Detectability of Exoplanets in the Beta Pic Moving Group with the Gemini Planet Imager

We model the detectability of exoplanets around stars in the Beta Pic Moving Group (BPMG) using the Gemini Planet Imager (GPI), a coronagraphic instrument designed to detect companions by imaging. Members of the BPMG are considered promising targets for exoplanet searches because of their youth (~12 MY) and proximity (median distance ~35 pc). We wrote a modeling procedure to generate hypothetical companions of given mass, age, eccentricity, and semi-major axis, and place them around BPMG members that fall within the V-band range of the GPI. We count as possible detections companions lying within the GPI's field of view and H-band fluxes that have a host-companion flux ratio placing them within its sensitivity. The fraction of companions that could be detected depends on their brightness at 12 Myr, and hence formation mechanism, and on their distribution of semi-major axes. We used brightness models for formation by disk instability and core-accretion. We considered the two extreme cases of the semi-major axis distribution - the log-normal distribution of the nearby F and G type stars and a power-law distribution indicated by the exoplanets detected by the radial velocity technique. We find that the GPI could detect exoplanets of all the F and G spectral type stars in the BPMG sample with a probability that depends on the brightness model and semi-major axis distribution. At spectral type K to M1, exoplanet detectability depends on brightness and hence distance of the host star. GPI will be able to detect the companions of M stars later than M1 only if they are closer than 10 pc. Of the four A stars in BPMG sample, only one has V-band brightness in the range of GPI; the others are too bright.Comment: Accepted for publication in the Astronomical Journa

Young Binary Stars and Associated Disks

The typical product of the star formation process is a binary star. Binaries have provided the first dynamical measures of the masses of pre-main-sequence (PMS) stars, providing support for the calibrations of PMS evolutionary tracks. Surprisingly, in some star-forming regions PMS binary frequencies are higher than among main-sequence solar-type stars. The difference in PMS and main-sequence binary frequencies is apparently not an evolutionary effect; recent attention has focussed on correlations between binary frequency and stellar density or cloud temperatures. Accretion disks are common among young binary stars. Binaries with separations between 1 AU and 100 AU have substantially less submillimeter emission than closer or wider binaries, suggesting that they have truncated their disks. Evidence of dynamical clearing has been seen in several binaries. Remarkably, PMS binaries of all separations show evidence of circumstellar disks and continued accretion. This suggests that the circumstellar disks are replenished from circumbinary disks or envelopes. The frequent presence of disks suggests that planet formation can occur in binary environments, and formation of planets in wide binaries is already established by their discovery. Circumbinary disk masses around very short period binaries are ample to form planetary systems such as our own. The nature of planetary systems among the most common binaries, with separations between 10 AU and 100 AU, is less clear given the observed reduction in disk mass, though they may have disk masses adequate for the formation of terrestrial-like planets.Comment: 32 pages, including 6 Postscript figures (TeX, uses psfig.sty); to appear in "Protostars & Planets IV". Gif figures with captions and high-res Postscript color figure available at http://hven.swarthmore.edu/~jensen/preprints/ppiv.htm

Truthful Matching with Online Items and Offline Agents

We study truthful mechanisms for welfare maximization in online bipartite matching. In our (multi-parameter) setting, every buyer is associated with a (possibly private) desired set of items, and has a private value for being assigned an item in her desired set. Unlike most online matching settings, where agents arrive online, in our setting the items arrive online in an adversarial order while the buyers are present for the entire duration of the process. This poses a significant challenge to the design of truthful mechanisms, due to the ability of buyers to strategize over future rounds. We provide an almost full picture of the competitive ratios in different scenarios, including myopic vs. non-myopic agents, tardy vs. prompt payments, and private vs. public desired sets. Among other results, we identify the frontier up to which the celebrated e/(e-1) competitive ratio for the vertex-weighted online matching of Karp, Vazirani and Vazirani extends to truthful agents and online items

Dimension of the repeller for a piecewise expanding affine map

In this paper, we study the dimension theory of a class of piecewise affine systems in euclidean spaces suggested by Barnsley, with some applications to the fractal image compression. It is a more general version of the class considered in the work of Keane, Simon and Solomyak and can be considered as the continuation of the works by the authors. We also present some applications of our results for generalized Takagi functions and fractal interpolation functions

On the dimension of triangular self-affine sets

As a continuation of a recent work [Bárány et al, On the dimension of self-affine sets and measures with overlaps. Proc. Amer. Math. Soc. 144 (2016) 4427–4440] of the same authors, in this note we study the dimension theory of diagonally homogeneous triangular planar self-affine iterated function systems