# Posts Tagged mass ratio

## Recent Postings from mass ratio

### 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.

### 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.

### 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.

### 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.

### 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.

### 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.

### Lattice QCD estimate of the $\eta_{c}(2S)\to J/\psi\gamma$ decay rate [Cross-Listing]

We compute the hadronic matrix element relevant to the physical radiative decay $\eta_{c}(2S)\to J/\psi\gamma$ by means of lattice QCD. We use the (maximally) twisted mass QCD action with Nf=2 light dynamical quarks and from the computations made at four lattice spacings we were able to take the continuum limit. The value of the mass ratio $m_{\eta_c(2S)}/m_{\eta_c(1S)}$ we obtain is consistent with the experimental value, and our prediction for the form factor is $V^{\eta_{c}(2S)\to J/\psi\gamma}(0)\equiv V_{12}(0)=0.32(6)(2)$, leading to $\Gamma(\eta_c (2S) \to J/\psi\gamma) = (15.7\pm 5.7)$ keV, which is much larger than $\Gamma(\psi (2S) \to \eta_c\gamma)$ and within reach of modern experiments.

### Super-massive black hole mass scaling relations

Using black hole masses which span 10^5 to 10^(10) solar masses, the distribution of galaxies in the (host spheroid stellar mass)-(black hole mass) diagram is shown to be strongly bent. While the core-Sersic galaxies follow a near-linear relation, having a mean M_(bh)/M_(sph) mass ratio of ~0.5%, the Sersic galaxies follow a near-quadratic relation: M_bh~M_sph^(2.22+\-0.58). This is not due to offset pseudobulges, but is instead an expected result arising from the long-known bend in the M_(sph)-sigma relation and the log-linear M_(bh)-sigma relation.

### Effective potentials and morphological transitions for binary black-hole spin precession

Binary black holes (BBHs) on quasicircular orbits are fully characterized by their total mass $M$, mass ratio $q$, spins $\mathbf{S}_1$ and $\mathbf{S}_2$, and orbital angular momentum $\mathbf{L}$. When the binary separation $r \gg GM/c^2$, the precession timescale is much shorter than the radiation-reaction time on which $L = |\mathbf{L}|$ decreases due to gravitational-wave (GW) emission. We use conservation of the total angular momentum $\mathbf{J} = \mathbf{L} + \mathbf{S}_1 + \mathbf{S}_2$ (with magnitude $J$) and the projected effective spin $\xi \equiv M^{-2} [(1+q) \mathbf{S}_1 + (1+q^{-1})\mathbf{S}_2] \cdot \hat{\mathbf{L}}$ on the precession time to derive an effective potential for BBH spin precession. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a period $\tau(L, J, \xi)$ the angular momenta return to their initial relative orientations and precess about $\mathbf{J}$ by an angle $\alpha(L, J, \xi)$. We classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. Our new solutions constitute fundamental progress in our understanding of BBH spin precession and also have important astrophysical applications. We derive a precession-averaged evolution equation $dJ/dL$ that can be numerically integrated on the radiation-reaction time, allowing us to statistically track BBH spins from formation to merger far more efficiently than was possible with previous orbit-averaged precession equations. This will greatly help us predict the signatures of BBH formation in the GWs emitted near merger and the distributions of final spins and gravitational recoils. The solutions may also help efforts to model and interpret GWs from generic BBH mergers.

### Effective potentials and morphological transitions for binary black-hole spin precession [Cross-Listing]

Binary black holes (BBHs) on quasicircular orbits are fully characterized by their total mass $M$, mass ratio $q$, spins $\mathbf{S}_1$ and $\mathbf{S}_2$, and orbital angular momentum $\mathbf{L}$. When the binary separation $r \gg GM/c^2$, the precession timescale is much shorter than the radiation-reaction time on which $L = |\mathbf{L}|$ decreases due to gravitational-wave (GW) emission. We use conservation of the total angular momentum $\mathbf{J} = \mathbf{L} + \mathbf{S}_1 + \mathbf{S}_2$ (with magnitude $J$) and the projected effective spin $\xi \equiv M^{-2} [(1+q) \mathbf{S}_1 + (1+q^{-1})\mathbf{S}_2] \cdot \hat{\mathbf{L}}$ on the precession time to derive an effective potential for BBH spin precession. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a period $\tau(L, J, \xi)$ the angular momenta return to their initial relative orientations and precess about $\mathbf{J}$ by an angle $\alpha(L, J, \xi)$. We classify BBH spin precession into three distinct morphologies between which BBHs can transition during their inspiral. Our new solutions constitute fundamental progress in our understanding of BBH spin precession and also have important astrophysical applications. We derive a precession-averaged evolution equation $dJ/dL$ that can be numerically integrated on the radiation-reaction time, allowing us to statistically track BBH spins from formation to merger far more efficiently than was possible with previous orbit-averaged precession equations. This will greatly help us predict the signatures of BBH formation in the GWs emitted near merger and the distributions of final spins and gravitational recoils. The solutions may also help efforts to model and interpret GWs from generic BBH mergers.

### The rise and fall of a challenger: the Bullet Cluster in {\Lambda} Cold Dark Matter simulations

The Bullet Cluster has provided some of the best evidence for the {\Lambda} Cold Dark Matter ({\Lambda}CDM) model via direct empirical proof of the existence of collisionless dark matter, while posing a serious challenge owing to the unusually high inferred pairwise velocities of its progenitor clusters. Here we investigate the probability of finding such a high-velocity pair in large-volume N-body simulations, particularly focusing on differences between halo finding algorithms. We find that algorithms that do not account for the kinematics of infalling groups yield vastly different statistics and probabilities. When employing the ROCKSTAR halo finder that considers particle velocities, we find numerous Bullet-like pair candidates that closely match not only the high pairwise velocity, but also the mass, mass ratio, separation distance, and collision angle of the initial conditions that have been shown to produce the Bullet Cluster in non-cosmological hydrodynamic simulations. The probability of finding a massive, high pairwise velocity pair among halos with M$_{\rm halo}\geq10^{14}$M$_{\odot}$ is $4.6\times10^{-4}$ using ROCKSTAR, while it is $\approx45\times$ lower using a friends-of-friends (FOF) based approach as in previous studies. This is because the typical spatial extent of Bullet progenitors is such that FOF tends to group them into a single halo despite clearly distinct kinematics. Further requiring an appropriately high average mass among the two progenitors, we find the number density of Bullet-like candidates to be $3.2\times10^{-10}h^{3}$Mpc$^{-3}$. Our findings suggest that {\Lambda}CDM straightforwardly produces massive, high relative velocity halo pairs analogous to the Bullet Cluster progenitors, and hence the Bullet Cluster does not present a challenge to the {\Lambda}CDM model.

### Relativistic simulations of black hole-neutron star coalescence: the jet emerges [Cross-Listing]

We perform magnetohydrodynamic simulations in full general relativity of an initially quasiequilibrium binary black hole-neutron star on a quasicircular orbit that undergoes merger. The binary mass ratio is $3:1$, the black hole has initial spin parameter $a/m=0.75$ aligned with the orbital angular momentum, and the neutron star is modeled as an irrotational $\Gamma=2$ polytrope. About two orbits prior to merger (at time $t=t_B$), we seed the neutron star with a dynamically weak dipolar magnetic field [${B}_{pole}\sim 10^{14}(1.4M_\odot/M_{\rm NS})$ G] that extends from the stellar interior into the exterior. At $t=t_B$ the exterior is characterized by a low density atmosphere with constant plasma parameter $\beta\equiv P_{\rm gas}/P_{\rm mag}$. Varying $\beta$ at $t_B$ in the exterior from $0.1$ to $0.01$, we find that at $\sim 4000M \sim 100(M_{\rm NS}/1.4M_\odot)$ms following the onset of accretion of tidally disrupted debris, magnetic field winding above the remnant black hole poles builds up the magnetic field sufficiently to launch a mildly relativistic, collimated outflow – an incipient jet. The duration of the accretion and the lifetime of the jet is $\Delta t\sim 0.5(M_{\rm NS}/1.4M_\odot)$s. Our simulations are the first self-consistent calculations in full general relativity that provide theoretical corroboration that mergers of black hole-neutron stars can launch jets and be the central engines that power short-hard gamma ray bursts.

### Relativistic simulations of black hole-neutron star coalescence: the jet emerges

We perform magnetohydrodynamic simulations in full general relativity of an initially quasiequilibrium binary black hole-neutron star on a quasicircular orbit that undergoes merger. The binary mass ratio is $3:1$, the black hole has initial spin parameter $a/m=0.75$ aligned with the orbital angular momentum, and the neutron star is modeled as an irrotational $\Gamma=2$ polytrope. About two orbits prior to merger (at time $t=t_B$), we seed the neutron star with a dynamically weak dipolar magnetic field [${B}_{pole}\sim 10^{14}(1.4M_\odot/M_{\rm NS})$ G] that extends from the stellar interior into the exterior. At $t=t_B$ the exterior is characterized by a low density atmosphere with constant plasma parameter $\beta\equiv P_{\rm gas}/P_{\rm mag}$. Varying $\beta$ at $t_B$ in the exterior from $0.1$ to $0.01$, we find that at $\sim 4000M \sim 100(M_{\rm NS}/1.4M_\odot)$ms following the onset of accretion of tidally disrupted debris, magnetic field winding above the remnant black hole poles builds up the magnetic field sufficiently to launch a mildly relativistic, collimated outflow – an incipient jet. The duration of the accretion and the lifetime of the jet is $\Delta t\sim 0.5(M_{\rm NS}/1.4M_\odot)$s. Our simulations are the first self-consistent calculations in full general relativity that provide theoretical corroboration that mergers of black hole-neutron stars can launch jets and be the central engines that power short-hard gamma ray bursts.

### Herbig AeBe stars: Multiplicity and consequences

By virtue of their young age and intermediate mass, Herbig AeBe stars represent a cornerstone for our understanding of the mass-dependency of both the stellar and planetary formation processes. In this contribution, I review the current state-of-the-art multiplicity surveys of Herbig AeBe stars to assess both the overall frequency of companions and the distribution of key orbital parameters (separation, mass ratio and eccentricity). In a second part, I focus on the interplay between the multiplicity of Herbig AeBe stars and the presence and properties of their protoplanetary disks. Overall, it appears that both star and planet formation in the context of intermediate-mass stars proceeds following similar mechanisms as lower-mass stars.

### 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 [Replacement]

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 [Replacement]

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

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.

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

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 [Replacement]

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 of $q = 0.13$ 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 $M_{1} = 0.096 \pm 0.013~M_{\odot}$ and $M_{2} = 0.012 \pm 0.002~M_{\odot}$, which correspond to near the hydrogen-burning and deuterium-burning mass limits, respectively. The distance to the lens is $3.04 \pm 0.31~{\rm kpc}$ and the projected separation between the lens components is $0.80 \pm 0.08~{\rm AU}$.

### 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.