# Posts Tagged mass ratio

## Recent Postings from mass ratio

### The evolution of a binary in a retrograde circular orbit embedded in an accretion disk

Supermassive black hole binaries may form as a consequence of galaxy mergers. Both prograde and retrograde orbits have been proposed. We study a binary of a small mass ratio, q, in a retrograde orbit immersed in and interacting with a gaseous accretion disk in order to estimate time scales for inward migration leading to coalescence and the accretion rate to the secondary component. We employ both semi-analytic methods and two dimensional numerical simulations, focusing on the case where the binary mass ratio is small but large enough to significantly perturb the disk. We develop the theory of type I migration for this case and determine conditions for gap formation finding that then inward migration occurs on a time scale equal to the time required for one half of the secondary mass to be accreted through the unperturbed disk, with accretion onto the secondary playing only a minor role. The semi-analytic and fully numerical approaches are in good agreement, the former being applicable over long time scales. Inward migration induced by interaction with the disk alleviates the final parsec problem. Accretion onto the secondary does not significantly affect the orbital evolution, but may have observational consequences for high accretion efficiency. The binary may then appear as two sources of radiation rotating around each other. This study should be extended to consider orbits with significant eccentricity and the effects of gravitational radiation at small length scales. Note too that torques acting between a circumbinary disk and a retrograde binary orbit may cause the mutual inclination to increase on a timescale that can be similar to, or smaller than that for orbital evolution, depending on detailed parameters. This is also an aspect for future study (abridged).

### The Size Evolution of Elliptical Galaxies

Recent work has suggested that the amplitude of the size mass relation of massive early type galaxies evolves with redshift. Here we use a semi-analytical galaxy formation model to study the size evolution of massive early type galaxies. We find this model is able to reproduce the amplitude of present day amplitude and slope of the relation between size and stellar mass for these galaxies, as well as its evolution. The amplitude of this relation reflects the typical compactness of dark halos at the time when most of the stars are formed. This link between size and star formation epoch is propagated in galaxy mergers. Mergers of high or moderate mass ratio (less than 1:3) become increasingly important with increasing present day stellar mass for galaxies more massive than $10^{11.4}M_{\odot}$. At lower masses, low mass ratio mergers play a more important role. In situ star formation contribute more to the size growth than it does to stellar mass growth. We also find that, for ETGs identified at $z=2$, minor mergers dominate subsequent growth both for stellar mass and in size, consistent with earlier theoretical results.

### Testing the nonlinear stability of Kerr-Newman black holes

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$) ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm max}$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.

### Testing the nonlinear stability of Kerr-Newman black holes [Cross-Listing]

The nonlinear stability of Kerr-Newman black holes (KNBHs) is investigated by performing numerical simulations within the full Einstein-Maxwell theory. We take as initial data a KNBH with mass $M$, angular momentum to mass ratio $a$ and charge $Q$. Evolutions are performed to scan this parameter space within the intervals $0\le a/M\le 0.994$ and $0\le Q/M\le 0.996$, corresponding to an extremality parameter $a/a_{\rm max}$ ($a_{\rm max} \equiv \sqrt{M^2-Q^2}$) ranging from $0$ to $0.995$. These KNBHs are evolved, together with a small bar-mode perturbation, up to a time of order $120M$. Our results suggest that for small $Q/a$, the quadrupolar oscillation modes depend solely on $a/a_{\rm max}$, a universality also apparent in previous perturbative studies in the regime of small rotation. Using as a stability criterion the absence of significant relative variations in the horizon areal radius and BH spin, we find no evidence for any developing instability.

### CC Sculptoris: Eclipsing SU UMa-Type Intermediate Polar

We observed the 2014 superoutburst of the SU UMa-type intermediate polar CC Scl. We detected superhumps with a mean period of 0.05998(2) d during the superoutburst plateau and during three nights after the fading. During the post-superoutburst stage after three nights, a stable superhump period of 0.059523(6) d was detected. We found that this object is an eclipsing system with an orbital period of 0.058567233(8) d. By assuming that the disk radius in the post-superoutburst phase is similar to those in other SU UMa-type dwarf novae, we obtained a mass ratio of q=0.072(3) from the dynamical precession rate of the accretion disk. The eclipse profile during outbursts can be modeled by an inclination of 80.6+/-0.5 deg. The 2014 superoutburst was preceded by a precursor outburst and the overall appearance of the outburst was similar to superoutbursts in ordinary SU UMa-type dwarf novae. We showed that the standard thermal-tidal instability model can explain the outburst behavior in this system and suggest that inner truncation of the disk by magnetism of the white dwarf does not strongly affect the behavior in the outer part of the disk.

### Discovery of a deep, low mass ratio overcontact binary GSC 03517-00663

When observing the blazars, we identified a new eclipsing binary GSC 03517-00663. The light curves of GSC 03517-00663 are typical EW-type light curves. Based on the observation using the 1m telescope at Weihai Observatory of Shandong University, complete VRI light curves were determined. Then, we analyzed the multiple light curves using the W-D program. It is found that GSC 03517-00663 has a mass ratio of q=0.164 and a contact degree of f=69.2%. GSC 03517-00663 is a deep, low mass ratio overcontact binary. The light curves of GSC 03517-00663 show strong O’Connell effect, it was explained by employing a dark spot on the secondary component.

### Gravitational self-force corrections to two-body tidal interactions and the effective one-body formalism

Tidal interactions have a significant influence on the late dynamics of compact binary systems, which constitute the prime targets of the upcoming network of gravitational-wave detectors. We refine the theoretical description of tidal interactions (hitherto known only to the second post-Newtonian level) by extending our recently developed analytic self-force formalism, for extreme mass-ratio binary systems, to the computation of several tidal invariants. Specifically, we compute, to linear order in the mass ratio and to the 7.5$^{\rm th}$ post-Newtonian order, the following tidal invariants: the square and the cube of the gravitoelectric quadrupolar tidal tensor, the square of the gravitomagnetic quadrupolar tidal tensor, and the square of the gravitoelectric octupolar tidal tensor. Our high-accuracy analytic results are compared to recent numerical self-force tidal data by Dolan et al. \cite{Dolan:2014pja}, and, notably, provide an analytic understanding of the light ring asymptotic behavior found by them. We transcribe our kinematical tidal-invariant results in the more dynamically significant effective one-body description of the tidal interaction energy. By combining, in a synergetic manner, analytical and numerical results, we provide simple, accurate analytic representations of the global, strong-field behavior of the gravitoelectric quadrupolar tidal factor. A striking finding is that the linear-in-mass-ratio piece in the latter tidal factor changes sign in the strong-field domain, to become negative (while its previously known second post-Newtonian approximant was always positive). We, however, argue that this will be more than compensated by a probable fast growth, in the strong-field domain, of the nonlinear-in-mass-ratio contributions in the tidal factor.

### Growth and activity of black holes in galaxy mergers with varying mass ratios

We study supermassive black holes (BHs) in merging galaxies, using a suite of hydrodynamical simulations with very high spatial (~10 pc) and temporal (~1 Myr) resolution, where we vary the initial mass ratio, the orbital configuration, and the gas fraction. (i) We address the question of when and why, during a merger, increased BH accretion occurs, quantifying gas inflows and BH accretion rates. (ii) We also quantify the relative effectiveness in inducing AGN activity of merger-related versus secular-related causes, by studying different stages of the encounter: the stochastic (or early) stage, the (proper) merger stage, and the remnant (or late) stage. (iii) We assess which galaxy mergers preferentially enhance BH accretion, finding that the initial mass ratio is the most important factor. (iv) We study the evolution of the BH masses, finding that the BH mass contrast tends to decrease in minor mergers and to increase in major mergers. This effect hints at the existence of a preferential range of mass ratios for BHs in the final pairing stages. (v) In both merging and dynamically quiescent galaxies, the gas accreted by the BH is not necessarily the gas with $low$ angular momentum, but the gas that $loses$ angular momentum.

### Some Aspects of Strange Matter in Astrophysics

The present work is connected with the investigation of the origin and properties of compact astrophysical objects endowed with strangeness, with the objective of finding out their relevance in the formation and evolution of the universe. In the first part of the thesis, Chap.~1-3, we discuss a model, proposed by us, to describe the propagation of small lumps of Strange Quark Matter (SQM) or strangelets, through the Terrestrial atmosphere. The theoretical results were found to be well correlated with exotic cosmic ray events characterized by very low charge to mass ratio. In the next part, we have investigated the other end of the mass spectrum of SQM. In Chap 5, we have developed an analytical expression for the Chandrasekhar Limit of Strange Quark Stars. The limit is found to depend on the fundamental constants (including the bag constant). In the last chapter we have endeavored to show that the quark nuggets, surviving the quark-hadron phase transition in the millisecond era of the early Universe can provide the required closure density and can merge to form compact quark matter objects, whose maximum mass would be governed by the formulation laid out in the preceding chapter. We have also found that these Cold Dark Matter objects can explain the recent astronomical observations of MACHOS by gravitational micro-lensing techniques in the Large Magellanic clouds in the Halo of our Galaxy.

### Effect of quintessence on the energy of the Reissner-Nordstrom black hole [Cross-Listing]

The energy content of the Reissner-Nordstrom black hole surrounded by quintessence is investigated using approximate Lie symmetry methods. It is mainly done by assuming mass and charge of the black hole as small quantities ($\epsilon$), and by retaining its second power in the perturbed geodesic equations for such black hole while neglecting its higher powers. Due to the presence of trivial second-order approximate Lie symmetries of these perturbed geodesic equations, a rescaling of the geodetic parameter gives a rescaling of the energy in this black hole. Interestingly we obtain an explicit relation of the rescaling factor that depends on the square of the charge to mass ratio of the black hole, the normalization factor $\alpha$, which is related to the state parameter of the quintessence matter, and the coordinate $r$. A comparison of this rescaling factor with that of the Reissner-Nordstrom black hole (Hussain et. al SIGMA, 2007), without quintessence is given. It is observed that the presence of the quintessence field reduces the energy in this black hole spacetime. Further it is found that there exists a point outside the event horizon of this black hole where the effect of quintessence balances the energy content in this black hole without quintessence, and where the total energy of the underlying spacetime becomes zero.

### Effect of quintessence on the energy of the Reissner-Nordstrom black hole

The energy content of the Reissner-Nordstrom black hole surrounded by quintessence is investigated using approximate Lie symmetry methods. It is mainly done by assuming mass and charge of the black hole as small quantities ($\epsilon$), and by retaining its second power in the perturbed geodesic equations for such black hole while neglecting its higher powers. Due to the presence of trivial second-order approximate Lie symmetries of these perturbed geodesic equations, a rescaling of the geodetic parameter gives a rescaling of the energy in this black hole. Interestingly we obtain an explicit relation of the rescaling factor that depends on the square of the charge to mass ratio of the black hole, the normalization factor $\alpha$, which is related to the state parameter of the quintessence matter, and the coordinate $r$. A comparison of this rescaling factor with that of the Reissner-Nordstrom black hole (Hussain et. al SIGMA, 2007), without quintessence is given. It is observed that the presence of the quintessence field reduces the energy in this black hole spacetime. Further it is found that there exists a point outside the event horizon of this black hole where the effect of quintessence balances the energy content in this black hole without quintessence, and where the total energy of the underlying spacetime becomes zero.

### HD 152246 - a new high-mass triple system and its basic properties

Analyses of multi-epoch, high-resolution (R ~ 50.000) optical spectra of the O-type star HD 152246 (O9 IV according to the most recent classification), complemented by a limited number of earlier published radial velocities, led to the finding that the object is a hierarchical triple system, where a close inner pair (Ba-Bb) with a slightly eccentric orbit (e = 0.11) and a period of 6.0049 days revolves in a 470-day highly eccentric orbit (e = 0.865) with another massive and brighter component A. The mass ratio of the inner system must be low since we were unable to find any traces of the secondary spectrum. The mass ratio A/(Ba+Bb) is 0.89. The outer system has recently been resolved using long-baseline interferometry on three occasions. The interferometry confirms the spectroscopic results and specifies elements of the system. Our orbital solutions, including the combined radial-velocity and interferometric solution indicate an orbital inclination of the outer orbit of 112{\deg} and stellar masses of 20.4 and 22.8 solar masses. We also disentangled the spectra of components A and Ba and compare them to synthetic spectra from two independent programmes, TLUSTY and FASTWIND. In either case, the fit was not satisfactory and we postpone a better determination of the system properties for a future study, after obtaining observations during the periastron passage of the outer orbit (the nearest chance being March 2015). For the moment, we can only conclude that component A is an O9 IV star with v*sin(i) = 210 +\- 10 km/s and effective temperature of 33000 +\- 500 K, while component Ba is an O9 V object with v*sin(i) = 65 +/- 3 km/s and T_eff = 33600 +\- 600 K.

### OGLE-2013-BLG-0102La,b: Microlensing binary with components at star/brown-dwarf and brown-dwarf/planet boundaries

We present the analysis of the gravitational microlensing event OGLE-2013-BLG-0102. The light curve of the event is characterized by a strong short-term anomaly superposed on a smoothly varying lensing curve with a moderate magnification $A_{\rm max}\sim 1.5$. It is found that the event was produced by a binary lens with a mass ratio between the components is $q = 0.13$ and the anomaly was caused by the passage of the source trajectory over a caustic located away from the barycenter of the binary. From the analysis of the effects on the light curve due to the finite size of the source and the parallactic motion of the Earth, the physical parameters of the lens system are determined. The measured masses of the lens components are $M_{1} = 0.097 \pm 0.011~M_{\odot}$ and $M_{2} = 0.013 \pm 0.002~M_{\odot}$, which correspond to the upper and lower limits of brown dwarfs, respectively. The distance to the lens is $3.02 \pm 0.21~{\rm kpc}$ and the projected separation between the lens components is $0.80 \pm 0.04~{\rm AU}$. These physical parameters lie beyond the detection ranges of other methods, demonstrating that microlensing is a useful method in detecting very low-mass binaries.

### Superoutburst of SDSS J090221.35+381941.9: First Measurement of Mass Ratio in an AM CVn-Type Object using Growing Superhumps

We report on a superoutburst of the AM CVn-type object SDSS J090221.35+381941.9 [J0902; orbital period 0.03355(6) d] in 2014 March-April. The entire outburst consisted of a precursor outburst and the main superoutburst, followed by a short rebrightening. During the rising branch of the main superoutburst, we detected growing superhumps (stage A superhumps) with a period of 0.03409(1) d. During the plateau phase of the superoutburst, superhumps with a shorter period (stage B superhumps) were observed. Using the orbital period and the period of the stage A superhumps, we were able to measure the dynamical precession rate of the accretion disk at the 3:1 resonance, and obtained a mass ratio (q) of 0.041(7). This is the first successful measurement of the mass ratio in an AM CVn-type object using the recently developed stage A superhump method. The value is generally in good agreement with the theoretical evolutionary model. The orbital period of J0902 is the longest among the outbursting AM CVn-type objects, and the borderline between the outbursting systems and systems with stable cool disks appears to be longer than had been supposed.

### Water Delivery and Giant Impacts in the 'Grand Tack' Scenario

A new model for terrestrial planet formation (Hansen 2009, Walsh et al. 2011) has explored accretion in a truncated protoplanetary disk, and found that such a configuration is able to reproduce the distribution of mass among the planets in the Solar System, especially the Earth/Mars mass ratio, which earlier simulations have generally not been able to match. Walsh et al. tested a possible mechanism to truncate the disk–a two-stage, inward-then-outward migration of Jupiter and Saturn, as found in numerous hydrodynamical simulations of giant planet formation. In addition to truncating the disk and producing a more realistic Earth/Mars mass ratio, the migration of the giant planets also populates the asteroid belt with two distinct populations of bodies–the inner belt is filled by bodies originating inside of 3 AU, and the outer belt is filled with bodies originating from between and beyond the giant planets (which are hereafter referred to as primitive’ bodies). We find here that the planets will accrete on order 1-2% of their total mass from primitive planetesimals scattered onto planet-crossing orbits during the formation of the planets. For an assumed value of 10% for the water mass fraction of the primitive planetesimals, this model delivers a total amount of water comparable to that estimated to be on the Earth today. While the radial distribution of the planetary masses and the dynamical excitation of their orbits are a good match to the observed system, we find that the last giant impact is typically earlier than 20 Myr, and a substantial amount of mass is accreted after that event. However, 5 of the 27 planets larger than half an Earth mass formed in all simulations do experience large late impacts and subsequent accretion consistent with the dating of the Moon-forming impact and the estimated amount of mass accreted by Earth following that event.

### Vertical instability and inclination excitation during planetary migration

We consider a two-planet system, which migrates under the influence of dissipative forces that mimic the effects of gas-driven (Type II) migration. It has been shown that, in the planar case, migration leads to resonant capture after an evolution that forces the system to follow families of periodic orbits. Starting with planets that differ slightly from a coplanar configuration, capture can, also, occur and, additionally, excitation of planetary inclinations has been observed in some cases. We show that excitation of inclinations occurs, when the planar families of periodic orbits, which are followed during the initial stages of planetary migration, become vertically unstable. At these points, {\em vertical critical orbits} may give rise to generating stable families of $3D$ periodic orbits, which drive the evolution of the migrating planets to non-coplanar motion. We have computed and present here the vertical critical orbits of the $2/1$ and $3/1$ resonances, for various values of the planetary mass ratio. Moreover, we determine the limiting values of eccentricity for which the "inclination resonance" occurs.

### Vertical instability and inclination excitation during planetary migration [Replacement]

We consider a two-planet system, which migrates under the influence of dissipative forces that mimic the effects of gas-driven (Type II) migration. It has been shown that, in the planar case, migration leads to resonant capture after an evolution that forces the system to follow families of periodic orbits. Starting with planets that differ slightly from a coplanar configuration, capture can, also, occur and, additionally, excitation of planetary inclinations has been observed in some cases. We show that excitation of inclinations occurs, when the planar families of periodic orbits, which are followed during the initial stages of planetary migration, become vertically unstable. At these points, {\em vertical critical orbits} may give rise to generating stable families of $3D$ periodic orbits, which drive the evolution of the migrating planets to non-coplanar motion. We have computed and present here the vertical critical orbits of the $2/1$ and $3/1$ resonances, for various values of the planetary mass ratio. Moreover, we determine the limiting values of eccentricity for which the "inclination resonance" occurs.

### Remnant mass, spin, and recoil from spin aligned black-hole binaries [Cross-Listing]

We perform a set of 36 nonprecessing black-hole binary simulations with spins either aligned or counteraligned with the orbital angular momentum in order to model the final mass, spin, and recoil of the merged black hole as a function of the individual black hole spin magnitudes and the mass ratio of the progenitors. We find that the maximum recoil for these configurations is $V_{max}=526\pm23\,km/s$, which occurs when the progenitor spins are maximal, the mass ratio is $q_{max}=m_1/m_2=0.623\pm0.038$, the smaller black-hole spin is aligned with the orbital angular momentum, and the larger black-hole spin is counteraligned ($\alpha_1=-\alpha_2=1$). This maximum recoil is about $80\,km/s$ larger than previous estimates, but most importantly, because the maximum occurs for smaller mass ratios, the probability for a merging binary to recoil faster than $400\,km/s$ can be as large as $17\%$, while the probability for recoils faster than $250\, km/s$ can be as large as $45\%$. We provide explicit phenomenological formulas for the final mass, spin, and recoil as a function of the individual BH spins and the mass difference between the two black holes. Here we include terms up through fourth-order in the initial spins and mass difference, and find excellent agreement (within a few percent) with independent results available in the literature. The maximum radiated energy is $E_{\rm rad}/m\approx11.3\%$ and final spin $\alpha_{\rm rem}^{\rm max}\approx0.952$ for equal mass, aligned maximally spinning binaries.

### The baryonic mass assembly of low-mass halos in a Lambda-CDM Universe

We analyse the dark, gas, and stellar mass assembly histories of low-mass halos (Mvir ~ 10^10.3 – 10^12.3 M_sun) identified at redshift z = 0 in cosmological numerical simulations. Our results indicate that for halos in a given present-day mass bin, the gas-to-baryon fraction inside the virial radius does not evolve significantly with time, ranging from ~0.8 for smaller halos to ~0.5 for the largest ones. Most of the baryons are located actually not in the galaxies but in the intrahalo gas; for the more massive halos, the intrahalo gas-to-galaxy mass ratio is approximately the same at all redshifts, z, but for the least massive halos, it strongly increases with z. The intrahalo gas in the former halos gets hotter with time, being dominant at z = 0, while in the latter halos, it is mostly cold at all epochs. The multiphase ISM and thermal feedback models in our simulations work in the direction of delaying the stellar mass growth of low-mass galaxies.

### Universal Profiles of the Intracluster Medium from Suzaku X-Ray and Subaru Weak Lensing Obesrvations [Replacement]

We conduct a joint X-ray and weak-lensing study of four relaxed galaxy clusters (Hydra A, A478, A1689 and A1835) observed by both Suzaku and Subaru out to virial radii, with an aim to understand recently-discovered unexpected feature of the ICM in cluster outskirts. We show that the average hydrostatic-to-lensing total mass ratio for the four clusters decreases from \sim 70% to \sim 40% as the overdensity contrast decreases from 500 to the virial value.The average gas mass fraction from lensing total mass estimates increases with cluster radius and agrees with the cosmic mean baryon fraction within the virial radius, whereas the X-ray-based gas fraction considerably exceeds the cosmic values due to underestimation of the hydrostatic mass. We also develop a new advanced method for determining normalized cluster radial profiles for multiple X-ray observables by simultaneously taking into account both their radial dependence and multivariate scaling relations with weak-lensing masses. Although the four clusters span a range of halo mass, concentration, X-ray luminosity and redshift, we find that the gas entropy, pressure, temperature and density profiles are all remarkably self-similar when scaled with the lensing M_200 mass and r_200 radius.The entropy monotonically increases out to \sim 0.5r_200 following the accretion shock heating model K(r)\propto r^1.1, and flattens at \simgt 0.5r_200.The universality of the scaled entropy profiles indicates that the thermalization mechanism over the entire cluster region (>0.1r_200) is controlled by gravitation in a common to all clusters, although the heating efficiency in the outskirts needs to be modified from the standard law.The bivariate scaling functions of the gas density and temperature reveal that the flattening of the outskirts entropy profile is caused by the steepening of the temperature, rather than the flattening of the gas density.

### Universal Profiles of the Intracluster Medium from Suzaku X-Ray and Subaru Weak Lensing Obesrvations

We conduct a joint X-ray and weak-lensing study of four relaxed galaxy clusters (Hydra A, A478, A1689 and A1835) observed by both Suzaku and Subaru out to virial radii, with an aim to understand recently-discovered unexpected feature of the ICM in cluster outskirts. We show that the average hydrostatic-to-lensing total mass ratio for the four clusters decreases from \sim 70% to \sim 40% as the overdensity contrast decreases from 500 to the virial value.The average gas mass fraction from lensing total mass estimates increases with cluster radius and agrees with the cosmic mean baryon fraction within the virial radius, whereas the X-ray-based gas fraction considerably exceeds the cosmic values due to underestimation of the hydrostatic mass. We also develop a new advanced method for determining normalized cluster radial profiles for multiple X-ray observables by simultaneously taking into account both their radial dependence and multivariate scaling relations with weak-lensing masses. Although the four clusters span a range of halo mass, concentration, X-ray luminosity and redshift, we find that the gas entropy, pressure, temperature and density profiles are all remarkably self-similar when scaled with the lensing M_200 mass and r_200 radius.The entropy monotonically increases out to \sim 0.5r_200 following the accretion shock heating model K(r)\propto r^1.1, and flattens at \simgt 0.5r_200.The universality of the scaled entropy profiles indicates that the thermalization mechanism over the entire cluster region (>0.1r_200) is controlled by gravitation in a common to all clusters, although the heating efficiency in the outskirts needs to be modified from the standard law.The bivariate scaling functions of the gas density and temperature reveal that the flattening of the outskirts entropy profile is caused by the steepening of the temperature, rather than the flattening of the gas density.

### A parameter study of the eclipsing CV in the Kepler field, KIS J192748.53+444724.5

We present high-speed, three-colour photometry of the eclipsing dwarf nova KIS J192748.53+444724.5 which is located in the Kepler field. Our data reveal sharp features corresponding to the eclipses of the accreting white dwarf followed by the bright spot where the gas stream joins the accretion disc. We determine the system parameters via a parameterized model of the eclipse fitted to the observed lightcurve. We obtain a mass ratio of q = 0.570 +/- 0.011 and an orbital inclination of 84.6 +/- 0.3 degrees. The primary mass is M_w = 0.69 +/- 0.07 Msun. The donor star’s mass and radius are found to be M_d = 0.39 +/- 0.04 Msun and R_d = 0.43 +/- 0.01 Rsun, respectively. From the fluxes of the white dwarf eclipse we find a white dwarf temperature of T_w = 23000 +/- 3000 K, and a photometric distance to the system of 1600 +/- 200 pc, neglecting the effects of interstellar reddening. The white dwarf temperature in KISJ1927 implies the white dwarf is accreting at an average rate of Mdot = (1.4 +/- 0.8) x10e-9 Msun/yr, in agreement with estimates of the secular mass loss rate from the donor.

### Lunar and Terrestrial Planet Formation in the Grand Tack Scenario

We present conclusions from a large number of N-body simulations of the giant impact phase of terrestrial planet formation. We focus on new results obtained from the recently proposed Grand Tack model, which couples the gas-driven migration of giant planets to the accretion of the terrestrial planets. The giant impact phase follows the oligarchic growth phase, which builds a bi-modal mass distribution within the disc of embryos and planetesimals. By varying the ratio of the total mass in the embryo population to the total mass in the planetesimal population and the mass of the individual embryos, we explore how different disc conditions control the final planets. The total mass ratio of embryos to planetesimals controls the timing of the last giant (Moon forming) impact and its violence. The initial embryo mass sets the size of the lunar impactor and the growth rate of Mars. After comparing our simulated outcomes with the actual orbits of the terrestrial planets (angular momentum deficit, mass concentration) and taking into account independent geochemical constraints on the mass accreted by the Earth after the Moon forming event and on the timescale for the growth of Mars, we conclude that the protoplanetary disc at the beginning of the giant impact phase must have had most of its mass in Mars-sized embryos and only a small fraction of the total disc mass in the planetesimal population. From this, we infer that the Moon forming event occurred between $\sim$60 and $\sim$130 My after the formation of the first solids, and was caused most likely by an object with a mass similar to that of Mars.

### CLASH-X: A Comparison of Lensing and X-ray Techniques for Measuring the Mass Profiles of Galaxy Clusters

We present profiles of temperature, gas mass, and hydrostatic mass estimated from X-ray observations of CLASH clusters. We compare measurements from XMM and Chandra and compare both sets to CLASH gravitational lensing mass profiles. We find that Chandra and XMM measurements of electron density and enclosed gas mass as functions of radius are nearly identical, indicating that any differences in hydrostatic masses inferred from X-ray observations arise from differences in gas-temperature estimates. Encouragingly, gas temperatures measured in clusters by XMM and Chandra are consistent with one another at ~100 kpc radii but XMM temperatures systematically decline relative to Chandra temperatures as the radius of the temperature measurement increases. One plausible reason for this trend is large-angle scattering of soft X-ray photons in excess of that amount expected from the standard XMM PSF correction. We present the CLASH-X mass-profile comparisons in the form of cosmology-independent and redshift-independent circular-velocity profiles, which are the most robust way to assess mass bias. Chandra HSE mass to CLASH lensing mass ratio profiles show no obvious radial dependence in the 0.3-0.8 Mpc range. However, the mean mass biases inferred from the WL and SaWLens data are different, with a weighted-mean value at 0.5 Mpc of <b>=0.12 for the WL comparison and <b>= -0.11 for the SaWLens comparison. XMM HSE mass to CLASH lensing mass ratio profiles show a pronounced radial dependence in the 0.3-1.0 Mpc range, with a weighted-mean mass bias of value rising to b>0.3 at ~1 Mpc for the WL comparison and b~0.25 for the SaWLens comparison. The enclosed gas mass profiles from both Chandra and XMM rise to a value ~1/8 times the total-mass profiles inferred from lensing at ~0.5 Mpc, suggesting that 8 M_gas profiles may be an excellent proxy for total-mass profiles at >~0.5 Mpc in massive galaxy clusters.

### Orbital masses of nearby luminous galaxies

We use observational properties of galaxies accumulated in the Updated Nearby Galaxy Catalog to derive a dark matter mass of luminous galaxies via motions of their companions. The data on orbital-to-stellar mass ratio are presented for 15 luminous galaxies situated within 11 Mpc from us: the Milky Way, M31, M81, NGC5128, IC342, NGC253, NGC4736, NGC5236, NGC6946, M101, NGC4258, NGC4594, NGC3115, NGC3627 and NGC3368, as well as for a composit suite around other nearby galaxies of moderate and low luminosity. The typical ratio for them is M_{orb}/M* = 31, corresponding to the mean local density of matter Omega_m = 0.09, i.e 1/3 of the global cosmic density. This quantity seems to be rather an upper limit of dark matter density, since the peripheric population of the suites may suffer from the presence of fictitious unbound members. We notice that the Milky Way and M31 haloes have lower dimensions and lower stellar masses than those of other 13 nearby luminous galaxies. However, the dark-to-stellar mass ratio for both the Milky Way and M31 is the typical one for other neighboring luminous galaxies. The distortion in the Hubble flow, observed around the Local Group and five other neighboring groups yields their total masses within the radius of zero velocity surface,R_0, which are slightly lower than the orbital and virial values. This difference may be due to the effect of dark energy, producing a kind of "mass defect" within R_0.

### High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries [Replacement]

The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision. In this paper, we build upon earlier work to carry this comparison still further, by examining next-to-next-to-leading order contributions beyond the half integral 5.5PN conservative effect, which arise from terms to cubic and higher orders in the metric and its multipole moments, thus extending scrutiny of the post-Newtonian methods to one of the highest orders yet achieved. We do this by explicitly constructing tail-of-tail terms at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in the small mass ratio limit, and comparing directly with numerically and analytically computed terms in the self-force approach, obtained using solutions for metric perturbations in the Schwarzschild space-time, and a combination of exact series representations possibly with more typical PN expansions. While self-force results may be relativistic but with restricted mass ratio, our methods, valid primarily in the weak-field slowly-moving regime, are nevertheless in principle applicable for arbitrary mass ratios.

### High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio. Within many of its applications, it is often required to use a regularization procedure. Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies. In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision. In this paper, we build upon earlier work to carry this comparison still further, by examining next-to-next-to-leading order contributions beyond the half integral 5.5PN conservative effect, which arise from terms to cubic and higher orders in the metric and its multipole moments, thus extending scrutiny of the post-Newtonian methods to one of the highest orders yet achieved. We do this by explicitly constructing tail-of-tail terms at 6.5PN and 7.5PN order, computing the redshift factor for compact binaries in the small mass ratio limit, and comparing directly with numerically and analytically computed terms in the self-force approach, obtained using solutions for metric perturbations in the Schwarzschild space-time, and a combination of exact series representations possibly with more typical PN expansions. While self force results may be relativistic but with restricted mass ratio, our methods, valid primarily in the weak-field slowly-moving regime, are nevertheless in principle applicable for arbitrary mass ratios.

### Balancing mass and momentum in the Local Group [Replacement]

In the rest frame of the Local Group (LG), the total momentum of the Milky Way (MW) and Andromeda (M31) should balance to zero. We use this fact to constrain new solutions for the solar motion with respect to the LG centre-of-mass, the total mass of the LG, and the individual masses of M31 and the MW. Using the set of remote LG galaxies at $>350$ kpc from the MW and M31, we find that the solar motion has amplitude $V_{\odot}=299\pm 15 {\rm ~km~s^{-1}}$ in a direction pointing toward galactic longitude $l_{\odot}=98.4^{\circ}\pm 3.6^{\circ}$ and galactic latitude $b_{\odot}=-5.9^{\circ}\pm 3.0^{\circ}$. The velocities of M31 and the MW in this rest frame give a direct measurement of their mass ratio, for which we find $\log_{10} (M_{\rm M31}/M_{\rm MW})=0.36 \pm 0.29$. We combine these measurements with the virial theorem to estimate the total mass within the LG as $M_{\rm LG}=(2.5\pm 0.4)\times 10^{12}~{\rm M}_{\odot}$. Our value for $M_{\rm LG}$ is consistent with the sum of literature values for $M_{\rm MW}$ and $M_{\rm M31}$. This suggests that the mass of the LG is almost entirely located within the two largest galaxies rather than being dispersed on larger scales or in a background medium. The outskirts of the LG are seemingly rather empty. Combining our measurement for $M_{\rm LG}$ and the mass ratio, we estimate the individual masses of the MW and M31 to be $M_{\rm MW}=(0.8\pm 0.5)\times 10^{12}~{\rm M}_{\odot}$ and $M_{\rm M31}=(1.7\pm 0.3)\times 10^{12}~{\rm M}_{\odot}$, respectively. Our analysis favours M31 being more massive than the MW by a factor of $\sim$2.3, and the uncertainties allow only a small probability (9.8%) that the MW is more massive. This is consistent with other properties such as the maximum rotational velocities, total stellar content, and numbers of globular clusters and dwarf satellites, which all suggest that $M_{\rm M31}/M_{\rm MW}>1$.

### Balancing mass and momentum in the Local Group

In the rest frame of the Local Group (LG), the total momentum of the Milky Way (MW) and Andromeda (M31) should balance to zero. We use this fact to constrain new solutions for the solar motion with respect to the LG centre-of-mass, the total mass of the LG, and the individual masses of M31 and the MW. Using the set of remote LG galaxies at $>350$ kpc from the MW and M31, we find that the solar motion has amplitude $V_{\odot}=299\pm 15 {\rm ~km~s^{-1}}$ in a direction pointing toward galactic longitude $l_{\odot}=98.4^{\circ}\pm 3.6^{\circ}$ and galactic latitude $b_{\odot}=-5.9^{\circ}\pm 3.0^{\circ}$. The velocities of M31 and the MW in this rest frame give a direct measurement of their mass ratio, for which we find $\log_{10} (M_{\rm M31}/M_{\rm MW})=0.36 \pm 0.29$. We combine these measurements with the virial theorem to estimate the total mass within the LG as $M_{\rm LG}=(2.5\pm 0.4)\times 10^{12}~{\rm M}_{\odot}$. Our value for $M_{\rm LG}$ is consistent with the sum of literature values for $M_{\rm MW}$ and $M_{\rm M31}$. This suggests that the mass of the LG is almost entirely located within the two largest galaxies rather than being dispersed on larger scales or in a background medium. The outskirts of the LG are seemingly rather empty. Combining our measurement for $M_{\rm LG}$ and the mass ratio, we estimate the individual masses of the MW and M31 to be $M_{\rm MW}=(0.8\pm 0.5)\times 10^{12}~{\rm M}_{\odot}$ and $M_{\rm M31}=(1.7\pm 0.3)\times 10^{12}~{\rm M}_{\odot}$, respectively. Our analysis favours M31 being more massive than the MW by a factor of $\sim$2.3, and the uncertainties allow only a small probability (9.8%) that the MW is more massive. This is consistent with other properties such as the maximum rotational velocities, total stellar content, and numbers of globular clusters and dwarf satellites, which all suggest that $M_{\rm M31}/M_{\rm MW}>1$.

### An interaction scenario of the galaxy pair NGC 3893/96 (KPG 302). A single passage?

Using the data obtained previously from Fabry-Perot interferometry, we study the orbital characteristics of the interacting pair of galaxies KPG 302 with the aim to estimate a possible interaction history, the conditions necessary for the spiral arms formation and initial satellite mass. We found by performing N-body/SPH simulations of the interaction that a single passage can produce a grand design spiral pattern in less than 1 Gyr. Althought we reproduce most of the features with the single passage, the required satellite to host mass ratio should be 1:5, which is not confirmed with the dynamical mass estimate made from the measured rotation curve. We conclude that a more realistic interaction scenario would require several passages in order to explain the mass ratio discrepancy.

### Spectroscopic Orbital Elements for the Helium-Rich Subdwarf Binary PG1544+488

PG1544+488 is an exceptional short-period spectroscopic binary containing two subdwarf B stars. It is also exceptional because the surfaces of both components are extremely helium-rich. We present a new analysis of spectroscopy of PG1544+488 obtained with the William Herschel Telescope. We obtain improved orbital parameters and atmospheric parameters for each component. The orbital period $P=0.496\pm0.002$\,d, dynamical mass ratio $M_{\rm B}/M_{\rm A}=0.911\pm0.015$, and spectroscopic radius ratio $R_{\rm B}/R_{\rm A}=0.939\pm0.004$ indicate a binary consisting of nearly identical twins. The data are insufficient to distinguish any difference in surface composition between the components, which are slightly metal-poor (1/3 solar) and carbon-rich (0.3% by number). The latter indicates that the hotter component, at least, has ignited helium. The best theoretical model for the origin of PG1544+488 is by the ejection of a common envelope from a binary system in which both components are giants with helium cores of nearly equal mass. Since precise tuning is necessary to yield two helium cores of similar masses at the same epoch, the mass ratio places very tight constraints on the dimensions of the progenitor system and on the physics of the common-envelope ejection mechanism.

### A dynamical model of the local cosmic expansion

We combine the equations of motion that govern the dynamics of galaxies in the local volume with Bayesian techniques in order to fit orbits to published distances and velocities of galaxies within 3 Mpc. We find a Local Group (LG) mass $2.1^{+0.7}_{-0.6}\times 10^{12}{\rm M}_\odot$ that is consistent with the combined dynamical masses of M31 and the Milky Way, and a mass ratio $1.29^{+0.24}_{-0.16}$ that rules out models where M31 is more massive than our Galaxy with $\sim 95%$ confidence. The Milky Way’s circular velocity at the solar radius is relatively high, $251\pm 23 {\rm km s}^{-1}$, which helps to reconcile the mass derived from the local Hubble flow with the larger value suggested by the timing argument’. Adopting {\it Planck}’s bounds on $\Omega_\Lambda$ yields a (local) Hubble constant $H_0=67\pm 5{\rm km s}^{-1}{\rm Mpc}^{-1}$ which is consistent with the value found on cosmological scales. Restricted N-body experiments show that substructures tend to fall onto the LG along the Milky Way-M31 axis, where the quadrupole attraction is maximum. Tests against mock data indicate that neglecting this effect slightly overestimates the LG mass without biasing the rest of model parameters. We also show that both the time-dependence of the LG potential and the cosmological constant have little impact on the observed local Hubble flow.

### A dynamical model of the local cosmic expansion [Replacement]

We combine the equations of motion that govern the dynamics of galaxies in the local volume with Bayesian techniques in order to fit orbits to published distances and velocities of galaxies within 3~Mpc. We find a Local Group (LG) mass $2.3\pm 0.7\times 10^{12}{\rm M}_\odot$ that is consistent with the combined dynamical masses of M31 and the Milky Way, and a mass ratio $0.54^{+0.23}_{-0.17}$ that rules out models where our Galaxy is more massive than M31 with $\sim 95\%$ confidence. The Milky Way’s circular velocity at the solar radius is relatively high, $245\pm 23$ km/s, which helps to reconcile the mass derived from the local Hubble flow with the larger value suggested by the timing argument’. Adopting {\it Planck}’s bounds on $\Omega_\Lambda$ yields a (local) Hubble constant $H_0=67\pm 5$km/s/Mpc which is consistent with the value found on cosmological scales. Restricted N-body experiments show that substructures tend to fall onto the LG along the Milky Way-M31 axis, where the quadrupole attraction is maximum. Tests against mock data indicate that neglecting this effect slightly overestimates the LG mass without biasing the rest of model parameters. We also show that both the time-dependence of the LG potential and the cosmological constant have little impact on the observed local Hubble flow.

### A dynamical model of the local cosmic expansion [Replacement]

We combine the equations of motion that govern the dynamics of galaxies in the local volume with Bayesian techniques in order to fit orbits to published distances and velocities of galaxies within $\sim 3$ Mpc. We find a Local Group (LG) mass $2.3\pm 0.7\times 10^{12}{\rm M}_\odot$ that is consistent with the combined dynamical masses of M31 and the Milky Way, and a mass ratio $0.54^{+0.23}_{-0.17}$ that rules out models where our Galaxy is more massive than M31 with $\sim 95\%$ confidence. The Milky Way’s circular velocity at the solar radius is relatively high, $245\pm 23$ km/s, which helps to reconcile the mass derived from the local Hubble flow with the larger value suggested by the timing argument’. Adopting {\it Planck}’s bounds on $\Omega_\Lambda$ yields a (local) Hubble constant $H_0=67\pm 5$km/s/Mpc which is consistent with the value found on cosmological scales. Restricted N-body experiments show that substructures tend to fall onto the LG along the Milky Way-M31 axis, where the quadrupole attraction is maximum. Tests against mock data indicate that neglecting this effect slightly overestimates the LG mass without biasing the rest of model parameters. We also show that both the time-dependence of the LG potential and the cosmological constant have little impact on the observed local Hubble flow.

### The Universal Relation of Galactic Chemical Evolution: The Origin of the Mass-Metallicity Relation

We examine the mass-metallicity relation for $z\lesssim 1.6$. The mass-metallicity relation follows a steep slope with a turnover or knee’ at stellar masses around $10^{10} M_\odot$. At stellar masses higher than the characteristic turnover mass, the mass-metallicity relation flattens as metallicities begin to saturate. We show that the redshift evolution of the mass-metallicity relation depends only on evolution of the characteristic turnover mass. The relationship between metallicity and the stellar mass normalized to the characteristic turnover mass is independent of redshift. We find that the redshift independent slope of the mass-metallicity relation is set by the slope of the relationship between gas mass and stellar mass. The turnover in the mass-metallicity relation occurs when the gas-phase oxygen abundance is high enough that the amount of oxygen locked up in low mass stars is an appreciable fraction of the amount of oxygen produced by massive stars. The characteristic turnover mass is the stellar mass where the stellar-to-gas mass ratio is unity. Numerical modeling suggests that the relationship between metallicity and stellar-to-gas mass ratio is a redshift independent, universal relationship followed by all galaxies as they evolve. The mass-metallicity relation originates from this more fundamental universal relationship between metallicity and stellar-to-gas mass ratio. We test the validity of this universal metallicity relation in local galaxies where stellar mass, metallicity and gas mass measurements are available. The data are consistent with a universal metallicity relation. We derive an equation for estimating the hydrogen gas mass from measurements of stellar mass and metallicity valid for $z\lesssim1.6$ and predict the cosmological evolution of galactic gas masses.

### The Universal Relation of Galactic Chemical Evolution: The Origin of the Mass-Metallicity Relation [Replacement]

We examine the mass-metallicity relation for $z\lesssim 1.6$. The mass-metallicity relation follows a steep slope with a turnover or knee’ at stellar masses around $10^{10} M_\odot$. At stellar masses higher than the characteristic turnover mass, the mass-metallicity relation flattens as metallicities begin to saturate. We show that the redshift evolution of the mass-metallicity relation depends only on evolution of the characteristic turnover mass. The relationship between metallicity and the stellar mass normalized to the characteristic turnover mass is independent of redshift. We find that the redshift independent slope of the mass-metallicity relation is set by the slope of the relationship between gas mass and stellar mass. The turnover in the mass-metallicity relation occurs when the gas-phase oxygen abundance is high enough that the amount of oxygen locked up in low mass stars is an appreciable fraction of the amount of oxygen produced by massive stars. The characteristic turnover mass is the stellar mass where the stellar-to-gas mass ratio is unity. Numerical modeling suggests that the relationship between metallicity and stellar-to-gas mass ratio is a redshift independent, universal relationship followed by all galaxies as they evolve. The mass-metallicity relation originates from this more fundamental universal relationship between metallicity and stellar-to-gas mass ratio. We test the validity of this universal metallicity relation in local galaxies where stellar mass, metallicity and gas mass measurements are available. The data are consistent with a universal metallicity relation. We derive an equation for estimating the hydrogen gas mass from measurements of stellar mass and metallicity valid for $z\lesssim1.6$ and predict the cosmological evolution of galactic gas masses.

### The Universal Relation of Galactic Chemical Evolution: The Origin of the Mass-Metallicity Relation [Replacement]

We examine the mass-metallicity relation for $z\lesssim 1.6$. The mass-metallicity relation follows a steep slope with a turnover or `knee’ at stellar masses around $10^{10} M_\odot$. At stellar masses higher than the characteristic turnover mass, the mass-metallicity relation flattens as metallicities begin to saturate. We show that the redshift evolution of the mass-metallicity relation depends only on evolution of the characteristic turnover mass. The relationship between metallicity and the stellar mass normalized to the characteristic turnover mass is independent of redshift. We find that the redshift independent slope of the mass-metallicity relation is set by the slope of the relationship between gas mass and stellar mass. The turnover in the mass-metallicity relation occurs when the gas-phase oxygen abundance is high enough that the amount of oxygen locked up in low mass stars is an appreciable fraction of the amount of oxygen produced by massive stars. The characteristic turnover mass is the stellar mass where the stellar-to-gas mass ratio is unity. Numerical modeling suggests that the relationship between metallicity and stellar-to-gas mass ratio is a redshift independent, universal relationship followed by all galaxies as they evolve. The mass-metallicity relation originates from this more fundamental universal relationship between metallicity and stellar-to-gas mass ratio. We test the validity of this universal metallicity relation in local galaxies where stellar mass, metallicity and gas mass measurements are available. The data are consistent with a universal metallicity relation. We derive an equation for estimating the hydrogen gas mass from measurements of stellar mass and metallicity valid for $z\lesssim1.6$ and predict the cosmological evolution of galactic gas masses.

### On the Spin-axis Dynamics of a Moonless Earth

The variation of a planet’s obliquity is influenced by the existence of satellites with a high mass ratio. For instance, the Earth’s obliquity is stabilized by the Moon, and would undergo chaotic variations in the Moon’s absence. In turn, such variations can lead to large-scale changes in the atmospheric circulation, rendering spin-axis dynamics a central issue for understanding climate. The relevant quantity for dynamically-forced climate change is the rate of chaotic diffusion. Accordingly, here we reexamine the spin-axis evolution of a Moonless Earth within the context of a simplified perturbative framework. We present analytical estimates of the characteristic Lyapunov coefficient as well as the chaotic diffusion rate and demonstrate that even in absence of the Moon, the stochastic change in the Earth’s obliquity is sufficiently slow to not preclude long-term habitability. Our calculations are consistent with published numerical experiments and illustrate the putative system’s underlying dynamical structure in a simple and intuitive manner.

### A mass-dependent density profile for dark matter haloes including the influence of galaxy formation

We introduce a mass dependent density profile to describe the distribution of dark matter within galaxies, which takes into account the stellar-to-halo mass dependence of the response of dark matter to baryonic processes. The study is based on the analysis of hydrodynamically simulated galaxies from dwarf to Milky Way mass, drawn from the MaGICC project, which have been shown to match a wide range of disk scaling relationships. We find that the best fit parameters of a generic double power-law density profile vary in a systematic manner that depends on the stellar-to-halo mass ratio of each galaxy. Thus, the quantity Mstar/Mhalo constrains the inner ($\gamma$) and outer ($\beta$) slopes of dark matter density, and the sharpness of transition between the slopes($\alpha$), reducing the number of free parameters of the model to two. Due to the tight relation between stellar mass and halo mass, either of these quantities is sufficient to describe the dark matter halo profile including the effects of baryons. The concentration of the haloes in the hydrodynamical simulations is consistent with N-body expectations up to Milky Way mass galaxies, at which mass the haloes become twice as concentrated as compared with pure dark matter runs. This mass dependent density profile can be directly applied to rotation curve data of observed galaxies and to semi analytic galaxy formation models as a significant improvement over the commonly used NFW profile.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

### Observational Signatures of Binary Supermassive Black Holes

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

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

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

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

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

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

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