Near-infrared emission from sublimating dust in collisionally active debris disks

Hot exozodiacal dust is thought to be responsible for excess near-infrared (NIR) emission emanating from the innermost parts of some debris disks. The origin of this dust, however, is still a matter of debate. We test whether hot exozodiacal dust can be supplied from an exterior parent belt by Poynting-Robertson (P-R) drag, paying special attention to the pile-up of dust that occurs due to the interplay of P-R drag and dust sublimation. Specifically, we investigate whether pile-ups still occur when collisions are taken into account, and if they can explain the observed NIR excess. We compute the steady-state distribution of dust in the inner disk by solving the continuity equation. First, we derive an analytical solution under a number of simplifying assumptions. Second, we develop a numerical debris disk model that for the first time treats the complex interaction of collisions, P-R drag, and sublimation in a self-consistent way. From the resulting dust distributions we generate thermal emission spectra and compare these to observed excess NIR fluxes. We confirm that P-R drag always supplies a small amount of dust to the sublimation zone, but find that a fully consistent treatment yields a maximum amount of dust that is about 7 times lower than that given by analytical estimates. The NIR excess due this material is much smaller (<10^-3 for A-type stars with parent belts at >1 AU) than the values derived from interferometric observations (~10^-2). Pile-up of dust still occurs when collisions are considered, but its effect on the NIR flux is insignificant. Finally, the cross-section in the innermost regions is clearly dominated by barely bound grains.Comment: 18 pages, 10 figures, A&A accepte

Detecting planets around stars in nearby galaxies

The only way to detect planets around stars at distances of several kpc is by (photometric or astrometric) microlensing observations. In this paper, we show that the capability of photometric microlensing extends to the detection of signals caused by planets around stars in nearby galaxies (e.g. M31) and that there is no other method that can achieve this. Due to the large crowding, microlensing experiments towards M31 can only observe the high-magnification part of a lensing light curve. Therefore, the dominating channel for microlensing signals by planets is in distortions near the peak of high-magnification events as discussed by Griest and Safizadeh. We calculate the probability to detect planetary anomalies for microlensing experiments towards M31 and find that jupiter-like planets around stars in M31 can be detected. Though the characterization of the planet(s) involved in this signal will be difficult, the absence of such signals can yield strong constraints on the abundance of jupiter-like planets.Comment: 16 LaTex Pages, including 1 Postscript Figures, submitted to A&A; title changed, one more author added, completely revised version: central point is detecting planet in nearby galaxies and one more technique is taken into consideratio

Angular Radii of Stars via Microlensing

We outline a method by which the angular radii of giant and main sequence stars in the Galactic bulge can be measured to a few percent accuracy. The method combines ground-based photometry of caustic-crossing bulge microlensing events, with a handful of precise astrometric measurements of the lensed star during the event, to measure the angular radius of the source, theta_*. Dense photometric coverage of one caustic crossing yields the crossing timescale dt. Less frequent coverage of the entire event yields the Einstein timescale t_E and the angle phi of source trajectory with respect to the caustic. The photometric light curve solution predicts the motion of the source centroid up to an orientation on the sky and overall scale. A few precise astrometric measurements therefore yield theta_E, the angular Einstein ring radius. Then the angular radius of the source is obtained by theta_*=theta_E(dt/t_E) sin(phi). We argue that theta_* should be measurable to a few percent accuracy for Galactic bulge giant stars using ground-based photometry from a network of small (1m-class) telescopes, combined with astrometric observations with a precision of ~10 microarcsec to measure theta_E. We find that a factor of ~50 times fewer photons are required to measure theta_E to a given precision for binary-lens events than single-lens events. Adopting parameters appropriate to the Space Interferometry Mission (SIM), ~7 min of SIM time is required to measure theta_E to ~5% accuracy for giant sources in the bulge. For main-sequence sources, theta_E can be measured to ~15% accuracy in ~1.4 hours. With 10 hrs of SIM time, it should be possible to measure theta_* to ~5% for \~80 giant stars, or to 15% for ~7 main sequence stars. A byproduct of such a campaign is a significant sample of precise binary-lens mass measurements.Comment: 13 pages, 3 figures. Revised version, minor changes, required SIM integration times revised upward by ~60%. Accepted to ApJ, to appear in the March 20, 2003 issue (v586

Microscopic gauge-invariant theory of the c-axis infrared response of bilayer cuprate superconductors and the origin of the superconductivity induced absorption bands

We report on results of our theoretical study of the c-axis infrared conductivity of bilayer high-Tc cuprate superconductors using a microscopic model involving the bilayer-split (bonding and antibonding) bands. An emphasis is on the gauge-invariance of the theory, which turns out to be essential for the physical understanding of the electrodynamics of these compounds. The description of the optical response involves local (intra-bilayer and inter-bilayer) current densities and local conductivities. The local conductivities are obtained using a microscopic theory, where the quasiparticles of the two bands are coupled to spin fluctuations. The coupling leads to superconductivity and is described at the level of generalized Eliashberg theory. Also addressed is the simpler case of quasiparticles coupled by a separable and nonretarded interaction. The gauge invariance of the theory is achieved by including a suitable class of vertex corrections. The resulting response of the model is studied in detail and an interpretation of two superconductivity-induced peaks in the experimental data of the real part of the c-axis conductivity is proposed. The peak around 400/cm is attributed to a collective mode of the intra-bilayer regions, that is an analogue of the Bogolyubov-Anderson mode playing a crucial role in the theory of the longitudinal response of superconductors. For small values of the bilayer splitting, its nature is similar to that of the transverse plasmon of the phenomenological Josephson superlattice model. The peak around 1000/cm is interpreted as a pair breaking-feature that is related to the electronic coupling through the spacing layers separating the bilayers.Comment: 18 pages, 15 figures, submitted to Phys. Rev.

Better safe than sorry: Risky function exploitation through safe optimization

Exploration-exploitation of functions, that is learning and optimizing a mapping between inputs and expected outputs, is ubiquitous to many real world situations. These situations sometimes require us to avoid certain outcomes at all cost, for example because they are poisonous, harmful, or otherwise dangerous. We test participants' behavior in scenarios in which they have to find the optimum of a function while at the same time avoid outputs below a certain threshold. In two experiments, we find that Safe-Optimization, a Gaussian Process-based exploration-exploitation algorithm, describes participants' behavior well and that participants seem to care firstly whether a point is safe and then try to pick the optimal point from all such safe points. This means that their trade-off between exploration and exploitation can be seen as an intelligent, approximate, and homeostasis-driven strategy.Comment: 6 pages, submitted to Cognitive Science Conferenc

Observations of Dense Molecular Gas in a Quasar Host Galaxy at z=6.42: Further Evidence for a Non-Linear Dense Gas - Star Formation Relation at Early Cosmic Times

We report a sensitive search for the HCN(J=2-1) emission line towards SDSS J1148+5251 at z=6.42 with the VLA. HCN emission is a star formation indicator, tracing dense molecular hydrogen gas (n(H2) >= 10^4 cm^-3) within star-forming molecular clouds. No emission was detected in the deep interferometer maps of J1148+5251. We derive a limit for the HCN line luminosity of L'(HCN) < 3.3 x 10^9 K km/s pc^2, corresponding to a HCN/CO luminosity ratio of L'(HCN)/L'(CO) < 0.13. This limit is consistent with a fraction of dense molecular gas in J1148+5251 within the range of nearby ultraluminous infrared galaxies (ULIRGs; median value: L'(HCN)/L'(CO) = 0.17 {+0.05/-0.08}) and HCN-detected z>2 galaxies (0.17 {+0.09/-0.08}). The relationship between L'(HCN) and L(FIR) is considered to be a measure for the efficiency at which stars form out of dense gas. In the nearby universe, these quantities show a linear correlation, and thus, a practically constant average ratio. In J1148+5251, we find L(FIR)/L'(HCN) > 6600. This is significantly higher than the average ratios for normal nearby spiral galaxies (L(FIR)/L'(HCN) = 580 {+510/-270}) and ULIRGs (740 {+505/-50}), but consistent with a rising trend as indicated by other z>2 galaxies (predominantly quasars; 1525 {+1300/-475}). It is unlikely that this rising trend can be accounted for by a contribution of AGN heating to L(FIR) alone, and may hint at a higher median gas density and/or elevated star-formation efficiency toward the more luminous high-redshift systems. There is marginal evidence that the L(FIR)/L'(HCN) ratio in J1148+5251 may even exceed the rising trend set by other z>2 galaxies; however, only future facilities with very large collecting areas such as the SKA will offer the sensitivity required to further investigate this question.Comment: 5 pages, 2 figures, 2 tables, to appear in ApJL (accepted October 24, 2007

A Complete Set of Solutions For Caustic-Crossing Binary Microlensing Events

We present a method to analyze binary-lens microlensing light curves with one well-sampled fold caustic crossing. In general, the surface of chi^2 shows extremely complicated behavior over the 9-parameter space that characterizes binary lenses. This makes it difficult to systematically search the space and verify that a given local minimum is a global minimum. We show that for events with well-monitored caustics, the caustic-crossing region can be isolated from the rest of the light curve and easily fit to a 5-parameter function. Four of these caustic-crossing parameters can then be used to constrain the search in the larger 9-parameter space. This allows a systematic search for all solutions and thus identification of all local minima. We illustrate this technique using the PLANET data for MACHO 98-SMC-1, an excellent and publicly available caustic-crossing data set. We show that a very broad range of parameter combinations are compatible with the PLANET data set, demonstrating that observations of binary-lens lightcurves with sampling of only one caustic crossing do not yield unique solutions. The corollary to this is that the time of the second caustic crossing cannot be reliably predicted on the basis of early data including the first caustic crossing alone. We investigate the requirements for determination of a unique solution and find that occasional observations of the first caustic crossing may be sufficient to derive a complete solution.Comment: 31 pages + 8 figures + 2 table

Scale dependence of cosmological backreaction

Due to the non-commutation of spatial averaging and temporal evolution, inhomogeneities and anisotropies (cosmic structures) influence the evolution of the averaged Universe via the cosmological backreaction mechanism. We study the backreaction effect as a function of averaging scale in a perturbative approach up to higher orders. We calculate the hierarchy of the critical scales, at which 10% effects show up from averaging at different orders. The dominant contribution comes from the averaged spatial curvature, observable up to scales of 200 Mpc. The cosmic variance of the local Hubble rate is 10% (5%) for spherical regions of radius 40 (60) Mpc. We compare our result to the one from Newtonian cosmology and Hubble Space Telescope Key Project data.Comment: 6 pages, 2 figures; v3: substantial modifications, new figure