Where have all the black holes gone?

We have calculated stationary models for accretion disks around super-massive black holes in galactic nuclei. Our models show that below a critical mass flow rate of ~3 10**-3 M_Edd advection will dominate the energy budget while above that rate all the viscously liberated energy is radiated. The radiation efficiency declines steeply below that critical rate. This leads to a clear dichotomy between AGN and normal galaxies which is not so much given by differences in the mass flow rate but by the radiation efficiency. At very low mass accretion rates below 5 10**-5 M_Edd synchrotron emission and Bremsstrahlung dominate the SED, while above 2 10**-4 M Edd the inverse Compton radiation from synchrotron seed photons produce flat to inverted SEDs from the radio to X-rays. Finally we discuss the implications of these findings for AGN duty cycles and the long-term AGN evolution.Comment: 7 pages, 5 figures, accepted for publication in A&

Determining the sign of Δ31\Delta_{31} at long baseline neutrino experiments

Recently it is advocated that high intensity and low energy $(E_\nu \sim 2 GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $\phi$ to a level of a few parts in $10^4$. Experiments using such beams will have better signal to background ratio in searches for $\nu_\mu \to \nu_e$ oscillations. We propose that such experiments can also determine the sign of $\Delta_{31}$ even if the beam consists of {\it neutrinos} only. By measuring the $\nu_\mu \to \nu_e$ transitions in two different energy ranges, the effects due to propagation of neutrinos through earth's crust can be isolated and the sign of $\Delta_{31}$ can be determined. If the sensitivity of an experiment to $\phi$ is $\epsilon$, then the same experiment is automatically sensitive to matter effects and the sign of $\Delta_{31}$ for values of $\phi \geq 2 \epsilon$.Comment: Title changed and paper rewritten. 4 pages, 1 figure, revte

The Effect of Poloidal Magnetic Field on Type I Planetary Migration: Significance of Magnetic Resonance

We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis in the shearing-sheet approximation and the analytic results are compared with numerical calculations. In contrast to the unmagnetized case, the basic equations that describe the wake due to the planet in the disk allow magnetic resonances at which density perturbation diverges. In order to simplify the problem, we consider the case without magneto-rotational instability. We perform two sets of analyses: two-dimensional and three-dimensional. In two-dimensional analysis, we find the generalization of the torque formula previously known in unmagnetized case. In three-dimensional calculations, we focus on the disk with very strong magnetic field and derive a new analytic formula for the torque exerted on the planet. We find that when Alfven velocity is much larger than sound speed, two-dimensional torque is suppressed and three-dimensional modes dominate, in contrast to the unmagnetized case.Comment: 33 pages, 10 figures, typos corrected, discussion added, reference added, Accepted for publication in Ap

Solar Neutrinos and the Eclipse Effect

The solar neutrino counting rate in a real time detector like Super--Kamiokanda, SNO, or Borexino is enhanced due to neutrino oscillations in the Moon during a partial or total solar eclipse. The enhancement is calculated as a function of the neutrino parameters in the case of three flavor mixing. This enhancement, if seen, can further help to determine the neutrino parameters.Comment: 24 Pages Revtex, 8 figures as one ps file. To appear in Phys. Rev. D; Some typos corrected and a reference adde

Lensing and the Centers of Distant Early-Type Galaxies

Gravitational lensing provides a unique probe of the inner 10-1000 pc of distant galaxies (z=0.2-1). Lens theory predicts that every strong lens system should have a faint image near the center of the lens galaxy, which should be visible in radio lenses but have not been observed. We study these ``core'' images using models derived from the stellar distributions in nearby early-type galaxies. We find that realistic galaxies predict a remarkably wide range of core images, with lensing magnifications spanning some six orders of magnitude. More concentrated galaxies produce fainter core images, although not with any simple, quantitative, model independent relation. Some real galaxies have diffuse cores and predict bright core images (magnification mu>~0.1), but more common are galaxies that predict faint core images (mu<~0.001). Thus, stellar mass distributions alone are probably concentrated enough to explain the lack of observed core images, and may require observational sensitivity to improve by an order of magnitude before detections of core images become common. Two-image lenses will tend to have brighter core images than four-image lenses, so they will be the better targets for finding core images and exploiting these tools for studying the central mass distributions of distant galaxies.Comment: 13 pages, emulateapj; submitted to Ap

String spectra near some null cosmological singularities

We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.Comment: Latex, 30pgs; v2. minor clarifications, references adde

Hybrid Thermal-Nonthermal Synchrotron Emission from Hot Accretion Flows

We investigate the effect of a hybrid electron population, consisting of both thermal and non-thermal particles, on the synchrotron spectrum, image size, and image shape of a hot accretion flow onto a supermassive black hole. We find two universal features in the emitted synchrotron spectrum: (i) a prominent shoulder at low (< 10^11 Hz) frequencies that is weakly dependent on the shape of the electron energy distribution, and (ii) an extended tail of emission at high (> 10^13 Hz) frequencies whose spectral slope depends on the slope of the power-law energy distribution of the electrons. In the low-frequency shoulder, the luminosity can be up to two orders of magnitude greater than with a purely thermal plasma even if only a small fraction (< 1%) of the steady-state electron energy is in the non-thermal electrons. We apply the hybrid model to the Galactic center source, Sgr A*. The observed radio and IR spectra imply that at most 1% of the steady-state electron energy is present in a power-law tail in this source. This corresponds to no more than 10% of the electron energy injected into the non-thermal electrons and hence 90% into the thermal electrons. We show that such a hybrid distribution can be sustained in the flow because thermalization via Coulomb collisions and synchrotron self-absorption are both inefficient. The presence of non-thermal electrons enlarges the size of the radio image at low frequencies and alters the frequency dependence of the brightness temperature. A purely thermal electron distributions produces a sharp-edged image while a hybrid distribution causes strong limb brightening. These effects can be seen up to frequencies ~10^11 Hz and are accessible to radio interferometers.Comment: 33 pages with figures, to appear in the Astrophysical Journa

The hard to soft spectral transition in LMXBs - affected by recondensation of gas into an inner disk

Soft and hard spectral states of X-ray transient sources reflect two modes of accretion, accretion via a geometrically thin, optically thick disk or an advection-dominated accretion flow (ADAF). The luminosity at transition between these two states seems to vary from source to source, or even for the same source during different outbursts, as observed for GX 339-4. We investigate how the existence of an inner weak disk in the hard state affects the transition luminosity. We evaluate the structure of the corona above an outer truncated disk and the resulting disk evaporation rate for different irradiation. In some cases, recent observations of X-ray transients indicate the presence of an inner cool disk during the hard state. Such a disk can remain during quiescence after the last outburst as long as the luminosity does not drop to very low values (10^-4 to 10^-3 of the Eddington luminosity). Consequently, as part of the matter accretes via the inner disk, the hard irradiation is reduced. The hard irradiation is further reduced, occulted and partly reflected by the inner disk. This leads to a hard-soft transition at a lower luminosity if an inner disk exists below the ADAF. This seems to be supported by observations for GX 339-4.Comment: 9 pages, 4 figures, accepted for publication in Astronomy and Astrophysic

Marginal Release Under Local Differential Privacy

Many analysis and machine learning tasks require the availability of marginal statistics on multidimensional datasets while providing strong privacy guarantees for the data subjects. Applications for these statistics range from finding correlations in the data to fitting sophisticated prediction models. In this paper, we provide a set of algorithms for materializing marginal statistics under the strong model of local differential privacy. We prove the first tight theoretical bounds on the accuracy of marginals compiled under each approach, perform empirical evaluation to confirm these bounds, and evaluate them for tasks such as modeling and correlation testing. Our results show that releasing information based on (local) Fourier transformations of the input is preferable to alternatives based directly on (local) marginals