# Posts Tagged mass ratio

## Recent Postings from mass ratio

### 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.

### 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

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 [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 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.

### 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.

### 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.

### 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

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.

### 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.

### The ecology of dark matter haloes I: The rates and types of halo interactions

Interactions such as mergers and flybys play a fundamental role in shaping galaxy morphology. Using the Horizon Run 4 cosmological N-body simulation, we studied the frequency and type of halo interactions, and their redshift evolution as a function of the environment defined by the large-scale density, pair separation, mass ratio, and target halo mass. Most interactions happen at large-scale density contrast $\delta \approx 20$, regardless of the redshift, corresponding to groups and relatively dense part of filaments. However, the fraction of interacting target is maximum at $\delta \approx 1000$. We provide a new empirical fitting form for the interaction rate as a function of the halo mass, large-scale density, and redshift. We also report the existence of two modes of interactions from the distributions of mass ratio and relative distance, implying two different physical origins of the interaction. Satellite targets lose their mass as they proceed deeper into the host halo. The relative importance of these two trends strongly depends on the large-scale density, target mass, and redshift.

### PHL 1445: An eclipsing cataclysmic variable with a substellar donor near the period minimum

We present high-speed, three-colour photometry of the eclipsing dwarf nova PHL 1445, which, with an orbital period of 76.3 min, lies just below the period minimum of ~82 min for cataclysmic variable stars. Averaging four eclipses reveals resolved eclipses of the white dwarf and bright spot. We determined the system parameters by fitting a parameterised eclipse model to the averaged lightcurve. We obtain a mass ratio of q = 0.087 +- 0.006 and inclination i = 85.2 +- 0.9 degrees. The primary and donor masses were found to be Mw = 0.73 +- 0.03 Msun and Md = 0.064 +- 0.005 Msun, respectively. Through multicolour photometry a temperature of the white dwarf of Tw = 13200 +- 700 K and a distance of 220 +- 50 pc were determined. The evolutionary state of PHL 1445 is uncertain. We are able to rule out a significantly evolved donor, but not one that is slightly evolved. Formation with a brown dwarf donor is plausible; though the brown dwarf would need to be no older than 600 Myrs at the start of mass transfer, requiring an extremely low mass ratio (q = 0.025) progenitor system. PHL 1445 joins SDSS 1433 as a sub-period minimum CV with a substellar donor. These existence of two such systems raises an alternative possibility; that current estimates for the intrinsic scatter and/or position of the period minimum may be in error.

### On the Influence of Minor Mergers on the Radial Abundance Gradient in Disks of Milky Way-like Galaxies

We investigate the influence of stellar migration caused by minor mergers (mass ratio from 1:70 to 1:8) on the radial distribution of chemical abundances in the disks of Milky Way-like galaxies during the last four Gyr. A GPU-based pure N-body tree-code model without hydrodynamics and star formation was used. We computed a large set of mergers with different initial satellite masses, positions, and orbital velocities. We find that there is no significant metallicity change at any radius of the primary galaxy in the case of accretion of a low-mass satellite of 10$^9$ M$_{\odot}$ (mass ratio 1:70) except for the special case of prograde satellite motion in the disk plane of the host galaxy. The accretion of a satellite of a mass $\gtrsim3\times10^9$ M$_{\odot}$ (mass ratio 1:23) results in an appreciable increase of the chemical abundances at galactocentric distances larger than $\sim10$ kpc. The radial abundance gradient flattens in the range of galactocentric distances from 5 to 15 kpc in the case of a merger with a satellite with a mass $\gtrsim3\times10^9$ M$_{\odot}$. There is no significant change in the abundance gradient slope in the outer disk (from $\sim15$ kpc up to 25 kpc) in any merger while the scatter in metallicities at a given radius significantly increases for most of the satellite’s initial masses/positions compared to the case of an isolated galaxy. This argues against attributing the break (flattening) of the abundance gradient near the optical radius observed in the extended disks of Milky Way-like galaxies only to merger-induced stellar migration.

### On the Influence of Minor Mergers on the Radial Abundance Gradient in Disks of Milky Way-like Galaxies [Replacement]

We investigate the influence of stellar migration caused by minor mergers (mass ratio from 1:70 to 1:8) on the radial distribution of chemical abundances in the disks of Milky Way-like galaxies during the last four Gyr. A GPU-based pure N-body tree-code model without hydrodynamics and star formation was used. We computed a large set of mergers with different initial satellite masses, positions, and orbital velocities. We find that there is no significant metallicity change at any radius of the primary galaxy in the case of accretion of a low-mass satellite of 10$^9$ M$_{\odot}$ (mass ratio 1:70) except for the special case of prograde satellite motion in the disk plane of the host galaxy. The accretion of a satellite of a mass $\gtrsim3\times10^9$ M$_{\odot}$ (mass ratio 1:23) results in an appreciable increase of the chemical abundances at galactocentric distances larger than $\sim10$ kpc. The radial abundance gradient flattens in the range of galactocentric distances from 5 to 15 kpc in the case of a merger with a satellite with a mass $\gtrsim3\times10^9$ M$_{\odot}$. There is no significant change in the abundance gradient slope in the outer disk (from $\sim15$ kpc up to 25 kpc) in any merger while the scatter in metallicities at a given radius significantly increases for most of the satellite’s initial masses/positions compared to the case of an isolated galaxy. This argues against attributing the break (flattening) of the abundance gradient near the optical radius observed in the extended disks of Milky Way-like galaxies only to merger-induced stellar migration.

### The Missing Link: Bayesian Detection and Measurement of Intermediate-Mass Black-Hole Binaries

We perform Bayesian analysis of gravitational-wave signals from non-spinning, intermediate-mass black-hole binaries (IMBHBs) with observed total mass, $M_{\mathrm{obs}}$, from $50\mathrm{M}_{\odot}$ to $500\mathrm{M}_{\odot}$ and mass ratio $1\mbox{–}4$ using advanced LIGO and Virgo detectors. We employ inspiral-merger-ringdown waveform models based on the effective-one-body formalism and include subleading modes of radiation beyond the leading $(2,2)$ mode. The presence of subleading modes increases signal power for inclined binaries and allows for improved accuracy and precision in measurements of the masses as well as breaking of extrinsic parameter degeneracies. For low total masses, $M_{\mathrm{obs}} \lesssim 50 \mathrm{M}_{\odot}$, the observed chirp mass $\mathcal{M}_{\rm obs} = M_{\mathrm{obs}}\,\eta^{3/5}$ ($\eta$ being the symmetric mass ratio) is better measured. In contrast, as increasing power comes from merger and ringdown, we find that the total mass $M_{\mathrm{obs}}$ has better relative precision than $\mathcal{M}_{\rm obs}$. Indeed, at high $M_{\mathrm{obs}}$ ($\geq 300 \mathrm{M}_{\odot}$), the signal resembles a burst and the measurement thus extracts the dominant frequency of the signal that depends on $M_{\mathrm{obs}}$. Depending on the binary’s inclination, at signal-to-noise ratio (SNR) of $12$, uncertainties in $M_{\mathrm{obs}}$ can be as large as $\sim 20 \mbox{–}25\%$ while uncertainties in $\mathcal{M}_{\rm obs}$ are $\sim 50 \mbox{–}60\%$ in binaries with unequal masses (those numbers become $\sim 17\%$ versus $\sim22\%$ in more symmetric binaries). Although large, those uncertainties will establish the existence of IMBHs. Our results show that gravitational-wave observations can offer a unique tool to observe and understand the formation, evolution and demographics of IMBHs, which are difficult to observe in the electromagnetic window. (abridged)

### Synergy between ground and space based gravitational wave detectors for estimation of binary coalescence parameters

We study the advantage of the co-existence of future ground and space based gravitational wave detectors, in estimating the parameters of a binary coalescence. Using the post-Newtonian waveform for the inspiral of non-spinning neutron star-black hole pairs in circular orbits, we study how the estimates for chirp mass, symmetric mass ratio, and time and phase at coalescence are improved by combining the data from different space-ground detector pairs. Since the gravitational waves produced by binary coalescence also provide a suitable domain where we can study strong field gravity, we also study the deviations from general relativity using the parameterized post-Einsteinian framework. As an example, focusing on the Einstein telescope and DECIGO pair, we demonstrate that there exists a sweet spot range of sensitivity in the pre-DECIGO phase where the best enhancement due to the synergy effect can be obtained for the estimates of the post-Newtonian waveform parameters as well as the modification parameters to general relativity.

### Orientation of x-lines in asymmetric magnetic reconnection - mass ratio dependency [Cross-Listing]

Using fully kinetic simulations, we study the x-line orientation of magnetic reconnection in an asymmetric configuration. A spatially localized perturbation is employed to induce a single x-line, that has sufficient freedom to choose its orientation in three-dimensional systems. The effect of ion to electron mass ratio is investigated, and the x-line appears to bisect the magnetic shear angle across the current sheet in the large mass ratio limit. The orientation can generally be deduced by scanning through corresponding 2D simulations to find the reconnection plane that maximizes the peak reconnection electric field. The deviation from the bisection angle in the lower mass ratio limit can be explained by the physics of tearing instability.

### Suzaku observations of subhalos in the Coma cluster

We observed three massive subhalos in the Coma cluster with {\it Suzaku}. These subhalos, labeled "ID 1", "ID 2", and "ID 32", were detected with a weak-lensing survey using the Subaru/Suprime-Cam (Okabe et al. 2014a), and are located at the projected distances of 1.4 $r_{500}$, 1.2 $r_{500}$, and 1.6 $r_{500}$ from the center of the Coma cluster, respectively. The subhalo "ID 1" has a compact X-ray excess emission close to the center of the weak-lensing mass contour, and the gas mass to weak-lensing mass ratio is about 0.001. The temperature of the emission is about 3 keV, which is slightly lower than that of the surrounding intracluster medium (ICM) and that expected for the temperature vs. mass relation of clusters of galaxies. The subhalo "ID 32" shows an excess emission whose peak is shifted toward the opposite direction from the center of the Coma cluster. The gas mass to weak-lensing mass ratio is also about 0.001, which is significantly smaller than regular galaxy groups. The temperature of the excess is about 0.5 keV and significantly lower than that of the surrounding ICM and far from the temperature vs. mass relation of clusters. However, there is no significant excess X-ray emission in the "ID 2" subhalo. Assuming an infall velocity of about 2000 $\rm km~s^{-1}$, at the border of the excess X-ray emission, the ram pressures for "ID 1" and "ID 32" are comparable to the gravitational restoring force per area. We also studied the effect of the Kelvin-Helmholtz instability to strip the gas. Although we found X-ray clumps associated with the weak-lensing subhalos, their X-ray luminosities are much lower than the total ICM luminosity in the cluster outskirts.

### Small-N collisional dynamics II: Roaming the realm of not-so-small-N

We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate probabilities for direct stellar collisions; however our method is in principle valid for larger particle numbers. Our method relies on the binomial theorem, and is applicable to encounters involving any combination of particle radii. We further demonstrate that our base model is valid to within a few percent for any combination of particle masses, provided the minimum mass ratio is within a factor of a few from unity. This method is particularly suitable for models of collisional systems involving large numbers of stars, such as globular clusters, old open clusters and galactic nuclei, where small subsets of stars may regularly have very close encounters, and the direct integration of all such encounters is computationally expensive. Variations of our method may also be used to treat other encounter outcomes, such as ejections and exchanges.

### Recoils from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime [Cross-Listing]

We revisit the modeling of the properties of the black-hole remnant resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 126 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.

### Recoils from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime

We revisit the modeling of the properties of the black-hole remnant resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 126 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.

### Modeling the remnant mass, spin, and recoil from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime [Replacement]

We revisit the modeling of the properties of the remnant black hole resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.

### Modeling the remnant mass, spin, and recoil from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime [Replacement]

We revisit the modeling of the properties of the remnant black hole resulting the merger of a black-hole binary as a function of the parameters of the binary. We provide a set of empirical formulas for the final mass, spin and recoil velocity of the final black hole as a function of the mass ratio and individual spins of the progenitor. In order to determine the fitting coefficients for these formulas, we perform a set of 128 new numerical evolutions of precessing, unequal-mass black-hole binaries, and fit to the resulting remnant mass, spin, and recoil. In order to reduce the complexity of the analysis, we chose configurations that have one of the black holes spinning, with dimensionless spin alpha=0.8, at different angles with respect to the orbital angular momentum, and the other non-spinning. In addition to evolving families of binaries with different spin-inclination angles, we also evolved binaries with mass ratios as small as q=1/6. We use the resulting empirical formulas to predict the probabilities of black hole mergers leading to a given recoil velocity, total radiated gravitational energy, and final black hole spin.

### Supernova remnant mass cumulated along the star formation history of the z=3.8 radiogalaxies 4C41.17 and TN J2007-1316

In this paper, we show that the supernova remnant (SNR) masses cumulated from core-collapse supernovae along the star formation history of two powerful z=3.8 radio galaxies 4C41.17 and TN J2007-1316 reach up to > 10^9 Msun, comparable with supermassive black hole (SMBH) masses measured from the SDSS sample at similar redshifts. The SNR mass is measured from the already exploded supernova mass after subtraction of ejecta at the galaxy age where the mass of still luminous stars fits at best the observed spectral energy distribution (SED), continuously extended to the optical-Spitzer-Herschel-submm domains, with the help of the galaxy evolution model P\’egase.3. For the recent and old stellar populations, SNR masses vary on 10^(9 to 10) Msun and the SNR-to-star mass ratio between 1 and 0.1 percent is comparable to the observed low-z SMBH-to-star mass ratio. For the template radio galaxy 4C41.17, SNR and stellar population masses estimated from large aperture (>4arcsec=30kpc) observations are compatible, within one mass order, with the total mass of multiple optical HST (~700pc) structures, associated with VLA radio emissions, both at 0.1 arcsec. Probing the SNR accretion by central black holes is a simple explanation for SMBH growth, requiring physics on star formation, stellar and galaxy dynamics with consequences on various processes (quenching, mergers, negative feedback) and a key to the relation bulge-SMBH.

### The Mass-Luminosity Relation in the L/T Transition: Individual Dynamical Masses for the New J-Band Flux Reversal Binary SDSSJ105213.51+442255.7AB

We have discovered that SDSSJ105213.51+442255.7 (T0.5$\pm$1.0) is a binary in Keck laser guide star adaptive optics imaging, displaying a large J-to-K-band flux reversal ($\Delta$J = -0.45$\pm$0.09 mag, $\Delta$K = 0.52$\pm$0.05 mag). We determine a total dynamical mass from Keck orbital monitoring (88$\pm$5 $M_{\rm Jup}$) and a mass ratio by measuring the photocenter orbit from CFHT/WIRCam absolute astrometry ($M_B/M_A$ = 0.78$\pm$0.07). Combining these provides the first individual dynamical masses for any field L or T dwarfs, 49$\pm$3 $M_{\rm Jup}$ for the L6.5$\pm$1.5 primary and 39$\pm$3 $M_{\rm Jup}$ for the T1.5$\pm$1.0 secondary. Such a low mass ratio for a nearly equal luminosity binary implies a shallow mass$-$luminosity relation over the L/T transition ($\Delta$log$L_{\rm bol}$/$\Delta$log$M = 0.6^{+0.6}_{-0.8}$). This provides the first observational support that cloud dispersal plays a significant role in the luminosity evolution of substellar objects. Fully cloudy models fail our coevality test for this binary, giving ages for the two components that disagree by 0.2 dex (2.0$\sigma$). In contrast, our observed masses and luminosities can be reproduced at a single age by "hybrid" evolutionary tracks where a smooth change from a cloudy to cloudless photosphere around 1300 K causes slowing of luminosity evolution. Remarkably, such models also match our observed JHK flux ratios and colors well. Overall, it seems that the distinguishing features SDSSJ1052+4422AB, like a J-band flux reversal and high-amplitude variability, are normal for a field L/T binary caught during the process of cloud dispersal, given that the age (1.11$^{+0.17}_{-0.20}$ Gyr) and surface gravity (log$g$ = 5.0$-$5.2) of SDSSJ1052+4422AB are typical for field ultracool dwarfs.

### Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III: Spin-orbit coupling revisited [Replacement]

The first- and second-order dissipative self force and the first order conservative self force are applied together with spin-orbit coupling to the quasi-circular motion of a test mass in the spacetime of a Schwarzschild black hole, for extreme or intermediate mass ratios. The partial dephasing of the gravitational waveform (at the order that is independent of the system’s mass ratio) due to the self force is compared with that of spin-orbit coupling. We find that accurate waveforms for parameter estimation need to include both effects. Specifically, we find a particular value for the spin parameter such that the spin-orbit effect cancels out the self-force effect on the waveform. Exclusion of dephasing effects that are independent of the mass ratio therefore might lead to a non-perturbative error in the estimation of the system’s parameters.

### Self-force gravitational waveforms for extreme and intermediate mass ratio inspirals. III: Spin-orbit coupling revisited

The first- and second-order dissipative self force and the first order conservative self force are applied together with spin-orbit coupling to the quasi-circular motion of a test mass in the spacetime of a Schwarzschild black hole, for extreme or intermediate mass ratios. The partial dephasing of the gravitational waveform (at the order that is independent of the system’s mass ratio) due to the self force is compared with that of spin-orbit coupling. We find that accurate waveforms for parameter estimation need to include both effects. Specifically, we find a particular value for the spin parameter such that the spin-orbit effect cancels out the self-force effect on the waveform. Exclusion of dephasing effects that are independent of the mass ratio therefore might lead to a non-perturbative error in the estimation of the system’s parameters.

### Is motion under the conservative self-force in black hole spacetimes an integrable Hamiltonian system?

A point-like object moving in a background black hole spacetime experiences a gravitational self-force which can be expressed as a local function of the object’s instantaneous position and velocity, to linear order in the mass ratio. We consider the worldline dynamics defined by the conservative part of the local self-force, turning off the dissipative part, and we ask: Is that dynamical system a Hamiltonian system, and if so, is it integrable? In the Schwarzschild spacetime, we show that the system is Hamiltonian and integrable, to linear order in the mass ratio, for generic (but not necessarily all) stable bound orbits. There exist an energy and an angular momentum, being perturbed versions of their counterparts for geodesic motion, which are conserved under the forced motion. We also discuss difficulties associated with establishing analogous results in the Kerr spacetime. This result may be useful for future computational schemes, based on a local Hamiltonian description, for calculating the conservative self-force and its observable effects. It is also relevant to the assumption of the existence of a Hamiltonian for the conservative dynamics for generic orbits in the effective-one-body formalism, to linear order in the mass ratio, but to all orders in the post-Newtonian expansion.

### Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits

The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modelling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods, and can be used to enhance their accuracy, e.g.\ via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits—specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity $\langle U \rangle$ that generalizes Detweiler’s redshift invariant. The functional relationship $\langle U \rangle(\Omr,\Omph)$, where $\Omr$ and $\Omph$ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute $\langle U \rangle(\Omr,\Omph)$ numerically through linear order in the mass ratio $q$, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive $\langle U \rangle(\Omr,\Omph)$ analytically through 3PN order, for an arbitrary $q$, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the $\ord(q)$ piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at $\ord(q)$.

### Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits [Replacement]

The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modelling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods, and can be used to enhance their accuracy, e.g. via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits—specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity $\langle U \rangle$ that generalizes Detweiler’s redshift invariant. The functional relationship $\langle U \rangle(\Omega_r,\Omega_\phi)$, where $\Omega_r$ and $\Omega_\phi$ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute $\langle U \rangle(\Omega_r,\Omega_\phi)$ numerically through linear order in the mass ratio $q$, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive $\langle U \rangle(\Omega_r,\Omega_\phi)$ analytically through 3PN order, for an arbitrary $q$, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the $\mathcal{O}(q)$ piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at $\mathcal{O}(q)$.