Algebraic Properties of the Real Quintic Equation for a Binary Gravitational Lens

It has been recently shown that the lens equation for a binary gravitational lens, which is apparently a coupled system, can be reduced to a real fifth-order (quintic) algebraic equation. Some algebraic properties of the real quintic equation are revealed. We find that the number of images on each side of the separation axis is independent of the mass ratio and separation unless the source crosses the caustics. Furthermore, the discriminant of the quintic equation enables us to study changes in the number of solutions, namely in the number of images. It is shown that this discriminant can be factorized into two parts: One represents the condition that the lens equation can be reduced to a single quintic equation, while the other corresponds to the caustics.Comment: 7 pages (PTPTeX); accepted for publication in Prog. Theor. Phy

The Legal Framework for States as Employers-of-Choice in Workplace Flexibility: A Case Study of Arizona and Michigan

Outlines the statutes, regulations, executive actions, and collective bargaining agreements that authorize flexible work arrangements, time off, and career flexibility in the two state workforces; the elements of model programs; and their benefits

Some Bright Stars with Smooth Continua for Calibrating the Response of High Resolution Spectrographs

When characterizing a high resolution echelle spectrograph, for instance for precise Doppler work, it is useful to observe featureless sources such as quartz lamps or hot stars to determine the response of the instrument. Such sources provide a way to determine the blaze function of the orders, pixel-to-pixel variations in the detector, fringing in the system, and other important characteristics. In practice, however, many B or early A stars do not provide a smooth continuum, whether because they are not rotating rapidly enough or for some other reason. In fact, we have found that published rotational velocities and temperatures are not a specific and sensitive guide to whether a star's continuum will be smooth. A useful resource for observers, therefore, is a list of "good" hot stars: bright, blue stars known empirically to have no lines or other spectral features beyond the Balmer series with minima below 95% of the continuum. We have compiled a list of such stars visible from Northern Hemisphere telescopes. This list includes all stars listed in the Yale Bright Star Catalog (Hoffleit & Jaschek 1991) as being single with V 175 km/s, and declination > -30, and many other hot stars that we have found useful for calibration purposes. The list here of "bad" stars may also be of interest in studies of hot, slowly rotating stars

The HARPS search for southern extra-solar planets. VI. A Neptune-mass planet around the nearby M dwarf Gl 581

We report the discovery of a Neptune-mass planet around Gl 581 (M3V, M = 0.31 Msol), based on precise Doppler measurements with the HARPS spectrograph at La Silla Observatory. The radial velocities reveal a circular orbit of period P = 5.366 days and semi-amplitude K1 = 13.2 m/s. The resulting minimum mass of the planet (m2 sin i) is only 0.052 Mjup = 0.97 Mnep = 16.6 Mearth making Gl 581b one of the lightest extra-solar planet known to date. The Gl 581 planetary system is only the third centered on an M dwarf, joining the Gl 876 three-planet system and the lone planet around Gl 436. Its discovery reinforces the emerging tendency of such planets to be of low mass, and found at short orbital periods. The statistical properties of the planets orbiting M dwarfs do not seem to match a simple mass scaling of their counterparts around solar-type stars.Comment: letter submitted to A&

Two Exoplanets Discovered at Keck Observatory

We present two exoplanets detected at Keck Observatory. HD 179079 is a G5 subgiant that hosts a hot Neptune planet with Msini = 27.5 M_earth in a 14.48 d, low-eccentricity orbit. The stellar reflex velocity induced by this planet has a semiamplitude of K = 6.6 m/s. HD 73534 is a G5 subgiant with a Jupiter-like planet of Msini = 1.1 M_jup and K = 16 m/s in a nearly circular 4.85 yr orbit. Both stars are chromospherically inactive and metal-rich. We discuss a known, classical bias in measuring eccentricities for orbits with velocity semiamplitudes, K, comparable to the radial velocity uncertainties. For exoplanets with periods longer than 10 days, the observed exoplanet eccentricity distribution is nearly flat for large amplitude systems (K > 80 m/s), but rises linearly toward low eccentricity for lower amplitude systems (K > 20 m/s).Comment: 8 figures, 6 tables, accepted, Ap

Five planets and an independent confirmation of HD 196885Ab from Lick Observatory

We present time series Doppler data from Lick Observatory that reveal the presence of long-period planetary companions orbiting nearby stars. The typical eccentricity of these massive planets are greater than the mean eccentricity of known exoplanets. HD30562b has Msini = 1.29 Mjup, with semi-major axis of 2.3 AU and eccentricity 0.76. The host star has a spectral type F8V and is metal rich. HD86264b has Msini = 7.0 Mjup, arel = 2.86 AU, an eccentricity, e = 0.7 and orbits a metal-rich, F7V star. HD87883b has Msini = 1.78 Mjup, arel = 3.6 AU, e = 0.53 and orbits a metal-rich K0V star. HD89307b has Msini = 1.78 Mjup, arel = 3.3 AU, e = 0.24 and orbits a G0V star with slightly subsolar metallicity. HD148427b has Msini = 0.96 Mjup, arel = 0.93 AU, eccentricity of 0.16 and orbits a metal rich K0 subgiant. We also present velocities for a planet orbiting the F8V metal-rich binary star, HD196885A. The planet has Msini = 2.58 Mjup, arel = 2.37 AU, and orbital eccentricity of 0.48, in agreement with the independent discovery by Correia et al. 2008.Comment: 12 figures, 8 tables, accepted Ap

A High Eccentricity Component in the Double Planet System Around HD 163607 and a Planet Around HD 164509

We report the detection of three new exoplanets from Keck Observatory. HD 163607 is a metal-rich G5IV star with two planets. The inner planet has an observed orbital period of 75.29 $\pm$ 0.02 days, a semi-amplitude of 51.1 $\pm$ 1.4 \ms, an eccentricity of 0.73 $\pm$ 0.02 and a derived minimum mass of \msini = 0.77 $\pm$ 0.02 \mjup. This is the largest eccentricity of any known planet in a multi-planet system. The argument of periastron passage is 78.7 $\pm$ 2.0$^{\circ}$; consequently, the planet's closest approach to its parent star is very near the line of sight, leading to a relatively high transit probability of 8%. The outer planet has an orbital period of 3.60 $\pm$ 0.02 years, an orbital eccentricity of 0.12 $\pm$ 0.06 and a semi-amplitude of 40.4 $\pm$ 1.3 \ms. The minimum mass is \msini = 2.29 $\pm$ 0.16 \mjup. HD 164509 is a metal-rich G5V star with a planet in an orbital period of 282.4 $\pm$ 3.8 days and an eccentricity of 0.26 $\pm$ 0.14. The semi-amplitude of 14.2 $\pm$ 2.7 \ms\ implies a minimum mass of 0.48 $\pm$ 0.09 \mjup. The radial velocities of HD 164509 also exhibit a residual linear trend of -5.1 $\pm$ 0.7 \ms\ per year, indicating the presence of an additional longer period companion in the system. Photometric observations demonstrate that HD 163607 and HD 164509 are constant in brightness to sub-millimag levels on their radial velocity periods. This provides strong support for planetary reflex motion as the cause of the radial velocity variations.Comment: 10 pages, 8 figures, accepted to Ap

The Evolution of Protoplanetary Disks Around Millisecond Pulsars: The PSR 1257 +12 System

We model the evolution of protoplanetary disks surrounding millisecond pulsars, using PSR 1257+12 as a test case. Initial conditions were chosen to correspond to initial angular momenta expected for supernova-fallback disks and disks formed from the tidal disruption of a companion star. Models were run under two models for the viscous evolution of disks: fully viscous and layered accretion disk models. Supernova-fallback disks result in a distribution of solids confined to within 1-2 AU and produce the requisite material to form the three known planets surrounding PSR 1257+12. Tidal disruption disks tend to slightly underproduce solids interior to 1 AU, required for forming the pulsar planets, while overproducing the amount of solids where no body, lunar mass or greater, exists. Disks evolving under 'layered' accretion spread somewhat less and deposit a higher column density of solids into the disk. In all cases, circumpulsar gas dissipates on $\lesssim 10^{5}$ year timescales, making formation of gas giant planets highly unlikely.Comment: 16 pages, 17 figures, Accepted for publication in The Astrophysical Journal (September 20, 2007 issue

The TRENDS High-Contrast Imaging Survey. V. Discovery of an Old and Cold Benchmark T-dwarf Orbiting the Nearby G-star HD 19467

The nearby Sun-like star HD 19467 shows a subtle radial velocity (RV) acceleration of -1.37+/-0.09 m/s/yr over an 16.9 year time baseline (an RV trend), hinting at the existence of a distant orbiting companion. We have obtained high-contrast adaptive optics images of the star using NIRC2 at Keck Observatory and report the direct detection of the body that causes the acceleration. The companion, HD 19467 B, is dK=12.57+/-0.09 mag fainter than its parent star (contrast ratio of 9.4e-6), has blue colors J-K_s=-0.36+/-0.14 (J-H=-0.29+/-0.15), and is separated by 1.653+/-0.004" (51.1+/-1.0 AU). Follow-up astrometric measurements obtained over an 1.1 year time baseline demonstrate physical association through common parallactic and proper motion. We calculate a firm lower-limit of m>51.9^{+3.6}_{-4.3}Mjup for the companion mass from orbital dynamics using a combination of Doppler observations and imaging. We estimate a model-dependent mass of m=56.7^{+4.6}_{-7.2}Mjup from a gyrochronological age of 4.3^{+1.0}_{-1.2} Gyr. Isochronal analysis suggests a much older age of $9\pm1$ Gyr, which corresponds to a mass of m=67.4^{+0.9}_{-1.5}Mjup. HD 19467 B's measured colors and absolute magnitude are consistent with a late T-dwarf [~T5-T7]. We may infer a low metallicity of [Fe/H]=-0.15+/-0.04 for the companion from its G3V parent star. HD 19467 B is the first directly imaged benchmark T-dwarf found orbiting a Sun-like star with a measured RV acceleration.Comment: Updated to reflect ApJ versio

The California Planet Survey IV: A Planet Orbiting the Giant Star HD 145934 and Updates to Seven Systems with Long-Period Planets

We present an update to seven stars with long-period planets or planetary candidates using new and archival radial velocities from Keck-HIRES and literature velocities from other telescopes. Our updated analysis better constrains orbital parameters for these planets, four of which are known multi-planet systems. HD 24040 b and HD 183263 c are super-Jupiters with circular orbits and periods longer than 8 yr. We present a previously unseen linear trend in the residuals of HD 66428 indicative on an additional planetary companion. We confirm that GJ 849 is a multi-planet system and find a good orbital solution for the c component: it is a $1 M_{\rm Jup}$ planet in a 15 yr orbit (the longest known for a planet orbiting an M dwarf). We update the HD 74156 double-planet system. We also announce the detection of HD 145934 b, a $2 M_{\rm Jup}$ planet in a 7.5 yr orbit around a giant star. Two of our stars, HD 187123 and HD 217107, at present host the only known examples of systems comprising a hot Jupiter and a planet with a well constrained period $> 5$ yr, and with no evidence of giant planets in between. Our enlargement and improvement of long-period planet parameters will aid future analysis of origins, diversity, and evolution of planetary systems.Comment: 16 pages, 13 figures. Accepted for publication in Ap