Spatial clustering and its effect on perceived clustering, numerosity, and dispersion

Human observers are able to estimate the numerosity of large sets of visual elements. The occupancy model of perceived numerosity in intermediate numerical ranges is based on overlapping regions of influence. The key idea is that items within a certain range count for less than their actual numerical value and more so the closer they are to their neighbours. Therefore occupancy is sensitive to the grouping of elements, but there are other spatial properties of configurations that could also influence perceived numerosity, such as: area of convex hull, occupancy area, total degree of connectivity, and local clustering For all indices apart from convex hull, we varied the radius of the area that defined neighbours. We tested perceived numerosity using a fixed number of elements placed at random within a circular region. Observers compared two patterns (presented in two intervals) and chose the one that appeared more numerous. The same observers performed two other separate tasks in which they judged which pattern appeared more dispersed or more clustered. In each pair of images, the number was always the same (22, 28, 34, or 40 items), because we were interested in which "appeared" more numerous on the basis of spatial configuration. The results suggest that estimates of numerosity, dispersion, and clustering are based on different spatial information, that there are alternative approaches to quantifying clustering, and that in all cases clustering is linked to a decrease in perceived numerosity. The alternative measures have different properties and different practical and computational advantages.</p

Imaging X-ray, Optical, and Infrared Observations of the Transient Anomalous X-ray Pulsar XTE J1810-197

We report X-ray imaging, timing, and spectral studies of XTE J1810-197, a 5.54s pulsar discovered by Ibrahim et al. (2003) in recent RXTE observations. In a set of short exposures with the Chandra HRC camera we detect a strongly modulated signal (55+/-4% pulsed fraction) with the expected period located at (J2000) 18:09:51.08, -19:43:51.7, with a uncertainty radius of 0.6 arcsec (90% C.L.). Spectra obtained with XMM-Newton are well fitted by a two-component model that typically describes anomalous X-ray pulsars (AXPs), an absorbed blackbody plus power law with parameters kT = 0.67+/-0.01 keV, Gamma=3.7+/-0.2, N_H=(1.05+/-0.05)E22 cm^-2, and Fx(0.5-10 keV) = 3.98E-11 ergs/cm2/s. Alternatively, a 2T blackbody fit is just as acceptable. The location of CXOU J180951.1-194351 is consistent with a point source seen in archival Einstein, Rosat, & ASCA images, when its flux was nearly two orders-of-magnitude fainter, and from which no pulsations are found. The spectrum changed dramatically between the "quiescent" and "active" states, the former can be modeled as a softer blackbody. Using XMM timing data, we place an upper limit of 0.03 lt-s on any orbital motion in the period range 10m-8hr. Optical and infrared images obtained on the SMARTS 1.3m telescope at CTIO show no object in the Chandra error circle to limits V=22.5, I=21.3, J=18.9, & K=17.5. Together, these results argue that CXOU J180951.1-194351 is an isolated neutron star, one most similar to the transient AXP AX J1844.8-0256. Continuing study of XTE J1810-197 in various states of luminosity is important for understanding and possibly unifying a growing class of isolated, young neutron stars that are not powered by rotation.Comment: 12 pages, 7 figures, AAS LaTex, uses emulateapj5.sty. Updated to include additional archival data and a new HRC observation. To appear in The Astrophysical Journa

The Giant Flare of 1998 August 27 from SGR 1900+14: II. Radiative Mechanism and Physical Constraints on the Source

(ABBREVIATED) The extraordinary 1998 August 27 giant flare places strong constraints on the physical properties of its source, SGR 1900+14. We make detailed comparisons of the published data with the magnetar model. The giant flare evolved through three stages, whose radiative mechanisms we address in turn. A triggering mechanism is proposed, whereby a helical distortion of the core magnetic field induces large-scale fracturing in the crust and a twisting deformation of the crust and exterior magnetic field. The envelope of the pulsating tail of the August 27 flare can be accurately fit, after ~40 s, by the contracting surface of a relativistically hot, but inhomogeneous, trapped fireball. We quantify the effects of direct neutrino-pair emission, thereby deducing a lower bound ~ 10^{32} G-cm^3 to the magnetic moment of the confining field. The radiative flux during the intermediate ~40 s of the burst appears to exceed the trapped fireball fit. The spectrum and lightcurve of this smooth tail are consistent with heating in an extended pair corona, possibly powered by continuing seismic activity in the star. We consider in detail the critical luminosity, below which a stable balance can be maintained between heating and radiative cooling in a confined, magnetized pair plasma; but above which the confined plasma runs away to local thermodynamic equilibrium. In the later pulsating tail, the best fit temperature equilibrates at a value which agrees well with the regulating effect of photon splitting. The remarkable four-peaked substructure within each 5.16-s pulse provides strong evidence for the presence of higher magnetic multipoles in SGR 1900+14. The corresponding collimation of the X-ray flux is related to radiative transport in a super-QED magnetic field.Comment: 11 July 2001, accepted for publication in the Astrophysical Journa

Foot placement variables of pedestrians in community setting during curve walking

Background: There is no precise description of changes of gait during curve walking. Research in curve walking is exclusively performed in clinical settings. Research question: Is there a difference in foot placement variables between the inner- and the outer leg during curve walking in a natural environment? And are these differences correlated with time or the curvature of the path? Method: During this observational study, camera footage was shot on a crossing where pedestrians were not aware of being filmed. Participants (n = 21, male, 18?40 yrs) were selected from this video footage. Using the software package ?Movieprocessing?, the kinematic variables (time, curvature, stride length, step length, step width and relative foot angle (RFA)) were extracted from the collected data. A MANOVA and Pearson correlation test were performed to explore the data. Results: MANOVA showed no significant differences in stride length and step length between inner- and outer leg. In contrast, a significant difference between the inner (M = 0.06, SD = 0.05) and outer leg (M = 0.10, SD = 0.06, F(20,256) = 3.577, p < .001) for the step width, and the inner (M = 11.72, SD = 7.99) and outer leg (M = 11.30, SD = 8.07, F(20,256) = 4.542, p < .001) for RFA was found. Pearson correlation was significant for curvature and step width for both legs pooled (r = .28, p < .01) and the outer leg (r = .64, p < .01), as well for time and RFA in the inner (r= -.25, p < .01) and outer leg (r = .213, p < .01). Significance: This research funds further research in curve walking in natural conditions, since curve walking is found to be performed non-symmetrically and not determined by geometrics but by choice. Foot placement variables change gradually and differently for both legs during walking a curve

Discovery of a 6.4 keV Emission Line in a Burst from SGR 1900+14

We present evidence of a 6.4 keV emission line during a burst from the soft gamma-ray repeater SGR 1900+14. The Rossi X-ray Timing Explorer (RXTE) monitored this source extensively during its outburst in the summer of 1998. A strong burst observed on August 29, 1998 revealed a number of unique properties. The burst exhibits a precursor and is followed by a long (~ 1000 s) tail modulated at the 5.16 s stellar rotation period. The precursor has a duration of 0.85 s and shows both significant spectral evolution as well as an emission feature centered near 6.4 keV during the first 0.3 s of the event, when the X-ray spectrum was hardest. The continuum during the burst is well fit with an optically thin thermal bremsstrahlung (OTTB) spectrum with the temperature ranging from about 40 to 10 keV. The line is strong, with an equivalent width of 400 eV, and is consistent with Fe K-alpha fluorescence from relatively cool material. If the rest-frame energy is indeed 6.4 keV, then the lack of an observed redshift indicates that the source is at least 80 km above the neutron star surface. We discuss the implications of the line detection in the context of models for SGRs.Comment: AASTex preprint, 14 pages, 3 embedded figures. Accepted for Publication in Astrophysical Journal Letter

General Relativistic Constraints on Emission Models of Anomalous X-ray Pulsars

Most models of anomalous X-ray pulsars (AXPs) account for the observed X-ray spectra and pulsations by means of radiation processes that occur on the surfaces of neutron stars. For any such model, general relativistic deflection of light severely suppresses the amplitude of the observed pulsations. We calculate the expected pulsation amplitudes of AXPs according to various models and compare the results with observations. We show that the high (<= 70%) pulse amplitudes observed in some AXPs can be accounted for only if the surface emission is localized (spot radius <40 degrees) and strongly beamed (cos^n[theta'] with n>2, where theta' is the angle to the normal). These constraints are incompatible with those cooling and magnetar models in which the observed X-rays originate as thermal emission from the neutron-star surface. Accretion models, on the other hand, are compatible with observations for a wide range of parameters. Finally, definitive conclusions cannot be reached on magnetospheric models, since their localization and beaming properties are not well understood.Comment: 7 pages, 9 figures, submitted to The Astrophysical Journa

Anomalous X-ray Pulsars and Soft gamma-ray Repeaters: Spectral Fits and the Magnetar Model

The energy source powering the X-ray emission from anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) is still uncertain. In one scenario, the presence of an ultramagnetized neutron star, or ``magnetar'', with B on the order of 10^{14} - 10^{15} G is invoked. To investigate this hypothesis, we have analyzed archival ASCA data for several known AXPs and SGRs, and fitted them with a model in which all or part of the X-ray flux originates as thermal emission from a magnetar. Our magnetar spectral model includes the effects of the anisotropy of the heat flow through an ultramagnetized neutron star envelope, reprocessing by a light element atmosphere, and general relativistic corrections to the observed spectrum. We obtain good fits to the data with radii for the emitting areas which are generally consistent with those expected for neutron stars, in contrast to blackbody (BB) fits, which imply much smaller radii. Furthermore, the inclusion of atmospheric effects results in inferred temperatures which are lower than those implied by BB fits, but however still too high to be accounted by thermal cooling alone. An extra source of heating (possibly due to magnetic field decay) is needed. Despite the harder tail in the spectrum produced by reprocessing of the outgoing flux through the atmosphere, spectral fits still require a considerable fraction of the flux to be in a power-law component.Comment: 14 pages, 2 tables, 1 figure, ApJ in press; note added to Table

Large Torque Variations in Two Soft Gamma Repeaters

We have monitored the pulse frequencies of the two soft gamma repeaters SGR 1806-20 and SGR 1900+14 through the beginning of year 2001 using primarily Rossi X-ray Timing Explorer Proportional Counter Array observations. In both sources, we observe large changes in the spin-down torque up to a factor of ~4, which persist for several months. Using long baseline phase-connected timing solutions as well as the overall frequency histories, we construct torque noise power spectra for each SGR. The power spectrum of each source is very red (power-law slope ~-3.5). The torque noise power levels are consistent with some accreting systems on time scales of ~1 year, yet the full power spectrum is much steeper in frequency than any known accreting source. To the best of our knowledge, torque noise power spectra with a comparably steep frequency dependence have only been seen in young, glitching radio pulsars (e.g. Vela). The observed changes in spin-down rate do not correlate with burst activity, therefore, the physical mechanisms behind each phenomenon are also likely unrelated. Within the context of the magnetar model, seismic activity cannot account for both the bursts and the long-term torque changes unless the seismically active regions are decoupled from one another.Comment: 26 pages, 11 figures included, accepted for publication in ApJ, analysis of torque noise power density spectra is revised from previous version and minor text changes were mad

Precise Localization of the Soft Gamma Repeater SGR 1627-41 and the Anomalous X-ray Pulsar AXP 1E1841-045 with Chandra

We present precise localizations of AXP 1E1841-045 and SGR 1627-41 with Chandra. We obtained new infrared observations of SGR 1627-41 and reanalyzed archival observations of AXP 1E1841-045 in order to refine their positions and search for infrared counterparts. A faint source is detected inside the error circle of AXP 1E1841-045. In the case of SGR 1627-41, several sources are located within the error radius of the X-ray position and we discuss the likelihood of one of them being the counterpart. We compare the properties of our candidates to those of other known AXP and SGR counterparts. We find that the counterpart candidates for SGR 1627-41 and SGR 1806-20 would have to be intrinsically much brighter than AXPs to have detectable counterparts with the observational limits currently available for these sources. To confirm the reported counterpart of SGR 1806-20, we obtained new IR observations during the July 2003 burst activation of the source. No brightening of the suggested counterpart is detected, implying that the counterpart of SGR 1806-20 remains yet to be identified.Comment: 29 pages, 4 figures, accepted for publication in Ap