Interferometric Astrometry of Proxima Centauri and Barnard's Star Using Hubble Space Telescope Fine Guidance Sensor 3: Detection Limits for sub-Stellar Companions

We report on a sub-stellar companion search utilizing interferometric fringe-tracking astrometry acquired with Fine Guidance Sensor 3 (FGS 3) on the Hubble Space Telescope. Our targets were Proxima Centauri and Barnard's Star. We obtain absolute parallax values for Proxima Cen pi_{abs} = 0.7687 arcsecond and for Barnard's Star pi_{abs} = 0.5454 arcsecond. Once low-amplitude instrumental systematic errors are identified and removed, our companion detection sensitivity is less than or equal to one Jupiter mass for periods longer than 60 days for Proxima Cen. Between the astrometry and the radial velocity results we exclude all companions with M > 0.8M_{Jup} for the range of periods 1 < P < 1000 days. For Barnard's Star our companion detection sensitivity is less than or equal to one Jupiter mass for periods long er than 150 days. Our null results for Barnard's Star are consistent with those of Gatewood (1995).Comment: 35 pages, 13 figures, to appear in August 1999 A

Photometry of Proxima Centauri and Barnard's Star Using HST Fine Guidance Sensor 3: A Search for Periodic Variations

We have observed Proxima Centauri and Barnard's Star with Hubble Space Telescope Fine Guidance Sensor 3. Proxima Centauri exhibits small-amplitude, periodic photometric variations. Once several sources of systematic photometric error are corrected, we obtain 2 milli-magnitude internal photometric precision. We identify two distinct behavior modes over the past four years: higher amplitude, longer period; smaller amplitude, shorter period. Within the errors one period (P ~ 83d) is twice the other. Barnard's Star shows very weak evidence for periodicity on a timescale of approximately 130 days. If we interpret these periodic phenomena as rotational modulation of star spots, we identify three discrete spots on Proxima Cen and possibly one spot on Barnard's Star. We find that the disturbances change significantly on time scales as short as one rotation period.Comment: 39 pages, 17 figure

The Distance To The Hyades Cluster Based On Hubble Space Telescope Fine Guidance Sensor Parallaxes

Trigonometric parallax observations made with the Hubble Space Telescope (HST) Fine Guidance Sensor (FGS) 3 of seven Hyades members in six fields of view have been analyzed along with their proper motions to determine the distance to the cluster. Knowledge of the convergent point and mean proper motion of the Hyades is critical to the derivation of the distance to the center of the cluster. Depending on the choice of the proper-motion system, the derived cluster center distance varies by 9%. Adopting a reference distance of 46.1 pc or m - M = 3.32, which is derived from the ground-based parallaxes in the General Catalogue of Trigonometric Stellar Parallaxes (1995 edition), the FK5/PPM proper-motion system yields a distance 4% larger, while the Hanson system yields a distance 2% smaller. The HST FGS parallaxes reported here yield either a 14% or 5% larger distance, depending on the choice of the proper-motion system. Orbital parallaxes (Torres et al.) yield an average distance 4% larger than the reference distance. The variation in the distance derived from the HST data illustrates the importance of the proper-motion system and the individual proper motions to the derivation of the distance to the Hyades center; therefore, a full utilization of the HST FGS parallaxes awaits the establishment of an accurate and consistent proper-motion system.NASA HST GTO, HF-1042.01-93A, HF-1046.01-93A, NAS526555Astronom

Atmospheric Density Uncertainty Quantification for Satellite Conjunction Assessment

Conjunction assessment requires knowledge of the uncertainty in the predicted orbit. Errors in the atmospheric density are a major source of error in the prediction of low Earth orbits. Therefore, accurate estimation of the density and quantification of the uncertainty in the density is required. Most atmospheric density models, however, do not provide an estimate of the uncertainty in the density. In this work, we present a new approach to quantify uncertainties in the density and to include these for calculating the probability of collision Pc. For this, we employ a recently developed dynamic reduced-order density model that enables efficient prediction of the thermospheric density. First, the model is used to obtain accurate estimates of the density and of the uncertainty in the estimates. Second, the density uncertainties are propagated forward simultaneously with orbit propagation to include the density uncertainties for Pc calculation. For this, we account for the effect of cross-correlation in position uncertainties due to density errors on the Pc. Finally, the effect of density uncertainties and cross-correlation on the Pc is assessed. The presented approach provides the distinctive capability to quantify the uncertainty in atmospheric density and to include this uncertainty for conjunction assessment while taking into account the dependence of the density errors on location and time. In addition, the results show that it is important to consider the effect of cross-correlation on the Pc, because ignoring this effect can result in severe underestimation of the collision probability.Comment: 15 pages, 6 figures, 5 table

Photometry of Proxima Centauri and Barnard\u27s Star Using Hubble Space Telescope Fine Guidance Sensor 3: A Search for Periodic Variations

We have observed Proxima Centauri and Barnard\u27s star with the Hubble Space Telescope Fine Guidance Sensor 3. Proxima Cen exhibits small-amplitude, periodic photometric variations. Once several sources of systematic photometric error are corrected, we obtain 2 mmag internal photometric precision. We identify two distinct behavior modes over the past 4 years: higher amplitude, longer period and smaller amplitude, shorter period. Within the errors, one period (P ~ 83 days) is twice the other. Barnard\u27s star shows very weak evidence for periodicity on a timescale of approximately 130 days. If we interpret these periodic phenomena as rotational modulation of starspots, we identify three discrete spots on Proxima Cen and possibly one spot on Barnard\u27s star. We find that the disturbances change significantly on timescales as short as one rotation period

Adaptively Indistinguishable Garbled Circuits

A garbling scheme is used to garble a circuit $C$ and an input $x$ in a way that reveals the output $C(x)$ but hides everything else. An adaptively secure scheme allows the adversary to specify the input $x$ after seeing the garbled circuit. Applebaum et al. (CRYPTO \u2713) showed that in any garbling scheme with adaptive simulation-based security, the size of the garbled input must exceed the output size of the circuit. Here we show how to circumvent this lower bound and achieve significantly better efficiency under the minimal assumption that one-way functions exist by relaxing the security notion from simulation-based to indistinguishability-based. We rely on the recent work of Hemenway et al. (CRYPTO \u2716) which constructed an adaptive simulation-based garbling scheme under one-way functions. The size of the garbled input in their scheme is as large as the output size of the circuit plus a certain pebble complexity of the circuit, where the latter is (e.g.,) bounded by the space complexity of the computation. By building on top of their construction and adapting their proof technique, we show how to remove the output size dependence in their result when considering indistinguishability-based security. As an application of the above result, we get a symmetric-key functional encryption based on one-way functions, with indistinguishability-based security where the adversary can obtain an unbounded number of function secret keys and then adaptively a single challenge ciphertext. The size of the ciphertext only depends on the maximal pebble complexity of each of the functions but not on the number of functions or their circuit size

Astrometry with Hubble Space Telescope: A Parallax of the Fundamental Distance Calibrator RR Lyrae

We present an absolute parallax and relative proper motion for the fundamental distance scale calibrator, RR Lyr. We obtain these with astrometric data from FGS 3, a white-light interferometer on HST. We find $\pi_{abs} = 3.82 \pm 0.2$ mas. Spectral classifications and VRIJHKT$_2$M and DDO51 photometry of the astrometric reference frame surrounding RR Lyr indicate that field extinction is low along this line of sight. We estimate =0.07\pm0.03 for these reference stars. The extinction suffered by RR Lyr becomes one of the dominant contributors to the uncertainty in its absolute magnitude. Adopting the average field absorption, =0.07 \pm 0.03, we obtain M_V^{RR} = 0.61 ^{-0.11}_{+0.10}. This provides a distance modulus for the LMC, m-M = 18.38 - 18.53^{-0.11}_{+0.10} with the average extinction-corrected magnitude of RR Lyr variables in the LMC, , remaining a significant uncertainty. We compare this result to more than 80 other determinations of the distance modulus of the LMC.Comment: Several typos corrected. To appear in The Astronomical Journal, January 200

Precise Masses for Wolf 1062 AB from Hubble Space Telescope Interferometric Astrometry and McDonald Observatory Radial Velocities

We present an analysis of astrometric data from FGS 3, a white-light interferometer on {\it HST}, and of radial velocity data from two ground-based campaigns. We model the astrometric and radial velocity measurements simultaneously to obtain parallax, proper motion and component masses for Wolf 1062 = Gl 748 AB (M3.5V). To derive the mass fraction, we relate FGS 3 fringe scanning observations of the science target to a reference frame provided by fringe tracking observations of a surrounding star field. We obtain an absolute parallax $\pi_{abs} = 98.0 \pm 0.4$ milliseconds of arc, yielding {\cal M}_A = 0.379 \pm 0.005{\cal M}_{\sun} and {\cal M}_B= 0.192 \pm 0.003 {\cal M}_{\sun}, high quality component masses with errors of only 1.5%.Comment: 13 pages, 7 figures. To appear in AJ March 200