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# 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.


text:
mersenneforum.org GIMPS fundraising/prizes as incentives
 Register FAQ Search Today's Posts Mark Forums Read

 View Poll Results: should GIMPS give rewards for contributing? Support 3 12.00% Oppose 20 80.00% Neutral 1 4.00% Support, but raffles only (no flat payment) 1 4.00% Voters: 25. You may not vote on this poll

 2007-09-16, 00:52 #1 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 22×54 Posts GIMPS fundraising/prizes as incentives For non-profit organizations, web hosting costs can be pretty high. That is one of the reasons that the GIMPS forum has limited functionality, as having many features definitely consumes more resources and thus raises bandwidth costs. One thing users could do is donate money to GIMPS. However, as there is no formal way of donation (probably except for working out a deal with George via e-mail), there aren't going to be many users who will donate. There are a few ways for GIMPS to make money (for covering its costs) and remain a non-profit organization. One possible way is to offer more forum functionality for donors. Personally, I think that a reasonable donation for enhanced services would be a one-time payment of $30. Free members: search limited to an interval of 60 seconds no automatic signature 1,000 private messages limited poll options (5) limited functionality Supporting members (proposed): no search limit automatic signature 5,000 private messages more poll options (up to 10) special "Supporting Member" rank increased functionality (blogs, etc) There could be other GIMPS-only features that other forums don't offer, such as dynamic images that show users' exponents and their progress, that can be placed into the signature. Another idea for fundraising would be to sell GIMPS merchandise. I mean, who could resist a t-shirt with a picture of Marin Mersenne with something like "Because bigger is better" as the caption? Now, on to the next part: Last year, there was talk about GIMPS offering payment for sending in results. The good thing is that this would encourage more people to join, and many users would be happy at getting some money back for their computing costs. On the other hand, I personally oppose this system. GIMPS is supposed to be a volunteer project, and I feel that money should not be involved. This would also attract all kinds of unwanted people who are just looking for money. Finally, the costs of paying users for their work are very high, and I don't think that we want to make GIMPS look too commercialized anyway. However, I do have an "in between" idea. Perhaps we could hold "raffles" (prizes donated by members) for those who turn in work units. Each work unit would count as a "ticket," and once used, cannot be used in another "raffle." To encourage other activities besides LL-testing, there should be prizes for each category (LL-testing, double-checking, and trial factoring). Each TF-ed exponent (without factor) would count as one "ticket" and each exponent cleared by TF-ing would be five "tickets." Example prizes: TF-ing prizes: GIMPS t-shirts or other similar merchandise (20 winners) DC-ing prizes:$100 gift certificates (10 winners oer raffle) a new processor (2 winners) What do you think? Just a crazy idea from me. :D
 2007-09-16, 02:43 #2 Xyzzy     Aug 2002 3·2,861 Posts Please note that the the forum is a separate entity from the GIMPS project, although if George says to jump, we do. (We can't remember him asking us to, though.) The forum has functionality built in to accept various forms of payment and various levels of membership. http://www.vbulletin.com/docs/html/subscriptions Most of the ideas you suggested for higher levels of membership are not available, but there are a few that are. However, the forum only costs a few dollars a month. To get all the goodies turned on we'd have to upgrade to a dedicated server that would cost more than a hundred dollars a month. Plus, it would be a lot more work to manage, and more work is always bad in our book. Personally, we like the forum the way it is now. It is inexpensive, fast, simple and the content of the forum is not obscured by excessive features. Is it really worth spending a lot more money to get a little bit more speed or functionality? We've tried to not limit our users in any way unless it directly affects performance. Members already have 1,000 private messages, which seems like a lot to us. All users are pretty much treated equally, except moderators get a few additional editing options and super moderators get 10,000 private messages and, of course, keys to the magnificent Hasselhoff forum. We have forum maintenance and upkeep down to about an hour a day. The forum runs stable, is up 99.9% of the time (hidden at the bottom of every page is a link to our uptime stats) and the cost is easily hidden amongst our stack of monthly bills that we pass off to the wife. That's our opinion. We're lazy and we have a menagerie of assistants to help us and they don't like change either. Especially the trolls. If you think Bob is gruff then obviously you've never lived with a family of trolls. PS - If you need more poll options or private message storage, let us know. If you can make a good argument for it we can try to make it happen.
 2007-09-16, 03:14 #3 Xyzzy     Aug 2002 218716 Posts Here is a current list of our private message usage. The first column is the number of messages and the second column is the number of users who have that many. Code: 421 1 383 1 281 1 265 1 215 1 192 1 184 1 160 1 152 1 144 1 141 1 137 1 123 1 116 1 111 1 110 1 109 1 107 1 104 1 101 1 99 2 96 2 87 1 84 1 83 1 82 1 81 1 78 1 76 1 75 1 74 1 73 1 72 1 71 1 70 2 69 1 67 1 64 1 63 4 62 2 61 2 60 1 59 1 55 1 54 3 53 1 52 2 50 1 45 1 43 3 42 1 41 2 38 1 36 1 32 3 30 1 29 5 28 4 27 6 26 2 25 4 24 1 22 5 21 7 20 5 19 9 18 6 17 8 16 9 15 3 14 6 13 10 12 5 11 10 10 16 9 8 8 10 7 15 6 22 5 26 4 19 3 45 2 62 1 76
 2007-09-16, 05:35 #4 jinydu     Dec 2003 Hopefully Near M48 2×3×293 Posts I personally don't like the idea of rewards for turning in results because it may encourage cheating. As it is now, the only incentive to turn it fake results is to move up the rankings. But it might be a lot worse if there is a material (especially monetary) incentive to do so.
 2007-09-16, 13:37 #5 Fusion_power     Aug 2003 Snicker, AL 26×3×5 Posts If there is a real need for money to help run the show, I would prefer to see a donation based system. We had a donation round a few years ago to buy a new computer for George to test code on. I don't see a reason why we could not do that again. I contributed a few dollars for that computer and would contribute again if needed. Paying for exponents completed is IMHO not worth considering. It would run into quite a few dollars, there would be questions if - as some of us do - someone else's computers are used, it would attract people who were not really serious about doing the work increasing churn of exponents. This is too much trouble for any gain made. Besides, it would reduce my chances of winning the big prize! There are very few incentives for "increased functionality". One major forum I frequent uses an advertisement blitz on all non-contributing members. You pay the danegeld and you gets rid of the ads. It didn't take long for some of us to come up with ways to block the ads eliminating that problem. Modifying the hosts file on your computer or using Firefox with adblock are easy to implement. I would hate! for this forum to become an advertising nightmare. From my perspective, this forum is pretty nice as is, barring the occasional gremlin or even troll attack. Just for curiosity, xyzzy, would you mind posting (or maybe pm'ing me) the amount it costs to have the forum per month? I'm curious because my website costs $5 per month or$60 per year. This is entirely reasonable from my perspective. Fusion Last fiddled with by WraithX on 2016-02-15 at 05:06
 2007-09-16, 18:10 #6 ixfd64 Bemusing Prompter     "Danny" Dec 2002 California 9C416 Posts I definitely agree that such incentives are not worth the trouble. On another note, there are EFF prizes of $100k,$150k, and $250k given for the discovery of the first known primes with at least 10m, 100m, and 1b digits, respectively. GIMPS may be within a year of winning the$100k prize, half of which will be given to the user who discovers the winning number. The EFF prizes are given by an outside entity and GIMPS isn't guaranteed to win them, although it is commonly believed that GIMPS will win at least the $100k prize. What I think that GIMPS needs is more publicity. Since GIMPS is a non-profit project, other websites might be more inclined to offer us free/discounted advertising. Last fiddled with by WraithX on 2016-02-15 at 05:07 2007-09-17, 04:41 #7 Mr. P-1 Jun 2003 7×167 Posts Quote:  Originally Posted by Fusion_power ...I'm curious because my website costs$5 per month or $60 per year... If your site uses less than 5GB/Month bandwidth, and doesn't require a huge amount of filespace, then have a look at https://www.nearlyfreespeech.net. They charge no minimum monthly fee, only for what you use. I'm not connected with the company, other than as a satisfied customer Last fiddled with by WraithX on 2016-02-15 at 05:07 2007-09-17, 12:26 #8 R.D. Silverman "Bob Silverman" Nov 2003 North of Boston 11101010110002 Posts Quote:  Originally Posted by ixfd64 What I think that GIMPS needs is more publicity. Since GIMPS is a non-profit project, other websites might be more inclined to offer us free/discounted advertising. Please explain *why* you think GIMPS needs more publicity. What would it accomplish?? Current resources certainly seem adequate. I view the cash prizes with hostility. People should participate out of interest and not because they hope to win a lottery. If the purpose of the cash prizes is to spur research into better methods than LL, I see no evidence that this is happening. Indeed, the few people who are competent to do this kind of research do not do it for money. Furthermore, there are strong arguments that LL is theoretically the best possible algorithm already. 2007-09-17, 12:49 #9 TimSorbet Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 11×389 Posts Quote:  Originally Posted by R.D. Silverman Current resources certainly seem adequate. There are a few things you can never have enough of, and one of them is people/computers contributing to GIMPS. Are you saying that we don't need or want more people to join? Imagine how quickly we could find new primes of ever-increasing size if there were many more people in GIMPS. 2007-09-17, 13:25 #10 R.D. Silverman "Bob Silverman" Nov 2003 North of Boston 23×3×313 Posts Quote:  Originally Posted by Mini-Geek There are a few things you can never have enough of, and one of them is people/computers contributing to GIMPS. Are you saying that we don't need or want more people to join? Imagine how quickly we could find new primes of ever-increasing size if there were many more people in GIMPS. And??? So we find more primes. So we do it a little quicker. BFD. Neither finding more primes nor doing it faster will add to our UNDERSTANDING of the mathematics. So what value does it have??? If, on the other hand, participants want to improve George's code, I am all for that. Computational number theorists really don't care about new Mersenne primes unless it leads to better METHODS. Simply throwing more machines at the search does nothing. I for one certainly do NOT want more people to join, especially if they are doing it for money. It takes ZERO intelligence to take someone else's code and run it on a computer, and makes no intellectual contribution to mankind's knowledge base. I also believe that the$100K prize for a 10M digit prime should only be given
if the discoverer wrote his/her own code or contributed in some way to
the GIMPS code. Otherwise, the prize is nothing more than a lottery.

We should encourage intellectual contributions to the art, and not just
the blind running of someone else's code. (hoping thereby to get lucky)

2007-09-17, 13:42   #11
akruppa

"Nancy"
Aug 2002
Alexandria

2,467 Posts

Quote:
 Originally Posted by Xyzzy Code: 421 1

Alex

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Cryptology ePrint Archive: Report 2017/1104

Efficient provable-secure NTRUEncrypt over any cyclotomic field

Yang Wang and Mingqiang Wang

Abstract: NTRUEncrypt is a fast lattice-based cryptosystem and a probable alternative of the existing public key schemes. The existing provable-secure NTRUEncrypts are limited by the cyclotomic field it works on - the prime-power cyclotomic field. This is worth worrying, due to the subfield attack methods proposed in $2016$. Also, the module used in computation and security parameters rely heavily on the choice of plaintext space. These disadvantages restrict the applications of NTRUEncrypt.

In this paper, we give a new provable secure NTRUEncrypt in standard model under canonical embedding over any cyclotomic field. We give an reduction from a simple variant of RLWE - an error distribution discretized version of RLWE, hence from worst-case ideal lattice problems, to our NTRUEncrypt. In particular, we get a union bound for reduction parameters and module for all choices of plaintext space, so that our NTRUEncrypt can send more encrypted bits in one encrypt process with higher efficiency and stronger security. Furthermore, our scheme's decryption algorithm succeeds with probability $1-n^{\o(\sqrt{n\log n})}$ comparing with the previous works' $1-n^{-\o(1)}$, making our scheme more practical in theory.

Category / Keywords: public-key cryptography / NTRU, Ideal lattice, Canonical embedding, Cyclotomic fields, RLWE


text:
# How do you find the slope and y intercept for y-2x=3?

You can write your equation in Slope-Intercept form, isolating $y$ on one side as:
$y = \textcolor{red}{2} x + \textcolor{red}{3}$
Slope$= 2$
Y-intercept$= 3$


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×

# Physical Chemistry - Electrochemistry - 2

Before reading this post, please read the first post here : Physical Chemistry - Electrochemistry - 1

STANDARD HYDROGEN ELECTRODE
A standard hydrogen electrode is prepared by dipping a Platinum strip in $$1M HCl$$ around which $$H_2$$ gas at $$1$$ atm pressure is bubbled in an inverted test tube. At $$25^oC$$, its standard reduction potential is defined to be zero.

STANDARD ELECTRODE POTENTIALS
As discussed in the previous post, the potential of any electrode is the potential difference between it and the electrolyte surrounding the electrode.
However, this potential depends upon the nature of the metal, concentration of the metallic ions in solution and the temperature of the solution.

Hence, again, we have to define a standard.
When the ions are at unit activity and the temperature is $$25^oC$$ ($$298K$$), the potential difference is called a Standard Electrode Potential ($$E_o$$).

Now,
the potential of a single electrode cannot be determined, but the potential difference between two electrodes can be accurately measured.
By convention, the electrode potential of S.H.E has been assigned a value of zero Volts.

POSITIVE(+) AND NEGATIVE(-) POTENTIALS
$$\bullet$$ If, on combining an electrode $$A$$ with the S.H.E, a reduction process (gain of electrons) occurs at the electrode, the potential of the electrode is called as reduction potential.
It is given a "+" sign as reduction potential or a "-" sign as oxidation potential.

$$\bullet$$ On the other hand, if, on combining an electrode $$B$$ with the S.H.E, an oxidation process (loss of electrons) occurs at $$B$$, the electrode potential (half-cell potential) is called as the oxidation potential.
It is given a "+" sign as oxidation potential or a "-" sign as reduction potential.

Thus, in short,
at Standard conditions,
Oxidation Potential for any half cell $$=$$ $$-$$(Reduction Potential)
Reduction Potential for any half cell $$=$$ $$-$$(Oxidation Potential)

In the next post, we shall discuss, the experimentally determined Electrochemical Series, and how it is used to determine the EMF of any cell.

Read the next post here : Physical Chemistry - Electrochemistry - 3

Note by Anish Puthuraya
3 years, 1 month ago

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Why they use Hydrogen electrode as a standard? I thought gases is harder to handle than solid? · 3 years, 1 month ago

It is generally done to form a good standard basis. This kind of stuff is done a lot, especially on linear algebra and it makes it somewhat "elegant". So this is something that we kinda agreed upon. To make a reference electrode because as this note says, we can't determine the potential of a single electrode... And really, it just forms a sort of like a baseline originating historically. Like "building" electrochemistry from scratch. I guess, think of it like 360$$^\circ$$ is one circle, why 360? Because of something people agreed upon years before (Babylonians had base 60 and ~360 days per year). x'D Hopefully, that's satisfying. I probably might've even interpreted your question incorrectly, but anyways, that's all I can say. ^^ · 3 years, 1 month ago

Well said. · 3 years, 1 month ago

Well, Hydrogen is the first element, so I guess it is fair to choose it as a standard. I cant think of any other reason. If you don't choose Hydrogen as standard, what else would you choose? I dont know. · 3 years, 1 month ago

×


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Book section Open Access

# Definite Integration of Parametric Rational Functions: Applying a DITLU

### Dublin Core Export

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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:contributor>Kerber, M.</dc:contributor>
<dc:contributor>Kohlhase, M.</dc:contributor>
<dc:date>2001-01-01</dc:date>
<dc:description>In [2] we presented a Definite Integral Table Lookup (the DITLU) for parametric functions, including a minimal prototype implementation demonstrating its capabilities. In this paper we present a possible application of a DITLU, which would extend its utility for a modest investment of effort. The naive algorithm for indefinite integration of rational functions (see e.g. [12, �2.10]) can be implemented for parametric rational functions. This involves splitting the rational function integrand using partial fractions. The resulting integrands all fall within a limited class which may be covered in a DITLU by a very small number of table entries. Extensions of this idea to less naive integration algorithms, and the number of table entries required to implement them, are also considered. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down.</dc:description>
<dc:identifier>https://zenodo.org/record/810877</dc:identifier>
<dc:identifier>10.5281/zenodo.810877</dc:identifier>
<dc:identifier>oai:zenodo.org:810877</dc:identifier>
<dc:publisher>A. K. Peters</dc:publisher>
<dc:relation>doi:10.5281/zenodo.810876</dc:relation>
<dc:relation>url:https://zenodo.org/communities/opendepot</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:title>Definite Integration of Parametric Rational Functions: Applying a DITLU</dc:title>
<dc:type>info:eu-repo/semantics/bookPart</dc:type>
<dc:type>publication-section</dc:type>
</oai_dc:dc>

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text: I'm having a ros system consiting of different nodes. Each of these nodes has a calback-class that does all the calculations. I define multiple std::couts in the destructors of the classes so that I can get some statistics output of what happened during the execution. This was working fine so far, because I only had one such DTOR defined. But now I thought it might be a good idea to have such statistics for each of my nodes and therefor I added those DTOR to all callback-classes. Now it frequently happens that one DTOR outputs it's first couple of lines, then another DTOR outputs a few lines and then the first DTOR again. Is there a way of making sure, that the output of each DTOR will not be interupted by the output of other DTORs?