Time variability of accretion flows: effects of the adiabatic index and gas temperature

We report on next phase of our study of rotating accretion flows onto black holes. We consider hydrodynamical (HD) accretion flows with a spherically symmetric density distribution at the outer boundary but with spherical symmetry broken by the introduction of a small, latitude-dependent angular momentum. We study accretion flows by means of numerical two-dimensional, axisymmetric, HD simulations for variety of the adiabatic index, $\gamma$ and the gas temperature at infinity, $c_\infty$. Our work is an extension of work done by Proga & Begelman who consider models for only $\gamma=5/3$. Our main result is that the flow properties such as the topology of the sonic surface and time behavior strongly depend on $\gamma$ but little on $c_\infty$. In particular, for $1 < \gamma < 5/3$, the mass accretion rate shows large amplitude, slow time-variability which is a result of mixing between slow and fast rotating gas. This temporal behavior differs significantly from that in models with \gamma\simless 5/3 where the accretion rate is relatively constant and from that in models with \gamma\simgreat 1 where the accretion exhibits small amplitude quasi-periodic oscillations. The key parameter responsible for the differences is the sound speed of the accretion flow which in turn determines whether the flow is dominated by gas pressure, radiation pressure or rotation. Despite these differences the time-averaged mass accretion rate in units of the corresponding Bondi rate is a weak function of $\gamma$ and $c_\infty$.Comment: 31 pages, 14 figures, accepted for publication in ApJ, for full resolution version goto http://users.camk.edu.pl/mmosc/ms.pd

The X-ray Outburst of H1743-322: High-Frequency QPOs with a 3:2 Frequency Ratio

We observed the 2003 X-ray outburst of H1743-322 in a series of 130 pointed observation with RXTE. We searched individual observations for high-frequency QPOs (HFQPOs) and found only weak or marginal detections near 240 and 160 Hz. We next grouped the observations in several different ways and computed the average power-density spectra (PDS) in a search for further evidence of HFQPOs. This effort yielded two significant results for those observations defined by the presence of low-frequency QPOs (0.1-20 Hz) and an absence of ``band-limited'' power continua: (1) The 9 time intervals with the highest 7-35 keV count rates yielded an average PDS with a QPO at $166 \pm 5$ Hz. ($4.1 \sigma$; 3--35 keV); and (2) a second group with lower 7-35 keV count rates (26 intervals) produced an average PDS with a QPO at $242 \pm 3$ Hz ($6.0 \sigma$; 7--35 keV). The ratio of these two frequencies is $1.46 \pm 0.05$. This finding is consistent with results obtained for three other black hole systems that exhibit commensurate HFQPOs in a 3:2 ratio. Furthermore, the occurrence of H1743-322's slower HFQPO at times of higher X-ray luminosity closely resembles the behavior of XTE J1550-564 and GRO J1655-40. We discuss our results in terms of a resonance model that invokes frequencies set by general relativity for orbital motions near a black-hole event horizon.Comment: 12 pages, 3 figures, submitted to Ap

Recurrent Nova IM Normae

We detected the second historical outburst of the 1920 nova IM Nor. Accurate astrometry of the outbursting object revealed the true quiescent counterpart having a magnitude of R=17.0 mag and B=18.0 mag. We show that the quiescent counterpart shows a noticeable variation. From the comparison of light curves and spectroscopic signatures, we propose that IM Nor and CI Aql comprise a new class of recurrent novae bearing some characteristics similar to those of classical novae. We interpret that the noticeable quiescent variation can be a result of either high orbital inclination, which may be also responsible for the low quiescent brightness, or the presence of high/low states. If the second possibility is confirmed by future observations, IM Nor becomes the first recurrent nova showing state changes in quiescence. Such state changes may provide a missing link between recurrent novae and supersoft X-ray sources.Comment: 4 pages, 3 figures, submitted to Astronomy and Astrophysics Letter

Excitation of Trapped Waves in Simulations of Tilted Black Hole Accretion Disks with Magnetorotational Turbulence

We analyze the time dependence of fluid variables in general relativistic, magnetohydrodynamic simulations of accretion flows onto a black hole with dimensionless spin parameter a/M=0.9. We consider both the case where the angular momentum of the accretion material is aligned with the black hole spin axis (an untilted flow) and where it is misaligned by 15 degrees (a tilted flow). In comparison to the untilted simulation, the tilted simulation exhibits a clear excess of inertial variability, that is, variability at frequencies below the local radial epicyclic frequency. We further study the radial structure of this inertial-like power by focusing on a radially extended band at 118 (M/10Msol)^-1 Hz found in each of the three analyzed fluid variables. The three dimensional density structure at this frequency suggests that the power is a composite oscillation whose dominant components are an over dense clump corotating with the background flow, a low order inertial wave, and a low order inertial-acoustic wave. Our results provide preliminary confirmation of earlier suggestions that disk tilt can be an important excitation mechanism for inertial waves.Comment: 8 Pages, 6 Figures, accepted for publication in Ap

Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method

Hole propagator of spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator on Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator on gl_2-Jack polynomials by the mapping. The resultant expression for hole propagator for finite-size system is written in terms of renormalized momenta and spin of quasi-holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of spin Calogero-Sutherland model becomes equivalent to dynamical colour correlation function of SU(3) Haldane-Shastry model.Comment: 36 pages, 8 figure

A generalized virial theorem and the balance of kinetic and potential energies in the semiclassical limit

We obtain two-sided bounds on kinetic and potential energies of a bound state of a quantum particle in the semiclassical limit, as the Planck constant \hbar\ri 0. Proofs of these results rely on the generalized virial theorem obtained in the paper as well as on a decay of eigenfunctions in the classically forbidden region

Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here, we investigate some properties of the derived value function. In particular, we show that the function is continuous and has the semigroup property, which is strongly related to the Hamilton-Jacobi-Bellman quasi-variational inequality. Moreover, we show that noise in market impact causes risk-neutral assessment to underestimate the impact cost. We also study typical examples under a log-linear/quadratic market impact function with Gamma-distributed noise.Comment: 24 pages, 14 figures. Continuation of the paper arXiv:1301.648

Existence of Density Functionals for Excited States and Resonances

We show how every bound state of a finite system of identical fermions, whether a ground state or an excited one, defines a density functional. Degeneracies created by a symmetry group can be trivially lifted by a pseudo-Zeeman effect. When complex scaling can be used to regularize a resonance into a square integrable state, a DF also exists.Comment: 4 pages, no figure

Exceptional Points in Atomic Spectra

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an experiment with atoms is proposed.Comment: 4 pages, 4 figures, 1 table, to be published in Physical Review Letter

Extended Weak Coupling Limit for Friedrichs Hamiltonians

We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a ``Friedrichs Hamiltonian'', has a small coupling constant in front of its off-diagonal term. It is well known that under some conditions in the weak coupling limit the appropriately rescaled evolution in the interaction picture converges to a contractive semigroup when restricted to the subsystem. We show that in this model, the properly renormalized and rescaled evolution converges on the whole space to a new unitary evolution, which is a dilation of the above mentioned semigroup. Similar results have been studied before \cite{AFL} in more complicated models and they are usually referred to as "stochastic Limit".Comment: changes in notation and title, minor correction