Evolution of the Cluster Correlation Function

We study the evolution of the cluster correlation function and its richness-dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with \Omega_m = 0.3 and, for comparison, a tilted \Omega_m = 1 model, TSCDM, are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high redshift clusters are clustered more strongly (in comoving scale) than low redshift clusters of the same mass. The increased correlations with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation-scale versus cluster mean separation relation, R_0 - d, is found to be, remarkably, independent of redshift to z <~ 2 for LCDM and z <~ 1 for TCDM (for a fixed correlation function slope and cluster mass within a fixed comoving radius). The non-evolving R_0 - d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters so that the R_0 - d relation remains essentially unchanged. The evolution of the R_0 - d relation from z ~ 0 to z ~ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ~ 0 and provide precise determination of cosmological parameters.Comment: AASTeX, 15 pages, including 5 figures, accepted version for publication in ApJ, vol.603, March 200

Hubble Space Telescope Imaging of the Expanding Nebular Remnant of the Recurrent Nova RS Ophiuchi (2006)

We report Hubble Space Telescope imaging obtained 155 days after the 2006 outburst of RS Ophiuchi. We detect extended emission in both [O III] and [Ne V] lines. In both lines, the remnant has a double ring structure. The E-W orientation and total extent of these structures (580+-50 AU at d=1.6kpc) is consistent with that expected due to expansion of emitting regions imaged earlier in the outburst at radio wavelengths. Expansion at high velocity appears to have been roughly constant in the E-W direction (v_{exp} = 3200+-300 km/s in the plane of the sky), with tentative evidence of deceleration N-S. We present a bipolar model of the remnant whose inclination is consistent with that of the central binary. The true expansion velocities of the polar components are then v = 5600+-1100 km/s. We suggest that the bipolar morphology of the remnant results from interaction of the outburst ejecta with a circumstellar medium that is significantly denser in the equatorial regions of the binary than at the poles. This is also consistent with observations of shock evolution in the X-ray and the possible presence of dust in the infrared. Furthermore, it is in line with models of the shaping of planetary nebulae with close binary central systems, and also with recent observations relating to the progenitors of Type Ia supernovae, for which recurrent novae are a proposed candidate. Our observations also reveal more extended structures to the S and E of the remnant whose possible origin is briefly discussed.Comment: 13 pages, 2 figures, accepted for publication in ApJ

GMRT Observations of the 2006 outburst of the Nova RS Ophiuchi: First detection of emission at radio frequencies < 1.4 GHz

The first low radio frequency (<1.4 GHz) detection of the outburst of the recurrent nova RS Ophiuchi is presented in this letter. Radio emission was detected at 0.61 GHz on day 20 with a flux density of ~48 mJy and at 0.325 GHz on day 38 with a flux density of ~ 44 mJy. This is in contrast with the 1985 outburst when it was not detected at 0.327 GHz even on day 66. The emission at low radio frequencies is clearly non-thermal and is well-explained by a synchrotron spectrum of index alpha ~ -0.8 (S propto nu^alpha) suffering foreground absorption due to the pre-existing, ionized, warm, clumpy red giant wind. The absence of low frequency radio emission in 1985 and the earlier turn-on of the radio flux in the current outburst are interpreted as being due to higher foreground absorption in 1985 compared to that in 2006, suggesting that the overlying wind densities in 2006 are only ~30% of those in 1985.Comment: 14 pages, 1 figure. Accepted for publication in ApJ

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr

We report the use of photoassociative spectroscopy to determine the ground state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red-detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494+/-5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Multi-Phase Patterns in Periodically Forced Oscillatory Systems

Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency (the 4:1 resonance). These systems possess four coexisting stable states, corresponding to uniform oscillations with successive phase shifts of $\pi/2$. Using an amplitude equation approach near a Hopf bifurcation to uniform oscillations, we study front solutions connecting different phase states. These solutions divide into two groups: $\pi$-fronts separating states with a phase shift of $\pi$ and $\pi/2$-fronts separating states with a phase shift of $\pi/2$. We find a new type of front instability where a stationary $\pi$-front ``decomposes'' into a pair of traveling $\pi/2$-fronts as the forcing strength is decreased. The instability is degenerate for an amplitude equation with cubic nonlinearities. At the instability point a continuous family of pair solutions exists, consisting of $\pi/2$-fronts separated by distances ranging from zero to infinity. Quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability. We conjecture the existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where stationary $\pi$-fronts decompose into n traveling $\pi/n$-fronts. The instabilities designate transitions from stationary two-phase patterns to traveling 2n-phase patterns. As an example, we demonstrate with a numerical solution the collapse of a four-phase spiral wave into a stationary two-phase pattern as the forcing strength within the 4:1 resonance is increased

The Critical Hopping Parameter in O(a) improved Lattice QCD

We calculate the critical value of the hopping parameter, $\kappa_c$, in O(a) improved Lattice QCD, to two loops in perturbation theory. We employ the Sheikholeslami-Wohlert (clover) improved action for Wilson fermions. The quantity which we study is a typical case of a vacuum expectation value resulting in an additive renormalization; as such, it is characterized by a power (linear) divergence in the lattice spacing, and its calculation lies at the limits of applicability of perturbation theory. The dependence of our results on the number of colors $N$, the number of fermionic flavors $N_f$, and the clover parameter $c_{SW}$, is shown explicitly. We compare our results to non perturbative evaluations of $\kappa_c$ coming from Monte Carlo simulations.Comment: 11 pages, 2 EPS figures. The only change with respect to the original version is inclusion of the standard formulae for the gauge fixing and ghost parts of the action. Accepted for publication in Physical Review

Double radio peak and non-thermal collimated ejecta in RS Ophiuchi following the 2006 outburst

We report Multi-Element Radio-Linked Interferometer Network, Very Large Array, One-Centimetre Radio Array, Very Long Baseline Array (VLBA), Effelsberg and Giant Metrewave Radio Telescope observations beginning 4.5 days after the discovery of RS Ophiuchi undergoing its 2006 recurrent nova outburst. Observations over the first 9 weeks are included, enabling us to follow spectral development throughout the three phases of the remnant development. We see dramatic brightening on days 4 to 7 at 6 GHz and an accompanying increase in other bands, particularly 1.46 GHz, consistent with transition from the initial ‘free expansion’ phase to the adiabatic expansion phase. This is complete by day 13 when the flux density at 5 GHz is apparently declining from an unexpectedly early maximum (compared with expectations from observations of the 1985 outburst). The flux density recovered to a second peak by approximately day 40, consistent with behaviour observed in 1985. At all times the spectral index is consistent with mixed non-thermal and thermal emission. The spectral indices are consistent with a non-thermal component at lower frequencies on all dates, and the spectral index changes show that the two components are clearly variable. The estimated extent of the emission at 22 GHz on day 59 is consistent with the extended east and west features seen at 1.7 GHz with the VLBA on day 63 being entirely non-thermal. We suggest a two-component model, consisting of a decelerating shell seen in mixed thermal and non-thermal emission plus faster bipolar ejecta generating the non-thermal emission, as seen in contemporaneous VLBA observations. Our estimated ejecta mass of 4 ± 2 × 10−7 M⊙ is consistent with a white dwarf (WD) mass of 1.4 M⊙. It may be that this ejecta mass estimate is a lower limit, in which case a lower WD mass would be consistent with the data

Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi: II. 1D hydrodynamical models of wind driven shocks

Following the early Swift X-ray observations of the latest outburst of the recurrent nova RS Ophiuchi in February 2006 (Paper I), we present new 1D hydrodynamical models of the system which take into account all three phases of the remnant evolution. The models suggest a novel way of modelling the system by treating the outburst as a sudden increase then decrease in wind mass-loss rate and velocity. The differences between this wind model and previous Primakoff-type simulations are described. A more complex structure, even in 1D, is revealed through the presence of both forward and reverse shocks, with a separating contact discontinuity. The effects of radiative cooling are investigated and key outburst parameters such as mass-loss rate, ejecta velocity and mass are varied. The shock velocities as a function of time are compared to the ones derived in Paper I. We show how the manner in which the matter is ejected controls the evolution of the shock and that for a well-cooled remnant, the shock deceleration rate depends on the amount of energy that is radiated away.Comment: 9 pages, 5 figure

Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi: I. Early X-ray emission from the shocked ejecta and red giant wind

RS Ophiuchi began its latest outburst on 2006 February 12. Previous outbursts have indicated that high velocity ejecta interact with a pre-existing red giant wind, setting up shock systems analogous to those seen in Supernova Remnants. However, in the previous outburst in 1985, X-ray observations did not commence until 55 days after the initial explosion. Here we report on Swift observations covering the first month of the 2006 outburst with the Burst Alert (BAT) and X-ray Telescope (XRT) instruments. RS Oph was clearly detected in the BAT 14-25 keV band from t=0 to $t\sim6$ days. XRT observationsfrom 0.3-10 keV, started at 3.17 days after outburst. The rapidly evolving XRT spectra clearly show the presence of both line and continuum emission which can be fitted by thermal emission from hot gas whose characteristic temperature, overlying absorbing column, $[N_H]_W$, and resulting unabsorbed total flux decline monotonically after the first few days. Derived shock velocities are in good agreement with those found from observations at other wavelengths. Similarly, $[N_H]_W$ is in accord with that expected from the red giant wind ahead of the forward shock. We confirm the basic models of the 1985 outburst and conclude that standard Phase I remnant evolution terminated by $t\sim10$ days and the remnant then rapidly evolved to display behaviour characteristic of Phase III. Around t=26 days however, a new, luminous and highly variable soft X-ray source began to appear whose origin will be explored in a subsequent paper.Comment: 20 pages, 4 figures (2 updated), accepted by Ap