Perelomov problem and inversion of the Segal-Bargmann transform

We reconstruct a function by values of its Segal-Bargmann transform at points of a lattice.Comment: 4pp, final varian

X-ray Variability Characteristics of the Seyfert 1 Galaxy NGC 3783

We have characterized the energy-dependent X-ray variability properties of the Seyfert~1 galaxy NGC 3783 using archival XMM-Newton and Rossi X-ray Timing Explorer data. The high-frequency fluctuation power spectral density function (PSD) slope is consistent with flattening towards higher energies. Light curve cross correlation functions yield no significant lags, but peak coefficients generally decrease as energy separation of the bands increases on both short and long timescales. We have measured the coherence between various X-ray bands over the temporal frequency range of 6e-8 to 1e-4 Hz; this range includes the temporal frequency of the low-frequency power spectral density function (PSD) break tentatively detected by Markowitz et al. and includes the lowest temporal frequency over which coherence has been measured in any AGN to date. Coherence is generally near unity at these temporal frequencies, though it decreases slightly as energy separation of the bands increases. Temporal frequency-dependent phase lags are detected on short time scales; phase lags are consistent with increasing as energy separation increases or as temporal frequency decreases. All of these results are similar to those obtained previously for several Seyfert galaxies and stellar-mass black hole systems. Qualitatively, these results are consistent with the variability models of Kotov et al. and Lyubarskii, wherein the X-ray variability is due to inwardly propagating variations in the local mass accretion rate.Comment: Accepted for publication in The Astrophysical Journal, 2005, vol. 635, p. 180; version 2 has minor grammatical changes; 23 pages; uses emulateapj

Disk Diffusion Propagation Model for the Outburst of XTE J1118+480

We present a linear diffusion model for the evolution of the double-peaked outburst in the transient source XTEJ1118+480. The model treats the two outbursts as episodic mass deposition at the outer radius of the disk followed by evolution of disk structure according to a diffusion process. We demonstrate that light curves with fast-rise, exponential decay profile are a general consequence of the diffusion process. Deconvolution of the light curve proves to be feasible and gives an input function specifying mass deposition at the outer disk edge as well as the total mass of the disk, both as functions of time. The derived evolution of total disk mass can be correlated with the observed evolution of the ~0.1 Hz QPO in the source reported in Wood et al. (2000).Comment: 26 pages, 6 figures, accepted for publication in Ap

Damped harmonic oscillator interpretation of the soft-state power spectra of Cyg X-1

We develop a model of an accretion disc in which the variability induced at a given radius is governed by a damped harmonic oscillator at the corresponding epicyclic frequency. That variability induces both linear and non-linear responses in the locally emitted radiation. The total observed variability of a source is the sum of these contributions over the disc radius weighted by the energy dissipation rate at each radius. It is shown that this simple model, which effectively has only three parameters including the normalization, can explain the range of the power spectra observed from Cyg X-1 in the soft state. Although a degeneracy between the black hole mass and the strength of the damping does not allow a unique determination of the mass, we can still constrain it to <16--20 solar masses. We also show that our model preserves the observed linear rms-flux relationship even in the presence of the non-linear flux response.Comment: MNRAS (Letters), in pres

Fourier-resolved energy spectra of the Narrow Line Seyfert 1 Mkn 766

We compute Fourier-resolved X-ray spectra of the Seyfert 1 Markarian 766 to study the shape of the variable components contributing to the 0.3-10 keV energy spectrum and their time-scale dependence. The fractional variability spectra peak at 1-3 keV, as in other Seyfert 1 galaxies, consistent with either a constant contribution from a soft excess component below 1 keV and Compton reflection component above 2 keV, or variable warm absorption enhancing the variability in the 1-3 keV range. The rms spectra, which shows the shape of the variable components only, is well described by a single power law with an absorption feature around 0.7 keV, which gives it an apparent soft excess. This spectral shape can be produced by a power law varying in normalisation, affected by an approximately constant (within each orbit) warm absorber, with parameters similar to those found by Turner et al. for the warm-absorber layer covering all spectral components in their scattering scenario. The total soft excess in the average spectrum can therefore be produced by a combination of constant warm absorption on the power law plus an additional less variable component. On shorter time-scales, the rms spectrum hardens and this evolution is well described by a change in power law slope, while the absorption parameters remain the same. The frequency dependence of the rms spectra can be interpreted as variability arising from propagating fluctuations through an extended emitting region, whose emitted spectrum is a power law that hardens towards the centre. This scenario reduces the short time-scale variability of lower energy bands making the variable spectrum harder on shorter time-scales and at the same time explains the hard lags found in these data by Markowitz et al.Comment: accepted for publication in MNRA

Discovery of multiple Lorentzian components in the X-ray timing properties of the Narrow Line Seyfert 1 Ark 564

We present a power spectral analysis of a 100 ksec XMM-Newton observation of the narrow line Seyfert 1 galaxy Ark~564. When combined with earlier RXTE and ASCA observations, these data produce a power spectrum covering seven decades of frequency which is well described by a power law with two very clear breaks. This shape is unlike the power spectra of almost all other AGN observed so far, which have only one detected break, and resemble Galactic binary systems in a soft state. The power spectrum can also be well described by the sum of two Lorentzian-shaped components, the one at higher frequencies having a hard spectrum, similar to those seen in Galactic binary systems. Previously we have demonstrated that the lag of the hard band variations relative to the soft band in Ark 564 is dependent on variability time-scale, as seen in Galactic binary sources. Here we show that the time-scale dependence of the lags can be described well using the same two-Lorentzian model which describes the power spectrum, assuming that each Lorentzian component has a distinct time lag. Thus all X-ray timing evidence points strongly to two discrete, localised, regions as the origin of most of the variability. Similar behaviour is seen in Galactic X-ray binary systems in most states other than the soft state, i.e. in the low-hard and intermediate/very high states. Given the very high accretion rate of Ark 564 the closest analogy is with the very high (intermediate) state rather than the low-hard state. We therefore strengthen the comparison between AGN and Galactic binary sources beyond previous studies by extending it to the previously poorly studied very high accretion rate regime.Comment: 11 pages, 11 figures, accepted for publication in MNRA

Analytic Representation of Finite Quantum Systems

A transform between functions in R and functions in Zd is used to define the analogue of number and coherent states in the context of finite d-dimensional quantum systems. The coherent states are used to define an analytic representation in terms of theta functions. All states are represented by entire functions with growth of order 2, which have exactly d zeros in each cell. The analytic function of a state is constructed from its zeros. Results about the completeness of finite sets of coherent states within a cell are derived

Aperiodic optical variability of intermediate polars - cataclysmic variables with truncated accretion disks

We study the power spectra of the variability of seven intermediate polars containing magnetized asynchronous accreting white dwarfs, XSS J00564+4548,IGR J00234+6141, DO Dra, V1223 Sgr, IGR J15094-6649, IGR J16500-3307 and IGR J17195-4100, in the optical band and demonstrate that their variability can be well described by a model based on fluctuations propagating in a truncated accretion disk. The power spectra have breaks at Fourier frequencies, which we associate with the Keplerian frequency of the disk at the boundary of the white dwarfs' magnetospheres. We propose that the properties of the optical power spectra can be used to deduce the geometry of the inner parts of the accretion disk, in particular: 1) truncation radii of the magnetically disrupted accretion disks in intermediate polars, 2) the truncation radii of the accretion disk in quiescent states of dwarf novaeComment: Accepted for publication in A&

Analyzing X-Ray Pulsar Profiles: Geometry and Beam Pattern of EXO 2030+375

The pulse profiles of the transient Be/X-ray binary EXO 2030+375 show strong dependence on energy, as well as on its luminosity state, and are asymmetric in shape. We want to identify the emission components of the two magnetic poles in the pulsed emission to understand the geometry of the neutron star and its beam pattern. We utilize a pulse-profile decomposition method that enables us to find two symmetric pulse profiles from the magnetic poles of the neutron star. The symmetry characteristics of these single-pole pulse profiles give information about the position of the magnetic poles of the neutron star relative to its rotation axis. We find a possible geometry for the neutron star in EXO 2030+375 through the decomposition of the pulse profiles, which suggests that one pole gets closer to the line of sight than the other and that, during the revolution of the neutron star, both poles disappear behind the horizon for a short period of time. A considerable fraction of the emission arises from a halo while the pole is facing the observer and from the accretion stream of the other pole while it is behind the neutron star, but the gravitational line bending makes the emission visible to us.Comment: 8 pages, 9 figures, accepted for publication in A&

Fast optical variability of SS 433

We study the optical variability of the peculiar Galactic source SS 433 using the observations made with the Russian Turkish 1.5-m telescope (RTT150). A simple technique which allows to obtain high-quality photometric measurements with 0.3-1 s time resolution using ordinary CCD is described in detail. Using the test observations of nonvariable stars, we show that the atmospheric turbulence introduces no significant distortions into the measured light curves. Therefore, the data obtained in this way are well suited for studying the aperiodic variability of various objects. The large amount of SS 433 optical light curve measurements obtained in this way allowed us to obtain the power spectra of its flux variability with a record sensitivity up to frequencies of ~0.5 Hz and to detect its break at frequency =~2.4e-3 Hz. We suggest that this break in the power spectrum results from the smoothing of the optical flux variability due to a finite size of the emitting region. Based on our measurement of the break frequency in the power spectrum, we estimated the size of the accretion-disk photosphere as 2e12 cm. We show that the amplitude of the variability in SS 433 decreases sharply during accretion-disk eclipses, but it does not disappear completely. This suggests that the size of the variable optical emission source is comparable to that of the normal star whose size is therefore R_O \approx 2e12 cm \approx 30 R_sun. The decrease in flux variability amplitude during eclipses suggests the presence of a nonvariable optical emission component with a magnitude m_R=~13.2.Comment: 12 pages, 11 figures. Accepted for publication in Astronomy Letters. The original version in Russian is available at http://hea.iki.rssi.ru/rtt150/ru/ss433_pazh10/pss433_fast.pd