Fast directional continuous spherical wavelet transform algorithms

We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al. Fast algorithms for performing the directional continuous wavelet analysis on the unit sphere are presented. The fast directional algorithm, based on the fast spherical convolution algorithm developed by Wandelt and Gorski, provides a saving of O(sqrt(Npix)) over a direct quadrature implementation for Npix pixels on the sphere, and allows one to perform a directional spherical wavelet analysis of a 10^6 pixel map on a personal computer.Comment: 10 pages, 3 figures, replaced to match version accepted by IEEE Trans. Sig. Pro

Binary quasars

Quasar pairs are either physically distinct binary quasars or the result of gravitational lensing. The majority of known pairs are in fact lenses, with a few confirmed as binaries, leaving a population of objects that have not yet been successfully classified. Building on the arguments of Kochanek, Falco & Munoz (1999), it is shown that there are no objective reasons to reject the binary interpretation for most of these. In particular, the similarity of the spectra of the quasar pairs appears to be an artifact of the generic nature of quasar spectra. The two ambiguous pairs discovered as part of the Large Bright Quasar Survey (Q 1429-053 and Q 2153-0256) are analysed using principle components analysis, which shows that their spectral similarities are not greater than expected for a randomly chosen pair of quasars from the survey. The assumption of the binary hypothesis allows the dynamics, time-scales and separation distribution of binary quasars to be investigated and constrained. The most plausible model is that the quasars' activity is triggered by tidal interactions in a galatic merger, but that the (re-)activation of the galactic nuclei occurs quite late in the interaction, when the nuclei are within 80+/-30 kpc of each other. A simple dynamical friction model for the decaying orbits reproduces the observed distribution of projected separations, but the decay time inferred is comparable to a Hubble time. Hence it is predicted that binary quasars are only observable as such in the early stages of galactic collisions, after which the quiescent super-massive black holes orbit in the merger remnant for some time.Comment: 12 pages, 12 figure

How neutral is the intergalactic medium surrounding the redshift z=7.085 quasar ULAS J1120+0641?

The quasar ULAS J1120+0641 at redshift z=7.085 has a highly ionised near zone which is smaller than those around quasars of similar luminosity at z~6. The spectrum also exhibits evidence for a damping wing extending redward of the systemic Lya redshift. We use radiative transfer simulations in a cosmological context to investigate the implications for the ionisation state of the inhomogeneous IGM surrounding this quasar. Our simulations show that the transmission profile is consistent with an IGM in the vicinity of the quasar with a volume averaged HI fraction of f_HI>0.1 and that ULAS J1120+0641 has been bright for 10^6--10^7 yr. The observed spectrum is also consistent with smaller IGM neutral fractions, f_HI ~ 10^-3--10-4, if a damped Lya system in an otherwise highly ionised IGM lies within 5 proper Mpc of the quasar. This is, however, predicted to occur in only ~5 per cent of our simulated sight-lines for a bright phase of 10^6--10^7 yr. Unless ULAS J1120+0641 grows during a previous optically obscured phase, the low age inferred for the quasar adds to the theoretical challenge of forming a 2x10^9 M_sol black hole at this high redshift.Comment: 5 pages, 4 figures, accepted to MNRAS letter

No excess of bright galaxies around the redshift 7.1 quasar ULAS J1120+0641

We present optical and near-infrared imaging of the field of the z = 7.0842 quasar ULAS J112001.48+064124.3 taken with the Hubble Space Telescope. We use these data to search for galaxies that may be physically associated with the quasar, using the Lyman break technique, and find three such objects, although the detection of one in Spitzer Space Telescope imaging strongly suggests it lies at z ∼ 2. This is consistent with the field luminosity function and indicates that there is no excess of >L★ galaxies within 1 Mpc of the quasar. A detection of the quasar shortwards of the Lyα line is consistent with the previously observed evolution of the intergalactic medium at z > 5.5.SC acknowledges support from the NSF grant AST-1010004 and NASA HST grant GO-13033.06-A, RJM acknowledges ERC funding via the award of a consolidator grant, and BV has been supported by the ERC grant ‘Cosmic Dawn’.This is the final published version. It originally appeared in MNRAS at http://www.mnras.org/content/442/4/3454.full

Limits on non-Gaussianities from WMAP data

We develop a method to constrain the level of non-Gaussianity of density perturbations when the 3-point function is of the "equilateral" type. Departures from Gaussianity of this form are produced by single field models such as ghost or DBI inflation and in general by the presence of higher order derivative operators in the effective Lagrangian of the inflaton. We show that the induced shape of the 3-point function can be very well approximated by a factorizable form, making the analysis practical. We also show that, unless one has a full sky map with uniform noise, in order to saturate the Cramer-Rao bound for the error on the amplitude of the 3-point function, the estimator must contain a piece that is linear in the data. We apply our technique to the WMAP data obtaining a constraint on the amplitude f_NL^equil of "equilateral" non-Gaussianity: -366 < f_NL^equil < 238 at 95% C.L. We also apply our technique to constrain the so-called "local" shape, which is predicted for example by the curvaton and variable decay width models. We show that the inclusion of the linear piece in the estimator improves the constraint over those obtained by the WMAP team, to -27 < f_NL^local < 121 at 95% C.L.Comment: 20 pages, 12 eps figure

Estimators for local non-Gaussianities

We study the Likelihood function of data given f_NL for the so-called local type of non-Gaussianity. In this case the curvature perturbation is a non-linear function, local in real space, of a Gaussian random field. We compute the Cramer-Rao bound for f_NL and show that for small values of f_NL the 3-point function estimator saturates the bound and is equivalent to calculating the full Likelihood of the data. However, for sufficiently large f_NL, the naive 3-point function estimator has a much larger variance than previously thought. In the limit in which the departure from Gaussianity is detected with high confidence, error bars on f_NL only decrease as 1/ln Npix rather than Npix^-1/2 as the size of the data set increases. We identify the physical origin of this behavior and explain why it only affects the local type of non-Gaussianity, where the contribution of the first multipoles is always relevant. We find a simple improvement to the 3-point function estimator that makes the square root of its variance decrease as Npix^-1/2 even for large f_NL, asymptotically approaching the Cramer-Rao bound. We show that using the modified estimator is practically equivalent to computing the full Likelihood of f_NL given the data. Thus other statistics of the data, such as the 4-point function and Minkowski functionals, contain no additional information on f_NL. In particular, we explicitly show that the recent claims about the relevance of the 4-point function are not correct. By direct inspection of the Likelihood, we show that the data do not contain enough information for any statistic to be able to constrain higher order terms in the relation between the Gaussian field and the curvature perturbation, unless these are orders of magnitude larger than the size suggested by the current limits on f_NL.Comment: 26 pages. v2: added comments about the approximations used, published JCAP versio

LBQS 1429-0053: a binary quasar rather than a lensed quasar

Very deep ESO/VLT FORS1 and ISAAC images, as well as HST NICMOS2 data are used to infer the nature of the quasar pair LBQS 1429-0053 A and B, either a binary quasar or a doubly-imaged lensed quasar. Direct search of a putative lensing galaxy is unsuccessful . Moreover, no galaxy overdensity close to the quasar pair is found. A weak shear analysis of the field also fails at detecting any concentration of dark matter and weakens the hypothesis of a dark lens. The only sign of a possible lens consists in a group of 5 objects at z~1, within a radius of 5'', from the quasar pair. Considering this group as the lensing potential does not allow to reproduce the image position and flux ratio of the quasars. Our deep R-band image shows a blue, extended object at the position of quasar A, which is consistent with either being the lensed quasar A host, or being an intervening galaxy at lower redshift. Unless future very deep optical images demonstrate that this object is actually the lensed host of LBQS 1429-0053, we conclude that there is very little evidence for this quasar being lensed. Therefore, we are led to declare LBQS 1429-0053 A and B a genuine binary quasar.Comment: 9 pages, 6 jpg images, accepted for publication in A&

Long-distance optical-conveyor-belt transport of ultracold 133 Cs and 87 Rb atoms

We report on the transport of a thermal cloud of ultracold cesium and rubidium atoms over about 37 cm in under 25 ms using an optical conveyor belt formed by two counterpropagating beams with a controllable frequency difference that generate a movable optical lattice. By carefully selecting the waists and focus positions, we are able to use two static Gaussian beams for the transport, avoiding the need for a Bessel beam or variable-focus lenses. We characterize the transport efficiency for both species, including a comparison of different transport trajectories, gaining insight into the loss mechanisms and finding the minimum jerk trajectory to be optimum. Using the optimized parameters, we are able to transport up to 7×106 cesium or rubidium atoms with an efficiency up to 75%. To demonstrate the viability of our transport scheme for experiments employing quantum gas microscopy, we produce Bose-Einstein condensates of either species after transport and present measurements of the simultaneous transport of both species

The spectral energy distribution of the redshift 7.1 quasar ULAS J1120+0641

We present new observations of the highest-redshift quasar known, ULAS J1120+0641, redshift $z=7.084$, obtained in the optical, at near-, mid-, and far-infrared wavelengths, and in the sub-mm. We combine these results with published X-ray and radio observations to create the multiwavelength spectral energy distribution (SED), with the goals of measuring the bolometric luminosity $L_{\rm bol}$, and quantifying the respective contributions from the AGN and star formation. We find three components are needed to fit the data over the wavelength range $0.12-1000\,\mu$m: the unobscured quasar accretion disk and broad-line region, a dusty clumpy AGN torus, and a cool 47K modified black body to characterise star formation. Despite the low signal-to-noise ratio of the new long-wavelength data, the normalisation of any dusty torus model is constrained within $\pm40\%$. We measure a bolometric luminosity $L_{\rm bol}=2.6\pm0.6\times10^{47}\,$erg$\,$s$^{-1}=6.7 \pm 1.6\times10^{13}L_{\odot}$, to which the three components contribute $31\%,32\%,3\%$, respectively, with the remainder provided by the extreme UV $<0.12\,\mu$m. We tabulate the best-fit model SED. We use local scaling relations to estimate a star formation rate (SFR) in the range $60-270\,{\rm M}_\odot$/yr from the [C$\,{\scriptsize \rm II}$] line luminosity and the $158\,\mu$m continuum luminosity. An analysis of the equivalent widths of the [C$\,{\scriptsize \rm II}$] line in a sample of $z>5.7$ quasars suggests that these indicators are promising tools for estimating the SFR in high-redshift quasars in general. At the time observed the black hole was growing in mass more than 100 times faster than the stellar bulge, relative to the mass ratio measured in the local universe, i.e. compared to ${M_{\rm BH}}/{M_{\rm bulge}} \simeq 1.4\times10^{-3}$, for ULAS J1120+0641 we measure ${\dot{M}_{\rm BH}}/{\dot{M}_{\rm bulge}} \simeq 0.2$.Comment: Accepted for publication in A&A. 10 pages, 5 figures, 5 table

Molecular evolution of HoxA13 and the multiple origins of limbless morphologies in amphibians and reptiles

Developmental processes and their results, morphological characters, are inherited through transmission of genes regulating development. While there is ample evidence that cis-regulatory elements tend to be modular, with sequence segments dedicated to different roles, the situation for proteins is less clear, being particularly complex for transcription factors with multiple functions. Some motifs mediating protein-protein interactions may be exclusive to particular developmental roles, but it is also possible that motifs are mostly shared among different processes. Here we focus on HoxA13, a protein essential for limb development. We asked whether the HoxA13 amino acid sequence evolved similarly in three limbless clades: Gymnophiona, Amphisbaenia and Serpentes. We explored variation in ω (dN/dS) using a maximum-likelihood framework and HoxA13sequences from 47 species. Comparisons of evolutionary models provided low ω global values and no evidence that HoxA13 experienced relaxed selection in limbless clades. Branch-site models failed to detect evidence for positive selection acting on any site along branches of Amphisbaena and Gymnophiona, while three sites were identified in Serpentes. Examination of alignments did not reveal consistent sequence differences between limbed and limbless species. We conclude that HoxA13 has no modules exclusive to limb development, which may be explained by its involvement in multiple developmental processes