High Resolution X-ray Imaging of a Globular Cluster Core: Compact Binaries in 47Tuc

We have obtained high resolution (<1") deep x-ray images of the globular cluster 47Tucanae (NGC 104) with the Chandra X-ray Observatory to study the population of compact binaries in the high stellar density core. A 70 kilosec exposure of the cluster reveals a centrally concentrated population of faint (Lx ~10^{30-33} erg/s) x-ray sources, with at least 108 located within the central 2arcmin X 2.5arcmin and at least half with Lx <10^{30.5} erg/s. All 15 millisecond pulsars (MSPs) recently located precisely by radio observations are identified, though two are unresolved by Chandra. The x-ray spectral and temporal characteristics, as well as initial optical identifications with the Hubble Space Telescope, suggest that >~50% are millisecond pulsars, ~30% are accreting white dwarfs, ~15% are main sequence binaries in flare outbursts and only 2 to 3 are quiescent low mass x-ray binaries containing neutron stars, the conventional progenitors of MSPs. An approximate upper limit of ~470Msun for the mass of an accreting central black hole in the cluster is derived. These observations provide the first x-ray "color-magnitude" diagram for a globular cluster and census of its compact object and binary population.Comment: 19 pages, 7 figures, 1 table (as supplementary file). Published online in Science Express on May 17, 2001 (reference: 10.1126/science.1061135). To appear in Science (print version) in late June, 200

The Formation Rate of Blue Stragglers in 47 Tucanae

We investigate the effects of changes in the blue straggler formation rate in globular clusters on the blue straggler distribution in the color-magnitude diagram. We find that the blue straggler distribution is highly sensitive to the past formation rate. Comparing our models to new UBV observations of a region close to the core of 47 Tucanae suggests that this cluster may have stopped forming blue straggler formation several Gyr ago. This cessation of formation can be associated with an epoch of primordial binary burning which has been invoked in other clusters to infer the imminence of core collapse.Comment: 17 pages, 9 figures, submitted to the Astrophysical Journa

An Extensive Census of HST Counterparts to Chandra X-ray Sources in the Globular Cluster 47 Tucanae. I. Astrometry and Photometry

We report the largest number of optical identifications of X-ray sources yet obtained in a single globular cluster. Using deep Chandra/ACIS-I imaging and extensive HST studies with WFPC2, we have detected optical counterparts to at least 22 cataclysmic variables (CVs) and 29 chromospherically active binaries (BY Dras and RS CVns) in 47 Tuc. These identifications are all based on tight astrometric matches between X-ray sources and objects with unusual (non main sequence) optical colors and/or optical variability. In the U vs U-V color magnitude diagram (CMD), the CVs all show evidence for blue colors compared to the main sequence, but most of them fall close to the main sequence in the V vs V-I CMD, showing that the secondary stars dominate the optical light. The X-ray detected active binaries have magnitude offsets above the main sequence that are indistinguishable from those of the much larger sample of optical variables (eclipsing and contact binaries and BY Dras) detected in the WFPC2 studies of Albrow et al. (2001). We also present the results of a new, deeper search for optical companions to MSPs. One possible optical companion to an MSP (47 Tuc T) was found, adding to the two optical companions already known. Finally, we study several blue stars with periodic variability from Albrow et al. (2001) that show little or no evidence for X-ray emission. The optical colors of these objects differ from those of 47 Tuc (and field) CVs.Comment: Accepted for publication in Astrophysical Journal. 25 pages, 12 figures, 3 tables, abridged abstract. Some figures at reduced resolutio

The hard quiescent spectrum of the neutron-star X-ray transient EXO 1745-248 in the globular cluster Terzan 5

We present a Chandra observation of the globular cluster Terzan 5 during times when the neutron-star X-ray transient EXO 1745-248 located in this cluster was in its quiescent state. We detected the quiescent system with a (0.5-10 keV) luminosity of ~2 x 10^{33} ergs/s. This is similar to several other neutron-star transients observed in their quiescent states. However, the quiescent X-ray spectrum of EXO 1745--48 was dominated by a hard power-law component instead of the soft component that usually dominates the quiescent emission of other neutron-star X-ray transients. This soft component could not conclusively be detected in EXO 1745-248 and we conclude that it contributed at most 10% of the quiescent flux in the energy range 0.5-10 keV. EXO 1745-248 is only the second neutron-star transient whose quiescent spectrum is dominated by the hard component (SAX J1808.4-3658 is the other one). We discuss possible explanations for this unusual behavior of EXO 1745-248, its relationship to other quiescent neutron-star systems, and the impact of our results on understanding quiescent X-ray binaries. We also discuss the implications of our results on the way the low-luminosity X-ray sources in globular clusters are classified.Comment: Accepted by ApJ Main Journal, September 22, 2004. Figure 2 is a color figur

An exactly solvable limit of low energy QCD

Starting from the QCD Hamiltonian, we derive a schematic Hamiltonian for low energy quark dynamics with quarks restricted to the lowest s-level. The resulting eigenvalue problem can be solved analytically. Even though the Hamiltonian exhibits explicit chiral symmetry the severe restriction of the number of degrees of freedom breaks the pattern of chiral symmetry breaking for finite quark masses.Comment: 7 page

Stellar Variability in the Globular Cluster Terzan 5

We present the results of a search for variability in and near the core of the metal-rich, obscured globular cluster Terzan 5, using NICMOS on HST. This extreme cluster has approximately solar metallicity and a central density that places it in the upper few percent of all clusters. It is estimated to have the highest interaction rate of any galactic globular cluster. The large extinction towards Terzan 5 and the severe stellar crowding near the cluster center present a substantial observational challenge. Using time series analysis we discovered two variable stars in this cluster. The first is a RRab Lyrae variable with a period of ~0.61 days, a longer period than that of field stars with similar high metallicities. This period is, however, shorter than the average periods of RR Lyraes found in the metal-rich globular clusters NGC 6441, NGC 6388 and 47 Tuc. The second variable is a blue star with a 7-hour period sinusoidal variation and a likely orbital period of 14 hours. This star is probably an eclipsing blue straggler, or (less likely) the infrared counterpart to the low mass X-ray binary known in Terzan 5. Due to the extreme crowding and overlapping Airy profile of the IR PSF, we fall short of our original goal of detecting CVs via Palpha emission and detecting variable infrared emission from the location of the binary MSP in Terzan 5.Comment: 17 pages including 12 figures. Accepted for publication in Ap

Entanglement in SO(3)-invariant bipartite quantum systems

The structure of the state spaces of bipartite (N tensor N) quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of arbitrary spin j which transform according to an irreducible representation of the rotation group. A positive map theta is introduced which describes the time reversal symmetry of the local states and which is unitarily equivalent to the transposition of matrices. It is shown that the partial time reversal transformation theta_2 = (I tensor theta) acting on the composite system can be expressed in terms of the invariant 6-j symbols introduced by Wigner into the quantum theory of angular momentum. This fact enables a complete geometrical construction of the manifold of states with positive partial transposition and of the sets of separable and entangled states of (4 tensor 4) systems. The separable states are shown to form a three-dimensional prism and a three-dimensional manifold of bound entangled states is identified. A positive maps is obtained which yields, together with the time reversal, a necessary and sufficient condition for the separability of states of (4 tensor 4) systems. The relations to the reduction criterion and to the recently proposed cross norm criterion for separability are discussed.Comment: 15 pages, 3 figure

Thermal structure of a gas-permeable lava dome and timescale separation in its response to perturbation

The thermal boundary layer at the surface of a volcanic lava dome is investigated through a continuum model of the thermodynamic advection diffusion processes resulting from magmatic gas flow through the dome matrix. The magmatic gas mass flux, porosity and permeability of the rock are identified as key parameters. New, theoretical, nonlinear steady-state thermal profiles are reported which give a realistic surface temperature of 210 degC for a region of lava dome surface through which a gas flux of 3.5 x 10-3 kg s-1 m-2 passes. This contrasts favourably with earlier purely diffusive thermal models, which cool too quickly. Results are presented for time-dependent perturbations of the steady states as a response to: changes in surface pressure, a sudden rockfall from the lava dome surface, and a change in the magmatic gas mass flux at depth. Together with a generalized analysis using the method of multiple scales, this identifies two characteristic time scales associated with the thermal evolution of a dome carapace: a short time scale of several minutes, over which the magmatic gas mass flux, density, and pressure change to a new quasi-steady-state, and a longer time scale of several days, over which the thermal profile changes to a new equilibrium distribution. Over the longer time scale the dynamic properties of the dome continue to evolve, but only in slavish response to the ongoing temperature evolution. In the light of this time scale separation, the use of surface temperature measurements to infer changes in the magmatic gas flux for use in volcanic hazard prediction is discussed

Chandra X-ray Sources in the Collapsed-Core Globular Cluster M30 (NGC 7099)

We report the detection of six discrete, low-luminosity (Lx < 10^33 erg/s) X-ray sources, located within 12 arcsec of the center of the collapsed-core globular cluster M30 (NGC 7099), and a total of 13 sources within the half-mass radius, from a 50 ksec Chandra ACIS-S exposure. Three sources lie within the very small upper limit of 1.9 arcsec on the core radius. The brightest of the three core sources has a luminosity of Lx (0.5-6 keV) = 6x10^32 erg/s and a blackbody-like soft X-ray spectrum, which are both consistent with it being a quiescent low-mass X-ray binary (qLMXB). We have identified optical counterparts to four of the six central sources and a number of the outlying sources, using deep Hubble Space Telescope and ground-based imaging. While the two proposed counterparts that lie within the core may represent chance superpositions, the two identified central sources that lie outside of the core have X-ray and optical properties consistent with being CVs. Two additional sources outside of the core have possible active binary counterparts. We discuss the X-ray source population of M30 in light of its collapsed-core status.Comment: 18 pages, 13 figures (8 color), resubmitted to ApJ after incorporating referee comment