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Yasuhiro Ohta

Publications and source records attributed to Yasuhiro Ohta.

At least 55 records · Page 3Linked to original sources
arXiv2008

An integrable semi-discretization of the Camassa-Holm equation and its determinant solution

An integrable semi-discretization of the Camassa-Holm equation is presented. The keys of its construction are bilinear forms and determinant structure of solutions of the CH equation. Determinant formulas of $N$-soliton solutions of the continuous and semi-discrete Camassa-Holm equations are presented. Based on determinant formulas, we can generate multi-soliton, multi-cuspon and multi-soliton-cuspon solutions. Numerical computations using the integrable semi-discrete Camassa-Holm equation are performed. It is shown that the integrable semi-discrete Camassa-Holm equation gives very accurate numerical results even in the cases of cuspon-cuspon and soliton-cuspon interactions. The numerical computation for an initial value condition, which is not an exact solution, is also presented.

nlin.SI↗
arXiv2008

Measurement of the Spin-Orbit Angle of Exoplanet HAT-P-1b

We present new spectroscopic and photometric observations of the HAT-P-1 planetary system. Spectra obtained during three transits exhibit the Rossiter-McLaughlin effect, allowing us to measure the angle between the sky projections of the stellar spin axis and orbit normal, λ= 3.7 +/- 2.1 degrees. The small value of λfor this and other systems suggests that the dominant planet migration mechanism preserves spin-orbit alignment. Using two new transit light curves, we refine the transit ephemeris and reduce the uncertainty in the orbital period by an order of magnitude. We find a upper limit on the orbital eccentricity of 0.067, with 99% confidence, by combining our new radial-velocity measurements with those obtained previously.

astro-ph↗
arXiv2007

Measurement of the Rossiter--McLaughlin Effect in the Transiting Exoplanetary System TrES-1

We report a measurement of the Rossiter--McLaughlin effect in the transiting extrasolar planetary system TrES-1, via simultaneous spectroscopic and photometric observations with the Subaru and MAGNUM telescopes. By modeling the radial velocity anomaly that was observed during a transit, we determine the sky-projected angle between the stellar spin axis and the planetary orbital axis to be $λ= 30 \pm 21$ [deg]. This is the third case for which $λ$ has been measured in a transiting exoplanetary system, and the first demonstration that such measurements are possible for relatively faint host stars ($V \sim 12$, as compared to $V \sim 8$ for the other systems). We also derive a time of mid-transit, constraints on the eccentricity of the TrES-1b orbit ($e = 0.048 \pm 0.025$), and upper limits on the mass of the Trojan companions ($\lesssim$14 $M_{\oplus}$) at the 3$σ$ level.

astro-ph↗
arXiv2007

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $τ$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $τ$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlevé II and IV equations are recovered. The case of finite lattice is also discussed.

nlin.SI↗
arXiv2005

Measurement of Spin-Orbit Alignment in an Extrasolar Planetary System

We determine the stellar, planetary, and orbital properties of the transiting planetary system HD 209458, through a joint analysis of high-precision radial velocities, photometry, and timing of the secondary eclipse. Of primary interest is the strong detection of the Rossiter-McLaughlin effect, the alteration of photospheric line profiles that occurs because the planet occults part of the rotating surface of the star. We develop a new technique for modeling this effect, and use it to determine the inclination of the planetary orbit relative to the apparent stellar equator [lambda = (-4.4 +/- 1.4) degrees], and the line-of-sight rotation speed of the star [v*sin(I) = (4.70 +/- 0.16) km/s]. The uncertainty in these quantities has been reduced by an order of magnitude relative to the pioneering measurements by Queloz and collaborators. The small but nonzero misalignment is probably a relic of the planet formation epoch, because the expected timescale for tidal coplanarization is larger than the age of the star. Our determination of v*sin(I) is a rare case in which rotational line broadening has been isolated from other broadening mechanisms.

astro-ph↗
arXiv2005

The Rossiter-McLaughlin effect and analytic radial velocity curves for transiting extrasolar planetary systems

A transiting extrasolar planet sequentially blocks off the light coming from the different parts of the disk of the host star in a time dependent manner. Due to the spin of the star, this produces an asymmetric distortion in the line profiles of the stellar spectrum, leading to an apparent anomaly of the radial velocity curves, known as the Rossiter - McLaughlin effect. Here, we derive approximate but accurate analytic formulae for the anomaly of radial velocity curves taking account of the stellar limb darkening. The formulae are particularly useful in extracting information of the projected angle between the planetary orbit axis and the stellar spin axis, λ, and the projected stellar spin velocity, V sin I_s. We create mock samples for the radial curves for the transiting extrasolar system HD209458, and demonstrate that constraints on the spin parameters (V sin I_s, λ) may be significantly improved by combining our analytic template formulae and the precision velocity curves from high-resolution spectroscopic observations with 8-10 m class telescopes. Thus future observational exploration of transiting systems using the Rossiter - McLaughlin effect is one of the most important probes to better understanding of the origin of extrasolar planetary systems, especially the origin of their angular momentum.

astro-ph↗
arXiv2004

Hypergeometric solutions to the q-Painlevé equations

Hypergeometric solutions to seven q-Painlevé equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painlevé equations to the three-term recurrence relations for q-hypergeometric functions.

nlin.SI↗
arXiv2004

Cubic Pencils and Painlevé Hamiltonians

We present a simple heuristic method to derive the Painlevé differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.

nlin.SI↗
arXiv2004

Cosmological Density Distribution Function from the Ellipsoidal Collapse Model in Real Space

We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the Lagrangian local dynamics with finite degrees of freedom, the analytic expressions of PDF are derived taking account of the smoothing effect. The validity and the usefulness of the local approximation are then discussed comparing those results with N-body simulations in a Gaussian initial condition. Adopting the ellipsoidal collapse model (ECM) and the spherical collapse model (SCM) as Lagrangian local dynamics, we found that the PDFs from the local approximation excellently match the simulation results in the case of the cold dark matter initial spectrum. As for the scale-free initial spectra given by $P(k)\propto k^n$, N-body result suffers from spurious numerical effects, which prevent us to give a detailed comparison. Nevertheless, at the quality of N-body data, the model predictions based on the ECM and the SCM quantitatively agree with N-body results in cases with spectral index n<0. For the index n>=0, choice of the Lagrangian local dynamics becomes crucial for an accurate prediction and a more delicate modeling is required, however, we find that the model prediction based on the ECM provides a better approximation to the N-body results of cumulants and PDFs.

astro-ph↗
arXiv2003

Exact Localized Solutions of Quintic Discrete Nonlinear Schrödinger Equation

We study a new quintic discrete nonlinear Schrödinger (QDNLS) equation which reduces naturally to an interesting symmetric difference equation of the form $ϕ_{n+1}+ϕ_{n-1}=F(ϕ_n)$. Integrability of the symmetric mapping is checked by singularity confinement criteria and growth properties. Some new exact localized solutions for integrable cases are presented for certain sets of parameters. Although these exact localized solutions represent only a small subset of the large variety of possible solutions admitted by the QDNLS equation, those solutions presented here are the first example of exact localized solutions of the QDNLS equation. We also find chaotic behavior for certain parameters of nonintegrable case.

nlin.PS↗
arXiv2003

_10E_9 solution to the elliptic Painlev'e equation

A $τ$ function formalism for Sakai's elliptic Painlev'e equation is presented. This establishes the equivalence between the two formulations by Sakai and by Ohta-Ramani-Grammaticos. We also give a simple geometric description of the elliptic Painlev'e equation as a non-autonomous deformation of the addition formula on elliptic curves. By using these formulations, we construct a particular solution of the elliptic Painlev'e equation expressed in terms of the elliptic hypergeometric function_10E_9.

nlin.SI↗
arXiv2003

Evolution of Cosmological Density Distribution Function from the Local Collapse Model

We present a general framework to treat the evolution of one-point probability distribution function (PDF) for cosmic density $δ$ and velocity-divergence fields $θ$. In particular, we derive an evolution equation for the one-point PDFs and consider the stochastic nature associated with these quantities. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the Lagrangian local dynamics with finite degrees of freedom, evolution equation for PDFs becomes a closed form and consistent formal solutions are constructed. Adopting this local approximation, we explicitly evaluate the one-point PDFs $P(δ)$ and $P(θ)$ from the spherical and the ellipsoidal collapse models as the representative Lagrangian local dynamics. In a Gaussian initial condition, while the local density PDF from the ellipsoidal model almost coincides with the that of the spherical model, differences between spherical and ellipsoidal collapse model are found in the velocity-divergence PDF. Importantly, the joint PDF of local density, $P(δ,t;δ',t')$, evaluated at the same Lagrangian position but at the different times $t$ and $t'$ from the ellipsoidal collapse model exhibits a large amount of scatter. The mean relation between $δ$ and $δ'$ does fail to match the one-to-one mapping obtained from spherical collapse model. Moreover, the joint PDF $P(δ;θ)$ from the ellipsoidal collapse model shows a similar stochastic feature, both of which are indeed consistent with the recent result from N-body simulations.

astro-ph↗
arXiv2001

Differential-difference system related to toroidal Lie algebra

We present a novel differential-difference system in (2+1)-dimensional space-time (one discrete, two continuum), arisen from the Bogoyavlensky's (2+1)-dimensional KdV hierarchy. Our method is based on the bilinear identity of the hierarchy, which is related to the vertex operator representation of the toroidal Lie algebra $\sl_2^{tor}$.

nlin.SI↗