# Posts Tagged mass ratio

## Recent Postings from mass ratio

### Superoutburst of WZ Sge-type Dwarf Nova Below the Period Minimum: ASASSN-15po

We report on a superoutburst of a WZ Sge-type dwarf nova (DN), ASASSN-15po. The light curve showed the main superoutburst and multiple rebrightenings. In this outburst, we observed early superhumps and growing (stage A) superhumps with periods of 0.050454(2) and 0.051809(13) d, respectively. We estimated that the mass ratio of secondary to primary ($q$) is 0.0699(8) by using $P_{\rm orb}$ and a superhump period $P_{\rm SH}$ of stage A. ASASSN-15po [$P_{\rm orb} \sim$ 72.6 min] is the first DN with the orbital period between 67--76 min. Although the theoretical predicted period minimum $P_{\rm min}$ of hydrogen-rich cataclysmic variables (CVs) is about 65--70 min, the observational cut-off of the orbital period distribution at 80 min implies that the period minimum is about 82 min, and the value is widely accepted. We suggest the following four possibilities: the object is (1) a theoretical period minimum object (2) a binary with a evolved secondary (3) a binary with a metal-poor (Popullation II) seconday (4) a binary which was born with a brown-dwarf donor below the period minimum.

### A possible formation channel for blue hook stars in globular cluster - II. Effects of metallicity, mass ratio, tidal enhancement efficiency and helium abundance

Employing tidally enhanced stellar wind, we studied in binaries the effects of metallicity, mass ratio of primary to secondary, tidal enhancement efficiency and helium abundance on the formation of blue hook (BHk) stars in globular clusters (GCs). A total of 28 sets of binary models combined with different input parameters are studied. For each set of binary model, we presented a range of initial orbital periods that is needed to produce BHk stars in binaries. All the binary models could produce BHk stars within different range of initial orbital periods. We also compared our results with the observation in the Teff-logg diagram of GC NGC 2808 and {\omega} Cen. Most of the BHk stars in these two GCs locate well in the region predicted by our theoretical models, especially when C/N-enhanced model atmospheres are considered. We found that mass ratio of primary to secondary and tidal enhancement efficiency have little effects on the formation of BHk stars in binaries, while metallicity and helium abundance would play important roles, especially for helium abundance. Specifically, with helium abundance increasing in binary models, the space range of initial orbital periods needed to produce BHk stars becomes obviously wider, regardless of other input parameters adopted. Our results were discussed with recent observations and other theoretical models.

### RZ Leonis Minoris Bridging between ER Ursae Majoris-Type Dwarf Nova and Novalike System

We observed RZ LMi, which is renowned for the extremely (~19d) short supercycle and is a member of a small, unusual class of cataclysmic variables called ER UMa-type dwarf novae, in 2013 and 2016. In 2016, the supercycles of this object substantially lengthened in comparison to the previous measurements to 35, 32, 60d for three consecutive superoutbursts. We consider that the object virtually experienced a transition to the novalike state (permanent superhumper). This observed behavior extremely well reproduced the prediction of the thermal-tidal instability model. We detected a precursor in the 2016 superoutburst and detected growing (stage A) superhumps with a mean period of 0.0602(1)d in 2016 and in 2013. Combined with the period of superhumps immediately after the superoutburst, the mass ratio is not as small as in WZ Sge-type dwarf novae, having orbital periods similar to RZ LMi. By using least absolute shrinkage and selection operator (Lasso) two-dimensional power spectra, we detected possible negative superhumps with a period of 0.05710(1)d. We estimated the orbital period of 0.05792d, which suggests a mass ratio of 0.105(5). This relatively large mass ratio is even above ordinary SU UMa-type dwarf novae, and it is also possible that the exceptionally high mass-transfer rate in RZ LMi may be a result of a stripped core evolved secondary which are evolving toward an AM CVn-type object.

### WR 148: Identifying the companion of an extreme runaway massive binary

WR 148 (HD 197406) is an extreme runaway system considered to be a potential candidate for a short-period (4.3173 d) rare WR + compact object binary. Provided with new high resolution, high signal-to-noise spectra from the Keck observatory, we determine the orbital parameters for both the primary WR and the secondary, yielding respective projected orbital velocity amplitudes of $88.1\pm3.8$ km s$^{-1}$ and $79.2\pm3.1$ km s$^{-1}$ and implying a mass ratio of $1.1\pm0.1$. We then apply the shift-and-add technique to disentangle the spectra and obtain spectra compatible with a WN7ha and an O4-6 star. Considering an orbital inclination of $\sim67^\circ$, derived from previous polarimetry observations, the system's total mass would be a mere 2-3 M$_{\odot}$ , an unprecedented result for a putative massive binary system. However, a system comprising a 37 M$_{\odot}$ secondary (typical mass of an O5V star) and a 33 M$_{\odot}$ primary (given the mass ratio) would infer an inclination of $\sim18^\circ$. We therefore reconsider the previous methods of deriving the orbital inclination based on time-dependent polarimetry and photometry. While the polarimetric results are inconclusive requiring better data, the photometric results favour low inclinations. Finally, we compute WR 148's space velocity and retrace the runaway's trajectory back to the Galactic plane (GP). With an ejection velocity of $198\pm27$ km s$^{-1}$ and a travel time of $4.7\pm0.8$ Myr to reach its current location, WR 148 was most likely ejected via dynamical interactions in a young cluster.

### Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

### Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations [Cross-Listing]

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

### Deriving analytic solutions for compact binary inspirals without recourse to adiabatic approximations [Cross-Listing]

We utilize the dynamical renormalization group formalism to calculate the real space trajectory of a compact binary inspiral for long times via a systematic resummation of secularly growing terms. This method generates closed form solutions without orbit averaging, and the accuracy can be systematically improved. The expansion parameter is $v^5 \nu \Omega(t-t_0)$ where $t_0$ is the initial time, $t$ is the time elapsed, and $\Omega$ and $v$ are the angular orbital frequency and initial speed, respectively, and $\nu$ is the binary's symmetric mass ratio. We demonstrate how to apply the renormalization group method to resum solutions beyond leading order in two ways. First, we calculate the second order corrections of the leading radiation reaction force, which involves highly non-trivial checks of the formalism (i.e. its renormalizability). Second, we show how to systematically include post-Newtonian corrections to the radiation reaction force. By avoiding orbit averaging we gain predictive power and eliminate ambiguities in the initial conditions. Finally, we discuss how this methodology can be used to find analytic solutions to the spin equations of motion that are valid over long times.

### Relic abundance of MeV millicharged particles

The relic abundance of light millicharged particles (MCP) with the electric charge $e' = 5\cdot 10^{-5} e$ and with the mass slightly below or above the electron mass is calculated. The abundance depends on the mass ratio $\eta=m_X/m_e$ and for $\eta<1$ can be high enough to allow MCP to be the cosmological dark matter or to make a noticeable contribution to it. On the other hand, for $\eta \gtrsim 1$ the cosmological energy density of MCPs can be quite low, $\Omega_X h_0^2 \simeq 0.02$ for scalar MCPs, and $\Omega_X h_0^2 \simeq 0.001$ for spin 1/2 fermions. But even the lowest value of $\Omega_X h_0^2$ is in tension with several existing limits on the MCP abundances and parameters. However, these limits have been derived under some natural or reasonable assumptions on the properties of MCPs. If these assumptions are relaxed, a patch in the mass-charge plot of MCPs may appear, permitting them to be dark matter particles.

### The First Circumbinary Planet Found by Microlensing: OGLE-2007-BLG-349L(AB)c

We present the analysis of the first circumbinary planet microlensing event, OGLE-2007-BLG-349. This event has a strong planetary signal that is best fit with a mass ratio of $q \approx 3.4\times 10^{-4}$, but there is an additional signal due to an additional lens mass, either another planet or another star. We find acceptable light curve fits with two classes of models: 2-planet models (with a single host star) and circumbinary planet models. The light curve also reveals a significant microlensing parallax effect, which constraints the mass of the lens system to be $M_L \approx 0.7 M_\odot$. Hubble Space Telescope images resolve the lens and source stars from their neighbors, and indicate excess flux due to the star(s) in the lens system. This is consistent with the predicted flux from the circumbinary models, where the lens mass is shared between two stars, but there is not enough flux to be consistent with the 2-planet, 1-star models. So, only the circumbinary models are consistent with the HST data. They indicate a planet of mass $m_c = 80\pm 13 M_\oplus$, orbiting a pair of M-dwarfs with masses of $M_A = 0.41\pm 0.07 M_\odot$ and $M_B = 0.30\pm 0.07 M_\odot$, which makes this the lowest mass circumbinary planet system known. The ratio of the planet:center-of-mass separation to the separations of the two stars is ~40, so unlike most of the circumbinary planets found by Kepler, the planet does not orbit near the stability limit.

### Rotating systems, universal features in dragging and anti-dragging effects, and bounds onto angular momentum

We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular momentum accumulates almost exclusively within toroids. It appears that various types of dragging (anti-dragging) effects are positively correlated with the ratio $M_\mathrm{D}/m$ ($M_\mathrm{D}$ is the mass of a toroid and $m$ is the mass of the black hole) - moreover, their maxima are proportional to $M_\mathrm{D}/m$. The horizontal sizes of investigated toroids range from c. 50 to c. 450 of Schwarzschild radii $R_\mathrm{S}$ of the central black hole; their mass $M_\mathrm{D} \in (10^{-4}m, 40m)$ and the radial size of the system is c. 500 $R_\mathrm{S}$. We found that the relative strength of various dragging (anti-dragging) effects does not change with the mass ratio, but it depends on the size of toroids. Several isoperimetric inequalities involving angular momentum are shown to hold true.

### Why are pulsar planets rare?

Pulsar timing observations have revealed planets around only a few pulsars. We suggest that the rarity of these planets is due mainly to two effects. First, we show that the most likely formation mechanism requires the destruction of a companion star. Only pulsars with a suitable companion (with an extreme mass ratio) are able to form planets. Second, while a dead zone (a region of low turbulence) in the disk is generally thought to be essential for planet formation, it is most probably rare in disks around pulsars because of the irradiation from the pulsar. The irradiation strongly heats the inner parts of the disk pushing the inner boundary of the dead zone out. We suggest that the rarity of pulsar planets can be explained by the low probability for these two requirements - a very low-mass companion and a dead zone - to be satisfied.

### $\gamma$ Doradus Pulsations in the Eclipsing Binary Star KIC 6048106

We present the ${\it Kepler}$ photometry of KIC 6048106 exhibiting O'Connell effect and multiperiodic pulsations. Including a starspot on either of the components, light-curve synthesis indicates that this system is a semi-detached Algol with a mass ratio of 0.211, an orbital inclination of 73.9 deg, and a large temperature difference of 2,534 K. To examine in detail both spot variations and pulsations, we separately analyzed the {\it Kepler} time-series data at the interval of an orbital period by an iterative way. The results reveal that the variable asymmetries of the light maxima can be interpreted as the changes of a magnetic cool spot on the secondary component with time. Multiple frequency analyses were performed in the outside-eclipse light residuals after removal of the binarity effects from the observed {\it Kepler} data. We detected 30 frequencies with signal to noise amplitude ratios larger than 4.0, of which six ($f_2$--$f_6$ and $f_{10}$) can be identified as high-order (17 $\le n \le$ 25) low-degree ($\ell$ = 2) gravity-mode pulsations that were stable during the observing run of 200 d. In contrast, the other frequencies may be harmonic and combination terms. For the six frequencies, the pulsation periods and pulsation constants are in the ranges of 0.352$-$0.506 d and 0.232$-$0.333 d, respectively. These values and the position on the HR diagram demonstrate that the primary star is a $\gamma$ Dor variable. The evolutionary status and the pulsation nature of KIC 6048106 are discussed.

### The Post-Starburst Evolution of Tidal Disruption Event Host Galaxies

Tidal Disruption Events (TDEs) favor quiescent host galaxies with strong Balmer absorption lines. Here we study eight hosts of optical/UV-detected TDEs to determine the duration of the recent star formation episode, the time elapsed since it ended, and the fraction of stellar mass produced. Most hosts (6/8) have had short recent starbursts of <200 Myr as opposed to a slower decline in star formation. TDE host galaxies span a wide range of post-starburst ages (60-600 Myr for 6/8 galaxies), indicating that TDEs are not limited to a specific time in their hosts' post-starburst evolution. If the disrupted star was a main sequence star that formed in the burst or before, the post-burst ages provide an independent constraint on its likely mass, excluding O, B and the most massive A stars. If the starburst arose from a galaxy merger, the time elapsed since the starburst began constrains the coalescence timescale and thus limits the merger mass ratio to more equal than 12:1 in most (7/8) TDE hosts. This uncommon ratio, if it also reflects that of the central SMBH binary, disfavors the scenario in which the TDE rate is boosted by the binary but is insensitive to its mass ratio. The fraction of stellar mass created in the burst is 0.5 - 10% for most (7/8) of the TDE hosts, not large enough to explain the increased TDE rate. If more stars are required to boost the TDE rate, the stellar concentration in the core must be more important. TDE host galaxies have stellar masses 10^9.4 - 10^10.3 M$_\odot$, consistent with the SDSS volume-corrected comparison sample and implying central black hole masses of 10^5.5 - 10^7.5 M$_\odot$. Subtracting the absorption line spectra, we uncover hidden emission lines; at least 5 of 8 hosts have ionization sources inconsistent with star formation. These ionization sources may be related to circumnuclear gas, merger shocks, or post-AGB stars.

### A numerical investigation of wind accretion in persistent Supergiant X-ray Binaries I - Structure of the flow at the orbital scale

Classical Supergiant X-ray Binaries host a neutron star orbiting a supergiant OB star and display persistent X-ray luminosities of 10$^{35}$ to 10$^{37}$ erg/s. The stellar wind from the massive companion is believed to be the main source of matter accreted by the compact object. With this first paper, we introduce a ballistic model to characterize the structure of the wind at the orbital scale as it accelerates, from the stellar surface to the vicinity of the accretor. Thanks to the parametrization we retained and the numerical pipeline we designed, we can investigate the supersonic flow and the subsequent observables as a function of a reduced set of characteristic numbers and scales. We show that the shape of the permanent flow is entirely determined by the mass ratio, the filling factor, the Eddington factor and the $\alpha$-force multiplier which drives the stellar wind acceleration. Provided scales such as the orbital period are known, we can trace back the observables to evaluate the mass accretion rates, the accretion mechanism, the shearing of the inflow and the stellar parameters. We confront our model to three persistent Supergiant X-ray Binaries (Vela X-1, IGR J18027-2016, XTE J1855-026) and discuss the likelihood of wind-formed accretion discs around the accretors in each case, further investigated in a following paper.

### Fractal basins of attraction in the planar circular restricted three-body problem with oblateness and radiation pressure

In this paper we use the planar circular restricted three-body problem where one of the primary bodies is an oblate spheroid or an emitter of radiation in order to determine the basins of attraction associated with the equilibrium points. The evolution of the position of the five Lagrange points is monitored when the values of the mass ratio $\mu$, the oblateness coefficient $A_1$, and the radiation pressure factor $q$ vary in predefined intervals. The regions on the configuration $(x,y)$ plane occupied by the basins of attraction are revealed using the multivariate version of the Newton-Raphson method. The correlations between the basins of convergence of the equilibrium points and the corresponding number of iterations needed in order to obtain the desired accuracy are also illustrated. We conduct a thorough and systematic numerical investigation demonstrating how the dynamical quantities $\mu$, $A_1$, and $q$ influence the basins of attractions. Our results suggest that the mass ratio and the radiation pressure factor are the most influential parameters, while on the other hand the structure of the basins of convergence are much less affected by the oblateness coefficient.

### Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio [Replacement]

We consider spin-orbit ("geodetic") precession for a compact binary in strong-field gravity. Specifically, we compute $\psi$, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body orbiting a non-rotating black hole. We show that $\psi$ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for $\psi$ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for $\psi$ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the Effective One-Body model of the gravitational two-body problem. We conclude that $\psi$ complements the Detweiler redshift $z$ as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.

### Spin-orbit precession for eccentric black hole binaries at first order in the mass ratio

We consider spin-orbit ("geodetic") precession for a compact binary in strong-field gravity. Specifically, we compute $\psi$, the ratio of the accumulated spin-precession and orbital angles over one radial period, for a spinning compact body orbiting a non-rotating black hole. We show that $\psi$ can be computed for eccentric orbits in both the gravitational self-force and post-Newtonian frameworks, and that the results appear to be consistent. We present a post-Newtonian expansion for $\psi$ at next-to-next-to-leading order, and a Lorenz-gauge gravitational self-force calculation for $\psi$ at first order in the mass ratio. The latter provides new numerical data in the strong-field regime to inform the Effective One-Body model of the gravitational two-body problem. We conclude that $\psi$ complements the Detweiler redshift $z$ as a key invariant quantity characterizing eccentric orbits in the gravitational two-body problem.

### Improved next-to-leading order tidal heating and torquing of a Kerr black hole

We calculate the energy and angular momentum fluxes across the event horizon of a tidally deformed, rapidly rotating black hole to next-to-leading order in the curvature of the external spacetime. These are expressed in terms of tidal quadrupole moments and their time derivatives, which provide a characterization of a generic tidal environment. As an application of our results, we provide an expression for the energy and angular-momentum fluxes across the horizon when the black hole is a member of a binary system on a slowly-moving, quasi-circular orbit. Our expressions are accurate to 1.5 post-Newtonian order beyond the leading-order fluxes, but they are valid for arbitrary mass ratios. We compare our results to those previously obtained in the case of an extreme mass ratio binary, and find that they do not agree at the 1.5 post-Newtonian order. We investigate a number of possible sources for this discrepancy, but are ultimately unable to resolve it.

### Modeling Mergers of Known Galactic Systems of Binary Neutron Stars [Cross-Listing]

We present a study of the merger of six different known galactic systems of binary neutron stars (BNS) of unequal mass with a mass ratio between $0.75$ and $0.99$. Specifically, these systems are J1756-2251, J0737-3039A, J1906+0746, B1534+12, J0453+1559 and B1913+16. We follow the dynamics of the merger from the late stage of the inspiral process up to $\sim$ 20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH), using a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLy with a thermal component. For the most extreme of these systems ($q=0.75$, J0453+1559), we also investigate the effects of different EOSs: APR4, H4, and MS1. Our numerical simulations are performed using only publicly available open source code such as, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. We show results on the gravitational wave signals, spectrogram and frequencies of the BNS after the merger and the BH properties in the two cases in which the system collapse within the simulated time.

### Modeling Mergers of Known Galactic Systems of Binary Neutron Stars

We present a study of the merger of six different known galactic systems of binary neutron stars (BNS) of unequal mass with a mass ratio between $0.75$ and $0.99$. Specifically, these systems are J1756-2251, J0737-3039A, J1906+0746, B1534+12, J0453+1559 and B1913+16. We follow the dynamics of the merger from the late stage of the inspiral process up to $\sim$ 20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH), using a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLy with a thermal component. For the most extreme of these systems ($q=0.75$, J0453+1559), we also investigate the effects of different EOSs: APR4, H4, and MS1. Our numerical simulations are performed using only publicly available open source code such as, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. We show results on the gravitational wave signals, spectrogram and frequencies of the BNS after the merger and the BH properties in the two cases in which the system collapse within the simulated time.

### Modeling Mergers of Known Galactic Systems of Binary Neutron Stars [Cross-Listing]

We present a study of the merger of six different known galactic systems of binary neutron stars (BNS) of unequal mass with a mass ratio between $0.75$ and $0.99$. Specifically, these systems are J1756-2251, J0737-3039A, J1906+0746, B1534+12, J0453+1559 and B1913+16. We follow the dynamics of the merger from the late stage of the inspiral process up to $\sim$ 20 ms after the system has merged, either to form a hyper-massive neutron star (NS) or a rotating black hole (BH), using a semi-realistic equation of state (EOS), namely the seven-segment piece-wise polytropic SLy with a thermal component. For the most extreme of these systems ($q=0.75$, J0453+1559), we also investigate the effects of different EOSs: APR4, H4, and MS1. Our numerical simulations are performed using only publicly available open source code such as, the Einstein Toolkit code deployed for the dynamical evolution and the LORENE code for the generation of the initial models. We show results on the gravitational wave signals, spectrogram and frequencies of the BNS after the merger and the BH properties in the two cases in which the system collapse within the simulated time.

### Parameter estimates in binary black hole collisions using neural networks [Cross-Listing]

We present an algorithm based on artificial neural networks (ANNs), that estimates the mass ratio in a binary black hole collision out of given Gravitational Wave (GW) strains. In this analysis, the ANN is trained with a sample of GW signals generated with numerical simulations. The effectiveness of the algorithm is evaluated with GWs generated also with simulations for given mass ratios unknown to the ANN. We measure the accuracy of the algorithm in the interpolation and extrapolation regimes. We present the results for noise free signals and signals contaminated with Gaussian noise, in order to foresee the dependence of the method accuracy in terms of the signal to noise ratio.

### Parameter estimates in binary black hole collisions using neural networks

We present an algorithm based on artificial neural networks (ANNs), that estimates the mass ratio in a binary black hole collision out of given Gravitational Wave (GW) strains. In this analysis, the ANN is trained with a sample of GW signals generated with numerical simulations. The effectiveness of the algorithm is evaluated with GWs generated also with simulations for given mass ratios unknown to the ANN. We measure the accuracy of the algorithm in the interpolation and extrapolation regimes. We present the results for noise free signals and signals contaminated with Gaussian noise, in order to foresee the dependence of the method accuracy in terms of the signal to noise ratio.

### Whimper of a Bang: Documenting the Final Days of the Nearby Type Ia Supernova 2011fe

Using the Hubble Space Telescope (HST) and the Large Binocular Telescope, we followed the evolution of the Type Ia supernova (SN Ia) 2011fe for an unprecedented 1622 days past B-band maximum light and over a factor of 5 million in flux. At 1622 days, the 4000 - 17000 \AA{} quasi-bolometric luminosity is just ($710 \pm 30$ $L_{\odot}$). By measuring the late-time quasi-bolometric light curve we present the first confident detection of 57Co decay in a SN Ia light curve and estimate a mass ratio of log(57Co/56Co) = -1.62+0.08. We do not have a clean detection of 55Fe, but find a limit of 55Fe/57Co $< 0.3$ with 90$\%$ confidence. These abundance ratios provide unique constraints on the progenitor system because the central density of the exploding white dwarf(s) dictates these nucleosynthetic yields. The observed ratios strongly prefer the lower central densities of double-degenerate models (55Fe/57Co = 0.27) over the higher central densities of near Chandrasekhar-mass single-degenerate models (55Fe/57Co = 0.68). We will continue to observe SN 2011fe for another $\sim$900 days with HST and possibly beyond.

### The photometric investigation of the newly discovered W UMa type binary system GSC 03122-02426

The $B$ $V$ $R_c$ $I_c$ bands light curves of the newly discovered binary system \astrobj{GSC 03122-02426} are obtained and analyzed using the Wilson-Devinney (W-D) code. The solutions suggest that the mass ratio of the binary system is $q = 2.70$ and the less massive component is $422K$ hotter than the more massive one. We conclude that \astrobj{GSC 03122-02426} is a W-subtype shallow contact (with a contact degree of $f = 15.3\,\%$) binary system. It may be a newly formed contact binary system which is just under geometrical contact and will evolve to be a thermal contact binary system. The high orbital inclination ($i = 81.6^{\circ}$) implies that \astrobj{GSC 03122-02426} is a total eclipsing binary system and the photometric parameters obtained by us are quite reliable. We also estimate the absolute physical parameters of the two components in \astrobj{GSC 03122-02426}, which will provide fundamental information for the research of contact binary systems. The formation and evolutionary scenario of \astrobj{GSC 03122-02426} is discussed.

### The first photometric analysis of the W-subtype contact binary UCAC4 436-062932 with O'Connell effect

Two sets of light curves in $V$ $R_c$ $I_c$ bands for a newly discovered binary system UCAC4 436-062932 are obtained and analyzed using the Wilson-Devinney (W-D) code. The two sets of light curves get almost consistent results. The determined mass ratio is about $q = 2.7$ and the less massive component is nearly $250K$ hotter than the more massive one. The solutions conclude that UCAC4 436-062932 is a W-subtype shallow contact (with a contact degree of $f = 20\,\%$) binary system. Since the O'Connell effect appears on one set of the light curves, theories proposed to explain the effect are discussed. We assume that spot model may be the more plausible one to the O'Connell effect appeared on the asymmetric light curves of the binary system UCAC4 436-062932. Therefore, we add a cool spot on the surface of the more massive star (component with lower effective temperature) and get a quite approving results for the light curve fitting. It will provide evidence to support the spot model in the explanatory mechanism of O'Connell effect.

### A Solar-type Stellar Companion to a Deep Contact Binary in a Quadruple System

The four-color ($B$ $V$ $R_c$ $I_c$) light curves of V776 Cas are presented and analyzed using the Wilson-Devinney (W-D) method. It is discovered that V776 Cas is an early F-type (F2V) overcontact binary with a very high contact degree ($f=64.6\,\%$) and an extremely low mass ratio ($q=0.130$), which indicate that it is at the final evolutionary stage of cool short-period binaries. The mass of the primary and secondary stars are calculated to be $M_1 = 1.55(\pm0.04)M_\odot$, $M_2 = 0.20(\pm0.01)M_\odot$. V776 Cas is supposed to be formed from an initially detached binary system via the loss of angular momentum due to the magnetic wind. The initial mass of the present primary and secondary components are calculated to be $M_{1i} = 0.86(\pm0.10)M_\odot$ and $M_{2i} = 2.13(\pm0.04)M_\odot$. The observed-calculated ($O$-$C$) curve exhibits a cyclic period variation, which is due to the light-travel time effect (LTTE) caused by the presence of a third component with a period of 23.7 years. The mass of the third component is estimated to be $M_3 = 1.04(\pm0.03)M_\odot$ and the orbital inclination of the third component is calculated to be $i' = 33.1^{\circ}$. The distance of the binary system to the mass center of the triple system is calculated to be $a'_{12} = 3.45AU$. The presence of the close-in tertiary component may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system.

### Photometric and period investigation of the late F-type overcontact binary II UMa

II UMa is a late F-type (F5) contact binary with a close-in tertiary and a distant visual companion. According to the four-color ($B$ $V$ $R_c$ $I_c$) light curves' solutions of II UMa, it is a high fill-out (f=$86.6\,\%$) and low mass ratio ($q = 0.172$) contact binary system, which indicate that it is at the late evolutionary stage of late-type tidal-locked binary stars. The mass of the primary star and secondary one are calculated to be $M_1 = 1.99M_\odot$, $M_2 = 0.34M_\odot$. The primary star has evolved from ZAMS, but it is still before TAMS, and the secondary star is even more evolved. Considering the mass ratio ($M_3/M_1 = 0.67$) obtained by spectroscopic observations, the mass of the close-in tertiary is estimated to be $M_3 = 1.34M_\odot$. The period variations of the binary system is investigated for the first time. According to the observed-calculated ($O$-$C$) curve analysis, a continuous period increase at a rate of $dP/dt=4.88\times{10^{-7}}day\cdot year^{-1}$ is determined. It may be just a part of a cyclic period change, or the combinational period change of a parabolic variation and a cyclic one. More times of minimum light are needed to confirm this. The presence of the tertiary component may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system during the pre-contact stage.

### Gravitational-wave tail effects to quartic non-linear order

Gravitational-wave tails are due to the backscattering of linear waves onto the space-time curvature generated by the total mass of the matter source. The dominant tails correspond to quadratic non-linear interactions and arise at the one-and-a-half post-Newtonian (1.5PN) order in the gravitational waveform. Also known are the "tails-of-tails", which are cubically non-linear effects appearing at the 3PN order in the waveform. Here we derive still higher non-linear tail effects, namely those associated with quartic non-linear interactions or "tails-of-tails-of-tails", which are shown to arise at the 4.5PN order. As an application we obtain at that order the complete coefficient in the total gravitational-wave energy flux of compact binary systems moving on circular orbits. Our result perfectly agrees with black-hole perturbation calculations in the limit of extreme mass ratio of the two compact objects.

### Evolution of binary seeds in collapsing protostellar gas clouds

We perform three dimensional smoothed particle hydrodynamics (SPH) simulations of gas accretion onto the seeds of binary stars to investigate their short-term evolution. Our simulation setup is more realistic compared to the previous works by taking into account of dynamically evolving envelope with non-uniform distribution of gas density and angular momentum of accreting flow. Our initial condition includes a seed binary and a surrounding gas envelope, modelling the phase of core collapse of gas cloud when the fragmentation has already occurred. We assume that the seed binary has no eccentricity and no growth by gas accretion. The envelope is assumed to be an isothermal gas with no self-gravity. We run multiple simulations with different values of initial mass ratio $q_0$ (the ratio of secondary over primary mass) and gas temperature, and find a critical value of $q_{\rm c} = 0.25$ which distinguishes the later evolution of mass ratio $q$ as a function of time. If $q_0 \ga q_{\rm c}$, the secondary seed grows faster and $q$ increases monotonically towards unity. If $q_0 \la q_{\rm c}$, on the other hand, the primary seed grows faster and $q$ is lower than $q_0$ at the end of the simulation. Based on our numerical results, we analytically calculate the long-term evolution of the seed binary including the growth of binary by gas accretion. We find that the seed binary with $q_0 \ga q_{\rm c}$ evolves towards an equal-mass binary star, and that with $q_0 \la q_{\rm c}$ evolves to a binary with an extreme value of $q$. Binary separation is a monotonically increasing function of time for any $q_0$, suggesting that the binary growth by accretion does not lead to the formation of close binaries.

### OGLE-2016-BLG-0596Lb: High-Mass Planet From High-Magnification Pure-Survey Microlensing Event

We report the discovery of a high mass-ratio planet $q=0.012$, i.e., 13 times higher than the Jupiter/Sun ratio. The host mass is not presently measured but can be determined or strongly constrained from adaptive optics imaging. The planet was discovered in a small archival study of high-magnification events in pure-survey microlensing data, which was unbiased by the presence of anomalies. The fact that it was previously unnoticed may indicate that more such planets lie in archival data and could be discovered by similar systematic study. In order to understand the transition from predominantly survey+followup to predominately survey-only planet detections, we conduct the first analysis of these detections in the observational $(s,q)$ plane. Here $s$ is projected separation in units of the Einstein radius. We find some evidence that survey+followup is relatively more sensitive to planets near the Einstein ring, but that there is no statistical difference in sensitivity by mass ratio.

### Binary Neutron Star Mergers and Short Gamma-Ray Bursts: Effects of Magnetic Field Orientation, Equation of State, and Mass Ratio

We present fully GRMHD simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we found the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to BH. Such larger fields make it possible, for at least one of our models, to resolve the MRI and hence further amplify the magnetic field. However, by the end of our simulations, we do not observe a magnetically dominated funnel and hence neither a relativistic outflow. With respect to the recent simulations of Ruiz et al 2016, we evolve models with lower and more realistic initial magnetic field strengths and, because of computational reasons, we do not evolve the accretion disk for the long timescales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure, we expect that the results found in Ruiz et al 2016, where they only considered an equal-mass system with an ideal fluid EOS, should be general and, at least from a qualitative point of view, independent from mass-ratio, magnetic field orientation, and EOS.

### Binary Neutron Star Mergers and Short Gamma-Ray Bursts: Effects of Magnetic Field Orientation, Equation of State, and Mass Ratio [Cross-Listing]

We present fully GRMHD simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we found the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to BH. Such larger fields make it possible, for at least one of our models, to resolve the MRI and hence further amplify the magnetic field. However, by the end of our simulations, we do not observe a magnetically dominated funnel and hence neither a relativistic outflow. With respect to the recent simulations of Ruiz et al 2016, we evolve models with lower and more realistic initial magnetic field strengths and, because of computational reasons, we do not evolve the accretion disk for the long timescales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure, we expect that the results found in Ruiz et al 2016, where they only considered an equal-mass system with an ideal fluid EOS, should be general and, at least from a qualitative point of view, independent from mass-ratio, magnetic field orientation, and EOS.

### Photometric and H-alpha studies of two extreme mass-ratio short period contact binaries in the direction of open cluster Praesepe

We present the high precession photometric studies in V band and spectroscopic studies centered around H-alpha line for two extreme mass-ratio short period contact binaries ASAS J082243+1927.0 (V1) and ASAS J085710+1856.8 (V2). The variables in study are in the direction of open cluster Praesepe. From the light curve analysis V1 was found to be a low mass-ratio over-contact binary of A-type, with a mass ratio q 0.121 and fill-out factor f 72%, and V2 was found to be a low mass contact binary of W-type, with a mass-ratio q 1.29 and fill-out factor f 11% (marginal contact). The study of H-alpha absorption line profile of both the variables shows variation in equivalent widths (EWs) with orbital phases. The mean EWs of the H-alpha line were obtained as 1.6+or-0.13 A and 1.18+or-0.12 A for V1 and V2 respectively. The variation of H-alpha absorption with respect to phase is explained to be due to chromospheric activity in V1, as evident from the O Connell effect and that due to chromospheric flares, winds or photospheric source in V2. The parameters for both the binaries are also studied with respect to the large sample of well-studied contact binaries and possible mechanisms for merger in contact binaries of both low and high mass ratios emphasized.

### Post-merger analytic templates for GW150914

Following the new analytic description of the postmerger (ringdown) waveform of coalescing, nonprecessing, spinning, black hole binaries (BBHs) introduced in Phys.~Rev.~D~90, 024054 (2014), we propose an analytic, closed form, time-domain, representation of the $\ell=m=2$ gravitational radiation mode emitted after merger. This expression is given as a function of the masses and dimensionless spins $(m_{1,2},\chi_{1,2})$ of the two inspiralling objects, as well as of the mass $M_{\rm BH}$ and (complex) frequency $\sigma_{1}$ of the fundamental quasi-normal mode of the final black hole. It is obtained by first fitting the postmerger waveform part of several numerical relativity simulations of the Simulating eXtreme Spacetimes (SXS) catalog and then suitably interpolating over (symmetric) mass ratio and spins. It is demonstrated that this analytic expression reproduces rather accurately the post-merger waveform of other SXS datasets not used to build it and, notably, the dataset SXS:BBH:0305, corresponding to a BBH with mass ratio $m_{1}/m_{2}=1.221$, $\chi_{1}=+0.33$ and $\chi_{2}=-0.4399$, which gives the closest match to the observed signal of GW150914. It would be interesting to use the postmerger analytic waveform template introduced here to perform a new measure of the frequency and damping time of the fundamental quasi-normal mode (and possibly also of individual masses and spins) of GW150914 that exploits the complete post-merger waveform signal and that is not restricted to only the late-time ringdown tail. In addition, the same analytic template could also be used to measure the damping time of the second quasi-normal mode, helping then to test the general-relativistic no-hair theorem.

### Simulating the dust content of galaxies: successes and failures

We present full volume cosmological simulations using the moving-mesh code AREPO to study the coevolution of dust and galaxies. We extend the dust model in AREPO to include thermal sputtering of grains and investigate the evolution of the dust mass function, the cosmic distribution of dust beyond the interstellar medium, and the dependence of dust-to-stellar mass ratio on galactic properties. The simulated dust mass function is well-described by a Schechter fit and lies closest to observations at $z = 0$. The radial scaling of projected dust surface density out to distances of $10 \, \text{Mpc}$ around galaxies with magnitudes $17 < i < 21$ is similar to that seen in Sloan Digital Sky Survey data. At $z = 0$, the predicted dust density of $\Omega_\text{dust} \approx 1.9 \times 10^{-6}$ lies in the range of $\Omega_\text{dust}$ values seen in low-redshift observations. We find that dust-to-stellar mass ratio anti-correlates with stellar mass for galaxies living along the star formation main sequence. Moreover, we estimate the $850 \, \mu\text{m}$ and $1.1 \, \text{mm}$ number density functions for simulated galaxies at $z = 1$ and analyse the relation between dust-to-stellar flux and mass ratios at $z = 0$. At high redshift, our model fails to produce enough dust-rich galaxies, and this tension is not alleviated by adopting a top-heavy initial mass function. We do not capture a decline in $\Omega_\text{dust}$ from $z = 2$ to $z = 0$, which suggests that dust production mechanisms more strongly dependent on star formation may help to produce the observed number of dusty galaxies near the peak of cosmic star formation.

### Be discs in binary systems I. Coplanar orbits

Be stars are surrounded by outflowing circumstellar matter structured in the form of decretion discs. They are often members of binary systems, where it is expected that the decretion disc interacts both radiatively and gravitationally with the companion. In this work we study how various orbital (period, mass ratio, eccentricity) and disc (viscosity) parameters affect the disc structure in coplanar systems. We simulate such binaries with the use of a smoothed particle hydrodynamics code. The main effects of the secondary on the disc are its truncation and the accumulation of material inwards of truncation. In circular or nearly circular prograde orbits, the disc maintains a rotating, constant in shape, configuration, which is locked to the orbital phase. The disc is smaller in size, more elongated and more massive for low viscosity parameter, small orbital separation and/or high mass ratio. Highly eccentric orbits are more complex, with the disc structure and total mass strongly dependent on the orbital phase. We also studied the effects of binarity in the disc continuum emission. Since the infrared and radio SED are sensitive to the disc size and density slope, the truncation and matter accumulation result in considerable modifications in the emergent spectrum. The decretion disc in circular binaries remains constant in shape and phase-locked. Eccentric binaries exhibit strong dependence on the distance to the secondary. We conclude that binarity can serve as an explanation for the variability exhibited in observations of Be stars, and that our model can be used to detect invisible companions.

### Be discs in binary systems I. Coplanar orbits [Replacement]

Be stars are surrounded by outflowing circumstellar matter structured in the form of decretion discs. They are often members of binary systems, where it is expected that the decretion disc interacts both radiatively and gravitationally with the companion. In this work we study how various orbital (period, mass ratio and eccentricity) and disc (viscosity) parameters affect the disc structure in coplanar systems. We simulate such binaries with the use of a smoothed particle hydrodynamics code. The main effects of the secondary on the disc are its truncation and the accumulation of material inwards of truncation. We find two cases with respect to the effects of eccentricity: (i) In circular or nearly circular prograde orbits, the disc maintains a rotating, constant in shape, configuration, which is locked to the orbital phase. The disc is smaller in size, more elongated and more massive for low viscosity parameter, small orbital separation and/or high mass ratio. (ii) Highly eccentric orbits are more complex, with the disc structure and total mass strongly dependent on the orbital phase and the distance to the secondary. We also study the effects of binarity in the disc continuum emission. Since the infrared and radio SED are sensitive to the disc size and density slope, the truncation and matter accumulation result in considerable modifications in the emergent spectrum. We conclude that binarity can serve as an explanation for the variability exhibited in observations of Be stars, and that our model can be used to detect invisible companions.

### Matching asteroid population characteristics with a model constructed from the YORP-induced rotational fission hypothesis

From the results of a comprehensive asteroid population evolution model, we conclude that the YORP-induced rotational fission hypothesis can be consistent with the observed population statistics of small asteroids in the main belt including binaries and contact binaries. The foundation of this model is the asteroid rotation model of Marzari et al. (2011), which incorporates both the YORP effect and collisional evolution. This work adds to that model the rotational fission hypothesis and the binary evolution model of Jacobson & Scheeres (2011). The asteroid population evolution model is highly constrained by these and other previous works, and therefore it has only two significant free parameters: the ratio of low to high mass ratio binaries formed after rotational fission events and the mean strength of the binary YORP (BYORP) effect. We successfully reproduce characteristic statistics of the small asteroid population: the binary fraction, the fast binary fraction, steady-state mass ratio fraction and the contact binary fraction. We find that in order for the model to best match observations, rotational fission produces high mass ratio ($> 0.2$) binary components with four to eight times the frequency as low mass ratio ($< 0.2$) components, where the mass ratio is the mass of the secondary component divided by the mass of the primary component. This is consistent with post-rotational fission binary system mass ratio being drawn from either a flat or a positive and shallow distribution, since the high mass ratio bin is four times the size of the low mass ratio bin; this is in contrast to the observed steady-state binary mass ratio, which has a negative and steep distribution. This can be understood in the context of the BYORP-tidal equilibrium hypothesis, which predicts that low mass ratio binaries survive for a significantly longer period of time than high mass ratio systems.

### Superoutburst of CR Bootis: Estimation of Mass Ratio of a typical AM CVn star by Stage A Superhumps

We report on two superoutbursts of the AM CVn-type object CR Boo in 2014 April--March and 2015 May--June. A precursor outburst acompanied both of these superoutbursts. During the rising branch of the main superoutburst in 2014, we detected growing superhumps (stage A superhumps) whose period was $0.017669(24)$ d. Assuming that this period reflects the dynamical precession rate at the radius of the 3:1 resonance, we could estimate the mass ratio ($q=M_2/M_1$) of 0.101(4) by using the stage A superhump period and the orbital one of 0.0170290(6) d. This mass ratio is consistent with that expected by the theoretical evolutionary model of AM CVn-type objects. The detection of precursor outbursts and stage A superhumps is the second case in AM CVn-type objects. There are two interpretations of the outbursts of AM CVn-type objects. One is a dwarf nova (DN) outbursts analogy, which is caused by thermal and tidal instabilities. Another is the VY Scl-type variation, which is caused by the variation of the mass-transfer rate of the secondary. This detection of the superhump variations strongly suggests the former interpretation.

### Large mass hierarchies from strongly-coupled dynamics [Cross-Listing]

Besides the Higgs particle discovered in 2012, with mass 125 GeV, recent LHC data show tentative signals for new resonances in diboson as well as diphoton searches at high center-of-mass energies (2 TeV and 750 GeV, respectively). If these signals are confirmed (or other new resonances are discovered at the TeV scale), the large hierarchies between masses of new bosons require a dynamical explanation. Motivated by these tentative signals of new physics, we investigate the theoretical possibility that large hierarchies in the masses of glueballs could arise dynamically in new strongly-coupled gauge theories extending the standard model of particle physics. We study lattice data on non-Abelian gauge theories in the (near-)conformal regime as well as a simple toy model in the context of gauge/gravity dualities. We focus our attention on the ratio $R$ between the mass of the lightest spin-2 and spin-0 resonances, that for technical reasons is a particularly convenient and clean observable to study. For models in which (non-perturbative) large anomalous dimensions arise dynamically, we show indications that this mass ratio can be large, with $R>5$. Moreover, our results suggest that $R$ might be related to universal properties of the IR fixed point. Our findings provide an interesting step towards understanding large mass ratios in the non-perturbative regime of quantum field theories with (near) IR conformal behaviour.

### Large mass hierarchies from strongly-coupled dynamics

Besides the Higgs particle discovered in 2012, with mass 125 GeV, recent LHC data show tentative signals for new resonances in diboson as well as diphoton searches at high center-of-mass energies (2 TeV and 750 GeV, respectively). If these signals are confirmed (or other new resonances are discovered at the TeV scale), the large hierarchies between masses of new bosons require a dynamical explanation. Motivated by these tentative signals of new physics, we investigate the theoretical possibility that large hierarchies in the masses of glueballs could arise dynamically in new strongly-coupled gauge theories extending the standard model of particle physics. We study lattice data on non-Abelian gauge theories in the (near-)conformal regime as well as a simple toy model in the context of gauge/gravity dualities. We focus our attention on the ratio $R$ between the mass of the lightest spin-2 and spin-0 resonances, that for technical reasons is a particularly convenient and clean observable to study. For models in which (non-perturbative) large anomalous dimensions arise dynamically, we show indications that this mass ratio can be large, with $R>5$. Moreover, our results suggest that $R$ might be related to universal properties of the IR fixed point. Our findings provide an interesting step towards understanding large mass ratios in the non-perturbative regime of quantum field theories with (near) IR conformal behaviour.

### Large mass hierarchies from strongly-coupled dynamics [Cross-Listing]

Besides the Higgs particle discovered in 2012, with mass 125 GeV, recent LHC data show tentative signals for new resonances in diboson as well as diphoton searches at high center-of-mass energies (2 TeV and 750 GeV, respectively). If these signals are confirmed (or other new resonances are discovered at the TeV scale), the large hierarchies between masses of new bosons require a dynamical explanation. Motivated by these tentative signals of new physics, we investigate the theoretical possibility that large hierarchies in the masses of glueballs could arise dynamically in new strongly-coupled gauge theories extending the standard model of particle physics. We study lattice data on non-Abelian gauge theories in the (near-)conformal regime as well as a simple toy model in the context of gauge/gravity dualities. We focus our attention on the ratio $R$ between the mass of the lightest spin-2 and spin-0 resonances, that for technical reasons is a particularly convenient and clean observable to study. For models in which (non-perturbative) large anomalous dimensions arise dynamically, we show indications that this mass ratio can be large, with $R>5$. Moreover, our results suggest that $R$ might be related to universal properties of the IR fixed point. Our findings provide an interesting step towards understanding large mass ratios in the non-perturbative regime of quantum field theories with (near) IR conformal behaviour.

### The realm of the Galactic globular clusters and the mass of their primordial clouds

By adopting the empirical constraints related to the estimates of Helium enhancement ($\Delta Y$), present mass ratio between first and second stellar generations ($M_{1G}/M_{2G}$) and the actual mass of Galactic globular clusters ($M_{GC}$), we envisage a possible scenario for the formation of these stellar systems. Our approach allows for the possible loss of stars through evaporation or tidal interactions and different star formation efficiencies. In our approach the star formation efficiency of the first generation ($\epsilon_{1G}$) is the central factor that links the stellar generations as it not only defines both the mass in stars of the first generation and the remaining mass available for further star formation, but it also fixes the amount of matter required to contaminate the second stellar generation. In this way, $\epsilon_{1G}$ is fully defined by the He enhancement between successive generations in a GC. We also show that globular clusters fit well within a $\Delta Y$ {\it vs} $M_{1G}/M_{2G}$ diagram which indicates three different evolutionary paths. The central one is for clusters that have not loss stars, through tidal interactions, from either of their stellar generations, and thus their present $M_{GC}$ value is identical to the amount of low mass stars ($M_* \le$ 1 M$_\odot$) that resulted from both stellar generations. Other possible evolutions imply either the loss of first generation stars or the combination of a low star formation efficiency in the second stellar generation and/or a loss of stars from the second generation. From these considerations we derive a lower limit to the mass ($M_{tot}$) of the individual primordial clouds that gave origin to globular clusters.

### Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes

Based on the result of classification in our previous work, we exhaustively investigate Yukawa sector of $U(8)$ model on magnetized orbifolds $T^{2}/Z_{2}$, $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$ by evaluating ratios of the mass eigenvalues of the three states in all the possible configurations with one and two Higgs pairs where three generations are realized in fermions. Because of smearing effect via kinetic mixing, one can realize a hierarchy such as $10^{-2}$-$10^{-3}$, but it is very difficult to achieve the mass ratio between the up and top quarks ($m_{\text{up}}/m_{\text{top}} \sim 10^{-5}$) on the complicated magnetized orbifolds $T^{2}/Z_{N}\,(N=3,4,6)$.

### Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes [Replacement]

Based on the result of classification in our previous work, we exhaustively investigate Yukawa sector of $U(8)$ model on magnetized orbifolds $T^{2}/Z_{2}$, $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$ by evaluating ratios of the mass eigenvalues of the three states in all the possible configurations with one and two Higgs pairs where three generations are realized in fermions. Because of smearing effect via kinetic mixing, one can realize a hierarchy such as $10^{-2}$-$10^{-3}$, but it is very difficult to achieve the mass ratio between the up and top quarks ($m_{\text{up}}/m_{\text{top}} \sim 10^{-5}$) on the complicated magnetized orbifolds $T^{2}/Z_{N}\,(N=3,4,6)$.

### Secular models and Kozai resonance for planets in coorbital non-coplanar motion

In this work, we construct and test an analytical and a semianalytical secular models for two planets locked in a coorbital non-coplanar motion, comparing some results with the case of restricted three body problem. The analytical average model replicates the numerical N-body integrations, even for moderate eccentricities ($\lesssim$ 0.3) and inclinations ($\lesssim10^\circ$), except for the regions corresponding to quasi-satellite and Lidov-Kozai configurations. Furthermore, this model is also useful in the restricted three body problem, assuming very low mass ratio between the planets. We also describe a four-degree-of-freedom semianalytical model valid for any type of coorbital configuration in a wide range of eccentricities and inclinations. {Using a N-body integrator, we have found that the phase space of the General Three Body Problem is different to the restricted case for inclined systems, and establish the location of the Lidov-Kozai equilibrium configurations depending on mass ratio. We study the stability of periodic orbits in the inclined systems, and find that apart from the robust configurations $L_4$, $AL_4$, and $QS$ is possible to harbour two Earth-like planets in orbits previously identified as unstable $U$ and also in Euler $L_3$ configurations, with bounded chaos.

### ASASSN-15jd: WZ Sge-type star with intermediate superoutburst between single and double ones

We present optical photometry of a WZ Sge-type dwarf nova (DN), ASASSN-15jd. Its light curve showed a small dip in the middle of the superoutburst in 2015 for the first time among WZ Sge-type DNe. The unusual light curve implies a delay in the growth of the 3:1 resonance tidal instability. Also, the light curve is similar to those of other two WZ Sge-type stars, SSS J122221.7$-$311523 and OT J184228.1$+$483742, which are believed to be the best candidates for a period bouncer on the basis of their small values of the mass ratio ($q \equiv M_{2}/M_{1}$). Additionally, the small mean superhump amplitude ($<$ 0.1 mag) and the long duration of no ordinary superhumps at the early stage of the superoutburst are common to the best candidates for a period bouncer. The average superhump period was $P_{\rm sh}$ = 0.0649810(78) d and no early superhumps were detected. Although we could not estimate the mass ratio of ASASSN-15jd with high accuracy, this object is expected to be a candidate for a period bouncer, a binary accounting for the missing population of post-period minimum cataclysmic variables, based on the above characteristics.

### OGLE-2012-BLG-0724Lb: A Saturn-mass Planet around an M-dwarf

We report the discovery of a planet by the microlensing method, OGLE-2012-BLG-0724Lb. Although the duration of the planetary signal for this event was one of the shortest seen for a planetary event, the anomaly was well covered thanks to high cadence observations taken by the survey groups OGLE and MOA. By analyzing the light curve, this planetary system is found to have a mass ratio $q=(1.58\pm0.15)\times10^{-3}$. By conducting a Bayesian analysis, we estimate that the host star is an M-dwarf star with a mass of $M_{\rm L}=0.29_{-0.16}^{+0.33} \ M_{\odot}$ located at $D_{\rm L}=6.7_{-1.2}^{+1.1} \ {\rm kpc}$ away from the Earth and the companion's mass is $m_{\rm P}=0.47_{-0.26}^{+0.54} \ M_{\rm Jup}$. The projected planet-host separation is $a_{\perp}=1.6_{-0.3}^{+0.4} \ {\rm AU}$. Because the lens-source relative proper motion is relatively high, future high resolution images would detect the lens host star and determine the lens properties uniquely. This system is likely a Saturn-mass exoplanet around an M-dwarf and such systems are commonly detected by gravitational microlensing. This adds an another example of a possible pileup of sub-Jupiters $(0.2 < m_{\rm P}/M_{\rm Jup} < 1)$ in contrast to a lack of Jupiters ($\sim 1 - 2 \ M_{\rm Jup}$) around M-dwarfs, supporting the prediction by core accretion models that Jupiter-mass or more massive planets are unlikely to form around M-dwarfs.