# Posts Tagged mass ratio

## Recent Postings from mass ratio

### 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.

### 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

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 [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.

### 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 $\mathcal{O}(q)$.

### How elevated is the dynamical-to-stellar mass ratio of the ultra-compact dwarf S999?

Here we present new Keck ESI high-resolution spectroscopy and deep archival HST/ACS imaging for S999, an ultra-compact dwarf in the vicinity of M87, which was claimed to have an extremely high dynamical-to-stellar mass ratio. Our data increase the total integration times by a factor of 5 and 60 for spectroscopy and imaging, respectively. This allows us to constrain the stellar population parameters for the first time (simple stellar population equivalent age $=7.6^{+2.0}_{-1.6}$ Gyr; $[Z/\textrm{H}]=-0.95^{+0.12}_{-0.10}$; $[\alpha/\textrm{Fe}]=0.34^{+0.10}_{-0.12}$). Assuming a Kroupa stellar initial mass function, the stellar population parameters and luminosity ($M_{F814W}=-12.13\pm0.06$ mag) yield a stellar mass of $M_*=3.9^{+0.9}_{-0.6}\times10^6 M_{\odot}$, which we also find to be consistent with near-infrared data. Via mass modelling, with our new measurements of velocity dispersion ($\sigma_{ap}=27\pm2$ km s$^{-1}$) and size ($R_e=20.9\pm1.0$ pc), we obtain an elevated dynamical-to-stellar mass ratio $M_{dyn}/M_*=8.2$ (with a range $5.6\le M_{dyn}/M_* \le 11.2$). Furthermore, we analyse the surface brightness profile of S999, finding only a small excess of light in the outer parts with respect to the fitted S\’ersic profile, and a positive colour gradient. Taken together these observations suggest that S999 is the remnant of a much larger galaxy that has been tidally stripped. If so, the observed elevated mass ratio may be caused by mechanisms related to the stripping process: the existence of an massive central black hole or internal kinematics that are out of equilibrium due to the stripping event. Given the observed dynamical-to-stellar mass ratio we suggest that S999 is an ideal candidate to search for the presence of an overly massive central black hole.

### Dynamical mass ejection from black hole-neutron star binaries [Cross-Listing]

We investigate properties of material ejected dynamically in the merger of black hole-neutron star binaries by numerical-relativity simulations. We systematically study dependence of ejecta properties on the mass ratio of the binary, spin of the black hole, and equation of state of the neutron-star matter. Dynamical mass ejection is driven primarily by tidal torque, and the ejecta is much more anisotropic than that from binary neutron star mergers. In particular, the dynamical ejecta is concentrated around the orbital plane with a half opening angle of 10deg–20deg and often sweeps only a half of the plane. The ejecta mass can be as large as ~0.1M_sun, and the velocity is subrelativistic with ~0.2–0.3c for typical cases. The ratio of the ejecta mass to the bound mass (disk and fallback components) becomes high and the ejecta velocity is large when the binary mass ratio is large, i.e., the black hole is massive. The remnant black hole-disk system receives a kick velocity of O(100)km/s due to the ejecta linear momentum, and this easily dominates the kick velocity due to gravitational radiation. Structures of postmerger material, velocity distribution of the dynamical ejecta, and fallback rates are also investigated. Tight correlations are suggested to exist between the gravitational-wave frequency at the maximum amplitude and tidal coupling constant. We also discuss the effect of ejecta anisotropy on electromagnetic counterparts, specifically a macronova/kilonova and synchrotron radio emission.

### Every interacting double white dwarf binary may merge [Replacement]

Interacting double white dwarf binaries can give rise to a wide variety of astrophysical outcomes ranging from faint thermonuclear and Type Ia supernovae to the formation of neutron stars and stably accreting AM Canum Venaticorum systems. One key factor affecting the final outcome is whether mass transfer remains dynamically stable or instead diverges, leading to the tidal disruption of the donor and the merger of the binary. It is typically thought that for low ratios of the donor mass to the accretor mass, mass transfer remains stable, especially if accretion occurs via a disk. In this Letter, we examine low mass ratio double white dwarf binaries and find that the initial phase of hydrogen-rich mass transfer leads to a classical nova-like outburst on the accretor. Dynamical friction within the expanding nova shell shrinks the orbit and causes the mass transfer rate to increase dramatically above the accretor’s Eddington limit, possibly resulting in a binary merger. If the binary survives the first hydrogen-rich nova outbursts, dynamical friction within the subsequent helium-powered nova shells pushes the system even more strongly towards merger. While further calculations are necessary to confirm this outcome for the entire range of binaries previously thought to be dynamically stable, it appears likely that most, if not all, interacting double white dwarf binaries will merge during the course of their evolution.

### The Mass Distribution Function of Planets [Replacement]

The distribution of orbital period ratios of adjacent planets in extra-solar planetary systems discovered by the {\it Kepler} space telescope exhibits a peak near $\sim1.5$–$2$, a long tail of larger period ratios, and a steep drop-off in the number of systems with period ratios below $\sim1.5$. We find from this data that the dimensionless orbital separations have an approximately log-normal distribution. Using Hill’s criterion for the dynamical stability of two planets, we find an upper bound on planet masses such that the most common planet mass does not exceed $10^{-3.2}m_*$, or about two-thirds Jupiter mass for solar mass stars. Assuming that the mass ratio and the dynamical separation (orbital spacings in units of mutual Hill radius) of adjacent planets are independent random variates, and adopting empirical distributions for these, we use Hill’s criterion in a statistical way to estimate the planet mass distribution function from the observed distribution of orbital separations. We find that the planet mass function is peaked in logarithm of mass, with a peak value and standard deviation of $\log m/M_\oplus$ of $\sim(0.6-1.0)$ and $\sim(1.1-1.2)$, respectively.

### The merger rate of galaxies in the Illustris Simulation: a comparison with observations and semi-empirical models [Replacement]

We have constructed merger trees for galaxies in the Illustris Simulation by directly tracking the baryonic content of subhalos. These merger trees are used to calculate the galaxy-galaxy merger rate as a function of descendant stellar mass, progenitor stellar mass ratio, and redshift. We demonstrate that the most appropriate definition for the mass ratio of a galaxy-galaxy merger consists in taking both progenitor masses at the time when the secondary progenitor reaches its maximum stellar mass. Additionally, we avoid effects from orphaned’ galaxies by allowing some objects to skip’ a snapshot when finding a descendant, and by only considering mergers which show a well-defined infall’ moment. Adopting these definitions, we obtain well-converged predictions for the galaxy-galaxy merger rate with the following main features, which are qualitatively similar to the halo-halo merger rate except for the last one: a strong correlation with redshift that evolves as $\sim (1+z)^{2.4-2.8}$, a power law with respect to mass ratio, and an increasing dependence on descendant stellar mass, which steepens significantly for descendant stellar masses greater than $\sim 2 \times 10^{11} \, {\rm M_{\odot}}$. These trends are consistent with observational constraints for medium-sized galaxies ($M_{\ast} \gtrsim 10^{10} \, {\rm M_{\odot}}$), but in tension with some recent observations of the close pair fraction for massive galaxies ($M_{\ast} \gtrsim 10^{11} \, {\rm M_{\odot}}$), which report a nearly constant or decreasing evolution with redshift. Finally, we provide a fitting function for the galaxy-galaxy merger rate which is accurate over a wide range of stellar masses, progenitor mass ratios, and redshifts.

### The merger rate of galaxies in the Illustris Simulation: a comparison with observations and semi-empirical models

We have constructed merger trees for galaxies in the Illustris Simulation by directly tracking the baryonic content of subhalos. These merger trees are used to calculate the galaxy-galaxy merger rate as a function of descendant stellar mass, progenitor stellar mass ratio, and redshift. We demonstrate that the most appropriate definition for the mass ratio of a galaxy-galaxy merger consists in taking both progenitor masses at the time when the secondary progenitor reaches its maximum stellar mass. Additionally, we avoid effects from orphaned’ galaxies by allowing some objects to skip’ a snapshot when finding a descendant, and by only considering mergers which show a well-defined `infall’ moment. Adopting these definitions, we obtain well-converged predictions for the galaxy-galaxy merger rate with the following main features, which are qualitatively similar to the halo-halo merger rate except for the last one: a strong correlation with redshift that evolves as $\sim (1+z)^{2.4-2.8}$, a power law with respect to mass ratio, and an increasing dependence on descendant stellar mass, which steepens significantly for descendant stellar masses greater than $\sim 2 \times 10^{11} \, {\rm M_{\odot}}$. These trends are consistent with observational constraints for medium-sized galaxies ($M_{\ast} \gtrsim 10^{10} \, {\rm M_{\odot}}$), but in tension with some recent observations of the close pair fraction for massive galaxies ($M_{\ast} \gtrsim 10^{11} \, {\rm M_{\odot}}$), which report a nearly constant or decreasing evolution with redshift. Finally, we provide a fitting function for the galaxy-galaxy merger rate which is accurate over a wide range of stellar masses, progenitor mass ratios, and redshifts.

### Light curve solutions of six eclipsing binaries at the lower limit of periods of the W UMa stars

Photometric observations in V and I bands of six eclipsing binaries at the lower limit of the orbital periods of W UMa stars are presented. Three of them are newly discovered eclipsing systems. The light curve solutions revealed that all short-period targets were contact or overcontact binaries and added new six binaries to the family of short-period systems with estimated parameters. Four binaries have equal in size components and mass ratio near 1. The phase variability of the V-I colors of all targets may be explained by lower temperatures of their back surfaces than those of their side surfaces. Five systems revealed O’Connell effect that was reproduced by cool spots on the side surfaces of their primary components. The light curves of V1067 Her in 2011 and 2012 were fitted by diametrically opposite spots. The applying of the criteria for subdivision of the W UMa stars to our targets led to ambiguous results.

### The Mass-Concentration Relation and the Stellar-to-Halo Mass Ratio in the CFHT Stripe 82 Survey

We present a new measurement of the mass-concentration relation and the stellar-to-halo mass ratio over a 5*10^(12) solar mass to 2*10^(14) solar mass range. To achieve this, we use the CFHT Stripe 82 Survey (CS82) weak lensing data combined with a well defined catalog of clusters (the redMaPPer catalogue) and the LOWZ/CMASS galaxies of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Tenth Data Release (SDSS-III BOSS DR10). The stacked lensing signals around these samples are modeled as a sum of contributions from the central galaxy, the dark matter halo, and the neighboring halos. We measure the mass-concentration relation: c200(M)=A(M200/M0)^(B) with A=5.25+/-1.67, B=-0.13+/-0.12 for 0.2<z<0.4 and A=6.77+/-1.13, B=-0.15+/-0.06 for 0.4<z<0.6. We conclude that the amplitude A and slope B are both consistent with the simulation predictions by Klypin et al. (2014) within the errors. We also measure the stellar-to-halo mass ratio and find it to be flatter than previous measurement for high stellar masses because of the complex structures and merger history in massive dark matter halos.

### Resonances in retrograde circumbinary discs

We analyse the interaction of an eccentric binary with a circular coplanar circumbinary disc that rotates in a retrograde sense with respect to the binary. In the circular binary case, no Lindblad resonances lie within the disc and no Lindblad resonant torques are produced, as was previously known. By analytic means, we show that when the binary orbit is eccentric, there exist components of the gravitational potential of the binary which rotate in a retrograde sense to the binary orbit and so rotate progradely with respect to this disc, allowing a resonant interaction to occur between the binary and the disc. The resulting resonant torques distinctly alter the disc response from the circular binary case. We describe results of three-dimensional hydrodynamic simulations to explore this effect and categorise the response of the disc in terms of modes whose strengths vary as a function of binary mass ratio and eccentricity. These mode strengths are weak compared to the largest mode strengths expected in the prograde case where the binary and disc rotate in the same sense. However, for sufficiently high binary eccentricity, resonant torques open a gap in a retrograde circumbinary disc, while permitting gas inflow on to the binary via gas streams. The inflow results in a time varying accretion rate on to the binary that is modulated over the binary orbital period, as was previously found to occur in the prograde case.

### A constraint on a varying proton--electron mass ratio 1.5 billion years after the Big Bang

A molecular hydrogen absorber at a lookback time of 12.4 billion years, corresponding to 10$\%$ of the age of the universe today, is analyzed to put a constraint on a varying proton–electron mass ratio, $\mu$. A high resolution spectrum of the J1443$+$2724 quasar, which was observed with the Very Large Telescope, is used to create an accurate model of 89 Lyman and Werner band transitions whose relative frequencies are sensitive to $\mu$, yielding a limit on the relative deviation from the current laboratory value of $\Delta\mu/\mu=(-9.5\pm5.4_{\textrm{stat}} \pm 5.3_{\textrm{sys}})\times 10^{-6}$.

### Relative distribution of dark matter and stellar mass in three massive galaxy clusters

This work observationally addresses the relative distribution of total and optically luminous matter in galaxy clusters by computing the radial profile of the stellar-to-total mass ratio. We adopt state-of-the-art accurate lensing masses free from assumptions about the mass radial profile and we use extremely deep multicolor wide–field optical images to distinguish star formation from stellar mass, to properly calculate the mass in galaxies of low mass, those outside the red sequence, and to allow a contribution from galaxies of low mass that is clustercentric dependent. We pay special attention to issues and contributions that are usually underrated, yet are major sources of uncertainty, and we present an approach that allows us to account for all of them. Here we present the results for three very massive clusters at $z\sim0.45$, MACSJ1206.2-0847, MACSJ0329.6-0211, and RXJ1347.5-1145. We find that stellar mass and total matter are closely distributed on scales from about 150 kpc to 2.5 Mpc: the stellar-to-total mass ratio is radially constant. We find that the characteristic mass stays constant across clustercentric radii and clusters, but that the less-massive end of the galaxy mass function is dependent on the environment.

### Constraints on changes in the proton-electron mass ratio using methanol lines

We report Karl G. Jansky Very Large Array (VLA) absorption spectroscopy in four methanol (CH$_3$OH) lines in the $z = 0.88582$ gravitational lens towards PKS1830-211. Three of the four lines have very different sensitivity coefficients $K_\mu$ to changes in the proton-electron mass ratio $\mu$; a comparison between the line redshifts thus allows us to test for temporal evolution in $\mu$. We obtain a stringent statistical constraint on changes in $\mu$ by comparing the redshifted 12.179 GHz and 60.531 GHz lines, $[\Delta mu/\mu] \leq 1.1 \times 10^{-7}$ ($2\sigma$) over $0 < z \leq 0.88582$, a factor of $\approx 2.5$ more sensitive than the best earlier results. However, the higher signal-to-noise ratio (by a factor of $\approx 2$) of the VLA spectrum in the 12.179 GHz transition also indicates that this line has a different shape from that of the other three CH$_3$OH lines (at $> 4\sigma$ significance). The sensitivity of the above result, and that of all earlier CH$_3$OH studies, is thus likely to be limited by unknown systematic errors, probably arising due to the frequency-dependent structure of PKS1830-211. A robust result is obtained by combining the three lines at similar frequencies, 48.372, 48.377 and 60.531 GHz, whose line profiles are found to be in good agreement. This yields the $2\sigma$ constraint $[\Delta \mu/\mu] \lesssim 4 \times 10^{-7}$, the most stringent current constraint on changes in $\mu$. We thus find no evidence for changes in the proton-electron mass ratio over a lookback time of $\approx 7.5$ Gyrs.

### H$_2$ Lyman and Werner band lines and their sensitivity for a variation of the proton-electron mass ratio in the gravitational potential of white dwarfs [Cross-Listing]

Recently an accurate analysis of absorption spectra of molecular hydrogen, observed with the Cosmic Origins Spectrograph aboard the Hubble Space Telescope, in the photosphere of white dwarf stars GD133 and GD29-38 was published in a Letter [Phys. Rev. Lett. 113, 123002 (2014)], yielding a constraint on a possible dependence of the proton-electron mass ratio on a gravitational field of strength 10,000 times that at the Earth’s surface. In the present paper further details of that study are presented, in particular a re-evaluation of the spectrum of the $B^1\Sigma_u^+ – X^1\Sigma_g^+ (v’,v”)$ Lyman bands relevant for the prevailing temperatures (12,000 – 14,000 K) of the photospheres. An emphasis is on the calculation of so-called $K_i$-coefficients, that represent the sensitivity of each individual line to a possible change in the proton-electron mass ratio. Such calculations were performed by semi-empirical methods and by ab initio methods providing accurate and consistent values. A full listing is provided for the molecular physics data on the Lyman bands (wavelengths $\lambda_i$, line oscillator strengths $f_i$, radiative damping rates $\Gamma_i$, and sensitivity coefficients $K_i$) as required for the analyses of H$_2$-spectra in hot dwarf stars. A similar listing of the molecular physics parameters for the $C^1\Pi_u – X^1\Sigma_g^+ (v’,v”)$ Werner bands is provided for future use in the analysis of white dwarf spectra.

### The evolution of the mass ratio of accreting binaries: the role of gas temperature

We explore an unresolved controversy in the literature about the accuracy of Smoothed Particle Hydrodynamics (SPH) in modeling the accretion of gas onto a binary system, a problem with important applications to the evolution of proto-binaries as well as accreting binary super massive black holes. It has previously been suggested that SPH fails to model the flow of loosely bound material from the secondary to primary Roche lobe and that its general prediction that accretion drives mass ratios upwards is numerically flawed. Here we show with 2D SPH that this flow from secondary to primary Roche lobe is a sensitive function of gas temperature and that this largely explains the conflicting claims in the literature which have hitherto been based on either ‘cold’ SPH simulations or ‘hot’ grid based calculations. We present simulations of a specimen ‘cold’ and ‘hot’ accretion scenario which are numerically converged and evolved into a steady state. Our analysis of the conservation of the Jacobi integral of accreting particles indicates that our results are not strongly compromised by numerical dissipation. We also explore the low resolution limit and find that simulations where the ratio of SPH smoothing length to disc scale height at the edge of the circumsecondary is less than 1 accurately capture binary accretion rates.

### A method to deconvolve mass ratio distribution from binary stars

To better understand the evolution of stars in binary systems as well as to constrain the formation of binary stars, it is important to know the binary mass-ratio distribution. However, in most cases, i.e. for single-lined spectroscopic binaries, the mass ratio cannot be measured directly but only derived as the convolution of a function that depends on the mass ratio and the unknown inclination angle of the orbit on the plane of the sky. We extend our previous method to deconvolve this inverse problem (Cure et al. 2014), i.e., we obtain as an integral the cumulative distribution function (CDF) for the mass ratio distribution. After a suitable transformation of variables it turns out that this problem is the same as the one for rotational velocities $v \sin i$, allowing a close analytic formulation for the CDF. We then apply our method to two real datasets: a sample of Am stars binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 Association.} {We are able to reproduce the previous results of Boffin (2010) for the sample of Am stars, while we show that the mass ratio distribution of massive stars shows an excess of small mass ratio systems, contrarily to what was claimed by Kobulnicky et al. (2014). Our method proves very robust and deconvolves the distribution from a sample in just a single step.