Station-Keeping Requirements for Constellations of Free-Flying Collectors Used for Astronomical Imaging in Space

The accuracy requirements on station-keeping for constellations of free-flying collectors coupled as (future) imaging arrays in space for astrophysics applications are examined. The basic imaging element of these arrays is the two-element interferometer. Accurate knowledge of two quantities is required: the \textit{projected baseline length}, which is the distance between the two interferometer elements projected on the plane tranverse to the line of sight to the target; and the \textit{optical path difference}, which is the difference in the distances from that transverse plane to the beam combiner. ``Rules-of-thumb'' are determined for the typical accuracy required on these parameters. The requirement on the projected baseline length is a \textit{knowledge} requirement and depends on the angular size of the targets of interest; it is generally at a level of half a meter for typical stellar targets, decreasing to perhaps a few centimeters only for the widest attainable fields of view. The requirement on the optical path difference is a \textit{control} requirement and is much tighter, depending on the bandwidth of the signal; it is at a level of half a wavelength for narrow (few %) signal bands, decreasing to $\approx 0.2 \lambda$ for the broadest bandwidths expected to be useful. Translation of these requirements into engineering requirements on station-keeping accuracy depends on the specific details of the collector constellation geometry. Several examples are provided to guide future application of the criteria presented here. Some implications for the design of such collector constellations and for the methods used to transform the information acquired into images are discussed.Comment: 13 pages, 6 figures, accepted 6/29/07 for the August 2007 issue of PAS

Calibration of Low-Frequency, Wide-Field Radio Interferometers Using Delay/Delay-Rate Filtering

We present a filtering technique that can be applied to individual baselines of wide-bandwidth, wide-field interferometric data to geometrically select regions on the celestial sphere that contain primary calibration sources. The technique relies on the Fourier transformation of wide-band frequency spectra from a given baseline to obtain one-dimensional "delay images", and then the transformation of a time-series of delay images to obtain two-dimensional "delay/delay-rate images." Source selection is possible in these images given appropriate combinations of baseline, bandwidth, integration time and source location. Strong and persistent radio frequency interference (RFI) limits the effectiveness of this source selection owing to the removal of data by RFI excision algorithms. A one-dimensional, complex CLEAN algorithm has been developed to compensate for RFI-excision effects. This approach allows CLEANed, source-isolated data to be used to isolate bandpass and primary beam gain functions. These techniques are applied to data from the Precision Array for Probing the Epoch of Reionization (PAPER) as a demonstration of their value in calibrating a new generation of low-frequency radio interferometers with wide relative bandwidths and large fields-of-view.Comment: 17 pages, 6 figures, 2009AJ....138..219

Comments on the tethered galaxy problem

In a recent paper Davis et al. make the counter intuitive assertion that a galaxy held `tethered' at a fixed distance from our own could emit blueshifted light. Moreover, this effect may be derived from the simplest Friedmann-Robertson-Walker spacetimes and the (0.3,0.7) case which is believed to be a good late time model of our own universe. In this paper we recover the previous authors' results in a more transparent form. We show how their results rely on a choice of cosmological distance scale and revise the calculations in terms of observable quantities which are coordinate independent. By this method we see that, although such a tethering would reduce the redshift of a receding object, it would not do so sufficiently to cause the proposed blueshift. The effect is also demonstrated to be much smaller than conjectured below the largest intergalactic scales. We also discuss some important issues, raised by this scenario, relating to the interpretation of redshift and distance in relativistic cosmology.Comment: 6 pages, 3 figures, submitted to Am.J.Phy

The Importance of Phase in Nulling Interferometry and a Three Telescope Closure-Phase Nulling Interferometer Concept

We discuss the theory of the Bracewell nulling interferometer and explicitly demonstrate that the phase of the "white light" null fringe is the same as the phase of the bright output from an ordinary stellar interferometer. As a consequence a "closure phase" exists for a nulling interferometer with three or more telescopes. We calculate the phase offset as a function of baseline length for an Earth-like planet around the Sun at 10 pc, with a contrast ratio of $10^{-6}$ at 10 $\mu$m. The magnitude of the phase due to the planet is $\sim 10^{-6}$ radians, assuming the star is at the phase center of the array. Although this is small, this phase may be observable in a three-telescope nulling interferometer that measures the closure phase. We propose a simple non-redundant three-telescope nulling interferometer that can perform this measurement. This configuration is expected to have improved characteristics compared to other nulling interferometer concepts, such as a relaxation of pathlength tolerances, through the use of the "ratio of wavelengths" technique, a closure phase, and better discrimination between exodiacal dust and planets

Displacement- and Timing-Noise Free Gravitational-Wave Detection

Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus realizable by shot-noise-limited laser interferometry. This is possible due to two reasons: first, gravitational waves and displacement disturbances contribute to light propagation times in different manners; second, for an N-detector system, the number of signal channels is of the order O(N^2), while the total number of timing- and displacement-noise channels is of the order O(N).Comment: 4 pages, 3 figures; mistake correcte

Boundary crossing Random Walks, clinical trials and multinomial sequential estimation

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or multinomial Random Walks which are observed until they reach a boundary. An application to clinical trials is presented

Bringing closure to microlensing mass measurement

Interferometers offer multiple methods for studying microlensing events and determining the properties of the lenses. We investigate the study of microlensing events with optical interferometers, focusing on narrow-angle astrometry, visibility, and closure phase. After introducing the basics of microlensing and interferometry, we derive expressions for the signals in each of these three channels. For various forecasts of the instrumental performance, we discuss which method provides the best means of measuring the lens angular Einstein radius theta_E, a prerequisite for determining the lens mass. If the upcoming generation of large-aperture, AO-corrected long baseline interferometers (e.g. VLTI, Keck, OHANA) perform as well as expected, theta_E may be determined with signal-to-noise greater than 10 for all bright events. We estimate that roughly a dozen events per year will be sufficiciently bright and have long enough durations to allow the measurement of the lens mass and distance from the ground. We also consider the prospects for a VLTI survey of all bright lensing events using a Fisher matrix analysis, and find that even without individual masses, interesting constraints may be placed on the bulge mass function, although large numbers of events would be required.Comment: 23 pages, aastex, submitted to Ap

Direct Detection of the Brown Dwarf GJ 802B with Adaptive Optics Masking Interferometry

We have used the Palomar 200" Adaptive Optics (AO) system to directly detect the astrometric brown dwarf GJ 802B reported by Pravdo et al. 2005. This observation is achieved with a novel combination of aperture masking interferometry and AO. The dynamical masses are 0.175$\pm$0.021 M$_\odot$ and 0.064$\pm$0.032 M$_\odot$ for the primary and secondary respectively. The inferred absolute H band magnitude of GJ 802B is M$_H$=12.8 resulting in a model-dependent T$_\mathrm{eff}$ of 1850 $\pm$ 50K and mass range of 0.057--0.074 M$_\odot$.Comment: 4 Pages, 5 figures, emulateapj format, submitted to ApJ

The last gasps of VY CMa: Aperture synthesis and adaptive optics imagery

We present new observations of the red supergiant VY CMa at 1.25 micron, 1.65 micron, 2.26 micron, 3.08 micron and 4.8 micron. Two complementary observational techniques were utilized: non-redundant aperture masking on the 10-m Keck-I telescope yielding images of the innermost regions at unprecedented resolution, and adaptive optics imaging on the ESO 3.6-m telescope at La Silla attaining extremely high (~10^5) peak-to-noise dynamic range over a wide field. For the first time the inner dust shell has been resolved in the near-infrared to reveal a one-sided extension of circumstellar emission within 0.1" (~15 R_star) of the star. The line-of-sight optical depths of the circumstellar dust shell at 1.65 micron, 2.26 micron, and 3.08 micron have been estimated to be 1.86 +/- 0.42, 0.85 +/- 0.20, and 0.44 +/- 0.11. These new results allow the bolometric luminosity of VY~CMa to be estimated independent of the dust shell geometry, yielding L_star ~ 2x10^5 L_sun. A variety of dust condensations, including a large scattering plume and a bow-shaped dust feature, were observed in the faint, extended nebula up to 4" from the central source. While the origin of the nebulous plume remains uncertain, a geometrical model is developed assuming the plume is produced by radially-driven dust grains forming at a rotating flow insertion point with a rotational period between 1200-4200 years, which is perhaps the stellar rotational period or the orbital period of an unseen companion.Comment: 25 pages total with 1 table and 5 figures. Accepted by Astrophysical Journal (to appear in February 1999

A toy model of the five-dimensional universe with the cosmological constant

A value of the cosmological constant in a toy model of the five-dimensional universe is calculated in such a manner that it remains in agreement with both astronomical observations and the quantum field theory concerning the zero-point fluctuations of the vacuum. The (negative) cosmological constant is equal to the inverse of the Planck length squared, which means that in the toy model the vanishing of the observed value of the cosmological constant is a consequence of the existence of an energy cutoff exactly at the level of the Planck scale. In turn, a model for both a virtual and a real particle-antiparticle pair is proposed which describes properly some energetic properties of both the vacuum fluctuations and created particles, as well as it allows one to calculate the discrete "bare" values of an elementary-particle mass, electric charge and intrinsic angular momentum (spin) at the energy cutoff. The relationships between the discussed model and some phenomena such as the Zitterbewegung and the Unruh-Davies effect are briefly analyzed, too. The proposed model also allows one to derive the Lorentz transformation and the Maxwell equations while considering the properties of the vacuum filled with the sea of virtual particles and their antiparticles. Finally, the existence of a finite value of the vacuum-energy density resulting from the toy model leads us to the formulation of dimensionless Einstein field equations which can be derived from the Lagrangian with a dimensionless (naively renormalized) coupling constant.Comment: 52 pages, 1 figure; a post-final, rewritten version with a number of new remarks and conclusion