ Sct pulsating star. Only four R CMa stars have been identified, three of which exhibit $\delta$ Sct-type oscillations. These findings make KIC 4739791 an attractive target for studies of stellar interior structure and evolution.

### Structures of GMC W 37

We carried out observations toward the giant molecular cloud W 37 with the $J = 1 - 0$ transitions of $^{12}$CO, $^{13}$CO, and C$^{18}$O using the 13.7 m single-dish telescope at the Delingha station of Purple Mountain Observatory. Based on the three CO lines, we calculated the column densities, cloud masses for the molecular clouds with radial velocities at around $+20 \mathrm{km s}^{-1}$. The gas mass of W 37, calculated from $^{13}$CO emission, is $1.7\times10^5 M_\odot$, above the criteria of giant molecular cloud. The dense ridge of W 37 is a dense filament, which is supercritical in linear mass ratio. Dense clumps found by C$^{18}$O emission are aligned along the dense ridge with a regular interval about 2.8 pc, similar to the clump separation caused by large-scale sausage instability'. We confirm the identification of the giant molecular filament (GMF) G 18.0-16.8 by \cite{2014A&A...568A..73R} and find a new giant filament, G16.5-15.8, located in the west 0.8 degree of G 18.0-16.8. Both GMFs are not gravitationally bound, as indicated by their low linear mass ratio ($\sim80 M_\odot \mathrm{pc}^{-1}$). We compared the gas temperature map with the dust temperature map from \emph{Herschel} images, and find similar structures. The spatial distributions of class I objects and the dense clumps is reminiscent of triggered star formation occurring in the northwestern part of W 37, which is close to NGC 6611.

### Multiple origins of asteroid pairs

Rotationally fissioned asteroids produce unbound daughter asteroids that have very similar heliocentric orbits. Backward integration of their current heliocentric orbits provides an age of closest proximity that can be used to date the rotational fission event. Most asteroid pairs follow a predicted theoretical relationship between the primary spin period and the mass ratio of the two pair members that is a direct consequence of the YORP-induced rotational fission hypothesis. If the progenitor asteroid has strength, asteroid pairs may have high mass ratios with possibly fast rotating primaries. However, secondary fission leaves the originally predicted trend unaltered. We also describe the characteristics of pair members produced by four alternative routes from a rotational fission event to an asteroid pair. Unlike direct formation from the event itself, the age of closest proximity of these pairs cannot generally be used to date the rotational fission event since considerable time may have passed.

### Constraints on Individual Supermassive Black Hole Binaries from Pulsar Timing Array Limits on Continuous Gravitational Waves

Pulsar timing arrays (PTAs) are placing increasingly stringent constraints on the strain amplitude of continuous gravitational waves emitted by supermassive black hole binaries on subparsec scales. In this paper, we incorporate independent measurements of the dynamical masses $M_{\rm bh}$ of supermassive black holes in specific galaxies at known distances and leverage this additional information to further constrain whether or not those galaxies could host a detectable supermassive black hole binary. We estimate the strain amplitudes from individual binaries as a function of binary mass ratio for two samples of nearby galaxies: (1) those with direct dynamical measurements of $M_{\rm bh}$ in the literature, and (2) the 116 most massive early-type galaxies (and thus likely hosts of the most massive black holes) within 108 Mpc from the MASSIVE Survey. Our exploratory analysis shows that the current PTA upper limits on continuous waves can already constrain the mass ratios of hypothetical black hole binaries in a dozen galaxies in our samples. The constraints are stronger for galaxies with larger $M_{\rm bh}$ and at smaller distances. For the black holes with $M_{\rm bh} \gtrsim 5\times 10^9 M_\odot$ at the centers of NGC 4889, NGC 4486 (M87) and NGC 4649 (M60), any binary companion in orbit within the PTA frequency bands would have to have a mass ratio of less than about 1:10.

### Black hole accretion disc impacts

We present an analytic model for computing the luminosity and spectral evolution of flares caused by a supermassive black hole impacting the accretion disc of another supermassive black hole. Our model includes photon diffusion, emission from optically thin regions and relativistic corrections to the observed spectrum and time-scales. We test the observability of the impact scenario with a simulated population of quasars hosting supermassive black hole binaries. The results indicate that for a moderate binary mass ratio of 0.3, and impact distances of 100 primary Schwarzschild radii, the accretion disc impacts can be expected to equal or exceed the host quasar in brightness at observed wavelength {\lambda} = 510 nm up to z = 0.6. We conclude that accretion disc impacts may function as an independent probe for supermassive black hole binaries. We release the code used for computing the model light curves to the community.

### Curvature of the pseudocritical line in (2+1)-flavor QCD with HISQ fermions

We study QCD with (2+1)-HISQ fermions at nonzero temperature and nonzero imaginary baryon chemical potential. Monte Carlo simulations are performed using the MILC code along the line of constant physics with a light to strange mass ratio of $m_l/m_s=1/20$ on lattices up to $48^3 \times 12$ to check for finite cutoff effects. We determine the curvature of the pseudocritical line extrapolated to the continuum limit.

### MOA-2010-BLG-353Lb A Possible Saturn Revealed

We report the discovery of a possible planet in microlensing event MOA-2010-BLG-353. This event was only recognised as having a planetary signal after the microlensing event had finished, and following a systematic analysis of all archival data for binary lens microlensing events collected to date. Data for event MOA-2010-BLG-353 were only recorded by the high cadence observations of the OGLE and MOA survey groups. If we make the assumptions that the probability of the lens star hosting a planet of the measured mass ratio is independent of the lens star mass or distance, and that the source star is in the Galactic bulge, a probability density analysis indicates the planetary system comprises a 0.9^{+1.6}_{-0.53} M_{Saturn} mass planet orbiting a 0.18^{+0.32}_{-0.11} M_{sun} red dwarf star, 6.43^{+1.09}_{-1.15} kpc away. The projected separation of the planet from the host star is 1.72^{+0.56}_{-0.48} AU. Under the additional assumption that the source is on the far side of the Galactic bulge, the probability density analysis favours a lens system comprising a slightly lighter planet.

### Pulsar J0453+1559: A Double Neutron Star System with a Large Mass Asymmetry

To understand the nature of supernovae and neutron star (NS) formation, as well as binary stellar evolution and their interactions, it is important to probe the distribution of NS masses. Until now, all double NS (DNS) systems have been measured to have a mass ratio close to unity (q $\geq$ 0.91). Here we report the measurement of the individual masses of the 4.07-day binary pulsar J0453+1559 from measurements of the rate of advance of periastron and Shapiro delay: The mass of the pulsar is 1.559(5) $M_{\odot}$ and that of its companion is 1.174(4) $M_{\odot}$; q = 0.75. If this companion is also a neutron star (NS), as indicated by the orbital eccentricity of the system (e=0.11), then its mass is the smallest precisely measured for any such object. The pulsar has a spin period of 45.7 ms and a spin derivative of 1.8616(7) x$10^-19$; from these we derive a characteristic age of ~ 4.1 x $10^9$ years and a magnetic field of ~ 2.9 x $10^9$ G,i.e, this pulsar was mildly recycled by accretion of matter from the progenitor of the companion star. This suggests that it was formed with (very approximately) its current mass. Thus NSs form with a wide range of masses, which is important for understanding their formation in supernovae. It is also important for the search for gravitational waves released during a NS-NS merger: it is now evident that we should not assume all DNS systems are symmetric.

### Modeling Equal and Unequal Mass Binary Neutron Star Mergers Using Public Codes [Cross-Listing]

We present three-dimensional simulations of the dynamics of binary neutron star (BNS) mergers from the late stage of the inspiral process up to $\sim 20$ ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH). We investigate five equal-mass models of total gravitational mass $2.207$, $2.373$, $2.537$, $2.697$ and $2.854 M_\odot$, respectively, and four unequal mass models with $M_{\mathrm{ADM}}\simeq 2.53\ M_\odot$ and $q\simeq 0.94$, $0.88$, $0.82$, and $0.77$ (where $q = M^{(1)}/M^{(2)}$ is the mass ratio). We use a semi-realistic equation of state (EOS) namely, the seven-segment piece-wise polytropic SLyPP with a thermal component given by $\Gamma_{th} = 1.8$. We have also compared the resulting dynamics (for one model) using both, the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector, and also different reconstruction methods for the matter sector, namely PPM, WENO and MP5. Our results show agreement and high resolution, but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions. One of the important characteristics of the present investigation is that, for the first time, this has been done using only publicly available open source software, in particular, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. All of the source code and parameters used for the simulations have been made publicly available. This not only makes it possible to re-run and re-analyze our data; it also enables others to directly build upon this work for future research.

### Modeling Equal and Unequal Mass Binary Neutron Star Mergers Using Public Codes [Replacement]

We present three-dimensional simulations of the dynamics of binary neutron star (BNS) mergers from the late stage of the inspiral process up to $\sim 20$ ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH). We investigate five equal-mass models of total gravitational mass $2.207$, $2.373$, $2.537$, $2.697$ and $2.854 M_\odot$, respectively, and four unequal mass models with $M_{\mathrm{ADM}}\simeq 2.53\ M_\odot$ and $q\simeq 0.94$, $0.88$, $0.82$, and $0.77$ (where $q = M^{(1)}/M^{(2)}$ is the mass ratio). We use a semi-realistic equation of state (EOS) namely, the seven-segment piece-wise polytropic SLyPP with a thermal component given by $\Gamma_{th} = 1.8$. We have also compared the resulting dynamics (for one model) using both, the BSSN-NOK and CCZ4 methods for the evolution of the gravitational sector, and also different reconstruction methods for the matter sector, namely PPM, WENO and MP5. Our results show agreement and high resolution, but superiority of BSSN-NOK supplemented by WENO reconstruction at lower resolutions. One of the important characteristics of the present investigation is that, for the first time, this has been done using only publicly available open source software, in particular, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. All of the source code and parameters used for the simulations have been made publicly available. This not only makes it possible to re-run and re-analyze our data; it also enables others to directly build upon this work for future research.

### Fractal structures for the Jacobi Hamiltonian of restricted three-body problem

We study the dynamical chaos and integrable motion in the planar circular restricted three-body problem and determine the fractal dimension of the spiral strange repeller set of non-escaping orbits at different values of mass ratio of binary bodies and of Jacobi integral of motion. We find that the spiral fractal structure of the Poincar\'e section leads to a spiral density distribution of particles remaining in the system. We also show that the initial exponential drop of survival probability with time is followed by the algebraic decay related to the universal algebraic statistics of Poincar\'e recurrences in generic symplectic maps.

### Gravitational-wave cutoff frequencies of tidally disruptive neutron star-black hole binary mergers [Cross-Listing]

Tidal disruption has a dramatic impact on the outcome of neutron star-black hole mergers. The phenomenology of these systems can be divided in three classes: nondisruptive, mildly disruptive or disruptive. The cutoff frequency of the gravitational radiation produced during the merger (which is potentially measurable by interferometric detectors) is very different in each regime, and when the merger is disuptive it carries information on the neutron star equation of state. Here we use semianalytical tools to derive a formula for the critical binary mass ratio $Q=M_{\rm BH}/M_{\rm NS}$ below which mergers are disruptive as a function of the stellar compactness $\mathcal{C}=M_{\rm NS}/R_{\rm NS}$ and the dimensionless black hole spin $\chi$. We then employ a new gravitational waveform amplitude model, calibrated to $134$ general relativistic numerical simulations of binaries with black hole spin (anti-)aligned with the orbital angular momentum, to obtain a fit to the gravitational-wave cutoff frequency in the disruptive regime as a function of $\mathcal{C}$, $Q$ and $\chi$. Our findings are important to build gravitational wave template banks, to determine whether neutron star-black hole mergers can emit electromagnetic radiation (thus helping multimessenger searches), and to improve event rate calculations for these systems.

### Stellar Dynamics around a Massive Black Hole I: Secular Collisionless Theory

We present a theory in 3 parts, of the long-term (or secular) evolution of stellar systems orbiting within the sphere of influence of massive black holes in galactic nuclei. Here we describe the secular collisionless dynamics of a (Keplerian) stellar system of mass $M$ orbiting a black hole of mass $M_\bullet \gg M$. The stellar distribution function (DF) $f$ obeys the collisionless Boltzmann equation (CBE) in 6-dim phase space. The small mass ratio, $\varepsilon = M/M_\bullet \ll 1$, implies a separation of time scales in the motions of stars: the fast Kepler orbital periods and the secular time scale which is longer by a factor $\varepsilon^{-1}$. We orbit-average the CBE over the fast Keplerian orbital phase using the Method of Multiple Scales. Then $f$ is expressed as the sum of a secular DF $F$ in a 5-dim (Gaussian Ring) space, and small fluctuations that remain of $O(\varepsilon)$ over secular times. $F$ obeys a secular CBE that includes stellar self-gravity, general relativistic corrections up to 1.5 post-Newtonian order, and external sources. Secular dynamics conserves the semi-major axis of every star. This additional integral of motion promotes extra regularity of the stellar orbits, and enables the construction of secular equilibrium DFs ($F_0$) through a Secular Jeans theorem. Secular equilibria allow for varied spatial geometries including figure rotation. A linearized secular CBE determines the linear response and stability of $F_0$. Spherical, non-rotating equilibria may support small-amplitude, long-lived, warp-like distortions. We also prove that an axisymmetric, zero-thickness, flat disc is secularly stable to all in-plane perturbations, when its DF $F_0$ is a monotonic function of the angular momentum at fixed energy.

### Mergers and Star Formation: The environment and Stellar Mass Growth of the Progenitors of Ultra-Massive Galaxies since z = 2

The growth of galaxies is a key problem in understanding the structure and evolution of the universe. Galaxies grow their stellar mass by a combination of star formation and mergers, with a relative importance that is redshift dependent. Theoretical models predict quantitatively different contributions from the two channels; measuring these from the data is a crucial constraint. Exploiting the UltraVISTA catalog and a unique sample of progenitors of local ultra massive galaxies selected with an abundance matching approach, we quantify the role of the two mechanisms from z = 2 to 0. We also compare our results to two independent incarnations of semi-analytic models. At all redshifts, progenitors are found in a variety of environments, ranging from being isolated to having 5-10 companions with mass ratio at least 1:10 within a projected radius of 500 kpc. In models, progenitors have a systematically larger number of companions, entailing a larger mass growth for mergers than in observations, at all redshifts. In observations, the total mass growth is slightly smaller than the expected growth, while in both models it agrees, within the uncertainties. Overall, our analysis confirms the model predictions, showing how the growth history of massive galaxies is dominated by in situ star formation at z = 2, both star-formation and mergers at 1 < z < 2, and by mergers alone at z < 1. Nonetheless, detailed comparisons still point out to tensions between the expected mass growth and our results, which might be due to either an incorrect progenitors-descendants selection, uncertainties on star formation rate and mass estimates, or the adopted assumptions on merger rates.

### Mergers and Star Formation: The environment and Stellar Mass Growth of the Progenitors of Ultra-Massive Galaxies since z = 2 [Replacement]

The growth of galaxies is a key problem in understanding the structure and evolution of the universe. Galaxies grow their stellar mass by a combination of star formation and mergers, with a relative importance that is redshift dependent. Theoretical models predict quantitatively different contributions from the two channels; measuring these from the data is a crucial constraint. Exploiting the UltraVISTA catalog and a unique sample of progenitors of local ultra massive galaxies selected with an abundance matching approach, we quantify the role of the two mechanisms from z=2 to 0. We also compare our results to two independent incarnations of semi-analytic models. At all redshifts, progenitors are found in a variety of environments, ranging from being isolated to having 5-10 companions with mass ratio at least 1:10 within a projected radius of 500 kpc. In models, progenitors have a systematically larger number of companions, entailing a larger mass growth for mergers than in observations, at all redshifts. Generally, in both observations and models, the inferred and the expected mass growth roughly agree, within the uncertainties. Overall, our analysis confirms the model predictions, showing how the growth history of massive galaxies is dominated by in situ star formation at z~2, both star-formation and mergers at 1<z<2, and by mergers alone at z<1. Nonetheless, detailed comparisons still point out to tensions between the expected mass growth and our results, which might be due to either an incorrect progenitors-descendants selection, uncertainties on star formation rate and mass estimates, or the adopted assumptions on merger rates.

### Mergers and Star Formation: The environment and Stellar Mass Growth of the Progenitors of Ultra-Massive Galaxies since z = 2 [Replacement]

The growth of galaxies is a key problem in understanding the structure and evolution of the universe. Galaxies grow their stellar mass by a combination of star formation and mergers, with a relative importance that is redshift dependent. Theoretical models predict quantitatively different contributions from the two channels; measuring these from the data is a crucial constraint. Exploiting the UltraVISTA catalog and a unique sample of progenitors of local ultra massive galaxies selected with an abundance matching approach, we quantify the role of the two mechanisms from z=2 to 0. We also compare our results to two independent incarnations of semi-analytic models. At all redshifts, progenitors are found in a variety of environments, ranging from being isolated to having 5-10 companions with mass ratio at least 1:10 within a projected radius of 500 kpc. In models, progenitors have a systematically larger number of companions, entailing a larger mass growth for mergers than in observations, at all redshifts. Generally, in both observations and models, the inferred and the expected mass growth roughly agree, within the uncertainties. Overall, our analysis confirms the model predictions, showing how the growth history of massive galaxies is dominated by in situ star formation at z~2, both star-formation and mergers at 1<z<2, and by mergers alone at z<1. Nonetheless, detailed comparisons still point out to tensions between the expected mass growth and our results, which might be due to either an incorrect progenitors-descendants selection, uncertainties on star formation rate and mass estimates, or the adopted assumptions on merger rates.

### Exploring properties of high-density matter through remnants of neutron-star mergers

Remnants of neutron-star mergers are essentially massive, hot, differentially rotating neutron stars, which are initially strongly oscillating. They represent a unique probe for high-density matter because the oscillations are detectable via gravitational-wave measurements and are strongly dependent on the equation of state. The impact of the equation of state is apparent in the frequency of the dominant oscillation mode of the remnant. For a fixed total binary mass a tight relation between the dominant postmerger frequency and the radii of nonrotating neutron stars exists. Inferring observationally the dominant postmerger frequency thus determines neutron star radii with high accuracy of the order of a few hundred meters. By considering symmetric and asymmetric binaries of the same chirp mass, we show that the knowledge of the binary mass ratio is not critical for this kind of radius measurements. We summarize different possibilities to deduce the maximum mass of nonrotating neutron stars. We clarify the nature of the three most prominent features of the postmerger gravitational-wave spectrum and argue that the merger remnant can be considered to be a single, isolated, self-gravitating object that can be described by concepts of asteroseismology. The understanding of the different mechanisms shaping the gravitational-wave signal yields a physically motivated analytic model of the gravitational-wave emission, which may form the basis for template-based gravitational-wave data analysis. We explore the observational consequences of a scenario of two families of compact stars including hadronic and quark stars. We find that this scenario leaves a distinctive imprint on the postmerger gravitational-wave signal. In particular, a strong discontinuity in the dominant postmerger frequency as function of the total mass will be a strong indication for two families of compact stars. (abridged)

### Exploring properties of high-density matter through remnants of neutron-star mergers [Cross-Listing]

Remnants of neutron-star mergers are essentially massive, hot, differentially rotating neutron stars, which are initially strongly oscillating. They represent a unique probe for high-density matter because the oscillations are detectable via gravitational-wave measurements and are strongly dependent on the equation of state. The impact of the equation of state is apparent in the frequency of the dominant oscillation mode of the remnant. For a fixed total binary mass a tight relation between the dominant postmerger frequency and the radii of nonrotating neutron stars exists. Inferring observationally the dominant postmerger frequency thus determines neutron star radii with high accuracy of the order of a few hundred meters. By considering symmetric and asymmetric binaries of the same chirp mass, we show that the knowledge of the binary mass ratio is not critical for this kind of radius measurements. We summarize different possibilities to deduce the maximum mass of nonrotating neutron stars. We clarify the nature of the three most prominent features of the postmerger gravitational-wave spectrum and argue that the merger remnant can be considered to be a single, isolated, self-gravitating object that can be described by concepts of asteroseismology. The understanding of the different mechanisms shaping the gravitational-wave signal yields a physically motivated analytic model of the gravitational-wave emission, which may form the basis for template-based gravitational-wave data analysis. We explore the observational consequences of a scenario of two families of compact stars including hadronic and quark stars. We find that this scenario leaves a distinctive imprint on the postmerger gravitational-wave signal. In particular, a strong discontinuity in the dominant postmerger frequency as function of the total mass will be a strong indication for two families of compact stars. (abridged)

### Is Main Sequence Galaxy Star Formation Controlled by Halo Mass Accretion?

It is known that the galaxy stellar-to-halo mass ratio (SHMR) is nearly independent of redshift from z=0-4. This motivates us to construct a toy model in which we assume that the SMHR for central galaxies measured at redshift z~0 is independent of redshift, which implies that the star formation rate (SFR) is determined by the halo mass accretion rate, a phenomenon we call Stellar-Halo Accretion Rate Coevolution (SHARC). Moreover, we show here that the ~0.3 dex dispersion of the halo mass accretion rate (MAR) is similar to the observed dispersion of the SFR on the main sequence. In the context of bathtub-type models of galaxy formation, SHARC leads to mass-dependent constraints on the relation between SFR and MAR. The SHARC assumption is no doubt over-simplified, but we expect it to be possibly valid for central galaxies with stellar masses of 10^9 - 10^10.5 M_sol that are on the star formation main sequence. Such galaxies represent most of the life history of M_* galaxies, and therefore most of the star formation in the Universe. The predictions from SHARC agree remarkably well with the observed SFR of galaxies on the main sequence at low redshifts and fairly well out to higher redshifts, although the predicted SFR exceeds observations at z<4. If we also assume that the interstellar gas mass is constant for each galaxy, equilibrium condition, the SHARC model allows calculation of mass loading factors for inflowing and outflowing gas. With assumptions about preventive feedback based on simulations, the model allows calculation of galaxy metallicity evolution. If the SFR in star-forming galaxies is indeed largely regulated by halo mass accretion, especially at low redshifts, that may help to explain the success of models that tie galaxy properties to those of their host halos, such as age matching and the relation between two-halo galaxy conformity and halo mass accretion conformity.

### Identifying mergers using non-parametric morphological classification at high redshifts

We investigate the time evolution of non-parametric morphological quantities and their relationship to major mergers between $4\geq z \geq 2$ in high-resolution cosmological zoom simulations of disk galaxies that implement kinetic wind feedback, $H_2$-based star formation, and minimal ISM pressurisation. We show that the resulting galaxies broadly match basic observed physical properties of $z\sim 2$ objects. We measure the galaxies' concentrations ($C$), asymmetries ($A$), and $Gini$ ($G$) and $M_{20}$ coefficients, and correlate these with major merger events identified from the mass growth history. We find that high values of asymmetry provide the best indicator for identifying major mergers of $>1:4$ mass ratio within our sample, with $Gini$-$M_{20}\,$ merger classification only as effective for face-on systems and much less effective for edge-on or randomly-oriented galaxies. The canonical asymmetry cut of $A\geq0.35$, however, is only able to correctly identify major mergers $\sim 10\%$ of the time, while a higher cut of $A\geq 0.8$ more efficiently picks out mergers at this epoch. We further examine the temporal correlation between morphological statistics and mergers, and show that for randomly-oriented galaxies, half the galaxies with $A\geq0.8$ undergo a merger within $\pm0.2\,{\rm Gyr}$, whereas $Gini$-$M_{20}\,$ identification only identifies about a third correctly. The fraction improves further using $A\geq 1.5$, but about the half the mergers are missed by this stringent cut.

### Terrestrial Planet Formation Constrained by Mars and the Structure of the Asteroid Belt

Reproducing the large Earth/Mars mass ratio requires a strong mass depletion in solids within the protoplanetary disk between 1 and 3 AU. The Grand Tack model invokes a specific migration history of the giant planets to remove most of the mass initially beyond 1 AU and to dynamically excite the asteroid belt. However, one could also invoke a steep density gradient created by inward drift and pile-up of small particles induced by gas-drag, as has been proposed to explain the formation of close-in super Earths. Here we show that the asteroid belt's orbital excitation provides a crucial constraint against this scenario for the Solar System. We performed a series of simulations of terrestrial planet formation and asteroid belt evolution starting from disks of planetesimals and planetary embryos with various radial density gradients and including Jupiter and Saturn on nearly circular and coplanar orbits. Disks with shallow density gradients reproduce the dynamical excitation of the asteroid belt by gravitational self-stirring but form Mars analogs significantly more massive than the real planet. In contrast, a disk with a surface density gradient proportional to $r^{-5.5}$ reproduces the Earth/Mars mass ratio but leaves the asteroid belt in a dynamical state that is far colder than the real belt. We conclude that no disk profile can simultaneously explain the structure of the terrestrial planets and asteroid belt. The asteroid belt must have been depleted and dynamically excited by a different mechanism such as, for instance, in the Grand Tack scenario.

### Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions [Cross-Listing]

Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasi-equilibrium configurations and dynamical evolutions. In this article, we construct quasi-equilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the SGRID code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity reduced data; we present the possibility of computing data for significantly unequal-mass binaries; and we create equal-mass binaries with individual compactness up to 0.23. As a proof of principle, we explore the dynamical evolution of three new configurations. First, we simulate a $q=2.06$ mass ratio which is the highest mass ratio for a binary neutron star evolved in numerical relativity to date. We find that mass transfer from the companion star sets in a few revolutions before merger and a rest mass of $\sim10^{-2}M_\odot$ is transferred between the two stars. This configuration also ejects a large amount of material during merger, imparting a substantial kick to the remnant. Second, we simulate the first merger of a precessing binary neutron star. We present the dominant modes of the gravitational waves for the precessing simulation, where a clear imprint of the precession is visible in the (2,1) mode. Finally, we quantify the effect of an eccentricity reduction procedure on the gravitational waveform. The procedure improves the waveform quality and should be employed in future precision studies, but also other errors, notably truncation errors, need to be reduced in order for the improvement due to eccentricity reduction to be effective. [abridged]

### Binary Neutron Stars with Generic Spin, Eccentricity, Mass ratio, and Compactness - Quasi-equilibrium Sequences and First Evolutions

Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasi-equilibrium configurations and dynamical evolutions. In this article, we construct quasi-equilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the SGRID code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity reduced data; we present the possibility of computing data for significantly unequal-mass binaries; and we create equal-mass binaries with individual compactness up to 0.23. As a proof of principle, we explore the dynamical evolution of three new configurations. First, we simulate a $q=2.06$ mass ratio which is the highest mass ratio for a binary neutron star evolved in numerical relativity to date. We find that mass transfer from the companion star sets in a few revolutions before merger and a rest mass of $\sim10^{-2}M_\odot$ is transferred between the two stars. This configuration also ejects a large amount of material during merger, imparting a substantial kick to the remnant. Second, we simulate the first merger of a precessing binary neutron star. We present the dominant modes of the gravitational waves for the precessing simulation, where a clear imprint of the precession is visible in the (2,1) mode. Finally, we quantify the effect of an eccentricity reduction procedure on the gravitational waveform. The procedure improves the waveform quality and should be employed in future precision studies, but also other errors, notably truncation errors, need to be reduced in order for the improvement due to eccentricity reduction to be effective. [abridged]

### Analysis of the exoplanet containing system Kepler 91 [Replacement]

We have applied the graphical user interfaced close binary system analysis program WinFitter to an intensive study of Kepler 91 using all the available photometry from the NASA Exoplanet Archive (NEA) at the Caltech website: http://exoplanetarchive.ipac.caltech.edu . Our fitting function for the tidal distortion derives from the relevant Radau equation and includes terms up to the fifth power of the fractional radius. This results in a systematic improvement in the mass ratio estimation over that of Lillo Box et al (2014a) and our derived value for the mass ratio is in close agreement with that inferred from recent high-resolution spectroscopic data. It is clear that the data analysis in terms of simply an eclipsing binary system is compromised by the presence of significant other causes of light variation, in particular non-radial pulsations. We apply a low-frequency filtering procedure to separate out some of this additional light variation. Whilst the derived eccentricity appears then reduced, an eccentric effect remains in the light curve. We consider how this may be maintained in spite of likely frictional effects operating over a long time. There are also indications of the possible effects of Trojan or other period-resonant mass concentrations. Suggestions of a possible secular period variation are briefly discussed.

### Binary accretion rates: dependence on temperature and mass-ratio

We perform a series of 2D smoothed particle hydrodynamics (SPH) simulations of gas accretion onto binaries via a circumbinary disc, for a range of gas temperatures and binary mass ratios ($q$). We show that increasing the gas temperature increases the accretion rate onto the primary for all values of the binary mass ratio: for example, for $q=0.1$ and a fixed binary separation, an increase of normalised sound speed by a factor of $5$ (from our "cold" to "hot" simulations) changes the fraction of the accreted gas that flows on to the primary from $10\%$ to $\sim40\%$. We present a simple parametrisation for the average accretion rate of each binary component accurate to within a few percent and argue that this parametrisation (rather than those in the literature based on warmer simulations) is relevant to supermassive black hole accretion and all but the widest stellar binaries. We present trajectories for the growth of $q$ during circumbinary disc accretion and argue that the period distribution of stellar "twin" binaries is strong evidence for the importance of circumbinary accretion. We also show that our parametrisation of binary accretion increases the minimum mass ratio needed for spin alignment of supermassive black holes to $q \sim 0.4$, with potentially important implications for the magnitude of velocity kicks acquired during black hole mergers.

### Precessional instability in binary black holes with aligned spins [Cross-Listing]

Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been testbeds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is anti-aligned. Spins in these configurations are unstable to precession to large misalignment when the binary separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{\chi_1} \pm \sqrt{q \chi_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is the mass ratio, and $\chi_1$ ($\chi_2$) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.

### Precessional instability in binary black holes with aligned spins

Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been testbeds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is anti-aligned. Spins in these configurations are unstable to precession to large misalignment when the binary separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{\chi_1} \pm \sqrt{q \chi_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is the mass ratio, and $\chi_1$ ($\chi_2$) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.

### Precessional instability in binary black holes with aligned spins [Replacement]

Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been testbeds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is anti-aligned. Spins in these configurations are unstable to precession to large misalignment when the binary separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{\chi_1} \pm \sqrt{q \chi_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is the mass ratio, and $\chi_1$ ($\chi_2$) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.

### OGLE-2012-BLG-0563Lb: a Saturn-mass Planet around an M Dwarf with the Mass Constrained by Subaru AO imaging [Replacement]

We report the discovery of a microlensing exoplanet OGLE-2012-BLG-0563Lb with the planet-star mass ratio ~1 x 10^{-3}. Intensive photometric observations of a high-magnification microlensing event allow us to detect a clear signal of the planet. Although no parallax signal is detected in the light curve, we instead succeed at detecting the flux from the host star in high-resolution JHK'-band images obtained by the Subaru/AO188 and IRCS instruments, allowing us to constrain the absolute physical parameters of the planetary system. With the help of a spectroscopic information of the source star obtained during the high-magnification state by Bensby et al. (2013), we find that the lens system is located at 1.3^{+0.6}_{-0.8} kpc from us, and consists of an M dwarf (0.34^{+0.12}_{-0.20} M_sun) orbited by a Saturn-mass planet (0.39^{+0.14}_{-0.23} M_Jup) at the projected separation of 0.74^{+0.26}_{-0.42} AU (close model) or 4.3^{+1.5}_{-2.5} AU (wide model). The probability of contamination in the host star's flux, which would reduce the masses by a factor of up to 3, is estimated to be 17%. This possibility can be tested by future high-resolution imaging. We also estimate the (J-Ks) and (H-Ks) colors of the host star, which are marginally consistent with a low-metallicity mid-to-early M dwarf, although further observations are required for the metallicity to be conclusive. This is the fifth sub-Jupiter-mass (0.2<m_p/M_Jup<1) microlensing planet around an M dwarf with the mass well constrained. The relatively rich harvest of sub-Jupiters around M dwarfs is contrasted with a possible paucity of ~1--2 Jupiter-mass planets around the same type of star, which can be explained by the planetary formation process in the core accretion scheme.

### OGLE-2012-BLG-0563Lb: a Saturn-mass Planet around an M Dwarf with the Mass Constrained by Subaru AO imaging

We report the discovery of a microlensing exoplanet OGLE-2012-BLG-0563Lb with the planet-star mass ratio ~1 x 10^{-3}. Intensive photometric observations of a high-magnification microlensing event allow us to detect a clear signal of the planet. Although no parallax signal is detected in the light curve, we instead succeed at detecting the flux from the host star in high-resolution JHK'-band images obtained by the Subaru/AO188 and IRCS instruments, allowing us to constrain the absolute physical parameters of the planetary system. With the help of a spectroscopic information of the source star obtained during the high-magnification state by Bensby et al. (2013), we find that the lens system is located at 1.3^{+0.6}_{-0.8} kpc from us, and consists of an M dwarf (0.34^{+0.12}_{-0.20} M_sun) orbited by a Saturn-mass planet (0.39^{+0.14}_{-0.23} M_Jup) at the projected separation of 0.74^{+0.26}_{-0.42} AU (close model) or 4.3^{+1.5}_{-2.5} AU (wide model). The probability of contamination in the host star's flux, which would reduce the masses by a factor of up to 3, is estimated to be 17%. This possibility can be tested by future high-resolution imaging. We also estimate the (J-Ks) and (H-Ks) colors of the host star, which are marginally consistent with a low-metallicity mid-to-early M dwarf, although further observations are required for the metallicity to be conclusive. This is the fifth sub-Jupiter-mass (0.2<m_p/M_Jup<1) microlensing planet around an M dwarf with the mass well constrained. The relatively rich harvest of sub-Jupiters around M dwarfs is contrasted with a possible paucity of ~1--2 Jupiter-mass planets around the same type of star, which can be explained by the planetary formation process in the core accretion scheme.

### What are Protoclusters? -- Defining High Redshift Galaxy Clusters and Protoclusters

We explore the structures of protoclusters and their relationship with high redshift clusters using the Millennium Simulation combined with a semi-analytic model. We find that protoclusters are very extended, with 90 per cent of their mass spread across $\sim35\,h^{-1}{\rm Mpc}$ comoving at $z=2$ ($\sim30\, \rm{arcmin}$). The main halo', which can manifest as a high redshift cluster or group, is only a minor feature of the protocluster, containing less than 20 per cent of all protocluster galaxies at $z=2$. Furthermore, many protoclusters do not contain a main halo that is massive enough to be identified as a high redshift cluster. Protoclusters exist in a range of evolutionary states at high redshift, independent of the mass they will evolve to at $z=0$. We show that the evolutionary state of a protocluster can be approximated by the mass ratio of the first and second most massive haloes within the protocluster, and the $z=0$ mass of a protocluster can be estimated to within 0.2 dex accuracy if both the mass of the main halo and the evolutionary state is known. We also investigate the biases introduced by only observing star-forming protocluster members within small fields. The star formation rate required for line-emitting galaxies to be detected is typically high, which leads to the artificial loss of low mass galaxies from the protocluster sample. This effect is stronger for observations of the centre of the protocluster, where the quenched galaxy fraction is higher. This loss of low mass galaxies, relative to the field, distorts the size of the galaxy overdensity, which in turn can contribute to errors in predicting the $z=0$ evolved mass.

### Mass ratio of the 2 pc binary brown dwarf LUH16 and limits on planetary companions from astrometry [Replacement]

We analyse FORS2/VLT $I$-band imaging data to monitor the motions of both components in the nearest known binary brown dwarf WISE J104915.57-531906.1AB (LUH16) over one year. The astrometry is dominated by parallax and proper motion, but with a precision of $\sim$0.2 milli-arcsecond per epoch we accurately measure the relative position change caused by the orbital motion of the pair. This allows us to directly measure a mass ratio of $q=0.78\pm0.10$ for this system. We also search for the signature of a planetary-mass companion around either of the A and B component and exclude at 3-$\sigma$ the presence of planets with masses larger than $2\,M_\mathrm{Jup}$ and orbital periods of 20--300 d. We update the parallax of LUH16 to $500.51\pm0.11$ mas, i.e. just within 2 pc. This study yields the first direct constraint on the mass ratio of LUH16 and shows that the system does not harbour any close-in giant planets.

### Mass ratio of the 2 pc binary brown dwarf LUH16 and limits on planetary companions from astrometry

We analyse FORS2/VLT I-band imaging data to monitor the motions of both components in the most nearby known binary brown dwarf WISE J104915.57-531906.1AB (LUH16) over one year. The astrometry is dominated by parallax and proper motion, but with a precision of $\sim$0.2 milli-arcsecond per epoch we accurately measure the relative position change caused by the orbital motion of the pair. This allows us to directly determine a mass ratio of $q=0.78\pm0.10$ for this system. We also search for the signature of a planetary-mass companion around either of the A and B component and exclude at 3-$\sigma$ the presence of planets with masses larger than $2\,M_\mathrm{Jup}$ and orbital periods of 20-300 d. We update the parallax of LUH16 to $500.51\pm0.11$ mas, i.e. just within 2 pc. This study yields the first direct constraint on the mass ratio of LUH16 and shows that the system does not harbour any close-in giant planets.

### Black hole-neutron star binary merger: Dependence on black hole spin orientation and equations of state

We systematically performed numerical-relativity simulations for black hole (BH) - neutron star (NS) binary mergers with a variety of the BH spin orientation and equations of state (EOS) of the NS. The initial misalignment angles of the BH spin are chosen in the range of i_tilt,0 = 30--90[deg.]. We employed four models of NS EOS with which the compactness of the NS is in the range of C = M_NS/R_NS = 0.138--0.180, where M_NS and R_NS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q = M_BH/M_NS, and the dimensionless spin parameter of the BH, chi, are chosen to be Q = 5 and chi = 0.75, together with M_NS = 1.35 M_sun. We obtain the following results: (i) The inclination angle of i_tilt,0 < 70[deg.] and i_tilt,0 < 50[deg.] are required for the formation of a remnant disk with its mass larger than 0.1 M_sun for the case C = 0.140 and C = 0.160, respectively, while the disk mass is always smaller than 0.1M_sun for C = 0.175. The ejecta with its mass larger than 0.01 M_sun is obtained for i_tilt,0 < 85[deg.] with C = 0.140, for i_tilt,0 < 65[deg.] with C = 0.160, and for i_tilt,0 < 30[deg.] with C = 0.175. (ii) The rotational axis of the dense part of the remnant disk is approximately aligned with the remnant BH spin for i_tilt,0 = 30[deg.]. On the other hand, the disk axis is misaligned initially with ~ 30[deg.] for i_tilt,0 = 60[deg.], and the alignment with the remnant BH spin is achieved at ~ 50--60 ms after the onset of merger. The accretion time scale of the remnant disk is typically ~ 100 ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically ~ 0.2--0.3c and depends only weakly on i_tilt,0 and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for i_tilt,0 < 60[deg.].

### Black hole-neutron star binary merger: Dependence on black hole spin orientation and equations of state [Cross-Listing]

We systematically performed numerical-relativity simulations for black hole (BH) - neutron star (NS) binary mergers with a variety of the BH spin orientation and equations of state (EOS) of the NS. The initial misalignment angles of the BH spin are chosen in the range of i_tilt,0 = 30--90[deg.]. We employed four models of NS EOS with which the compactness of the NS is in the range of C = M_NS/R_NS = 0.138--0.180, where M_NS and R_NS are the mass and the radius of the NS, respectively. The mass ratio of the BH to the NS, Q = M_BH/M_NS, and the dimensionless spin parameter of the BH, chi, are chosen to be Q = 5 and chi = 0.75, together with M_NS = 1.35 M_sun. We obtain the following results: (i) The inclination angle of i_tilt,0 < 70[deg.] and i_tilt,0 < 50[deg.] are required for the formation of a remnant disk with its mass larger than 0.1 M_sun for the case C = 0.140 and C = 0.160, respectively, while the disk mass is always smaller than 0.1M_sun for C = 0.175. The ejecta with its mass larger than 0.01 M_sun is obtained for i_tilt,0 < 85[deg.] with C = 0.140, for i_tilt,0 < 65[deg.] with C = 0.160, and for i_tilt,0 < 30[deg.] with C = 0.175. (ii) The rotational axis of the dense part of the remnant disk is approximately aligned with the remnant BH spin for i_tilt,0 = 30[deg.]. On the other hand, the disk axis is misaligned initially with ~ 30[deg.] for i_tilt,0 = 60[deg.], and the alignment with the remnant BH spin is achieved at ~ 50--60 ms after the onset of merger. The accretion time scale of the remnant disk is typically ~ 100 ms and depends only weakly on the misalignment angle and the EOS. (iii) The ejecta velocity is typically ~ 0.2--0.3c and depends only weakly on i_tilt,0 and the EOS of the NS, while the morphology of the ejecta depends on its mass. (iv) The gravitational-wave spectra contains the information of the NS compactness in the cutoff frequency for i_tilt,0 < 60[deg.].

### Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar $\psi_4$ using semi-analytical methods. The metric perturbation is then reconstructed from $\psi_4$ in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies $\Omega_r$ and $\Omega_\phi$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

### Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole [Replacement]

We present the first numerical calculation of the (local) metric perturbation produced by a small compact object moving on an eccentric equatorial geodesic around a Kerr black hole, accurate to first order in the mass ratio. The procedure starts by first solving the Teukolsky equation to obtain the Weyl scalar $\psi_4$ using semi-analytical methods. The metric perturbation is then reconstructed from $\psi_4$ in an (outgoing) radiation gauge, adding the appropriate non-radiative contributions arising from the shifts in mass and angular momentum of the spacetime. As a demonstration we calculate the generalized redshift $U$ as a function of the orbital frequencies $\Omega_r$ and $\Omega_\phi$ to linear order in the mass ratio, a gauge invariant measure of the conservative corrections to the orbit due to self-interactions. In Schwarzschild, the results surpass the existing result in the literature in accuracy, and we find new estimates for some of the unknown 4PN and 5PN terms in the post-Newtonian expansion of $U$. In Kerr, we provide completely novel values of $U$ for eccentric equatorial orbits. Calculation of the full self-force will appear in a forthcoming paper.

### Migration of two massive planets into (and out of) first order mean motion resonances

We consider the dynamical evolution of two planets orbiting in the vicinity of a first order mean motion reso- nance while simultaneously undergoing eccentricity damping and convergent migration. Following Goldreich & Schlichting (2014), we include a coupling between the dissipative semimajor axis evolution and the damping of the eccentricities. In agreement with past studies, we find that this coupling can lead to overstability of the resonance and that for a certain range of parameters capture into resonance is only temporary. Using a more general model, we show that whether overstable motion can occur depends in a characteristic way on the mass ratio between the two planets as well as their relative eccentricity damping timescales. Moreover, we show that even when escape from resonance does occur, the timescale for escape is long enough such at any given time a pair of planets is more likely to be found in a resonance rather than migrating between them. Thus, we argue that overstability of resonances cannot singlehandedly reconcile convergent migration with the observed lack of Kepler planet pairs found near resonances. However, it is possible that overstable motion in combination with other effects such as large scale orbital instability could produce the observed period ratio distribution.

### Merging galaxies produce outliers from the Fundamental Metallicity Relation [Replacement]

From a large sample of $\approx 170,000$ local SDSS galaxies, we find that the Fundamental Metallicity Relation (FMR) has an overabundance of outliers, compared to what would be expected from a Gaussian distribution of residuals, with significantly lower metallicities than predicted from their stellar mass and star formation rate (SFR). This low-metallicity population has lower stellar masses, bimodial specific SFRs with enhanced star formation within the aperture and smaller half-light radii than the general sample, and is hence a physically distinct population. We show that they are consistent with being galaxies that are merging or have recently merged with a satellite galaxy. In this scenario, low-metallicity gas flows in from large radii, diluting the metallicity of star-forming regions and enhancing the specific SFR until the inflowing gas is processed and the metallicity has recovered. We introduce a simple model in which mergers with a mass ratio larger than a minimum dilute the central galaxy's metallicity by an amount that is proportional to the stellar mass ratio for a constant time, and show that it provides an excellent fit to the distribution of FMR residuals. We find the dilution time-scale to be $\tau=1.568_{-0.027}^{+0.029}$ Gyr, the average metallicity depression caused by a 1:1 merger to be $\alpha=0.2480_{-0.0020}^{+0.0017}$ dex and the minimum mass ratio merger that can be discerned from the intrinsic Gaussian scatter in the FMR to be $\xi_\text{min}=0.2030_{-0.0095}^{+0.0127}$ (these are statistical errors only). From this we derive that the average metallicity depression caused by a merger with mass ratio between 1:5 and 1:1 is 0.114 dex.

### Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium

We consider hard three-loop corrections to hyperfine splitting in muonium and positronium generated by the diagrams with closed electron loops. There are six gauge-invariant sets of such diagrams that generate corrections of order $m\alpha^7$. The contributions of these diagrams are calculated for an arbitrary electron-muon mass ratio without expansion in the small mass ratio. We obtain the formulae for contributions to hyperfine splitting that in the case of small mass ratio describe corrections for muonium and in the case of equal masses describe corrections for positronium. First few terms of the expansion of hard corrections in the small mass ratio were earlier calculated for muonium analytically. We check numerically that the new results coincide with the sum of the known terms of the expansion in the case of small mass ratio. In the case of equal masses we obtain hard nonlogarithmic corrections of order $m\alpha^7$ to hyperfine splitting in positronium.

### Search for associations containing young stars (SACY). VI. Is multiplicity universal? Stellar multiplicity in the range 3-1000 au from adaptive-optics observations

Context. Young loose nearby associations are unique samples of close (<150 pc), young (approx 5-100 Myr) pre-main sequence (PMS) stars. A significant number of members of these associations have been identified in the SACY collaboration. We can use the proximity and youth of these members to investigate key ingredients in star formation processes, such as multiplicity. Aims. We present the statistics of identified multiple systems from 113 confirmed SACY members. We derive multiplicity frequencies, mass-ratio, and physical separation distributions in a consistent parameter space, and compare our results to other PMS populations and the field. Methods. We have obtained adaptive-optics assisted near-infrared observations with NACO (ESO/VLT) and IRCAL (Lick Observatory) for at least one epoch of all 113 SACY members. We have identified multiple systems using co-moving proper-motion analysis and using contamination estimates. We have explored ranges in projected separation and mass-ratio of a [3-1000 au], and q [0.1-1], respectively. Results. We have identified 31 multiple systems (28 binaries and 3 triples). We derive a multiplicity frequency (MF) of MF_(3-1000au)=28.4 +4.7, -3.9% and a triple frequency (TF) of TF_(3-1000au)=2.8 +2.5, -0.8% in the separation range of 3-1000 au. We do not find any evidence for an increase in the MF with primary mass. The estimated mass-ratio of our statistical sample (with power-law index gamma=-0.04 +/- 0.14) is consistent with a flat distribution (gamma = 0). Conclusions. We show further similarities (but also hints of discrepancies) between SACY and the Taurus region: flat mass-ratio distributions and statistically similar MF and TF values. We also compared the SACY sample to the field (in the separation range of 19-100 au), finding that the two distributions are indistinguishable, suggesting a similar formation mechanism.

### On the potentially dramatic history of the super-Earth rho 55 Cancri e

We demonstrate that tidal evolution of the inner planet (`e') of the system orbiting the star rho 55 Cancri could have led to passage through two secular resonances with other planets in the system. The consequence of this evolution is excitation of both the planetary eccentricity and inclination relative to the original orbital plane. The large mass ratio between the innermost planet and the others means that these excitations can be of substantial amplitude and can have dramatic consequences for the system organisation. Such evolution can potentially explain the large observed mutual inclination between the innermost and outermost planets in the system, and implies that tidal heating could have substantially modified the structure of planet e, and possibly reduced its mass by Roche lobe overflow. Similar inner secular resonances may be found in many multiple planet systems and suggest that many of the innermost planets in these systems could have suffered similar evolutions.

### Effects of hot halo gas on the star formation and mass transfer during distant galaxy-galaxy encounters

We use $N$-body/smoothed particle hydrodynamics simulations of encounters between an early-type galaxy (ETG) and a late-type galaxy (LTG) to study the effects of hot halo gas on the evolution for a case with the mass ratio of the ETG to LTG of 2:1 and the closest approach distance of $\sim$100 kpc. We find that the dynamics of the cold disk gas in the tidal bridge and the amount of the newly formed stars depend strongly on the existence of a gas halo. In the run of interacting galaxies not having a hot gas halo, the gas and stars accreted into the ETG do not include newly formed stars. However, in the run using the ETG with a gas halo and the LTG without a gas halo, a shock forms along the disk gas tidal bridge and induces star formation near the closest approach. The shock front is parallel to a channel along which the cold gas flows toward the center of the ETG. As a result, the ETG can accrete star-forming cold gas and newly born stars at and near its center. When both galaxies have hot gas halos, a shock is formed between the two gas halos somewhat before the closest approach. The shock hinders the growth of the cold gas bridge to the ETG and also ionizes it. Only some of the disk stars transfer through the stellar bridge. We conclude that the hot halo gas can give significant hydrodynamic effects during distant encounters.

### PZ Mon is a new RS CVn synchronous binary giant with low mass ratio

Analysis of new radial velocity measurements of the active giant PZ Mon is presented. We estimated the radial velocity of center of mass 25.5$\pm$0.3 km s$^{-1}$, the period on the circular orbit $P=34.14\pm0.02$ days, and parameters of the secondary component including the mass $M_2$=0.14 M$_\odot$ which is a smallest among known components of RS CVn type giants. Combined with photometric data we conclude that PZ Mon is a system with synchronous rotation, and there is a big cool spotted area on PZ Mon surface towards to secondary component that provides optical variability.

### PZ Mon is a new synchronous binary with low mass ratio [Replacement]

Analysis of new radial velocity measurements of the active giant PZ Mon is presented. Only in 2015 was reported that PZ Mon may be classified as RS CVn giant. At the same time was discovered the variability of radial velocity. However, lack of the data is not allowed to determine parameters of the system. The measurements of radial velocity were performed using Radial Velocity Meter installed at the Simeiz 1-m telescope of the Crimean Astrophysical Observatory and using echelle spectrographs installed at the 2-m Zeiss telescope of the Terskol Observatory and the 6-m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. We estimated parameters of this binary system including the $\gamma$-velocity 25.5$\pm$0.3 kms, the period on the circular orbit $P=34.15\pm0.02$ days, the mass of the secondary component $M_2$=0.14 \Mo, and the mass ratio $q=0.09$ The mass ratio is a smallest value among known RS CVn type giants. Combined with photometric data we conclude that PZ Mon is a system with synchronous rotation, and there is a big cool spotted area on the stellar surface towards to the secondary component that provides the optical variability.

### Detection of radial velocity shifts due to black hole binaries near merger

The barycenter of a massive black hole binary will lie outside the event horizon of the primary black hole for modest values of mass ratio and binary separation. Analagous to radial velocity shifts in stellar emission lines caused by the tug of planets, the radial velocity of the primary black hole around the barycenter can leave a tell-tale oscillation in the broad component of Fe K$\alpha$ emission from accreting gas. Near-future X-ray telescopes such as Astro-H and Athena will have the energy resolution ($\delta E/E \lesssim 10^{-3}$) to search nearby active galactic nuclei (AGN) for the presence of binaries with mass ratios $q \gtrsim 0.01$, separated by several hundred gravitational radii. The general-relativistic and Lense-Thirring precession of the periapse of the secondary orbit imprints a detectable modulation on the oscillations. The lowest mass binaries in AGN will oscillate many times within typical X-ray exposures, leading to a broadening of the line wings and an over-estimate of black hole spin in these sources. Detection of periodic oscillations in the AGN line centroid energy will reveal a massive black hole binary close to merger and will provide an early warning of gravitational radiation emission.

### Sharp bounds on the radius of relativistic charged spheres: Guilfoyle's stars saturate the Buchdahl-Andr\'easson bound [Cross-Listing]

Buchdahl, by imposing a few physical assumptions on the matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution, found that the radius $r_0$ to mass $m$ ratio of a star would obey the Buchdahl bound $r_0/m\geq9/4$. He noted that the bound was saturated by the Schwarzschild interior solution, the solution with $\rho_{\rm m}(r)= {\rm constant}$, where $\rho_{\rm m}(r)$ is the energy density of the matter at $r$, when the central central pressure blows to infinity. Generalizations of this bound have been studied. One generalization was given by Andr\'easson by including electrically charged matter and imposing that $p+2p_T \leq\rho_{\rm m}$, where $p$ is the radial pressure and $p_T$ the tangential pressure. His bound is given by $r_0/m\geq9/\left(1+\sqrt{1+3\,q^2/r_0^2}\right)^{2}$, the Buchdahl-Andr\'easson bound, with $q$ being the star's total electric charge. Following Andr\'easson's proof, the configuration that saturates the Buchdahl bound is an uncharged shell, rather than the Schwarzschild interior solution. By extension, the configurations that saturate the Buchdahl-Andr\'easson bound are charged shells. One expects then, in turn, that there should exist an electrically charged equivalent to the interior Schwarzschild limit. We find here that this equivalent is provided by the equation $\rho_{\rm m}(r) + {Q^2(r)}/ {\left(8\pi\,r^4\right)}= {\rm constant}$, where $Q(r)$ is the electric charge at $r$. This equation was put forward by Cooperstock and de la Cruz, and Florides, and realized in Guilfoyle's stars. When the central pressure goes to infinity Guilfoyle's stars are configurations that saturate the Buchdahl-Andr\'easson bound. It remains to find a proof in Buchdahl's manner such that these configurations are the limiting configurations of the bound.

### Sharp bounds on the radius of relativistic charged spheres: Guilfoyle's stars saturate the Buchdahl-Andr\'easson bound

Buchdahl, by imposing a few physical assumptions on the matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution, found that the radius $r_0$ to mass $m$ ratio of a star would obey the Buchdahl bound $r_0/m\geq9/4$. He noted that the bound was saturated by the Schwarzschild interior solution, the solution with $\rho_{\rm m}(r)= {\rm constant}$, where $\rho_{\rm m}(r)$ is the energy density of the matter at $r$, when the central central pressure blows to infinity. Generalizations of this bound have been studied. One generalization was given by Andr\'easson by including electrically charged matter and imposing that $p+2p_T \leq\rho_{\rm m}$, where $p$ is the radial pressure and $p_T$ the tangential pressure. His bound is given by $r_0/m\geq9/\left(1+\sqrt{1+3\,q^2/r_0^2}\right)^{2}$, the Buchdahl-Andr\'easson bound, with $q$ being the star's total electric charge. Following Andr\'easson's proof, the configuration that saturates the Buchdahl bound is an uncharged shell, rather than the Schwarzschild interior solution. By extension, the configurations that saturate the Buchdahl-Andr\'easson bound are charged shells. One expects then, in turn, that there should exist an electrically charged equivalent to the interior Schwarzschild limit. We find here that this equivalent is provided by the equation $\rho_{\rm m}(r) + {Q^2(r)}/ {\left(8\pi\,r^4\right)}= {\rm constant}$, where $Q(r)$ is the electric charge at $r$. This equation was put forward by Cooperstock and de la Cruz, and Florides, and realized in Guilfoyle's stars. When the central pressure goes to infinity Guilfoyle's stars are configurations that saturate the Buchdahl-Andr\'easson bound. It remains to find a proof in Buchdahl's manner such that these configurations are the limiting configurations of the bound.

### Sharp bounds on the radius of relativistic charged spheres: Guilfoyle's stars saturate the Buchdahl-Andr\'easson bound [Cross-Listing]

Buchdahl, by imposing a few physical assumptions on the matter, i.e., its density is a nonincreasing function of the radius and the fluid is a perfect fluid, and on the configuration, such as the exterior is the Schwarzschild solution, found that the radius $r_0$ to mass $m$ ratio of a star would obey the Buchdahl bound $r_0/m\geq9/4$. He noted that the bound was saturated by the Schwarzschild interior solution, the solution with $\rho_{\rm m}(r)= {\rm constant}$, where $\rho_{\rm m}(r)$ is the energy density of the matter at $r$, when the central central pressure blows to infinity. Generalizations of this bound have been studied. One generalization was given by Andr\'easson by including electrically charged matter and imposing that $p+2p_T \leq\rho_{\rm m}$, where $p$ is the radial pressure and $p_T$ the tangential pressure. His bound is given by $r_0/m\geq9/\left(1+\sqrt{1+3\,q^2/r_0^2}\right)^{2}$, the Buchdahl-Andr\'easson bound, with $q$ being the star's total electric charge. Following Andr\'easson's proof, the configuration that saturates the Buchdahl bound is an uncharged shell, rather than the Schwarzschild interior solution. By extension, the configurations that saturate the Buchdahl-Andr\'easson bound are charged shells. One expects then, in turn, that there should exist an electrically charged equivalent to the interior Schwarzschild limit. We find here that this equivalent is provided by the equation $\rho_{\rm m}(r) + {Q^2(r)}/ {\left(8\pi\,r^4\right)}= {\rm constant}$, where $Q(r)$ is the electric charge at $r$. This equation was put forward by Cooperstock and de la Cruz, and Florides, and realized in Guilfoyle's stars. When the central pressure goes to infinity Guilfoyle's stars are configurations that saturate the Buchdahl-Andr\'easson bound. It remains to find a proof in Buchdahl's manner such that these configurations are the limiting configurations of the bound.