Direct imaging constraints on planet populations detected by microlensing

Results from gravitational microlensing suggested the existence of a large population of free-floating planetary mass objects. The main conclusion from this work was partly based on constraints from a direct imaging survey. This survey determined upper limits for the frequency of stars that harbor giant exoplanets at large orbital separations. Aims. We want to verify to what extent upper limits from direct imaging do indeed constrain the microlensing results. We examine the current derivation of the upper limits used in the microlensing study and re-analyze the data from the corresponding imaging survey. We focus on the mass and semi-major axis ranges that are most relevant in context of the microlensing results. We also consider new results from a recent M-dwarf imaging survey as these objects are typically the host stars for planets detected by microlensing. We find that the upper limits currently applied in context of the microlensing results are probably underestimated. This means that a larger fraction of stars than assumed may harbor gas giant planets at larger orbital separations. Also, the way the upper limit is currently used to estimate the fraction of free-floating objects is not strictly correct. If the planetary surface density of giant planets around M-dwarfs is described as df_Planet ~ a^beta da, we find that beta ~ 0.5 - 0.6 is consistent with results from different observational studies probing semi-major axes between ~0.03 - 30 AU. Having a higher upper limit on the fraction of stars that may have gas giant planets at orbital separations probed by the microlensing data implies that more of the planets detected in the microlensing study are potentially bound to stars rather than free-floating. The current observational data are consistent with a rising planetary surface density for giant exoplanets around M-dwarfs out to ~30 AU.Comment: Accepted for publication in A&A as Research Note, 3 page

Comparison of two models for bridge-assisted charge transfer

Based on the reduced density matrix method, we compare two different approaches to calculate the dynamics of the electron transfer in systems with donor, bridge, and acceptor. In the first approach a vibrational substructure is taken into account for each electronic state and the corresponding states are displaced along a common reaction coordinate. In the second approach it is assumed that vibrational relaxation is much faster than the electron transfer and therefore the states are modeled by electronic levels only. In both approaches the system is coupled to a bath of harmonic oscillators but the way of relaxation is quite different. The theory is applied to the electron transfer in ${\rm H_2P}-{\rm ZnP}-{\rm Q}$ with free-base porphyrin (${\rm H_2P}$) being the donor, zinc porphyrin (${\rm ZnP}$) being the bridge and quinone (${\rm Q}$) the acceptor. The parameters are chosen as similar as possible for both approaches and the quality of the agreement is discussed.Comment: 12 pages including 4 figures, 1 table, 26 references. For more info see http://eee.tu-chemnitz.de/~kili

About the maximal rank of 3-tensors over the real and the complex number field

High dimensional array data, tensor data, is becoming important in recent days. Then maximal rank of tensors is important in theory and applications. In this paper we consider the maximal rank of 3 tensors. It can be attacked from various viewpoints, however, we trace the method of Atkinson-Stephens(1979) and Atkinson-Lloyd(1980). They treated the problem in the complex field, and we will present various bounds over the real field by proving several lemmas and propositions, which is real counterparts of their results.Comment: 13 pages, no figure v2: correction and improvemen

Optical properties of small polarons from dynamical mean-field theory

The optical properties of polarons are studied in the framework of the Holstein model by applying the dynamical mean-field theory. This approach allows to enlighten important quantitative and qualitative deviations from the limiting treatments of small polaron theory, that should be considered when interpreting experimental data. In the antiadiabatic regime, accounting on the same footing for a finite phonon frequency and a finite electron bandwidth allows to address the evolution of the optical absorption away from the well-understood molecular limit. It is shown that the width of the multiphonon peaks in the optical spectra depends on the temperature and on the frequency in a way that contradicts the commonly accepted results, most notably in the strong coupling case. In the adiabatic regime, on the other hand, the present method allows to identify a wide range of parameters of experimental interest, where the electron bandwidth is comparable or larger than the broadening of the Franck-Condon line, leading to a strong modification of both the position and the shape of the polaronic absorption. An analytical expression is derived in the limit of vanishing broadening, which improves over the existing formulas and whose validity extends to any finite-dimensional lattice. In the same adiabatic regime, at intermediate values of the interaction strength, the optical absorption exhibits a characteristic reentrant behavior, with the emergence of sharp features upon increasing the temperature -- polaron interband transitions -- which are peculiar of the polaron crossover, and for which analytical expressions are provided.Comment: 16 pages, 6 figure

High precision microlensing maps of the Galactic bulge

We present detailed maps of the microlensing optical depth and event density over an area of 195 sq. deg towards the Galactic bulge. The maps are computed from synthetic stellar catalogues generated from the Besancon Galaxy Model, which comprises four stellar populations and a three-dimensional extinction map calibrated against the Two-Micron All-Sky Survey. The optical depth maps have a resolution of 15 arcminutes, corresponding to the angular resolution of the extinction map. We compute optical depth and event density maps for all resolved sources above I=19, for unresolved (difference image) sources magnified above this limit, and for bright standard candle sources in the bulge. We show that the resulting optical depth contours are dominated by extinction effects, exhibiting fine structure in stark contrast to previous theoretical optical depth maps. Optical depth comparisons between Galactic models and optical microlensing survey measurements cannot safely ignore extinction or assume it to be smooth. We show how the event distribution for hypothetical J and K-band microlensing surveys, using existing ground-based facilities such as VISTA, UKIRT or CFHT, would be much less affected by extinction, especially in the K band. The near infrared provides a substantial sensitivity increase over current I-band surveys and a more faithful tracer of the underlying stellar distribution, something which upcoming variability surveys such as VVV will be able to exploit. Synthetic population models offer a promising way forward to fully exploit large microlensing datasets for Galactic structure studies.Comment: 8 pages, submitted to MNRA

The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

MOA-2011-BLG-293Lb: First Microlensing Planet possibly in the Habitable Zone

We used Keck adaptive optics observations to identify the first planet discovered by microlensing to lie in or near the habitable zone, i.e., at projected separation $r_\perp=1.1\pm 0.1\,$AU from its $M_{L}=0.86\pm 0.06\,M_\odot$ host, being the highest microlensing mass definitely identified. The planet has a mass $m_p = 4.8\pm 0.3\,M_{\rm Jup}$, and could in principle have habitable moons. This is also the first planet to be identified as being in the Galactic bulge with good confidence: $D_L=7.72\pm 0.44$ kpc. The planet/host masses and distance were previously not known, but only estimated using Bayesian priors based on a Galactic model (Yee et al. 2012). These estimates had suggested that the planet might be a super-Jupiter orbiting an M dwarf, a very rare class of planets. We obtained high-resolution $JHK$ images using Keck adaptive optics to detect the lens and so test this hypothesis. We clearly detect light from a G dwarf at the position of the event, and exclude all interpretations other than that this is the lens with high confidence (95%), using a new astrometric technique. The calibrated magnitude of the planet host star is $H_{L}=19.16\pm 0.13$. We infer the following probabilities for the three possible orbital configurations of the gas giant planet: 53% to be in the habitable zone, 35% to be near the habitable zone, and 12% to be beyond the snow line, depending on the atmospherical conditions and the uncertainties on the semimajor axis.Comment: Accepted by ApJ, 21 pages, 4 figure

Chebyshev approach to quantum systems coupled to a bath

We propose a new concept for the dynamics of a quantum bath, the Chebyshev space, and a new method based on this concept, the Chebyshev space method. The Chebyshev space is an abstract vector space that exactly represents the fermionic or bosonic bath degrees of freedom, without a discretization of the bath density of states. Relying on Chebyshev expansions the Chebyshev space representation of a bath has very favorable properties with respect to extremely precise and efficient calculations of groundstate properties, static and dynamical correlations, and time-evolution for a great variety of quantum systems. The aim of the present work is to introduce the Chebyshev space in detail and to demonstrate the capabilities of the Chebyshev space method. Although the central idea is derived in full generality the focus is on model systems coupled to fermionic baths. In particular we address quantum impurity problems, such as an impurity in a host or a bosonic impurity with a static barrier, and the motion of a wave packet on a chain coupled to leads. For the bosonic impurity, the phase transition from a delocalized electron to a localized polaron in arbitrary dimension is detected. For the wave packet on a chain, we show how the Chebyshev space method implements different boundary conditions, including transparent boundary conditions replacing infinite leads. Furthermore the self-consistent solution of the Holstein model in infinite dimension is calculated. With the examples we demonstrate how highly accurate results for system energies, correlation and spectral functions, and time-dependence of observables are obtained with modest computational effort.Comment: 18 pages, 13 figures, to appear in Phys. Rev.

Galactic bulge giants: probing stellar and galactic evolution I. Catalogue of Spitzer IRAC and MIPS sources

Aims: We aim at measuring mass-loss rates and the luminosities of a statistically large sample of Galactic bulge stars at several galactocentric radii. The sensitivity of previous infrared surveys of the bulge has been rather limited, thus fundamental questions for late stellar evolution, such as the stage at which substantial mass-loss begins on the red giant branch and its dependence on fundamental stellar properties, remain unanswered. We aim at providing evidence and answers to these questions. Methods: To this end, we observed seven 15 times 15 arcmin^2 fields in the nuclear bulge and its vicinity with unprecedented sensitivity using the IRAC and MIPS imaging instruments on-board the Spitzer Space Telescope. In each of the fields, tens of thousands of point sources were detected. Results: In the first paper based on this data set, we present the observations, data reduction, the final catalogue of sources, and a detailed comparison to previous mid-IR surveys of the Galactic bulge, as well as to theoretical isochrones. We find in general good agreement with other surveys and the isochrones, supporting the high quality of our catalogue.Comment: 21 pages, accepted for publication in A&A. A version with high-resolution figures, as well as the data catalogues (including cross-id with GLIMPSE and GALCEN) and image mosaics are available at the anonymous ftp://ftp.ster.kuleuven.be/dist/stefan/Spitzer