Primordial non-Gaussianity: local curvature method and statistical significance of constraints on fNL from WMAP data

We test the consistency of estimates of the non-linear coupling constant f _NL using non-Gaussian cosmic microwave background (CMB) maps generated by the method described in the work of Liguori, Matarrese & Moscardini. This procedure to obtain non-Gaussian maps differs significantly from the method used in previous works on the estimation of f _NL. Nevertheless, using spherical wavelets, we find results in very good agreement with Mukherjee & Wang, showing that the two ways of generating primordial non-Gaussian maps give equivalent results. Moreover, we introduce a new method for estimating the non-linear coupling constant from CMB observations by using the local curvature of the temperature fluctuation field. We present both Bayesian credible regions (assuming a flat prior) and proper (frequentist) confidence intervals on f _NL, and discuss the relation between the two approaches. The Bayesian approach tends to yield lower error bars than the frequentist approach, suggesting that a careful analysis of the different interpretations is needed. Using this method, we estimate   f _NL=−10⁺²⁷⁰₋₂₆₀  at the 2σ level (Bayesian) and   f _NL=−10⁺³¹⁰₋₂₇₀  (frequentist). Moreover, we find that the wavelet and the local curvature approaches, which provide similar error bars, yield approximately uncorrelated estimates of f _NL and therefore, as advocated in the work of Cabella et al., the estimates may be combined to reduce the error bars. In this way, we obtain   f _NL=−5 ± 85  and   f _NL=−5 ± 175  at the 1σ and 2σ level respectively using the frequentist approach.     

Constraints on primordial non-Gaussianity from a needlet analysis of the WMAP-5 data

We look for a non-Gaussian signal in the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year temperature anisotropy maps by performing a needlet-based data analysis. We use the foreground-reduced maps obtained by the WMAP team through the optimal combination of the W, V and Q channels, and perform realistic non-Gaussian simulations in order to constrain the non-linear coupling parameter f _NL. We apply a third-order estimator of the needlet coefficients skewness and compute the  χ²  statistics of its distribution. We obtain  −80 < f _NL < 120  at 95 per cent confidence level, which is consistent with a Gaussian distribution and comparable to previous constraints on the non-linear coupling. We then develop an estimator of f _NL based on the same simulations and we find consistent constraints on primordial non-Gaussianity. We finally compute the three-point correlation function in needlet space: the constraints on f _NL improve to  −50 < f _NL < 110  at 95 per cent confidence level.     

The effect of primordial non-Gaussianity on the topology of large-scale structure

We study the effect of primordial non-Gaussianity on the development of large-scale cosmic structure using high-resolution N -body simulations. In particular, we focus on the topological properties of the 'cosmic web', quantitatively characterized by the Minkowski functionals (MFs), for models with quadratic non-linearities with different values of the usual non-Gaussianity parameter f _NL. In the weakly non-linear regime (the amplitude of mass density fluctuations σ₀ < 0.1), we find that analytic formulae derived from perturbation theory agree with the numerical results within a few per cent of the amplitude of each MF when | f _NL| < 1000. In the non-linear regime, the detailed behaviour of the MFs as functions of threshold density deviates more strongly from the analytical curves, while the overall amplitude of the primordial non-Gaussian effect remains comparable to the perturbative prediction. When smaller-scale information is included, the influence of primordial non-Gaussianity becomes increasingly significant statistically due to decreasing sample variance. We find that the effect of the primordial non-Gaussianity with  | f _NL| = 50  is comparable to the sample variance of mass density fields with a volume of 0.125( h ⁻¹ Gpc)³ when they are smoothed by Gaussian filter at a scale of 5  h ⁻¹ Mpc. The detectability of this effect in actual galaxy surveys will strongly depend on residual uncertainties in cosmological parameters and galaxy biasing.     

Scale-dependent bias induced by local non-Gaussianity: a comparison to N-body simulations

We investigate the effect of primordial non-Gaussianity of the local f _NL type on the auto- and cross-power spectra of dark matter haloes using simulations of the Λ cold dark matter cosmology. We perform a series of large N -body simulations of both positive and negative f _NL, spanning the range between 10 and 100. Theoretical models predict a scale-dependent bias correction  Δ b ( k , f _NL)  that depends on the linear halo bias   b ( M )  . We measure the power spectra for a range of halo mass and redshifts covering the relevant range of existing galaxy and quasar populations. We show that auto- and cross-correlation analyses of bias are consistent with each other. We find that for low wavenumbers with   k < 0.03  h  Mpc⁻¹  the theory and the simulations agree well with each other for biased haloes with   b ( M ) > 1.5  . We show that a scale-independent bias correction improves the comparison between theory and simulations on smaller scales, where the scale-dependent effect rapidly becomes negligible. The current limits on f _NL from Slosar et al. come mostly from very large scales   k < 0.01  h  Mpc⁻¹  and, therefore, remain valid. For the halo samples with   b ( M ) < 1.5 − 2  , we find that the scale-dependent bias from non-Gaussianity actually exceeds the theoretical predictions. Our results are consistent with the bias correction scaling linearly with f _NL.     

Primordial non-Gaussianities in the intergalactic medium

We present results from the first high-resolution hydrodynamical simulations of non-Gaussian cosmological models. We focus on the statistical properties of the transmitted Lyman-α flux in the high-redshift intergalactic medium. Imprints of non-Gaussianity are present and are larger at high redshifts. Differences larger than 20 per cent at   z > 3  in the flux probability distribution function for high-transmissivity regions (voids) are expected for values of the non-linearity parameter   f _NL=±100  when compared to a standard Λ cold dark matter cosmology with   f _NL= 0  . We also investigate the one-dimensional flux bispectrum: at the largest scales (corresponding to tens of Mpc), we expect deviations in the flux bispectrum up to 20 per cent at   z ∼ 4  (for   f _NL=±100  ), significantly larger than deviations of ∼3 per cent in the flux power spectrum. We briefly discuss possible systematic errors that can contaminate the signal. Although challenging, a detection of non-Gaussianities in the interesting regime of scales and redshifts probed by the Lyman-α forest could be possible with future data sets.     

Limits on isocurvature perturbations from non-Gaussianity in WMAP temperature anisotropy

We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB) temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable  σ,  S =σ²−〈σ²〉  , can give the same signal-to-noise ratio as   f _NL= 30  even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe ( WMAP ) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model, we obtain a stringent upper limit on the isocurvature fraction  α < 0.070  (95 per cent CL) for a scale-invariant spectrum which is comparable to the limit obtained from the power spectrum.     

The effects of primordial non-Gaussianity on the cosmological reionization

We investigate the effects of non-Gaussianity in the primordial density field on the reionization history. We rely on a semi-analytic method to describe the processes acting on the intergalactic medium (IGM), relating the distribution of the ionizing sources to that of dark matter haloes. Extending previous work in the literature, we consider models in which the primordial non-Gaussianity is measured by the dimensionless non-linearity parameter f _NL, using the constraints recently obtained from cosmic microwave background data. We predict the ionized fraction and the optical depth at different cosmological epochs assuming two different kinds of non-Gaussianity characterized by a scale-independent and a scale-dependent f _NL and comparing the results to those for the standard Gaussian scenario. We find that a positive f _NL enhances the formation of high-mass haloes at early epochs when reionization begins, and, as a consequence, the IGM ionized fraction can grow by a factor of up to 5 with respect to the corresponding Gaussian model. The increase of the filling factor has a small impact on the reionization optical depth and is of the order of ∼10 per cent if a scale-dependent non-Gaussianity is assumed. Our predictions for non-Gaussian models are in agreement with the latest Wilkinson Microwave Anisotropy Probe results within the error bars, but a higher precision is required to constrain the scale dependence of non-Gaussianity.     

A Bayesian Kepler periodogram detects a second planet in HD 208487

An automatic Bayesian Kepler periodogram has been developed for identifying and characterizing multiple planetary orbits in precision radial velocity data. The periodogram is powered by a parallel tempering Markov chain Monte Carlo (MCMC) algorithm which is capable of efficiently exploring a multiplanet model parameter space. The periodogram employs an alternative method for converting the time of an observation to true anomaly that enables it to handle much larger data sets without a significant increase in computation time. Improvements in the periodogram and further tests using data from HD 208487 have resulted in the detection of a second planet with a period of 909⁸²₋₉₂ d, an eccentricity of 0.37^0.26_−0.20, a semimajor axis of 1.87^0.13_−0.14 au and an M sin  i = 0.45^+0.11_−0.13 M _J. The revised parameters of the first planet are period = 129.8 ± 0.4 d, eccentricity = 0.20 ± 0.09, semimajor axis = 0.51 ± 0.02 au and M sin  i = 0.41 ± 0.05  M _J. Particular attention is paid to several methods for calculating the model marginal likelihood which is used to compare the probabilities of models with different numbers of planets.     

Spectroscopic and photometric observations of the eclipsing star UV Leo

High-resolution spectroscopic observations around the Hα line and BVRI photometry of the eclipsing short-period RS CVn star UV Leo are presented. The simultaneous light-curve solution and radial velocity-curve solution led to the following values of the global parameters of the binary: temperatures   T ₁= 6000 ± 100 K  and   T ₂= 5970 ± 20 K  ; masses   M ₁= 0.976 ± 0.067 M_⊙  and   M ₂= 0.931 ± 0.052 M_⊙  ; separation   a = 3.716 ± 0.048 R_⊙  ; orbital inclination     ; radii   R ₁= 1.115 ± 0.052 R_⊙  and   R ₂= 1.078 ± 0.051 R_⊙  ; equatorial velocities   V ₁= 98.8 ± 2.3 km s⁻¹  and   V ₂= 89.6 ± 2.7 km s⁻¹  . These results lead to the conclusion that the two components of UV Leo are slightly oversized for their masses and lie within the main-sequence band on the mass–radius diagram, close to the isochrone 9 × 10¹⁰ yr.     

An iterative filter to reconstruct planetary transit signals in the presence of stellar variability

We report the identification, from a photometric, astrometric and spectroscopic study, of a massive white dwarf member of the nearby, approximately solar metallicity, Coma Berenices open star cluster (Melotte 111). We find the optical to near-infrared energy distribution of WD 1216+260 to be entirely consistent with that of an isolated DA and determine the effective temperature and surface gravity of this object to be   T _eff= 15 739⁺¹⁹⁷₋₁₉₆ K  and  log  g = 8.46^+0.03_−0.02  . We set tight limits on the mass of a putative cool companion,   M ≳ 0.036 M_⊙  (spatially unresolved) and   M ≳ 0.034 M_⊙  (spatially resolved and   a ≲ 2500 au  ). Based on the predictions of CO core, thick H layer evolutionary models we determine the mass and cooling time of WD 1216+260 to be   M _WD= 0.90 ± 0.04 M_⊙  and  τ_cool= 363⁺⁴⁶₋₄₁ Myr  , respectively. For an adopted cluster age of  τ= 500 ± 100 Myr  we infer the mass of its progenitor star to be   M _init= 4.77^+5.37_−0.97 M_⊙  . We briefly discuss this result in the context of the form of the stellar initial mass–final mass relation.     

Using the minimum spanning tree to trace mass segregation

We present a new method to detect and quantify mass segregation in star clusters. It compares the minimum spanning tree (MST) of massive stars with that of random stars. If mass segregation is present, the MST length of the most massive stars will be shorter than that of random stars. This difference can be quantified (with an associated significance) to measure the degree of mass segregation. We test the method on simulated clusters in both 2D and 3D and show that the method works as expected.
We apply the method to the Orion Nebula Cluster (ONC) and show that the method is able to detect the mass segregation in the Trapezium with a 'mass segregation ratio (MSR)'  Λ_MSR= 8.0 ± 3.5  (where  Λ_MSR= 1  is no mass segregation) down to  16 M_⊙  , and also that the ONC is mass segregated at a lower level  (∼2.0 ± 0.5)  down to  5 M_⊙  . Below  5 M_⊙  we find no evidence for any further mass segregation in the ONC.     

Structural parameters of Mayall II = G1 in M31

Mayall II = G1 is one of the most luminous globular clusters (GCs) known in M31. New deep, high-resolution observations with the Advanced Camera for Surveys on the Hubble Space Telescope are used to provide accurate photometric data to the smallest radii yet. In particular, we present the precise variation of ellipticity and position angle, and of surface brightness for the core of the object. Based on these accurate photometric data, we redetermine the structural parameters of G1 by fitting a single-mass isotropic King model. We derive a core radius,   r _c= 0.21 ± 0.01  arcsec (= 0.78 ± 0.04  pc)  , a tidal radius,   r _t= 21.8 ± 1.1  arcsec (= 80.7 ± 3.9  pc)  , and a concentration index   c = log ( r _t/ r _c) = 2.01 ± 0.02  . The central surface brightness is 13.510 mag arcsec⁻². We also calculate the half-light radius, at   r _h= 1.73 ± 0.07  arcsec (= 6.5 ± 0.3  pc)  . The results show that, within 10 core radii, a King model fits the surface brightness distribution well. We find that this object falls in the same region of the   M_V   versus  log   R _h  diagram as ω Centauri, M54 and NGC 2419 in the Milky Way. All three of these objects have been claimed to be the stripped cores of now defunct dwarf galaxies. We discuss in detail whether GCs, stripped cores of dwarf spheroidals and normal dwarf galaxies form a continuous distribution in the   M_V   versus  log   R _h  plane, or if GCs and dwarf spheroidals constitute distinct classes of objects; we present arguments in favour of this latter view.     

Spectroscopic solution of the star QX Cas

High-resolution spectroscopic observations around the Hα line of the binary star QX Cas covering the whole orbital period are presented. Our radial velocity solution, the first ever determined, requires an eccentric orbit with the following orbital parameters: eccentricity,   e = 0.22 ± 0.01  ; longitude of periastron,  ω= 45°± 5°  ; semi-amplitudes of the radial velocity curves of the primary and secondary stars,   K ₁ sin  i = 125.8 ± 0.9 km s⁻¹  and   K ₂ sin  i = 144.8 ± 1.1 km s⁻¹  ; gamma velocity,   V ₀= 65.1 ± 0.5 km s⁻¹  ; and mass ratio,   q = 0.869 ± 0.013  . The corresponding lower limits of the masses of the components and their separation are         , and   a sin  i = 31.34 ± 0.48 R_⊙  .     

The binary star population of the young cluster NGC 1818 in the Large Magellanic Cloud

We determine the binary star fraction as a function of radius in NGC 1818, a young rich cluster in the Large Magellanic Cloud, using Hubble Space Telescope images in bands F336W (∼ U ) and F555W (∼ V ). Our sample includes binaries with M _primary ∼ 2–5.5 M_⊙ and M _secondary ≳ 0.7 M_primary. The binary fraction increases towards the cluster centre, from ∼ 20 ± 5 per cent in the outer parts, to ∼ 35 ± 5 per cent inside the core. This increase is consistent with dynamical mass segregation and need not be primordial. We compare our results with expectations from N -body models, and discuss the implications for the formation and early evolution of such clusters.     

The component masses of the cataclysmic variable V347 Puppis

We present time-resolved spectroscopy and photometry of the double-lined eclipsing cataclysmic variable V347 Pup (=LB 1800). There is evidence of irradiation on the inner hemisphere of the secondary star, which we correct for using a model to give a secondary-star radial velocity of   K _R= 198 ± 5 km s⁻¹  . The rotational velocity of the secondary star in V347 Pup is found to be   v sin  i = 131 ± 5 km s⁻¹  and the system inclination is   i = 840 ± 23  . From these parameters we obtain masses of   M ₁= 0.63 ± 0.04 M_⊙  for the white dwarf primary and   M ₂= 0.52 ± 0.06 M_⊙  for the M0.5V secondary star, giving a mass ratio of   q = 0.83 ± 0.05  . On the basis of the component masses, and the spectral type and radius of the secondary star in V347 Pup, we find tentative evidence for an evolved companion. V347 Pup shows many of the characteristics of the SW Sex stars, exhibiting single-peaked emission lines, high-velocity S-wave components and phase-offsets in the radial velocity curve. We find spiral arms in the accretion disc of V347 Pup and measure the disc radius to be close to the maximum allowed in a pressureless disc.     

The minimum mass ratio of W UMa-type binary systems

When the total angular momentum of a binary system   J _tot= J _orb+ J _spin  is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when   J _orb= 3 J _spin  , which in the case of contact binaries corresponds to a minimum mass ratio   q _min≈  0.071–0.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have   R ₂= R ₂( R ₁, a , q )  . By finding a new criterion for contact binaries, which arises from  d J _tot= 0  , and assuming   k ²₁≠ k ²₂  for the component's dimensionless gyration radii, a theoretical lower limit   q _min= 0.094–0.109  for overcontact degree   f = 0–1  is obtained.     

The mass ratio and the orbital parameters of the sdOB binary AA Doradus

The time sequence of 105 spectra covering one full orbital period of AA Dor has been analysed. Direct determination of   V  sin  i   for the sdOB component from 97 spectra outside of the eclipse for the lines Mg  ii 4481 Å and Si  iv 4089 Å clearly indicated a substantially smaller value than estimated before. Detailed modelling of line-profile variations for eight spectra during the eclipse for the Mg  ii 4481 Å line, combined with the out-of-eclipse fits, gave   V  sin  i = 31.8 ± 1.8 km s⁻¹  . The previous determinations of   V  sin  i   , based on the He  ii 4686 Å line, appear to be invalid because of the large natural broadening of the line. With the assumption of the solid-body, synchronous rotation of the sdOB primary, the measured values of the semi-amplitude K ₁ and   V  sin  i   lead to the mass ratio   q = 0.213 ± 0.013  which in turn gives K ₂ and thus the masses and radii of both components. The sdOB component appears to be less massive than assumed before,   M ₁= 0.25 ± 0.05 M_⊙  , but the secondary has its mass–radius parameters close to theoretically predicted for a brown dwarf,   M ₂= 0.054 ± 0.010 M_⊙  and   R ₂= 0.089 ± 0.005 R_⊙  . Our results do not agree with the recent determination of Vŭcković et al. based on a K ₂ estimate from line-profile asymmetries.     

New constraints on turbulent transport in accretion discs

Many objects studied in astronomy follow a power-law distribution function (DF), for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The parameters obtained in this way can be severely biased, and the properties of the underlying DF, such as its shape or a possible upper limit, are difficult to extract. In this work, we review techniques available in the literature and present newly developed (effectively) bias-free estimators for the exponent and the upper limit. Furthermore, we discuss various graphical representations of the data and powerful goodness-of-fit tests to assess the validity of a power law for describing the distribution of data. As an example, we apply the presented methods to the data set of massive stars in R136 and the young star clusters in the Large Magellanic Cloud. For R136 we confirm the result of Koen of a truncated power law with a bias-free estimate for the exponent of  2.20 ± 0.78/2.87 ± 0.98  (where the Salpeter–Massey value is 2.35) and for the upper limit of  143 ± 9/163 ± 9 M_⊙  , depending on the stellar models used. The star clusters in the Large Magellanic Cloud (with ages up to  10^7.5 yr  ) follow a truncated power-law distribution with exponent  1.62 ± 0.06  and upper limit  68 ± 12 × 10³ M_⊙  . Using the graphical data representation, a significant change in the form of the mass function below  10^2.5 M_⊙  can be detected, which is likely caused by incompleteness in the data.     

Physical parameters of the O6.5V+B1V eclipsing binary system LS 1135

The 'All Sky Automated Survey' (ASAS) photometric observations of LS 1135, an O-type single-lined binary (SB1) system with an orbital period of 2.7 d, show that the system is also eclipsing performing a numerical model of this binary based on the Wilson–Devinney method. We obtained an orbital inclination     . With this value of the inclination, we deduced masses   M ₁∼ 30 ± 1 M_⊙  and   M ₂∼ 9 ± 1 M_⊙  , and radii   R ₁∼ 12 ± 1 R_⊙  and   R ₂∼ 5 ± 1 R_⊙  for primary and secondary components, respectively. Both the components are well inside their respective Roche lobes. Fixing the T _eff of the primary to the value corresponding to its spectral type (O6.5V), the T _eff obtained for the secondary component corresponds approximately to a spectral type of B1V. The mass ratio   M ₂/ M ₁∼ 0.3  is among the lowest known values for spectroscopic binaries with O-type components.