Sylvain G. Korzennik

Helioseismic Studies of Differential Rotation in the Solar Envelope by the Solar Oscillations Investigation Using the Michelson Doppler Imager

The splitting of the frequencies of the global resonant acoustic modes of the Sun by large-scale flows and rotation permits study of the variation of angular velocity Ω with both radius and latitude within the turbulent convection zone and the deeper radiative interior. The nearly uninterrupted Doppler imaging observations, provided by the Solar Oscillations Investigation (SOI) using the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO) spacecraft positioned at the L1 Lagrangian point in continuous sunlight, yield oscillation power spectra with very high signal-to-noise ratios that allow frequency splittings to be determined with exceptional accuracy. This paper reports on joint helioseismic analyses of solar rotation in the convection zone and in the outer part of the radiative core. Inversions have been obtained for a medium-l mode set (involving modes of angular degree l extending to about 250) obtained from the first 144 day interval of SOI-MDI observations in 1996. Drawing inferences about the solar internal rotation from the splitting data is a subtle process. By applying more than one inversion technique to the data, we get some indication of what are the more robust and less robust features of our inversion solutions. Here we have used seven different inversion methods. To test the reliability and sensitivity of these methods, we have performed a set of controlled experiments utilizing artificial data. This gives us some confidence in the inferences we can draw from the real solar data. The inversions of SOI-MDI data have confirmed that the decrease of Ω with latitude seen at the surface extends with little radial variation through much of the convection zone, at the base of which is an adjustment layer, called the tachocline, leading to nearly uniform rotation deeper in the radiative interior. A prominent rotational shearing layer in which Ω increases just below the surface is discernible at low to mid latitudes. Using the new data, we have also been able to study the solar rotation closer to the poles than has been achieved in previous investigations. The data have revealed that the angular velocity is distinctly lower at high latitudes than the values previously extrapolated from measurements at lower latitudes based on surface Doppler observations and helioseismology. Furthermore, we have found some evidence near latitudes of 75° of a submerged polar jet which is rotating more rapidly than its immediate surroundings. Superposed on the relatively smooth latitudinal variation in Ω are alternating zonal bands of slightly faster and slower rotation, each extending some 10° to 15° in latitude. These relatively weak banded flows have been followed by inversion to a depth of about 5% of the solar radius and appear to coincide with the evolving pattern of torsional oscillations reported from earlier surface Doppler studies.

Evidence for Multiple Companions to υ Andromedae

The bright F8 V star t Andromedae was previously reported to have a 4.6 day Doppler velocity periodicity, consistent with having a Jupiter-mass companion orbiting at 0.059 AU. Follow-up obser- vations by both the Lick and Advanced Fiber-Optic Echelle spectrometer (AFOE) planet survey pro- grams con—rm this periodicity and reveal additional periodicities at 241 and 1267 days. These periodicities are consistent with Keplerian orbital motion and imply two additional companions orbiting at 0.83 and 2.5 AU, with minimum (M sin i) masses of 2.0 and 4.6 respectively. Non-Keplerian M JUP , explanations for the observed Doppler velocity variations, including radial and nonradial pulsations, rotational modulation of surface features, and stellar magnetic cycles, are examined. These explanations seem unlikely based on the observed photometric and chromospheric stability of the star. This putative three-planet system is found to be dynamically stable by both analytic techniques and numerical simula- tions. The outer two companions both reside in eccentric orbits, as do all nine known extrasolar planet candidates in distant orbits. If real, this multiple-planet system is the —rst around a main-sequence star, and its study should oUer insights into planet formation, planet-planet interactions, and the observed eccentricities of planetary orbits. Subject headings: binaries: spectroscopicplanetary systemsstars: individual (t Andromedae)

Differential rotation and dynamics of the solar interior

Splitting of the suns global oscillation frequencies by large-scale flows can be used to investigate how rotation varies with radius and latitude within the solar interior. The nearly uninterrupted observations by the Global Oscillation Network Group (GONG) yield oscillation power spectra with high duty cycles and high signal-to-noise ratios. Frequency splittings derived from GONG observations confirm that the variation of rotation rate with latitude seen at the surface carries through much of the convection zone, at the base of which is an adjustment layer leading to latitudinally independent rotation at greater depths. A distinctive shear layer just below the surface is discernible at low to mid-latitudes.

A Planet Orbiting the Star ρ Coronae Borealis

We report the discovery of near-sinusoidal radial velocity variations of the G0V star ρ CrB, with period 39.6 days and amplitude 67 m s-1. These variations are consistent with the existence of an orbital companion in a circular orbit. Adopting a mass of 1.0 M☉ for the primary, the companion has minimum mass about 1.1 Jupiter masses and orbital radius about 0.23 AU. Such an orbital radius is too large for tidal circularization of an initially eccentric orbit during the lifetime of the star, and hence we suggest that the low eccentricity is primordial, as would be expected for a planet formed in a dissipative circumstellar disk.

An Upper Limit on the Reflected Light from the Planet Orbiting the Star τ Bootis

The planet orbiting ??Boo at a separation of 0.046 AU could produce a reflected light flux as bright as 1 × 10-4 relative to that of the star. A spectrum of the system will contain a reflected light component which varies in amplitude and Doppler shift as the planet orbits the star. Assuming the secondary spectrum is primarily the reflected stellar spectrum, we can limit the relative reflected light flux to be less than 5 × 10-5. This implies an upper limit of 0.3 for the planetary geometric albedo near 480?nm, assuming a planetary radius of 1.2 RJup. This albedo is significantly less than that of any of the giant planets of the solar system and is not consistent with certain published theoretical predictions.

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.

The Solar Acoustic Spectrum and Eigenmode Parameters

The Global Oscillation Network Group (GONG) project estimates the frequencies, amplitudes, and linewidths of more than 250,000 acoustic resonances of the sun from data sets lasting 36 days. The frequency resolution of a single data set is 0.321 microhertz. For frequencies averaged over the azimuthal order m, the median formal error is 0.044 microhertz, and the associated median fractional error is 1.6 × 10−5. For a 3-year data set, the fractional error is expected to be 3 × 10−6. The GONG m-averaged frequency measurements differ from other helioseismic data sets by 0.03 to 0.08 microhertz. The differences arise from a combination of systematic errors, random errors, and possible changes in solar structure.

On the Determination of Michelson Doppler Imager High-Degree Mode Frequencies

The characteristics of the solar acoustic spectrum are such that mode lifetimes get shorter and spatial leaks get closer in frequency as the degree of a mode increases for a given order. A direct consequence of this property is that individual p-modes are resolved only at low and intermediate degrees and that at high degrees individual modes blend into ridges. Once modes have blended into ridges, the power distribution of the ridge defines the ridge central frequency, and it will mask the true underlying mode frequency. An accurate model of the amplitude of the peaks that contribute to the ridge power distribution is needed to recover the underlying mode frequency from fitting the ridge. We present the results of fitting high-degree power ridges (up to l = 900) computed from several 2-3 month long time series of full-disk observations taken with the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory between 1996 and 1999. We also present a detailed discussion of the modeling of the ridge power distribution, and the contribution of the various observational and instrumental effects on the spatial leakage, in the context of the MDI instrument. We have constructed a physically motivated model (rather than some ad hoc correction scheme) that we believe results in a methodology that can produce an unbiased determination of high-degree modes once the instrumental characteristics are well understood. Finally, we present preliminary estimates of changes in high-degree mode parameters with epoch and thus solar activity level and discuss their significance. These estimates are preliminary because they rely on a simple—if not simplistic—ridge-to-mode correction scheme to account for errors in the plate scale used for the spherical harmonic decomposition. Such a correction scheme produced residual systematics that, as we show, are not always constant with time. These cannot be properly corrected without reprocessing the data back to the level of the spherical harmonic decomposition.

THE AFOE: A SPECTROGRAPH FOR PRECISION DOPPLER STUDIES

The Advanced Fiber Optic Echelle (AFOE) is a fiber-fed echelle spectrograph designed for the measurement of stellar Doppler shifts. Using a 2k x 2k CCD detector, it samples about 55% of the wavelength range between 450 nm and 700 nm (20 echelle orders) at a single shot, with spectral resolution R = 32000 to 70000 at 500 nm, depending on the slit width employed. The AFOE employs a number of devices to assure that the calibrations necessary for accurate Doppler measurements can be properly performed. The most important of these are: (1) coupling to the telescope via a double-scrambling optical fiber system; (2) continuous calibration of the wavelength scale and point-spread function by means of an atomic emission lamp entering the spectrograph via a separate fiber and/or a molecular iodine absorption cell; (3) availability of fiber-coupled sunlight for regular calibration against the solar spectrum; (4) appropriate mechanical design and active thermal control, yielding good mechanical stability. The AFOE is coupled to the Tillinghast 1.5-m telescope at the F. L. Whipple Observatory. It presently achieves S/N = 500 in the continuum near 500 nm in 60s when observing Arcturus (alpha-Boo, mV = -0.04). This noise level sets a limit of about 0.7 ms-1 to the Doppler precision attainable in this length of observing time. Currently, our actual frame-to-frame repeatability is worse than the photon noise limited value by about a factor of 3 for this bright star, and about 1.5 for stars with mV = 4. Work is continuing to refine data processing methods so that the ultimate noise limit may be approached more closely, and to improve the spectrographs relatively low efficiency.

p-mode frequencies in solar-like stars. I. Procyon A

As a part of an on-going program to explore the signature of p -modes in solar-like stars by means of high-resolution absorption line spectroscopy, we have studied four stars ( α  CMi, η  Cas A, ζ  Her A and β  Vir). We present here new results from two-site observations of Procyon A acquired over twelve nights in 1999. Oscillation frequencies for