Photonic Band Tuning in 2D Photonic Crystals by Atomic Layer Deposition

Atomic layer deposition (ALD) has become a powerful tool for the fabrication of high quality 3-dimentional photonic crystals (PCs) from both inorganic (opal) and organic (holographically patterned polymer) templates [1,2]. With ALD, highly conformal films can be grown with a precision of 0.05 nm, which, when combined with the availability of a wide range of low temperature film growth protocols, enables a high degree of control over material and structural properties to precisely tune optical properties [3]. Two-dimensional photonic crystals have been developed extensively for applications in optical interconnects, beam steering, and sensor devices; and are predominantly fabricated by electron-beam lithography. The optical properties of 2D photonic crystal slab waveguides are determined by the precision of the lithography process, with limited post fabrication tunability

The Kepler Follow-up Observation Program

The Kepler Mission was launched on March 6, 2009 to perform a photometric survey of more than 100,000 dwarf stars to search for terrestrial-size planets with the transit technique. Follow-up observations of planetary candidates identified by detection of transit-like events are needed both for identification of astrophysical phenomena that mimic planetary transits and for characterization of the true planets and planetary systems found by Kepler. We have developed techniques and protocols for detection of false planetary transits and are currently conducting observations on 177 Kepler targets that have been selected for follow-up. A preliminary estimate indicates that between 24% and 62% of planetary candidates selected for follow-up will turn out to be true planets.Comment: 12 pages, submitted to the Astrophysical Journal Letter

Results of two multi-chord stellar occultations by dwarf planet (1) Ceres

We report the results of two multi-chord stellar occultations by the dwarf planet (1) Ceres that were observed from Brazil on 2010 August 17, and from the USA on 2013 October 25. Four positive detections were obtained for the 2010 occultation, and nine for the 2013 occultation. Elliptical models were adjusted to the observed chords to obtain Ceres' size and shape. Two limb fitting solutions were studied for each event. The first one is a nominal solution with an indeterminate polar aspect angle. The second one was constrained by the pole coordinates as given by Drummond et al. Assuming a Maclaurin spheroid, we determine an equatorial diameter of 972 $\pm$ 6 km and an apparent oblateness of 0.08 $\pm$ 0.03 as our best solution. These results are compared to all available size and shape determinations for Ceres made so far, and shall be confirmed by the NASA's Dawn space mission.Comment: 9 pages, 6 figures. Accepted for publication in MNRA

Thirty-two Goldbach Variations

We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.Comment: v1: 34 pages AMSLaTeX. v2: 41 pages AMSLaTeX. New introductory material added and material on inequalities, Hilbert matrix and Witten zeta functions. Errors in the second section on Complex Line Integrals are corrected. To appear in International Journal of Number Theory. Title change

Kepler-4B: A Hot Neptune-Like Planet of A G0 Star Near Main-Sequence Turnoff

Early time-series photometry from NASA's Kepler spacecraft has revealed a planet transiting the star we term Kepler-4, at R.A. = 19(h)02(m)27.(s)68, delta = +50 degrees 08'08 '' 7. The planet has an orbital period of 3.213 days and shows transits with a relative depth of 0.87 x 10(-3) and a duration of about 3.95 hr. Radial velocity (RV) measurements from the Keck High Resolution Echelle Spectrometer show a reflex Doppler signal of 9.3(-1.9)(+1.1) m s(-1), consistent with a low-eccentricity orbit with the phase expected from the transits. Various tests show no evidence for any companion star near enough to affect the light curve or the RVs for this system. From a transit-based estimate of the host star's mean density, combined with analysis of high-resolution spectra, we infer that the host star is near turnoff from the main sequence, with estimated mass and radius of 1.223(-0.091)(+0.053) M(circle dot) and 1.487(-0.084)(+0.071) R(circle dot).We estimate the planet mass and radius to be {M(P), R(P)} = {24.5 +/- 3.8 M(circle plus), 3.99 +/- 0.21 R(circle plus)}. The planet's density is near 1.9 g cm(-3); it is thus slightly denser and more massive than Neptune, but about the same size.W. M. Keck FoundationNASA's Science Mission DirectorateAstronom

Integrals Over Polytopes, Multiple Zeta Values and Polylogarithms, and Euler's Constant

Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in single zeta values. We obtain asymptotic expansions of the integrals, and of sums of certain multiple zeta values with constant weight. We also give related expressions for Euler's constant. In the final section, we evaluate more general integrals -- one is a Chen (Drinfeld-Kontsevich) iterated integral -- over some polytopes that are higher-dimensional analogs of $T$. This leads to a relation between certain multiple polylogarithm values and multiple zeta values.Comment: 19 pages, to appear in Mat Zametki. Ver 2.: Added Remark 3 on a Chen (Drinfeld-Kontsevich) iterated integral; simplified Proposition 2; gave reference for (19); corrected [16]; fixed typ

A New Spectroscopic and Photometric Analysis of the Transiting Planet Systems TrES-3 and TrES-4

We report new spectroscopic and photometric observations of the parent stars of the recently discovered transiting planets TrES-3 and TrES-4. A detailed abundance analysis based on high-resolution spectra yields [Fe/H] $= -0.19\pm 0.08$, $T_\mathrm{eff} = 5650\pm 75$ K, and $\log g = 4.4\pm 0.1$ for TrES-3, and [Fe/H] $= +0.14\pm 0.09$, $T_\mathrm{eff} = 6200\pm 75$ K, and $\log g = 4.0\pm0.1$ for TrES-4. The accuracy of the effective temperatures is supported by a number of independent consistency checks. The spectroscopic orbital solution for TrES-3 is improved with our new radial-velocity measurements of that system, as are the light-curve parameters for both systems based on newly acquired photometry for TrES-3 and a reanalysis of existing photometry for TrES-4. We have redetermined the stellar parameters taking advantage of the strong constraint provided by the light curves in the form of the normalized separation $a/R_\star$ (related to the stellar density) in conjunction with our new temperatures and metallicities. The masses and radii we derive are M_\star=0.928_{-0.048}^{+0.028} M_{\sun},R_\star = 0.829_{-0.022}^{+0.015} R_{\sun}, and M_\star = 1.404_{-0.134}^{+0.066} M_{\sun}, R_\star=1.846_{-0.087}^{+0.096} R_{\sun} for TrES-3 and TrES-4, respectively. With these revised stellar parameters we obtain improved values for the planetary masses and radii. We find $M_p = 1.910_{-0.080}^{+0.075} M_\mathrm{Jup}$, $R_p=1.336_{-0.036}^{+0.031} R_\mathrm{Jup}$ for TrES-3, and $M_p=0.925 \pm 0.082 M_\mathrm{Jup}$, $R_p=1.783_{-0.086}^{+0.093} R_\mathrm{Jup}$ for TrES-4. We confirm TrES-4 as the planet with the largest radius among the currently known transiting hot Jupiters.Comment: 42 pages, 10 tables, 8 figures. Accepted for publication in the Astrophysical Journa

A New Spectroscopic and Photometric Analysis of the Transiting Planet Systems TrES-3 and TrES-4

We report new spectroscopic and photometric observations of the parent stars of the recently discovered transiting planets TrES-3 and TrES-4. A detailed abundance analysis based on high-resolution spectra yields [Fe/H] = –0.19 ± 0.08, T_(eff) = 5650 ± 75 K, and log g = 4.4 ± 0.1 for TrES-3, and [Fe/H] = +0.14 ± 0.09, T_(eff) = 6200 ± 75 K, and log g = 4.0 ± 0.1 for TrES-4. The accuracy of the effective temperatures is supported by a number of independent consistency checks. The spectroscopic orbital solution for TrES-3 is improved with our new radial velocity measurements of that system, as are the light-curve parameters for both systems based on newly acquired photometry for TrES-3 and a reanalysis of existing photometry for TrES-4. We have redetermined the stellar parameters taking advantage of the strong constraint provided by the light curves in the form of the normalized separation a/R_* (related to the stellar density) in conjunction with our new temperatures and metallicities. The masses and radii we derive are M_* = 0.928^(+0.028)_(–0.048) M_⊙, R_* = 0.829^(+0.015)_(–0.022) R_⊙, and M_* = 1.404^(+0.066)_(–0.134) M_⊙, R_* = 1.846^(+0.096)_(–0.087) R_⊙ for TrES-3 and TrES-4, respectively. With these revised stellar parameters, we obtain improved values for the planetary masses and radii. We find M_p = 1.910^(+0.075)_(–0.080) M_(Jup), R_p = 1.336^(+0.031)_(–0.036) R_(Jup) for TrES-3, and M_p = 0.925 ± 0.082 M_(Jup), R_p = 1.783^(+0.093)_(–0.086) R_(Jup) for TrES-4. We confirm TrES-4 as the planet with the largest radius among the currently known transiting hot Jupiters

Discovery of the Transiting Planet Kepler-5B

We present 44 days of high duty cycle, ultra precise photometry of the 13th magnitude star Kepler-5 (KIC 8191672, T(eff) = 6300 K, log g = 4.1), which exhibits periodic transits with a depth of 0.7%. Detailed modeling of the transit is consistent with a planetary companion with an orbital period of 3.548460 +/- 0.000032 days and a radius of 1.431(-0.052)(+0.041) R(J). Follow-up radial velocity measurements with the Keck HIRES spectrograph on nine separate nights demonstrate that the planet is more than twice as massive as Jupiter with a mass of 2.114(-0.059)(+0.056) M(J) and a mean density of 0.894 +/- 0.079 g cm(-3).NASA's Science Mission DirectorateAstronom

Kepler-7b: A Transiting Planet with Unusually Low Density

We report the discovery and confirmation of Kepler-7b, a transiting planet with unusually low density. The mass is less than half that of Jupiter, Mp = 0.43 Mj, but the radius is fifty percent larger, Rp = 1.48 Rj. The resulting density, 0.17 g/cc, is the second lowest reported so far for an extrasolar planet. The orbital period is fairly long, P = 4.886 days, and the host star is not much hotter than the Sun, Teff = 6000 K. However, it is more massive and considerably larger than the sun, Mstar = 1.35 Msun and Rstar = 1.84 Rsun, and must be near the end of its life on the Main Sequence.Comment: 19 pages, 3 figure