Model Checkers Are Cool: How to Model Check Voting Protocols in Uppaal

The design and implementation of an e-voting system is a challenging task. Formal analysis can be of great help here. In particular, it can lead to a better understanding of how the voting system works, and what requirements on the system are relevant. In this paper, we propose that the state-of-art model checker Uppaal provides a good environment for modelling and preliminary verification of voting protocols. To illustrate this, we present an Uppaal model of Pr\^et \`a Voter, together with some natural extensions. We also show how to verify a variant of receipt-freeness, despite the severe limitations of the property specification language in the model checker

Sgr A* Polarization: No ADAF, Low Accretion Rate, and Non-Thermal Synchrotron Emission

The recent detection of polarized radiation from Sgr A* requires a non-thermal electron distribution for the emitting plasma. The Faraday rotation measure must be small, placing strong limits on the density and magnetic field strength. We show that these constraints rule out advection-dominated accretion flow models. We construct a simple two-component model which can reproduce both the radio to mm spectrum and the polarization. This model predicts that the polarization should rise to nearly 100% at shorter wavelengths. The first component, possibly a black-hole powered jet, is compact, low density, and self-absorbed near 1 mm with ordered magnetic field, relativistic Alfven speed, and a non-thermal electron distribution. The second component is poorly constrained, but may be a convection-dominated accretion flow with dM/dt~10^-9 M_Sun/yr, in which feedback from accretion onto the black hole suppresses the accretion rate at large radii. The black hole shadow should be detectable with sub-mm VLBI.Comment: 4 pages, 1 figure, accepted by ApJL, several changes from submitted versio

The origin of emission and absorption features in Ton S180 Chandra observations

We present new interpretation of Ton S180 spectrum obtained by {\it Chandra} Spectrometer (Low Energy Transmission Grating). Several narrow absorption lines and a few emission disk lines have been successfully fitted to the data. We have not found any significant edges accompanying line emission. We propose the interpretation of narrow lines consistent with the paper recently written by Krolik (2002), where warm absorber is strongly inhomogeneous. Such situation is possible in so called multi-phase medium, where regions with different ionization states, densities and temperatures may coexist in thermal equilibrium under constant pressure. We illustrate this scenario with theoretical spectra of radiation transfered through a stratified cloud with constant pressure (instead of constant density) computed by code {\sc titan} in plane parallel approximation. Detected spectral features are faint and their presence do not alter the broad band continuum. We model the broad band continuum of Ton S180 assuming an irradiated accretion disk with a dissipative warm skin. The set of parameters appropriate for the data cannot be determined uniquely but models with low values of the black hole mass have too hot and radially extended warm skin to explain the formation of soft X-ray disk lines seen in the data.Comment: accepted to Ap

General-relativistic model of hot accretion flows with global Compton cooling

We present a model of optically thin, two-temperature, accretion flows using an exact Monte Carlo treatment of global Comptonization, with seed photons from synchrotron and bremsstrahlung emission, as well as with a fully general relativistic description of both the radiative and hydrodynamic processes. We consider accretion rates for which the luminosities of the flows are between ~0.001 and 0.01 of the Eddington luminosity. The black hole spin parameter strongly affects the flow structure within the innermost 10 gravitational radii. The resulting large difference between the Coulomb heating in models with a non-rotating and a rapidly rotating black hole is, however, outweighed by a strong contribution of compression work, much less dependent on spin. The consequent reduction of effects related to the value of the black spin is more significant at smaller accretion rates. For a non-rotating black hole, the compressive heating of electrons dominates over their Coulomb heating, and results in an approximately constant radiative efficiency of approximately 0.4 per cent in the considered range of luminosities. For a rapidly rotating black hole, the Coulomb heating dominates, the radiative efficiency is ~1 per cent and it slightly increases (but less significantly than estimated in some previous works) with increasing accretion rate. We find an agreement between our model, in which the synchrotron emission is the main source of seed photons, and observations of black-hole binaries in their hard states and AGNs at low luminosities. In particular, our model predicts a hardening of the X-ray spectrum with increasing luminosity, as indeed observed below ~0.01 of the Eddington luminosity in both black-hole binaries and AGNs. Also, our model approximately reproduces the luminosity and the slope of the X-ray emission in Cen A.Comment: 13 pages, MNRAS, accepte

A Structure for Quasars

This paper proposes a simple, empirically derived, unifying structure for the inner regions of quasars. This structure is constructed to explain the broad absorption line (BAL) regions, the narrow `associated' ultraviolet and X-ray warm absorbers (NALs); and is also found to explain the broad emission line regions (BELR), and several scattering features, including a substantial fraction of the broad X-ray Iron-K emission line, and the bi-conical extended narrow emission line region (ENLR) structures seen on large kiloparsec scales in Seyfert images. Small extensions of the model to allow luminosity dependent changes in the structure may explain the UV and X-ray Baldwin effects and the greater prevalence of obscuration in low luminosity AGN.Comment: 35 pages, including 8 color figures (figures 4abc are big). Astrophysical Journal, in press. Expanded version of conference paper astro-ph/000516

Monte Carlo simulations of global Compton cooling in inner regions of hot accretion flows

Hot accretion flows such as advection-dominated accretion flows are generally optically thin in the radial direction. Thus photons generated at some radii can cool or heat electrons at other radii via Compton scattering. Such global Compton scattering has previously been shown to be important for the dynamics of accretion flows. Here, we extend previous treatments of this problem by using accurate global general relativistic Monte Carlo simulations. We focus on an inner region of the accretion flow (R < 600R_g), for which we obtain a global self-consistent solution. As compared to the initial, not self-consistent solution, the final solution has both the cooling rate and the electron temperature significantly reduced at radii >=10 gravitational radii. On the other hand, the radiation spectrum of the self-consistent solution has the shape similar to that of the initial iteration, except for the high-energy cut-off being at an energy lower by a factor of ~2 and the bolometric luminosity decreased by a factor of ~2. We also compare the global Compton scattering model with local models in spherical and slab geometry. We find that the slab model approximates the global model significantly better than the spherical one. Still, neither local model gives a good approximation to the radial profile of the cooling rate, and the differences can be up to two orders of magnitude. The local slab model underestimates the cooling rate at outer regions whereas it overestimates that rate at inner regions. We compare our modelling results to observed hard-state spectra of black-hole binaries and find an overall good agreement provided any disc outflow is weak. We find that general-relativistic effects in flows which dynamics is modified by global Comptonization is crucial in approaching this agreement.Comment: 9 pages, 4 figures. Accepted to MNRAS. Add a new section to discuss on the impact of outflow and viscous electron heatin

Peering through the dust: Evidence for a supermassive Black Hole at the nucleus of Centaurus A from VLT IR spectroscopy

We used the near infrared spectrometer ISAAC at the ESO 'Very Large Telescope' to map the velocity field of Centaurus A (NGC 5128) at several position angles and locations in the central 20" of the galaxy. The high spatial resolution (~0.5") velocity fields from both ionized and molecular gas (PaBeta, [FeII], BrGamma, and H2) are not compromised by either excitation effects or obscuration. We identify three distinct kinematical systems: (i) a rotating 'nuclear disk' of ionized gas, confined to the inner 2", the counterpart of the PaAlpha feature previously revealed by HST/NICMOS imaging; (ii) a ring-like system with a ~6" inner radius detected only in H2, likely the counterpart of the 100pc-scale structure detected in CO by other authors; (iii) a normal extended component of gas rotating in the galactic potential. The nuclear disk is in keplerian rotation around a central mass concentration, dark (M/L>20 Msun/LsunK) and point-like at the spatial resolution of the data (R<0.25" ~4pc). We interpret this mass concentration as a supermassive black hole. Its dynamical mass based on the line velocities and disk inclination (i>15deg) is M=2(+3.0;-1.4) 10^8 Msun. The ring-like system is probably characterized by non-circular motions; a 'figure-of-8' pattern observed in the H2 position-velocity diagram might provide kinematical evidence for the presence of a nuclear bar.Comment: 43 pages, 19 figures, Astrophysical Journal in press, higher quality figures available at http://www.arcetri.astro.it/~marconi/pubs.htm