Toward High-Precision Astrometry with WFPC2. I. Deriving an Accurate PSF

The first step toward doing high-precision astrometry is the measurement of individual stars in individual images, a step that is fraught with dangers when the images are undersampled. The key to avoiding systematic positional error in undersampled images is to determine an extremely accurate point-spread function (PSF). We apply the concept of the {\it effective} PSF, and show that in images that consist of pixels it is the ePSF, rather than the often-used instrumental PSF, that embodies the information from which accurate star positions and magnitudes can be derived. We show how, in a rich star field, one can use the information from dithered exposures to derive an extremely accurate effective PSF by iterating between the PSF itself and the star positions that we measure with it. We also give a simple but effective procedure for representing spatial variations of the HST PSF. With such attention to the PSF, we find that we are able to measure the position of a single reasonably bright star in a single image with a precision of 0.02 pixel (2 mas in WF frames, 1 mas in PC), but with a systematic accuracy better than 0.002 pixel (0.2 mas in WF, 0.1 mas in PC), so that multiple observations can reliably be combined to improve the accuracy by $\surd N$.Comment: 33 pp. text + 15 figs.; accepted by PAS

Accurate Internal Proper Motions of Globular Clusters

We have undertaken a long term program to measure high precision proper motions of nearby Galactic globular cluster (GC) stars using multi-epoch observations with the WFPC2 and the ACS cameras on-board the Hubble Space Telescope. The proper motions are used to study the internal cluster kinematics, and to obtain accurate cluster distances. In this paper, we also show how the proper motions of the field stars projected in the direction of the studied clusters can be used to set constraints on the Galaxy kinematics.Comment: 4 pages, 2 figures, A.S.P. Conf. Ser., in press in Vol. 296, 200

A preliminary survey of collapsed cores in globular clusters

This is a preliminary report on surface photometry of the major fraction of known globular clusters, to see which of them show the signs of a collapsed core. The authors find more than 20 examples, or one-fifth of the total. Core classifications are given for all clusters examined. The fraction of collapsed-core clusters may be an index of how long a cluster takes to reexpand after collapse

Deep HST/FOC Imaging of the Central Density Cusp of the Globular Cluster M15

Using the Faint Object Camera on the repaired Hubble Space Telescope, we have observed two fields in the globular cluster M15: the central density cusp, and a field at r = 20''. These are the highest-resolution images ever taken of this cluster's dense core, and are the first to probe the distribution of stars well below the main-sequence turnoff. After correction for incompleteness, we measure a logarithmic cusp slope (d log \sigma / d log r) of -0.70 +- 0.05 (1-sigma) for turnoff (~ 0.8 \Msun) stars over the radial range from 0.3'' to 10''; this slope is consistent with previous measurements. We also set an approximate upper limit of ~1.5'' (90% confidence limit) on the size of any possible constant-surface-density core, but discuss uncertainties in this limit that arise from crowding corrections. We find that fainter stars in the cusp also have power-law density profiles: a mass group near 0.7 \Msun has a logarithmic slope of -0.56 +- 0.05 (1-sigma) over the radial range from 2'' to 10''. Taken together, the two slopes are not well matched by the simplest core-collapse or black-hole models. We also measure a mass function at r = 20'', outside of the central cusp. Both of the FOC fields show substantial mass segregation, when compared with a mass function measured with the WFPC2 at r = 5'. In comparing the overall mass functions of the two FOC fields and the r = 5' field, we find that the radial variation of the mass function is somewhat less than that predicted by a King-Michie model of the cluster, but greater than that predicted by a Fokker-Planck model taken from the literature.Comment: 40 pages single-spaced, including 12 figures; to appear in AJ, April 199

Is Your Wireless Network Being Hacked?

Wireless networks provide vulnerable gateways for unauthorised entry to networks or even a standalone wireless computer. The independent radio signals that constitute wireless communications have no physical boundary to keep them in check. This allows a third party to easily eavesdrop on communications sessions and by capturing the data packets, they can break the encryption keys and access the data within the network. The public awareness of the insecurity of wireless networks is surprisingly poor despite frequent news media reports of the vulnerabilities of the equipment and the activities of the criminals prepare to exploit it. In this paper we review the security protocols commonly used on wireless networks and investigate their weaknesses by showing how easy it is to crack the codes using tools freely available on the Internet

Color and population gradients in the core of the postcollapse globular cluster M30

We have developed a new technique for seeking color gradients in multicolor CCD images of a globular cluster. Application of this technique to M30 confirms the radial color gradient reported by others. The B - V and V - R colors show linear gradients, when plotted against log r, that are many times their statistical errors. In the radial range ~ 3-100 arcsec, the B - V and V - R colors increase outwards by about (0.18 ± 0.015) mag/dex and (0.09 ± 0.01) mag/dex, respectively. Color-magnitude arrays of the central region show that the Balmer-line strength that accompanies the central blueness is due to an increased proportion of blue-horizontal-branch starlight in the center. This excess does not appear to be statistically significant in terms of star numbers, even though the color gradient is so highly significant. The authors are divided among themselves as to whether the color and spectrum gradients observed here and in other clusters are due only to random statistical fluctuations, or whether they might have a physical significance

HST Astrometry of M4 and the Galactic Constant V_0/R_0

From multi-epoch WFPC2/HST observations we present astrometric measurements of stars in the Galactic globular cluster M4 (NGC 6121) and in the foreground/background. The presence of an extragalactic point source allows us to determine the absolute proper motion of the cluster, and, through use of the field stars in this region only 18 degree from the Galactic center, to measure the difference between the Oort constants, A-B. We find: (mu_alpha cos dec, mu_dec)_J2000 = (-13.21 +/- 0.35, -19.28 +/- 0.35) mas/yr, and A-B = V_0/R_0 = 27.6 +/- 1.7 km / s / kpc.Comment: 20 pages, 6 figures, A.J.__ACCEPTED__, 1 April, 2003, (...!

A Re-examination of the "Planetary" Lensing Events in M22

We have carried out further analysis of the tentative, short-term brightenings reported by Sahu et al. (2001), which were suggested to be possible lensings of Galactic-bulge stars by free-floating planets in the globular cluster M22. Closer examination shows that--unlikely as it may seem--small, point-like cosmic rays had hit very close to the same star in both of a pair of cosmic-ray-split images, which cause the apparent brightenings of stars at the times and locations reported. We show that the observed number of double hits is consistent with the frequency of cosmic rays in WFPC2 images, given the number of stars and epochs observed. Finally, we point to ways in which cosmic rays can be more directly distinguished.Comment: Accepted Dec 11, 2001 by ApJ Letter