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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 379 records · Page 21
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NASA NTRS1994

Upper limits on metals in quasar Lyman-alpha forest clouds: Absence of C 5 lines in echelle spectra

Recently Lu presented tentative evidence for C IV lines in Quasi-Stellar Object (QSO) Ly-alpha forest systems with strong lines. We have performed a similar search for C IV in our 10 km/s resolution echelle spectra of the bright QSO HS 1946+7658. We shifted the spectra to align the expected positions of the C IV lines in 65 Ly-alpha systems and then added them. The resulting composite spectrum, equivalent to 390 hr of exposure time on the Lick 3 m telescope, has a signal-to-noise ratio of 80 per 0.025 A in the rest frame of the absorbers. We do not see any C IV lines down to a 2 sigma limit of W(1548) less than or equal to 1.4 mA, about one fifth of the strength of the lines seen by Lu. The C IV lines that Lu saw must be restricted to rare Ly-alpha systems with large H I column densities greater than or equal to 10(exp 14)/sq cm, which are too rare to show C IV in our sample. More common Ly-alpha systems with H I column densities of 10(exp 13)-10(exp 14)/sq cm do not show C IV lines. If their ionization is H/H I = 10(exp 4) then they have (C/H) less than or equal to -2.0.

Tytler, David↗
NASA NTRS1994

The Fe XIV spectrum: Predicted line intensities and solar identifications

Level populations and line intensities have been calculated in a 40-level model of Fe XIV which includes the configuations 3p(exp 3) and 3s3p3d. The results have been compared against intensities of weaker, unidentified, or tentatively classified lines in published solar line lists including a recent Goddard Space Flight Center/Solar Extreme Ultraviolet Telescope and Spectrograph (GSFC/SERTS) high-resolution list, and in presently measured archival Naval Research Laboratory (NRL)/S082A active region spectra. Seven new lines are identified as Fe XIV transitions; five other observed, unidentified lines are considered to be Fe XIV transitions on the basis of wavelength coincidence, but require further observations to obtain photometric intensities for verification; one line at 216.93 A is shown to be due to some other ion than Fe XIV. In addition, a unique forbidden infrared (approx. equal to 1.25 micrometer(s)) line originating in the high metastable level 3s3p3d(F(sub 9/2)-4) is found to have an unusual intensity dependence on electron density.

Bhatia, A. K.↗
NASA NTRS1994

Emission lines in the long-period Cepheid l Carinae

For the Cepheid l Carinae, with a pulsation period of 35.5 days, we have studied the emission-line fluxes as a function of pulsational phase in order to find out whether we see chromospheric and transition-layer emission due to an outward-moving shock. All emission lines show a steep increase in flux shortly before maximum light, suggestive of a shock moving through the surface layers. The large ratio of C IV to C II line fluxes shows that these are not transition-layer lines. During maximum light the large ratio of the large ratio of the C IV to C II line fluxes also suggests that we see emission from a shock with velocities greater than 100 km/s such that C IV emission can be excited. With such velocities mass outflow appears possible. The variations seen in the MG II line profiles show that there is an external absorption over a broad velocity band independent of the pulsation phase. We attribute this absorption to a circumstellar 'shell.' This 'shell' appears to be seen also as spatially extended emission in the O I line at 1300 A, which is probably excited by resonance with Ly beta.

Bohm-Vitense, Erika↗
NASA NTRS1994

Dynamic processes in Be star atmospheres. 2: He I 2P-nD line formation in lambda Eridani (outburst)

The He I lambda 6678 line of early Be stars generally shows violet (V) and red (R) emission whenever hydrogen alpha emission is present, but its use as a diagnostic has been handicapped by a poor understanding of the processes that drive it into emission. In an attempt to address this problem we obtained three series of eschelle spectra of the first two members of the singlet and triplet 2P-nD series of lambda Eri (B2e) during 1992 November 3-5 at Kitt Peak. During these observations lambda 6678 showed substantial emission variability in both the wings and central profile, providing an opportunity to compare its behavior with that of the lambda 4922, lambda 5876, and lambda 4471 lines. We found that the responses of the lines were different in several respects. Whereas the emissions in the V wings of all four lines scaled together, the R wing of the lambda 4922 line invariably responded with increased absorption whenever the R wing of lambda 6678 line showed increased emission. These same trends occurred within the central photospheric profiles. The R-wing behavior shows that much, but not all of the emission in lambda 6678 is caused by matter projected against the stellar disk. The excitation temperatures of the neighboring 2(sup 1) P transitions, lambda 6678 and lambda 4922 must be greater than and less than the photospheric continuum temperature, respectively. We have investigated departures from local thermodynamic equilibrium (LTE) for the He I spectrum in a variety of ad hoc, perturbed model atmospheres. We have found only one way to cause the source function of lambda 6678 to increase so strongly, namely, by increasing the atmospheric temperature in the line formation region to 30,000 - 40,000 K. This effect was discovered by Auer and Mihalas for O3-O4 atmospheric models, but it has not been applied to active B stars. Our models suggest that lambda 6678 emission in Be stars can be used as a sensitive monitor of localized hot spots on these stars' surfaces. The energies involved in heating the active portions of the atmosphere are too high to be produced by gravitational infall. This leaves magnetically induced flares among the few known processes on the surfaces of stars capable of sustaining this energy level.

Smith, Myron A.↗
NASA NTRS1993

Absence of magnetic trapping on closed field lines at Neptune

The large offset of Neptune's magnetic field in an offset tilted dipole (OTD) approximation allows some fraction of magnetospheric field lines to have monotonically increasing field magnitude over their entire length in the magnetosphere. The usual magnetic trapping is impossible on such field lines, meaning that all charged particles on these field lines will precipitate after mirroring at most once. These field lines can be thought of as the part of the global magnetic anomaly where no particles on the corresponding drift shells remain trapped for an entire rotation of the planet. In this paper we examine both the morphology and size of the affected surface area in the OTD2 and O8 magnetic field models. For regions where there are indications that part of the aurora could be due to monotonic field line precipitation we analyze whether these field lines could be sufficiently populated to produce auroral signatures by considering photoelectron production rates and radial diffusion. We conclude that monotonic field line precipitation may contribute to the observed Neptune aurora but does not explain the global phenomenon.

Paranicas, C.↗
NASA NTRS1994

The characteristic of the magnetopause reconnection X-line deduced from low-altitude satellite observations of cusp ions

We present an analysis of a 'quasi-steady' cusp ion dispersion signature observed at low altitudes. We reconstruct the field-parallel part of the Cowley-D ion distribution function, injected into the open low-latitude boundary layer (LLBL) in the vicinity of the reconnection X-line. From this we find the field parallel magnetosheath flow at the X-line was only 20 +/- 60 km/s, placing the reconnection site close to the flow streamline which is perpendicular to the magnetosheath field. Using interplanetary data and assuming the subsolar magnetopause is in pressure balance, we derive a wealth of information about the X-line, including: the density, flow, magnetic field and Alfven speed of the magnetosheath; the magnetic shear across the X-line; the de-Hoffman Teller speed with which field lines emerge from the X-line; the magnetospheric field; and the ion transmission factor across the magnetopause. The results indicate that some heating takes place near the X-line as the ions cross the magnetopause, and that sheath densities may be reduced in a plasma depletion layer. We also compute the reconnection rate. Despite its quasi-steady appearance on an ion spectrogram, this cusp is found to reveal a large pulse of enhanced reconnection rate.

Lockwood, M.↗
NASA NTRS1995

The variability of the double-peaked Balmer lines in the active nucleus of NGC 1097

We present spectroscopic observations of the nucleus of the Seyfert/low-ionization nuclear emission-line region galaxy NGC 1097 spanning the period 1991-1994. The goal was to monitor anticipated variations of the broad, double-peaked Balmer lines which appeared abruptly in 1991. We find that the broad Balmer lines have varied significantly over the monitoring period, both in their integrated fluxes and in their profile shapes. The integrated H-alpha flux has decreased by a factor of 2, the (H-alpha)/(H-beta) ratio has increased, and the originally asymmetric H-alpha profile has become symmetric. The decline of the H-alpha flux and the change in the (H-alpha)/(H-beta) ratio can be interpreted as consequences of either increased obscuration along the line of sight, or a decline in the ionizing continuum, but neither of these scenarios can account for the change in profile shapes. A model attributing the line emission to a precessing elliptical ring around a 10(exp 6) solar mass nuclear black hole can reproduce the observed profile variations. In this scenario, the line-emitting ring is the result of the tidal disruption of a star by the black hole. Alternative scenarios associating the broad-line emission with a collimated bipolar outflow also remain viable, but binary black holes and inhomogeneous accretion disks are disfavored by the observed pattern of variability.

Storchi-Bergmann, Thaisa↗
NASA NTRS1995

Emission line signatures of anisotropic turbulence in accretion disks

We investigate observable effects of anisotropic turbulence on the velocity profiles and eclipse behavior of emission lines from accretion disks. Turbulence expands the local line broadening profile, enhancing the surface brightness of saturated emission lines. Anisotropic turbulence produces anisotropic emission in such lines. The effects become observable when the turbulence exceeds the thermal velocity. Each term in the velocity-velocity correlation matrix produces a distinctive azimuthal pattern of enhanced emission-line surface brightness on the face of the accretion disk. These patterns express themselves as changes in the observable shapes of the disk's emission lines. The best place to look for turbulence effects is in saturated emission lines of heavy elements such as Ca, Mg, and Fe, which have a smaller thermal velocity at a given sound speed and at moderate inclination (60-70 degrees), since the Keplerian shear broadening dominates at higher inclinations.

Horne, Keith↗
NASA NTRS1994

Steps toward determination of the size and structure of the broad-line region in active galactic nuclei. 8: An intensive HST, IUE, and ground-based study of NGC 5548

We present the data and initial results from a combined HST/IUE/ground-based spectroscopic monitoring campaign on the Seyfert 1 galaxy NGC 5548 that was undertaken in order to address questions that require both higher temporal resolution and higher signal-to-noise ratios than were obtained in our previous multiwavelength monitoring of this galaxy in 1988-89. IUE spectra were obtained once every two days for a period of 74 days beginning on 14 March 1993. During the last 39 days of this campaign, spectroscopic observations were also made with the HST Faint Object Spectrograph (FOS) on a daily basis. Ground-based observations, consisting of 165 optical spectra and 77 photometric observations (both CCD imaging and aperture photometry), are reported for the period 1992 October to 1993 September, although much of the data are concentrated around the time of the satellite-based program. These data constitute a fifth year of intensive optical monitoring of this galaxy. In this contribution, we describe the acquisition and reduction of all of the satellite and ground-based data obtained in this program. We describe in detail various photometric problems with the FOS and explain how we identified and corrected for various anomalies. During the HST portion of the monitoring campaign, the 1350 A continuum flux is found to have varied by nearly a factor of two. In other wavebands, the continuum shows nearly identical behavior, except that the amplitude of variability is larger at shorter wavelengths, and the continuum light curves appear to show more short time-scale variability at shorter wavelengths. The broad emission lines also vary in flux, with amplitudes that are slightly smaller than the UV continuum variations and with a small time delay relative to the UV continuum. On the basis of simple time-series analysis of the UV and optical continuum and emission line light curves, we find (1) that the ultraviolet and optical continuum variations are virtually simultaneous, with any lag between the 1350 A continuum and the 5100 A continuum amounting to less than about one day; (2) that the variations in the highest ionization lines observed, He II lambda 1640 and N V lambda 1240, lag behind the continuum variations by somewhat less than 2 days, and (3) that the velocity field of the C IV-emitting region is not dominated by radial motion. The results on the C IV velocity field are preliminary and quite uncertain, but there are some weak indications that the emission-line (wings absolute value of Delta upsilon is greater than or equal to 3000 km/s) respond to continuum variations slightly more rapidly than does the core. The optical observations show that the variations in the broad H beta line flux follow the continuum variations with a time lag of around two weeks, about twice the lag for Ly alpha and C IV, as in our previous monitoring campaign on this same galaxy. However, the lags measured for Ly alpha, C IV, and H Beta are each slightly smaller than previously determined. We confirm two trends reported earlier, namely (1) that the UV/optical continuum becomes 'harder' as it gets brighter, and (2) that the highest ionization emission lines have the shortest lags, thus indicating radial ionization stratificatin of a broad-line region that spans over an order of magnitude range in radius.

Korista, K.↗
NASA NTRS1995

Thermal Line Shift and Broadening of Ho(3+) in Y3AI5O12 and Lu3AIO12

The interaction between the active ion and the host lattice manifests itself in two distinct ways: the static interaction with the crystal field that causes the splitting of the free ion energy levels and the active interaction through the surrounding phonon system that produces temperature dependent characteristics in the optical spectrum of the ion (e.g. line broadening and line shift). The strength of the splitting depends heavily on the electronic configuration of the atom. The model give by McCumber and Sturge describes the thermal effects on line width and position above 77 K with Raman scattering of Debye model phonons. These processes predict a Lorentzian line shape. However, below 77 K the principal contributions are from crystal inhomogeneities that result in a Gaussian line shape. We have investigated the experimental Stark levels as well as the thermal effects on the line width and the position of trivalent holmium ions in both yttrium aluminum garnet, Y3Al5O12 (YAG) and lutetium aluminum garnet, Lu3Al5O12 (LuAG) crystals. We have compared the Stark levels of the (5)I(6) state, and the thermal line shift and broadening of an isolated transition (Z2 to X13) between the (5)I(8) and (5)I(6) stark levels in these crystals. This transition occurs in the near infrared region at approximately 1117 nm.

Snoke, Elizabeth R.↗
NASA NTRS1995

Flow properties along field lines in a 3-D tilted-dipole geometry

A 3-D MHD simulation of a global, tilted-dipole solar wind flow pattern is analyzed to determine flow properties along individual magnetic field lines. In the model, flow conditions near the Sun are chosen to provide a reasonable match to the interplanetary configuration prevailing during the recent south polar passage by Ulysses, i.e., a streamer belt inclined approximately 30 deg to the solar equator and speeds ranging from 325-800 km/s. Field lines all across the stream pattern are traced from 1 to 10 AU by following the motion of marker particles embedded in the flow. It is found that those field lines threading the core of the interaction region are subject to significant latitudinal and relative longitudinal displacement over this range of heliocentric distance. Thus, observations taken at a fixed latitude in the inner solar system sample, over the course of a solar rotation, field lines which connect to a range of latitudes in the outer heliosphere. Maps of the field line displacements are presented to help visualize these connections. In addition, it is found that depending upon the location relative to the CIR structure, the radial evolution of fluid elements frozen to different field lines can deviate considerably from that of the canonical solar wind. That is, for selected subsets of field lines, large speed changes (not just at shocks) can be experienced; the density variation can be far from 1/r(exp 2), and the magnetic field intensity need not decay monotonically with distance.

Pizzo, V. J.↗
NASA NTRS1996

The Micromechanics of the Moving Contact Line

The proposed research is divided into three components concerned with molecular structure, molecular orientation, and continuum averages of discrete systems. In the experimental program, we propose exploring how changes in interfacial molecular structure generate contact line motion. Rather than rely on the electrostatic and electrokinetic fields arising from the molecules themselves, we augment their interactions by an imposed field at the solid/liquid interface. By controling the field, we can manipulate the molecular structure at the solid/liquid interface. In response to controlled changes in molecular structure, we observe the resultant contact line motion. In the analytical portion of the proposed research we seek to formulate a system of equations governing fluid motion which accounts for the orientation of fluid molecules. In preliminary work, we have focused on describing how molecular orientation affects the forces generated at the moving contact line. Ideally, as assumed above, the discrete behavior of molecules can be averaged into a continuum theory. In the numerical portion of the proposed research, we inquire whether the contact line region is, in fact, large enough to possess a well-defined average. Additionally, we ask what types of behavior distinguish discrete systems from continuum systems. Might the smallness of the contact line region, in itself, lead to behavior different from that in the bulk? Taken together, our proposed research seeks to identify and accurately account for some of the molecular dynamics of the moving contact line, and attempts to formulate a description from which one can compute the forces at the moving contact line.

Han, Minsub↗
NASA NTRS1997

Evaluating Possible Heating Mechanisms Using the Transition Region Line Profiles of Late-Type Stars

Our analysis of high-resolution Goddard High-Resolution Spectrograph (GHRS) spectra of late-type stars shows that the Si IV and C IV lines formed near 10(exp 5) K can be decomposed into the sum of two Gaussians, a broad component and a narrow component. We find that the flux contribution of the broad components is correlated with both the C IV and X-ray surface fluxes. For main-sequence stars, the widths of the narrow components suggest subsonic nonthermal velocities, and there appears to be a tight correlation between these nonthermal velocities and stellar surface gravity [xi(sub nc) varies as g(sup (-.68 +/-.07))]. For evolved stars with lower surface gravities, the nonthermal velocities suggested by the narrow components are at or just above the sound speed. Nonthermal velocities computed from the widths of the broad components are always highly supersonic. We propose that the broad components are diagnostics for microflare heating. Turbulent dissipation and Alfven waves are both viable candidates for the narrow component heating mechanism. A solar analog for the broad components might be the 'explosive events' detected by the High-Resolution Telescope and Spectrograph (HRTS) experiment. The broad component we observe for the Si IV lambda 1394 line of alpha Cen A, a star that is nearly identical to the Sun, has a FWHM of 109 +/- 10 km/s and is blueshifted by 9 +/- 3 km/s relative to the narrow component. Both of these properties are consistent with the properties of the solar explosive events. However, the alpha Cen A broad component accounts for 25% +/- 4% of the total Si IV line flux, while solar explosive events are currently thought to account for no more than 5% of the Sun's total transition region emission. This discrepancy must be resolved before the connection between broad components and explosive events can be positively established. In addition to our analysis of the Si IV and C IV lines of many stars, we also provide a more thorough analysis of all of the available GHRS data for alpha Cen A (G2 V) and alpha Cen B (K1 V). We find that the transition region lines of both stars have redshifts almost identical to those observed on the Sun: showing an increase with line formation temperature up to about log T = 5.2 and then a rapid decrease. Using the O IV] lines as density diagnostics, we compute electron densities of log n(sub e) = 9.65 +/- 0.20 and log n(sub e) = 9.50 +/- 0.30 for alpha Cen A and alpha Cen B, respectively.

Wood, Brian E.↗
NASA NTRS1996

Line Profile of H Lyman-Beta Emission from Dissociative Excitation of H2

A high-resolution ultraviolet spectrometer was employed for a measurement of the H Lyman-Beta(H L(sub Beta)) emission Doppler line profile at 1025.7 A from dissociative excitation of H2 by electron impact. Analysis of the deconvolved line profile reveals the existence of a narrow central peak, less than 30 mA full width at half maximum (FWHM), and a broad pedestal base about 260 mA FWHM. Analysis of the red wing of the line profile is complicated by a group of Wemer and Lyman rotational lines 160-220 mA from the line center. Analysis of the blue wing of the line profile gives the kinetic-energy distribution. There are two main kinetic-energy components to the H(3p) distribution: (1) a slow distribution with a peak value near 0 eV from singly excited states, and (2) a fast distribution with a peak contribution near 7 eV from doubly excited states. Using two different techniques, the absolute cross section of H L(sub Beta)p is found to be 3.2+/-.8 x 10(exp -19)sq cm at 100-eV electron impact energy. The experimental cross-section and line-profile results can be compared to previous studies of H(alpha) (6563.7 A) for principal quantum number n=3 and L(sub alpha)(1215.7 A) for n=2.

Ajello, Joseph M.↗
NASA NTRS1997

Using Strong Solar Coronal Emission Lines as Coronal Flux Proxies

A comparison of Skylab results with observations of the strong EUV lines of Fe XVI at 335 A and 361 A from the Goddard Solar EUV Rocket Telescope and Spectrograph (SERTS) flight of 1989 suggests that these lines, and perhaps others observed with SERTS, might offer good proxies for estimating the total coronal flux over important wavelength ranges. In this paper, we compare SERTS observations from a later, 1993 flight with simultaneous cospatial Yohkoh soft X-ray observations to test this suggestion over the energy range of the Soft X-ray Telescope (SXT) on Yohkoh. Both polynomial and power-law fits are obtained, and errors are estimated, for the SERTS lines of Fe XVI 335 A and 361 A, Fe XV 284 A and 417 A, and Mg IX 368 A. It is found that the power-law fits best cover the full range of solar conditions from quiet Sun through active region, though not surprisingly the 'cooler' Mg IX 368 A line proves to be a poor proxy. The quadratic polynomial fits yield fair agreement over a large range for all but the Mg IX line, but the linear fits fail conspicuously when extrapolated into the quiet Sun regime. The implications of this work for the He 11 304 A line formation problem are briefly considered. The paper concludes with a discussion of the value of these iron lines observed with SERTS for estimating stellar coronal fluxes, as observed for example with the EUVE satellite.

Falconer, David A.↗
NASA NTRS1999

The Role of Velocity Redistribution in Enhancing the Intensity of the He II 304 A Line in the Quiet Sun Spectrum

We present observational evidence of the effect of small scale ("microturbulent") velocities in enhancing the intensity of the He II lambda304 line with respect to other transition region emission lines, a process we call "velocity redistribution". We first show results from the 1991 and 1993 flights of SERTS (Solar EUV Rocket Telescope and Spectrograph). The spectral resolution of the SERTS instrument was sufficient to infer that, at the spatial resolution of 5", the line profile is nearly gaussian both in the quiet Sun and in active regions. We were then able to determine, for the quiet Sun, a lower limit for the amplitude of non-thermal motions in the region of formation of the 304 A line of the order of 10 km/s. We estimated that, in the presence of the steep temperature gradients of the solar Transition Region (TR), velocities of this magnitude can significantly enhance the intensity of that line, thus at least helping to bridge the gap between calculated and observed values. We also estimated the functional dependence of such an enhancement on the relevant parameters (non-thermal velocities, temperature gradient, and pressure). We then present results from a coordinated campaign, using SOHO/CDS and H-alpha spectroheliograms from Coimbra Observatory, aimed at determining the relationship between regions of enhanced helium emission and chromospheric velocity fields and transition region emission in the quiescent atmosphere. Using these data, we examined the behavior of the He II lambda304 line in the quiet Sun supergranular network and compared it with other TR lines, in particular with O III lambda600. We also examined the association of 304 A emission with the so-called "coarse dark mottle", chromospheric structures seen in H-alpha red wing images and associated with spicules. We found that all these observations are consistent with the velocity redistribution picture.

Andretta, Vincenzo↗
NASA NTRS2000

Emission Line Spectra from Low-Density Laboratory Plasmas

Using spectroscopic equipment optimized for laboratory astrophysics, we are performing systematic measurements of the line emission from astrophysically relevant ions in the wavelength band between 1 and 400 Angstroms important to X-ray missions such as Chandra, XMM, Astro-E, and EUVE. Obtained in a controlled laboratory setting at electron densities similar to those found in stellar coronae, the data are used to test spectral modeling codes for accuracy and completeness. Our effort includes the compilation of the iron L-shell emission lines from 6-18 Angstroms and the iron M-shell emission lines from 50-200 Angstroms. Many lines have been identified for the first time, and the fluxes from lines missing in the spectral modeling codes are assessed. Our measurements also assess the accuracy of line excitation calculations, including direct electron-impact excitation, dielectronic recombination, and resonance excitation. These measurements yield a calibration of specific diagnostic line ratios. Examples of our current measurements are given.

Beiersdorfer, P.↗
NASA NTRS2000

Limits on Line Bisector Variability for Stars with Extrasolar Planets

We present an analysis of high-resolution synoptic spectra of ten F- and G-type stars, seven of which exhibit periodic radial velocity variations due to the presence of one or more substellar companions. We searched for subtle periodic variations in photospheric line asymmetry, as characterized by line bisectors. In principle, periodic variations in line asymmetry observed at lower spectral resolution could mimic the radial velocity signature of a companion, but we find no significant evidence of such behavior in our data. Observations were obtained from 1998 March to 1999 February using the National Solar Observatory (NSO) 1.52-m McMath-Pierce Solar Telescope Facility on Kitt Peak in conjunction with the solar-stellar spectrograph, achieving a resolving power of 1.2x10(exp5). To characterize line asymmetry, we first measured line bisectors for the unblended Fe I photospheric line at 625.26 nm. To improve sensitivity to small fluctuations, we then combined points in each bisector to form a velocity displacement with respect to the line core. We searched for periodic variations in this displacement, finding no substantial difference between stars with substellar companions and those without reported companions. We find no correlation between bisector velocity displacement and the known orbital phase of substellar companions around our target stars. Simulations of a periodic signal with noise levels that mimic our measurement errors suggest that we can exclude bisector variations with amplitudes greater than about 20 m/s. These results support the conclusion that extrasolar planets best explain the observed periodic variations in radial velocity.

Povich, M. S.↗