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In searches for planetary transits in the field, well over half of the survey stars are typically giants or other stars that are too large to permit straightforward detection of planets. For all-sky searches of bright V<~11 stars, the fraction is ~90%. We show that the great majority of these contaminants can be removed from the sample by analyzing their reduced proper motions (RPMs): giants have much lower RPMs than dwarfs of the same color. We use Hipparcos data to design a RPM selection function that eliminates most evolved stars, while rejecting only 9% of viable transit targets. Our method can be applied using existing or soon-to-be-released all-sky data to stars V<12.5 in the northern hemisphere and V<12 in the south. The method degrades at fainter magnitudes, but does so gracefully. For example, at V=14 it can still be used to eliminate giants redward of V-I~0.95, that is, the blue edge of the red giant clump.
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New astrometric reductions of the US Naval Observatory CCD Astrograph Catalog (UCAC) all-sky observations were performed from first principles using the TGAS stars in the 8 to 11 magnitude range as reference star catalog. Significant improvements in the astrometric solutions were obtained and the UCAC5 catalog of mean positions at a mean epoch near 2001 was generated. By combining UCAC5 with Gaia DR1 data new proper motions on the Gaia coordinate system for over 107 million stars were obtained with typical accuracies of 1 to 2 mas/yr (R = 11 to 15 mag), and about 5 mas/yr at 16th mag. Proper motions of most TGAS stars are improved over their Gaia data and the precision level of TGAS proper motions is extended to many millions more, fainter stars. External comparisons were made using stellar cluster fields and extragalactic sources. The TGAS data allow us to derive the limiting precision of the UCAC x,y data, which is significantly better than 1/100 pixel.
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in cite{BCDDPW,DPW}, where it is shown that the reduced basis space $V_n$ of dimension $n$, constructed by a certain greedy strategy, has approximation error similar to that of the optimal space associated to the Kolmogorov $n$-width of the solution manifold. The greedy construction of the reduced basis space is performed in an offline stage which requires at each step a maximization of the current error over the parameter space. For the purpose of numerical computation, this maximization is performed over a finite {em training set} obtained through a discretization. of the parameter domain. To guarantee a final approximation error $varepsilon$ for the space generated by the greedy algorithm requires in principle that the snapshots associated to this training set constitute an approximation net for the solution manifold with accuracy or order $varepsilon$. Hence, the size of the training set is the $varepsilon$ covering number for $mathcal{M}$ and this covering number typically behaves like $exp(Cvarepsilon^{-1/s})$ for some $C>0$ when the solution manifold has $n$-width decay $O(n^{-s})$. Thus, the shear size of the training set prohibits implementation of the algorithm when $varepsilon$ is small. The main result of this paper shows that, if one is willing to accept results which hold with high probability, rather than with certainty, then for a large class of relevant problems one may replace the fine discretization by a random training set of size polynomial in $varepsilon^{-1}$. Our proof of this fact is established by using inverse inequalities for polynomials in high dimensions.
With the release of Gaia DR2, it is now possible to measure the proper motions (PMs) of the lowest mass, ultra-faint satellite galaxies in the Milky Ways (MW) halo for the first time. Many of these faint satellites are posited to have been accreted as satellites of the Magellanic Clouds (MCs). Using their 6-dimensional phase space information, we calculate the orbital histories of 13 ultra-faint satellites and five classical dwarf spheroidals in a combined MW+LMC+SMC potential to determine which galaxies are dynamically associated with the MCs. These 18 galaxies are separated into four classes: i.) long-term Magellanic satellites that have been bound to the MCs for at least the last two consecutive orbits around the MCs (Carina 2, Carina 3, Horologium 1, Hydrus 1); ii.) Magellanic satellites that were recently captured by the MCs $<$ 1 Gyr ago (Reticulum 2, Phoenix 2); iii.) MW satellites that have interacted with the MCs (Sculptor 1, Tucana 3, Segue 1); and iv.) MW satellites (Aquarius 2, Canes Venatici 2, Crater 2, Draco 1, Draco 2, Hydra 2, Carina, Fornax, Ursa Minor). Results are reported for a range of MW and LMC masses. Contrary to previous work, we find no dynamical association between Carina, Fornax, and the MCs. Finally, we determine that the addition of the SMCs gravitational potential affects the longevity of satellites as members of the Magellanic system (long-term versus recently captured), but it does not change the total number of Magellanic satellites.
We quantify and correct systematic errors in PPMXL proper motions using extragalactic sources from the first two LAMOST data releases and the Veron-Cetty & Veron Catalog of Quasars. Although the majority of the sources are from the Veron catalog, LAMOST makes important contributions in regions that are not well-sampled by previous catalogs, particularly at low Galactic latitudes and in the south Galactic cap. We show that quasars in PPMXL have measureable and significant proper motions, which reflect the systematic zero-point offsets present in the catalog. We confirm the global proper motion shifts seen by Wu, Ma, & Zhou (2011), and additionally find smaller-scale fluctuations of the QSO-derived corrections to an absolute frame. We average the proper motions of 158,106 extragalactic objects in bins of 3x3 degrees and present a table of proper motion corrections.
This article presents results of VLBI observations of regions of H2O maser activity in the Local Group galaxies M33 and IC10. Since all position measurements were made relative to extragalactic background sources, the proper motions of the two galaxies could be measured. For M33, this provides this galaxys three dimensional velocity, showing that this galaxy is moving with a velocity of 190 +/- 59 kms relative to the Milky Way. For IC10, we obtain a motion of 215 +/- 42 km/s relative to the Milky Way. These measurements promise a new handle on dynamical models for the Local Group and the mass and dark matter halo of Andromeda and the Milky Way.
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