Frequency Limits on Naked-Eye Optical Transients Lasting from Minutes to Years

How often do bright optical transients occur on the sky but go unreported? To constrain the bright end of the astronomical transient function, a systematic search for transients that become bright enough to be noticed by the unaided eye was conducted using the all-sky monitors of the Night Sky Live network. Two fisheye continuous cameras (CONCAMs) operating over three years created a data base that was searched for transients that appeared in time-contiguous CCD frames. Although a single candidate transient was found (Nemiroff and Shamir 2006), the lack of more transients is used here to deduce upper limits to the general frequency of bright transients. To be detected, a transient must have increased by over three visual magnitudes to become brighter than visual magnitude 5.5 on the time scale of minutes to years. It is concluded that, on the average, fewer than 0.0040 ($t_{dur} / 60$ seconds) transients with duration $t_{dur}$ between minutes and hours, occur anywhere on the sky at any one time. For transients on the order of months to years, fewer than 160 ($t_{dur} / 1$ year) occur, while for transients on the order of years to millennia, fewer than 50 ($t_{dur}/1$ year)$^2$ occur.Comment: Accepted for publication in A

Extension of an Exponential Light Curve GRB Pulse Model Across Energy Bands

A simple mathematical model of GRB pulses in time, suggested in Norris et al. (2005), is extended across energy. For a class of isolated pulses, two of those parameters appear effectively independent of energy. Specifically, statistical fits indicate that pulse amplitude $A$ and pulse width $\tau$ are energy dependent, while pulse start time and pulse shape are effectively energy independent. These results bolster the Pulse Start and Pulse Scale conjectures of Nemiroff (2000) and add a new Pulse Shape conjecture which states that a class of pulses all have the same shape. The simple resulting pulse counts model is $P(t,E) = A(E) \ {\rm exp} (-t/\tau(E) - \tau(E)/t)$, where $t$ is the time since the start of the pulse. This pulse model is found to be an acceptable statistical fit to many of the fluent separable BATSE pulses listed in Norris et al. (2005). Even without theoretical interpretation, this cross-energy extension may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters.Comment: 11 pages, 5 figures. Accepted by MNRA

Visual Distortions Near a Neutron Star and Black Hole

The visual distortion effects visible to an observer traveling around and descending to the surface of an extremely compact star are described. Specifically, trips to a ``normal" neutron star, a black hole, and an ultracompact neutron star with extremely high surface gravity, are described. Concepts such as multiple imaging, red- and blue-shifting, conservation of surface brightness, the photon sphere, and the existence of multiple Einstein rings are discussed in terms of what the viewer would see. Computer generated, general relativistically accurate illustrations highlighting the distortion effects are presented and discussed. A short movie (VHS) depicting many of these effects is available to those interested free of charge.Comment: 23 pages, Plain TeX (v. 3.0), figures in American Journal of Physics, 61, 619, 1993, video available upon written (hard copy) request onl

Towards Locating the Brightest Microlensing Events on the Sky

It is estimated that a star brighter than visual magnitude 17 is undergoing a detectable gravitational microlensing event, somewhere on the sky, at any given time. It is assumed that both lenses and sources are normal stars drawn from a standard Bahcall-Soneira model of our Galaxy. Furthermore, over the time scale of a year, a star 15th magnitude or brighter should undergo a detectable gravitational lens amplification. Detecting and studying the microlensing event rate among the brightest 10$^8$ stars could yield a better understanding of Galactic stellar and dark matter distributions. Diligent tracking of bright microlensing events with even small telescopes might detect planets orbiting these stellar lenses.Comment: 19 pages, 4 figures, accepted by Ap

Superluminal Spot Pair Events in Astronomical Settings: Sweeping Beams

Sweeping beams of light can cast spots moving with superluminal speeds across scattering surfaces. Such faster-than-light speeds are well-known phenomena that do not violate special relativity. It is shown here that under certain circumstances, superluminal spot pair creation and annihilation events can occur that provide unique information to observers. These spot pair events are {\it not} particle pair events -- they are the sudden creation or annihilation of a pair of relatively illuminated spots on a scattering surface. Real spot pair illumination events occur unambiguously on the scattering surface when spot speeds diverge, while virtual spot pair events are observer dependent and perceived only when real spot radial speeds cross the speed of light. Specifically, a virtual spot pair creation event will be observed when a real spot's speed toward the observer drops below $c$, while a virtual spot pair annihilation event will be observed when a real spot's radial speed away from the observer rises above $c$. Superluminal spot pair events might be found angularly, photometrically, or polarimetrically, and might carry useful geometry or distance information. Two example scenarios are briefly considered. The first is a beam swept across a scattering spherical object, exemplified by spots of light moving across Earth's Moon and pulsar companions. The second is a beam swept across a scattering planar wall or linear filament, exemplified by spots of light moving across variable nebulae including Hubble's Variable Nebula. In local cases where the sweeping beam can be controlled and repeated, a three-dimensional map of a target object can be constructed. Used tomographically, this imaging technique is fundamentally different from lens photography, radar, and conventional lidar.Comment: 30 pages, 8 figures, accepted for publication in PAS

Tile or Stare? Cadence and Sky Monitoring Observing Strategies that Maximize the Number of Discovered Transients

To maximize the number of transients discovered on the sky, should sky-monitoring projects stare at one location or continually jump from location to location, tiling the sky? If tiling is preferred, what cadence maximizes the discovery rate? As sky monitoring is a growing part of astronomical observing, utilized to find such phenomena as supernovae, microlensing, and planet transits, well thought out answers to these questions are increasingly important. Answers are sky, source, and telescope dependent and should include information about the source luminosity distribution near the observation limit, the duration of variability, the nature of the dominant noise, and the magnitude of down and slew times. Usually, a critical slope of the effective cumulative transient apparent luminosity distribution (Log N - Log S) at the limiting magnitude will define when "tile" or "stare" is superior. For shallower slopes, when "tile" is superior, optimal cadences and pointing algorithms are discussed. For transients discovered on a single exposure or time-contiguous series of exposures, when down and slew times are small and the character of the noise is unchanged, the most productive cadence for isotropic power-law luminosity distributions is the duration of the transient -- faster cadences waste time re-discovering known transients, while slower cadences neglect transients occurring in other fields. A "cadence creep" strategy might find an optimal discovery cadence experimentally when one is not uniquely predetermined theoretically. Guest investigator programs might diversify previously dedicated sky monitoring telescopes by implementing bandpasses and cadences chosen to optimize the discovery of different types of transients. Example analyses are given for SuperMACHO, LSST, and GLAST.Comment: 28 pages, 4 figures. Accepted to Astronomical Journal. Mission specific correspondence welcome (to [email protected]

Attributes of Gravitational Lensing Parallax

The density of stars and MACHOs in the universe could theoretically be determined or limited by simultaneous measurements of compact sources by well separated observers. A gravitational lens effect would be expected to create a slight differential amplification between the observers detectable with sufficiently sensitive relative photometry: "lensing parallax." When applied to expanding fireballs such as those from GRBs and supernovae, the mass of the lens can be indicated by the end of lensing parallax, when the angular size of the source becomes much greater than the angular size of the Einstein ring of the lens.Comment: 7 pages, to be published in Astrophysics and Space Scienc