The number of point-splitting circles

Let S be a set of 2n+1 points in the plane such that no three are collinear and no four are concyclic. A circle will be called point-splitting if it has 3 points of S on its circumference, n-1 points in its interior and n-1 in its exterior. We show the surprising property that S always has exactly n^2 point- splitting circles, and prove a more general result.Comment: 12 pages, 4 figure

Tropical eigenwave and intermediate Jacobians

Tropical manifolds are polyhedral complexes enhanced with certain kind of affine structure. This structure manifests itself through a particular cohomology class which we call the eigenwave of a tropical manifold. Other wave classes of similar type are responsible for deformations of the tropical structure. If a tropical manifold is approximable by a 1-parametric family of complex manifolds then the eigenwave records the monodromy of the family around the tropical limit. With the help of tropical homology and the eigenwave we define tropical intermediate Jacobians which can be viewed as tropical analogs of classical intermediate Jacobians.Comment: 38 pages, 8 figure

Extended Coronal Emission Lines in Active Galactic Nuclei

VLT and NTT spectra are used to examine the nuclear and extended coronal line emission in a sample of well-known Seyfert 1 and 2 galaxies. The excellent spatial resolution obtained with VLT allowed us to map [SiVI] 1.963 $\mu$m and [SiVII] 2.48 $\mu$m on scales of up to 20 pc. Coronal line emission, extended to distances of $\sim$100 pc, is detected in some of the lines analyzed, particularly in [FeX] 6374\AA, [FeXI] 7891\AA, and [SiVII] 2.48$\mu$m. Most coronal lines are strongly asymmetric towards the blue and broader than low-ionization lines. This result is particularly important for Circinus, where previous observations had failed at detecting larger widths for high-ionization lines. Photoionization models are used to investigate the physical conditions and continuum luminosities necessary to produced the observed coronal emission. We found that an ionization parameter U> 0.10 is necessary to reproduce the observations, although the clouds should be located at distances < 30 pc.Comment: 4 pages, 6 figures, to appear in proceedings of IAU Symposium No. 222, The Interplay Among Black Holes, Stars and ISM in Galacti Nucle

A Consistent Model of the Accretion Shock Region in Classical T Tauri Stars

We develop a consistent model of the accretion shock region in Classical T Tauri Stars (CTTSs). The initial conditions of the post-shock flow are determined by the irradiated shock precursor and the ionization state is calculated without assuming ionization equilibrium. Comparison with observations of the C IV resonance lines (λλ 1550 Å) for CTTSs indicate that the post-shock emission predicted by the model is too large, for a reasonable range of parameters. If the model is to reproduce the observations, C IV emission from CTTSs has to be dominated by pre-shock emission, for stars with moderate to large accretion rates. For stars with low accretion rates, the observations suggest a comparable contribution between the pre- and post-shock regions. These conclusions are consistent with previous results indicating that the post-shock will be buried under the stellar photosphere for moderate to large accretion rates

The Narrow Line Region of Ark 564

The continuum and emission-line spectrum of the narrow-line Seyfert 1 galaxy Ark 564 is used to investigate, for the first time, the physical conditions and structure of its narrow line region (NLR). For this purpose, composite models, accounting for the coupled effect of photoionization and shocks, are employed. The emission-line spectrum of Ark 564, which ranges from the ultraviolet to the near-infrared, shows a rich forbidden line spectrum. Strong emphasis is given to the study of the coronal line region. The diversity of physical conditions deduced from the observations requires multi-cloud models to reproduce the observed lines and continuum. We find that a combination of high velocity (Vs = 1500 km/s) shock-dominated clouds as well as low velocity (Vs = 150 km/s) radiation-dominated clouds explains the coronal lines, while the optical low-ionization lines are mainly explained by shock-dominated clouds. The results for Ark 564 are compared with those obtained for other Seyfert galaxies previously analyzed such as NGC 5252, Circinus, NGC 4051 and NGC 4151. The model results for the ultraviolet and optical permitted lines suggest that the broad line region may contribute up to 80%, depending on the emission-line, being of about 30% for Hbeta. The consistency of the multi-cloud model is checked by comparing the predicted and observed continuum, from radio to X-ray, and indicate that the dust-to-gas ratio in the clouds varies from 10^{-15} to 10^{-12}.Comment: 18 pages, 1 figure. Accepted in A&

Ysovar: The First Sensitive, Wide-area, Mid-infrared Photometric Monitoring of the Orion Nebula Cluster

We present initial results from time-series imaging at infrared wavelengths of 0.9 deg^2 in the Orion Nebula Cluster (ONC). During Fall 2009 we obtained 81 epochs of Spitzer 3.6 and 4.5 μm data over 40 consecutive days. We extracted light curves with ~3% photometric accuracy for ~2000 ONC members ranging from several solar masses down to well below the hydrogen-burning mass limit. For many of the stars, we also have time-series photometry obtained at optical (I_c) and/or near-infrared (JK_s ) wavelengths. Our data set can be mined to determine stellar rotation periods, identify new pre-main-sequence eclipsing binaries, search for new substellar Orion members, and help better determine the frequency of circumstellar disks as a function of stellar mass in the ONC. Our primary focus is the unique ability of 3.6 and 4.5 μm variability information to improve our understanding of inner disk processes and structure in the Class I and II young stellar objects (YSOs). In this paper, we provide a brief overview of the YSOVAR Orion data obtained in Fall 2009 and highlight our light curves for AA-Tau analogs—YSOs with narrow dips in flux, most probably due to disk density structures passing through our line of sight. Detailed follow-up observations are needed in order to better quantify the nature of the obscuring bodies and what this implies for the structure of the inner disks of YSOs